Nanoscopic description of biomembrane electrostatics: results of molecular dynamics simulations and fluorescence probing

Chemistry and Physics of Lipids 160 (2009) 63–84

Contents lists available at ScienceDirect

Chemistry and Physics of Lipids journal homepage: www.elsevier.com/locate/chemphyslip

Review

Nanoscopic description of biomembrane electrostatics: results of molecular dynamics simulations and fluorescence probing Alexander P. Demchenko a , Semen O. Yesylevskyy b,∗ a b

A.V. Palladin Institute of Biochemistry, National Academy of Sciences of Ukraine, Leontovicha st. 9, Kiev 01601, Ukraine Institute of Physics, National Academy of Sciences of Ukraine, Prospect Nauki, 46, Kiev 03039, Ukraine

a r t i c l e

i n f o

Article history: Received 23 March 2009 Received in revised form 18 May 2009 Accepted 19 May 2009 Available online 27 May 2009 Keywords: Lipid membranes Electrostatic potential Molecular dynamics Fluorescent probing Electrochromic dyes

a b s t r a c t Electrostatic fields generated on and inside biological membranes are recognized to play a fundamental role in key processes of cell functioning. Their understanding requires an adequate description on the level of elementary charges and the reconstruction of electrostatic potentials by integration over all elementary interactions. Out of all the available research tools, only molecular dynamics simulations are capable of this, extending from the atomic to the mesoscopic level of description on the required time and space scale. A complementary approach is that offered by molecular probe methods, with the application of electrochromic dyes. Highly sensitive to intermolecular interactions, they generate integrated signals arising from electric fields produced by elementary charges at the sites of their location. This review is an attempt to provide a critical analysis of these two approaches and their present and potential applications. The results obtained by both methods are consistent in that they both show an extremely complex profile of the electric field in the membrane. The nanoscopic view, with two-dimensional averaging over the bilayer plane and formal separation of the electrostatic potential into surface ( s ), dipole ( d ) and transmembrane ( t ) potentials, is constructive in the analysis of different functional properties of membranes. © 2009 Published by Elsevier Ireland Ltd.

Contents 1. 2.

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecular dynamics simulations of biomembrane electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Methodological issues in MD simulations of membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Resolution of components of biomembrane electrostatic potential (dipole, surface and transmembrane potentials) . . . . . . . . . . . . . . . . . . . . . 2.2.1. Dipole potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2. Surface potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3. Transmembrane potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Influence of small molecules and ions on electrostatic potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The principles behind the applications of fluorescent probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Slow responding potential-sensitive probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. The pH-sensitive probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. The probes with response based on electrochromism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrochromic probes in action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Styryl dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Hydroxychromone dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. The limitations in application of electrochromic dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. MD simulations of location and dynamics of fluorescence probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abbreviations: MD, molecular dynamics; PME, Particle-Mesh Evald; RF, Reaction Field; PC, phosphatidylcholine; DPPC, dipalmitoylphosphatidylcholine; SDPC, stearoyldocosahexaenoylglycerophosphocholine; POPC, palmitoyloleoylphosphatidylcholine; POPG, palmitoyloleoylphosphatidylglycerol; POPE, palmitoyloleoylphosphatidylethanolamine; POPS, palmitoyloleoylphosphatidylserine; DMPC, dimyristoylphosphatidylcholine; DMTAP, dimyristoyltrimethylammonium propane; FRET, Förster resonance energy transfer; ESIPT, excited-state intramolecular proton transfer; 3HC, 3-hydroxychromone; PTD, protein transduction domain; CPP, cell-penetrating peptide. ∗ Corresponding author. E-mail addresses: [email protected] (A.P. Demchenko), [email protected] (S.O. Yesylevskyy). 0009-3084/$ – see front matter © 2009 Published by Elsevier Ireland Ltd. doi:10.1016/j.chemphyslip.2009.05.002

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Membrane electrostatics and cell functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Binding and translocation of ions and small molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Interactions between membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Asymmetry of lipids and their translocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Translocation of peptides and proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Ionic channel activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions and prospects for future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction At the beginning of 21st century biological membranes still contain a lot of mysteries. Discussions continue around the fluid–mosaic biomembrane model with the emphasis that real membranes are more mosaic than fluid (Vereb et al., 2003; Engelman, 2005). The role of fluid and rigid domains (rafts) is not fully understood; neither is the functional role of lipid asymmetry which results in asymmetry in surface charges. It is still not clear how membrane proteins fold. Do they fold first and then incorporate themselves into the membrane or are they able to fold in the biomembrane milieu? (Stanley and Fleming, 2008). The membrane interior is hydrophobic in nature and poorly permeable to ions. Why then do membranes allow the translocation of lipophilic anions with a rate that is one million times faster than that of cations? (Brockman, 1994) In contrast, only cationic but not anionic peptides are able to penetrate cell membranes even in the absence of specific receptors (Patel et al., 2007). This is a new mystery. Electrostatic interactions must play a crucial role in these and many other biomembrane processes. Membrane stability, flexibility and fusion, which govern the processes of membrane transport, energy generation and its utilization, depend strongly on these interactions. Membrane electrostatics can be studied on several levels of detail. The first level is the macroscopic one (McLaughlin, 1989; Cevc, 1990). In this approach the membrane is considered to be a featureless continuous medium, which segregates two different solutions. Characteristic for the macroscopic approach is the operation with such macroscopic variables as polarity and viscosity. Regarding electrostatics, such models are useful in electrophysiology and general physical theory of membrane thermodynamics. However, they do not provide a clue to the understanding of the phenomena observed on molecular level. Another macroscopic model of limited utility is that of a capacitor with conducting plates approximating biomembrane surfaces separated by a hydrophobic dielectric approximating the membrane interior. The second level is the level in which the membrane is considered in atomic detail. Each atom is the source of an electrostatic field and it “feels” the electrostatic field of all other atoms. At this level of description it is hard to operate based on the information available about the membrane as an integral assembly possessing integrated functional properties. This approach is used in molecular dynamics simulations to compute the forces between all atoms in the system and to study their motion at times up to hundreds of nanoseconds. However, this approach usually gives little insight into the fundamental physical processes in the membranes, since the numerous atomic details mask the general picture. Finally, there is a mesoscopic level of detail (Grochowski and Trylska, 2008), which is probably the most useful approach for understanding membrane phenomena. In this approach the membrane is viewed as an integral but non-homogeneous system and the electrostatic potential is integrated over elementary interactions, but the spatial resolution is not lost. The more detailed (“lower”) part of the mesoscopic level of detail is often called the nanoscopic level because it allows the analysis of elementary interactions on the nanometer length scale (Hell, 2003; Schonle and

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Hell, 2007). Introduction of the nanoscopic level allows the spatial scale of the studied phenomena to be reduced and places them in the realm of nano-science and nano-technology. On the nanoscopic level the contributions to the electrostatics of different structural components of the membrane can be studied with atomic resolution while considering the membrane as an integral structure. On this level of description one may achieve an understanding of many functional properties, such as the mechanism of operation of voltage-gated ionic channels or the mechanism of penetration of cationic peptides through phospholipid bilayers. The nanoscopic level can be reached either “from above” by increasing the sensitivity and resolution of experimental techniques or “from below” by analyzing and interpreting the atomic-level data of molecular dynamics and quantum–chemical simulations. Such formal classification of the levels of detail is a useful abstraction, which helps in understanding the roles of different research methods. A comprehensive description of electrostatic biomembrane properties is highly needed, but it is not easily achievable due to technical limitations associated with every method of study and problems arising in the comparison of results obtained by different methods. Traditional experimental methods of studying biomembrane electrostatics do not allow the nanoscopic level of description to be reached. Microelectrode techniques can only detect the transmembrane potential between two media separated by a membrane. They have an insufficiently low spatial resolution and do not allow the profile of the electrostatic gradient across the membrane to be obtained. The surface potential, as determined by the ␨-potential technique, also lacks high structural resolution, and, basically, there is no possibility to improve it. Therefore, the focus of this review will be on the results and prospects of application of the methods that allow membrane electrostatics to be studied at the nanoscopic level. These are the in silico-based method of molecular dynamics (MD) simulations and the experimental technique of the application of voltage-sensitive fluorescent dyes. Potentially, these methods show a high degree of complementarity. Fluorescent probes allow a very high resolution in interaction energy to be achieved, but their structural resolution is relatively poor. In contrast, MD simulations allow atomic spatial resolution to be achieved, but the energies calculated depend strongly on the simulation setup and the applied parameters. These problems do not exist in spectroscopic studies, which use the concept of a collective reactive field (Liptay, 1969; Suppan and Ghoneim, 1997), so that real intermolecular electrostatic interactions are sensed as macroscopic electric fields acting on probe molecules at the site of their location. The latter methods can in principle provide data on the electrostatic potential in the microenvironment of the probe. However, in order to obtain detailed data, the probes should be localized in the membrane at a particular site and in a specified orientation. MD simulations may help to determine this location and provide the reference that is needed for the quantitative analysis of probe effects. Using these methods as the research tools we will discuss different possibilities of describing the effects of electric fields in membranes and characterize three important com-

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ponents of electrostatic potentials in membranes—the dipole ( d ), transmembrane ( t ) and surface ( s ) potentials. 2. Molecular dynamics simulations of biomembrane electrostatics Molecular dynamics (MD) simulations provide an unique opportunity to study the membrane at the all-atom level of details, which is not accessible and will probably never be accessible for experimental techniques (Berendsen, 1996; van Gunsteren et al., 2006). MD is based on classical mechanics in which the interactions between the atoms are described using semi-empirical force fields. Such force fields use simple chemical concepts to describe the potential energy of the system in terms of the Cartesian coordinates of the atoms. Newton’s equations of motion are then solved iteratively to simulate the time evolution of the system. Applying the concepts from statistical mechanics, the resulting trajectory can be used to evaluate various time-dependent structural, dynamic, and thermodynamic properties of the system. Biophysical applications of MD simulations have started several decades ago from the studies of internal dynamics of small proteins and developed in the direction of more complicated protein structures and longer times. In contrast, the field of the membrane MD simulations is rather young mainly because of the large system sizes needed for consistent modeling (Tieleman et al., 1997). Once the advances of computer hardware allowed the simulations of the membrane systems, the number of computational studies of various aspects of the membrane functioning started growing extremely fast. MD simulations provide the trajectories of all particles in the system over time. This information can be transformed to electrostatic potentials easily by first computing the time-averaged charge density in the simulation box and then solving Poisson equation, which relates the charge density in the system with the electrostatic potential. In the planar bilayer the electrostatic potential across the bilayer  (z) as a function of bilayer normal z is the most useful. In this case the charge density (z) is computed in a series of narrow slabs perpendicular to bilayer normal by averaging the charges of all atoms, which fall into a given slab, over simulated trajectory. The electrostatic potential is then obtained by integrating this charge density twice (Pandit et al., 2003) −1 (z) = ε0

z z (z  ) dz  dz  ,

(1)

z0 z0

where ε0 is the electrostatic permittivity of vacuum, z0 is the position of the membrane boundary at which the potential is assumed to be zero. 2.1. Methodological issues in MD simulations of membranes Modern MD techniques still have some limitations. Below we briefly discuss several issues, which are important for the membrane simulations. The reliability of the results from MD simulations depends primarily on two factors, (a) the accuracy of the function describing inter-atomic interactions (the force field) and (b) the time scale over which the simulations of atomic motions can be performed (Berendsen, 1996; Karplus, 2002; Mackerell, 2004). Conventional MD force fields contain several energy terms, which determine the interactions between the atoms of certain pre-defined types. These types are the abstractions based on the chemical identity of real atoms (element, valence, functional group, etc.). The number of atom types varies for different force fields but remains of the order of 100. Any force field contains the so-called bonded energy terms (describing the covalent bonds stretching,

