Protein conformational transitions coupling with ligand interactions: Simulations from molecules to medicine

Journal Pre-proof Protein conformational transitions coupling with ligand interactions: simulations from molecules to medicine Dechang Li, Baohua Ji PII:

S2590-0935(19)30026-8

DOI:

https://doi.org/10.1016/j.medntd.2019.100026

Reference:

MEDNTD 100026

To appear in:

Medicine in Novel Technology and Devices

Received Date: 2 October 2019 Revised Date:

6 December 2019

Accepted Date: 18 December 2019

Please cite this article as: Li D, Ji B, Protein conformational transitions coupling with ligand interactions: simulations from molecules to medicine, Medicine in Novel Technology and Devices, https:// doi.org/10.1016/j.medntd.2019.100026. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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. © 2019 The Author(s). Published by Elsevier B.V.

Protein conformational transitions coupling with ligand interactions: simulations from molecules to medicine

Dechang Li1* and Baohua Ji1,2* 1

Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China

2

Beijing Advanced Innovation Center for Biomedical Engineering, Beijing 100191,

China

*Corresponding authors: [email protected]; [email protected].

Abstract: The functions and activities of proteins are closely related to their structures and dynamics, and their interactions with ligands. Knowledge of the mechanistic events of proteins’ conformational transitions and interactions with ligands is crucially important to understand the functions and biological activities of proteins and thus to the design of novel inhibitors of the targeted receptor. In this review article, taking two important systems as examples, i.e., human immunodeficiency virus type 1 protease (HIV-1 PR) and adenylate kinase (AdK), and focusing on the molecular dynamics simulations of the conformational transitions of protein and the protein-ligand association/dissociation, we explain how the conformational transitions of proteins influence the interactions with their ligands, and how the ligands impact the function and dynamics of proteins. These results of structural dynamics of HIV-1 PR and AdK and their interactions with ligands

can help to understand the principle of conformational transitions of proteins, or the interactions of ligands to their biological targets, and thus provide meaningful message in chemistry and biology of drug design and discovery.

Keywords: conformational transition, protein-ligand interaction, drug design, molecular dynamics simulation, HIV-1 protease, adenylate kinase

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1 Introduction It is well known that the functions and biological activities of proteins are closely related to their structures and dynamics [1-4]. Understanding the function and biological activities of proteins requires an investigation of the dynamics of the structural fluctuations and their relations to conformational transitions [2, 5]. Of particular importance, many kinds of vital diseases are related to the misfunction of proteins, most of which are caused by the sophisticated changes of their structure and dynamics. For example, one residue mutation of haemoglobin, such as E6V, would have a great impact on the protein structure and dynamics and thus influence its functions and biological activities, which can lead to the sickle-cell disease [6, 7].

On the other hand, the functions and biological activities of protein are highly dependent on the association and dissociation with other molecules, called ligands [8]. In proteinligand binding, the ligand is a molecule binds to a particular site on a target protein that serves as the receptor. The protein-ligand binding usually produces chemical signals, which are crucial for lots of physiological processes, including enzyme reactions, folding of intrinsically disordered proteins, gene expression, etc [9-11]. The kinetics of proteinligand binding can be descript as

kon  → PL P + L ←  koff

(1)

where P represents the protein, L represents the ligand, and PL represents the bound complex. The constant kon and koff are the association and dissociation rates, respectively.

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The binding of ligands and the conformational transitions of proteins always go hand in hand. In some cases, the ligand selectively binds to a state of the targeted protein that is present only in small amounts and eventually converting the state to the ligand-bound conformation. That is the so-called conformational selection binding mode [12]. Alternatively, the ligand binds to the predominant free conformation followed by a conformational transition in the protein to a preferred ligand-bound conformation, which is the so-called induced fit mode [13]. In both of the two binding modes, protein structural fluctuations and conformational transitions significantly affect the association processes and influence the kinetics [14, 15]. Understanding the ligand binding strategy (e.g., induced fit or conformational selection) is crucial for structure-based drug design [16-18]. For example, to promote the target recognition, structure-based drug design should consider all the equilibrium conformations if the association process follows the conformational selection mode [18].

The binding of ligands typically results in changes in the dynamics and conformational states of the target proteins. As a result, the biological activities of proteins can be regulated by the binding and unbinding of ligands. In such a way, many diseases can be treated clinically by delivering designed ligands (i.e., drugs/inhibitors) to specific protein targets. For example, the inhibiting therapy of Acquired Immune Deficiency Syndrome (AIDS) can be achieved by designing effective inhibitors to bind with the protease of the human immunodeficiency virus (HIV) [19, 20]. To form specific interactions with the targets, the molecules of the inhibitors/drugs are expected to be complementary in shape and/or charge to the targets (e.g., proteins) [21]. Once the ligand binds tightly with the

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targeted molecule, the function of the targeted protein would be inhibited. Understanding the underlying mechanism that protein receptors recognize, interact, and associate/ dissociate with ligands (e.g., substrates and inhibitors) is of paramount importance in drug discovery efforts [22]. Rational drug design should be based upon both structure and structural dynamics of the targeted proteins and the ligands.

The X-ray crystallography and nuclear magnetic resonance (NMR) studies demonstrate their power to provide atomic details of the three-dimensional structure of the free proteins and complexes bound with ligands. However, the available structures for free and bound states of protein systems from X-ray crystallography and NMR studies show limited information about their dynamics, e.g., the conformational transitions of proteins and the binding/unbinding pathways. Alternatively, molecular simulation method can provide an effective way of gaining insight into the details of the dynamics of proteins and the association/dissociation with the ligands. In this review, taking two important systems as examples, i.e., human immunodeficiency virus type 1 protease (HIV-1 PR) and adenylate kinase (AdK), we explain how the conformational transitions of proteins influence the association/dissociation of its ligands and how the binding of ligand impacts on the dynamics of proteins with molecular dynamics simulations.

HIV-1 PR and AdK represent two different typical protein structures. HIV-1 PR is a dimeric aspartic protease, which is critical in the virus replication cycle to cleave the gag and pol polyprotein to process viral maturation [23]. Each monomer of HIV-1 PR contains 99 amino residues and the active site is caved by two flexible β-hairpin flaps as a

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gate to control the association of ligands (as shown in Fig. 1(a) and 1(b)) [24, 25]. The HIV virus is noninfectious without HIV-1 PR [7]. As a result, one of the major inhibiting therapy methods of AIDS is to design potent inhibitors to occupy the active site of HIV-1 PR. The binding of inhibitor will block the binding of substrates (see Fig. 1(b)). The other case, AdK is an ubiquitous cellular energy homeostasis enzyme. AdK catalyzes the Mg2+dependent phosphoryl transfer reaction Mg2++2ADP ↔Mg2++ATP + AMP in cellular systems [26, 27]. It was found that some of the residue mutations of AdK would cause abnormal conformational transitions of AdK, leading to severe human disease phenotypes such as dysgenesis associated with immunodeficiency and sensorineural hearing loss [28]. In contract to HIV-1 PR that has only one binding site, AdK consists of two binding sites and three major domains: a CORE domain, an ATP-binding domain (LID), and an AMP-binding domain (NMP) [26, 27] (see Fig. 1(c) and 1(d)). The crystallographic structures showed that AdK has open conformation (i.e., the unbound state, see Fig. 1(c)) as well as closed conformation [26, 27] (i.e., with substrates, see Fig. 1(d)). Overall, HIV-1 PR and AdK are two benchmark models for developing new molecular modelling methods and studying protein-ligand interactions. Studies of the dynamics of there two protein and their interactions with ligands can provide meaningful message in physics, chemistry, and biology for drug design and discovery.

