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Molecular simulation of peptides coming of age: Accurate prediction of folding, dynamics and structures
Accepted Manuscript Molecular simulation of peptides coming of age: Accurate prediction of folding, dynamics and structures Panagiota S. Georgoulia, Nicholas M. Glykos PII:
S0003-9861(18)30734-3
DOI:
https://doi.org/10.1016/j.abb.2019.01.033
Reference:
YABBI 7939
To appear in:
Archives of Biochemistry and Biophysics
Received Date: 14 September 2018 Revised Date:
23 January 2019
Accepted Date: 28 January 2019
Please cite this article as: P.S. Georgoulia, N.M. Glykos, Molecular simulation of peptides coming of age: Accurate prediction of folding, dynamics and structures, Archives of Biochemistry and Biophysics (2019), doi: https://doi.org/10.1016/j.abb.2019.01.033. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Molecular simulation of peptides coming of age: accurate prediction of folding, dynamics and structures. Department of Chemistry and Biomedical Sciences, Faculty of Health and Life Sciences, Linnæus University, Kalmar, 39182, Sweden 2 3
Linnæus University Centre of Excellence “Biomaterials Chemistry”, Kalmar, 3912, Sweden
Department of Molecular Biology and Genetics, Democritus University of Thrace, University Campus, Alexandroupolis, 68100, Greece
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Panagiota S. Georgoulia1,2 , Nicholas M. Glykos3 *
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Abstract
The application of molecular dynamics simulations to study the folding and dynamics of peptides has attracted a lot of interest in the last couple of decades. Following the successful prediction of the folding of several proteins using molecular simulation, foldable peptides emerged as a favourable system mainly due to their application in improving protein structure prediction methods and in drug design studies. However,
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their performance is inherently linked to the accuracy of the empirical force fields used
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in the simulations, whose optimisation and validation is of paramount importance. Here we review the most important findings in the field of molecular peptide simulations and highlight the significant advancements made over the last twenty years. Special
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reference is made on the simulation of disordered peptides and the remaining challenge to find a force field able to describe accurately their conformational landscape. Keywords:
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peptide simulations, peptide folding, peptide dynamics, empirical force fields, validation.
Preprint submitted to Archives in Biochemistry and Biophysics
January 30, 2019
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1. Overview Molecular simulations have evolved to a powerful theoretical technique to study
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peptide structure and dynamics, as indicated by the plethora of references in the lit-
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erature. The study of peptides thrived in the beginning of this millennium and still
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holds as an active field of research after 20 years. This interest is mainly due to the
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ability of foldable peptides to mimic essential characteristics of the much larger protein
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systems while at the same time maintaining the simplicity of smaller systems. This
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makes peptide systems not only easier to comprehend, but also cost efficient in terms
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of both computational power and experimental resources required. Their advantages
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as model systems have been eloquently presented in other reviews[24, 63]. Herein, we
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try to underline their vital role in the development and advancement of force fields
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through numerous cycles of validation and optimisation that lead to what we perceive
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to be significant improvements in the ability of simulations to capture and reproduce
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the experimentally accessible physical reality.
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2. Peptide folding simulations: two decades of continuous advancement
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Historically, the study of peptides was prompted by the fact that they resemble
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the early events in protein folding and thus offer an excellent opportunity to decipher
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protein-structure relationships[35, 75, 97]. Early studies suggested that peptides may
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serve as nucleation sites from where the folding is initiated[171, 200]. This paved the
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way to a number of studies aiming to characterise the timescales of the early folding
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events and to model them computationally.
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The speed limit of folding has been estimated to be N/100µs, where N is the number
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of residues[96], with its actual value being dependant on a number of events such as
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the formation of hydrophobic core, hydrogen bonds, electrostatic interactions, solvation
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energy, conformational entropy, diffusion, etc.[126]. The timescales for the formation
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of basic structural elements have been placed to the sub-second time-scale[20, 43]. The
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fastest early folding events were grouped by Gnanakaran et al.[63] based on the minimal
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sequence that can form each of these structures, from loop-closure events that can take
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place in the 10ns time-scale[103], to α-helix formation which takes place in the 100-
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200ns time-scale[57, 199] and to the slower β-hairpin formation that may require several
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microseconds[132]. The Eaton group contributed with extensive studies on the speed of
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folding, setting an upper limit for a 50-residue protein to 1 microsecond[42, 66]. This
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nano- to micro-second regime allowed a unique opportunity for a direct comparison
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between theoretical calculations and experimental measurements[27, 95, 103, 202]. The combination of these relatively short folding timescales with the increase of the
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computational power available to the research groups led to numerous peptide folding
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simulation studies which significantly advanced the field of peptide folding simulations.
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One of the pioneering studies was by Daura et al. that showed in atomistic detail the
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reversible folding of two β-peptides in solution[32]. Later, the Caflisch group showed the
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impressive, for that time, folding of a 20-residue peptide to a three-stranded antiparallel
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β-sheet through a cumulative simulation time of 4µs[49, 50]. Likewise, Pande et al.,
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illustrated the efficiency of using different starting conformations and high-temperature
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unfolding to study the folding pathway of a β-hairpin fragment of protein G[143].
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Challenging short peptides with many charged residues (10 out of 21 amino acids) were
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successfully computationally folded to the native structure in an attempt to describe
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the folding pathway and estimate folding rates that were experimentally difficult to
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access[194].
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In later years, the increase in available computational power made it possible for
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the molecular simulations to reach even higher time scales in the range of tens to
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hundreds of microseconds, approaching the folding times of longer peptides (20-60
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amino acids)[125]. One of the first notable studies was the milestone 1 microsecond
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single folding simulation of the 36 residue villin headpiece in explicit water by Duan and
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Kollman[38]. Shortly after that, the Pande group demonstrated the efficiency of using
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many short trajectories instead of a single long one to describe the folding pathway of
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small peptides like BBA and villin headpiece (23 and 36 residue long, respectively), an
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effort made possible through the development of distributed computing [45, 104, 167,
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175, 205].
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A few peptides served as preferable study systems due to their unique properties
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and abundance of experimental data, like the 20-residue peptide, Trp-cage, the smallest
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stably folded peptide showing two-state folding properties [28, 151, 170] and the WW
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domain (approximately 40 residues) of Pin1 protein[46, 52]. The later one served
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especially as a workhorse for small all beta-sheet peptides to examine force fields’ bias
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towards helical conformations[53, 131].
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All-atom molecular simulations in explicit solvent have nowadays reached the
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impressive millisecond timescale thanks to the improvement of the parallelization
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algorithms[2], the highly optimised GPU implementations[55, 159, 180] and special3
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purpose supercomputers like Anton[163, 164]. For an example of the latter, it was
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the increased simulation length afforded by the Anton machine, together with a better
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performing force field, that allowed the correct folding of both FiP35, the fastest fold-
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ing variant of WW domains, and BPTI (58 residues) to experimental resolution[164],
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overcoming deficiencies of previous trials[52, 53]. The Shaw group in 2011 took the
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whole field of molecular simulation a huge step forward by demonstrating the correct
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folding of 12 structurally diverse small proteins, ranging from 10 to 80 residues and
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from all structural classes[108]. Apart from the obvious significance of a successful in
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silico folding study, they demonstrated the transient formation of native-like structural
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elements already in the unfolded state, providing unprecedented insights into their
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folding mechanism.
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The small size of the peptides is counteracted by their high flexibility and increased dynamics which made the probing of their full conformational potential extremely dif-
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ficult with conventional unconstrained molecular dynamics simulations. Thus, and
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more often that not, enhanced methods are employed to study peptide systems. In
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fact most of the work cited in this review concerns studies that make use of some of the
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established accelerated dynamics techniques, such as the replica exchange molecular dy-
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namics (REMD)[181], simulated tempering (ST)[120] and adaptive tempering[206] to
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name but few. The common concept in all of these methods is to enhance the conforma-
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tional sampling through different biasing methods (for example umbrella sampling[182],
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metadynamics[100], and accelerated MD[68]) to achieve the desired long timescales and
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retrieve thermodynamic and kinetic properties for the system. Although an in-depth
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presentation of these techniques is beyond the scope of this review, we should empha-
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sise the contribution of these methods to the field of peptide folding[76, 179, 207]
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and refer the interested reader to some excellent reviews already available in the
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literature[36, 122, 130, 141].
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To summarise the progress outlined above, we believe that molecular simulation
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of peptides has reached the level of maturity where they can realistically describe in
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atomistic detail the structure and dynamics of peptides, justifying their naming as a
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computational microscope[37]. In the past, a folding simulation could have been char-
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acterised as successful based solely on its ability to locate the native (experimentally
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determined) structure. It is an indication of the maturity of the field that simply lo-
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cating the native peptide structure through simulation is no longer sufficient for an
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application to be considered successful. The major question for recent applications 4
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is how realistically can the simulation describe the folding mechanism and the corre-
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sponding folding landscape, including the transiently stable conformations. Present-
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day molecular simulations are performing relatively well in characterising structurally
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stable peptide conformations and in estimating rates and free energies of folding[149].
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However the unfolded state is still poorly understood. The inherent properties of the
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disordered state —with its multitude of conformations of similar energies which are
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separated by relatively low energy barriers— amplifies any small force field deficiencies
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but will most probably not prevent the native structure from being located. The ability
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to perform extremely long simulations of peptide systems will allow a more extensive
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sampling of the unfolded/disordered state and should, thus, allow further refinement
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of the empirical force fields.
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3. Molecular simulations of health-related peptides
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A great interest for the study of the structure and dynamics of peptides came
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from their applications in drug design, even leading to the creation of a new subfield
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aptly named “computational peptidology”[209]. Molecular dynamics are a powerful
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tool towards this means, whose contribution is increasingly being recognised[22, 41].
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Simulation-based methods are actively used both in early stages of drug discovery as
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well as in the final steps aiming to decipher binding mechanisms[208].
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Peptides are physiologically involved in many biological processes with vital roles
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in metabolism and signalling. In particular, they are long-recognised to have a well-
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established role as anti-cancer, anti-microbial, anti-viral, anti-angiogenic and anti-
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inflammatory agents. Their inherent capability to modulate protein function increases
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dramatically their druggability potency[89]. On top of that, they offer enhanced ac-
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tivity and specificity which is translated in smaller dosages and lower toxicity. How-
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ever, their susceptibility to proteases appears to be a major bottleneck, underlying
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the need for alternative administration routes to overcome their low bioavailability[44].
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Significant improvements in the synthesis and purification techniques have made the
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production of peptides up to 100 amino acids a routine, opening new horizons for their
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large-scale health-related applications. A comprehensive presentation of the peptide-
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based drug market is exhaustively analysed in other reviews[110, 188].
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Significant advancements have also been made concerning the availability of com-
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putational tools aiming to assist peptide-based drug design studies[90, 91]. However,
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most of these tools are limited in their general applicability by making the more often 5
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than not unjustified assumption that the peptides of interest will have stable (native-
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like) structures in water. In this connection, special mention must be made of the
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Rosetta suite of programs which have been catalytic in the field, with pioneering work
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in the de novo peptide (and protein) structure prediction accuracy as assessed by
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CASP (Critical Assessment of Structure Prediction)[21]. The Rosetta algorithm im-
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plemented the fundamental concept of peptide fragments, which are short fragments
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of known protein structures that are assembled by Monte Carlo methods to predict
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protein structures[7, 172]. There are also many other in silico tools dedicated to struc-
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ture prediction but only a handful are adapted for peptides. Their accuracy is limited
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and highly dependable on the availability of experimental data. The most promising
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representative of this class is the Pepfold server that is a bioinformatics-based de novo
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approach to predict tertiary peptide structures from sequence[124]. The algorithm uses
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Hidden Markov Models and non-overlapping peptide fragments of four amino acids. It
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should be noted, however, that all of these methods and programs, and irrespectively
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of their detailed algorithmic basis, utilise empirical force fields to refine their proposed
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structures, thus highlighting the substantial interplay of peptides with the force fields
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even in protein structure prediction methods.
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Health-related applications of peptides also involve the search for small foldable
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peptides with predefined structural characteristics. Identification of small stably folded
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and soluble peptides is not trivial[59]. Many small peptides (4-10 residues) of biological
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interest have been studied computationally but were found to be marginally stable in
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solution[171]. Well-known exceptions to this rule are the designed 10-residue peptides
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chignolin[77, 98, 160] and its variant, CLN025[70, 127, 157] that adopt a unique and
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outstandingly stable β-hairpin structure in water.
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The question that arises then, is how good are the empirical force fields in describ-
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ing the structure and dynamics of peptides, especially of those that are not stably
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folded, or have more than one stable conformation. Are, for example, the force fields
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sensitive enough to predict the structural plasticity of the peptides, or, the sometimes
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pronounced effect of mutations on the peptide structure and dynamics? Force field
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improvement and validation has gone hand-in-hand with peptide simulations. In the
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following section we present a historical perspective of the evolution of the force fields
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highlighting the parallel paths that accurate peptide structure predictions and force
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field development followed through the years.
