Influence of temperature, friction, and random forces on folding of the B-domain of staphylococcal protein A: All-atom molecular dynamics in implicit solvent

Evaluation of alternate hosts for recombinant expression of a reductive dehalogenase

Organohalides are recalcitrant, toxic environmental pollutants. Reductive dehalogenase enzymes (RDases) found in organohalide respiring bacteria (OHRB) utilise organohalides as electron acceptors for cellular energy and growth, producing lesser-halogenated compounds. Consequently, microbial reductive dehalogenation via organohalide respiration represents a promising solution for clean-up of organohalide pollutants. Dehalobacter sp. UNSWDHB is an OHRB capable of respiring highly toxic chloroform (CF) and converting it to dichloromethane (DCM). TmrA has been identified as an RDase responsible for this conversion and different strategies for generation of functional recombinant TmrA is the focus of this article. In this study, TmrA was recovered from inclusion bodies expressed in E. coli and refolded in the presence of FeCl3, Na2S and cobalamin to yield functional enzyme. TmrA has been previously expressed in a soluble and functional form in the corrinoid-producing Bacillus megaterium. Using a fractional experimental design for cultivation and induction combined with purification under anaerobic conditions resulted in substantially higher activity of recombinant and native TmrA than previously reported. TmrA was then expressed in a soluble and active form in Shimwellia blattae. Co-expression with two different putative chaperone proteins from the original host did not increase the level of soluble expression in S. blattae, however activity assays showed that removing the TAT signal from TmrA increases the dechlorination activity compared to when the TAT signal is present. Finally, TmrA was successfully expressed in a soluble and active form in the H2-oxidizing C. necator H16, a novel host for the expression of RDases.

A Closed-Form, Analytical Approximation for Apparent Surface Charge and Electric Field of Molecules

Closed-form, analytical approximations for electrostatic properties of molecules are of unique value as these can provide computational speed, versatility, and physical insight. Here, we have derived a simple, closed-form formula for the apparent surface charge (ASC) as well as for the electric field generated by a molecular charge distribution in aqueous solution. The approximation, with no fitted parameters, was tested against numerical solutions of the Poisson equation, where it has produced a significant speed-up. For neutral small molecules, the hydration free energies estimated from the closed-form ASC formula are within 0.8 kcal/mol RMSD from the numerical Poisson reference; the electric field at the surface is in quantitative agreement with the reference. Performance of the approximation was also tested on larger structures, including a protein, a DNA fragment, and a viral receptor-target complex. For all structures tested, a near-quantitative agreement with the numerical Poisson reference was achieved, except in regions of high negative curvature, where the new approximation is still qualitatively correct. A unique efficiency feature of the proposed "source-based″ closed-form approximation is that the ASC and electric field can be estimated individually at any point or surface patch, without the need to obtain the full global solution. An open-source software implementation of the method is available: https://people.cs.vt.edu/~onufriev/CODES/aasc.zip.

Implicit Solvent Model for Million-Atom Atomistic Simulations: Insights into the Organization of 30-nm Chromatin Fiber

