Simulations of apo and holo-fatty acid binding protein: structure and dynamics of protein, ligand and internal water

On the Dynamic Mechanism of Long-Flexible Fatty Acid Binding to Fatty Acid Binding Protein: Resolving the Long-Standing Debate

Fatty acids (FAs) are one of the essential energy sources for physiological processes, and they play a vital role in regulating immune and inflammatory responses, promoting cell differentiation and apoptosis, and inhibiting tumor growth. These functions are carried out by FA binding proteins (FABPs) that recognize and transport FAs. Although the crystal structure of the FA-FABPs complex has long been characterized, the mechanism behind FA binding and dissociation from FABP remains unclear. This study employed conventional MD simulations and enhanced sampling technologies to investigate the atomic-scale complexes of heart fatty acid binding proteins and stearic acid (SA). The results revealed two primary pathways for the binding or dissociation of the flexible long-chain ligand, with the orientation of the SA carboxyl head during dissociation determining the chosen path. Conformational changes in the portal region of FABP during the ligand binding/unbinding were found to be trivial, and the overturn of the ″cap″ or the unfolding of the α2 helix was not required. This study resolves the long-standing debate on the binding mechanism of SA with the long-flexible tail to FABP, which significantly improves the understanding of the transport mechanism of FABPs and the development of related therapeutic agents.

Identification of Structural transitions in bacterial fatty acid binding proteins that permit ligand entry and exit at membranes

Fatty acid (FA) transfer proteins extract FA from membranes and sequester them to facilitate their movement through the cytosol. Detailed structural information is available for these soluble protein–FA complexes, but the structure of the protein conformation responsible for FA exchange at the membrane is unknown. Staphylococcus aureus FakB1 is a prototypical bacterial FA transfer protein that binds palmitate within a narrow, buried tunnel. Here, we define the conformational change from a “closed” FakB1 state to an “open” state that associates with the membrane and provides a path for entry and egress of the FA. Using NMR spectroscopy, we identified a conformationally flexible dynamic region in FakB1, and X-ray crystallography of FakB1 mutants captured the conformation of the open state. In addition, molecular dynamics simulations show that the new amphipathic α-helix formed in the open state inserts below the phosphate plane of the bilayer to create a diffusion channel for the hydrophobic FA tail to access the hydrocarbon core and place the carboxyl group at the phosphate layer. The membrane binding and catalytic properties of site-directed mutants were consistent with the proposed membrane docked structure predicted by our molecular dynamics simulations. Finally, the structure of the bilayer-associated conformation of FakB1 has local similarities with mammalian FA binding proteins and provides a conceptual framework for how these proteins interact with the membrane to create a diffusion channel from the FA location in the bilayer to the protein interior.

Tardigrade Secretory-Abundant Heat-Soluble Protein Has a Flexible β-Barrel Structure in Solution and Keeps This Structure in Dehydration

Secretory-abundant heat-soluble (SAHS) proteins are unique heat-soluble proteins of Tardigrada and are believed to play an essential role in anhydrobiosis, a latent state of life induced by desiccation. To investigate the dynamic properties, molecular dynamics (MD) simulations of a SAHS protein, RvSAHS1, were performed in solution and under dehydrating conditions. For comparison purposes, MD simulations of a human liver-type fatty-acid binding protein (LFABP) were performed in solution. Furthermore, high-speed atomic force microscopy observations were conducted to ascertain the results of the MD simulations. Three properties of RvSAHS1 were found as follows. (1) The entrance region of RvSAHS1 is more flexible and can be more extensive in solutions compared with that of a human LFABP because there is no salt bridge between the βD and βE strands. (2) The intrinsically disordered domain in the N-terminal region significantly fluctuates and can form an amphiphilic α-helix. (3) The size of the entrance region gets smaller along with dehydration, keeping the β-barrel structure. Overall, the obtained results provide atomic-level dynamics of SAHS proteins.

Atomistic Insights into the Functional Instability of the Second Helix of Fatty Acid Binding Protein

Structural dynamics of fatty acid binding proteins (FABPs), which accommodate poorly soluble ligands in the internalized binding cavities, are intimately related to their function. Recently, local unfolding of the α-helical cap in a variant of human intestinal FABP (IFABP) has been shown to correlate with the kinetics of ligand association, shedding light on the nature of the critical conformational reorganization. Yet, the physical origin and mechanism of the functionally relevant transient unfolding remain elusive. Here, we investigate the intrinsic structural instability of the second helix (αII) of IFABP in comparison with other segments of the protein using hydrogen-exchange NMR spectroscopy, microsecond molecular dynamics simulations, and enhanced sampling techniques. Although tertiary interactions positively contribute to the stability of helices in IFABP, the intrinsic unfolding tendency of αII is encoded in its primary sequence and can be described by the Lifson-Roig theory in the absence of tertiary interactions. The unfolding pathway of αII in intact proteins involves an on-pathway intermediate state that is characterized with the fraying of the last helical turn, captured by independent enhanced sampling methods. The simulations in this work, combined with hydrogen-exchange NMR data, provide new, to our knowledge, atomistic insights into the functional local unfolding of FABPs.

The Observation of Ligand-Binding-Relevant Open States of Fatty Acid Binding Protein by Molecular Dynamics Simulations and a Markov State Model

As a member of the fatty acids transporter family, the heart fatty acid binding proteins (HFABPs) are responsible for many important biological activities. The binding mechanism of fatty acid with FABP is critical to the understanding of FABP functions. The uncovering of binding-relevant intermediate states and interactions would greatly increase our knowledge of the binding process. In this work, all-atom molecular dynamics (MD) simulations were performed to characterize the structural properties of nativelike intermediate states. Based on multiple 6 μs MD simulations and Markov state model (MSM) analysis, several "open" intermediate states were observed. The transition rates between these states and the native closed state are in good agreement with the experimental measurements, which indicates that these intermediate states are binding relevant. As a common property in the open states, the partially unfolded α2 helix generates a larger portal and provides the driving force to facilitate ligand binding. On the other side, there are two kinds of open states for the ligand-binding HFABP: one has the partially unfolded α2 helix, and the other has the looser β-barrel with disjointing βD-βE strands. Our results provide atomic-level descriptions of the binding-relevant intermediate states and could improve our understanding of the binding mechanism.