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4. Force fields: then and now A number of force fields have been developed over the years for the simulations of
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biological macromolecules. These can categorised in the families of CHARMM[114],
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AMBER[31], OPLS[85] and GROMOS[140]. The similarities and differences among
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them, especially regarding their parameterisation protocols can be found in other
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reviews[65, 153]. In what follows, we review the evolution of the force fields from
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their first appearance to the present, highlighting the pivotal role of peptides in their
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improvement.
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4.1. CHARMM force field
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Historically, the CHARMM (Chemistry at Harvard Macromolecular Mechan-
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ics) force field appeared in 1983[23] and was officially released in the version
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CHARMM19[134] (Figure 1). The published parameters comprised the so called ’ex-
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tended’ atom types and van der Waals parameters, wherein hydrogen atoms were in-
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cluded as part of their attached heavy atoms for sulfur and carbon, whereas for nitrogen
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and oxygen the hydrogen atoms were treated explicitly, hence the name united-atom
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potentials. One of the major features was the application of the partial atomic charges
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to fit ab initio calculations, using the TIP3P water model[84] to calibrate the inter-
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actions. The potential function also included internal energy terms for bonds, angles,
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dihedrals, improper dihedrals as well as the non-bonded terms for van der Waals and
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electrostatics, using a truncation cutoff for the latter. This basic form of the energy
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function has been carried-over to almost all present-day empirical force fields.
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CHARMM22[113][114] was later introduced as an ”additive” protein force field that included explicit parameters for all atoms (rendering the term ’extended atom’
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obsolete), emphasising on the balance of interactions involving the protein and the
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solvent and in-between. This was mainly achieved through a refinement of the non-
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bonded interactions already implemented in the CHARMM19 version, by broadening
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the experimental and ab initio data used. Backbone parameters were based on the
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N-methylacetamide (NMA) and the alanine dipeptide and the side chains were based
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on a number of small model compounds. Additive force fields do not allow however
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the change of the electrostatic parameters as a function of environment, neglecting
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the electronic polarisation phenomenon. The CHARMM22 protein parameters were
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maintained to the version that followed, CHARMM27, where only the nucleic acid
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and lipid parameters were updated together with parameters for a number of common
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ions[112]. This force field version remained prevalent for a decade until the introduction of
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the CHARMM22/CMAP version which incorporated the addition of a dihedral correc-
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tion map (CMAP)[115, 116]. CMAP is a two-dimensional grid of energy corrections
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in the dihedral space of φ/ψ angles added to the potential energy equation, which
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improved the secondary structure propensities and compensated for the demonstrated
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helical bias of the CHARMM force field[178]. The parameters for the CMAP term
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were derived from a big collection of protein x-ray crystallographic data[116]. The
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CHARMM22/CMAP version had an improved performance[25], but deficiencies in the
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equilibrium between helical and extended conformations were noted which affected the
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ability of the force field to correctly fold small peptides, mostly due to an increased heli-
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cal propensity[13, 52, 53]. Thus, further improvements were incorporated by correcting
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the backbone and side-chain dihedral angles to sample better the corresponding regions
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in the Ramachandran plot[19]. Corrections were based on experimental solution NMR
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data of weakly structured peptides for all residues except glycine and proline, for which
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QM-based corrections were made. We should note that this work was not based solely
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on alanine peptides but also on small helical and hairpin peptides.
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In later years, only non-protein parameters regarding lipids, carbohydrates,
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drug-like and cofactor molecules were implemented, giving rise consequently to
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CHARMM27r, CHARMM35 and the CHARMM General Force Field (CGenFF). To-
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gether they resulted in the latest great release of CHARMM36[19, 81] and a few years
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later of CHARMM36m for intrinsically disordered proteins[82]. In parallel, version
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CHARMM C22*[150] was presented that aimed towards a better helix-coil balance.
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This was achieved by replacing the CMAP correction for all residues except glycine and
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proline, and modifying the side-chain partial charges and torsional terms for residues
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aspartate, glutamate and arginine (following the philosophy of the ff99SB* and ff03*
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corrections in the AMBER family that is presented in the next section). A more com-
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prehensive presentation on each component of the CHARMM all-atom additive force
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field together with the parameterisation philosophy and methodology and the recently
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released CHARMM Drude polarizable force field can be found elsewhere[111, 187, 210].
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4.2. AMBER force field
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The AMBER (Assisted Model Building with Energy Refinement) force field first appeared also in the early 80s, sharing the united-atom idea[195] but was soon extended 8
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to an all-atom force field with recalibrated torsional and angle parameters based on
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experimental conformational energies[196] (Figure 2). A decade of improvements in
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the parameters and the algorithm gave rise to a second generation force field, named
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ff94[31]. Since then, the tradition has it that protein (and nucleic acid) force fields
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in the AMBER family are named with ”ff” followed by a two-digit number year. Up
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to this point, the parameterisation was focused on the gas phase behaviour, but the
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need to produce potentials that are suitable for condensed phase simulations became
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apparent for a more balanced modelling of biomolecules in solution. Unlike CHARMM
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though, the core parameterisation is different here, employing more adjustable empir-
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ical parameters that can be optimised. For example, the fixed atomic partial charges
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of CHARMM that are tightly connected to the TIP3P water model are not present
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here. Instead AMBER employed initially an ESP (electrostatic potential) fit for atomic
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centred charges and later an RESP fit (restrained ESP) where charges were fitted simul-
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taneously to several conformations to achieve a better average behaviour. The dihedral
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parameters were fit to relative QM energies of alternate rotamers of small molecules
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to represent several conformations of glycine and alanine. Unlike CHARMM, the AM-
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BER force fields underwent many optimisations and refinements to reach a satisfactory
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level of accuracy, giving rise to a large number of variants.
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The ff94 force field was shown to over-stabilise helical conformations and over-
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estimate computed melting temperatures in peptide simulations, sometimes even bias
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helices over the native β-hairpin conformation[57, 137, 170]. The ff94 version was soon
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replaced by ff96 and C96[93], which featured improved calculations for electrostatics
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and van der Waals interactions and better accounted of long-range effects. This resulted
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in better fitting to ab initio calculations on small peptides and more balanced solvent-
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solvent and solute-solvent interactions. One of the main drawbacks of this version
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was a bias towards β-structures this time[74, 88, 138]. The next version ff99[190]
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was yet another attempt to refit the backbone dihedral parameters using this time
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more representative structures of alanine and glycine in the form of tetrapeptides and
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dipeptides. At that time, generalised parameters for compounds beyond proteins and
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nucleic acids were also released. The new potential surfaces were significantly different
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of those of its predecessors.
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Force field optimisation was assisted by the longer simulation times that became fea-
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sible, which only uncovered more force field deficiencies. This opened up to a decade of
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numerous almost in-parallel efforts to improve AMBER force field, making it challeng9
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ing to keep up with them and even more to choose the appropriate one for a particular
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study. Despite the extended optimisation of the ff99 version, AMBER force fields con-
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tinued to suffer from an imbalance of secondary structural elements, over-stabilising
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α-helical peptides, like their ff94 counterpart[57, 137].
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A few years later ff03 was released, a so called third-generation point-charge all-atom
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force field[39]. The major contribution was the fitting of the electrostatic potential and
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main-chain torsion parameters to QM calculations of small peptides in condensed phase
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with continuum solvent models. Initial testing showed a satisfactory balance between
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helical and extended conformations and a better description of the polyproline II region.
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A united-atom counterpart was also released, ff03ua[201], where aliphatic hydrogens of
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α-carbon and aromatic hydrogens are explicitly represented whereas aliphatic hydro-
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gens of side-chains are represented united to their carbon atom, to improve speed for
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computationally demanding cases like folding simulations. A close variant of ff03, ff03*
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incorporated a correction to the backbone dihedral potential to fit experimental data
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of helix-coil transition, making it more transferable and able to fold peptides from both
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helical and beta structural classes[15]. The ff03w force field[16] is a slightly modified
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version of ff03*, with a backbone dihedral potential correction that allows the usage
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of the more accurate TIP4P/2005 water model[1]. This updated force field offered a
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better description of the folding thermodynamics and of the unfolded state as tested
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in small peptides, whilst preserving its ability to fold to the native structure larger
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peptides like the Trp cage and the GB1 hairpin. It still suffered though from poor
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solvation, with less favourable solvation free energies and too favorable protein asso-
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ciation. In an attempt to further improve the representation of these properties, the
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ff03ws force field[18] was released which essentially incorporated a tuning parameter
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for the Lennard-Jones protein-water interaction, specifically the water oxygen. The
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same scheme applied to the ff99SB force field, gave rise to version ff99SBws[18].
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The ff99SB force field[79] was a parallel effort focused largely on improving the φ/ψ
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dihedral terms of the previous ff94/ff99 energy functions, after showing that the inad-
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equate backbone dihedral parameterisation was indeed responsible for the weaknesses
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of that generation of force fields. The major realisation here was that the two sets
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of dihedral backbone parameters introduced in ff94 version have to be both individu-
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ally optimised for glycine and non-glycine residues. Glycine due to absence of a Cβ
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atom needs only one set of dihedral parameters, φ/ψ (defined as φ = C-N-Cα -C, ψ =
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N-Cα -C-N), whereas all other amino acids that harbor a side-chain need also a φ’/ψ’ 10
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term (defined as φ’ = C-N-Cα -Cβ , ψ’ = Cβ -Cα -C-N). Then the dihedral potential for
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the non-glycine residues will be the sum of them. This resulted in better agreement
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with the PDB data for the dihedral angles and consequently better description of the
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secondary structural preferences of small peptides as well as improved fitting to NMR
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observables of larger peptides, like trpzip2, trp cage, villin headpiece, ubiquitin and
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lysozyme.
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In the same spirit, there were some efforts like the AMBER-GS version[57], where the φ/ψ torsion potential was completely removed to fit better to experimental helix-
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coil parameters, but the α-helical bias was not removed as shown by long equilibrium
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ensemble simulations[177]. As a remedy, the ff99SB-φ’ force field[177] was proposed
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where they combined the low helicity of the ff99 potential with the high helicity of
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the ff94, by removing the additional barriers on the φ rotational degree of freedom.
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This version provided a better description of the helix-coil transition but its usage to
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non-helical peptides was not verified.
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The fast —almost chaotic— production of even more versions of AMBER force fields
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continued unimpeded in the years to come. All versions from this period shared the
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core potential function of ff99SB which demonstrated superior performance to previous
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versions[13], proving the significance of the proper backbone dihedral parameterisation.
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Next in line, came ff99SB* force field[15], which incorporated to 99SB potential the
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same backbone correction as the ff03* version described above. This improved the
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helical bias and showed better agreement to NMR data of peptides but with poor
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thermodynamics description.
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A different approach was introduced with the ff99SB-ILDN version[109], where the
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torsion potentials of side-chains were targeted this time. Especially four residue types,
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isoleucine (I), leucine (L), aspartate (D) and asparagine (N), where found to have
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considerably different rotamer distributions in the simulation in respect to the exper-
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imentally observed ones. So, the side-chain torsion potentials for these four residues
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were fitted to high-level QM calculations, improving considerably the agreement to
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NMR data for the rotamer distributions. Of course combinations of these optimisa-
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tions surfaced, like ff99SB*-ILDN[15] and later ff99SB*-ILDN-Q[14], which combined
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the global backbone correction and the modified torsion parameters for residues ILDN,
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with refitted charges for residues D, E, K, R.
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On another front, the Br¨ uschweiler group introduced the concept of employing experimental NMR data that are commonly used to cross-validate a force field’s per11
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formance, to optimise them instead. Thus they used a collection of NMR chemical
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shift data and RDCs for peptides to optimise and improve the ff99SB version using
337
an energy-based reweighting to match the experimental data in an iterative manner,
338
giving rise to the versions ff99SBnmr1[105] and ff99SB-φψ[106] that showed superior
339
performance when compared to its parent force field, ff99SB.
340
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Around that time, it became clear that it was imperative to produce a catholic AMBER version with carefully selected corrections that can reproduce faithfully ex-
342
perimental data for peptides from all structural classes that the developers can respon-
343
sibly recommend to general users of molecular simulations. Towards this direction, a
344
preliminary version, ff12SB, and nowadays ff14SB[118] were officially released. Taking
345
lessons from all the previous optimisation attempts, this version comprised a complete
346
refit of the side-chain dihedral potential of all amino acids, including alternate protona-
347
tion states for the ionizable ones, and empirical adjustments to the backbone dihedral
348
potential, including the φ rotational profile. The superiority of this updated version
349
was tested for reproducibility of the secondary structural content and NMR parameters
350
of peptides and proteins in solution. The ff12SB version was also optimised by adding
351
a CMAP-like correction, ff12SB-cMAP, for simulations with implicit solvent models,
352
when computational speed is a crucial factor[146].
