Concepts and protocols for electrostatic free energies

Alchemical Free Energy Calculations on Membrane-Associated Proteins

Membrane proteins have diverse functions within cells and are well-established drug targets. The advances in membrane protein structural biology have revealed drug and lipid binding sites on membrane proteins, while computational methods such as molecular simulations can resolve the thermodynamic basis of these interactions. Particularly, alchemical free energy calculations have shown promise in the calculation of reliable and reproducible binding free energies of protein-ligand and protein-lipid complexes in membrane-associated systems. In this review, we present an overview of representative alchemical free energy studies on G-protein-coupled receptors, ion channels, transporters as well as protein-lipid interactions, with emphasis on best practices and critical aspects of running these simulations. Additionally, we analyze challenges and successes when running alchemical free energy calculations on membrane-associated proteins. Finally, we highlight the value of alchemical free energy calculations calculations in drug discovery and their applicability in the pharmaceutical industry.

Accurate Host-Guest Binding Free Energies Using the AMOEBA Polarizable Force Field

A grand challenge of computational biophysics is accurate prediction of interactions between molecules. Molecular dynamics (MD) simulations have recently gained much interest as a tool to directly compute rigorous intermolecular binding affinities. The choice of a fixed point-charge or polarizable multipole force field used in MD is a topic of ongoing discussion. To compare alternative methods, we participated in the SAMPL7 and SAMPL8 Gibb octaacid host-guest challenges to assess the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) polarizable multipole force field. Advantages of AMOEBA over fixed charge models include improved representation of molecular electrostatic potentials and better description of water occupying the unligated host cavity. Prospective predictions for 26 host-guest systems exhibit a mean unsigned error vs experiment of 0.848 kcal/mol across all absolute binding free energies, demonstrating excellent agreement between computational and experimental results. In addition, we explore two topics related to the inclusion of ions in MD simulations: use of a neutral co-alchemical protocol and the effect of salt concentration on binding affinity. Use of the co-alchemical method minimally affects computed energies, but salt concentration significantly perturbs our binding results. Higher salt concentration strengthens binding through classical charge screening. In particular, added Na+ ions screen negatively charged carboxylate groups near the binding cavity, thereby diminishing repulsive coulomb interactions with negatively charged guests. Overall, the AMOEBA results demonstrate the accuracy available through a force field providing a detailed energetic description of the four octaacid hosts and 13 charged organic guests. Use of the AMOEBA polarizable atomic multipole force field in conjunction with an alchemical free energy protocol can achieve chemical accuracy in application to realistic molecular systems.

Consistent Picture of Phosphate-Divalent Cation Binding from Models with Implicit and Explicit Electronic Polarization

The binding of divalent cations to the ubiquitous phosphate group is essential for a number of key biological processes, such as DNA compaction, RNA folding, or interactions of some proteins with membranes. Yet, probing their binding sites, modes, and associated binding free energy is a challenge for both experiments and simulations. In simulations, standard force fields strongly overestimate the interaction between phosphate groups and divalent cations. Here, we examine how different strategies to include electronic polarization effects in force fields─implicitly, through the use of scaled charges or pair-specific Lennard-Jones parameters, or explicitly, with the polarizable force fields Drude and AMOEBA─capture the interactions of a model phosphate compound, dimethyl phosphate, with calcium and magnesium divalent cations. We show that both implicit and explicit approaches, when carefully parameterized, are successful in capturing the overall binding free energy and that common trends emerge from the comparison of different simulation approaches. Overall, the binding is very moderate, slightly weaker for Ca²⁺ than Mg²⁺, and the solvent-shared ion pair is slightly more stable than the contact monodentate ion pair. The bidentate ion pair is higher in energy (or even fully unstable for Mg²⁺). Our results thus suggest practical ways to capture the divalent cations with biomolecular phosphate groups in complex biochemical systems. In particular, the computational efficiency of implicit models makes them ideally suited for large-scale simulations of biological assemblies, with improved accuracy compared to state-of-the-art fixed-charge force fields.