Molecular mechanisms of Charcot-Marie-Tooth neuropathy linked to mutations in human myelin protein P2

Charcot-Marie-Tooth (CMT) disease is one of the most common inherited neuropathies. Recently, three CMT1-associated point mutations (I43N, T51P, and I52T) were discovered in the abundant peripheral myelin protein P2. These mutations trigger abnormal myelin structure, leading to reduced nerve conduction velocity, muscle weakness, and distal limb atrophy. P2 is a myelin-specific protein expressed by Schwann cells that binds to fatty acids and membranes, contributing to peripheral myelin lipid homeostasis. We studied the molecular basis of the P2 patient mutations. None of the CMT1-associated mutations alter the overall folding of P2 in the crystal state. P2 disease variants show increased aggregation tendency and remarkably reduced stability, T51P being most severe. In addition, P2 disease mutations affect protein dynamics. Both fatty acid binding by P2 and the kinetics of its membrane interactions are affected by the mutations. Experiments and simulations suggest opening of the β barrel in T51P, possibly representing a general mechanism in fatty acid-binding proteins. Our findings demonstrate that altered biophysical properties and functional dynamics of P2 may cause myelin defects in CMT1 patients. At the molecular level, a few malformed hydrogen bonds lead to structural instability and misregulation of conformational changes related to ligand exchange and membrane binding.

High-resolution neutron and X-ray diffraction room-temperature studies of an H-FABP-oleic acid complex: study of the internal water cluster and ligand binding by a transferred multipolar electron-density distribution

Crystal diffraction data of heart fatty acid binding protein (H-FABP) in complex with oleic acid were measured at room temperature with high-resolution X-ray and neutron protein crystallography (0.98 and 1.90 Å resolution, respectively). These data provided very detailed information about the cluster of water molecules and the bound oleic acid in the H-FABP large internal cavity. The jointly refined X-ray/neutron structure of H-FABP was complemented by a transferred multipolar electron-density distribution using the parameters of the ELMAMII library. The resulting electron density allowed a precise determination of the electrostatic potential in the fatty acid (FA) binding pocket. Bader's quantum theory of atoms in molecules was then used to study interactions involving the internal water molecules, the FA and the protein. This approach showed H⋯H contacts of the FA with highly conserved hydrophobic residues known to play a role in the stabilization of long-chain FAs in the binding cavity. The determination of water hydrogen (deuterium) positions allowed the analysis of the orientation and electrostatic properties of the water molecules in the very ordered cluster. As a result, a significant alignment of the permanent dipoles of the water molecules with the protein electrostatic field was observed. This can be related to the dielectric properties of hydration layers around proteins, where the shielding of electrostatic interactions depends directly on the rotational degrees of freedom of the water molecules in the interface.

Multiple Binding Poses in the Hydrophobic Cavity of Bee Odorant Binding Protein AmelOBP14

In the first step of olfaction, odorants are bound and solubilized by small globular odorant binding proteins (OBPs) which shuttle them to the membrane of a sensory neuron. Low ligand affinity and selectivity at this step enable the recognition of a wide range of chemicals. Honey bee Apis mellifera’s OBP14 (AmelOBP14) binds different plant odorants in a largely hydrophobic cavity. In long molecular dynamics simulations in the presence and absence of ligand eugenol, we observe a highly dynamic C-terminal region which forms one side of the ligand-binding cavity, and the ligand drifts away from its crystallized orientation. Hamiltonian replica exchange simulations, allowing exchanges of conformations sampled by the real ligand with those sampled by a noninteracting dummy molecule and several intermediates, suggest an alternative, quite different ligand pose which is adopted immediately and which is stable in long simulations. Thermodynamic integration yields binding free energies which are in reasonable agreement with experimental data.

Lipid binding protein response to a bile acid library: a combined NMR and statistical approach

Primary bile acids, differing in hydroxylation pattern, are synthesized from cholesterol in the liver and, once formed, can undergo extensive enzyme-catalysed glycine/taurine conjugation, giving rise to a complex mixture, the bile acid pool. Composition and concentration of the bile acid pool may be altered in diseases, posing a general question on the response of the carrier (bile acid binding protein) to the binding of ligands with different hydrophobic and steric profiles. A collection of NMR experiments (H/D exchange, HET-SOFAST, ePHOGSY NOESY/ROESY and (15) N relaxation measurements) was thus performed on apo and five different holo proteins, to monitor the binding pocket accessibility and dynamics. The ensemble of obtained data could be rationalized by a statistical approach, based on chemical shift covariance analysis, in terms of residue-specific correlations and collective protein response to ligand binding. The results indicate that the same residues are influenced by diverse chemical stresses: ligand binding always induces silencing of motions at the protein portal with a concomitant conformational rearrangement of a network of residues, located at the protein anti-portal region. This network of amino acids, which do not belong to the binding site, forms a contiguous surface, sensing the presence of the bound lipids, with a signalling role in switching protein-membrane interactions on and off.

Characterization of a novel water pocket inside the human Cx26 hemichannel structure

Connexins (Cxs) are a family of vertebrate proteins constituents of gap junction channels (GJCs) that connect the cytoplasm of adjacent cells by the end-to-end docking of two Cx hemichannels. The intercellular transfer through GJCs occurs by passive diffusion allowing the exchange of water, ions, and small molecules. Despite the broad interest to understand, at the molecular level, the functional state of Cx-based channels, there are still many unanswered questions regarding structure-function relationships, perm-selectivity, and gating mechanisms. In particular, the ordering, structure, and dynamics of water inside Cx GJCs and hemichannels remains largely unexplored. In this work, we describe the identification and characterization of a believed novel water pocket-termed the IC pocket-located in-between the four transmembrane helices of each human Cx26 (hCx26) monomer at the intracellular (IC) side. Using molecular dynamics (MD) simulations to characterize hCx26 internal water structure and dynamics, six IC pockets were identified per hemichannel. A detailed characterization of the dynamics and ordering of water including conformational variability of residues forming the IC pockets, together with multiple sequence alignments, allowed us to propose a functional role for this cavity. An in vitro assessment of tracer uptake suggests that the IC pocket residue Arg-143 plays an essential role on the modulation of the hCx26 hemichannel permeability.