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Although the ff14SB is the one officially still recommended by the developers at the
354
time of the writing, another version, ff15SB, came up for use in combination with the
355
TIP3P-FB water model[192]. This version comprised a complete refitting of the bonded
356
parameters of the parental ff99SB force field and was shown to retain the prediction
357
accuracy of equilibrium properties while improving the accuracy of the temperature
358
dependent ones[127]. Its broader application and establishment remains to be seen.
359
For completeness, there are nowadays available force fields that can also describe small
360
molecule ligands (General AMBER force field, GAFF), carbohydrates (GLYCAM),
361
lipids (lipid14) but also amber-compatible parameters for post-translational modifica-
362
tions (Forcefield PTM) and ff15ipq version for implicit polarised charges in explicit
363
solvent[34].
364
4.3. Force fields for disordered peptides
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Much of the current focus in the community of force field development has turned
366
towards the study of disordered peptides. An accurate description of the landscape of
367
these structurally challenging peptides is of paramount importance due to the increas-
368
ing acknowledgement of their abundance in protein structures as modular elements and 12
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their participation in many cellular processes[40]. Their main characteristic, the abil-
370
ity to interconvert between different conformations, also presents the greatest challenge
371
which is the requirement to transform force fields that underwent decades of optimisa-
372
tion cycles to model well-folded peptides, to now perform comparably well even with
373
disordered peptides.
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Disordered peptides present the additional challenge of interpreting complex experi-
375
mental observables that are averaged ensembles over transient conformations. The most
376
common experimental techniques used for validation of the simulation data comprise
377
NMR (nuclear magnetic resonance), usually amide proton exchange measurements, J-
378
couplings, chemical shifts, NOEs (nuclear Overhauser effect) and RDC (residual dipo-
379
lar coupling) constants, FRET (F¨orster resonance energy transfer) and SAXS (small
380
angle X-ray scattering), that have been reviewed recently[18, 26, 72, 80]. Infrared spec-
381
troscopy has emerged lately as a powerful tool to probe the conformational dynamics
382
of the disordered states, providing experimental evidence on the secondary structures
383
of sites that can be isolated by isotope labelling that can be compared with computa-
384
tionally modelled amide I spectra[48].
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Naturally, force fields had to embrace the need to represent the disordered state
386
as accurately as the well-structured state. The first attempt to produce such a force
387
field was based on the application of the CMAP correction method to the dihedral
388
potential of 8 disorder-promoting residues (A, G, P, R, Q, S, E, K), using as basis
389
the ff99SB-ildn force field, giving rise to the version ff99IDPs[193] (Figure 2). A later
390
validation study using a set of 3 representative IDPs showed a quantitative agreement
391
with the experimental NMR chemical shifts and more representative conformational
392
sampling, though still suffering from over-stabilisation of structured conformations,
393
most probably due to inadequate representation of polar interactions[203].
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A more comprehensive effort was presented through the refined CHARMM36m
395
(Figure 1) force field[82] that tried to address a reported bias for overpopulation of
396
the αL region of the Ramachandran plot[154]. The exhaustive benchmarking gave
397
satisfactory fitting to experimental parameters for IDPs while retaining consistency
398
with the CHARMM36 counterpart for folded peptides, folding kinetics and free energy
399
calculations. It removed the oversampling of the αL region observed in CHARMM36,
400
but also underestimated the β region as shown through simulations of peptides like
401
chignolin and CLN025. The main issue addressed was the over-compactness, a common
402
characteristic of all current generation empirical force fields when applied to studies of 13
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403 404
the disordered state. In the same spirit, and inspired by previous optimisation efforts, a force field termed a99SB-disp was released (Figure 2), the most recent to our knowledge empiri-
406
cal force field dedicated to accurately present both folded and unfolded conformational
407
states[156]. This force field is based on the ff99SB-ILDN version with necessary modi-
408
fications to employ the TIP4P-D water model. Its superior performance is attributed
409
to (a) an iterative scheme to optimise the backbone and side-chain torsion parame-
410
ters to represent better the protein-water van der Waals interactions inspired by the
411
ff99SB*-ILDN-Q version, and, (b) the modification of the strength of the Lennard-
412
Jones term for carbonyl oxygen and amide hydrogen pairs. Its performance remains to
413
be evaluated in the years to come.
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Amyloid (Aβ) peptides and in particular their assembly into fibrils, have been one of
415
the most challenging peptide systems to study with significant difficulties encountered
416
with both the experimental and computational approaches. The interested reader is re-
417
ferred to some excellent reviews of these Alzheimer’s disease-related peptides[133, 183].
418
A large number of studies appeared which attempted to computationally characterise
419
the peptides’ equilibrium conformations using the most advanced force fields. The great
420
discrepancy among the predicted structures of the monomers as well as of the various
421
oligomers only highlights the difficulty to describe the conformational preferences of
422
disordered peptides and the force field bias that needs yet to be addressed[136]. The
423
differences between the various force fields, sometimes in the context of different water
424
models as well, have been attributed to differing secondary structure biases as well
425
as the intrapeptide hydrogen bonding, with helix-overestimating force fields, like AM-
426
BER99SB and CHARMM22-CMAP, having the poorest agreement to experimentally
427
observed populations[174]. Later studies with improved force field versions accompa-
428
nied by different water models, such as OPLS-AA/TIP3P, AMBER99SB-ILDN/TIP4P-
429
Ew and CHARMM22*/TIP3SP demonstrated strongly converged structural properties
430
for these type of disordered peptides[158] and improved agreement with experimental
431
J-coupling constants, chemical shifts and CD data[176]. These encouraging findings
432
indicate that force field improvements may be heading in the correct direction. How-
433
ever, the force field validation is difficult due to the limited availability of experimental
434
observables for disordered peptide systems. This is particularly concerning when force
435
field performance is found to be dependent on the peptide system per se. For instance,
436
the CHARMM36/TIP3P combination was the most accurate in the case of Aβ10-
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40 peptide but not in the case of Aβ1-40 and Aβ1-42 peptides[173]. In a different
438
study, the most recent versions AMBER14SB and CHARMM22* with TIP3P water
439
model showed a helical overestimation compared to CD data, whereas OPLS-AA and
440
AMBER99SB-ILDN with the same water model represented conformational ensembles
441
closer to experiment[119]. Clearly further studies are needed to determine the source
442
of the force field discrepancies, but more importantly to also comprehend whether the
443
limited accuracy for disordered peptide systems is due to the interplay between the
444
force field and water model parameters.
445
4.4. Other biomolecular force fields
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The force field families of CHARMM and AMBER are the ones that underwent
447
through heavy optimisation and validation by the developers but also the rest of the
448
community in the peptide folding and dynamics field. For completeness we should also
449
mention two additional and significant contributions, those of the OPLS and GROMOS
450
force fields.
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The OPLS (optimised potentials for liquid simulations) made its appearance in
452
the 80s as well (OPLS-ua) and was initially intended for simulation of liquid-state
453
properties of water and other organic liquids[84] (Figure 3). A distinct feature was the
454
emphasis given to model the non-bonded interactions to fit liquid-state thermodynamic
455
properties, like density and heat of vaporisation. The first release was a combined
456
AMBER/OPLS force field[86] (AMBER ff94 was largely inspired by OPLS) and was
457
later updated to the all-atom version OPLS-AA[85]. An update of it came out a
458
few years later, where side-chain potentials were reparameterized based on QM-data
459
of small peptides[87]. The major contribution from this effort was, and still is, the
460
development of the water models TIP3P and TIP4P that are heavily used to the
461
present. It was only very recently that new OPLS versions emerged, like OPLS2.1 and
462
OPLS3, that are mostly optimised towards small molecules and protein-ligand binding
463
studies[69].
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Closing this section, we should refer to GROMOS (Groningen molecular simulation)
465
that appeared in the 90s together with the homonymous computer simulation program
466
with the most cited version being GROMOS96[186] (Figure 4). The newest release
467
appeared a few years ago as GROMOS11 with the parameter sets 54A7[161] and now
468
54A8[155]. Its inferior performance compared to other force fields in comparative
469
validation studies of peptide folding and dynamics prevented its broader use in the
470
specified field of peptide simulations and will not be further presented here. 15
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4.5. Water models for explicit representation of the solute in peptide folding simulations
472
This review is focused on peptide folding simulations that comprise explicit repre-
473
sentation of the solvent. Therefore, the ability of the force fields to describe accurately
474
the conformational landscape of the peptides is inextricably dependent on the ability
475
of the associated water model to describe the physical properties of water molecules in
476
the liquid phase. There are numerous water potentials that have been developed so far,
477
but we shall only mention here the empirical potentials that are used in biomolecular
478
simulations (Figure 5). Detailed presentation of all available water models and their
479
comparative performance can be found elsewhere[30, 64, 73, 139, 142, 185, 189].
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Their first appearance coincided with the early protein force field versions in the 80s and they all share the idea of a rigid water monomer with the non-bonded interac-
482
tions described by 3, 4, or 5 sites composed of Coulombic terms for the intermolecular
483
interaction pairs and a Lennard-Jones term for oxygen atoms upon dimerization. His-
484
torically, two quite similar 3-site models were introduced in parallel in 1981. These
485
were the TIPS (transferable intermolecular potential)[83] model, and the SPC (simple
486
point charge)[11] model, two of the most popular potentials for water molecules in
487
molecular simulations even to date[153]. The main difference between TIP and SPC
488
models is the tetrahedral shape geometry adapted by the latter and its ability to re-
489
produce the experimental radial distribution function (including the second peak) and
490
the self-diffusion coefficient. Later the SPC/E[10] model was released that comprised
491
an additional polarization correction leading to better representation of the density,
492
diffusion coefficient and dielectric constant for simulations of liquid water. Together
493
these features made the SPC models more appropriate for modeling the bulk properties
494
of water[121].
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Later reparameterisation of TIPS and addition of a Lennard-Jones term to the hy-
496
drogen atoms as well, lead to improved representation of the density of liquid water and
497
gave rise to what became the standard model for protein simulations, the TIP3P[84]
498
model. Concurrently with TIP3P, its 4-site version was released, the TIP4P model,
499
which also incorporated terms for the bisector of the H-O-H angle allowing a better
500
electrostatic distribution. The TIP4P model provided a better description of most of
501
the water’s properties (like the phase diagram) but not of its dielectric constant. The
502
increased computational cost (imposed by the larger number of interactions to be cal-
503
culated) prohibited its wider use in the early peptide folding studies. The most crucial
504
factor however for the wider application of TIP3P was its coupling to the vastly popular 16
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CHARMM22 force field. The 5-site interaction version, TIP5P[117] appeared in 2000,
506
which replaced the single negative charge on the bisector angle of TIP4P with two
507
single negative charges on the lone-pair electrons. The truncated tetrahedral geometry
508
showed excellent representation of the structure of water, matching the density and
509
radial distribution properties, but suffered in describing the gas phase. The increased
510
complexity also significantly increased the computational requirements. As a result,
511
SPC and TIP4P models provided a satisfying description of liquid’s water structural
512
and thermodynamic parameters at a much lower computational cost.
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The scenery changed with the increase in the available computational power but
514
most importantly the appearance of AMBER force field versions that gave more free-
515
dom on the choice of water model (RESP-fitted atomic charges). All aforementioned
516
water models utilise truncated Coulombic interactions. An improved treatment of the
517
long-range interactions with particle-mesh Ewald summation gave rise to the TIP4P-
518
Ew[78] model which improved the representation of liquid water’s thermodynamic pa-
519
rameters over a large temperature range but without adding significantly to the compu-
520
tational cost. On the same spirit was based the parameterisation of the TIP4P/2005[1]
521
model which reproduces temperature-dependent properties but underestimates the di-
522
electric constant. The TIP4P/ǫ[56] model is fine tuned to match exactly that property
523
in a large temperature regime. An equivalent version is the TIP4Q[4] model that
524
includes an additional charge to increase the dipole moment, but at an additional
525
computational expense compared to other TIP4P-based models. The common charac-
526
teristic of these water models is the larger enthalpy of solvation that leads to stronger
527
interactions between the water and the embedded protein. It is for that reason that
528
they have been lately employed in folding simulations of disordered less hydrophobic
529
peptides, facilitating a more accurate description of the expanded unfolded state. On
530
the same front, the TIP3P-FB and TIP4P-FB[191] models were introduced by applying
531
the so called ForceBalance method that combines reference data produced both exper-
532
imentally and theoretically to derive parameters for force fields. The resultant models,
533
and in particular the TIP4P-FB, manage to reproduce most of the kinetic and thermo-
534
dynamic properties of water, like the viscosity, diffusion coefficient, dielectric constant,
535
radial distribution function and heat of vaporization, in a variety of temperatures and
536
pressures.