Correction Schemes for Absolute Binding Free Energies Involving Lipid Bilayers

Absolute binding free-energy (ABFE) calculations are playing an increasing role in drug design, especially as they can be performed on a range of disparate compounds and direct comparisons between them can be made. It is, however, especially important to ensure that they are as accurate as possible, as unlike relative binding free-energy (RBFE) calculations, one does not benefit as much from a cancellation of errors during the calculations. In most modern implementations of ABFE calculations, a particle mesh Ewald scheme is typically used to treat the electrostatic contribution to the free energy. A central requirement of such schemes is that the box preserves neutrality throughout the calculation. There are many ways to deal with this problem that have been discussed over the years ranging from a neutralizing plasma with a post hoc correction term through to a simple co-alchemical ion within the same box. The post hoc correction approach is the most widespread. However, the vast majority of these studies have been applied to a soluble protein in a homogeneous solvent (water or salt solution). In this work, we explore which of the more common approaches would be the most suitable for a simulation box with a lipid bilayer within it. We further develop the idea of the so-called Rocklin correction for lipid-bilayer systems and show how such a correction could work. However, we also show that it will be difficult to make this generalizable in a practical way and thus we conclude that the use of a “co-alchemical ion” is the most useful approach for simulations involving lipid membrane systems.

Molecular Simulation of Stapled Peptides

Constrained peptides represent a relatively new class of biologic therapeutics, which have the potential to overcome several limitations of small-molecule drugs, and of designed antibodies. Because of their modest size, the rational design of such peptides is becoming increasingly amenable to computer simulation; multi-microsecond molecular dynamic (MD) simulations are now routinely possible on consumer-grade graphical processors (GPUs). Here, we describe the procedures for performing and analyzing MD simulations of hydrocarbon-stapled peptides using the CHARMM energy function, in isolation and in complex with a binding partner, to investigate their conformational properties and to compute changes in their binding affinity upon mutation.

Molecular dynamics free energy simulations of ATP:Mg2+ and ADP:Mg2+ using the polarizable force field AMOEBA

ATPases and GTPases are two important classes of protein that play critical roles in energy transduction, cellular signaling, gene regulation and catalysis. These proteins use cofactors such as nucleoside di and tri-phosphates (NTP, NDP) and can detect the difference between NDP and NTP which then induce different protein conformations. Mechanisms that drive proteins into the NTP or NDP conformation may depend on factors such as ligand structure and how Mg²⁺ coordinates with the ligand, amino acids in the pocket and water molecules. Here, we have used the advanced electrostatic and polarizable force field AMOEBA and molecular dynamics free energy simulations (MDFE) to examine the various binding mechanisms of ATP:Mg²⁺ and ADP:Mg²⁺.We compared the ATP:Mg²⁺ binding with previous studies using non-polarizable force fields and experimental data on the binding affinity. It was found that the total free energy of binding for ATP:Mg²⁺ (-7.00 ± 2.13 kcal/mol) is in good agreement with experimental values (-8.6 ± .2 kcal/mol)¹. In addition, parameters for relevant protonation states of ATP, ADP, GTP and GDP have been derived. These parameters will allow for researchers to investigate biochemical phenomena involving NTP's and NDP's with greater accuracy than previous studies involving non-polarizable force fields.

Building intuition for binding free energy calculations: Bound state definition, restraints, and symmetry

The theory behind computation of absolute binding free energies using explicit-solvent molecular simulations is well-established, yet somewhat complex, with counter-intuitive aspects. This leads to frequent frustration, common misconceptions, and sometimes erroneous numerical treatment. To improve this, we present the main practically relevant segments of the theory with constant reference to physical intuition. We pinpoint the role of the implicit or explicit definition of the bound state (or the binding site) to make a robust link between an experimental measurement and a computational result. We clarify the role of symmetry and discuss cases where symmetry number corrections have been misinterpreted. In particular, we argue that symmetry corrections as classically presented are a source of confusion and could be advantageously replaced by restraint free energy contributions. We establish that contrary to a common intuition, partial or missing sampling of some modes of symmetric bound states does not affect the calculated decoupling free energies. Finally, we review these questions and pitfalls in the context of a few common practical situations: binding to a symmetric receptor (equivalent binding sites), binding of a symmetric ligand (equivalent poses), and formation of a symmetric complex, in the case of homodimerization.