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the angle bending, dihedral angle torsions and possibly various cross-terms) and non-bonded terms (Coulomb and van der Waals interactions). The bonded terms include up to four atoms, while the non-bonded terms describe only additive pair interactions. The algebraic form of each energy term is defined in advance and contains several empirical constants, which depend on the type of interacting atoms. All these constants should be determined and optimized in the course of force field parameterization. For example, the parameterization of the van der Waals interactions requires the determination of two parameters for each atom type. Such parameterization usually employs diverse experimental data and the results of quantum–chemical calculations. Each atom in a particular molecule is assigned a partial point charge, which can be very different (up to a different sign) in different force fields. The procedure of determining partial charges depends strongly on the parameterization rules of particular force field and usually includes unphysical assumptions. For example, it is usually required that the total charge of the functional group (such as phosphate in a lipid or side chain in amino acid) should be an integer, so the charges of atoms are modified accordingly. This limitation is caused by purely “technical” reasons (the so-called “group cut-off” algorithms in MD can only work effectively with the groups of integer charge). Thus, it is important to remember that the charges of atoms in MD are also to a large extent empirically adjusted. It is necessary to note that formally there is no need to introduce a dielectric constant in MD simulations. All the charges interact in vacuum (ε = 1) and the dielectric screening is modeled by explicit motion of dipoles and charges. However, in view of cut-off of Coulomb interactions between distant atoms, the effective dielectric constant can be introduced for approximate treatment of the long-range electrostatics (see below). Conventional force fields include only pair-additive Coulomb potentials and point charges, which prevent them from describing realistic collective electrostatic effects, such as the electronic polarization, the charge transfer or the electronic excitations. The absence of the electronic polarization is often considered as a major limitation of the classical force fields. Many different ways of adding this missed component to the force field have been proposed (Halgren and Damm, 2001; Warshel et al., 2007), however none of them is widely used in large-scale simulations now. The main reasons are the dramatic increase of the computational intensity of simulation and additional complications with the parameterization of “polarizable” force fields. The latter problem can be solved by switching to purely quantum or mixed quantum–classical dynamic simulation (SinghKollman, 1986; Gao, 1995). However, this step will require another revolutionary advance in computational power. Modern force fields are quite accurate in reproducing the structural and thermodynamic properties of proteins, nucleic acids, lipids and their complexes. However, the membrane systems present a considerable challenge for the force field development. Interactions between the molecules of very different nature, such as lipids and proteins, are not easily parameterized, which leads to some disagreement between force fields suggested by different authors. Simulations of the non-standard membrane components, such as modified lipids or embedded synthetic molecular probes, remain a complicated problem because of laborious parameterization step for these compounds. Despite this fact, several force fields, such as GROMOS (van Gunsteren et al., 1998), CHARMM (MacKerell et al., 1998) and AMBER (Case et al., 1999; Rosso and Gould, 2008) are now routinely used for the simulations of membrane systems. The choice of the force field is often based on personal preferences and background of the researcher rather than on objective advantages of the particular force field. Limited support in the chosen MD software is also a major factor, which influences the usage of a particular force field. All this makes the comparison of force fields

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rather subjective matter. Several comprehensive comparisons of major MD force fields are available now (Mackerell, 2004; Guvench and MacKerell, 2008; Rosso and Gould, 2008). None of the force fields is able to reproduce all structural properties of the planar lipid bilayers with the same accuracy in comparison to experimental results (Benz et al., 2005). Better description of one property usually leads to larger error of the other. Despite this fact, modern force fields provide an adequate description of the properties of membrane systems and allow obtaining at least semi-quantitative data about membrane electrostatics. The time scales of hundreds of nanoseconds and even microseconds are currently accessible for MD simulations, which is usually enough to equilibrate the hydrated patch of lipid bilayer and to study its average properties and their fluctuations. However, many membrane phenomena, such as membrane fusion, pore formation or embedding of various molecules into the membranes are still far beyond the time scale accessible by atomistic MD simulations. The so-called coarse-grained MD is based on simplified united-atom force fields (Shelley et al., 2001; Izvekov and Voth, 2006; Marrink et al., 2007). It is actively used now to study slow large-scale phenomena in membranes. In these force fields, several atoms of the same functional group are combined into single bead called “united atom”. In this approach the head group of the choline lipid can be represented by just two particles (one for choline and the other for phosphate). Such coarse-grained representation reduces the computation time dramatically and even for very large systems allows reaching the time scales of tens of microseconds. This is sufficient to simulate such phenomena as vesicle fusion (Marrink and Mark, 2003a), spontaneous assembly of different lipid phases (Marrink et al., 2001; Shelley et al., 2001; Marrink and Mark, 2003b), etc. However, the coarse-graining has a significant drawback. The charge distribution inside the coarse-grained bead is completely neglected and the polar but uncharged groups become indistinguishable from non-polar ones in terms of electrostatics. In this work we will focus on traditional atomistic MD simulations, which provide more precise information about the membrane electrostatics. The size of the bilayer patch in the simulation unit cell determines the spatial scale of the effects studied in MD simulations. Typically, the patches with 64–256 lipids in each monolayer are used. All modern simulations of the membranes use the model systems with periodic boundary, which means that the patch of the bilayer in the simulated unit cell is in fact replicated infinitely in three dimensions. This produces the multilamellar system of parallel planar bilayers separated by relatively small slabs of water (Fig. 1). Such topology is obviously very different from that existing in experimental conditions, where single bilayers of artificial membranes, membrane vesicles (liposomes) or living cells are studied. The artifacts induced by artificial periodicity in MD simulations in general and in membrane simulations in particular are discussed extensively in the literature (Hünenbergera and McCammon, 1999; Monticelli and Colombo, 2004; Villarreal and Montich, 2005; van Gunsteren et al., 2006). In the context of this study the most important question is the treatment of the long-range electrostatic forces, which extend over the periodic boundaries and allow the periodic replicas of the unit cell to influence each other over large distance (Koehl, 2006; Karttunen et al., 2008). The electrostatics is the long-range interaction. Thus, in principle, the Coulomb interactions between all atoms in the system and all its periodic images should be computed. Unfortunately this is not feasible because of enormous amount of computer time required. Therefore the electrostatic interactions in all major MD programs are subdivided into short-range and long-range components. The short-range interactions include all atoms, which fall inside a certain cut-off distance from the given atom (typically 10–15 Å). The Coulomb interactions within this cut-off are computed explicitly.

Fig. 1. Periodicity in MD simulation of POPC bilayer. The black cube encloses the unit cell, which contains 200 lipids (100 in each monolayer). The unit cell is replicated infinitely in all three dimensions producing the multilamellar stack of infinite bilayers. The lipid heads are black and the tails are gray. Water molecules are not shown for clarity.

In order to reduce the computation time, the interactions with more distant atoms (including the periodic images) are treated approximately. The simplest possible approximation can be disregarding long-range electrostatic interactions beyond the cut-off distance. It was shown, however, that in the case of lipid bilayers this approach is not acceptable because of severe artifacts (Patra et al., 2003; Gurtovenko et al., 2004). Thus for computing the long-range electrostatics, in the majority of simulations either the Particle-Mesh Evald (PME) summation (Zhao et al., 2007) or the Reaction Field (RF) methods are used (Tironi et al., 1995). The latter is mostly used in combination with the GROMOS (van Gunsteren et al., 1998; Oostenbrink et al., 2004, 2005) force fields, which are usually parameterized with RF electrostatics in mind. The PME computes the formally infinite converging sum over all Coulomb interactions between the charges in the unit cell and their periodic images. In the RF technique the long-range Coulombic interactions are not computed exactly, but approximated by the additional correction term to electrostatic energy. The correction is derived from the mean-field-like theory based on the distance-dependent effective dielectric constant. Both techniques have specific pros and cons. The membrane regions with different effective dielectric constants contribute to the electrostatic potential in a “fair” way according to their distribution of charges in PME. However, PME allows very extended long-range interactions between the periodic images, which can lead to enhanced periodicity artifacts (Hünenbergera and McCammon, 1999). It is generally believed now that such artifacts, which were found in some early works (Hünenbergera and McCammon, 1999), are caused by incomplete sampling of the explicit solvent rather than by application of PME. In contrast, the RF method does not enforce any artificial periodicity by treating all surrounding periodic images as a continuous homogeneous medium. This also means, however, that for long-range electrostatics in RF the real charge distributions and different dielectric properties of the system components are neglected.

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Fig. 2. The scheme of the lipid bilayer and the membrane potential profile, which is the energy profile experienced by a point positive charge. Three components of the membrane potential are shown. The orange region represents the hydrophobic core of the bilayer. The scheme is drawn based on the data from several works (Pandit et al., 2003; Xu and Loew, 2003; Sachs et al., 2004a). Various components of the membrane potential are shown not to scale to visualize rather small contribution of the surface potential.

In the case of unperturbed planar bilayer both these techniques give comparable results (provided that the force field is compatible with both of them). However, if the transmembrane proteins or embedded charged molecules are studied, the situation becomes more complicated. Particularly, it was shown that PME overestimates significantly the energy barrier of translocation of the ion through the gramicidin channel due to unphysical interaction between the periodic images of the system (Allen et al., 2006b). In contrast, RF is free from such artifacts, but requires an empirical parameter, which is the effective dielectric constant, to be specified. The choice of this parameter is a guesswork and its influence on the membrane properties is hard to estimate. MD simulations provide computational means to obtain the absolute values of membrane potential and its components. Since these data are accessed experimentally only on a very limited scale, the results of MD simulations are considered to be of extreme value. Meanwhile, these data lack consistency and their comparisons with experimental ones show substantial deviations. 2.2. Resolution of components of biomembrane electrostatic potential (dipole, surface and transmembrane potentials) It is necessary to note that there is a terminological controversy in many MD studies. The terms “membrane potential”, “transmembrane potential” and “dipole potential” are often used synonymously in a particular context. This is a direct consequence of the fact, that only one total electrostatic potential is computed in MD, which can be subdivided for analysis. Confusion may arise also in the analysis of experimental data, since the new definitions appear based on the physical principle behind a particular method. Such are “boundary potential” analyzed in ion conductance experiments and -potential obtained in free electrophoresis. In our analysis we will follow the definitions of the components of electrostatic potential in membranes that are accepted by the majority of researchers (see, for example, Gross et al., 1994; Clarke, 1997). Three major components of membrane potential are distinguished: the dipole potential,  d , the surface potential,  s , and the transmembrane potential,  t . This division is rather arbitrary. From the physical point of view all of them are caused by the same Coulombic interactions of charges, and due to their long range, a

significant overlap in these contributions is expected. However the subsets of atoms, which create these potentials, and their locations are different, and MD simulations help to resolve them. Fig. 2 shows the schematic profile of the electrostatic potential across typical lipid bilayer and its decomposition into three major components. 2.2.1. Dipole potential The dipole potential,  d , is the potential formed between the highly hydrated lipid heads at the membrane surface and the lowpolar interior of the bilayer.  d arises from the aligned dipoles of phospholipid molecules, with the participation of hydration water molecules on the level of their carbonyl and phosphate groups. (Fig. 2) (Gawrisch et al., 1992; Tu et al., 1998; Saiz and Klein, 2002). It is not only the strongest but also the most obscure component of biomembrane electrostatics because of insufficient understanding of its origin and of the lack of experimental techniques for its direct measurements. Its characteristic feature is a rather weak dependence on the ionic composition of the surrounding medium. Therefore it was suggested that its origin is due to orientation of dipoles in the bilayer structure. The dipole potentials formed by two monolayers are of opposite sign, and their combination creates a strong virtual positive charge in the bilayer center. Due to this potential, a strong energy barrier exists for the penetration of ions, so that the penetration rate for hydrophobic cations is 105 –106 times lower than for the anions (Clarke, 1997). While the dipole potential was estimated in a number of molecular dynamics studies, only few of them were focused on this subject directly. Experiments and MD simulations show that the contributions of the dipoles of the lipid heads and the oriented water molecules are the major components of the dipole potential. These components are also most sensitive to the composition and environment of the lipid bilayer. The magnitude of the dipole potential caused by lipid carbonyls is controversial (Zheng and Vanderkooi, 1992) and MD is probably the only method that could resolve it. Experimental studies of the ether-linked dihexadecyl-PC bilayers, which lack the carbonyl groups, show that their dipole potential is by ∼120 mV smaller than those for the ester-linked DPPC bilayers (Gawrisch et al., 1992). These observations as well as the experiments with the