In this review, we will firstly introduce the dynamics of conformational transitions between the open and closed states of HIV-1 PR and AdK without ligands, and then we review how the dynamics of the ligand-free proteins influences the mechanics of proteinligand association. Finally, since the ligand dissociation kinetics closely related to the in

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vivo efficacy for drug design, we will introduce the recent progresses in studies of ligand dissociation processes by simulations and theoretical models for the single-molecule dynamic force spectroscopy (DFS) experiments.

Figure 1. Structures of HIV-1 PR and AdK and their interactions with ligands. (a) The semi-open state of HIV-1 PR. (b) The closed state of HIV-1 PR bound with an inhibitor. While the inhibitor occupies the active site, the binding of substrate is blocked and the function of the protease is inhibited. (c) The illustration of the open structure of AdK and the two ligands binding to the individual binding site. (d) The closed state of AdK bound with ligands. Figures adapted from References [29] and [30] with permission.

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2 Conformational transitions of ligand free proteins

2.1 Closed

open transitions of HIV-1 PR without ligands

The protein-ligand association can be simplified into three steps: (I) free diffusions of the ligand and the ligand-free protein molecules; (II) several intermediate states for the ligand and protein to rearrange their position and shape to form a loose complex when the two molecules contact; (III) conformational rearrangement to form sophisticated interactions in the bound complex [31-33]. In the second and the final steps, the conformational transitions of protein is crucial for the access of the ligand to the binding site.

The crystallographic and NMR structures showed that HIV-1 PR exists in large ensemble of conformations, mainly distinctive for a semi-open state (see Fig. 1(a), with the flaps packed loosely), and a closed state (see Fig. 1(b), with the ligand-bound at the binding site and the flaps packed tightly and blocked the binding of substrate) [24, 25]. It is expected there should be an open state of HIV-1 PR that the flaps in wide distance enable the access of the ligand to the binding site. Numerous computational studies have been aimed to understand the opening dynamics of the flexible flaps of HIV-1 PR [29, 34-40]. Especially, Hornak et al. showed that HIV-1 PR flaps can spontaneously open and reclose in MD simulations by using implicit solvent model [35]. The opening motion of flaps exposes the binding site for contacting with the ligand. It was found that there is a network of weakly polar interactions between the flap tips, which was proposed to be responsible for stabilizing the semi-open flap conformation [36]. This finding suggests that the polar interactions located at the flap tips could be responsible for making flaps

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opening as a highly sensitive gating mechanism which controls the access to the active site [36]. Li et al. showed that there are rapid, subnanosecond fluctuations located at the flap tips, caused by the dihedral angles rotation, would disrupt the polar interactions between the tips and then induce the opening of the flaps [29]. Importantly, the weak interaction between the tips may be affected by the contacts of ligands [29].

To simulate the long-time conformational transitions of HIV-1 PR, McCammon and coworkers developed a coarse-grained (CG) model for the protease [41-45]. In the CG model, each amino acid is represented by one bead of different size and weight. The bead is placed at the C-alpha position and connected by virtual bonds, angles, and dihedral angles, in which the CG force field parameterization is based on the crystallographic and NMR structure data, as well as all-atom simulation results [41-45]. According to the CG model, the conformational transitions between the semi-open, open, and closed states were observed by the microsecond time scale simulations (see Fig. 2) [41]. It showed that the predominant conformation of HIV-1 PR without ligand is the semi-open state, while sometimes it can transit to the closed and open states at the time scale of ~100 ns to microseconds. In the open state, the flaps move away far from the binding site so that the binding site is completely exposed for the binding of ligands (see Fig. 2).

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Figure 2. Conformational transitions of HIV-1 PR by CG model. Figure adapted from Reference [41] with permission.

2.2 Multi intermediate states and transition pathways of AdK In contrast to the HIV-1 PR case, AdK has two binding sites that are covered by LID and NMP domains in the closed state (see Fig. 1(c) and 1(d)), respectively. The movement of LID and NMP domains is in competitive order, which will lead to different pathways for conformational transitions in AdK: from the open (with both LID and NMP domains open), via NMP-open (with LID domain closed and NMP domain open) or alternatively via LID-open (the LID domain open with the NMP domain closed), through to the closed (with both domains closed); and vice versa [46]. The competitive order of conformational transitions of different domains affects the binding processes of the ligands. Previous studies have shown that some salt bridges located at the LID-CORE and NMP-CORE interfaces contributing to the stability of the open and closed state of AdK without ligands [47]. Interestingly, it was proposed that the conformational transitions caused by LID and NMP domains movements are coupling to the folding/unfolding of specific secondary structures (i.e., the cracking mechanism) [48].

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Recent study found there are multi conformational transition pathways of AdK [30] using a bias-exchange metadynamics simulation. As shown in Fig. 3, the LID and NMP domains of AdK undergo hinge motions towards and away from the CORE domain [30]. The simulation results indicate there are relatively small energy barrieres, around 1~2 kBT , need to overcome to transit between open and closed conformations in the ligand-

free AdK [30]. As a result, AdK equilibrates between the open and closed states in the absence of ligands. From the biological perspective, it was supposed that the relatively small free energy difference between different conformations can facilitate a fine control of transitions by environmental perturbations and signaling [49]. Most importantly, it was found that not only the open state but also some of the intermediate ones (e.g., the socalled semi-open-semi-closed states) expose the binding sites that enable the access of the ligands [30]. The recently extensive explicit solvent atomistic simulations confirmed that there are multiple pathways and time scales for conformational transitions in AdK [50].

The structures and dynamics of HIV-1 PR and AdK show the good examples that the proteins may have conformational transfer between varied conformational states even without ligands. The conformational transitions facilitate the proteins to expose the binding site to enable the access of the ligands.

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Figure 3. Conformational transitions of AdK by bias-exchange metadynamics simulation. (a) Free energy landscape of the conformational transitions of AdK between multi intermediate states. (b) A three-dimensional plot of free energy landscapes of the conformational transitions of AdK in the absence of ligands. (c) Corresponding structures of the intermediate states and the transition rates obtained by simulations. Figure adapted from Reference [30] with permission.