Ketamine Metabolite (2R,6R)-Hydroxynorketamine Interacts with μ and κ Opioid Receptors

Ketamine is an anesthetic, analgesic, and antidepressant whose secondary metabolite (2R,6R)-hydroxynorketamine (HNK) has N-methyl-d-aspartate-receptor-independent antidepressant activity in a rodent model. In humans, naltrexone attenuates its antidepressant effect, consistent with opioid pathway involvement. No detailed biophysical description is available of opioid receptor binding of ketamine or its metabolites. Using molecular dynamics simulations with free energy perturbation, we characterize the binding site and affinities of ketamine and metabolites in μ and κ opioid receptors, finding a profound effect of the protonation state. G-protein recruitment assays show that HNK is an inverse agonist, attenuated by naltrexone, in these receptors with IC₅₀ values congruous with our simulations. Overall, our findings are consistent with opioid pathway involvement in ketamine function.

A practical guide to biologically relevant molecular simulations with charge scaling for electronic polarization

Molecular simulations can elucidate atomistic-level mechanisms of key biological processes, which are often hardly accessible to experiment. However, the results of the simulations can only be as trustworthy as the underlying simulation model. In many of these processes, interactions between charged moieties play a critical role. Current empirical force fields tend to overestimate such interactions, often in a dramatic way, when polyvalent ions are involved. The source of this shortcoming is the missing electronic polarization in these models. Given the importance of such biomolecular systems, there is great interest in fixing this deficiency in a computationally inexpensive way without employing explicitly polarizable force fields. Here, we review the electronic continuum correction approach, which accounts for electronic polarization in a mean-field way, focusing on its charge scaling variant. We show that by pragmatically scaling only the charged molecular groups, we qualitatively improve the charge-charge interactions without extra computational costs and benefit from decades of force field development on biomolecular force fields.

SAMPL7 Host-Guest Challenge Overview: assessing the reliability of polarizable and non-polarizable methods for binding free energy calculations

The SAMPL challenges focus on testing and driving progress of computational methods to help guide pharmaceutical drug discovery. However, assessment of methods for predicting binding affinities is often hampered by computational challenges such as conformational sampling, protonation state uncertainties, variation in test sets selected, and even lack of high quality experimental data. SAMPL blind challenges have thus frequently included a component focusing on host-guest binding, which removes some of these challenges while still focusing on molecular recognition. Here, we report on the results of the SAMPL7 blind prediction challenge for host-guest affinity prediction. In this study, we focused on three different host-guest categories-a familiar deep cavity cavitand series which has been featured in several prior challenges (where we examine binding of a series of guests to two hosts), a new series of cyclodextrin derivatives which are monofunctionalized around the rim to add amino acid-like functionality (where we examine binding of two guests to a series of hosts), and binding of a series of guests to a new acyclic TrimerTrip host which is related to previous cucurbituril hosts. Many predictions used methods based on molecular simulations, and overall success was mixed, though several methods stood out. As in SAMPL6, we find that one strategy for achieving reasonable accuracy here was to make empirical corrections to binding predictions based on previous data for host categories which have been studied well before, though this can be of limited value when new systems are included. Additionally, we found that alchemical free energy methods using the AMOEBA polarizable force field had considerable success for the two host categories in which they participated. The new TrimerTrip system was also found to introduce some sampling problems, because multiple conformations may be relevant to binding and interconvert only slowly. Overall, results in this challenge tentatively suggest that further investigation of polarizable force fields for these challenges may be warranted.