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compounds, which bind to the carbonyls (Luzardo et al., 2000), show that the lipid carbonyl groups contribute to the dipole potential, but this contribution is not the major one. The spectroscopic studies suggest that the water molecules, which penetrate deeply into the bilayer, can hydrate the carbonyls and compensate the dipole of the carbonyl groups (Gawrisch et al., 2007). Recent combined spectroscopic and MD studies also suggest that the extent of this compensation effect is different for the two carbonyl groups (sn1 and sn2 ) of phospholipid molecules due to their different orientations with respect to the membrane normal (Gawrisch et al., 1992) and different propensity of forming hydrogen bonds with water (Volkov et al., 2006). Therefore polarized water molecules hydrating these carbonyls produce different effect on  d . Recent spectroscopic studies also demonstrate uneven contribution of the carbonyls of different chains to the dipole potential (Starke-Peterkovic and Clarke, 2009). However, these findings are in contrast to some early MD studies, which suggested that the carbonyl groups are not hydrated substantially (Tu et al., 1996). The reason for such discrepancy is, most probably, in insufficient sampling and underdeveloped methodological issues in those early MD simulations. Since in the bilayer the negatively charged phosphate group in phosphatidylcholine is located closer to the membrane interior than the positively charged choline, it can be expected that the projections of P− → N+ dipoles on the bilayer normal will have contribution to  d projecting negative potential to the membrane interior. Meanwhile, both experiments and simulations show that this effect is small, and it cannot overcompensate a more positive contribution from oriented water dipoles. Extensive analysis of the orientations of SDPC and POPC headgroups in MD simulations (Saiz and Klein, 2002; Sachs et al., 2004b) showed that both ordered and disordered lipid headgroup dipoles are present in the fluid lamellar phase of model membrane. Despite this fact, the water molecules are always ordered at the lipid–water interface (Fig. 3), creating a positive potential in the bilayer interior and excessively counteracting the negative potential created by the lipid heads. This gives rise to a considerable positive contribution to  d of ∼1200–1400 mV. These data about the contributions of water molecules and lipid head groups are especially useful because it is presently not possible to obtain them experimentally in such level of detail. It was determined that the dipole potential increases significantly (from ∼600 to ∼1000 mV) in mixed bilayers formed of neutral and charged lipids with the increase of mole fraction of the charged lipids (Gurtovenko et al., 2004). The authors of this paper claim that this increase is caused mainly by the reorientation of the

Fig. 3. The scheme illustrating the origin of dipole potential. Green arrows indicate relative magnitudes and orientations of the dipoles. The dipoles are fluctuating continuously, thus only the snapshot is shown. Time-averaged total dipole is shown below. The data from (Gawrisch et al., 1992; Tu et al., 1998; Saiz and Klein, 2002) are used to compose the scheme. Virtual positive charge in the center of the membrane produced by the dipole potential is shown.

neutral zwitterionic head groups and reordering of water molecules around the charged head groups. However, the total increase of the charge density on the membrane may also contribute to this effect. This result suggests that in the case of lipid asymmetry with a predominance of anionic lipids on one of the monolayers (and this is the real case with cell membranes) there must appear a static electric field gradient across the membrane. It is necessary to note that the discrepancy in the absolute values of the dipole potential (ranging from 600–1000 to 1200–1400 mV) is typical for MD studies. This is caused by the diversity of the studied lipids and also by the differences in simulation setups. The values of  d for common mono-unsaturated PC lipids are usually below 800 mV while the values higher than 1000 mV are observed for unsaturated lipids and are considered exceptional. This issue is discussed below. It is interesting that cholesterol is a small dipole, and its influence on  d has to be attributed to its influence on the structure and hydration of major constituents of membrane. Particularly, it decreases the amount of inter-lipid links (Pasenkiewicz-Gierula et al., 2000). This effect contributes to the total increase of the electrostatic potential observed in the presence of cholesterol (Tu et al., 1998). Another important effect of cholesterol is its dramatic influence on the orientation of head groups. The influence of this effect on the dipole potential comes from the simulations of the mixed DPPC–cholesterol bilayers (Tu et al., 1998). In this study the contribution of the headgroups and water molecules to the dipole potential were estimated independently, which is trivial in MD simulations but not possible in experiment. It was shown that the intercalation of the cholesterol molecules forces the head groups to lie flatter in the plane of membrane in order to fill the extra space between the lipids. This leads to decreased compensation by the lipid headgroups of the oriented water contribution to the membrane dipole potential and explains the experimentally observed increase of dipole potential by cholesterol (McIntosh et al., 1989). In this study it was shown that the addition of cholesterol can increase the dipole potential from ∼500 to ∼800 mV. This result agrees well with a recent experimental study of DMPC–cholesterol bilayers with di-8-ANEPPS fluorescent probe (Starke-Peterkovic et al., 2006), in which the depletion of cholesterol from cell membranes led to substantial decrease of  d . However, the increase of dipole potential in the presence of cholesterol has been questioned in some recent MD studies of the mixed DPPC–cholesterol bilayers (Hofsass et al., 2003). It was claimed that  d fluctuates rather irregularly from 600 to 700 mV in the range of cholesterol concentrations from 0 to 40%, which is within statistical error. The reduced total number of DPPC dipoles with increasing cholesterol concentration is compensated by a smaller area per lipid and by an increased tilt of the head group dipoles. It should be noted that the absolute values of the dipole potential that are commonly obtained in MD simulations (600–1000 mV) are much higher than the experimentally obtained values based on the rates of penetration of hydrophobic ions (200–350 mV). The sources of this discrepancy may lie both in experiment and in MD simulations. In experiments with hydrophobic ions the dipole potential is probably underestimated (Schamberger and Clarke, 2002). The conductance ratio of the negative (tetraphenylborate) and positive (tetraphenylarsonium or tetraphenylphosphonium) hydrophobic ions is measured in these experiments and the dipole potential is computed based on this ratio using simple thermodynamic considerations (Schamberger and Clarke, 2002). However, in order to compute the dipole potential one needs to know free energies of hydration of the negative and positive hydrophobic ions. In early works it was assumed that these hydration energies are equal, which led to the values of dipole potential of 110–230 mV depending on the bilayer (Pickar and Benz, 1978; Gawrisch et al.,

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1992). However later quantum–chemical calculations showed that this assumption is not justified (Schamberger and Clarke, 2002). Accounting for different hydration free energies of the hydrophobic ions allows refining the results and obtaining the dipole potentials of 230–350 mV (Schamberger and Clarke, 2002). It is still not known, however, if the quantum–chemical calculations, which rely on the choice of the level of theory and other numerous assumptions, give sufficiently accurate estimates of the hydration free energies of hydrophobic ions in real systems. It is also not known whether the hydrophobic ions dehydrate completely or partially during the translocation. Another possibility is that experimental techniques are not selective enough to filter out all electrostatic contributions except true dipole potential. These factors may lead to underestimation of the dipole potential in such experiments. It is not excluded, however, that the source of this discrepancy lies in the MD methodology. A small periodically replicated patch of the membrane, simulated in MD, is unlikely to possess absolutely the same properties as the membrane in experiment. Notably, there is also a large (up to 500 mV) discrepancy between the absolute values of the dipole potentials in different MD studies. The absolute value of the dipole potential depends significantly on the treatment of the long-range electrostatics in the MD simulations. It was shown that  d of the same pure DPPC bilayer is 620 ± 20 mV in the case of PME electrostatics, 720 ± 100 mV in the case of simple cut-off electrostatics and 830 ± 50 mV in the case of RF electrostatics (Anezo et al., 2003). This example shows convincingly that the absolute values of the electrostatic potentials obtained in MD simulations can differ by up to 200 mV depending on the simulation setup. The partial charges of individual atoms and the dipole moments of the lipid head groups vary substantially in different force fields. Different models of water molecules are used. This can explain an observed difference, at least partially. The electronic polarization effects are neglected completely in the above-cited MD studies, due to force field limitations, and this can also influence the results. It was shown recently that an introduction into MD analysis of the many-body polarization effects based on the model of classical Drude oscillators reduces  d substantially (Harder et al., 2009). In this work the  d of the lipid monolayer at the water–air interface was reduced from 800 to 350 mV after the introduction of the many-body polarizability. This fact suggests that  d can be overestimated significantly in conventional non-polarizable force fields. Despite these discrepancies in absolute values of the dipole potentials, the MD simulations and experiments with penetration of hydrophobic ions give consistent qualitative results. These results suggest that the dipole potential is usually several times larger than the transmembrane potential detected in living cells by the electrode technique. Therefore it should be considered as a major component of the total membrane potential. This potential is sensitive to the composition of the bilayer and the phase order of its lipids. This allows using  d as a measure of bilayer structure and its functional state. In this context the accurate reference values of  d could be valuable tools in experimental studies. Important is that both MD simulations and ion penetration experiment allow connecting the results of fluorescence probe experiments to an absolute scale. 2.2.2. Surface potential The membrane surface potential,  s , is created by the charges located at the lipid–water interface. This includes the uncompensated charges of the lipid head groups, adsorbed ions and the counter ions, which reside closely in the vicinity of the headgroups on both sides of the membrane. To characterize this part of membrane electrostatics,  s represents the electrostatic potential difference between the bulk aqueous phase, which is well

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defined, and the membrane surface, the assignment of which is more ambiguous. The surface potential depends on the amount and type of the charged lipids in the bilayer and the concentration of protons (measured in pH units) and of ions (often presented in terms of ionic strength). Since the biomembranes commonly bear a net negative charge (due to the presence of negatively charged lipid head groups and acidic groups on membrane-bound proteins), this leads to a higher concentration of adjacent to the surface protons and other cations (McLaughlin, 1989). The simplest continuous macroscopic description of the surface potential is given by the Gouy-Chapman-Stern theory (McLaughlin, 1989), which assumes that the surface charge is uniformly smeared over a perfect impenetrable planar surface. This theory gives the relationship between  s , the surface charge density and the ionic concentration in the aqueous phase (McLaughlin et al., 1971):



1 = 272

 i



Ci exp

−zi F RT



s

− 1,

(2)

where  is the surface charge density in unit charges per Angstrom squared, Ci is the concentration of the ith ionic species in the bulk solution and zi is the valence. R and T are the gas constant and the absolute temperature, respectively. The so-called -potential that is used in the analysis of results of electrokinetic experiments, such as electrophoresis of membrane particles and cells, is usually considered as a component of  s . -Potential is not the electrostatic potential at the interface of the membrane but a potential at some shear surface, which is the boundary that separates the mobile fluid and the immobilized surface layer that moves together with the particle or cell. The exact position of this boundary cannot be determined either by experiments or by computational means, and therefore, for obtaining  s from these data, additional assumptions need to be introduced (Sprycha and Matijevic, 1989; Ermakov, 1990). There are no experimental means for evaluating the contribution produced by -potential to electrostatic potential within the membrane. The surface potential plays an especially important role in the bilayers that contain charged lipids. The uncompensated charge of the lipid head groups alters the distribution of the counter ions significantly and changes the overall shape of the electrostatic potential across the membrane (Fig. 4). In comparative MD studies of negatively charged POPG and neutral POPC bilayers it was

Fig. 4. Schematic distribution of ions at the surface of lipid membrane (not to scale). The calcium ions bind strongly to phosphates at well-defined positions. Monovalent cations are somewhat looser distributed around phosphates. Anions form a loose atmosphere above the membrane. The dipoles of the lipid head groups and the total dipole are shown as green arrows. Virtual positive charge in the center of the membrane produced by the dipole potential is also shown.