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3 Association of ligands – induced fit or conformational selection?

3.1 Gating effect of the protein domains to ligand association Protein structural fluctuations and conformational transitions significantly affect the binding kinetics. For instance, the binding sites of proteins can be occluded by protein loops or domains. Such loops and domains act as a gate that can regulate the conformational transitions of protein between the open and closed states to influence the ligand binding kinetics. As a result, the association processes will be closely correlated to the conformational transitions of the proteins. Previous studies proposed that proteins with lid-gated binding sites must operate by an induced fit mode [51]. But recent studies suggested that it might not be true.

As shown in crystallographic and NMR structures, the binding site of HIV-1 PR is covered by two flexible flaps that behavior as a gate to control the binding of the substrate and the inhibitor. Previous studies indicated that HIV-1 PR undergoes conformational exchanges between the semi-open, open and closed states in ~100 nanoseconds and the binding process can be up to microseconds [29, 41]. To study the binding processes of ligands to HIV-1 PR, Li et al. calculated the binding energies of varied inhibitors and substrates of HIV-1 PR for constructing the CG model for the ligands and HIV-1 PR [52, 53]. Similar approach has been used to study the binding of carbon nanotubes as an inhibitor to HIV-1 PR [54]. According to the CG model simulations, it was found that the binding pathways strongly depend on the size of the ligands and the interaction energy between the ligand and the protease (see Fig. 4(a) and 4(b)). For instance, experiments showed that the small size ligands of HIV-1 PR, e.g.,

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XK263 and DMP323, exhibits fast association rates as kon = 109 M −1 s −1 , which is close to the diffusion limit [55]. In the CG simulations, because of its small size, it can be seem that sometimes the ligand can enter the binding cavity without the fully opening of the flaps, as shown in Fig. 4(c) [52, 53]. However, for a larger size ligand, e.g., Saquinavir (SQV), after the diffusion to the surface of HIV-1 PR, it needs to wait for a wide open conformation of the flaps, as shown in Fig. 4(d) [52, 53]. In this case, the association rate is governed by the rate of conformational transitions of protein, which is much slower than the diffusion limited rate [55]. Consequently, the gate effect of the flaps of HIV-1 PR depends on the size of the ligands.

On the other hand, it was also found that the binding energy is another critical parameter influencing the ligand's binding processes. For instance, the association rate constant decreases significantly with the decreasing of the binding energy (see Fig. 4(b)) [52, 53]. The underlying mechanism is that the stronger binding energy results in a larger driving force for the binding process. The ligand with a larger driving force can have a higher impact on the dynamics of flaps and accelerate the opening, while weaker driving force rarely affect the dynamics of the protein and the ligand needs to wait for the conformational transitions for exposing the binding site [52, 53].

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Figure 4. The conformational transitions of HIV-1 PR and the pathways of ligand association. (a) Correlation between the association rate constant and the radius of gyration of inhibitors. (b) Correlation between the association rate constant and the binding energy of inhibitors. The dash black lines are the trend lines, and the dash red circle highlights the region of FDA-approved inhibitors (represented by the solid pink color dots). (c) The ligand binding pathway without fully opening of the flaps. (d) The ligand binds to the binding site needing to wait for fully opening of the flaps. Figures adapted from References [53] and [52] with permission.

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An extremely long-time scale unbiased all-atom simulation study of ligands binding to HIV-1 PR was recently reported [56]. The timescale it simulated is up to 14 microseconds by using a special-purpose computer [56]. This state-of-art longest all-atom simulation confirmed that the small size ligand XK263 can bind with HIV-1 PR without the fully opening of the flaps. Furthermore, it showed that XK263 has a stronger capacity for desolvating surrounding water molecules [56], i.e., stronger driving force, can induce conformational transitions of the flaps for ligand binding. It seems that the small size ligand with stronger driving force binds to HIV-1 PR following the induced fit mechanism. In contrast, other ligands (e.g., Ritonavir and Saquinavir) with slow dehydration characteristic (i.e., larger size ligands with weaker driving force) only allows for a gradual association to HIV-1 PR when the protein’s flaps conformation is fully open, working as conformational selection mode [56].

3.2 Association coupling with conformational transitions In contrast to the case of HIV-1 PR, AdK equilibrates between the open and closed conformations without significant energy barrier even in the absence of ligands [30, 50]. Structurally, in the fully closed state, the LID and NMP domains cover on the binding sites and completely occlude the access pathways of the ligands. However, the semiopen–semi-closed intermediate states do not rule out the binding of ligands with these states (see Fig. 3(c)) [30]. It is possible to bind to the conformations that do not result in complete steric occlusion of the binding site, consistent with the conformational selection mode. Once the ligand binds to the intermediate states, it will induce the conformational

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transition of AdK toward the fully closed conformations (see Fig. 5), behaves as the induced fit mechanism [30]. Consequently, the mechanism of ligand binding to AdK could involve both conformational selection and induced fit operations [30]. Previously, Hammes et al. have proposed that both of the conformational selection and induced fit operations may occur through a flux description of the binding mechanism, which showed that the association of ligands switches from being dominated by the conformational selection pathway at low ligand concentration to induced fit at high ligand concentration [57]. In the case of AdK, when the ligand is in low concentration, because the binding of ligands is in low stochastic frequency compared with the conformational transitions of AdK, the conformational selection will be the dominate mode for binding [30]. In contrast, the binding mode will switch to be dominated by induced fit at high ligand concentration, as the protein and the ligand will encounter in high frequency [30]. Multiwell free energy landscape with low energy barriers of AdK let conformational selection and induced fit operations coexist in the ligand binding process, depending on the the ligand concentration [30].

There are also other systems that the association of ligands involves both of induced fit and conformational selection modes, e.g. the binding of nicotinamide adenine dinucleotide phosphate (NADP+) to dihydrofolate reductase (DHFR) [57], flavodoxin folding coupled to binding of its cofactor flavin mononucleotide (FMN) [57], the ligands bind to the Lysine-, Arginine-, Ornithine-binding (LAO) protein [58], and the binding of anti-cancer drug Imatinib to the c-Src Kinase [16]. The induced fit and conformational selection mechanisms are complementary rather than mutually exclusive models.

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Figure 5. Conformational transitions of AdK binding with ligands. (a) Free energy landscape of the conformational transitions of AdK between multi intermediate states. (b) A three-dimensional plot of free energy landscapes of the conformational transitions of AdK with ligands. (c) Representative conformational transition pathways derived from the free energy landscape. Figure adapted from Reference [30] with permission.