Molecular dynamics (MD) simulations based on the implicit solvent generalized Born (GB) models can provide significant computational advantages over the traditional explicit solvent simulations. However, the standard GB becomes prohibitively expensive for all-atom simulations of large structures; the model scales poorly, ∼n2, with the number of solute atoms. Here we combine our recently developed optimal point charge approximation (OPCA) with the hierarchical charge partitioning (HCP) approximation to present an ∼n log n multiscale, yet fully atomistic, GB model (GB-HCPO). The HCP approximation exploits the natural organization of biomolecules (atoms, groups, chains, and complexes) to partition the structure into multiple hierarchical levels of components. OPCA approximates the charge distribution for each of these components by a small number of point charges so that the low order multipole moments of these components are optimally reproduced. The approximate charges are then used for computing electrostatic interactions with distant components, while the full set of atomic charges are used for nearby components. We show that GB-HCPO can deliver up to 2 orders of magnitude speedup compared to the standard GB, with minimal impact on its accuracy. For large structures, GB-HCPO can approach the same nominal speed, as in nanoseconds per day, as the highly optimized explicit-solvent simulation based on particle mesh Ewald (PME). The increase in the nominal simulation speed, relative to the standard GB, coupled with substantially faster sampling of conformational space, relative to the explicit solvent, makes GB-HCPO a suitable candidate for MD simulation of large atomistic systems in implicit solvent. As a practical demonstration, we use GB-HCPO simulation to refine a ∼1.16 million atom structure of 30 nm chromatin fiber (40 nucleosomes). The refined structure suggests important details about spatial organization of the linker DNA and the histone tails in the fiber: (1) the linker DNA fills the core region, allowing the H3 histone tails to interact with the linker DNA, which is consistent with experiment; (2) H3 and H4 tails are found mostly in the core of the structure, closer to the helical axis of the fiber, while H2A and H2B are mostly solvent exposed. Potential functional consequences of these findings are discussed. GB-HCPO is implemented in the open source MD software NAB in Amber 2016.

Speed of conformational change: comparing explicit and implicit solvent molecular dynamics simulations

Adequate sampling of conformation space remains challenging in atomistic simulations, especially if the solvent is treated explicitly. Implicit-solvent simulations can speed up conformational sampling significantly. We compare the speed of conformational sampling between two commonly used methods of each class: the explicit-solvent particle mesh Ewald (PME) with TIP3P water model and a popular generalized Born (GB) implicit-solvent model, as implemented in the AMBER package. We systematically investigate small (dihedral angle flips in a protein), large (nucleosome tail collapse and DNA unwrapping), and mixed (folding of a miniprotein) conformational changes, with nominal simulation times ranging from nanoseconds to microseconds depending on system size. The speedups in conformational sampling for GB relative to PME simulations, are highly system- and problem-dependent. Where the simulation temperatures for PME and GB are the same, the corresponding speedups are approximately onefold (small conformational changes), between ∼1- and ∼100-fold (large changes), and approximately sevenfold (mixed case). The effects of temperature on speedup and free-energy landscapes, which may differ substantially between the solvent models, are discussed in detail for the case of miniprotein folding. In addition to speeding up conformational sampling, due to algorithmic differences, the implicit solvent model can be computationally faster for small systems or slower for large systems, depending on the number of solute and solvent atoms. For the conformational changes considered here, the combined speedups are approximately twofold, ∼1- to 60-fold, and ∼50-fold, respectively, in the low solvent viscosity regime afforded by the implicit solvent. For all the systems studied, 1) conformational sampling speedup increases as Langevin collision frequency (effective viscosity) decreases; and 2) conformational sampling speedup is mainly due to reduction in solvent viscosity rather than possible differences in free-energy landscapes between the solvent models.

Effect of fullerenol surface chemistry on nanoparticle binding-induced protein misfolding

Fullerene and its derivatives with different surface chemistry have great potential in biomedical applications. Accordingly, it is important to delineate the impact of these carbon-based nanoparticles on protein structure, dynamics, and subsequently function. Here, we focused on the effect of hydroxylation - a common strategy for solubilizing and functionalizing fullerene - on protein-nanoparticle interactions using a model protein, ubiquitin. We applied a set of complementary computational modeling methods, including docking and molecular dynamics simulations with both explicit and implicit solvent, to illustrate the impact of hydroxylated fullerenes on the structure and dynamics of ubiquitin. We found that all derivatives bound to the model protein. Specifically, the more hydrophilic nanoparticles with a higher number of hydroxyl groups bound to the surface of the protein via hydrogen bonds, which stabilized the protein without inducing large conformational changes in the protein structure. In contrast, fullerene derivatives with a smaller number of hydroxyl groups buried their hydrophobic surface inside the protein, thereby causing protein denaturation. Overall, our results revealed a distinct role of surface chemistry on nanoparticle-protein binding and binding-induced protein misfolding.