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The take-home message here is that there is no perfect water model that encapsu-
538
lates all of the experimental physical properties of water. Furthermore, the general 17
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users are highly restricted in their choice by the compatibility to the protein force
540
field of choice and whether it is implemented in a molecular mechanics program.
541
For example, the molecular dynamics simulation engine NAMD[147] only supports
542
TIP3P- and TIP4P-based models from the whole panel of non polarizable water
543
models. Gromacs[12, 184] on the other hand supports SPC, SPC/E, TIP3P, TIP4P
544
and TIP5P. It has thus become common knowledge in the field that the GROMOS
545
force fields should better be paired with the SPC water models, OPLS force fields
546
are recommended to be used with TIP4P, whilst the CHARMM family of force fields
547
should be paired with the TIP3P model to avoid inconsistencies.
548
fields, especially the latest versions, are more versatile. Despite the relatively poor
549
performance of some water models with respect to the description of the bulk solvent
550
properties, their success in the folding of proteins and peptides appears to indicate that
551
folding per se may not be as sensitive to the properties of bulk solvent. This finding is
552
probably the result of the protein force fields being developed given the available water
553
models, so their deficiencies could be masked in the empirical parameterization of the
554
force fields. As the observation that the main deficiency of current generation of force
555
fields is the poor description of the protein-water interactions, an effort in underway
556
to develop force fields that are parameterized in combination with the newly reported
557
water models. In that spirit the TIP4P-D[148] was recently released in an effort to
558
recapitulate the more extended conformational ensembles of the disordered state by
559
increasing the strength of the dispersion interaction (LJ-term) (see also section 6.
560
The future). As is always the case with molecular simulation, it will be the extensive
561
testing by the community that will define which of these models will survive the acid
562
test of a quantitative comparison with the experimental data, including the ability to
563
accurately describe the kinetics and thermodynamics of peptide folding.
565
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5. The unceasing quest for a balanced biomolecular force field
566
The previous sections clearly demonstrated that one of the main contributions
567
of peptide simulations is their continuing usage as test systems for the optimisation,
568
correction and validation of empirical force fields[5, 61, 107, 123, 175]. One of the
569
recurring challenges through all these studies has been to convincingly quantify force
570
field accuracy, especially in connection with the fact that the relatively limited simu-
571
lation timescales attainable are insufficient for guaranteeing a faithful configurational 18
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sampling of the peptides’ folding landscapes[51]. Soon it became clear in the litera-
573
ture that the initial force field versions from all families were suffering from helical
574
bias[13, 51, 53, 62, 79, 123, 137, 165, 178, 204]. A common remedy to tackle the helical
575
bias of the early force fields was to choose one with a bias towards the major secondary
576
structure of the protein under study. This was obviously highly unsatisfactory and
577
proved indeed ineffective, as demonstrated by the folding simulations of villin and Pin1
578
WW domain mentioned earlier with the CHARMM22/CMAP force field[115, 116]. In
579
these studies, villin folded to its native structure[54] but the WW domain, whose na-
580
tive structure is a 3-stranded β-sheet, did not[52]. The reason, of course, was that as
581
far the force field was concerned a misfolded conformation had lower free energy than
582
the native structure[47, 53]. Studies such as these highlight how small force field inac-
583
curacies can have an additive effect and can result in stabilising misfolded non-native
584
structures.
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AMBER’s ff99SB was the first successful version to convincingly compensate for
586
that and displayed superior performance over the rest of the force fields of its time:
587
literature consistently provided overwhelming evidence of significantly improved bal-
588
ance of secondary structural elements and reasonable agreement with experimental
589
data through multiple comparative validation studies comprising from short glycine
590
and alanine peptides to longer 10-20 residue peptides (disordered, helical, beta) up to
591
small proteins like lysozyme and ubiquitin[8, 58, 79, 92, 94, 99, 102, 123, 144, 145, 168,
592
168, 169, 197, 198].
TE
Follow-up studies suggested two more force fields, f99SB-ILDN-φ and ff99SB-ILDN-
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593
D
585
NMR, with significantly improved agreement with NMR observables, highlighting
595
though that large uncertainties accompany this agreement: statistical calculated er-
596
rors in the validation were in the margin of systematic experimental errors of these
597
parameters[9].
598
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The newer versions that surfaced, ff03/ff03* and ff99SB*-ILDN from AMBER, and
599
CHARMM22/CMAP and CHARMM22* from CHARMM, all succeeded in predicting
600
the native states and folding rates (for example the case of the model protein villin
601
headpiece), but displayed distinct discrepancies in the folding mechanism and in the
602
description of the unfolded state in particular, with ff99SB*-ILDN and CHARMM22*
603
being closer to the experiments[150]. CHARMM22* showed superior performance over
604
its counterparts in the CHARMM family in describing the free energy landscape of the
605
β-hairpin GB1[71]. Similarly, f99SB and its variants (ff99SB*, ff99SB-ILDN, ff99SB*19
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ILDN), ff03, ff03* and the GROMOS96 (43a1p,53a6) succeeded in finding the residual
607
β-hairpin preference of the disordered 16-mer Nrf2-derived peptide but with extremely
608
spurious results that were temperature dependent[29]. In accordance, a parallel study
609
with ff99SB-ILDN, ff99SB*-ILDN, CHARMM22/CMAP and CHARMM22* provided
610
accurate description of the native state of ubiquitin, GB3, villin and WW domain, but
611
force fields with better helix-coil balance, ff99SB*-ILDN, ff03* and CHARMM22* had
612
superior performance in the peptide systems[107]. Our personal recent work also lends
613
further support that for structurally challenging peptide systems, the ff99SB*-ILDN is
614
outperforming its counterparts in the AMBER 99SB family[3, 60, 162].
SC
615
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606
To summarise, our take on the current literature is that from the set of all extensively tested and validated force fields, there are nowadays versions from both AMBER
617
and CHARMM families that are shown to be balanced and well-performing in a wide
618
variety of tested systems, including cases of intrinsically disordered peptide systems,
619
like the RS repeats[154]. All that being said, we present in the next section our views
620
concerning the remaining challenges towards a universally useful biomolecular force
621
field.
622
6. The future
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616
We believe that a bird’s eye view of the recent literature leaves little doubt: peptide
624
simulations followed the rest of the molecular dynamics field in making a tremendous
625
progress towards accurate and physically relevant simulations. The development of
626
new algorithms, the production and validation of new robust and transferable force
627
fields, together with the increase of computational power available to the research
628
groups, completely transformed the field. Indeed, it is no longer an exaggeration to
629
state that we have reached the point where molecular simulations can faithfully predict
630
and reproduce the peptides’ native states, folding rates and in exceptional cases even
631
provide atomistic description of the folding mechanism in unprecedented detail, often
632
unreachable by experiments. Having said that, there are still a significant number of
633
unresolved issues and deficiencies, some of which are discussed in the paragraphs that
634
follow.
635
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Peptides with weak structural propensities are difficult systems to track computa-
636
tionally. The major challenge here is to describe, without overestimating, the residual
637
(if any) secondary structure present in the unfolded state, whilst retaining the fold-
638
ing performance for the folders. Some recently reported issues concern the observed 20
ACCEPTED MANUSCRIPT
temperature dependence of the conformational preferences of peptides and the weak
640
folding cooperativity, whose combination results in a relatively poor description of
641
the kinetics and thermodynamics[33]. As discussed in the previous section on water
642
potentials, the source of this ”overcompactness” compared to the experimental observ-
643
ables (SAXS, FRET, Rg) appears to be the inaccurate description of the solvation
644
of the unfolded chain, possibly due to systematically underestimating the dispersion
645
parameter in the protein-water interactions[18, 72, 148]. A number of approaches have
646
been proposed to remedy this, for example applying a scaling factor to the van der
647
Waals interaction parameter[18], or re-parameterizing the Lennard-Jones parameter
648
for water’s oxygen (TIP4P-D water model[148]) or hydrogen (mTIP3P)[82]. These ap-
649
proaches improved the agreement with the experimental observables for some peptide
650
cases but not for others, rendering this approach not universally applicable. For ex-
651
ample, recent studies showed that the more polar TIP3P model favours more compact
652
structures[176]. On the other hand, the treatment of the protein-water interactions
653
by the TIP4P-Ew and TIP4P/2005 water models, eases the hydrophobically-driven
654
collapse and improves sampling of the disordered state for peptides like Trp-cage and
655
GB1[17], with TIP4P/2005 giving less collapsed conformations[135]. The latest of
656
the released water models, TIP4P-D matched better the experimental Rg in a set of
657
disordered peptides[148].
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639
It has, thus, been realized that a new direction for further improvement of the
659
force fields is the one aiming towards an accurate description of the solvation effect
660
and better accounting for the long-range interactions. It is probably not surprising
661
that the newest of the empirical protein force field versions are adapting to new water
662
models that provide a better description of the total physical properties of the solvent.
663
However, obtaining a balance between the water model and the protein force field is
664
not a trivial exercise, especially with respect to peptide folding and dynamics. The
665
bulk properties of the solvent are experimentally tractable and thus it is straightfor-
666
ward to validate the available water models on how well they describe the solvent’s
667
molecular properties. However, the impact of the interactions between the solvent and
668
the biomolecules on the conformation of the latter is still poorly understood and needs
669
further exploration. A much different approach has been introduced with a force field
670
based on the Kirkwood-Buff theory (KBFF)[152] to retrieve force field parameters
671
that reproduce the microscopic characteristics of the solution to better describe the
672
protein-water interactions. This force field was found to compensate for the overcom-
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21
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pacteness and match the experimentally found dimensions of disordered peptides[128],
674
still though at the expense of partially unfolding peptides like GB1[129]. However, this
675
was partially rescued by increasing the interaction cut-off to strengthen the contribu-
676
tion of the long range interactions, like in the case of AMBER99SB*-ILDN with the
677
TIP4P-D water model for Nup peptides[148].
678
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673
Polarizable force fields might be an alternative route by accounting for the environmental effects. Their main asset is the ability to describe changes of the charge
680
distribution upon conformational changes of the molecules. This can be achieved via
681
fluctuating charge models, Drude oscillator-based models[101], inducible dipole models
682
or multipole electrostatics, like in AMOEBA[166], all of which are detailed in other
683
reviews[6, 67]. Their general applicability is hindered by the large computational bur-
684
den of the additional electrostatic interatomic forces calculations, barely reaching the
685
100ns timescale even for small peptide systems.
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679
The difficulty in approaching all those unresolved matters in a meaningful way is
687
that on one hand the disordered state is heavily undersampled computationally and on
688
the other hand complex experimental data of disordered peptides can have ambiguous
689
interpretations. We believe that peptides have and will continue to serve as an acid
690
test for the performance of molecular simulations and force fields to reproduce the
691
physical reality: small deficiencies in the force field parameterisation can be shielded
692
in the larger well-folded protein context. Further improvements could be of substantial
693
importance towards more accurate modelling of disease-related issues, like mutation
694
effects, misfolding, aggregation or alternative enzyme conformations that affect drug
695
binding. We hope that this review of the literature regarding molecular simulations
696
of peptides and associated force fields will aid the readers to wisely select a force field
697
suitable for a certain application in order to achieve high quality results.
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7. Author Information Corresponding Author
700
*Phone: +30-25510-30620. Fax: +30-25510-30620.
701
Web page: https://utopia.duth.gr/glykos/. E-mail: [email protected].
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ORCID
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Panagiota S. Georgoulia: 0000-0003-4573-8052
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Nicholas M. Glykos: 0000-0003-3782-206X
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Notes
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The authors declare no competing financial interest.
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Figure 1: CHARMM family of protein force fields. Circled tree map representation of the various protein-related force fields developed to present time. The size of the circle and the colour is analogous to the number of reported citations. Genealogically-related force field are encircled in the same hierarchical level, which is represented by the thickness of the lines. Force-fields are ordered chronologically from left to right by year of appearance.
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Figure 2: AMBER family of protein force fields. Circled tree map representation of the various protein force fields developed to present time as presented in Figure 1.
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Figure 3: OPLS family of protein force fields. Circled tree map representation of the various protein force fields developed to present time as presented in Figure 1.
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Figure 4: GROMOS family of protein force fields. Circled tree map representation of the various protein force fields developed to present time as presented in Figure 1.
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Figure 5: Water models for biomolecular simulations. Circled tree map representation of the water potentials used in simulations of proteins and peptides. The size and colour of the circles follows their popularity as expressed by the number of citations. Encircled are the models that can be used in conjunction with a specific family of force fields, with consecutive levels of hierarchy represented by the line colour.