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shown that the charge of the head groups alters the electrostatic potential in the inner side of the lipid–water interface region. In the case of POPG the potential barrier created by the adsorbed Na+ ions is much lower, which means that the positively charged ions can migrate deeper into the interfacial region (Zhao et al., 2007). This effect is believed to be caused by concerted change of the surface potential and the part of dipole potential created by ester carbonyls and oriented water molecules (Zhao et al., 2007). It was shown that the difference of the surface potentials between two monolayers could create significant driving force for the permeation of charged molecules even in the absence of ions in solutions. This effect is observed in asymmetric bilayers, which have different lipid compositions of the leaflets. The potentials of about 100 mV were observed in asymmetrically composed POPC-POPE (Gurtovenko and Vattulainen, 2007b) and POPC-POPS (Gurtovenko and Vattulainen, 2008c) bilayers. This potential contributes to  t , but its nature is the same as for the surface potential,  s . The wellknown fact that in normal cells the anionic lipids are commonly found in the intracellular leaflet of the cell membrane (Cerbon and Calderon, 1991) suggests that this mechanism may play an important role in the transmembrane transport in living cells. 2.2.3. Transmembrane potential The third component of membrane potential is the transmembrane potential,  t , which is often confused with the membrane potential itself. This is because in excitable cells it is subjective to rapid change on a sub-millisecond time scale. This potential is in focus of cellular research, and it is commonly detected by electrophysiological techniques (Schiller et al., 2007). In plasma membranes its value is approximately −70 mV (negative inside). It is formed mainly by a gradient of K+ , Na+ and Cl− ions, which is the result of their active transport process. The changes of this potential (hyperpolarization and depolarization) play a central role in many physiological processes, such as nerve impulse propagation, muscle contraction and ionic channel gating. According to the classical definition of the transmembrane potential,  t , it is the voltage (the difference of electrostatic potentials) between two liquid phases separated by the membrane. Since this potential drops over the whole membrane thickness (about 4 nm), its electric field gradient is estimated to be of 2.5 × 107 V/m, which is very high but still by one order of magnitude smaller than that produced by  d (Clarke, 1997). This is because  d drops at much shorter distances across the bilayer. The macroscopic electrodes are usually used to measure  t as the difference of electrostatic potentials between the bulk solutions (or the cell interior and exterior). Thus,  t measured in electrophysiological experiments is created by the difference of concentrations of free ions in two solutions, which are segregated by the membrane. It is clear, however, that there is no sharp distinction between the surface  s and the transmembrane  t potentials. Because the atmosphere of the counter ions is continuous, the determinations of free and adsorbed ions are very uncertain and the asymmetry of counter ions can be the result of asymmetry of charged components intrinsic to the membrane. Though transmembrane potential is simple to understand and to measure, it appeared to be the most challenging one for consistent modeling in MD simulations. The brute-force way of introducing the  t is simply the application of external electric field perpendicularly to the bilayer. Although such an approach works very well in the majority of MD studies, it contradicts the main paradigm of MD simulations, which states that there should be no any other forces except the atom–atom interactions. Even if this “extreme puristic” approach is used, there are still two major problems in realistic modeling of  t . The first one is related to the system size. Small volumes of the solvent slabs used in simulations (see Fig. 1) lead to unnatural congestion of the ions and unrealistically strong

forces between them. The second problem is the periodic boundary conditions, which transform two slabs of water into a single medium (the water molecules, which cross the periodic boundary in the direction perpendicular to the membrane plane, appear near the opposite side of the membrane). Nevertheless there are MD studies, in which  t is modeled quite accurately using the trick of double-bilayer geometry (Sachs et al., 2004a; Gurtovenko, 2005). In these simulations the periodic unit cell contains two bilayers and three slabs of water. In such setup the central slab of water corresponds to one solution, while two outer slabs (which constitute the single medium due to periodic boundary conditions) correspond to the other solution. Recently another approach was introduced, which allows maintaining different ion concentrations on the sides of the membrane without double-bilayer setup (Delemotte et al., 2008). In this approach the vacuum slab is added to the simulation cell in the direction perpendicular to the membrane, which separates the solutions with different ionic concentrations. Such simulations allow the study of all three components of the membrane potential simultaneously and to differentiate their influence on the studied phenomenon. 2.3. Influence of small molecules and ions on electrostatic potentials The interactions of small molecules and ions with the lipid bilayers are studied actively due to their great practical importance. The majority of MD studies on this subject are focused on structural changes of the bilayer, lateral mobility of the lipids and their phase transitions. The changes of membrane electrostatics are rarely considered as primary effects of various small molecules. The work of Hogberg and Lyubartsev (Hogberg and Lyubartsev, 2007) is exceptional in this respect. The authors studied the influence of widely used local anesthetic lidocaine on electrostatic properties of a lipid bilayer. Two forms of this anesthetic, charged and neutral, are known. It was shown that both charged and uncharged lidocaine cause significant increase in  d in the interior of the membrane, which is accompanied by the changes of charge densities and orientations of the head groups. The increase of  d in the presence of lidocaine reaches 220 mV, which is quite sufficient to affect the functioning of the voltage-gated ion channels. It is hypothesized that such mechanism can constitute the molecular basis of lidocaine action. The influence of the ions on electrostatic properties of the bilayers appears to be quite complicated and depends strongly on the nature of both ions and the lipid head groups (Gurtovenko and Vattulainen, 2008b). The contribution of sodium ions, which can be strongly bound to the head groups of neutral lipids, is compensated almost completely by a changed polarization of the water and the reorientation of the lipid dipoles. As a result, the total electrostatic potential changes only slightly, while the individual contributions are strongly affected (Bockmann et al., 2003). The distribution of counter ions in the membrane head group region depends strongly on the chemical nature of the head groups. Particularly, the dipole potential of the DPPC lipids is larger than one of DPPS in the presence of the counter ions due to deeper penetration of the counter ions and more diffuse ion distribution in the latter case (Pandit and Berkowitz, 2002). Molecular dynamics simulations allow studying the details of location and interactions of adsorbed ions at the bilayer surface. Pandit et al. (2003) compares the properties of the DPPC bilayer in the absence and in the presence of NaCl in solution. It was established that the Na+ ions are coordinated effectively by the phosphate groups of the lipid heads and carbonyl groups of their backbones. The hydration shell is rearranged substantially in the resulting lipid aggregates, which leads to the changes of dynamics and orientation of the lipid heads. It was established that the

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adsorbed Na+ ions locate just above the membrane surface creating the local positive potential of approximately 25 mV. In contrast, the Cl− ions do not bind to the bilayer significantly and tend to form the loose atmosphere in its surrounding. The nature of the positively charged ions plays an important role in their interaction with the bilayer. Different sizes of the Na+ and K+ ions and their different coordination (formation of hydration shells) with water molecules and binding to lipid head groups lead to significantly different surface potentials induced by these ions. The physiological difference in concentrations of these ions between the intra- and extra-cellular solutions can lead to significant electrostatic potential between the inner and outer leaflets of plasma cell membranes in living cells even if there is no total charge imbalance between the solutions (Gurtovenko and Vattulainen, 2008b). It was shown that divalent Ca2+ ions affect the bilayers to a much stronger extent than monovalent Na+ ions (Rainer and Bockmann, 2004; Pedersen et al., 2006). Calcium ions are found to bind tightly to the lipid phosphate groups. The distribution of these ions in the head group region is much narrower than that of sodium, which correlates with their much stronger binding. These ions enhance the packing of lipids and therefore they may be considered as an integral part of the membrane (Pedersen et al., 2006). Systematic comparison of MD simulation of DPPC bilayer with Li+ , Na+ , Ca2+ , Mg2+ , Sr2+ , Ba2+ , Ac 3+ , and K+ ions revealed that all of these ions change the electrostatic potential in the head group region of the membrane; however, the nature and the extent of these changes vary. Particularly, it was shown that potassium ions do not bind tightly to the head group oxygens, while all other studied ions do. It was shown that interaction of ions with the membrane depends strongly on the charge, radius, and the coordination properties of the ions (Cordomí et al., 2008). One of the most unexpected results of MD simulation in doublebilayer geometry is the fact, that the transmembrane potential,  t , can appear in the system with no global charge imbalance between the solutions on two sides of the membrane (Gurtovenko, 2005; Lee et al., 2008). The setup with the symmetric lipid bilayer, which separates two aqueous reservoirs with and without NaCl salt, allows demonstrating this effect. The charges in the system were perfectly balanced globally. However, one leaflet of the bilayer was exposed to the counter ions, while the other one was not. In this system, the Na+ ions bind tightly to the head groups of exposed leaflet, while the Cl− ions remain distributed in the solution (Pandit et al., 2003). As a result, the bulk solution that contains the salt becomes negatively charged, while the other solution remains neutral. This effect results in the transmembrane potential of about 85 mV between two water phases. The unnatural lipids with positively charged heads are used in many experiments. Their presence in the membrane affects the binding of ions significantly because they prevent the positively charged ions from tight binding to the heads of neutral lipids. Thus, the high mole fractions of the DMTAP lipids in mixed DMPC/DMTAP bilayers (50–75%) suppress the changes in bilayer structure and electrostatic properties induced by the monovalent salt (Gurtovenko et al., 2005a). Thus, the results of MD simulations allow us to conclude that both surface and dipole potentials are sensitive to the ion binding to the membranes, however the nature and the extent of this sensitivity is different. The surface potential is very sensitive to the ionic composition of the solutions and the nature of positively charged ions that bind tightly to the lipid head groups. In contrast, the dipole potential is not influenced directly by the ion binding. It changes slightly due to reorientation of the head groups and reordering of water molecules caused by the ion binding. Another major result of MD simulations is that the cations and anions are not equivalent in their binding to the membranes. The energy minima for cations are located close to or between the lipid head groups, while the

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anions do not penetrate between the head groups and form a loose atmosphere of counter ions above the membrane plane (Fig. 4). 3. The principles behind the applications of fluorescent probes Fluorescence probing methods focus on nanoscopic properties of matter. They use different organic dyes, luminescent metal complexes, labeled macromolecules and different kinds of nanoparticles to evaluate local properties of their environment and of their intermolecular interactions. Description of the probed system on the level of atomic details here is not available (exceptions are the formations of strong complexes and of covalent bonds by the probes, which is generally outside the probing methodology). The focus here is made on characterizing the quasi-continuous properties of environment, such as polarity (Sykora et al., 2005). The macroscopically applied electric fields (such as in a capacitor) here are not distinguishable from that formed by molecular charges located nearby. There are three basic principles behind the application of fluorescence probe method to study electrostatics in biomembranes. One is based on the effects of probe re-location in the membrane or sorption–desorption from the membrane under the influence of electric fields. Such re-location, often coupled with the aggregation, changes the probe fluorescence response that can be detected and analyzed. The other is the use of pH-sensitive dyes located close to membrane surface that allows potential-dependent evaluation of concentration of protons. The third is based on direct response of ground and excited electronic state energies to electric field, resulting in the shifts of absorption and emission spectra (electrochromism). These principles and their realization are discussed below. 3.1. Slow responding potential-sensitive probes These probes should be necessarily charged, and their response to the change of electric field is based on the change of their interaction with the membrane (Fig. 5A). Several classes of organic dyes are used as these probes: cationic (carbocyanines, rhodamines) or anionic (oxonols). The advantages provided by them in many experimental studies on cells are due to a relatively high optical response, typically a 1% fluorescence change per mV (Plásek and Sigler, 1996). Meanwhile, this response is slow on a millisecond time scale because it is based on the ground-state diffusional relocation of the dyes, including their association–dissociation with the membrane, and (in some cases) on formation of the dye aggregates. One type of these aggregates (J-aggregates of cyanine dyes) is interesting due to the long-wavelength shift of the emission band of the aggregates that is convenient for two-wavelength observation of depolarization changes in cells and their mitochondria in flow cytometry (Salvioli et al., 1997). Since location of these probes in membrane and the amplitude of changes in fluorescence signal cannot be determined with high precision, they cannot be very useful for obtaining the absolute values of membrane potential and of its components. Commonly, their response is calibrated in  values by induction of the K+ ion gradient in the presence of valinomycin in model lipid vesicles. However, to a large extent these probes respond to different factors unrelated to membrane potential, and this produces problems in calibration. Some of these probes diffuse easily into the cell and can be used for evaluating the membrane potential of mitochondria (Solaini et al., 2007), which in normal conditions is in the range of 150–180 mV, negative inside the membrane matrix, resulting from the proton gradient across the inner membrane. Although providing very sensitive detection of changes in membrane potential, these