Introducing Charge Hydration Asymmetry into the Generalized Born Model

The effect of charge hydration asymmetry (CHA)-non-invariance of solvation free energy upon solute charge inversion-is missing from the standard linear response continuum electrostatics. The proposed charge hydration asymmetric-generalized Born (CHA-GB) approximation introduces this effect into the popular generalized Born (GB) model. The CHA is added to the GB equation via an analytical correction that quantifies the specific propensity of CHA of a given water model; the latter is determined by the charge distribution within the water model. Significant variations in CHA seen in explicit water (TIP3P, TIP4P-Ew, and TIP5P-E) free energy calculations on charge-inverted "molecular bracelets" are closely reproduced by CHA-GB, with the accuracy similar to models such as SEA and 3D-RISM that go beyond the linear response. Compared against reference explicit (TIP3P) electrostatic solvation free energies, CHA-GB shows about a 40% improvement in accuracy over the canonical GB, tested on a diverse set of 248 rigid small neutral molecules (root mean square error, rmse = 0.88 kcal/mol for CHA-GB vs 1.24 kcal/mol for GB) and 48 conformations of amino acid analogs (rmse = 0.81 kcal/mol vs 1.26 kcal/mol). CHA-GB employs a novel definition of the dielectric boundary that does not subsume the CHA effects into the intrinsic atomic radii. The strategy leads to finding a new set of intrinsic atomic radii optimized for CHA-GB; these radii show physically meaningful variation with the atom type, in contrast to the radii set optimized for GB. Compared to several popular radii sets used with the original GB model, the new radii set shows better transferability between different classes of molecules.

Hidden protein folding pathways in free-energy landscapes uncovered by network analysis

A network analysis is used to uncover hidden folding pathways in free-energy landscapes usually defined in terms of such arbitrary order parameters as root-mean-square deviation from the native structure, radius of gyration, etc. The analysis has been applied to molecular dynamics (MD) trajectories of the B-domain of staphylococcal protein A, generated with the coarse-grained united-residue (UNRES) force field in a broad range of temperatures (270K ≤ T ≤ 325K). Thousands of folding pathways have been identified at each temperature. Out of these many folding pathways, several most probable ones were selected for investigation of the conformational transitions during protein folding. Unlike other conformational space network (CSN) methods, a node in the CSN variant implemented in this work is defined according to the nativelikeness class of the structure, which defines the similarity of segments of the compared structures in terms of secondary-structure, contact-pattern, and local geometry, as well as the overall geometric similarity of the conformation under consideration to that of the reference (experimental) structure. Our previous findings, regarding the folding model and conformations found at the folding-transition temperature for protein A (Maisuradze et al., J. Am. Chem. Soc. 132, 9444, 2010), were confirmed by the conformational space network analysis. In the methodology and in the analysis of the results, the shortest path identified by using the shortest-path algorithm corresponds to the most probable folding pathway in the conformational space network.

A strategy for reducing gross errors in the generalized Born models of implicit solvation

The "canonical" generalized Born (GB) formula [C. Still, A. Tempczyk, R. C. Hawley, and T. Hendrickson, J. Am. Chem. Soc. 112, 6127 (1990)] is known to provide accurate estimates for total electrostatic solvation energies ΔG(el) of biomolecules if the corresponding effective Born radii are accurate. Here we show that even if the effective Born radii are perfectly accurate, the canonical formula still exhibits significant number of gross errors (errors larger than 2k(B)T relative to numerical Poisson equation reference) in pairwise interactions between individual atomic charges. Analysis of exact analytical solutions of the Poisson equation (PE) for several idealized nonspherical geometries reveals two distinct spatial modes of the PE solution; these modes are also found in realistic biomolecular shapes. The canonical GB Green function misses one of two modes seen in the exact PE solution, which explains the observed gross errors. To address the problem and reduce gross errors of the GB formalism, we have used exact PE solutions for idealized nonspherical geometries to suggest an alternative analytical Green function to replace the canonical GB formula. The proposed functional form is mathematically nearly as simple as the original, but depends not only on the effective Born radii but also on their gradients, which allows for better representation of details of nonspherical molecular shapes. In particular, the proposed functional form captures both modes of the PE solution seen in nonspherical geometries. Tests on realistic biomolecular structures ranging from small peptides to medium size proteins show that the proposed functional form reduces gross pairwise errors in all cases, with the amount of reduction varying from more than an order of magnitude for small structures to a factor of 2 for the largest ones.