4 Dissociation of the ligand from protein

4.1 Protein-ligand dissociation and single-molecule dynamic force spectroscopy (DFS) The ligands can form sophisticated interactions with the targeted protein after binding via, e.g. the hydrophobic interactions and the hydrogen bond (H-bond) network. The

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interactions help to restrain the ligands at the binding site. On the other hand, the ligand facilitates the restrain of the protein’s dynamics. For example, the fluctuations of the flap tips of HIV-1 PR are inhibited by the binding of the ligand, through the H-bond network formed between the ligand and the PR’s flap tips and active site. The hinge motions of the LID and NMP domains of AdK are also restrained by the binding of ligands, because of lots of H-bonds formed between the ligand and AdK that bridge the CORE domain and LID/NMP domains. In the ligand-bound AdK, a closed conformation is energetically favorable and requires a larger driving force to overcome the energy barrier (~13.5 kBT ) in order to induce an open conformation (see Fig. 5) [30]. In other words, it should need a sufficiently long time course, up to milliseconds to seconds, to have the bound complex dissociation for an open conformation under the thermal fluctuations.

The knowledge of the dissociation process of the ligand from the protein is important. We already know that a potent inhibitor with strong binding affinity is expected to have a large kon (fast association) and a small koff (slow dissociation), corresponding to a long residence time with the targeted protein [59]. Importantly, it was found that in some cases, koff is better correlated in vivo efficacy for drug design [60]. Furthermore, it was found that the rate limiting step in the catalysis cycle of AdK is related to the product release, and the slow product release is caused by the long-time scale re-opening of the substrate-binding subdomains [61, 62].

Because the time scale of the dissociation process is large, simulation of this process typically requires resorting to CG model. Trylska et al. studied the release of the product

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of HIV-1 PR by using a CG model [43], and they showed that the product can slide out from the binding cleft to the sides of the protease, not requiring the flap opening [43]. However, the CG model is lack of accurate atomic interactions between the ligand and protease. Alternatively, Gardner and Abrams applied the temperature acceleration MD technique to study the conformational changes associated with substrate unbinding of both wild-type and F99Y mutant HIV-1 PR, showing that the elbow engagement is a necessary and the limiting step in substrate movement into or out of the binding pocket [63]. Cui et al. employed metadynamics simulations in all-atom MD simulations to investigat the ADP release process and the coupled protein dynamics of AdK [64]. It was found that the ADP release requires to overcome a relatively high energy barrier, accompanied by a fully opening of the LID domain and partially opening of the NMP domain [64]. By using a so-called parallel cascade selection molecular dynamics method, Ye et al. showed that the electrostatic interactions determine the entrance/release order of substrates in the catalytic cycle of AdK [65]. However, the high energy barrier for protein-ligand dissociation makes a great challenge for all-atom MD simulations, indicating that the acceleration MD techniques are still highly desired.

To accelerate the dissociation process, an external load is applied to the ligand in the simulations, which is called the steered molecular dynamics (SMD) method, corresponding to the force-induced bond rupture in experiments [66-74]. In the SMD simulation, the center of mass (COM) of the pulled molecule is connected to a steered dummy atom via a spring, and the dummy atom moves at a constant velocity. As a result, a pull force

f = k spring ( vt − x0 )

is applied to the pulled molecule, where k spring is to mimic the

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stiffness of the loading device, v is the pulling velocity, t is the simulation time and x0 is the position of the pulled molecule [72]. Importantly, Colizzi et al. showed that mimicking the single-molecule pulling experiments, the SMD simulation results can be used to discern the active compounds from the inactive ones to a target protein [75]. For instance, SMD simulations were applied to study the dissociation of varied ligands from HIV-1 PR [66, 67]. It was shown that the dissociation process is accelerated significantly under the external force, by disrupting the critical interactions (see Fig. 7) [66]. It can be seen that different mean rupture forces indicate different binding interaction of the ligands, i.e., higher rupture forces denote stronger bound inhibitors, whereas the lower rupture forces denote the weaker bound ones [66]. More recently, Huang et al. showed that the SMD simulations combined with residue-based energy decomposition can accurately predict the dissociation rate constants of HIV-1 PR inhibitors [76].

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Figure 6. SMD simulation of dissociating the ligand from protein. (a) Snapshots of ligand dissociation from HIV-1 PR binding site under external force. The red lines indicate the H-bond network. (b) The pulling force applied to the protein-ligand complex. (c) The rupture forces of protein-ligand bonds of three inhibitor cases with HIV-1 PR. Figure adapted from Reference [66] with permission.

4.2 Single-molecule DFS for analysis of protein-ligand dissociation The single-molecule dynamic force spectroscopy (DFS) is a typical method for studying the protein-ligand interactions in single-molecule systems. The most prominent experimental tools in DFS studies are atomic force microscope (AFM), biomembrane

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force probe (BFP), laser optical tweezer (LOT), and magnetic tweezer (MT), as shown in Fig. 6(a) [77-80]. In theoretical studies of the DFS, the force-induced dissociation, i.e., the bond rupture, is treated as a thermally activated escape of a particle over a single energy barrier under the perturbation of an external force (see Fig. 6(b)) [78, 81]. Previously, Dudko et al. [82] showed that the mean rupture force for disrupting the ligand-receptor interaction can be expressed as

Frup

µ koff exp ( ∆Goff + γ )   ∆Goff   1   = ln 1 −  µ xβ   ∆Goff xβ Kv     

(2)

in which µ = 1 2 and µ = 2 3 correspond to the cusp [83] and linear-cubic energy surfaces [84], respectively. γ ≈ 0.577 is the Euler-Mascheroni constant, K is the loading stiffness of the pulling device, v is the pulling velocity, Kv represents the loading rate, ∆Goff is the energy barrier for the dissociation, xβ is the width of the energy well, and koff is the dissociation rate in the absence of external force. Equation (2) shows that the rupture forces to disrupt the ligand-receptor interactions non-linearly depend on the logarithm of loading rates. Equation (2) can reduce to the Bell’s [85] model when µ = 1 and ∆Goff → ∞ . The theoretical models have provided a variety of thought-provoking views in the DFS experiments, by which the energy landscape parameters (i.e. ∆Goff , koff and xβ ) can be extracted from the mean rupture forces under varied loading rates.

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Figure 6. DSF experiment and the corresponding theoretical model. (a) Schematic illustration of two major techniques for loading single molecules: AFM and LOT in DSF experiment. (b) Schematic representation of a particle escaping from an energy well to mimic the rupture of the receptor–ligand interaction under an external force. (c) The mean rupture force depends on the logarithm of the loading rate. (d) The relationship between the saturating rupture force and the stiffness of the spring constant K. Figure adapted from References [77] and [86] with permission.