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Fig. 5. The mechanisms of response of fluorescence probes to electrostatic effects in membranes. (A) Slow responding charged probes, which redistribute through the membrane and produce binding-release or concentration effects; (B) probes with the response to proton concentration based on protonation–deprotonation equilibrium; (C) electrochromic probes with fast and direct response to local electric field. Corresponding changes of the spectra are shown in right panels. The intracellular side of the membrane faces bottom.

probes are unable to characterize the potential profile across the membrane. The simultaneous use of two dyes, one being the movable transmembrane potential sensitive probe and the other an immobilized fluorescent donor, allows application of Förster resonance energy transfer (FRET) between these dyes with significant increase of sensitivity (Gonzalez and Tsien, 1997). When the low polar but negatively charged oxonol derivative is chosen as the FRET acceptor, it will distribute between two monolayers in a potential-dependent manner according to Nernst equation and respond to  t change by modulating FRET: the probe located at the proximal monolayer to the anchored donor will be within critical distance and display emission, and the probes at the opposite leaflet will be outside this distance and will not be excited via FRET (Steinberg et al., 2007). This allows use of this approach in cellular studies of genetically introduced fluorescent proteins serving as FRET donors and acceptors. Coupling one of them with voltage-gated ionic channel allows increasing both the sensitivity and time resolution (Tsutsui and Karasawa, 2008). Contributing to strong progress in the studies of living cells and their organelles, such systems are even less subjective for probing the depth-dependent gradients of electric field in membranes.

3.2. The pH-sensitive probes The surface potential, as well as the electrostatic potential in aqueous medium at a distance from the membrane, depends upon the local proton concentration, which can be evaluated by the pHsensitive probes (Fromherz, 1989; Kraayenhof et al., 1993). There are many dyes that are fluorescent both in protonated and protondissociated forms with a strong difference between these forms displayed by the positions of band maxima in both excitation and emission spectra, and therefore they can be used as such probes (Fig. 5). Their protonation–deprotonation equilibrium in the ground state is observed in excitation spectra. In the excited state, these dyes loose proton more easily and this equilibrium displayed in emission spectra can be observed at much lower pH values. For providing proper response, these dyes should be exposed to an aqueous medium. Their location with respect to the membrane can be established with the attachment of spacer groups of variable lengths and can be determined on a sub-nanometer scale with the use of specially designed fluorescence quenchers (Kachel et al., 1998). A strong correlation was found between surface potential produced by graded incorporation into the membrane vesicles of anionic lipid and the change of apparent pKa of these probes. In

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addition, with the aid of pH-sensitive 7-hydroxycoumarin probe the decrease of this dependence was seen with the distance from the membrane surface (Kraayenhof et al., 1993). Such correlations are expected from considerations based on a simple thermodynamic approach. The estimated  s and pKa values were in good harmony with the predictions based on the Gouy-Chapman-Stern theory. This approach has found application in the analysis of factors modulating  s or studying the processes that depend on it. For instance, the lipid with fluorescein-labeled head incorporated into bacterial membrane responds to binding of peptides by the change in protonation of xanthene ring of the label (Fitchen et al., 2003). Unfortunately, this approach cannot be applied for the study of electrostatic effects inside the membrane, where the proton activity and dielectric constant are unknown and very different from that in bulk water. 3.3. The probes with response based on electrochromism A different principle is behind the ‘fast-responding’ fluorescence probes. Their response is based on electrochromism (also known as Stark effect), which is the phenomenon of shifts of electronic (absorption and fluorescence) spectra under the influence of electric fields (Fig. 5C). These shifts occur due to differences in interaction with the field of the dye ␲-electronic systems in the ground and excited states, thus changing their relative energies (Bublitz and Boxer, 1997). The electrochromic dye senses the integrated electric field at the site of its location whenever this field is applied externally in a macroscopic device or internally, on a molecular level being produced by a nearby charge. This allows some averaging and integration of the electric field effects. The ‘mesoscopic’ approach (which considers the dye ␲-electronic system as a point dipole, the electric field as a vector F that averages all the fields influencing this system and its surrounding, with effective dielectric constant of the medium being εef can be used for the description of electrochromism in the simplest dipole approximation. The direction and magnitude of the shift, obs , is proportional (in this approximation) to the electric field vector F and the change of dipole  moment associated with the spectroscopic transition  : h vobs = −

1 εef

  · |F|cos( ), · | |

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4. Electrochromic probes in action The necessary condition for the design of electrochromic probes is their extended structure with the conjugated ␲-electronic system of the fluorophore and the substituents arranged in such a way that could provide efficient transfer of electronic charge along this structure. Regarding biomembrane applications, this structure should allow for its orthogonal incorporation into the bilayer for probing the electric field strength along the bilayer normal. If necessary, additional groups of atoms are introduced for proper location and fixation of the dye. 4.1. Styryl dyes Styryl dyes and particularly 4-dialkylaminostyrylpyridinium derivatives with electron-donor and electron-acceptor substituents at the opposite ends of their rod-shaped aromatic conjugated moieties are among the best known electrochromic dyes (Loew and Simpson, 1981; Gross et al., 1994; Clarke and Kane, 1997). They exhibit efficient excited-state re-location of electronic charge (Fig. 6). The change of dipole moment in such dyes on electronic excitation is one of the most dramatic. It is determined by a partial positive charge that is reversed in the excited state by electronic intramolecular charge transfer (ICT) from dialkylamino group to aromatic amine (Fig. 6). This electronic polarization along the extended ␲-electron system can be modulated in broad ranges by external electric field. Therefore these dyes can exhibit detectable spectral shifts, and these shifts can be modulated by the external electric fields operating on a molecular scale (Loew and Simpson, 1981). The best possibility to observe these shifts is by recording the excitation spectra, where the strong variations of intensities of fluorescence light can be recorded at the two slopes of these spectra. The ratio of these intensities provides ratiometric response, which does not depend on the probe concentration. Regarding the sensitivity to transmembrane potential, the magnitude of this twowavelength intensity ratio is still not very large, about 7–10% per 100 mV. These values are influenced by membrane composition and

(3)

 and F vectors. It follows that where is the angle between  in order to show maximal sensitivity to electrostatic potential, the  probe dye should exhibit substantial change of its dipole moment on electronic excitation, which implies a substantial redistribution of the electronic charge density. Furthermore, the dye should be located in low-polar environment (low εef ) and oriented parallel (cos = 1) or anti-parallel (cos = −1) to the electric field. It is also important that the correlation between the electric field strength and the spectroscopic effect within the applied approximation is linear, which allows, in principle, easy calibration of this effect in absolute values. Such electrochromic mechanism allows obtaining very fast response, which can be understood from its electronic nature that does not require re-location of molecules or of their groups. Besides, it is very general. It allows detecting the response to the changes in electric field in any medium. Therefore, there is no restriction for the location of electrochromic dyes in any depth and orientation in the membranes. Of course, their response to electric field is not free from involvement of interfering factors, and this issue will be discussed in the next section. Despite many problems, these probes offer the easiest possibility to correlate their response with the results of MD simulations, therefore we will concentrate on them in our discussions below.

Fig. 6. Translocation of electronic charge in the excited state of 4dialkylaminostyrylpyridinium dye di-ANEPPS on electronic excitation. The probe location is illustrated by showing two PC molecules constituting the outer monolayer to which these dyes are spontaneously inserted.

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fluidity (Clarke and Kane, 1997). The shifts in fluorescence spectra (Kao et al., 2001) are even smaller than in excitation. There are many possibilities for improving the properties of wavelength-shifting electrochromic probes, and some of them were realized in recent studies (Salama et al., 2005; Wuskell et al., 2006; Matiukas et al., 2007; Fromherz et al., 2008). In order to improve the sensitivity of electrochromic dyes to the transmembrane potential, much longer rigid analogues of styryl dyes (ANNINE probes) were developed, which, upon incorporation, span from the surface till almost the middle of the bilayer (Fromherz et al., 2008). This design improved the sensitivity to  t more than twice. However, as for their parent analogs, only the excitation spectra could be used. Some of these new developments allow increasing the probe solubility and shifting the wavelength of its emission to the near-IR for applications of two-photon spectroscopy and microscopy. This opens new prospects for biomembrane studies at cellular and tissue levels. Meanwhile, these probes do not allow overcoming several problems that seem to be very general: (1) The magnitude of wavelength-ratiometric response that is determined by the spectral shift in excitation spectra cannot be increased significantly. It is limited by the length of ␲-electronic system and its electronic charge-transfer ability that are limited by the dye structure. (2) A much smaller scale for a detection of spectral shifts is available on measurements of fluorescence emission spectra, which is more convenient for experiment. There were reports showing that unlike the excitation ratio, the emission ratio does not correlate with the dipole potential of vesicles made from different lipids (Vitha and Clarke, 2007). This ratio is subjective to important intervening factors operating in the excited state, such as segmental mobility, the change in hydrogen bonding or in the dielectric relaxations of dipoles in the probe environment. The dipoles surrounding the probe, interacting with its dipole, re-orient on time scale of emission (Liptay, 1969; Suppan and Ghoneim, 1997). In simple words, the fluorescence emission spectra of electrochromic dyes respond to polarity, segmental mobility and the presence of water producing the shifts of fluorescence spectra that cannot be distinguished from electrochromic shifts. (3) The asymmetric ground-state charge distribution on these probes does not allow locating them at will at any site of the biomembrane. Hopefully, their location site, in which the groundstate charge is hooked at the surface and the probe body extends into membrane interior, is probably optimal for detecting the changes of  d (Gross et al., 1994). The response to  t is by one order of magnitude smaller (Montana et al., 1989), probably because  d changes steeply within a few Angstroms and  t drops uniformly across the entire width of the bilayer. These probes are almost completely insensitive to the changes of  s , since due to dielectric screening this potential does not go deep into the bilayer, but  s asymmetry between monolayers can be detected (Xu and Loew, 2003). The broad-scale variation of dye locations that is highly needed for selective description of these effects is not achievable. These limitations are, of course, important. But the broad areas of applications of styryl probes exist. They arose mainly due to the possibility of their spontaneous incorporation into membranes of different types and to straightforward and ultra-fast mechanism of their response. 4.2. Hydroxychromone dyes From the above discussion we can derive that in several key properties the electrochromic styryl probes have probably reached the limit of their perfection. Trying to expand the possibilities of electrochromic dyes, we found an original pathway—to couple