Computational model for protein unfolding simulation

The protein folding problem is one of the fundamental and important questions in molecular biology. However, the all-atom molecular dynamics studies of protein folding and unfolding are still computationally expensive and severely limited by the time scale of simulation. In this paper, a simple and fast protein unfolding method is proposed based on the conformational stability analyses and structure modeling. In this method, two structure-based conditions are considered to identify the unstable regions of proteins during the unfolding processes. The protein unfolding trajectories are mimicked through iterative structure modeling according to conformational stability analyses. Two proteins, chymotrypsin inhibitor 2 (CI2) and α -spectrin SH3 domain (SH3) were simulated by this method. Their unfolding pathways are consistent with the previous molecular dynamics simulations. Furthermore, the transition states of the two proteins were identified in unfolding processes and the theoretical Φ values of these transition states showed significant correlations with the experimental data (the correlation coefficients are >0.8). The results indicate that this method is effective in studying protein unfolding. Moreover, we analyzed and discussed the influence of parameters on the unfolding simulation. This simple coarse-grained model may provide a general and fast approach for the mechanism studies of protein folding.

Evidence, from simulations, of a single state with residual native structure at the thermal denaturation midpoint of a small globular protein

The folding of the B-domain of staphylococcal protein A has been studied by coarse-grained canonical and multiplexed replica-exchange molecular dynamics simulations with the UNRES force field in a broad range of temperatures (270 K < or = T < or = 350 K). In canonical simulations, the folding was found to occur either directly to the native state or through kinetic traps, mainly the topological mirror image of the native three-helix bundle. The latter folding scenario was observed more frequently at low temperatures. With increase of temperature, the frequency of the transitions between the folded and misfolded/unfolded states increased and the folded state became more diffuse with conformations exhibiting increased root-mean-square deviations from the experimental structure (from about 4 A at T = 300 K to 8.7 A at T = 325 K). An analysis of the equilibrium conformational ensemble determined from multiplexed replica exchange simulations at the folding-transition temperature (T(f) = 325 K) showed that the conformational ensemble at this temperature is a collection of conformations with residual secondary structures, which possess native or near-native clusters of nonpolar residues in place, and not a 50-50% mixture of fully folded and fully unfolded conformations. These findings contradict the quasi-chemical picture of two- or multistate protein folding, which assumes an equilibrium between the folded, unfolded, and intermediate states, with equilibrium shifting with temperature but with the native conformations remaining essentially unchanged. Our results also suggest that long-range hydrophobic contacts are the essential factor to keep the structure of a protein thermally stable.