Correlation spectroscopy and molecular dynamics simulations to study the structural features of proteins

In this work, we used a combination of fluorescence correlation spectroscopy (FCS) and molecular dynamics (MD) simulation methodologies to acquire structural information on pH-induced unfolding of the maltotriose-binding protein from Thermus thermophilus (MalE2). FCS has emerged as a powerful technique for characterizing the dynamics of molecules and it is, in fact, used to study molecular diffusion on timescale of microsecond and longer. Our results showed that keeping temperature constant, the protein diffusion coefficient decreased from 84±4 µm²/s to 44±3 µm²/s when pH was changed from 7.0 to 4.0. An even more marked decrease of the MalE2 diffusion coefficient (31±3 µm²/s) was registered when pH was raised from 7.0 to 10.0. According to the size of MalE2 (a monomeric protein with a molecular weight of 43 kDa) as well as of its globular native shape, the values of 44 µm²/s and 31 µm²/s could be ascribed to deformations of the protein structure, which enhances its propensity to form aggregates at extreme pH values. The obtained fluorescence correlation data, corroborated by circular dichroism, fluorescence emission and light-scattering experiments, are discussed together with the MD simulations results.

The simulation approach to lipid-protein interactions

The interactions between lipids and proteins are crucial for a range of biological processes, from the folding and stability of membrane proteins to signaling and metabolism facilitated by lipid-binding proteins. However, high-resolution structural details concerning functional lipid/protein interactions are scarce due to barriers in both experimental isolation of native lipid-bound complexes and subsequent biophysical characterization. The molecular dynamics (MD) simulation approach provides a means to complement available structural data, yielding dynamic, structural, and thermodynamic data for a protein embedded within a physiologically realistic, modelled lipid environment. In this chapter, we provide a guide to current methods for setting up and running simulations of membrane proteins and soluble, lipid-binding proteins, using standard atomistically detailed representations, as well as simplified, coarse-grained models. In addition, we outline recent studies that illustrate the power of the simulation approach in the context of biologically relevant lipid/protein interactions.

Simulating electrostatic energies in proteins: perspectives and some recent studies of pKas, redox, and other crucial functional properties

Electrostatic energies provide what is arguably the most effective tool for structure-function correlation of biological molecules. Here, we provide an overview of the current state-of-the-art simulations of electrostatic energies in macromolecules, emphasizing the microscopic perspective but also relating it to macroscopic approaches. We comment on the convergence issue and other problems of the microscopic models and the ways of keeping the microscopic physics while moving to semi-macroscopic directions. We discuss the nature of the protein dielectric "constants" reiterating our long-standing point that the dielectric "constants" in semi-macroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering different functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding, and protein stability. We emphasize the microscopic overcharging approach for studying pK(a) 's of internal groups in proteins and give a demonstration of power of this approach. We also emphasize recent advances in coarse grained models with a physically based electrostatic treatment and provide some examples including further directions in treating voltage activated ion channels.

Paradynamics: an effective and reliable model for ab initio QM/MM free-energy calculations and related tasks

Recent years have seen tremendous effort in the development of approaches with which to obtain quantum mechanics/molecular mechanics (QM/MM) free energies for reactions in the condensed phase. Nevertheless, there remain significant challenges to address, particularly, the high computational cost involved in performing proper configurational sampling and, in particular, in obtaining ab initio QM/MM (QM(ai)/MM) free-energy surfaces. One increasingly popular approach that seems to offer an ideal way to progress in this direction is the elegant metadynamics (MTD) approach. However, in the current work, we point out the subtle efficiency problems associated with this approach and illustrate that we have at hand what is arguably a more powerful approach. More specifically, we demonstrate the effectiveness of an updated version of our original idea of using a classical reference potential for QM(ai)/MM calculations [J. Phys. Chem. 1995, 99, 17516)], which we refer to as paradynamics (PD). This approach is based on the use of an empirical valence bond (EVB) reference potential, which is already similar to the real ab initio potential. The reference potential is fitted to the ab initio potential by an iterative and, to a great degree, automated refinement procedure. The corresponding free-energy profile is then constructed using the refined EVB potential, and the linear response approximation (LRA) is used to evaluate the QM(ai)/MM activation free-energy barrier. The automated refinement of the EVB surface (and thus the reduction of the difference between the reference and ab initio potentials) is a key factor in accelerating the convergence of the LRA approach. We apply our PD approach to a test reaction, namely, the S(N)2 reaction between a chloride ion and methyl chloride, and demonstrate that, at present, this approach is far more powerful and cost-effective than the metadynamics approach (at least in its current implementation). We also discuss the general features of the PD approach in terms of its ability to explore complex systems and clarify that it is not a specialized approach limited to only accelerating QM(ai)/MM calculations with proper sampling, but rather can be used in a wide variety of applications. In fact, we point out that the use of a reference (CG) potential coupled with its PD refinement, as well as our renormalization approach, provides very general and powerful strategies that can be used very effectively to explore any property that has been studied by the MTD approach.

Dissection of the critical binding determinants of cellular retinoic acid binding protein II by mutagenesis and fluorescence binding assay

The binding of retinoic acid to mutants of Cellular Retinoic Acid Binding Protein II (CRABPII) was evaluated to better understand the importance of the direct protein/ligand interactions. The important role of Arg111 for the correct structure and function of the protein was verified and other residues that directly affect retinoic acid binding have been identified. Furthermore, retinoic acid binding to CRABPII mutants that lack all previously identified interacting amino acids was rescued by providing a carboxylic acid dimer partner in the form of a Glu residue.

Exploring the conserved water site and hydration of a coiled-coil trimerisation motif: a MD simulation study

The solvent structure and dynamics around ccbeta-p, a 17-residue peptide that forms a parallel three-stranded alpha-helical coiled coil in solution, was analysed through 10 ns explicit solvent molecular dynamics (MD) simulations at 278 and 330 K. Comparison with two corresponding simulations of the monomeric form of ccbeta-p was used to investigate the changes of hydration upon coiled-coil formation. Pronounced peaks in the solvent density distribution between residues Arg8 and Glu13 of neighbouring helices show the presence of water bridges between the helices of the ccbeta-p trimer; this is in agreement with the water sites observed in X-ray crystallography experiments. Interestingly, this water site is structurally conserved in many three-stranded coiled coils and, together with the Arg and Glu residues, forms part of a motif that determines three-stranded coiled-coil formation. Our findings show that little direct correlation exists between the solvent density distribution and the temporal ordering of water around the trimeric coiled coil. The MD-calculated effective residence times of up to 40 ps show rapid exchange of surface water molecules with the bulk phase, and indicate that the solvent distribution around biomolecules requires interpretation in terms of continuous density distributions rather than in terms of discrete molecules of water. Together, our study contributes to understanding the principles of three-stranded coiled-coil formation.