the electrochromic spectral shift to photochemical reaction, the excited-state intramolecular proton transfer (ESIPT) (Klymchenko et al., 2002). What was the reason for choosing the ESIPT reaction? It is known that other excited-state reactions, such as electron transfer (Kawabata et al., 2001) and excimer formation by pyrene (Ohta et al., 1997) can be also influenced by electric fields. But only the ESIPT reaction can satisfy the necessary requirements for the role of strongly amplified electrochromic probing. The two excited states coupled by this reaction are uncharged. Meanwhile, their intramolecular charge distributions are different, one of them being strongly electrochromic, and the other not. Fluorescence emission from both of these states can be strong, and its spectra are well separated on the wavelength scale. The ESIPT reaction can be reversible and very fast on a time scale of emission, in order to equilibrate the populations of species residing in these states (M’Baye et al., 2006). The balance in any reaction in the state of equilibrium between concentrations of reactant and product depends on the difference in free energies of correspondent states. If some, even weak, intermolecular interactions of reactant or product molecules change this energy balance, the corresponding balance in relative concentrations will also change. The stronger interacting state (possessing decreased free energy) will become more populated, just in accordance with the Boltzmann law. The population of excited-state species determines the fluorescence intensity of the corresponding band. Therefore, if one of the states existing in equilibrium is electrochromic and the other is not, the electrochromic shift of one band will produce redistribution of intensity between the two fluorescence bands. The intensity ratio between these bands demonstrates a strong amplification effect compared to this ratio obtained from the shift of a single excitation band (Demchenko, 2006). Fig. 7 is the simple illustration of a new effect in photochemistry, the electrochromic modulation of ESIPT reaction, which was first demonstrated on a series of 3-hydroxychromone (3HC) dyes (Klymchenko et al., 2002). Soon these dyes became basic for the development of electric field sensitive probes for biomembrane applications. They possess two bands in fluorescence emission. One appears due to emission from initially excited N* state and the other from tautomer T* state, which is the product of ESIPT reaction. Strong electrochromic shift of N* band is due to strongly increased dipole moment of this state, which can be achieved by proper substitution in chromone ring (Klymchenko et al., 2003; Yesylevskyy et al., 2005). In contrast, the properties of T* state that possesses very small charge asymmetry remain essentially unchanged with no significant electric field sensitivity. This allows to make not only the position of the N* band but, especially, the ratio of band intensities (IN* /IT* ) highly sensitive to interaction with the environment. Thus, if an electric field is applied to the “smart” 3HC dye, the N* state will be, depending on the direction of the field, either stabilized or destabilized with respect to the T* state and its relative intensity will be either increased or decreased (see Fig. 7). This provides the strong coupling between electrochromism and ESIPT (Klymchenko et al., 2002). The described effect can be illustrated by studying the 3HC derivatives (particularly, 4 -diethylamino-3-hydroxyflavone) in which the electric fields in opposite directions are induced by negative charges belonging to groups covalently attached at opposite sides of fluorophore through the spacers that do not allow direct electronic conjugation (Fig. 8). Notably, the N* band shifts much stronger than the T* band and due to rapid establishment of ESIPT equilibrium, the electric-field-induced change of the N* state energy is transformed directly into the change of relative populations in these states giving rise to two-band wavelength-ratiometric response changing the emission intensity between blue-green and orange-red bands. It is also practically important that this response is dye concentration-independent, so that the factors that induce

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Fig. 7. The modulation of ESIPT reaction caused by electric field. The shift of equilibrium of the ESIPT reaction results in the redistribution of fluorescence intensity of N* and T* forms. This is schematically shown by the arrows of different width for the opposite directions of the applied electric field E. Bottom panels show the free energies of N* and T* forms for the electric fields of different directions and magnitudes.

the quenching of one of the forms do not change this two-band ratiometry. As for every type of electrochromic dyes, the fluorescence spectra of 3HC probes exhibit not only the Stark effects. They are sensitive to polarity and also to hydrogen bonding in protic environments. The sensitivity to H-bonding is due to formation of

intermolecular H-bond by carbonyl group of the probe to generate additional fluorescence band (H–N*) shifted with respect to N* band to longer wavelengths (Klymchenko et al., 2004b). This bonding can be eliminated by chemical substitution providing steric protection of this carbonyl. The contribution of polarity factor can be estimated by locating the parent fluorophore at the same depth but in differ-

Fig. 8. The effect of covalently attached positively but electronically uncoupled charged groups on absorption and fluorescence spectra of strongly dipolar 3HC dye. The dye (1), in which the charged group is attached from the side of electron-donor dialkylamino group of dye (2) possesses the absorption spectrum strongly shifted to the blue. Its fluorescence spectrum possesses greatly decreased intensity of the N* band that is also shifted to the blue. The opposite effect is observed for dye (3), in which the positively charged group is attached through a spacer to the opposite side.

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Fig. 9. Series of 3-hydroxychromone probes developed for characterizing different components of electrostatic potential in membranes. The probe di-SFA with the deepest location senses transmembrane potential. Probes F8N1S and BPPZ located in opposite orientations close to and under the glycerol backbone sense dipole potential and probe F2N12S responds to the changes of surface potential/hydration. The probe locations are illustrated by showing two PC molecules constituting the outer monolayer to which these dyes are spontaneously inserted.

ent orientations with respect to bilayer (this was not possible with the fluorescence probes before). The scalar polarity function should not be influenced by its orientation, and the observed orientationdependent effects should be attributed to directional (see Eq. (3)) effect of electric field. The success in biomembrane applications can be achieved due to the fact that the ground-state forms of the parent 3HC fluorophores are electrically neutral and low polar. Such electric neutrality is retained in the excited state and it is not changed in ESIPT reaction: the proton transfer is intramolecular with no generation of charged species. With the aid of different substituents the probes can be obtained with the ability of spontaneous incorporation into the membrane at any depth and orientation from aqueous solution. This allowed, for the first time, reaching preferential (to an extent that could be achieved in spatial resolution) response from the components of membrane potential,  t ,  s , and  d. The design principle that has been followed in development of these probes does not involve modification of lipids or simulations of their structures. The incorporation of fluorophore into desired membrane site is achieved due to attachment of charged groups through a spacer of variable length from one side and of hydrophobic chains from the other side. Especially difficult was the task of selective probing of  t that requires its location in an apolar region close to the bilayer center. In this case extreme rigidity of the whole construction is needed, since it is known that the dyes attached to flexible phospholipid tails can bend over to appear at polar interface, and recent MD simulations predict such location (Loura and Ramalho, 2007). Therefore Klymchenko et al. (M’Baye et al., 2006) designed fully rigid two-armed structure di-SFA presented in Fig. 9. Due to such two-armed structure the dye attains a vertical orientation in the bilayer and in model and cellular membranes shows fluorescence spectra corresponding to a very low polar environment (ε ∼ 3–4) (M’Baye et al., 2006). In cell membranes, the probe response of 12% per 100 mV is larger than the corresponding response of the styryl probes (Montana et al., 1989), but still lesser than that of the new generation of ANNINE styryl analogs (Fromherz et al., 2008). The key advantages of the present 3HC probe are its smaller size that together with the absence of charge allows locating it remote from the interface. Also, as a technical advantage especially useful in cell microscopy, its two-band ratiometric response in emission allows using a single excitation source and a two-color fluorescence detection setup.

Probing  d needs location of the fluorophore in vertical orientation at the site of its steepest gradient, somewhere between the apolar bilayer center and the interface. The dyes with dipole moment oriented in opposite directions (such as the probes F4N1 and BBPZ used initially and their modified versions F8N1S and PPZ8 presented in Fig. 9) can be used to show that reversal of the dipole moment induces opposite effects on spectra of  d modifiers (Klymchenko et al., 2003). Observed as the changes in the N*/T* ratio of two emission bands, their strong responses can be recorded for measuring  d in living cells (M’Baye et al., 2006). For measuring the surface potential ( s ) those 3HC probes can be applied that are localized at the interface, such as F2N8 and F2N12S (Klymchenko et al., 2002). The latter probe, due to the presence of its charges (see Fig. 9) being incorporated into the outer leaflet of the cell membrane, has a decreased tendency to flip to the inner leaflet. This is important for studying cellular processes associated with the change of their surface potential. Meanwhile, being located at the interface these dyes are highly hydrated, which results in intermolecular hydrogen bonding of their 4-carbonyl with water and the appearance of additional H-N* fluorescence band. Spectral deconvolution is needed to recover the ratio of band intensities (N*/T*) that is strongly connected with the factors that affect the surface potential, such as the charge of the lipid head group (Klymchenko et al., 2004a,b). An important application of the F2N12S dye is in the detection of apoptosis, the biological process of programmed cell death. At its early step, apoptosis results in the loss of transbilayer asymmetry, which is accompanied by the changes in the surface charge (PS exposure), lipid order and hydration. Probe F2N12S is able to detect the exposure of anionic lipids at the outer leaflet of cell membranes producing easily recognizable change of color of their fluorescence (M’Baye et al., 2006). 4.3. The limitations in application of electrochromic dyes Electrochromic organic dyes exhibit two essential limitations that cannot be removed by their design. One is the size of these dyes, which being of the order of 1 nm and more does not allow, in principle, locating the point charges. Instead, their fluorescence parameters respond only to a portion of an electric field potential gradient that falls across the dimensions of their ␲-electron-polarizable part. Because of that, the resolution of different components of membrane potential is not ideal, which often complicates the interpretation of results. Molecular probes are not

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as large as microelectrodes but they are still not small enough to operate at inter-atomic distances. The other limitation appears due to the dependence of response on different factors beside the electrostatic potential. The spectral shifts that determine the probe response have as their origin the change of energy of electronic transitions between the ground and excited states. The magnitude of these shifts is limited by the electronic charge-transfer ability of these states and depends on different intermolecular interactions. Thus, electrochromism (the response to external electric field) and solvatochromism (the response to dielectric interactions with molecular environment) are based on the same photophysical mechanism. The reader interested in a deeper understanding of their connection is referred to a classic review (Liptay, 1969). In practice, the effects of dipoles chaotically surrounding the dye in a polar liquid (effects of polarity) are not basically distinguishable from that of dipoles arranged in organized ensemble and generating the electrostatic potential. The distinguishing feature can only be based on the fact of high structural anisotropy of membrane and the possibility of locating the probe also anisotropically, orienting it along, reverse or perpendicular to bilayer normal. Therefore the effects that do not depend on dye orientation should be attributed to the effects of polarity, and those that show such dependence – to electrostatic potentials. The real picture in biomembranes is definitely more complicated, since the gradient of polarity may extend on the length scale of the size of the dye. To go deeper into this aspect, there are two contributors to polarity that are used in quasi-continuous approximation: one is the electronic polarizability and the other – orientational polarizability (Mataga and Kubota, 1970). For a dye located in the bilayer the first factor is mainly related to the presence of lipid carbonyls and phosphate, and the second is predominantly due to rotating dipoles of hydration water, the concentration of which is strongly depth-variable (Erilov et al., 2005). Moreover, the rates of dielectric relaxations that determine the spectroscopic effects of polarity may change dramatically across the bilayer (Sykora et al., 2005, 2007), so that the charged probes located at the interface and neutral probes located deeper in the bilayer sense these dynamics on different time scales (Demchenko and Shcherbatska, 1985; Gakamsky et al., 1992) and therefore provide different contributions to overall spectroscopic effects. Due to these limitations, strong efforts should be made for designing the probes with more specified location and orientation in the membrane, and caution is always needed in the interpretation of the obtained data. To conclude this section on an optimistic note we emphasize that whereas the physical mechanisms of probe response are limited, the possibilities of organic synthesis to provide the optimal probe design are not. These efforts are justified by the facts that it is the fluorescence probes that offer a unique possibility to study electrostatics in membranes regardless of their complexity: from phospholipid vesicles to natural membranes, organelles, living cells and tissues. 4.4. MD simulations of location and dynamics of fluorescence probes From the previous discussion we infer that the precise location of the probe fluorophore in the bilayer can be engineered. This can be done by attachment of molecular segments of desired length, polarity and charge. The commonly used methods to control the depth of probe insertion, such as quenching by spin-labeled lipids (Kachel et al., 1998), are not sufficient for that. NMR methods offer better precision (Bammel et al., 1990). The MD simulations can be used to obtain detailed atomic-scale information on the location and orientation of the fluorescent probes in lipid bilayers as well as the information about their interactions and dynamics. Since the abso-