Folding simulations of a de novo designed protein with a betaalphabeta fold

betaalphabeta structural motifs are commonly used building blocks in protein structures containing parallel beta-sheets. However, to our knowledge, no stand-alone betaalphabeta structure has been observed in nature to date. Recently, for the first time that we know of, a small protein with an independent betaalphabeta structure (DS119) was successfully designed in our laboratory. To understand the folding mechanism of DS119, in the study described here, we carried out all-atom molecular dynamics and coarse-grained simulations to investigate its folding pathways and energy landscape. From all-atom simulations, we successfully observed the folding event and got a stable folded structure with a minimal root mean-square deviation of 2.6 A with respect to the NMR structure. The folding process can be described as a fast collapse phase followed by rapid formation of the central helix, and then slow formation of a parallel beta-sheet. By using a native-centric Gō-like model, the cooperativity of the system was characterized in terms of the calorimetric criterion, sigmoidal transitions, conformation distribution shifts, and free-energy profiles. DS119 was found to be an incipient downhill folder that folds more cooperatively than a downhill folder, but less cooperatively than a two-state folder. This may reflect the balance between the two structural elements of DS119: the rapidly formed alpha-helix and the slowly formed parallel beta-sheet. Folding times estimated from both the all-atom simulations and the coarse-grained model were at microsecond level, making DS119 another fast folder. Compared to fast folders reported previously, DS119 is, to the best of our knowledge, the first that exhibits a parallel beta-sheet.

A fast method for large-scale de novo peptide and miniprotein structure prediction

Although peptides have many biological and biomedical implications, an accurate method predicting their equilibrium structural ensembles from amino acid sequences and suitable for large-scale experiments is still missing. We introduce a new approach-PEP-FOLD-to the de novo prediction of peptides and miniproteins. It first predicts, in the terms of a Hidden Markov Model-derived structural alphabet, a limited number of local conformations at each position of the structure. It then performs their assembly using a greedy procedure driven by a coarse-grained energy score. On a benchmark of 52 peptides with 9-23 amino acids, PEP-FOLD generates lowest-energy conformations within 2.8 and 2.3 A Calpha root-mean-square deviation from the full nuclear magnetic resonance structures (NMR) and the NMR rigid cores, respectively, outperforming previous approaches. For 13 miniproteins with 27-49 amino acids, PEP-FOLD reaches an accuracy of 3.6 and 4.6 A Calpha root-mean-square deviation for the most-native and lowest-energy conformations, using the nonflexible regions identified by NMR. PEP-FOLD simulations are fast-a few minutes only-opening therefore, the door to in silico large-scale rational design of new bioactive peptides and miniproteins.

Investigation of protein folding by coarse-grained molecular dynamics with the UNRES force field

Coarse-grained molecular dynamics simulations offer a dramatic extension of the time-scale of simulations compared to all-atom approaches. In this article, we describe the use of the physics-based united-residue (UNRES) force field, developed in our laboratory, in protein-structure simulations. We demonstrate that this force field offers about a 4000-times extension of the simulation time scale; this feature arises both from averaging out the fast-moving degrees of freedom and reduction of the cost of energy and force calculations compared to all-atom approaches with explicit solvent. With massively parallel computers, microsecond folding simulation times of proteins containing about 1000 residues can be obtained in days. A straightforward application of canonical UNRES/MD simulations, demonstrated with the example of the N-terminal part of the B-domain of staphylococcal protein A (PDB code: 1BDD, a three-alpha-helix bundle), discerns the folding mechanism and determines kinetic parameters by parallel simulations of several hundred or more trajectories. Use of generalized-ensemble techniques, of which the multiplexed replica exchange method proved to be the most effective, enables us to compute thermodynamics of folding and carry out fully physics-based prediction of protein structure, in which the predicted structure is determined as a mean over the most populated ensemble below the folding-transition temperature. By using principal component analysis of the UNRES folding trajectories of the formin-binding protein WW domain (PDB code: 1E0L; a three-stranded antiparallel beta-sheet) and 1BDD, we identified representative structures along the folding pathways and demonstrated that only a few (low-indexed) principal components can capture the main structural features of a protein-folding trajectory; the potentials of mean force calculated along these essential modes exhibit multiple minima, as opposed to those along the remaining modes that are unimodal. In addition, a comparison between the structures that are representative of the minima in the free-energy profile along the essential collective coordinates of protein folding (computed by principal component analysis) and the free-energy profile projected along the virtual-bond dihedral angles gamma of the backbone revealed the key residues involved in the transitions between the different basins of the folding free-energy profile, in agreement with existing experimental data for 1E0L .