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S0003-9861(18)30734-3
DOI:
https://doi.org/10.1016/j.abb.2019.01.033
Reference:
YABBI 7939
To appear in:
Archives of Biochemistry and Biophysics
Received Date: 14 September 2018 Revised Date:
23 January 2019
Accepted Date: 28 January 2019
Please cite this article as: P.S. Georgoulia, N.M. Glykos, Molecular simulation of peptides coming of age: Accurate prediction of folding, dynamics and structures, Archives of Biochemistry and Biophysics (2019), doi: https://doi.org/10.1016/j.abb.2019.01.033. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Molecular simulation of peptides coming of age: accurate prediction of folding, dynamics and structures. Department of Chemistry and Biomedical Sciences, Faculty of Health and Life Sciences, Linnæus University, Kalmar, 39182, Sweden 2 3
Linnæus University Centre of Excellence “Biomaterials Chemistry”, Kalmar, 3912, Sweden
Department of Molecular Biology and Genetics, Democritus University of Thrace, University Campus, Alexandroupolis, 68100, Greece
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Panagiota S. Georgoulia1,2 , Nicholas M. Glykos3 *
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Abstract
The application of molecular dynamics simulations to study the folding and dynamics of peptides has attracted a lot of interest in the last couple of decades. Following the successful prediction of the folding of several proteins using molecular simulation, foldable peptides emerged as a favourable system mainly due to their application in improving protein structure prediction methods and in drug design studies. However,
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their performance is inherently linked to the accuracy of the empirical force fields used
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in the simulations, whose optimisation and validation is of paramount importance. Here we review the most important findings in the field of molecular peptide simulations and highlight the significant advancements made over the last twenty years. Special
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reference is made on the simulation of disordered peptides and the remaining challenge to find a force field able to describe accurately their conformational landscape. Keywords:
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peptide simulations, peptide folding, peptide dynamics, empirical force fields, validation.
Preprint submitted to Archives in Biochemistry and Biophysics
January 30, 2019
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1. Overview Molecular simulations have evolved to a powerful theoretical technique to study
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peptide structure and dynamics, as indicated by the plethora of references in the lit-
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erature. The study of peptides thrived in the beginning of this millennium and still
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holds as an active field of research after 20 years. This interest is mainly due to the
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ability of foldable peptides to mimic essential characteristics of the much larger protein
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systems while at the same time maintaining the simplicity of smaller systems. This
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makes peptide systems not only easier to comprehend, but also cost efficient in terms
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of both computational power and experimental resources required. Their advantages
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as model systems have been eloquently presented in other reviews[24, 63]. Herein, we
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try to underline their vital role in the development and advancement of force fields
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through numerous cycles of validation and optimisation that lead to what we perceive
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to be significant improvements in the ability of simulations to capture and reproduce
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the experimentally accessible physical reality.
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2. Peptide folding simulations: two decades of continuous advancement
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Historically, the study of peptides was prompted by the fact that they resemble
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the early events in protein folding and thus offer an excellent opportunity to decipher
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protein-structure relationships[35, 75, 97]. Early studies suggested that peptides may
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serve as nucleation sites from where the folding is initiated[171, 200]. This paved the
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way to a number of studies aiming to characterise the timescales of the early folding
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events and to model them computationally.
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The speed limit of folding has been estimated to be N/100µs, where N is the number
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of residues[96], with its actual value being dependant on a number of events such as
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the formation of hydrophobic core, hydrogen bonds, electrostatic interactions, solvation
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energy, conformational entropy, diffusion, etc.[126]. The timescales for the formation
26
of basic structural elements have been placed to the sub-second time-scale[20, 43]. The
27
fastest early folding events were grouped by Gnanakaran et al.[63] based on the minimal
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sequence that can form each of these structures, from loop-closure events that can take
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place in the 10ns time-scale[103], to α-helix formation which takes place in the 100-
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200ns time-scale[57, 199] and to the slower β-hairpin formation that may require several
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microseconds[132]. The Eaton group contributed with extensive studies on the speed of
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folding, setting an upper limit for a 50-residue protein to 1 microsecond[42, 66]. This
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nano- to micro-second regime allowed a unique opportunity for a direct comparison
34
between theoretical calculations and experimental measurements[27, 95, 103, 202]. The combination of these relatively short folding timescales with the increase of the
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computational power available to the research groups led to numerous peptide folding
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simulation studies which significantly advanced the field of peptide folding simulations.
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One of the pioneering studies was by Daura et al. that showed in atomistic detail the
39
reversible folding of two β-peptides in solution[32]. Later, the Caflisch group showed the
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impressive, for that time, folding of a 20-residue peptide to a three-stranded antiparallel
41
β-sheet through a cumulative simulation time of 4µs[49, 50]. Likewise, Pande et al.,
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illustrated the efficiency of using different starting conformations and high-temperature
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unfolding to study the folding pathway of a β-hairpin fragment of protein G[143].
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Challenging short peptides with many charged residues (10 out of 21 amino acids) were
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successfully computationally folded to the native structure in an attempt to describe
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the folding pathway and estimate folding rates that were experimentally difficult to
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access[194].
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In later years, the increase in available computational power made it possible for
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the molecular simulations to reach even higher time scales in the range of tens to
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hundreds of microseconds, approaching the folding times of longer peptides (20-60
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amino acids)[125]. One of the first notable studies was the milestone 1 microsecond
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single folding simulation of the 36 residue villin headpiece in explicit water by Duan and
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Kollman[38]. Shortly after that, the Pande group demonstrated the efficiency of using
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many short trajectories instead of a single long one to describe the folding pathway of
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small peptides like BBA and villin headpiece (23 and 36 residue long, respectively), an
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effort made possible through the development of distributed computing [45, 104, 167,
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175, 205].
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A few peptides served as preferable study systems due to their unique properties
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and abundance of experimental data, like the 20-residue peptide, Trp-cage, the smallest
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stably folded peptide showing two-state folding properties [28, 151, 170] and the WW
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domain (approximately 40 residues) of Pin1 protein[46, 52]. The later one served
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especially as a workhorse for small all beta-sheet peptides to examine force fields’ bias
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towards helical conformations[53, 131].
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All-atom molecular simulations in explicit solvent have nowadays reached the
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impressive millisecond timescale thanks to the improvement of the parallelization
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algorithms[2], the highly optimised GPU implementations[55, 159, 180] and special3
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purpose supercomputers like Anton[163, 164]. For an example of the latter, it was
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the increased simulation length afforded by the Anton machine, together with a better
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performing force field, that allowed the correct folding of both FiP35, the fastest fold-
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ing variant of WW domains, and BPTI (58 residues) to experimental resolution[164],
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overcoming deficiencies of previous trials[52, 53]. The Shaw group in 2011 took the
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whole field of molecular simulation a huge step forward by demonstrating the correct
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folding of 12 structurally diverse small proteins, ranging from 10 to 80 residues and
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from all structural classes[108]. Apart from the obvious significance of a successful in
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silico folding study, they demonstrated the transient formation of native-like structural
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elements already in the unfolded state, providing unprecedented insights into their
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folding mechanism.
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The small size of the peptides is counteracted by their high flexibility and increased dynamics which made the probing of their full conformational potential extremely dif-
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ficult with conventional unconstrained molecular dynamics simulations. Thus, and
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more often that not, enhanced methods are employed to study peptide systems. In
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fact most of the work cited in this review concerns studies that make use of some of the
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established accelerated dynamics techniques, such as the replica exchange molecular dy-
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namics (REMD)[181], simulated tempering (ST)[120] and adaptive tempering[206] to
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name but few. The common concept in all of these methods is to enhance the conforma-
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tional sampling through different biasing methods (for example umbrella sampling[182],
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metadynamics[100], and accelerated MD[68]) to achieve the desired long timescales and
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retrieve thermodynamic and kinetic properties for the system. Although an in-depth
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presentation of these techniques is beyond the scope of this review, we should empha-
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sise the contribution of these methods to the field of peptide folding[76, 179, 207]
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and refer the interested reader to some excellent reviews already available in the
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literature[36, 122, 130, 141].
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To summarise the progress outlined above, we believe that molecular simulation
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of peptides has reached the level of maturity where they can realistically describe in
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atomistic detail the structure and dynamics of peptides, justifying their naming as a
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computational microscope[37]. In the past, a folding simulation could have been char-
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acterised as successful based solely on its ability to locate the native (experimentally
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determined) structure. It is an indication of the maturity of the field that simply lo-
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cating the native peptide structure through simulation is no longer sufficient for an
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application to be considered successful. The major question for recent applications 4
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is how realistically can the simulation describe the folding mechanism and the corre-
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sponding folding landscape, including the transiently stable conformations. Present-
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day molecular simulations are performing relatively well in characterising structurally
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stable peptide conformations and in estimating rates and free energies of folding[149].
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However the unfolded state is still poorly understood. The inherent properties of the
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disordered state —with its multitude of conformations of similar energies which are
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separated by relatively low energy barriers— amplifies any small force field deficiencies
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but will most probably not prevent the native structure from being located. The ability
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to perform extremely long simulations of peptide systems will allow a more extensive
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sampling of the unfolded/disordered state and should, thus, allow further refinement
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of the empirical force fields.
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3. Molecular simulations of health-related peptides
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A great interest for the study of the structure and dynamics of peptides came
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from their applications in drug design, even leading to the creation of a new subfield
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aptly named “computational peptidology”[209]. Molecular dynamics are a powerful
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tool towards this means, whose contribution is increasingly being recognised[22, 41].
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Simulation-based methods are actively used both in early stages of drug discovery as
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well as in the final steps aiming to decipher binding mechanisms[208].
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Peptides are physiologically involved in many biological processes with vital roles
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in metabolism and signalling. In particular, they are long-recognised to have a well-
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established role as anti-cancer, anti-microbial, anti-viral, anti-angiogenic and anti-
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inflammatory agents. Their inherent capability to modulate protein function increases
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dramatically their druggability potency[89]. On top of that, they offer enhanced ac-
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tivity and specificity which is translated in smaller dosages and lower toxicity. How-
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ever, their susceptibility to proteases appears to be a major bottleneck, underlying
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the need for alternative administration routes to overcome their low bioavailability[44].
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Significant improvements in the synthesis and purification techniques have made the
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production of peptides up to 100 amino acids a routine, opening new horizons for their
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large-scale health-related applications. A comprehensive presentation of the peptide-
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based drug market is exhaustively analysed in other reviews[110, 188].
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Significant advancements have also been made concerning the availability of com-
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putational tools aiming to assist peptide-based drug design studies[90, 91]. However,
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most of these tools are limited in their general applicability by making the more often 5
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than not unjustified assumption that the peptides of interest will have stable (native-
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like) structures in water. In this connection, special mention must be made of the
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Rosetta suite of programs which have been catalytic in the field, with pioneering work
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in the de novo peptide (and protein) structure prediction accuracy as assessed by
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CASP (Critical Assessment of Structure Prediction)[21]. The Rosetta algorithm im-
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plemented the fundamental concept of peptide fragments, which are short fragments
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of known protein structures that are assembled by Monte Carlo methods to predict
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protein structures[7, 172]. There are also many other in silico tools dedicated to struc-
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ture prediction but only a handful are adapted for peptides. Their accuracy is limited
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and highly dependable on the availability of experimental data. The most promising
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representative of this class is the Pepfold server that is a bioinformatics-based de novo
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approach to predict tertiary peptide structures from sequence[124]. The algorithm uses
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Hidden Markov Models and non-overlapping peptide fragments of four amino acids. It
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should be noted, however, that all of these methods and programs, and irrespectively
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of their detailed algorithmic basis, utilise empirical force fields to refine their proposed
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structures, thus highlighting the substantial interplay of peptides with the force fields
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even in protein structure prediction methods.
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Health-related applications of peptides also involve the search for small foldable
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peptides with predefined structural characteristics. Identification of small stably folded
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and soluble peptides is not trivial[59]. Many small peptides (4-10 residues) of biological
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interest have been studied computationally but were found to be marginally stable in
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solution[171]. Well-known exceptions to this rule are the designed 10-residue peptides
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chignolin[77, 98, 160] and its variant, CLN025[70, 127, 157] that adopt a unique and
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outstandingly stable β-hairpin structure in water.
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The question that arises then, is how good are the empirical force fields in describ-
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ing the structure and dynamics of peptides, especially of those that are not stably
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folded, or have more than one stable conformation. Are, for example, the force fields
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sensitive enough to predict the structural plasticity of the peptides, or, the sometimes
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pronounced effect of mutations on the peptide structure and dynamics? Force field
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improvement and validation has gone hand-in-hand with peptide simulations. In the
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following section we present a historical perspective of the evolution of the force fields
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highlighting the parallel paths that accurate peptide structure predictions and force
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field development followed through the years.