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lute values of membrane potential and its components are accessed experimentally only on a very limited scale, the ability of MD simulations to provide these data are of extreme value. This makes MD a unique reference technique for verification of experimental results. The MD simulations have only started to be applied to this task. These simulations for the fluorescent probe DPH (Repáková et al., 2004; Repakova et al., 2005) and pyrene (Hoff et al., 2005) in lipid membranes were recently reported. In addition, these studies allow estimating the perturbation effect of the probe on the bilayer. In a series of recent works (Loura and Ramalho, 2007; Loura et al., 2008), MD simulations, differential scanning calorimetry and time-resolved fluorescence anisotropy methods were used in a complimentary manner to study several parameters of the bilayer with embedded NBD-based fluorescent phospholipid analogs C6NBD-PC and C12-NBD-PC. It was found that the incorporation of the fluorescent phospholipid analogs increases the average area per lipid molecule and decreases the order parameters of DPPC acyl chains. Moreover, incorporation of NBD-PC increases the electrostatic potential across the bilayer and slows lateral diffusion of DPPC molecules and rotational mobility of DPPC acyl chains. Although surprisingly few in number, these works showed the suitability of MD for calculation of a variety of properties of fluorescence probes in the bilayer, as well as their effect on the organization of the latter. 5. Membrane electrostatics and cell functions The discussion presented above demonstrates that the description of biomembrane electrostatics with nanoscopic view is a constructive language applicable for both MD simulations and fluorescence probing. Here we will show that, based on this description that distinguishes surface  s , transmembrane  t and dipole  d potentials, the different functional properties of membranes can be better described and understood. The number of experimental and simulation studies focused on different aspects of the cell functioning and revealing the important role of the membrane electrostatics, is so large that we do not even attempt to mention all of them in this review. We will focus on several representative processes, which can be approached by both fluorescent probing and MD simulations to show the complementarity of these techniques. 5.1. Binding and translocation of ions and small molecules Compared to anions, cations bind much more strongly to membrane surfaces, due to their negative  s, but their permeability is lower by many orders of magnitude due to strongly positive  d (see Figs. 2 and 3). Due to such energy profile, the permeability of Cl− or thiocyanate and nitrate ions is much higher when compared to Na+ or K+ cations. Although the spontaneous translocation of ions is still far beyond the time scales accessible for plain MD simulations, the free energy profiles of translocation could be obtained by means of umbrella sampling technique (Kumar et al., 2001). The idea of umbrella sampling is the following. The translocating molecule is restrained in some narrow region inside the membrane by applying strong external harmonic potential, which allows only small fluctuations around its center. The mean force, which acts on the molecule in such restrained simulation, consists of artificial restraining force (the “biasing” force) and the natural force caused by its membrane environment. The later can be recovered from a sequence of simulations with different positions of the restraining potentials using the so-called “unbiasing” techniques (Kumar et al., 2001; Kästner and Thiel, 2005). As a result, the potential of mean force across the membrane is obtained from the series of rather short restrained simulations. Restrain-

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ing potentials prevent the permeating molecule from escaping the unfavorable regions inside the membrane and allow accumulating statistically significant mean force for such regions. Sampling of such high-energy regions in plain MD simulations is prohibitively slow. The ions can also permeate through the pores in lipid bilayers, which either form spontaneously or are induced by various external conditions. Pore-mediated translocation of ions is much easier to study in MD simulations because the ions diffuse through the pore spontaneously (Gurtovenko and Vattulainen, 2005b; Gurtovenko and Anwar, 2007a; Leontiadou et al., 2007). Many events of translocation could be observed at the time scale from tens to hundreds of nanoseconds, which is easily accessible in plain MD simulations. One of experimental means to modulate  d that is actively used in fluorescence probing is the incorporation into the bilayer of small molecules that are strong dipoles able to increase or decrease  d . Their equilibrium location is studied by MD simulation. One of these compounds that dramatically increase  d is 6-ketocholestanol (Smondyrev and Berkowitz, 2001). Its difference from cholesterol is not only in a strong dipole moment but also in its more polar location in the bilayer. The popular lipophilic  d reducer, phloretin, changes also biomembrane head-group structure and hydration, as it is evidenced from the data of 2 H and 31 P NMR (Bechinger and Seelig, 1991). Therefore, interpretation of its effect in fluorescence studies needs caution, and MD simulations are expected to provide the necessary background. In addition to monitoring membrane potential and its components, fluorescence probing can be used in analogy to permeating lipophylic ions (Brockman, 1994) and their spin-labeled analogs (Matiukas et al., 2007) for evaluating the electrostatic-potentialdependent ion conduction profile. Permeation of the charged fluorescent dyes can be detected by their concentration-dependent quenching and application of membrane-impermeable quencher (e.g. iodine ions) located on one side of the membrane (Melikyan et al., 1996). Many small lipophilic molecules change the properties of biomembranes without binding to specific receptors, the most important of which are general anesthetics. Introduction of positively and negatively charged hydrophobic spin labels allowed revealing their strong influence on dipole potential (Matiukas et al., 2007). This technique cannot be extended to living cells, and for this research, electrochromic dyes of new generation are highly needed (Huang et al., 1995). 5.2. Interactions between membranes Electrostatic interactions in membranes play a critical role in such important functions as cell adhesion, cell spreading, chemotaxis and endo-exocytosis, membrane fusion, etc. Meanwhile, the exact mechanisms involving electric field effects in these processes are still poorly understood. For instance, there is a notion that dipole potential does not influence these processes since it does not extend out to the aqueous phase at the biomembrane surface and does not participate in generation of hydration forces between bilayers (Gawrisch et al., 1992). In contrast, some authors ascribe  d an important role in formation of a strong repulsive force between the bilayers (McIntosh et al., 1989). Analysis of their computations and comparison with experimental data indicates that the magnitude of the so-called “solvation pressure” is proportional to the square of the value of dipole potential. The electric field produced by interfacial dipoles polarizes the interbilayer solvent molecules and can give rise to such effects. Interesting in this respect is the observation made by atomic force microscopy (AFM) that a repulsive force between membranes appears not only due to their surface negative charge, but it also exists between membranes formed of neutral zwitterionic lipids. Its presence is explained by negative compo-

nent of dipole potential, extending from the bilayer (Yang et al., 2008). Direct molecular dynamics simulations of the membrane interactions become possible only recently because of large system sizes and long simulation times required. The spontaneous fusion of two mixed DPPC/palmitic acid vesicles was recently studies in atomic details (Knecht and Marrink, 2007). MD simulation of various fusion proteins, including the proteins playing an important role in virus infection, was also reported (Huang et al., 1995; Kamath and Wong, 2002; Knecht and Grubmuller, 2003). This field of simulation is progressing rapidly now, which allows us to say that the subtle electrostatic effects during the membrane interactions will become accessible in atomistic simulation in the nearest future. 5.3. Asymmetry of lipids and their translocation Asymmetric distribution of lipids between inner and outer monolayers of cell membranes is characteristic of living cells: the lipids with negative charge are predominantly located at the inner interface. Such asymmetry can be changed in a lipid flip–flop process in which the membrane integrity is retained; it is characteristic for different cell transformations (apoptosis, activation of trombocytes, cancer) (Wilton, 1998). Therefore this functionally important process has attracted the attention of researchers. Different properties of the asymmetric lipid bilayers were addressed in recent MD study of mixed DPPC–DPPS bilayer. It was shown that the order parameter of the lipid tails and the electrostatic potential of the leaflet, which contained charged DPPS lipids, differ significantly from these properties of the other leaflet, which contained only DPPC molecules (López Cascales et al., 2006). The flip–flop translocation of the lipids was recently studied in atomistic MD simulations using the umbrella sampling technique (Tieleman and Marrink, 2006). In this study the phosphate groups of two lipids were restrained in different positions in such a way that one of them samples configurations from the bulk water to the average position in the upper monolayer and the other samples configurations from the center of bilayer to the average position in the lower monolayer. Such intricate setup allows sampling the whole width of the membrane with the minimal number of umbrella sampling simulations. It was shown that the energy barrier for the flip–flop transition is approximately 80 kJ/mol, which correlates well with available experimental data. PME electrostatics was used in this study. The size of the bilayer patch was quite small (64 lipids), which means that quite strong interaction between the periodic images of the system was present. However, no specific attention was paid to the role of electrostatic interactions in the flip–flop process. The flip–flop events can also occur in spontaneously formed water pores in lipid bilayers. Although the spontaneous formation of the pore under physiological conditions is beyond the time scale of MD simulations, the pores could be induced artificially, i.e. by large transmembrane ion density gradients, which lead to electroporation, or certain amphiphilic compounds, which embed into the membrane and act as pore inductors. Once the pore is formed the spontaneous diffusion of lipids between the monolayers can be simulated successfully (Gurtovenko and Vattulainen, 2007c; Gurtovenko et al., 2008a). These studies suggest that the pore-mediated flip–flop is very fast process (of order of tens of nanoseconds), in contrast to the pore formation, which is the limiting step. Fluorescence probing of electric-field-dependent translocation of lipids allows application of two types of these probes: the electrochromic dyes for monitoring membrane potential and its components and the labeled lipids to observe the translocation process. The lipids are labeled at their polar heads, and their translo-

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cation can be monitored by their self-quenching and quenching by iodine ions. It was found that such translocation strongly depends on transmembrane potential (Leenhouts and De Kruijff, 1995). 5.4. Translocation of peptides and proteins The translocation of proteins and peptides through the membranes is vital for many cell processes such as signaling, secretion and viral infection. The problem of translocation of therapeutic peptides through the membrane is also very important for intracellular drug delivery and gene therapy. Proteins and peptides are usually huge molecules, which carry many charges and dipoles, thus the membranes seem to be completely impermeable for them. Indeed, the majority of proteins and peptides can be transferred by specialized membrane transporters only, however, some of them exhibit spontaneous insertion into or translocation through the bilayers. Various membrane-active peptides, such as mellitin (Hristova et al., 2001), are embedded spontaneously into the membranes forming water-filled pores, which facilitates their antimicrobial activity. Recently, a number of molecular dynamics studies of antimicrobial peptides were reported (Vereb et al., 2003; Leontiadou et al., 2006; Sengupta et al., 2008). Spontaneous pore formation was observed directly in these works, which allowed telling about simulating these peptides “in action” (Leontiadou et al., 2006). Although it is clear that the electrostatic effects play an important role in embedding of antimicrobial peptides into the membranes, to our knowledge no special attention was paid to this issue in simulations. Another intriguing group of peptides is the so-called protein transduction domains (PTDs) or cell-penetrating peptides (CPPs) (Lindgren et al., 2000; Magzoub and Gräslund, 2004). These peptides translocate through the membranes in apparently energy and receptor independent manner (Lindgren et al., 2000; Deshayes et al., 2005; Zorko and Langel, 2005). In addition, CPPs lead to the internalization of various cargos to which they are attached, which makes them very promising candidates for intracellular drug delivery agents. Although more than one hundred CPPs have been identified, only few of them, such as Penetratin (Derossi et al., 1994), the HIV-TAT peptide (Fawell et al., 1994), transportan (Pooga et al., 1998), MAP (Oehlke et al., 1998) and polyarginines of various lengths (Wender et al., 2000) have been studied in details. While CPPs in general possess a net positive charge and are amphipathic, they do not have a recognizable common sequence or structure motif. The mechanism of translocation of the CPPs is still unknown despite the variety of proposed models of this process (Zorko and Langel, 2005). It has been established both experimentally (Thorén et al., 2004) and by simulations (Lensink et al., 2005) that the binding of CPPs to the membranes increases with the increase of the negative charge of the membrane surface. Such behavior is expected because of the net positive charge of the CPPs. However, it is still unknown if the electrostatic effects play any role in the later stages of translocation. Recently, the translocation of two CPPs – Penetratin and the Tat peptide – was addressed in extensive MD study (Yesylevskyy et al., submitted for publication). Simulations of translocation of the CPPs impose significant methodological difficulties. Particularly, rotational diffusion of the peptides inside the membranes cannot be sampled adequately and the conformation of peptide during the translocation is not known. Despite these problems, the semi-quantitative free energy profiles of translocation of the PTDs were obtained in the series of umbrella sampling simulations. It was shown that the free energy barrier of translocation is approximately 70–100 kJ/mol for penetratin and 100–120 kJ/mol for Tat peptide. The height of this barrier will depend significantly on the value of the dipole potential, so the investigation of the influence