Modeling fatty acid delivery from intestinal fatty acid binding protein to a membrane

Intestinal fatty acid binding protein (IFABP) interacts with biological membranes and delivers fatty acid (FA) into them via a collisional mechanism. However, the membrane-bound structure of the protein and the pathway of FA transfer are not precisely known. We used molecular dynamics (MD) simulations with an implicit membrane model to determine the optimal orientation of apo- and holo-IFABP (bound with palmitate) on an anionic membrane. In this orientation, the helical portal region, delimited by the alphaII helix and the betaC-betaD and betaE-betaF turns, is oriented toward the membrane whereas the putative beta-strand portal, delimited by the betaB-betaC, betaF-betaG, betaH-betaI turns and the N terminus, is exposed to solvent. Starting from the MD structure of holo-IFABP in the optimal orientation relative to the membrane, we examined the release of palmitate via both pathways. Although the domains can widen enough to allow the passage of palmitate, fatty acid release through the helical portal region incurs smaller conformational changes and a lower energetic cost.

Role of flexibility and polarity as determinants of the hydration of internal cavities and pockets in proteins

Molecular dynamics simulations of Staphylococcal nuclease and of 10 variants with internal polar or ionizable groups were performed to investigate systematically the molecular determinants of hydration of internal cavities and pockets in proteins. In contrast to apolar cavities in rigid carbon structures, such as nanotubes or buckeyballs, internal cavities in proteins that are large enough to house a few water molecules will most likely be dehydrated unless they contain a source of polarity. The water content in the protein interior can be modulated by the flexibility of protein elements that interact with water, which can impart positional disorder to water molecules, or bias the pattern of internal hydration that is stabilized. This might explain differences in the patterns of hydration observed in crystal structures obtained at cryogenic and room temperature conditions. The ability of molecular dynamics simulations to determine the most likely sites of water binding in internal pockets and cavities depends on its efficiency in sampling the hydration of internal sites and alternative protein and water conformations. This can be enhanced significantly by performing multiple molecular dynamics simulations as well as simulations started from different initial hydration states.

Molecular Insight into the Interaction between IFABP and PA by Using MM−PBSA and Alanine Scanning Methods

The molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method combined with alanine-scanning mutagenesis is a very important tool for rational drug design. In this study, molecular dynamics (MD) and MM-PBSA were applied to calculate the binding free energy between the rat intestinal fatty acid binding protein (IFABP) and palmitic acid (PA) to gain insight to the interaction details. Equally spaced snapshots along the trajectory were chosen to perform the binding free energy calculation, which yields a result highly consistent with experimental value with a deviation of 0.4 kcal/mol. Computational alanine scanning was performed on the same set of snapshots by mutating the residues in IFABP to alanine and recomputing the DeltaDeltaG(binding). By postprocessing a single trajectory of the wild-type complex, the average unsigned error of our calculated DeltaDeltaG(binding) is below 1.5 kcal/mol for most of the alanine mutations of the noncharged residues (67% in total). To further investigate some particular mutants, three additional dynamical simulations of IFABP Arg126Ala, Arg106Ala, and Arg106Gln mutants were conducted. Recalculated binding free energies are well consistent with the experimental data. Moreover, the ambiguous role of Arg106 caused by the free energy change of the opposite sign when it is mutated to alanine and glutamine respectively is clarified both structurally and energetically. Typically, this can be attributed to the partial electrostatic compensation mainly from Arg56 and the obvious entropy gain in Arg106Ala mutant while not in Arg106Gln mutant. The presented structural model of IFABP-PA complex could be used to guide future studies.

Metastable water clusters in the nonpolar cavities of the thermostable protein tetrabrachion

Water expulsion from the protein core is a key step in protein folding. Nevertheless, unusually large water clusters confined into the nonpolar cavities have been observed in the X-ray crystal structures of tetrabrachion, a bacterial protein that is thermostable up to at least 403 K (130 degrees C). Here, we use molecular dynamics (MD) simulations to investigate the structure and thermodynamics of water filling the largest cavity of the right-handed coiled-coil stalk of tetrabrachion at 365 K (92 degrees C), the temperature of optimal bacterial growth, and at room temperature (298 K). Hydrogen-bonded water clusters of seven to nine water molecules are found to be thermodynamically stable in this cavity at both temperatures, confirming the X-ray studies. Stability, as measured by the transfer free energy of the optimal size cluster, decreases with increasing temperature. Water filling is thus driven by the energy of transfer and opposed by the transfer entropy, both depending only weakly on temperature. Our calculations suggest that cluster formation becomes unfavorable at approximately 384 K (110 degrees C), signaling the onset of drying just slightly above the temperature of optimal growth. "Drying" thus precedes protein denaturation. At room temperature, the second largest cavity in tetrabrachion accommodates a five water molecule cluster, as reported in the X-ray studies. However, the simulations show that at 365 K the cluster is unstable and breaks up. We suggest that the large hydrophobic cavities may act as binding sites for two proteases, possibly explaining the unusual thermostability of the resulting protease-stalk complexes (up to approximately 393 K, 120 degrees C).

Molecular dynamics simulations of palmitate entry into the hydrophobic pocket of the fatty acid binding protein

The entry of substrate into the active site is the first event in any enzymatic reaction. However, due to the short time interval between the encounter and the formation of the stable complex, the detailed steps are experimentally unobserved. In the present study, we report a molecular dynamics simulation of the encounter between palmitate molecule and the Toad Liver fatty acid binding protein, ending with the formation of a stable complex resemblance in structure of other proteins of this family. The forces operating on the system leading to the formation of the tight complex are discussed.