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4. Force fields: then and now A number of force fields have been developed over the years for the simulations of
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biological macromolecules. These can categorised in the families of CHARMM[114],
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AMBER[31], OPLS[85] and GROMOS[140]. The similarities and differences among
171
them, especially regarding their parameterisation protocols can be found in other
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reviews[65, 153]. In what follows, we review the evolution of the force fields from
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their first appearance to the present, highlighting the pivotal role of peptides in their
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improvement.
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4.1. CHARMM force field
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Historically, the CHARMM (Chemistry at Harvard Macromolecular Mechan-
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ics) force field appeared in 1983[23] and was officially released in the version
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CHARMM19[134] (Figure 1). The published parameters comprised the so called ’ex-
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tended’ atom types and van der Waals parameters, wherein hydrogen atoms were in-
180
cluded as part of their attached heavy atoms for sulfur and carbon, whereas for nitrogen
181
and oxygen the hydrogen atoms were treated explicitly, hence the name united-atom
182
potentials. One of the major features was the application of the partial atomic charges
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to fit ab initio calculations, using the TIP3P water model[84] to calibrate the inter-
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actions. The potential function also included internal energy terms for bonds, angles,
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dihedrals, improper dihedrals as well as the non-bonded terms for van der Waals and
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electrostatics, using a truncation cutoff for the latter. This basic form of the energy
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function has been carried-over to almost all present-day empirical force fields.
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CHARMM22[113][114] was later introduced as an ”additive” protein force field that included explicit parameters for all atoms (rendering the term ’extended atom’
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obsolete), emphasising on the balance of interactions involving the protein and the
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solvent and in-between. This was mainly achieved through a refinement of the non-
192
bonded interactions already implemented in the CHARMM19 version, by broadening
193
the experimental and ab initio data used. Backbone parameters were based on the
194
N-methylacetamide (NMA) and the alanine dipeptide and the side chains were based
195
on a number of small model compounds. Additive force fields do not allow however
196
the change of the electrostatic parameters as a function of environment, neglecting
197
the electronic polarisation phenomenon. The CHARMM22 protein parameters were
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maintained to the version that followed, CHARMM27, where only the nucleic acid
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and lipid parameters were updated together with parameters for a number of common
200
ions[112]. This force field version remained prevalent for a decade until the introduction of
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the CHARMM22/CMAP version which incorporated the addition of a dihedral correc-
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tion map (CMAP)[115, 116]. CMAP is a two-dimensional grid of energy corrections
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in the dihedral space of φ/ψ angles added to the potential energy equation, which
205
improved the secondary structure propensities and compensated for the demonstrated
206
helical bias of the CHARMM force field[178]. The parameters for the CMAP term
207
were derived from a big collection of protein x-ray crystallographic data[116]. The
208
CHARMM22/CMAP version had an improved performance[25], but deficiencies in the
209
equilibrium between helical and extended conformations were noted which affected the
210
ability of the force field to correctly fold small peptides, mostly due to an increased heli-
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cal propensity[13, 52, 53]. Thus, further improvements were incorporated by correcting
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the backbone and side-chain dihedral angles to sample better the corresponding regions
213
in the Ramachandran plot[19]. Corrections were based on experimental solution NMR
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data of weakly structured peptides for all residues except glycine and proline, for which
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QM-based corrections were made. We should note that this work was not based solely
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on alanine peptides but also on small helical and hairpin peptides.
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In later years, only non-protein parameters regarding lipids, carbohydrates,
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drug-like and cofactor molecules were implemented, giving rise consequently to
219
CHARMM27r, CHARMM35 and the CHARMM General Force Field (CGenFF). To-
220
gether they resulted in the latest great release of CHARMM36[19, 81] and a few years
221
later of CHARMM36m for intrinsically disordered proteins[82]. In parallel, version
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CHARMM C22*[150] was presented that aimed towards a better helix-coil balance.
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This was achieved by replacing the CMAP correction for all residues except glycine and
224
proline, and modifying the side-chain partial charges and torsional terms for residues
225
aspartate, glutamate and arginine (following the philosophy of the ff99SB* and ff03*
226
corrections in the AMBER family that is presented in the next section). A more com-
227
prehensive presentation on each component of the CHARMM all-atom additive force
228
field together with the parameterisation philosophy and methodology and the recently
229
released CHARMM Drude polarizable force field can be found elsewhere[111, 187, 210].
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4.2. AMBER force field
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The AMBER (Assisted Model Building with Energy Refinement) force field first appeared also in the early 80s, sharing the united-atom idea[195] but was soon extended 8
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to an all-atom force field with recalibrated torsional and angle parameters based on
234
experimental conformational energies[196] (Figure 2). A decade of improvements in
235
the parameters and the algorithm gave rise to a second generation force field, named
236
ff94[31]. Since then, the tradition has it that protein (and nucleic acid) force fields
237
in the AMBER family are named with ”ff” followed by a two-digit number year. Up
238
to this point, the parameterisation was focused on the gas phase behaviour, but the
239
need to produce potentials that are suitable for condensed phase simulations became
240
apparent for a more balanced modelling of biomolecules in solution. Unlike CHARMM
241
though, the core parameterisation is different here, employing more adjustable empir-
242
ical parameters that can be optimised. For example, the fixed atomic partial charges
243
of CHARMM that are tightly connected to the TIP3P water model are not present
244
here. Instead AMBER employed initially an ESP (electrostatic potential) fit for atomic
245
centred charges and later an RESP fit (restrained ESP) where charges were fitted simul-
246
taneously to several conformations to achieve a better average behaviour. The dihedral
247
parameters were fit to relative QM energies of alternate rotamers of small molecules
248
to represent several conformations of glycine and alanine. Unlike CHARMM, the AM-
249
BER force fields underwent many optimisations and refinements to reach a satisfactory
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level of accuracy, giving rise to a large number of variants.
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The ff94 force field was shown to over-stabilise helical conformations and over-
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estimate computed melting temperatures in peptide simulations, sometimes even bias
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helices over the native β-hairpin conformation[57, 137, 170]. The ff94 version was soon
254
replaced by ff96 and C96[93], which featured improved calculations for electrostatics
255
and van der Waals interactions and better accounted of long-range effects. This resulted
256
in better fitting to ab initio calculations on small peptides and more balanced solvent-
257
solvent and solute-solvent interactions. One of the main drawbacks of this version
258
was a bias towards β-structures this time[74, 88, 138]. The next version ff99[190]
259
was yet another attempt to refit the backbone dihedral parameters using this time
260
more representative structures of alanine and glycine in the form of tetrapeptides and
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dipeptides. At that time, generalised parameters for compounds beyond proteins and
262
nucleic acids were also released. The new potential surfaces were significantly different
263
of those of its predecessors.
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Force field optimisation was assisted by the longer simulation times that became fea-
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sible, which only uncovered more force field deficiencies. This opened up to a decade of
266
numerous almost in-parallel efforts to improve AMBER force field, making it challeng9
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ing to keep up with them and even more to choose the appropriate one for a particular
268
study. Despite the extended optimisation of the ff99 version, AMBER force fields con-
269
tinued to suffer from an imbalance of secondary structural elements, over-stabilising
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α-helical peptides, like their ff94 counterpart[57, 137].
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A few years later ff03 was released, a so called third-generation point-charge all-atom
272
force field[39]. The major contribution was the fitting of the electrostatic potential and
273
main-chain torsion parameters to QM calculations of small peptides in condensed phase
274
with continuum solvent models. Initial testing showed a satisfactory balance between
275
helical and extended conformations and a better description of the polyproline II region.
276
A united-atom counterpart was also released, ff03ua[201], where aliphatic hydrogens of
277
α-carbon and aromatic hydrogens are explicitly represented whereas aliphatic hydro-
278
gens of side-chains are represented united to their carbon atom, to improve speed for
279
computationally demanding cases like folding simulations. A close variant of ff03, ff03*
280
incorporated a correction to the backbone dihedral potential to fit experimental data
281
of helix-coil transition, making it more transferable and able to fold peptides from both
282
helical and beta structural classes[15]. The ff03w force field[16] is a slightly modified
283
version of ff03*, with a backbone dihedral potential correction that allows the usage
284
of the more accurate TIP4P/2005 water model[1]. This updated force field offered a
285
better description of the folding thermodynamics and of the unfolded state as tested
286
in small peptides, whilst preserving its ability to fold to the native structure larger
287
peptides like the Trp cage and the GB1 hairpin. It still suffered though from poor
288
solvation, with less favourable solvation free energies and too favorable protein asso-
289
ciation. In an attempt to further improve the representation of these properties, the
290
ff03ws force field[18] was released which essentially incorporated a tuning parameter
291
for the Lennard-Jones protein-water interaction, specifically the water oxygen. The
292
same scheme applied to the ff99SB force field, gave rise to version ff99SBws[18].
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The ff99SB force field[79] was a parallel effort focused largely on improving the φ/ψ
294
dihedral terms of the previous ff94/ff99 energy functions, after showing that the inad-
295
equate backbone dihedral parameterisation was indeed responsible for the weaknesses
296
of that generation of force fields. The major realisation here was that the two sets
297
of dihedral backbone parameters introduced in ff94 version have to be both individu-
298
ally optimised for glycine and non-glycine residues. Glycine due to absence of a Cβ
299
atom needs only one set of dihedral parameters, φ/ψ (defined as φ = C-N-Cα -C, ψ =
300
N-Cα -C-N), whereas all other amino acids that harbor a side-chain need also a φ’/ψ’ 10
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term (defined as φ’ = C-N-Cα -Cβ , ψ’ = Cβ -Cα -C-N). Then the dihedral potential for
302
the non-glycine residues will be the sum of them. This resulted in better agreement
303
with the PDB data for the dihedral angles and consequently better description of the
304
secondary structural preferences of small peptides as well as improved fitting to NMR
305
observables of larger peptides, like trpzip2, trp cage, villin headpiece, ubiquitin and
306
lysozyme.
307
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In the same spirit, there were some efforts like the AMBER-GS version[57], where the φ/ψ torsion potential was completely removed to fit better to experimental helix-
309
coil parameters, but the α-helical bias was not removed as shown by long equilibrium
310
ensemble simulations[177]. As a remedy, the ff99SB-φ’ force field[177] was proposed
311
where they combined the low helicity of the ff99 potential with the high helicity of
312
the ff94, by removing the additional barriers on the φ rotational degree of freedom.
313
This version provided a better description of the helix-coil transition but its usage to
314
non-helical peptides was not verified.
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The fast —almost chaotic— production of even more versions of AMBER force fields
316
continued unimpeded in the years to come. All versions from this period shared the
317
core potential function of ff99SB which demonstrated superior performance to previous
318
versions[13], proving the significance of the proper backbone dihedral parameterisation.
319
Next in line, came ff99SB* force field[15], which incorporated to 99SB potential the
320
same backbone correction as the ff03* version described above. This improved the
321
helical bias and showed better agreement to NMR data of peptides but with poor
322
thermodynamics description.
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A different approach was introduced with the ff99SB-ILDN version[109], where the
324
torsion potentials of side-chains were targeted this time. Especially four residue types,
325
isoleucine (I), leucine (L), aspartate (D) and asparagine (N), where found to have
326
considerably different rotamer distributions in the simulation in respect to the exper-
327
imentally observed ones. So, the side-chain torsion potentials for these four residues
328
were fitted to high-level QM calculations, improving considerably the agreement to
329
NMR data for the rotamer distributions. Of course combinations of these optimisa-
330
tions surfaced, like ff99SB*-ILDN[15] and later ff99SB*-ILDN-Q[14], which combined
331
the global backbone correction and the modified torsion parameters for residues ILDN,
332
with refitted charges for residues D, E, K, R.
333 334
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On another front, the Br¨ uschweiler group introduced the concept of employing experimental NMR data that are commonly used to cross-validate a force field’s per11
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formance, to optimise them instead. Thus they used a collection of NMR chemical
336
shift data and RDCs for peptides to optimise and improve the ff99SB version using
337
an energy-based reweighting to match the experimental data in an iterative manner,
338
giving rise to the versions ff99SBnmr1[105] and ff99SB-φψ[106] that showed superior
339
performance when compared to its parent force field, ff99SB.
340
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Around that time, it became clear that it was imperative to produce a catholic AMBER version with carefully selected corrections that can reproduce faithfully ex-
342
perimental data for peptides from all structural classes that the developers can respon-
343
sibly recommend to general users of molecular simulations. Towards this direction, a
344
preliminary version, ff12SB, and nowadays ff14SB[118] were officially released. Taking
345
lessons from all the previous optimisation attempts, this version comprised a complete
346
refit of the side-chain dihedral potential of all amino acids, including alternate protona-
347
tion states for the ionizable ones, and empirical adjustments to the backbone dihedral
348
potential, including the φ rotational profile. The superiority of this updated version
349
was tested for reproducibility of the secondary structural content and NMR parameters
350
of peptides and proteins in solution. The ff12SB version was also optimised by adding
351
a CMAP-like correction, ff12SB-cMAP, for simulations with implicit solvent models,
352
when computational speed is a crucial factor[146].