Relation between free energy landscapes of proteins and dynamics

By examining the molecular dynamics (MD) of protein folding trajectories, generated with the coarse-grained UNRES force field, for the B-domain of staphylococcal protein A and the triple β-strand WW domain from the Formin binding protein 28 (FBP), by principal component analysis (PCA), it is demonstrated how different free energy landscapes (FELs) and folding pathways of trajectories can be, even though they appear to be very similar by visual inspection of the time-dependence of the root-mean-square deviation (rmsd). Approaches to determine the minimal dimensionality of FELs for a correct description of protein folding dynamics are discussed. The correlation between the amplitude of the fluctuations of proteins and the dimensionality of the FELs is shown. The advantage of internal coordinate PCA over Cartesian PCA for small proteins is also illustrated.

Quantifying the structural requirements of the folding transition state of protein A and other systems

The B-domain of protein A is a small three-helix bundle that has been the subject of considerable experimental and theoretical investigation. Nevertheless, a unified view of the structure of the transition-state ensemble (TSE) is still lacking. To characterize the TSE of this surprisingly challenging protein, we apply a combination of psi analysis (which probes the role of specific side-chain to side-chain contacts) and kinetic H/D amide isotope effects (which measures hydrogen-bond content), building upon previous studies using mutational phi analysis (which probes the energetic influence of side-chain substitutions). The second helix is folded in the TSE, while helix formation appears just at the carboxy and amino termini of the first and third helices, respectively. The experimental data suggest a homogenous yet plastic TS with a native-like topology. This study generalizes our earlier conclusion, based on two larger alpha/beta proteins, that the TSEs of most small proteins achieve approximately 70% of their native state's relative contact order. This high percentage limits the degree of possible TS heterogeneity and requires a reevaluation of the structural content of the TSE of other proteins, especially when they are characterized as small or polarized.

Folding processes of the B domain of protein A to the native state observed in all-atom ab initio folding simulations

Reaching the native states of small proteins, a necessary step towards a comprehensive understanding of the folding mechanisms, has remained a tremendous challenge to ab initio protein folding simulations despite the extensive effort. In this work, the folding process of the B domain of protein A (BdpA) has been simulated by both conventional and replica exchange molecular dynamics using AMBER FF03 all-atom force field. Started from an extended chain, a total of 40 conventional (each to 1.0 micros) and two sets of replica exchange (each to 200.0 ns per replica) molecular dynamics simulations were performed with different generalized-Born solvation models and temperature control schemes. The improvements in both the force field and solvent model allowed successful simulations of the folding process to the native state as demonstrated by the 0.80 A C(alpha) root mean square deviation (RMSD) of the best folded structure. The most populated conformation was the native folded structure with a high population. This was a significant improvement over the 2.8 A C(alpha) RMSD of the best nativelike structures from previous ab initio folding studies on BdpA. To the best of our knowledge, our results demonstrate, for the first time, that ab initio simulations can reach the native state of BdpA. Consistent with experimental observations, including Phi-value analyses, formation of helix II/III hairpin was a crucial step that provides a template upon which helix I could form and the folding process could complete. Early formation of helix III was observed which is consistent with the experimental results of higher residual helical content of isolated helix III among the three helices. The calculated temperature-dependent profile and the melting temperature were in close agreement with the experimental results. The simulations further revealed that phenylalanine 31 may play critical to achieve the correct packing of the three helices which is consistent with the experimental observation. In addition to the mechanistic studies, an ab initio structure prediction was also conducted based on both the physical energy and a statistical potential. Based on the lowest physical energy, the predicted structure was 2.0 A C(alpha) RMSD away from the experimentally determined structure.