AMOEBA binding free energies for the SAMPL7 TrimerTrip host-guest challenge

As part of the SAMPL7 host-guest binding challenge, the AMOEBA force field was applied to calculate the absolute binding free energy for 16 charged organic ammonium guests to the TrimerTrip host, a recently reported acyclic cucurbituril-derived clip host structure with triptycene moieties at its termini. Here we report binding free energy calculations for this system using the AMOEBA polarizable atomic multipole force field and double annihilation free energy methodology. Conformational analysis of the host suggests three families of conformations that do not interconvert in solution on a time scale available to nanosecond molecular dynamics (MD) simulations. Two of these host conformers, referred to as the "indent" and "overlap" structures, are capable of binding guest molecules. As a result, the free energies of all 16 guests binding to both conformations were computed separately, and combined to produce values for comparison with experiment. Initial ranked results submitted as part of the SAMPL7 exercise had a mean unsigned error (MUE) from experimental binding data of 2.14 kcal/mol. Subsequently, a rigorous umbrella sampling reference calculation was used to better determine the free energy difference between unligated "indent" and "overlap" host conformations. Revised binding values for the 16 guests pegged to this umbrella sampling reference reduced the MUE to 1.41 kcal/mol, with a correlation coefficient (Pearson R) between calculated and experimental binding values of 0.832 and a rank correlation (Kendall τ) of 0.65. Overall, the AMOEBA results demonstrate no significant systematic error, suggesting the force field provides an accurate energetic description of the TrimerTrip host, and an appropriate balance of solvation and desolvation effects associated with guest binding.

Binding of divalent cations to acetate: molecular simulations guided by Raman spectroscopy

We combine Raman-MCR vibrational spectroscopy experiments with ab initio and classical MD simulations to gain molecular insights into carboxylate–cation binding.

Molecular Dynamics Study of the Hybridization between RNA and Modified Oligonucleotides

MicroRNAs (miRNAs) are attractive drug candidates for many diseases as they can modulate the expression of gene networks. Recently, we discovered that DNAs targeting microRNA-22-3p (miR-22-3p) hold the potential for treating obesity and related metabolic disorders (type 2 diabetes mellitus, hyperlipidemia, and nonalcoholic fatty liver disease (NAFLD)) by turning fat-storing white adipocytes into fat-burning adipocytes. In this work, we explored the effects of chemical modifications, including phosphorothioate (PS), locked nucleic acid (LNA), and peptide nucleic acid (PNA), on the structure and energy of DNA analogs by using molecular dynamics (MD) simulations. To achieve a reliable prediction of the hybridization free energy, the AMOEBA polarizable force field and the free energy perturbation technique were employed. The calculated hybridization free energies are generally compatible with previous experiments. For LNA and PNA, the enhanced duplex stability can be explained by the preorganization mechanism, i.e., the single strands adopt stable helical structures similar to those in the duplex. For PS, the S and R isomers (Sp and Rp) have preferences for C2'-endo and C3'-endo sugar puckering conformations, respectively, and therefore Sp is less stable than Rp in DNA/RNA hybrids. In addition, the solvation penalty of Rp accounts for its destabilization effect. PS-LNA is similar to LNA as the sugar puckering is dominated by the locked sugar ring. This work demonstrated that MD simulations with polarizable force fields are useful for the understanding and design of modified nucleic acids.