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Although the ff14SB is the one officially still recommended by the developers at the
354
time of the writing, another version, ff15SB, came up for use in combination with the
355
TIP3P-FB water model[192]. This version comprised a complete refitting of the bonded
356
parameters of the parental ff99SB force field and was shown to retain the prediction
357
accuracy of equilibrium properties while improving the accuracy of the temperature
358
dependent ones[127]. Its broader application and establishment remains to be seen.
359
For completeness, there are nowadays available force fields that can also describe small
360
molecule ligands (General AMBER force field, GAFF), carbohydrates (GLYCAM),
361
lipids (lipid14) but also amber-compatible parameters for post-translational modifica-
362
tions (Forcefield PTM) and ff15ipq version for implicit polarised charges in explicit
363
solvent[34].
364
4.3. Force fields for disordered peptides
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Much of the current focus in the community of force field development has turned
366
towards the study of disordered peptides. An accurate description of the landscape of
367
these structurally challenging peptides is of paramount importance due to the increas-
368
ing acknowledgement of their abundance in protein structures as modular elements and 12
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their participation in many cellular processes[40]. Their main characteristic, the abil-
370
ity to interconvert between different conformations, also presents the greatest challenge
371
which is the requirement to transform force fields that underwent decades of optimisa-
372
tion cycles to model well-folded peptides, to now perform comparably well even with
373
disordered peptides.
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Disordered peptides present the additional challenge of interpreting complex experi-
375
mental observables that are averaged ensembles over transient conformations. The most
376
common experimental techniques used for validation of the simulation data comprise
377
NMR (nuclear magnetic resonance), usually amide proton exchange measurements, J-
378
couplings, chemical shifts, NOEs (nuclear Overhauser effect) and RDC (residual dipo-
379
lar coupling) constants, FRET (F¨orster resonance energy transfer) and SAXS (small
380
angle X-ray scattering), that have been reviewed recently[18, 26, 72, 80]. Infrared spec-
381
troscopy has emerged lately as a powerful tool to probe the conformational dynamics
382
of the disordered states, providing experimental evidence on the secondary structures
383
of sites that can be isolated by isotope labelling that can be compared with computa-
384
tionally modelled amide I spectra[48].
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Naturally, force fields had to embrace the need to represent the disordered state
386
as accurately as the well-structured state. The first attempt to produce such a force
387
field was based on the application of the CMAP correction method to the dihedral
388
potential of 8 disorder-promoting residues (A, G, P, R, Q, S, E, K), using as basis
389
the ff99SB-ildn force field, giving rise to the version ff99IDPs[193] (Figure 2). A later
390
validation study using a set of 3 representative IDPs showed a quantitative agreement
391
with the experimental NMR chemical shifts and more representative conformational
392
sampling, though still suffering from over-stabilisation of structured conformations,
393
most probably due to inadequate representation of polar interactions[203].
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D
385
A more comprehensive effort was presented through the refined CHARMM36m
395
(Figure 1) force field[82] that tried to address a reported bias for overpopulation of
396
the αL region of the Ramachandran plot[154]. The exhaustive benchmarking gave
397
satisfactory fitting to experimental parameters for IDPs while retaining consistency
398
with the CHARMM36 counterpart for folded peptides, folding kinetics and free energy
399
calculations. It removed the oversampling of the αL region observed in CHARMM36,
400
but also underestimated the β region as shown through simulations of peptides like
401
chignolin and CLN025. The main issue addressed was the over-compactness, a common
402
characteristic of all current generation empirical force fields when applied to studies of 13
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403 404
the disordered state. In the same spirit, and inspired by previous optimisation efforts, a force field termed a99SB-disp was released (Figure 2), the most recent to our knowledge empiri-
406
cal force field dedicated to accurately present both folded and unfolded conformational
407
states[156]. This force field is based on the ff99SB-ILDN version with necessary modi-
408
fications to employ the TIP4P-D water model. Its superior performance is attributed
409
to (a) an iterative scheme to optimise the backbone and side-chain torsion parame-
410
ters to represent better the protein-water van der Waals interactions inspired by the
411
ff99SB*-ILDN-Q version, and, (b) the modification of the strength of the Lennard-
412
Jones term for carbonyl oxygen and amide hydrogen pairs. Its performance remains to
413
be evaluated in the years to come.
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Amyloid (Aβ) peptides and in particular their assembly into fibrils, have been one of
415
the most challenging peptide systems to study with significant difficulties encountered
416
with both the experimental and computational approaches. The interested reader is re-
417
ferred to some excellent reviews of these Alzheimer’s disease-related peptides[133, 183].
418
A large number of studies appeared which attempted to computationally characterise
419
the peptides’ equilibrium conformations using the most advanced force fields. The great
420
discrepancy among the predicted structures of the monomers as well as of the various
421
oligomers only highlights the difficulty to describe the conformational preferences of
422
disordered peptides and the force field bias that needs yet to be addressed[136]. The
423
differences between the various force fields, sometimes in the context of different water
424
models as well, have been attributed to differing secondary structure biases as well
425
as the intrapeptide hydrogen bonding, with helix-overestimating force fields, like AM-
426
BER99SB and CHARMM22-CMAP, having the poorest agreement to experimentally
427
observed populations[174]. Later studies with improved force field versions accompa-
428
nied by different water models, such as OPLS-AA/TIP3P, AMBER99SB-ILDN/TIP4P-
429
Ew and CHARMM22*/TIP3SP demonstrated strongly converged structural properties
430
for these type of disordered peptides[158] and improved agreement with experimental
431
J-coupling constants, chemical shifts and CD data[176]. These encouraging findings
432
indicate that force field improvements may be heading in the correct direction. How-
433
ever, the force field validation is difficult due to the limited availability of experimental
434
observables for disordered peptide systems. This is particularly concerning when force
435
field performance is found to be dependent on the peptide system per se. For instance,
436
the CHARMM36/TIP3P combination was the most accurate in the case of Aβ10-
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14
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40 peptide but not in the case of Aβ1-40 and Aβ1-42 peptides[173]. In a different
438
study, the most recent versions AMBER14SB and CHARMM22* with TIP3P water
439
model showed a helical overestimation compared to CD data, whereas OPLS-AA and
440
AMBER99SB-ILDN with the same water model represented conformational ensembles
441
closer to experiment[119]. Clearly further studies are needed to determine the source
442
of the force field discrepancies, but more importantly to also comprehend whether the
443
limited accuracy for disordered peptide systems is due to the interplay between the
444
force field and water model parameters.
445
4.4. Other biomolecular force fields
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The force field families of CHARMM and AMBER are the ones that underwent
447
through heavy optimisation and validation by the developers but also the rest of the
448
community in the peptide folding and dynamics field. For completeness we should also
449
mention two additional and significant contributions, those of the OPLS and GROMOS
450
force fields.
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The OPLS (optimised potentials for liquid simulations) made its appearance in
452
the 80s as well (OPLS-ua) and was initially intended for simulation of liquid-state
453
properties of water and other organic liquids[84] (Figure 3). A distinct feature was the
454
emphasis given to model the non-bonded interactions to fit liquid-state thermodynamic
455
properties, like density and heat of vaporisation. The first release was a combined
456
AMBER/OPLS force field[86] (AMBER ff94 was largely inspired by OPLS) and was
457
later updated to the all-atom version OPLS-AA[85]. An update of it came out a
458
few years later, where side-chain potentials were reparameterized based on QM-data
459
of small peptides[87]. The major contribution from this effort was, and still is, the
460
development of the water models TIP3P and TIP4P that are heavily used to the
461
present. It was only very recently that new OPLS versions emerged, like OPLS2.1 and
462
OPLS3, that are mostly optimised towards small molecules and protein-ligand binding
463
studies[69].
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Closing this section, we should refer to GROMOS (Groningen molecular simulation)
465
that appeared in the 90s together with the homonymous computer simulation program
466
with the most cited version being GROMOS96[186] (Figure 4). The newest release
467
appeared a few years ago as GROMOS11 with the parameter sets 54A7[161] and now
468
54A8[155]. Its inferior performance compared to other force fields in comparative
469
validation studies of peptide folding and dynamics prevented its broader use in the
470
specified field of peptide simulations and will not be further presented here. 15
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4.5. Water models for explicit representation of the solute in peptide folding simulations
472
This review is focused on peptide folding simulations that comprise explicit repre-
473
sentation of the solvent. Therefore, the ability of the force fields to describe accurately
474
the conformational landscape of the peptides is inextricably dependent on the ability
475
of the associated water model to describe the physical properties of water molecules in
476
the liquid phase. There are numerous water potentials that have been developed so far,
477
but we shall only mention here the empirical potentials that are used in biomolecular
478
simulations (Figure 5). Detailed presentation of all available water models and their
479
comparative performance can be found elsewhere[30, 64, 73, 139, 142, 185, 189].
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Their first appearance coincided with the early protein force field versions in the 80s and they all share the idea of a rigid water monomer with the non-bonded interac-
482
tions described by 3, 4, or 5 sites composed of Coulombic terms for the intermolecular
483
interaction pairs and a Lennard-Jones term for oxygen atoms upon dimerization. His-
484
torically, two quite similar 3-site models were introduced in parallel in 1981. These
485
were the TIPS (transferable intermolecular potential)[83] model, and the SPC (simple
486
point charge)[11] model, two of the most popular potentials for water molecules in
487
molecular simulations even to date[153]. The main difference between TIP and SPC
488
models is the tetrahedral shape geometry adapted by the latter and its ability to re-
489
produce the experimental radial distribution function (including the second peak) and
490
the self-diffusion coefficient. Later the SPC/E[10] model was released that comprised
491
an additional polarization correction leading to better representation of the density,
492
diffusion coefficient and dielectric constant for simulations of liquid water. Together
493
these features made the SPC models more appropriate for modeling the bulk properties
494
of water[121].
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Later reparameterisation of TIPS and addition of a Lennard-Jones term to the hy-
496
drogen atoms as well, lead to improved representation of the density of liquid water and
497
gave rise to what became the standard model for protein simulations, the TIP3P[84]
498
model. Concurrently with TIP3P, its 4-site version was released, the TIP4P model,
499
which also incorporated terms for the bisector of the H-O-H angle allowing a better
500
electrostatic distribution. The TIP4P model provided a better description of most of
501
the water’s properties (like the phase diagram) but not of its dielectric constant. The
502
increased computational cost (imposed by the larger number of interactions to be cal-
503
culated) prohibited its wider use in the early peptide folding studies. The most crucial
504
factor however for the wider application of TIP3P was its coupling to the vastly popular 16
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CHARMM22 force field. The 5-site interaction version, TIP5P[117] appeared in 2000,
506
which replaced the single negative charge on the bisector angle of TIP4P with two
507
single negative charges on the lone-pair electrons. The truncated tetrahedral geometry
508
showed excellent representation of the structure of water, matching the density and
509
radial distribution properties, but suffered in describing the gas phase. The increased
510
complexity also significantly increased the computational requirements. As a result,
511
SPC and TIP4P models provided a satisfying description of liquid’s water structural
512
and thermodynamic parameters at a much lower computational cost.
SC
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The scenery changed with the increase in the available computational power but
514
most importantly the appearance of AMBER force field versions that gave more free-
515
dom on the choice of water model (RESP-fitted atomic charges). All aforementioned
516
water models utilise truncated Coulombic interactions. An improved treatment of the
517
long-range interactions with particle-mesh Ewald summation gave rise to the TIP4P-
518
Ew[78] model which improved the representation of liquid water’s thermodynamic pa-
519
rameters over a large temperature range but without adding significantly to the compu-
520
tational cost. On the same spirit was based the parameterisation of the TIP4P/2005[1]
521
model which reproduces temperature-dependent properties but underestimates the di-
522
electric constant. The TIP4P/ǫ[56] model is fine tuned to match exactly that property
523
in a large temperature regime. An equivalent version is the TIP4Q[4] model that
524
includes an additional charge to increase the dipole moment, but at an additional
525
computational expense compared to other TIP4P-based models. The common charac-
526
teristic of these water models is the larger enthalpy of solvation that leads to stronger
527
interactions between the water and the embedded protein. It is for that reason that
528
they have been lately employed in folding simulations of disordered less hydrophobic
529
peptides, facilitating a more accurate description of the expanded unfolded state. On
530
the same front, the TIP3P-FB and TIP4P-FB[191] models were introduced by applying
531
the so called ForceBalance method that combines reference data produced both exper-
532
imentally and theoretically to derive parameters for force fields. The resultant models,
533
and in particular the TIP4P-FB, manage to reproduce most of the kinetic and thermo-
534
dynamic properties of water, like the viscosity, diffusion coefficient, dielectric constant,
535
radial distribution function and heat of vaporization, in a variety of temperatures and
536
pressures.