Electron donor solvent effects provide biosensing with quantum dots

A palmitate biosensor that uses the emission intensity of a semiconducting nanoparticle to report palmitate concentration is presented. This method uses electron transfer to quench the emission from a ZnS-coated CdSe nanoparticle. The fatty acid binding pocket of intestinal fatty acid binding protein is used to modulate the electron transfer properties of [Ru(L)(NH3)4](PF6)2 (L = 5-maleimido-1,10-phenanthroline) that is covalently attached within this pocket. Once the metal-complex-modified protein is attached to ZnS-coated CdSe nanoparticles, palmitate addition excludes water from around the metal complex and increases the electron transfer from the metal complex to the valence band hole of the nanoparticle excited state. A 1.6-fold change in emission intensity is observed upon adding a saturated amount (500 nM) of sodium palmitate. The dissociation constant was calculated as 5 nM with a 1 nM lower limit of detection. Since palmitate does not alter the global conformation of intestinal fatty acid binding protein, palmitate-mediated changes in pocket solvation are suggested. This represents a new method in biosensor construction with semiconducting nanoparticles. Including previous conformation-dependent biosensors, there are thousands of potential analytes that can be detected with these strategies. Such biosensors will provide fluorescence contrast imaging reagents for small molecule analytes.

Protein Dynamics Tightly Connected to the Dynamics of Surrounding and Internal Water Molecules

Proteins are key components of biological cells. For example, enzymes catalyze biochemical reactions, membrane transporters are responsible for uptake and release of critical and superfluous components from the cell environment, and structural proteins are responsible for the stability of the cell wall and cytoskeleton. Many of the diverse protein functions involve dynamic transitions ranging from small local atomic displacements up to large allosteric conformational changes. In any conformation, proteins are in contact with the universal solvent medium of cells, water. Water not only surrounds proteins but is often an integral part of proteins and also is involved in key mechanistic steps. This Minireview discusses recent experimental and theoretical results on the role of water for protein dynamics and function.

Calculations of solute and solvent entropies from molecular dynamics simulations

The translational, rotational and conformational (vibrational) entropy contributions to ligand-receptor binding free energies are analyzed within the standard formulation of statistical thermodynamics. It is shown that the partitioning of the binding entropy into different components is to some extent arbitrary, but an appropriate method to calculate both translational and rotational entropy contributions to noncovalent association is by estimating the configurational volumes of the ligand in the bound and free states. Different approaches to calculating solute entropies using free energy perturbation calculations, configurational volumes based on root-mean-square fluctuations and covariance matrix based quasiharmonic analysis are illustrated for some simple molecular systems. Numerical examples for the different contributions demonstrate that theoretically derived results are well reproduced by the approximations. Calculation of solvent entropies, either using total potential energy averages or van't Hoff plots, are carried out for the case of ion solvation in water. Although convergence problems will persist for large and complex simulation systems, good agreement with experiment is obtained here for relative and absolute ion hydration entropies. We also outline how solvent and solute entropic contributions are taken into account in empirical binding free energy calculations using the linear interaction energy method. In particular it is shown that empirical scaling of the nonpolar intermolecular ligand interaction energy effectively takes into account size dependent contributions to the binding free energy.

Modeling electrostatic effects in proteins

Electrostatic energies provide what is perhaps the most effective tool for structure-function correlation of biological molecules. This review considers the current state of simulations of electrostatic energies in macromolecules as well as the early developments of this field. We focus on the relationship between microscopic and macroscopic models, considering the convergence problems of the microscopic models and the fact that the dielectric 'constants' in semimacroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering a wide range of functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding and protein stability. We conclude by pointing out that, despite the current problems and the significant misunderstandings in the field, there is an overall progress that should lead eventually to quantitative descriptions of electrostatic effects in proteins and thus to quantitative descriptions of the function of proteins.

Molecular dynamics study of water penetration in staphylococcal nuclease

The ionization properties of Lys and Glu residues buried in the hydrophobic core of staphylococcal nuclease (SN) suggest that the interior of this protein behaves as a highly polarizable medium with an apparent dielectric constant near 10. This has been rationalized previously in terms of localized conformational relaxation concomitant with the ionization of the internal residue, and with contributions by internal water molecules. Paradoxically, the crystal structure of the SN V66E variant shows internal water molecules and the structure of the V66K variant does not. To assess the structural and dynamical character of interior water molecules in SN, a series of 10-ns-long molecular dynamics (MD) simulations was performed with wild-type SN, and with the V66E and V66K variants with Glu66 and Lys66 in the neutral form. Internal water molecules were identified based on their coordination state and characterized in terms of their residence times, average location, dipole moment fluctuations, hydrogen bonding interactions, and interaction energies. The locations of the water molecules that have residence times of several nanoseconds and display small mean-square displacements agree well with the locations of crystallographically observed water molecules. Additional, relatively disordered water molecules that are not observed crystallographically were found in internal hydrophobic locations. All of the interior water molecules that were analyzed in detail displayed a distribution of interaction energies with higher mean value and narrower width than a bulk water molecule. This underscores the importance of protein dynamics for hydration of the protein interior. Further analysis of the MD trajectories revealed that the fluctuations in the protein structure (especially the loop elements) can strongly influence protein hydration by changing the patterns or strengths of hydrogen bonding interactions between water molecules and the protein. To investigate the dynamical response of the protein to burial of charged groups in the protein interior, MD simulations were performed with Glu66 and Lys66 in the charged state. Overall, the MD simulations suggest that a conformational change rather than internal water molecules is the dominant determinant of the high apparent polarizability of the protein interior.

NMR dynamic studies suggest that allosteric activation regulates ligand binding in chicken liver bile acid-binding protein

Apo chicken liver bile acid-binding protein has been structurally characterized by NMR. The dynamic behavior of the protein in its apo- and holo-forms, complexed with chenodeoxycholate, has been determined via (15)N relaxation and steady state heteronuclear (15)N((1)H) nuclear Overhauser effect measurements. The dynamic parameters were obtained at two pH values (5.6 and 7.0) for the apoprotein and at pH 7.0 for the holoprotein, using the model free approach. Relaxation studies, performed at three different magnetic fields, revealed a substantial conformational flexibility on the microsecond to millisecond time scales, mainly localized in the C-terminal face of the beta-barrel. The observed dynamics are primarily caused by the protonation/deprotonation of a buried histidine residue, His(98), located on this flexible face. A network of polar buried side chains, defining a spine going from the E to J strand, is likely to provide the long range connectivity needed to communicate motion from His(98) to the EF loop region. NMR data are accompanied by molecular dynamics simulations, suggesting that His(98) protonation equilibrium is the triggering event for the modulation of a functionally important motion, i.e. the opening/closing at the protein open end, whereas ligand binding stabilizes one of the preexisting conformations (the open form). The results presented here, complemented with an analysis of proteins belonging to the intracellular lipid-binding protein family, are consistent with a model of allosteric activation governing the binding mechanism. The functional role of this mechanism is thoroughly discussed within the framework of the mechanism for the enterohepatic circulation of bile acids.