Computational and Experimental Studies of Inhibitor Design for Aldolase A

Glycolytic enzyme fructose-bisphosphate aldolase A is an emerging therapeutic target in cancer. Recently, we have solved the crystal structure of murine aldolase in complex with naphthalene-2,6-diyl bisphosphate (ND1) that served as a template of the design of bisphosphate-based inhibitors. In this work, a series of ND1 analogues containing difluoromethylene (-CF₂), methylene (-CH₂), or aldehyde substitutions were designed. All designed compounds were studied using molecular dynamics (MD) simulations with the AMOEBA force field. Both energetics and structural analyses have been done to understand the calculated binding free energies. The average distances between ligand and protein atoms for ND1 were very similar to those for the ND1 crystal structure, which indicates that our MD simulation is sampling the correct conformation well. CF₂ insertion lowers the binding free energy by 10-15 kcal/mol, while CF₂ substitution slightly increases the binding free energy, which matches the experimental measurement. In addition, we found that NDB with two CF₂ insertions, the strongest binder, is entropically driven, while others including NDA with one CF₂ insertion are all enthalpically driven. This work provides insights into the mechanisms underlying protein-phosphate binding and enhances the capability of applying computational and theoretical frameworks to model, predict, and design diagnostic strategies targeting cancer.

Free Energy Calculations Based on Coupling Proximal Distribution Functions and Thermodynamic Cycles

Techniques to calculate the free energy changes of a system are very useful in the study of biophysical and biochemical properties. In practice, free energy changes can be described with thermodynamic cycles, and the free energy change of an individual process can be computed by sufficiently sampling the corresponding configurations. However, this is still time-consuming especially for large biomolecular systems. Previously, we have shown that by utilizing precomputed solute-solvent correlations, so-called proximal distribution functions (pDF), we are capable of reconstructing the solvent environment near solute atoms, thus estimating the solute-solvent interactions and solvation free energies of molecules. In this contribution, we apply the technique of pDF-reconstructions to calculate chemical potentials and use this information in thermodynamic cycles. This illustrates how free energy changes of nontrivial chemical processes in aqueous solution systems can be rapidly estimated.

Accurate PDZ/Peptide Binding Specificity with Additive and Polarizable Free Energy Simulations

PDZ domains contain 80-100 amino acids and bind short C-terminal sequences of target proteins. Their specificity is essential for cellular signaling pathways. We studied the binding of the Tiam1 PDZ domain to peptides derived from the C-termini of its Syndecan-1 and Caspr4 targets. We used free energy perturbation (FEP) to characterize the binding energetics of one wild-type and 17 mutant complexes by simulating 21 alchemical transformations between pairs of complexes. Thirteen complexes had known experimental affinities. FEP is a powerful tool to understand protein/ligand binding. It depends, however, on the accuracy of molecular dynamics force fields and conformational sampling. Both aspects require continued testing, especially for ionic mutations. For six mutations that did not modify the net charge, we obtained excellent agreement with experiment using the additive, AMBER ff99SB force field, with a root mean square deviation (RMSD) of 0.37 kcal/mol. For six ionic mutations that modified the net charge, agreement was also good, with one large error (3 kcal/mol) and an RMSD of 0.9 kcal/mol for the other five. The large error arose from the overstabilization of a protein/peptide salt bridge by the additive force field. Four of the ionic mutations were also simulated with the polarizable Drude force field, which represents the first test of this force field for protein/ligand binding free energy changes. The large error was eliminated and the RMS error for the four mutations was reduced from 1.8 to 1.2 kcal/mol. The overall accuracy of FEP indicates it can be used to understand PDZ/peptide binding. Importantly, our results show that for ionic mutations in buried regions, electronic polarization plays a significant role.

Classical Drude Polarizable Force Field Model for Methyl Phosphate and Its Interactions with Mg2

Phosphate groups are essential components of nucleic acids and proteins, whose interactions with solvent, metal ions, and ionic side chains help control folding and binding. Methyl phosphate (MP) represents a simple analog of phosphate moieties that are post-translation modifications in proteins and present at the termini of nucleic acids, among other environments. In the present study, we optimized parameters for use in polarizable molecular dynamics simulations of MP in its mono- and dianionic forms, MP- ≡ CH3HPO4- and MP2- ≡ CH3PO42-, along with P i2- ≡ HPO42-, in the context of the classical Drude oscillator model. Parameter optimization was done in a manner consistent with the remainder of the Drude molecular mechanics force field, choosing atomic charges and polarizabilities to reproduce molecular properties from quantum mechanics as well as experimental hydration free energies. Optimized parameters were similar to existing dimethyl phosphate parameters, with a few significant differences. The developed parameters were then used to compute magnesium binding affinities in aqueous solution, using alchemical molecular dynamics free energy simulations. Good agreement with experiment was obtained, and outer sphere binding was shown to be predominant for MP- and MP2-.