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537
The take-home message here is that there is no perfect water model that encapsu-
538
lates all of the experimental physical properties of water. Furthermore, the general 17
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users are highly restricted in their choice by the compatibility to the protein force
540
field of choice and whether it is implemented in a molecular mechanics program.
541
For example, the molecular dynamics simulation engine NAMD[147] only supports
542
TIP3P- and TIP4P-based models from the whole panel of non polarizable water
543
models. Gromacs[12, 184] on the other hand supports SPC, SPC/E, TIP3P, TIP4P
544
and TIP5P. It has thus become common knowledge in the field that the GROMOS
545
force fields should better be paired with the SPC water models, OPLS force fields
546
are recommended to be used with TIP4P, whilst the CHARMM family of force fields
547
should be paired with the TIP3P model to avoid inconsistencies.
548
fields, especially the latest versions, are more versatile. Despite the relatively poor
549
performance of some water models with respect to the description of the bulk solvent
550
properties, their success in the folding of proteins and peptides appears to indicate that
551
folding per se may not be as sensitive to the properties of bulk solvent. This finding is
552
probably the result of the protein force fields being developed given the available water
553
models, so their deficiencies could be masked in the empirical parameterization of the
554
force fields. As the observation that the main deficiency of current generation of force
555
fields is the poor description of the protein-water interactions, an effort in underway
556
to develop force fields that are parameterized in combination with the newly reported
557
water models. In that spirit the TIP4P-D[148] was recently released in an effort to
558
recapitulate the more extended conformational ensembles of the disordered state by
559
increasing the strength of the dispersion interaction (LJ-term) (see also section 6.
560
The future). As is always the case with molecular simulation, it will be the extensive
561
testing by the community that will define which of these models will survive the acid
562
test of a quantitative comparison with the experimental data, including the ability to
563
accurately describe the kinetics and thermodynamics of peptide folding.
565
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5. The unceasing quest for a balanced biomolecular force field
566
The previous sections clearly demonstrated that one of the main contributions
567
of peptide simulations is their continuing usage as test systems for the optimisation,
568
correction and validation of empirical force fields[5, 61, 107, 123, 175]. One of the
569
recurring challenges through all these studies has been to convincingly quantify force
570
field accuracy, especially in connection with the fact that the relatively limited simu-
571
lation timescales attainable are insufficient for guaranteeing a faithful configurational 18
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sampling of the peptides’ folding landscapes[51]. Soon it became clear in the litera-
573
ture that the initial force field versions from all families were suffering from helical
574
bias[13, 51, 53, 62, 79, 123, 137, 165, 178, 204]. A common remedy to tackle the helical
575
bias of the early force fields was to choose one with a bias towards the major secondary
576
structure of the protein under study. This was obviously highly unsatisfactory and
577
proved indeed ineffective, as demonstrated by the folding simulations of villin and Pin1
578
WW domain mentioned earlier with the CHARMM22/CMAP force field[115, 116]. In
579
these studies, villin folded to its native structure[54] but the WW domain, whose na-
580
tive structure is a 3-stranded β-sheet, did not[52]. The reason, of course, was that as
581
far the force field was concerned a misfolded conformation had lower free energy than
582
the native structure[47, 53]. Studies such as these highlight how small force field inac-
583
curacies can have an additive effect and can result in stabilising misfolded non-native
584
structures.
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AMBER’s ff99SB was the first successful version to convincingly compensate for
586
that and displayed superior performance over the rest of the force fields of its time:
587
literature consistently provided overwhelming evidence of significantly improved bal-
588
ance of secondary structural elements and reasonable agreement with experimental
589
data through multiple comparative validation studies comprising from short glycine
590
and alanine peptides to longer 10-20 residue peptides (disordered, helical, beta) up to
591
small proteins like lysozyme and ubiquitin[8, 58, 79, 92, 94, 99, 102, 123, 144, 145, 168,
592
168, 169, 197, 198].
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Follow-up studies suggested two more force fields, f99SB-ILDN-φ and ff99SB-ILDN-
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593
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585
NMR, with significantly improved agreement with NMR observables, highlighting
595
though that large uncertainties accompany this agreement: statistical calculated er-
596
rors in the validation were in the margin of systematic experimental errors of these
597
parameters[9].
598
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The newer versions that surfaced, ff03/ff03* and ff99SB*-ILDN from AMBER, and
599
CHARMM22/CMAP and CHARMM22* from CHARMM, all succeeded in predicting
600
the native states and folding rates (for example the case of the model protein villin
601
headpiece), but displayed distinct discrepancies in the folding mechanism and in the
602
description of the unfolded state in particular, with ff99SB*-ILDN and CHARMM22*
603
being closer to the experiments[150]. CHARMM22* showed superior performance over
604
its counterparts in the CHARMM family in describing the free energy landscape of the
605
β-hairpin GB1[71]. Similarly, f99SB and its variants (ff99SB*, ff99SB-ILDN, ff99SB*19
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ILDN), ff03, ff03* and the GROMOS96 (43a1p,53a6) succeeded in finding the residual
607
β-hairpin preference of the disordered 16-mer Nrf2-derived peptide but with extremely
608
spurious results that were temperature dependent[29]. In accordance, a parallel study
609
with ff99SB-ILDN, ff99SB*-ILDN, CHARMM22/CMAP and CHARMM22* provided
610
accurate description of the native state of ubiquitin, GB3, villin and WW domain, but
611
force fields with better helix-coil balance, ff99SB*-ILDN, ff03* and CHARMM22* had
612
superior performance in the peptide systems[107]. Our personal recent work also lends
613
further support that for structurally challenging peptide systems, the ff99SB*-ILDN is
614
outperforming its counterparts in the AMBER 99SB family[3, 60, 162].
SC
615
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606
To summarise, our take on the current literature is that from the set of all extensively tested and validated force fields, there are nowadays versions from both AMBER
617
and CHARMM families that are shown to be balanced and well-performing in a wide
618
variety of tested systems, including cases of intrinsically disordered peptide systems,
619
like the RS repeats[154]. All that being said, we present in the next section our views
620
concerning the remaining challenges towards a universally useful biomolecular force
621
field.
622
6. The future
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616
We believe that a bird’s eye view of the recent literature leaves little doubt: peptide
624
simulations followed the rest of the molecular dynamics field in making a tremendous
625
progress towards accurate and physically relevant simulations. The development of
626
new algorithms, the production and validation of new robust and transferable force
627
fields, together with the increase of computational power available to the research
628
groups, completely transformed the field. Indeed, it is no longer an exaggeration to
629
state that we have reached the point where molecular simulations can faithfully predict
630
and reproduce the peptides’ native states, folding rates and in exceptional cases even
631
provide atomistic description of the folding mechanism in unprecedented detail, often
632
unreachable by experiments. Having said that, there are still a significant number of
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unresolved issues and deficiencies, some of which are discussed in the paragraphs that
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follow.
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Peptides with weak structural propensities are difficult systems to track computa-
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tionally. The major challenge here is to describe, without overestimating, the residual
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(if any) secondary structure present in the unfolded state, whilst retaining the fold-
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ing performance for the folders. Some recently reported issues concern the observed 20
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temperature dependence of the conformational preferences of peptides and the weak
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folding cooperativity, whose combination results in a relatively poor description of
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the kinetics and thermodynamics[33]. As discussed in the previous section on water
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potentials, the source of this ”overcompactness” compared to the experimental observ-
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ables (SAXS, FRET, Rg) appears to be the inaccurate description of the solvation
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of the unfolded chain, possibly due to systematically underestimating the dispersion
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parameter in the protein-water interactions[18, 72, 148]. A number of approaches have
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been proposed to remedy this, for example applying a scaling factor to the van der
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Waals interaction parameter[18], or re-parameterizing the Lennard-Jones parameter
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for water’s oxygen (TIP4P-D water model[148]) or hydrogen (mTIP3P)[82]. These ap-
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proaches improved the agreement with the experimental observables for some peptide
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cases but not for others, rendering this approach not universally applicable. For ex-
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ample, recent studies showed that the more polar TIP3P model favours more compact
652
structures[176]. On the other hand, the treatment of the protein-water interactions
653
by the TIP4P-Ew and TIP4P/2005 water models, eases the hydrophobically-driven
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collapse and improves sampling of the disordered state for peptides like Trp-cage and
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GB1[17], with TIP4P/2005 giving less collapsed conformations[135]. The latest of
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the released water models, TIP4P-D matched better the experimental Rg in a set of
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disordered peptides[148].
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It has, thus, been realized that a new direction for further improvement of the
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force fields is the one aiming towards an accurate description of the solvation effect
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and better accounting for the long-range interactions. It is probably not surprising
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that the newest of the empirical protein force field versions are adapting to new water
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models that provide a better description of the total physical properties of the solvent.
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However, obtaining a balance between the water model and the protein force field is
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not a trivial exercise, especially with respect to peptide folding and dynamics. The
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bulk properties of the solvent are experimentally tractable and thus it is straightfor-
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ward to validate the available water models on how well they describe the solvent’s
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molecular properties. However, the impact of the interactions between the solvent and
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the biomolecules on the conformation of the latter is still poorly understood and needs
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further exploration. A much different approach has been introduced with a force field
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based on the Kirkwood-Buff theory (KBFF)[152] to retrieve force field parameters
671
that reproduce the microscopic characteristics of the solution to better describe the
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protein-water interactions. This force field was found to compensate for the overcom-
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pacteness and match the experimentally found dimensions of disordered peptides[128],
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still though at the expense of partially unfolding peptides like GB1[129]. However, this
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was partially rescued by increasing the interaction cut-off to strengthen the contribu-
676
tion of the long range interactions, like in the case of AMBER99SB*-ILDN with the
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TIP4P-D water model for Nup peptides[148].
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Polarizable force fields might be an alternative route by accounting for the environmental effects. Their main asset is the ability to describe changes of the charge
680
distribution upon conformational changes of the molecules. This can be achieved via
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fluctuating charge models, Drude oscillator-based models[101], inducible dipole models
682
or multipole electrostatics, like in AMOEBA[166], all of which are detailed in other
683
reviews[6, 67]. Their general applicability is hindered by the large computational bur-
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den of the additional electrostatic interatomic forces calculations, barely reaching the
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100ns timescale even for small peptide systems.
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The difficulty in approaching all those unresolved matters in a meaningful way is
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that on one hand the disordered state is heavily undersampled computationally and on
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the other hand complex experimental data of disordered peptides can have ambiguous
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interpretations. We believe that peptides have and will continue to serve as an acid
690
test for the performance of molecular simulations and force fields to reproduce the
691
physical reality: small deficiencies in the force field parameterisation can be shielded
692
in the larger well-folded protein context. Further improvements could be of substantial
693
importance towards more accurate modelling of disease-related issues, like mutation
694
effects, misfolding, aggregation or alternative enzyme conformations that affect drug
695
binding. We hope that this review of the literature regarding molecular simulations
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of peptides and associated force fields will aid the readers to wisely select a force field
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suitable for a certain application in order to achieve high quality results.
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7. Author Information Corresponding Author
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*Phone: +30-25510-30620. Fax: +30-25510-30620.
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Web page: https://utopia.duth.gr/glykos/. E-mail: [email protected].
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ORCID
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Panagiota S. Georgoulia: 0000-0003-4573-8052
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Nicholas M. Glykos: 0000-0003-3782-206X
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Notes
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The authors declare no competing financial interest.
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Figure 1: CHARMM family of protein force fields. Circled tree map representation of the various protein-related force fields developed to present time. The size of the circle and the colour is analogous to the number of reported citations. Genealogically-related force field are encircled in the same hierarchical level, which is represented by the thickness of the lines. Force-fields are ordered chronologically from left to right by year of appearance.
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Figure 2: AMBER family of protein force fields. Circled tree map representation of the various protein force fields developed to present time as presented in Figure 1.
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Figure 3: OPLS family of protein force fields. Circled tree map representation of the various protein force fields developed to present time as presented in Figure 1.
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Figure 4: GROMOS family of protein force fields. Circled tree map representation of the various protein force fields developed to present time as presented in Figure 1.
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Figure 5: Water models for biomolecular simulations. Circled tree map representation of the water potentials used in simulations of proteins and peptides. The size and colour of the circles follows their popularity as expressed by the number of citations. Encircled are the models that can be used in conjunction with a specific family of force fields, with consecutive levels of hierarchy represented by the line colour.
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