Fatty acid binding proteins: same structure but different binding mechanisms? Molecular dynamics simulations of intestinal fatty acid binding protein

Fatty acid binding proteins (FABPs) carry fatty acids (FAs) and other lipids in the cellular environment, and are thus involved in processes such as FA uptake, transport, and oxidation. These proteins bind either one or two ligands in a binding site, which appears to be inaccessible from the bulk. Thus, the entry of the substrate necessitates a conformational change, whose nature is still unknown. A possible description of the ligand binding process is given by the portal hypothesis, which suggests that the FA enters the protein through a dynamic area known as the portal region. On the other hand, recent simulations of the adipocyte lipid binding protein (ALBP) suggested a different entry site (the alternative portal). In this article, we discuss molecular dynamics simulations of the apo-intestinal-FABP (I-FABP) in the presence of palmitate molecule(s) in the simulation box. The simulations were carried out to study whether the FA can enter the protein during the simulations (as in the ALBP) and where the ligand entry site is (the portal region, the alternative portal or a different domain). The analysis of the simulations revealed a clear difference between the ALBP and the I-FABP. In the latter case, the palmitate preferentially adsorbed to the portal region, which was more mobile than the rest of the protein. However, no ligand entry was observed in the multi-nanosecond-long simulations, in contrast to ALBP. These findings suggest that, although the main structural motif of the FABPs is common, the fine details of each individual protein structure grossly modulate its reactivity.

The GROMOS software for biomolecular simulation: GROMOS05

We present the latest version of the Groningen Molecular Simulation program package, GROMOS05. It has been developed for the dynamical modelling of (bio)molecules using the methods of molecular dynamics, stochastic dynamics, and energy minimization. An overview of GROMOS05 is given, highlighting features not present in the last major release, GROMOS96. The organization of the program package is outlined and the included analysis package GROMOS++ is described. Finally, some applications illustrating the various available functionalities are presented.

NMR studies of 4-19F-phenylalanine-labeled intestinal fatty acid binding protein: evidence for conformational heterogeneity in the native state

(19)F-Nuclear magnetic resonance (NMR) studies have been carried out after incorporation of 4-(19)F-phenylalanine into the intestinal fatty acid binding protein (IFABP), a protein composed of two beta-sheets containing a large hydrophobic cavity into which ligands bind. NMR spectra have been obtained with both the ligand-free and ligand-bound (oleate) forms. There are 29 residues involved in van der Waals or hydrophobic interactions or both to form a U-shaped ligand binding pocket (Sacchettni J. C., Scapin G., Gopaul D., and Gordon J. I. (1992) J. Biol. Chem. 267, 23534-23545). The protein contains eight phenylalanines, and all are included in those residues that line the pocket. Peak assignments were made using site-specific incorporation of 4-(19)F-phenylalanine. Fluorine is a highly sensitive probe to monitor the conformation and dynamics of the side chains in native state. We find that chemical exchange in the binding pocket exists in the native apo- and holo-state. Of the eight phenylalanine residues, Phe2, Phe47, Phe62, Phe68, and Phe93 are arranged on one side of the binding pocket, and all exist in two conformations with Phe2, Phe47, and Phe62 showing exchange cross-peaks with minor conformation in (19)F-(19)F nuclear Overhauser effect (NOESY) spectra. The line widths of Phe68 and Phe93 are broader than those of other phenylalanine residues and can be deconvoluted into two peaks. Phe47, Phe62, Phe68, Phe93, and Trp82 have been proposed to be involved in the early stage of collapse (Ropson, I. J., and Frieden, C. (1992) Proc. Natl. Acad. Sci U.S.A. 89, 7222-7226), but a temperature study suggests that Phe47 behaves differently than other residues and may be more involved in a later stage of folding, for example, side chain stabilization. In the holo-form, Phe17 shows an extra exchange cross-peak in addition to those exchange cross-peaks observed in apo-form. Holo-IFABP exhibits broader line width than the apo-form, suggesting more flexibility of the binding cavity upon ligand binding.

Validation of the 53A6 GROMOS force field

The quality of biomolecular dynamics simulations relies critically on the force field that is used to describe the interactions between particles in the system. Force fields, which are generally parameterized using experimental data on small molecules, can only prove themselves in realistic simulations of relevant biomolecular systems. In this work, we begin the validation of the new 53A6 GROMOS parameter set by examining three test cases. Simulations of the well-studied 129 residue protein hen egg-white lysozyme, of the DNA dodecamer d(CGCGAATTCGCG)(2), and a proteinogenic beta(3)-dodecapeptide were performed and analysed. It was found that the new parameter set performs as well as the previous parameter sets in terms of protein (45A3) and DNA (45A4) stability and that it is better at describing the folding-unfolding balance of the peptide. The latter is a property that is directly associated with the free enthalpy of hydration, to which the 53A6 parameter set was parameterized.

Absolute and Relative Entropies from Computer Simulation with Applications to Ligand Binding

A comparison between two related methods, Schlitter's formula and quasiharmonic analysis, for calculating absolute entropies from the covariance matrix of atomic fluctuations using molecular dynamics (MD) simulations is presented. Calculations for a set of organic compounds in the gas phase are compared to the corresponding statistical thermodynamics results for translational and rotational entropies and to experimental data for vibrational entropies. Encouraging agreement is obtained for translational entropies, but for the rotational contribution, both methods fail to reproduce the theoretically calculated values. Absolute and relative vibrational entropies are found to be better reproduced using quasiharmonic analysis compared to Schlitter's formula. For rotational entropies, we propose a method based on the variances in Euler angles, which gives good agreement with theory. Alternative methods for estimating translational entropies based on principal root mean-square (rms) fluctuations of the center of mass are also presented, and these reproduce theoretically calculated values well. These methodologies are applied to the binding of benzene to T4-lysozyme, where close agreement with the literature is obtained for translational and rotational entropies.