Note that the models by Dudko et al. [82] and Evans and Ritchie [81] predicted that the rupture force would diminish to zero or even negative value when the loading rate is vanishingly small by assuming an irreversible protein-ligand interaction. Comparing with the irreversible interaction model [82], Tshiprut et al. [87, 88] found that the rebinding of

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the molecular bond decreases the slopes of the rupture force - loading rate curve when the loading rates are small, indicating that the rebinding effect is important to the strength of single-molecular bond under the ultralow loading rate. Experiments also showed that the mean rupture force would not depend on the loading rates but on the stiffness of the loading device at ultralow loading rate [89-92]. To take into account the rebinding effect in DSF under ultralow loading rates, Li and Ji have recently developed a new theoretical model by allowing bond rebinding (see Fig. 6b) [86, 93]. They showed that when the loading rate is lower than a critical value, bond rebinding dominates the rupture process, resulting in a rate-independent rupture forces that correspond to nonzero interaction strength at an ultralow loading rate (Fig. 6(c)) [86, 93, 94], and the rupture force increases with the loading stiffness (Fig. 6(d)) [86, 93, 94]. The DFS theoretical models provide effective ways for studying protein-ligand interactions.

5 Conclusions and perspectives The functions of protein are closely related to their structures and dynamics. Understanding of the proteins’ conformational transitions in the presence of ligands is crucially important for the design of novel inhibitors of the targeted receptor. In this review, taken two important proteins, i.e., HIV-1 PR and AdK, as examples, we introduced the molecular simulation studies of proteins’ conformational transitions and their interactions with the ligands. Structurally, both of HIV-1 PR and AdK equilibrate between open and closed conformations even without binding of ligands. Large conformational transitions are triggered by local fluctuations, which facilitate the protein to expose the binding site to allow the access of the ligands. We showed that the

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conformational selection and induced fit mechanisms are complementary mechanisms for ligand association rather than mutually exclusive ones. The two cases of HIV-1 PR and AdK give good examples illustrating how the two mechanisms co-regulate the association of ligands, which depends on the structures of protein and ligand (e.g., the gating effect of domains in proteins and the size of ligands), the interactions (e.g., the strength of driving force) and the concentration of ligands. To study the dissociation process, the DFS experiment and SMD simulation are useful methods to accelerate the dissociation process of the ligand-bound complex. The SMD derived force profiles can be used to discern different binding strength of ligands and critical interactions during the dissociation process, as well as the dissociation rate contants. On the other hand, the protein-ligand interaction properties (e.g., the binding energy

∆G

, the width of the

energy well xβ and the self-dissociation rate koff ) can be extracted from the DFS theoretical model.

Molecular dynamic simulation method is a powerful tool for studying the atomistic details of the mechanics/dynamics of the proteins and their interactions with ligands [95, 96]. The long-time simulation with an accurate force field is still a challenge for studying large conformational transitions of proteins and the association/dissociation of ligands. The CG models have provided an effective way of gaining insight into the long-time scale events of biomolecular systems [97]. However, the achievement of the long-time scale of CG model is at the cost of the accurate description of interactions. In recent years, the so-called enhance sampling methods are established to accelerate the dynamic process in atomic details [98], e.g., replica-exchange molecular dynamics [99-101],

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accelerated molecular dynamics [38, 102], metadynamics [103-105] and etc., with which the long-time scale process can be achieved within current computational power. We expect that more advanced computational methods can be developed to take advantage of enhanced sampling and/or efficient representations of proteins’ conformational transitions and their interaction with ligands, which then provide the powerful tools for novel drug design using molecular simulations.

Conflict of Interest statement The authors declare that there are no conflicts of interest.

Acknowledgments This work was supported by the Natural Science Foundation of China (Grants No. 11932017, 11772055, 11772054, 11221202, 11202026, and 11532009), and the Fundamental Research Funds for the Central Universities (Grant No. 2019QNA4060).

References:

[1]

P.Y. Chou and G.D. Fasman, Empirical predictions of protein conformation. Annual review of biochemistry 47 (1978) 251-276.

[2]

M. Kurplus and J. McCammon, Dynamics of proteins: elements and function. Annual review of biochemistry 52 (1983) 263-300.

27

[3]

K.A. Henzler-Wildman, V. Thai, M. Lei, M. Ott, M. Wolf-Watz, T. Fenn, E. Pozharski, M.A. Wilson, G.A. Petsko, M. Karplus, C.G. Huebner, and D. Kern, Intrinsic motions along an enzymatic reaction trajectory. Nature 450 (2007) 838U13.

[4]

D. Kern and E.R.P. Zuiderweg, The role of dynamics in allosteric regulation. Current Opinion in Structural Biology 13 (2003) 748-757.

[5]

C.-J. Tsai, A. Del Sol, and R. Nussinov, Allostery: absence of a change in shape does not imply that allostery is not at play. Journal of Molecular Biology 378 (2008) 1-11.

[6]

R.A. Studer, B.H. Dessailly, and C.A. Orengo, Residue mutations and their impact on protein structure and function: detecting beneficial and pathogenic changes. Biochemical Journal 449 (2013) 581-594.

[7]

N.E. Kohl, E.A. Emini, W.A. Schleif, L.J. Davis, J.C. Heimbach, R.A.F. Dixon, E.M. Scolnick, and I.S. Sigal, Active Human Immunodeficiency Virus Protease Is Required for Viral Infectivity. Proceedings of the National Academy of Sciences of the United States of America 85 (1988) 4686-4690.

[8]

P. Bongrand, Ligand-receptor interactions. Reports on Progress in Physics 62 (1999) 921.

[9]

C.H. Henkels, J.C. Kurz, C.A. Fierke, and T.G. Oas, Linked folding and anion binding of the Bacillus subtilis ribonuclease P protein. Biochemistry 40 (2001) 2777-2789.

[10]

P.E. Wright and H.J. Dyson, Linking folding and binding. Current opinion in structural biology 19 (2009) 31-38.

28

[11]

M.F. Dunn, Protein–Ligand Interactions: General Description. In: Encyclopedia of Life Sciences (ELS). John Wiley & Sons, Ltd: Chichester. (2010).

[12]

J.P. Changeux and S. Edelstein, Conformational selection or induced fit? 50 years of debate resolved. F1000 Biol Rep 3 (2011) 19.

[13]

D. Koshland, The active site and enzyme action. Advances in Enzymology and Related Areas of Molecular Biology 22 (1960) 45-97.

[14]

K.G. Daniels, Y. Suo, and T.G. Oas, Conformational kinetics reveals affinities of protein conformational states. Proceedings of the National Academy of Sciences 112 (2015) 9352-9357.

[15]

A.M. Ruvinsky, T. Kirys, A.V. Tuzikov, and I.A. Vakser, Structure fluctuations and conformational changes in protein binding. Journal of bioinformatics and computational biology 10 (2012) 1241002.

[16]

M.A. Morando, G. Saladino, N. D'Amelio, E. Pucheta-Martinez, S. Lovera, M. Lelli, B. Lopez-Mendez, M. Marenchino, R. Campos-Olivas, and F.L. Gervasio, Conformational Selection and Induced Fit Mechanisms in the Binding of an Anticancer Drug to the c-Src Kinase. Scientific Reports 6 (2016) 24439.