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of the dipole potential on translocation is the most obvious future prospect of these studies. There are several experimental evidences of the major role of electrostatic effects in the interactions of other peptides and proteins with membranes. It was shown that the translocation of synthetic model peptides carrying a single positive charge into the unilamellar vesicles depends strongly on the transmembrane gradient of K+ ions (de Kroon et al., 1991). Insertion into the membrane and folding of the mitochondrial amphipathic signal sequence (known as p25 peptide) appeared to be strongly dependent on the dipole potential, which was modified by sterol derivatives (Cladera and O’Shea, 1998). It is shown that the variation of the membrane dipole potential affects the extent of the membrane fusion caused by the fusion domain of the simian immunodeficiency virus and implicates the dipolar properties of membranes in their fusion (Cladera et al., 1999). The dipole potential also affects the structure and function of membrane-incorporated proteins and peptides such as model amphiphilic peptide (Cladera and O’Shea, 1998), gramicidin A (Rokitskaya et al., 1997; Thompson et al., 2001), and phospholipase A (Maggio, 1999). It has also been suggested that the dipole potential may play a role in the function and conformation of proteins in lipid rafts, where the dipole potential is different from that of surrounding lipids because of associated sterols within the raft structure (O’Shea, 2005). From this brief survey it is possible to conclude that MD simulations in the area of protein–membrane interactions are not focused enough on the electrostatic effects, while experimental researches are not detailed enough to reveal the mechanisms by which various components of the membrane potential influence embedding and binding of the proteins and peptides. Close connections between the simulations and experimental techniques will definitely provide significant insights in this area in the future. 5.5. Ionic channel activity Phospholipid bilayers are highly simplified model systems. Real biological membranes contain many protein, glycolipid and glycoprotein components, electrostatic interactions in which are essential for the cell functions. Special attention of researchers is attracted to ion channels, concerted action of which is responsible for propagation of electric signal along the neuronal pathways. The negative surface potentials can affect the steady-state conductance of the ion channels in the membrane, inasmuch as (1), they determine the local ion concentration at the channel orifice; and (2), the difference in surface potentials between both sides of a membrane produces an electric potential drop across the membrane (intramembrane potential), thereby changing the electric driving forces within the membrane. In voltage-gated potassium channels both the channel conductance and its opening/closing (gating) are governed by transmembrane electric field. These channels respond to the changes in transmembrane potential by movement of their positively charged voltage sensing segments across this field. By attaching tethered charges to these segments, evidence was obtained that the electric field in the vicinity of the channel falls within a short distance of <4 Å (Ahern and Horn, 2005), which necessitates its probing with high spatial resolution. It is known from experiments that the membrane dipole potential influences significantly the conductance in gramicidin channels. Particularly it was reported that the decrease of  d resulted in a decrease in proton conductance and in an increase of alkali metal conductance (Rokitskaya et al., 2002). It was also established that the dipole potential affects the process of dissociation of the gramicidin channel. Presumably the motion of the gramicidin monomers is affected in the region near the membrane–water interface where the dipole potential changes significantly (Rokitskaya et al., 1997).

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The MD studies of the ion channels are so numerous and diverse that the specialized review is required to cover them. Unfortunately the electrostatic properties of the membranes, which surround the channel protein, are almost never discussed in these studies. The most severe limitation in the ions channel simulations is the limited time scale, which is currently not sufficient to study the gating phenomena and even multiple events of ion translocation through the selective channel. Thus, most of the MD studies of the ion channels are currently unable to address the dependence of the channel functioning on the electrostatics of the membrane directly. Despite these difficulties, attempts were made to compute the free energy profile of the permeating ions in the channel, which includes the contribution of the surrounding lipid membrane (Allen et al., 2006a). It was shown that the treatment of long-range electrostatic interactions and the finite-size effects affect the resulting free energy profile significantly. However, the components of the membrane electrostatic potential were not differentiated and their influence was not studied. The same is true for numerous simulations of the KcsA potassium channel (Shrivastava and Sansom, 2000; Chung et al., 2002). In these studies the membrane was considered as an integral part of the simulated system, but its influence was not studied. The electrostatic potential maps of the large-conductance ␣chemolysin channel and the surrounding DPPC membrane were recently computed in MD simulations (Aksimentiev and Schulten, 2005). It was shown that the membrane interior possesses the potential of approximately +800 mV, which is in good agreement with the value of the dipole potential of pure DPPC membrane. The influence of transmembrane potential (modeled by the uniform external electric field) on the conductance properties of the channel was investigated in this study. As it was stated above, this method of modeling the transmembrane potential is not very realistic, however, this work is probably the first example of MD simulation focused on the detailed study of electrostatic effects in ionic channels. Several attempts were made for covalent binding of electrochromic dyes at different sites of ionic channel membrane proteins for obtaining information on the changes of these fields in the course of protein functioning (Blunck et al., 2005). The problem here is the large size of these dyes that is comparable with the size of submolecular structures. A necessary sub-nanosecond time resolution can be easily achieved with these dyes (Asamoah et al., 2003). The measurements of transmembrane potential are routine for cell physiology. They are used on a large scale for screening of new pharmacological agents. Meanwhile, without knowledge of detailed membrane electrostatics it is hard to establish the mechanism of their action. For detecting the ion channel activity in the presence of test compounds, the voltage-sensitive electrochromic dyes are in active use (Wolff et al., 2003). Further progress in this methodology requires strong support from the side of MD simulations. 6. Conclusions and prospects for future research In this review we made an effort to tear down the barrier separating high-resolution computational and experimental studies of biomembrane electrostatics. These fields are hitherto seen as largely unconnected, but in our view they are closely related being focused on electrostatic and other nanoscale properties of membranes that are hardly available for accessing by other methods. As in any other area of science, in research on biomembranes the level of description and understanding of the studied system approaches steadily the level of complexity of this system. In this area, we clearly observe that simple macroscopic analogs and the models based on them do not allow understanding even the

basic phenomena. Therefore the nanoscopic way of thinking should be accepted by many researchers working with biomembranes. This should happen only because of the fact that the gradients of electric field across the membranes are nonlinear and, moreover, even on a short distance of several Angstroms they can reverse their sign. They are strongly connected to molecular level and, even more, to the level of groups of atoms that form very specific pattern of properties at every Angstrom of penetration into the bilayer. These membrane properties allow applying an approximation based on nanoscopic resolution in one dimension, along the membrane normal. An implicitly or explicitly applied averaging operates along the membrane plane at different depths. Already on such level of detail, such macroscopic variables as polarity, viscosity or hydration loose their meaning unless it becomes specified, to which particular site they refer and what kind of modeling brings their particular values. MD simulations and molecular probing are presently seen as the only methods that can allow providing in a consistent manner the analysis of structure, dynamics and interactions leading to this quasi-continuous description. It is interesting that for achieving such description (i.e. for calculating the local dielectric constants, “dielectric profile”), MD simulations have started to borrow the concept of molecular probing by applying a virtual charged particle at different membrane depths, and calculating its electrostatic interactions (Nymeyer and Zhou, 2008). It is surprising that these two very different methods suffer from similar type of limitations. Both of them are unable to describe elementary electrostatic interactions that depend on distribution and redistribution of electronic charge density. Such distribution cannot be described within MD formalism that operates only with point charges. This approximation does not allow adequate description of electronic polarization effects and of the dynamic phenomena in the membrane systems that involve motions of electrons, such as in charge transfer or on electronic excitations of natural membrane pigments or fluorescence probes. Likewise, presentation of fluorescence electrochromic dyes as permanent point dipoles is not sufficient for deriving and predicting the spectroscopic effects occurring on their interaction with other dipoles or charges. In principle, in MD the majority of these problems can be solved by switching to purely quantum or mixed quantum mechanics–classical MD simulation (SinghKollman, 1986; Gao, 1995), however this will require another revolutionary advance in the computer power. New methods are expected to start in the future an active competition with MD and fluorescence in the studies of membrane electrostatics. Primarily, they can be based on the observation of Stark effect shifts in vibrational spectra of compounds containing nitrile (R-CN) or azide (R-N3 ) groups (Oklejas et al., 2002; Webb and Boxer, 2008). Such electrochromic groups can be introduced into lipids, membrane proteins or compounds incorporated into bilayers with the observation of shifts of IR or Raman spectra. In view of small size of these groups, structural resolution should be substantially increased. Parameters of EPR spectra are known to be sensitive to electrostatic potentials (Gulla and Budil, 2001), and their possibilities must be explored in view of small size of stable nitroxide radicals that can be used in these studies. Meanwhile, the ‘dynamic’ methods based on determining collision frequencies between neutral fluorescent or paramagnetic probe and diffusing charged paramagnetic radical or fluorescence quencher suggested a decade ago (Likhtenshtein et al., 1999; Chung et al., 2002) are not expected to be of prospect in the studies of biomembrane electrostatics due to difficulties in interpretation of obtained data. It should be emphasized that MD techniques are approximate by definition. They are limited by the classical formalism of motion.

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Simulations of the non-standard membrane components, such as modified lipids or embedded synthetic probes, remain a complicated problem because of laborious parameterization step for these compounds and difficulties in constructing the correspondent force fields. With this technique the realistic collective (not pair-additive) electric field effects here are not studied explicitly, and nanoscopic-level electric field effects are obtained by averaging (integration). Being fully aware of these limitations, we can summarize the present and foreseen achievements. The formal separation of electrostatic field pattern across the membrane into three components, the surface  s , transmembrane  t and dipole  d potentials, that rely strongly on comparative experimental studies on model membranes with the variation of their chemical composition or by producing the binding and translocation of small charged and dipolar compounds, now got a strong support on a submolecular level. The novel simulations and probing demonstrate the possibility to estimate the quantitative value of electrostatic potential at any depth in the membrane and to determine the structural origin of its generation. Meanwhile, the long-range nature of electrostatic interactions does not allow making this separation ideal. Introduction of new research methods will allow characterizing both this separation and overlap in greater depth. The MD provides a unique opportunity to make any “experiments in silico” by manipulating with inter-atomic interactions. Particularly the interactions between different subsets of atoms could be switched off, particular degrees of freedom could be frozen and the charges of any atoms could be changed. This allows, for example, separating the electrostatic contributions of different parts of the system such as water molecules, lipid head groups, lipid carbonyls and tails, etc. The future prospects in this area include dedicated MD simulations of the systems, which correspond to experimental conditions as close as possible. Such simulations should be focused on the effects and quantities observed experimentally. This requires high-quality parameterization of the fluorescent probes and adequate models of their interaction with the lipid bilayers. The strong impulse provided by MD for enrichment of information provided by fluorescence probing is especially important, since the latter approach provides the most efficient means for studying membrane electrostatics in native membranes, cells and tissues. Acknowledgments Prof. Ronald Clarke and Prof. Pradeep K. Sengupta are acknowledged for critical reading of the manuscript and useful suggestions. References Ahern, C.A., Horn, R., 2005. Focused electric field across the voltage sensor of potassium channels. Neuron 48, 25–29. Aksimentiev, A., Schulten, K., 2005. Imaging {alpha}-hemolysin with molecular dynamics: ionic conductance, osmotic permeability, and the electrostatic potential map. Biophys. J. 88, 3745–3761. Allen, T.W., Andersen, O.S., Roux, B., 2006a. Ion permeation through a narrow channel: using gramicidin to ascertain all-atom molecular dynamics potential of mean force methodology and biomolecular force fields. Biophys. J. 90, 3447–3468. Allen, T.W., Andersen, O.S., Roux, B., 2006b. Molecular dynamics—potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels. Biophys. Chem. 124, 251–267. Anezo, C., de Vries, A.H., Holtje, H.-D., Tieleman, D.P., Marrink, S.J., 2003. Methodological issues in lipid bilayer simulations. J. Phys. Chem. B 107, 9424–9433. Asamoah, O.K., Wuskell, J.P., Loew, L.M., Bezanilla, F., 2003. A fluorometric approach to local electric field measurements in a voltage-gated ion channel. Neuron 37, 85–97. Bammel, B.P., Hamilton, D.D., Haugland, R.P., Hopkins, H.P., Schuette, J., Szalecki, W., Smith, J.C., 1990. NMR, calorimetric, spin-label, and optical studies on a trifluoromethyl-substituted styryl molecular probe in dimyristoylphosphatidylcholine vesicles and multilamellar suspensions: a model for location of optical probes. Biochim. Biophys. Acta 1024, 61–81.

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