Molecular Dynamics Simulations of the Adipocyte Lipid Binding Protein Reveal a Novel Entry Site for the Ligand,

The adipocyte lipid binding protein (ALBP) binds fatty acids (FA) in a cavity that is inaccessible from the bulk. Therefore, the penetration of the FA necessitates conformational changes whose nature is still unknown. It was suggested that the lipid first enters through a "portal region" which consists of the alphaII helix and the adjacent tight turns. The initial event in the ligand binding must be the interaction of the lipid with the protein surface. To analyze this interaction, we have carried out three molecular dynamics simulations of the apo-ALBP, with a palmitate ion initially located at different positions near the protein surface. The simulation indicated that the ligand could adsorb to the protein in more than one location. Yet, in one case, the ligand managed to penetrate the protein by entering a newly formed cavity some 10 A deep. The entry site is located near the N-terminus, at the junction between the loops connecting the beta-strands. Further progression of the penetration seems to be arrested by the need for desolvation of the COOH end of the headgroup. Evolutionary analysis showed that amino acids in this entry site are well conserved. On the basis of these observations, we suggest that the ligand may enter the protein from a site other than the portal region. Furthermore, the rate-limiting step is proposed to be the desolvation of the FA polar headgroup.

Validation of the GROMOS force-field parameter set 45Alpha3 against nuclear magnetic resonance data of hen egg lysozyme

The quality of molecular dynamics (MD) simulations of proteins depends critically on the biomolecular force field that is used. Such force fields are defined by force-field parameter sets, which are generally determined and improved through calibration of properties of small molecules against experimental or theoretical data. By application to large molecules such as proteins, a new force-field parameter set can be validated. We report two 3.5 ns molecular dynamics simulations of hen egg white lysozyme in water applying the widely used GROMOS force-field parameter set 43Alpha1 and a new set 45Alpha3. The two MD ensembles are evaluated against NMR spectroscopic data NOE atom-atom distance bounds, (3)J(NHalpha) and (3)J(alphabeta) coupling constants, and (15)N relaxation data. It is shown that the two sets reproduce structural properties about equally well. The 45Alpha3 ensemble fulfills the atom-atom distance bounds derived from NMR spectroscopy slightly less well than the 43Alpha1 ensemble, with most of the NOE distance violations in both ensembles involving residues located in loops or flexible regions of the protein. Convergence patterns are very similar in both simulations atom-positional root-mean-square differences (RMSD) with respect to the X-ray and NMR model structures and NOE inter-proton distances converge within 1.0-1.5 ns while backbone (3)J(HNalpha)-coupling constants and (1)H-(15)N order parameters take slightly longer, 1.0-2.0 ns. As expected, side-chain (3)J(alphabeta)-coupling constants and (1)H-(15)N order parameters do not reach full convergence for all residues in the time period simulated. This is particularly noticeable for side chains which display rare structural transitions. When comparing each simulation trajectory with an older and a newer set of experimental NOE data on lysozyme, it is found that the newer, larger, set of experimental data agrees as well with each of the simulations. In other words, the experimental data converged towards the theoretical result.

A biomolecular force field based on the free enthalpy of hydration and solvation: the GROMOS force-field parameter sets 53A5 and 53A6

Successive parameterizations of the GROMOS force field have been used successfully to simulate biomolecular systems over a long period of time. The continuing expansion of computational power with time makes it possible to compute ever more properties for an increasing variety of molecular systems with greater precision. This has led to recurrent parameterizations of the GROMOS force field all aimed at achieving better agreement with experimental data. Here we report the results of the latest, extensive reparameterization of the GROMOS force field. In contrast to the parameterization of other biomolecular force fields, this parameterization of the GROMOS force field is based primarily on reproducing the free enthalpies of hydration and apolar solvation for a range of compounds. This approach was chosen because the relative free enthalpy of solvation between polar and apolar environments is a key property in many biomolecular processes of interest, such as protein folding, biomolecular association, membrane formation, and transport over membranes. The newest parameter sets, 53A5 and 53A6, were optimized by first fitting to reproduce the thermodynamic properties of pure liquids of a range of small polar molecules and the solvation free enthalpies of amino acid analogs in cyclohexane (53A5). The partial charges were then adjusted to reproduce the hydration free enthalpies in water (53A6). Both parameter sets are fully documented, and the differences between these and previous parameter sets are discussed.

Dynamics of water molecules buried in cavities of apolipoprotein E studied by molecular dynamics simulations and continuum electrostatic calculations

Molecular dynamics (MD) simulations of several nanoseconds each were used to monitor the dynamic behavior of the five crystal water molecules buried in the interior of the N-terminal domain of apolipoprotein E. These crystal water molecules are fairly well conserved in several apolipoprotein E structures, suggesting that they are not an artifact of the crystal and that they may have a structural and/or functional role for the protein. All five buried crystal water molecules leave the protein interior in the course of the longest simulations and exchange with water molecules from the bulk. The free energies of binding evaluated from the electrostatic binding free energy computed using a continuum model and estimates of the binding entropy changes represent shallow minima. The corresponding calculated residence times of the buried water molecules range from tens of picoseconds to hundreds of nanoseconds, which denote rather short times as for buried water molecules. Several water exchanges monitored in the simulations show that water molecules along the exit/entrance pathway use a relay of H bonds primarily formed with charged residues which helps either the exit or the entrance from or into the buried site. The exit/entrance of water molecules from/into the sites is permitted essentially by local motions of, at most, two side chains, indicating that, in these cases, complex correlated atomic motions are not needed to open the buried site toward the surface of the protein. This provides a possible explanation for the short residence times.

Water and urea interactions with the native and unfolded forms of a beta-barrel protein

A fundamental understanding of protein stability and the mechanism of denaturant action must ultimately rest on detailed knowledge about the structure, solvation, and energetics of the denatured state. Here, we use (17)O and (2)H magnetic relaxation dispersion (MRD) to study urea-induced denaturation of intestinal fatty acid-binding protein (I-FABP). MRD is among the few methods that can provide molecular-level information about protein solvation in native as well as denatured states, and it is used here to simultaneously monitor the interactions of urea and water with the unfolding protein. Whereas CD shows an apparently two-state transition, MRD reveals a more complex process involving at least two intermediates. At least one water molecule binds persistently (with residence time >10 nsec) to the protein even in 7.5 M urea, where the large internal binding cavity is disrupted and CD indicates a fully denatured protein. This may be the water molecule buried near the small hydrophobic folding core at the D-E turn in the native protein. The MRD data also provide insights about transient (residence time <1 nsec) interactions of urea and water with the native and denatured protein. In the denatured state, both water and urea rotation is much more retarded than for a fully solvated polypeptide. The MRD results support a picture of the denatured state where solvent penetrates relatively compact clusters of polypeptide segments.