From helix-coil transitions to protein folding

An evolution of procedures to simulate protein structure and folding pathways is described. From an initial focus on the helix-coil transition and on hydrogen-bonding and hydrophobic interactions, our original attempts to determine protein structure and folding pathways were based on an experimental approach. Experiments on the oxidative folding of reduced bovine pancreatic ribonuclease A (RNase A) led to a mechanism by which the molecule folded to the native structure by a minimum of four different pathways. The experiments with RNase A were followed by development of a molecular mechanics approach, first, making use of global optimization procedures and then with molecular dynamics (MD), evolving from an all-atom to a united-residue model. This hierarchical MD approach facilitated probing of the folding trajectory to longer time scales than with all-atom MD, and hence led to the determination of complete folding trajectories, thus far for a protein containing as many as 75 amino acid residues. With increasing refinement of the computational procedures, the computed results are coming closer to experimental observations, providing an understanding as to how physics directs the folding process.

Recent advances in implicit solvent-based methods for biomolecular simulations

Implicit solvent-based methods play an increasingly important role in molecular modeling of biomolecular structure and dynamics. Recent methodological developments have mainly focused on the extension of the generalized Born (GB) formalism for variable dielectric environments and accurate treatment of nonpolar solvation. Extensive efforts in parameterization of GB models and implicit solvent force fields have enabled ab initio simulation of protein folding to native or near-native structures. Another exciting area that has benefited from the advances in implicit solvent models is the development of constant pH molecular dynamics methods, which have recently been applied to the calculations of protein pK(a) values and the studies of pH-dependent peptide and protein folding.

Implicit modeling of nonpolar solvation for simulating protein folding and conformational transitions

Accurate description of the solvent environment is critical in computer simulations of protein structure and dynamics. An implicit treatment of solvent aims to capture the mean influence of water molecules on the solute via direct estimation of the solvation free energy. It has emerged as a powerful alternative to explicit solvent, and provides a favorable compromise between computational cost and level of detail. We review the current theory and techniques for implicit modeling of nonpolar solvation in the context of simulating protein folding and conformational transitions, and discuss the main directions for further development. It is demonstrated that the current surface area based nonpolar models have severe limitations, including insufficient description of the conformational dependence of solvation, over-estimation of the strength of pair-wise nonpolar interactions, and incorrect prediction of anti-cooperativity for three-body hydrophobic associations. We argue that, to improve beyond current level of accuracy of implicit solvent models, two important aspects of nonpolar solvation need to be incorporated, namely, the length-scale dependence of hydrophobic association and solvent screening of solute-solute dispersion interactions. We recognize that substantial challenges exist in constructing a sufficiently balanced, yet reasonably efficient, implicit solvent protein force field. Nonetheless, most of the fundamental problems are understood, and exciting progress has been made over the last few years. We believe that continual work along the frontiers outlined will greatly improve one's ability to study protein folding and large conformational transitions at atomistic detail.

Revisiting the carboxylic acid dimers in aqueous solution: interplay of hydrogen bonding, hydrophobic interactions, and entropy

Carboxylic acid dimers are useful model systems for understanding the interplay of hydrogen bonding, hydrophobic effects, and entropy in self-association and assembly. Through extensive sampling with a classical force field and careful free energy analysis, it is demonstrated that both hydrogen bonding and hydrophobic interactions are indeed important for dimerization of carboxylic acids (except formic acid). The dimers are only weakly ordered, and the degree of ordering increases with stronger hydrophobic interactions between longer alkyl chains. Comparison of calculated and experimental dimerization constants reveals a systematic tendency for excessive self-aggregation in current classical force fields. Qualitative and quantitative information on the thermodynamics of hydrogen bonding and hydrophobic interactions derived from these simulations is in excellent agreement with existing results from experiment and theory. These results provide a verification from first principles of previous estimations based on two statistical mechanical hydrophobic theories. We also revisit and clarify the fundamental statistical thermodynamics formalism for calculating absolute binding constants, external entropy, and solvation entropy changes upon association from detailed free energy simulations. This analysis is believed to be useful for a wide range of applications including computational studies of protein-ligand and protein-protein binding.