[17]

Y.C. Xu, J.P. Colletier, H.L. Jiang, I. Silman, J.L. Sussman, and M. Weik, Induced-fit or preexisting equilibrium dynamics? Lessons from protein crystallography and MD simulations on acetylcholinesterase and implications for structure-based drug design. Protein Science 17 (2008) 601-605.

[18]

D.P. Fairlie, J.D.A. Tyndall, R.C. Reid, A.K. Wong, G. Abbenante, M.J. Scanlon, D.R. March, D.A. Bergman, C.L.L. Chai, and B.A. Burkett, Conformational selection of inhibitors and substrates by proteolytic enzymes: Implications for

29

drug design and polypeptide processing. Journal Of Medicinal Chemistry 43 (2000) 1271-1281. [19]

V. Hornak and C. Simmerling, Targeting structural flexibility in HIV-1 protease inhibitor binding. Drug Discovery Today 12 (2007) 132-138.

[20]

A. Wlodawer and J. Vondrasek, Inhibitors of HIV-1 protease: A major success of structure-assisted drug design. Annual Review of Biophysics and Biomolecular Structure 27 (1998) 249-284.

[21]

G. Sliwoski, S. Kothiwale, J. Meiler, and E.W. Lowe, Computational Methods in Drug Discovery. Pharmacological Reviews 66 (2014) 334-395.

[22]

S.F. Sousa, P.A. Fernandes, and M.J. Ramos, Protein–ligand docking: current status and future challenges. Proteins: Structure, Function, and Bioinformatics 65 (2006) 15-26.

[23]

R.A. Katz and A.M. Skalka, The Retroviral Enzymes. Annual Review of Biochemistry 63 (1994) 133-173.

[24]

S. Spinelli, Q.Z. Liu, P.M. Alzari, P.H. Hirel, and R.J. Poljak, The 3-Dimensional Structure of the Aspartyl Protease from the Hiv-1 Isolate Bru. Biochimie 73 (1991) 1391-1396.

[25]

P.Y.S. Lam, P.K. Jadhav, C.J. Eyermann, C.N. Hodge, Y. Ru, L.T. Bacheler, J.L. Meek, M.J. Otto, M.M. Rayner, Y.N. Wong, C.H. Chang, P.C. Weber, D.A. Jackson, T.R. Sharpe, and S. Ericksonviitanen, Rational Design of Potent, Bioavailable, Nonpeptide Cyclic Ureas as Hiv Protease Inhibitors. Science 263 (1994) 380-384.

30

[26]

C.W. Muller, G.J. Schlauderer, J. Reinstein, and G.E. Schulz, Adenylate kinase motions during catalysis: An energetic counterweight balancing substrate binding. Structure 4 (1996) 147-156.

[27]

C.W. Muller and G.E. Schulz, Structure of The Complex Between Adenylate Kinase From Escherichia-Coli And The Inhibitor Ap5a Refined At 1.9 A Resolution - A Model For A Catalytic Transition-State. Journal of Molecular Biology 224 (1992) 159-177.

[28]

S. Zhang, E. Nemutlu, A. Terzic, and P. Dzeja, Adenylate kinase isoform network: a major hub in cell energetics and metabolic signaling, in Systems Biology of Metabolic and Signaling Networks. 2014, Springer. p. 145-162.

[29]

D.C. Li, B.H. Ji, K. Hwang, and Y.G. Huang, Crucial Roles of the Subnanosecond Local Dynamics of the Flap Tips in the Global Conformational Changes of HIV-1 Protease. Journal of Physical Chemistry B 114 (2010) 30603069.

[30]

D. Li, Ming S. Liu, and B. Ji, Mapping the Dynamics Landscape of Conformational Transitions in Enzyme: The Adenylate Kinase Case. Biophysical Journal 109 (2015) 647-660.

[31]

G. Schreiber, G. Haran, and H.-X. Zhou, Fundamental aspects of protein− protein association kinetics. Chemical reviews 109 (2009) 839-860.

[32]

E.S. Furfine, E. Dsouza, K.J. Ingold, J.J. Leban, T. Spector, and D.J.T. Porter, Two-Step Binding Mechanism for Hiv Protease Inhibitors. Biochemistry 31 (1992) 7886-7891.

31

[33]

J.R. Horn, T.R. Sosnick, and A.A. Kossiakoff, Principal determinants leading to transition state formation of a protein–protein complex, orientation trumps sidechain interactions. Proceedings of the National Academy of Sciences 106 (2009) 2559-2564.

[34]

D.C. Li, B.H. Ji, K.C. Hwang, and Y.G. Huang, Coarse grained modeling of biopolymers and proteins: methods and applications. International Journal of Applied Mechanics 1 (2009) 113-136.

[35]

V. Hornak, A. Okur, R.C. Rizzo, and C. Simmerling, HIV-1 protease flaps spontaneously open and reclose in molecular dynamics simulations. Proceedings of the National Academy of Sciences of the United States of America 103 (2006) 915-920.

[36]

G. Toth and A. Borics, Flap opening mechanism of HIV-1 protease. Journal of Molecular Graphics & Modelling 24 (2006) 465-474.

[37]

W.R.P. Scott and C.A. Schiffer, Curling of flap tips in HIV-1 protease as a mechanism for substrate entry and tolerance of drug resistance. Structure 8 (2000) 1259-1265.

[38]

D. Hamelberg and J.A. McCammon, Fast peptidyl cis-trans isomerization within the flexible Gly-rich flaps of HIV-1 protease. Journal of the American Chemical Society 127 (2005) 13778-13779.

[39]

A.P. Wiley, S.L. Williams, and J.W. Essex, Conformational Motions of HIV-1 Protease Identified Using Reversible Digitally Filtered Molecular Dynamics. Journal of Chemical Theory and Computation 5 (2009) 1117-1128.

32

[40]

J.R. Collins, S.K. Burt, and J.W. Erickson, Flap Opening in Hiv-1 Protease Simulated by Activated Molecular-Dynamics. Nature Structural Biology 2 (1995) 334-338.

[41]

V. Tozzini, J. Trylska, C.E. Chang, and J.A. McCammon, Flap opening dynamics in HIV-1 protease explored with a coarse-grained model. Journal of Structural Biology 157 (2007) 606-615.

[42]

V. Tozzini and J.A. McCammon, A coarse grained model for the dynamics of flap opening in HIV-1 protease. Chemical Physics Letters 413 (2005) 123-128.

[43]

J. Trylska, V. Tozzini, C.A. Chang, and J.A. McCammon, HIV-1 protease substrate binding and product release pathways explored with coarse-grained molecular dynamics. Biophysical Journal 92 (2007) 4179-4187.

[44]

C.E.A. Chang, J. Trylska, V. Tozzini, and J.A. McCammon, Binding pathways of ligands to HIV-1 protease: Coarse-grained and atomistic simulations. Chemical Biology & Drug Design 69 (2007) 5-13.