MHC–Peptide Binding is Assisted by Bound Water Molecules

Water plays an important role in determining the high affinity of epitopes to the class I MHC complex. To study the energy and dynamics of water interactions in the complex we performed molecular dynamics simulation of the class I MHC-HLA2 complex bound to the HIV reverse transcriptase epitope, ILKEPVHGV, and in the absence of the epitope. Each simulation was extended for 5ns. We studied the processes of water penetration in the interface between MHC and peptide, and identified 14 water molecules that stay bound for periods longer than 1ns in regions previously identified by crystallography. These water molecules in the interface perform definite "tasks" contributing to the binding energy: hydrogen bond bridges between MHC and peptide and filling empty spaces in the groove which enhance affinity without contributing to epitope specificity. We calculate the binding energy for interfacial water molecules and find that there is an overall gain in free energy resulting from the formation of water clusters at the epitope-MHC interface. Water molecules serving the task of filling empty spaces bind at the interface with a net gain in entropy, relative to their entropy in bulk. We conclude that water molecules at the interface play the role of active mediators in the MHC-peptide interaction, and might be responsible for the large binding affinity of the MHC complex to a large number of epitope sequences.

Trifluoroethanol-induced beta --> alpha transition in beta-lactoglobulin: hydration and cosolvent binding studied by 2H, 17O, and 19F magnetic relaxation dispersion

Alcohols, such as 2,2,2-trifluoroethanol (TFE), have been shown to induce a cooperative transition to an open helical structure in many proteins, but the underlying molecular mechanism has not been identified. Here, we employ the technique of magnetic relaxation dispersion (MRD) to study the TFE-induced beta --> alpha transition of beta-lactoglobulin at pH 2.4. Unlike traditional techniques that focus on protein secondary structure, the MRD method directly monitors the solvent, providing quantitative information about preferential solvation and solvent penetration and about the overall size and structural integrity of the protein. In this multinuclear MRD study, we use the (2)H and (17)O resonances to examine hydration and the (19)F resonance to study TFE. The transformation from the native to the helical state via an intermediate state at 300 K is found to be accompanied by a progressive expansion of the protein and loss of specific long-lived hydration sites. The observation of (17)O and (19)F dispersions from the helical state shows that water and TFE penetrate the protein. The MRD data indicate a strong accumulation of TFE at the surface as well as in the interior of the protein. At 277 K, BLG is much less affected by TFE, remaining in the native state at 16% TFE, but adopting a nonnative structure at 30% TFE. This nonnative structure is not penetrated by long-lived water molecules. The implications of these findings for the mechanism of TFE-induced structural transformations are discussed.

Water dynamics in the large cavity of three lipid-binding proteins monitored by (17)O magnetic relaxation dispersion

Intracellular lipid-binding proteins contain a large binding cavity filled with water molecules. The role played by these water molecules in ligand binding is not well understood, but their energetic and dynamic properties must be important for protein function. Here, we use the magnetic relaxation dispersion (MRD) of the water 17O resonance to investigate the water molecules in the binding cavity of three different lipid-binding proteins: heart fatty acid-binding protein (H-FABP), ileal lipid-binding protein (I-LBP) and intestinal fatty acid-binding protein (I-FABP). Whereas about half of the crystallographically visible water molecules appear to be expelled by the ligand, we find that ligand binding actually increases the number of water molecules within the cavity. At 300 K, the water molecules in the cavity exchange positions on a time-scale of about 1ns and exchange with external water on longer time-scales (0.01-1 micros). Exchange of water molecules among hydration sites within the cavity should be strongly coupled to ligand motion. Whereas a recent MD simulation indicates that the structure of the cavity water resembles a bulk water droplet, the present MRD results show that its dynamics is more than two orders of magnitude slower than in the bulk. These findings may have significant implications for the strength, specificity and kinetics of lipid binding.

Protein stability and plasticity of the hydrophobic cavity in wheat ns-LTP

Plant ns-LTPs display an original structure with four helices and a flexible C-terminus, maintained together by four disulphide bridges and delineating an elongated central hydrophobic cavity. In order to relate these structural features to the protein stability and plasticity, combined molecular mechanics and simulated annealing calculations were undertaken on a wheat ns-LTP "mutant" with Cys-Ala replacement and with the application of core inter-residue restraints up to 2 A, reducing the cross-section size of the hydrophobic cavity. Analysis of the energy-minimized structures shows that removal of the disulphide bridges results in structures with a lower total energy and a smaller cavity volume. A 1-ns MD simulation at 300K in water, underlines that, despite the absence of a well-packed hydrophobic core, the native structure is extremely stable at room temperature and the cavity is not hydrated. This confirms that the disulphide bridges are essential for the existence of the cavity, whereas its plasticity depends both on the hydrophobic chain lining the cavity and on the C-terminal flexibility. A high temperature (500K) MD simulation confirms the stability of the secondary structure elements and the flexibility of the loops and of the C-terminal segment. Two important structural transitions during this simulation are discussed and possible routes for the insertion and release of hydrophobic ligands are suggested.

Static and dynamic water molecules in Cu,Zn superoxide dismutase

Understanding protein hydration is a crucial, and often underestimated issue, in unraveling protein function. Molecular dynamics (MD) computer simulation can provide a microscopic description of the water behavior. We have applied such a simulative approach to dimeric Photobacterium leiognathi Cu,Zn superoxide dismutase, comparing the water molecule sites determined using 1.0 ns MD simulation with those detected by X-ray crystallography. Of the water molecules detected by the two techniques, 20% fall at common sites. These are evenly distributed over the protein surface and located around crevices, which represent the preferred hydration sites. The water mean residence time, estimated by means of a survival probability function on a given protein hydration shell, is relatively short and increases for low accessibility sites constituted by polar atoms. Water molecules trapped in the dimeric protein intersubunit cavity, as identified in the crystal structure, display a trajectory mainly confined within the cavity. The simulation shows that these water molecules are characterized by relatively short residence times, because they continuously change from one site to another within the cavity, thus hinting at the absence of any relationship between spatial and temporal order for solvent molecules in proximity of protein surface.