[45]

C.E. Chang, T.Y. Shen, J. Trylska, V. Tozzini, and J.A. McCammon, Gated binding of ligands to HIV-1 protease: Brownian dynamics simulations in a coarse-grained model. Biophysical Journal 90 (2006) 3880-3885.

[46]

M.S. Liu, B.D. Todd, and R.J. Sadus, Allosteric Conformational Transition in Adenylate Kinase: Dynamic Correlations and Implication for Allostery. Australian Journal of Chemistry 63 (2010) 405-412.

[47]

H.D. Song and F. Zhu, Conformational Dynamics of a Ligand-Free Adenylate Kinase. PLoS ONE 8 (2013) e68023.

33

[48]

P.C. Whitford, O. Miyashita, Y. Levy, and J.N. Onuchic, Conformational transitions of adenylate kinase: Switching by cracking. Journal of Molecular Biology 366 (2007) 1661-1671.

[49]

D.A. Potoyan, P.I. Zhuravlev, and G.A. Papoian, Computing Free Energy of a Large-Scale Allosteric Transition in Adenylate Kinase Using All Atom Explicit Solvent Simulations. Journal of Physical Chemistry B 116 (2012) 1709-1715.

[50]

Y.Q. Zheng and Q. Cui, Multiple Pathways and Time Scales for Conformational Transitions in apo-Adenylate Kinase. Journal of Chemical Theory and Computation 14 (2018) 1716-1726.

[51]

S.M. Sullivan and T. Holyoak, Enzymes with lid-gated active sites must operate by an induced fit mechanism instead of conformational selection. Proceedings of the National Academy of Sciences of the United States of America 105 (2008) 13829-13834.

[52]

D.C. Li, M.S. Liu, B.H. Ji, K. Hwang, and Y.G. Huang, Coarse-grained molecular dynamics of ligands binding into protein: The case of HIV-1 protease inhibitors. Journal of Chemical Physics 130 (2009) 215102.

[53]

D. Li, M.S. Liu, B. Ji, K.C. Hwang, and Y. Huang, Identifying the Molecular Mechanics and Binding Dynamics Characteristics of Potent Inhibitors to HIV‐1 Protease. Chemical Biology & Drug Design 80 (2012) 440-454.

[54]

Y.A. Cheng, D.C. Li, B.H. Ji, X.H. Shi, and H.J. Gao, Structure-based design of carbon nanotubes as HIV-1 protease inhibitors: Atomistic and coarse-grained simulations. Journal of Molecular Graphics & Modelling 29 (2010) 171-177.

34

[55]

P.O. Markgren, W. Schaal, M. Hamalainen, A. Karlen, A. Hallberg, B. Samuelsson, and U.H. Danielson, Relationships between structure and interaction kinetics for HIV-1 protease inhibitors. Journal of Medicinal Chemistry 45 (2002) 5430-5439.

[56]

Y.-m.M. Huang, M.A.V. Raymundo, W. Chen, and C.-e.A. Chang, Mechanism of the association pathways for a pair of fast and slow binding ligands of HIV-1 protease. Biochemistry 56 (2017) 1311-1323.

[57]

G.G. Hammes, Y.-C. Chang, and T.G. Oas, Conformational selection or induced fit: a flux description of reaction mechanism. Proceedings of the National Academy of Sciences 106 (2009) 13737-13741.

[58]

D.A. Silva, G.R. Bowman, A. Sosa-Peinado, and X.H. Huang, A Role for Both Conformational Selection and Induced Fit in Ligand Binding by the LAO Protein. Plos Computational Biology 7 (2011).

[59]

H. Lu and P.J. Tonge, Drug–target residence time: critical information for lead optimization. Current opinion in chemical biology 14 (2010) 467-474.

[60]

G.K. Walkup, Z. You, P.L. Ross, E.K. Allen, F. Daryaee, M.R. Hale, J. O’Donnell, D.E. Ehmann, V.J. Schuck, and T. Buurman, Translating slowbinding inhibition kinetics into cellular and in vivo effects. Nature chemical biology 11 (2015) 416.

[61]

J.A. Hanson, K. Duderstadt, L.P. Watkins, S. Bhattacharyya, J. Brokaw, J.-W. Chu, and H. Yang, Illuminating the mechanistic roles of enzyme conformational dynamics. Proceedings of the National Academy of Sciences of the United States of America 104 (2007) 18055-18060.

35

[62]

M. Wolf-Watz, V. Thai, K. Henzler-Wildman, G. Hadjipavlou, E.Z. Eisenmesser, and D. Kern, Linkage between dynamics and catalysis in a thermophilicmesophilic enzyme pair. Nature structural & molecular biology 11 (2004) 945949.

[63]

J.M. Gardner and C.F. Abrams, Energetics of Flap Opening in HIV-1 Protease: String Method Calculations. J Phys Chem B 123 (2019) 9584-9591.

[64]

D. Cui, W. Ren, W. Li, and W. Wang, Molecular simulations of substrate release and coupled conformational motions in adenylate kinase. Journal of Theoretical and Computational Chemistry 15 (2016) 1650004.

[65]

C. Ye, C.T. Ding, R.S. Ma, J.F. Wang, and Z.Y. Zhang, Electrostatic interactions determine entrance/release order of substrates in the catalytic cycle of adenylate kinase. Proteins-Structure Function and Bioinformatics 87 (2019) 337-347.

[66]

D. Li, B. Ji, K.-C. Hwang, and Y. Huang, Strength of Hydrogen Bond Network Takes Crucial Roles in the Dissociation Process of Inhibitors from the HIV-1 Protease Binding Pocket. PLoS ONE 6 (2011) e19268.

[67]

D. Li and B. Ji, Free energy calculation of single molecular interaction using Jarzynski's identity method: the case of HIV-1 protease inhibitor system. Acta Mechanica Sinica 28 (2012) 891-903.

[68]

Z. Xu, D. Li, and J. Baohua, Quantification of the stiffness and strength of cadherin ectodomain binding with different ions. Theoretical and Applied Mechanics Letters 4 (2014) 034001.

36

[69]

Y. Cheng, L.-D. Koh, D. Li, B. Ji, M.-Y. Han, and Y.-W. Zhang, On the strength of β-sheet crystallites of Bombyx mori silk fibroin. Journal of the Royal Society Interface 11 (2014) 20140305.

[70]

C. Xu, D. Li, Y. Cheng, M. Liu, Y. Zhang, and B. Ji, Pulling out a peptide chain from β -sheet crystallite: Propagation of instability of H-bonds under shear force. Acta Mechanica Sinica 31 (2015) 416-424.

[71]

Y. Cheng, L.-D. Koh, D. Li, B. Ji, Y. Zhang, J. Yeo, G. Guan, M.-Y. Han, and Y.W. Zhang, Peptide-Graphene Interactions Enhance the Mechanical Properties of Silk Fibroin. ACS Applied Materials & Interfaces (2015) 21787-21796.

[72]

B. Isralewitz, M. Gao, and K. Schulten, Steered molecular dynamics and mechanical functions of proteins. Current Opinion In Structural Biology 11 (2001) 224-230.

[73]

Y. Cheng, L.-D. Koh, F. Wang, D. Li, B. Ji, J. Yeo, G. Guan, M. Han, and Y.-W. Zhang, Carbon Nanoscroll-Silk Crystallite Hybrid Structure with Controllable Hydration and Mechanical Properties. Nanoscale (2017) 9181-9189.

[74]

X.H. Zhou, D.C. Li, S.J. Wan, Q.F. Cheng, and B.H. Ji, In silicon testing of the mechanical properties of graphene oxide-silk nanocomposites. Acta Mechanica 230 (2019) 1413-1425.

[75]

F. Colizzi, R. Perozzo, L. Scapozza, M. Recanatini, and A. Cavalli, SingleMolecule Pulling Simulations Can Discern Active from Inactive Enzyme Inhibitors. Journal of the American Chemical Society 132 (2010) 7361-7371.

[76]

S.H. Huang, D. Zhang, H. Mei, M. Kevin, S.J. Qu, X.C. Pan, and L.C. Lu, SMDBased Interaction-Energy Fingerprints Can Predict Accurately the Dissociation

37

Rate Constants of HIV-1 Protease Inhibitors. Journal of Chemical Information and Modeling 59 (2019) 159-169. [77]

S. Kumar and M.S. Li, Biomolecules under mechanical force. Physics ReportsReview Section of Physics Letters 486 (2010) 1-74.

[78]

E. Evans, Probing the relation between force - Lifetime - and chemistry in single molecular bonds. Annual Review of Biophysics and Biomolecular Structure 30 (2001) 105-128.

[79]

T. Hugel and M. Seitz, The study of molecular interactions by AFM force spectroscopy. Macromolecular Rapid Communications 22 (2001) 989-1016.

[80]

K.C. Neuman and A. Nagy, Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy. Nature Methods 5 (2008) 491505.

[81]

E. Evans and K. Ritchie, Strength of a weak bond connecting flexible polymer chains. Biophysical Journal 76 (1999) 2439-2447.

[82]

O.K. Dudko, G. Hummer, and A. Szabo, Intrinsic rates and activation free energies from single-molecule pulling experiments. Physical Review Letters 96 (2006) 108101.

[83]

G. Hummer and A. Szabo, Kinetics from nonequilibrium single-molecule pulling experiments. Biophysical Journal 85 (2003) 5-15.

[84]

O.K. Dudko, A.E. Filippov, J. Klafter, and M. Urbakh, Beyond the conventional description of dynamic force spectroscopy of adhesion bonds. Proceedings of the National Academy of Sciences of the United States of America 100 (2003) 11378-11381.

38

[85]

G.I. Bell, Models for Specific Adhesion of Cells to Cells. Science 200 (1978) 618627.

[86]

D. Li and B. Ji, Predicted Rupture Force of a Single Molecular Bond Becomes Rate Independent at Ultralow Loading Rates. Physical Review Letters 112 (2014) 078302.

[87]

Z. Tshiprut, J. Klafter, and M. Urbakh, Single-molecule pulling experiments: When the stiffness of the pulling device matters. Biophysical Journal 95 (2008) L42-L44.

[88]

Z. Tshiprut and M. Urbakh, Exploring hysteresis and energy dissipation in singlemolecule force spectroscopy. Journal of Chemical Physics 130 (2009) 084703.

[89]

Y. Zhang, G.Y. Sun, S.Q. Lu, N. Li, and M.A. Long, Low Spring Constant Regulates P-Selectin-PSGL-1 Bond Rupture. Biophysical Journal 95 (2008) 54395448.

[90]

S. Zepeda, Y. Yeh, and A. Noy, Determination of energy barriers for intermolecular interactions by variable temperature dynamic force spectroscopy. Langmuir 19 (2003) 1457-1461.

[91]

A. Ptak, M. Kappl, S. Moreno-Flores, H. Gojzewski, and H.J. Butt, Quantitative Characterization of Nanoadhesion by Dynamic Force Spectroscopy. Langmuir 25 (2009) 256-261.

[92]

R.W. Friddle, P. Podsiadlo, A.B. Artyukhin, and A. Noy, Near-equilibrium chemical force microscopy. Journal Of Physical Chemistry C 112 (2008) 49864990.

39

[93]

D. Li and B. Ji, Crucial Roles of Bond Rebinding in Rupture Behaviors of Single Molecular Bond at Ultralow Loading Rates. International Journal of Applied Mechanics 7 (2015) 1550015.

[94]

X. Chen, D. Li, B. Ji, and B. Chen, Reconciling bond strength of a slip bond at low loading rates with rebinding. EPL (Europhysics Letters) 109 (2015) 68002.

[95]

S.A. Hollingsworth and R.O. Dror, Molecular Dynamics Simulation for All. Neuron 99 (2018) 1129-1143.

[96]

M. Karplus and J. Kuriyan, Molecular dynamics and protein function. Proceedings of the National Academy of Sciences of the United States of America 102 (2005) 6679-6685.

[97]

V. Tozzini, Coarse-grained models for proteins. Current Opinion in Structural Biology 15 (2005) 144-150.

[98]

H. Lei and Y. Duan, Improved sampling methods for molecular simulation. Current opinion in structural biology 17 (2007) 187-191.

[99]

A. Patriksson and D. van der Spoel, A temperature predictor for parallel tempering simulations. Physical Chemistry Chemical Physics 10 (2008) 20732077.

[100] B. Bu, X. Tong, D. Li, Y. Hu, W. He, C. Zhao, R. Hu, X. Li, Y. Shao, and C. Liu, N-Terminal Acetylation Preserves α -Synuclein from Oligomerization by Blocking Intermolecular Hydrogen Bonds. ACS Chemical Neuroscience (2017). [101] Z.H. Li and H. Kono, Investigating the Influence of Arginine Dimethylation on Nucleosome Dynamics Using All-Atom Simulations and Kinetic Analysis. Journal of Physical Chemistry B 122 (2018) 9625-9634.

40

[102] D. Hamelberg, J. Mongan, and J.A. McCammon, Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules. The Journal of chemical physics 120 (2004) 11919-11929. [103] A. Barducci, G. Bussi, and M. Parrinello, Well-tempered metadynamics: A smoothly converging and tunable free-energy method. Physical Review Letters 100 (2008) 020603. [104] A. Laio and F.L. Gervasio, Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science. Reports on Progress in Physics 71 (2008) 126601. [105] F. Pietrucci, F. Marinelli, P. Carloni, and A. Laio, Substrate Binding Mechanism of HIV-1 Protease from Explicit-Solvent Atomistic Simulations. Journal of the American Chemical Society 131 (2009) 11811-11818.

41

Conflict of Interest statement The authors declare that there are no conflicts of interest.