Charge Dispersion and Its Effects on the Reactivity of Thiamin-Derived Breslow Intermediates

The enzymic decarboxylation of 2-ketoacids proceeds via their C2-thiazolium adducts of thiamin diphosphate (ThDP). Loss of CO₂ from these adducts leads to reactive species that are known as Breslow intermediates. The protein-bound adducts of the 2-ketoacids and ThDP are several orders of magnitude more reactive than the synthetic analogues in solution. Studies of enzymes are consistent with formulation of protein-bound Breslow intermediates with localized carbanionic character at the reactive C2α position, reflecting the charge-stabilized transition state that leads to this form. Our study reveals that nonenzymic decarboxylation of the related thiamin adducts proceeds to the alternative charge-dispersed enol form of the Breslow intermediate. These differences suggest that the greatly enhanced rate of decarboxylation of the precursors to Breslow intermediates in enzymes arises from maintenance of the carbanionic character at the position from which the carboxyl group departs, avoiding charge dispersion by stabilizing electrostatic interactions with the protein as formulated by Warshel. Applying Guthrie's "no-barrier" addition to Marcus theory also leads to the conclusion that maintaining the tetrahedral carbanion at C2α of the resulting adduct minimizes associated kinetic barriers by avoiding rehybridization as part of steps to and from the intermediate. Finally, maintenance of the reactive energetic carbanion agrees with the concepts of Albery and Knowles as the outcome of evolved enzymic processes.

Binding affinities of the farnesoid X receptor in the D3R Grand Challenge 2 estimated by free-energy perturbation and docking

We have studied the binding of 102 ligands to the farnesoid X receptor within the D3R Grand Challenge 2016 blind-prediction competition. First, we employed docking with five different docking software and scoring functions. The selected docked poses gave an average root-mean-squared deviation of 4.2 Å. Consensus scoring gave decent results with a Kendall's τ of 0.26 ± 0.06 and a Spearman's ρ of 0.41 ± 0.08. For a subset of 33 ligands, we calculated relative binding free energies with free-energy perturbation. Five transformations between the ligands involved a change of the net charge and we implemented and benchmarked a semi-analytic correction (Rocklin et al., J Chem Phys 139:184103, 2013) for artifacts caused by the periodic boundary conditions and Ewald summation. The results gave a mean absolute deviation of 7.5 kJ/mol compared to the experimental estimates and a correlation coefficient of R 2 = 0.1. These results were among the four best in this competition out of 22 submissions. The charge corrections were significant (7-8 kJ/mol) and always improved the results. By employing 23 intermediate states in the free-energy perturbation, there was a proper overlap between all states and the precision was 0.1-0.7 kJ/mol. However, thermodynamic cycles indicate that the sampling was insufficient in some of the perturbations.

A Simple PB/LIE Free Energy Function Accurately Predicts the Peptide Binding Specificity of the Tiam1 PDZ Domain

PDZ domains generally bind short amino acid sequences at the C-terminus of target proteins, and short peptides can be used as inhibitors or model ligands. Here, we used experimental binding assays and molecular dynamics simulations to characterize 51 complexes involving the Tiam1 PDZ domain and to test the performance of a semi-empirical free energy function. The free energy function combined a Poisson-Boltzmann (PB) continuum electrostatic term, a van der Waals interaction energy, and a surface area term. Each term was empirically weighted, giving a Linear Interaction Energy or “PB/LIE” free energy. The model yielded a mean unsigned deviation of 0.43 kcal/mol and a Pearson correlation of 0.64 between experimental and computed free energies, which was superior to a Null model that assumes all complexes have the same affinity. Analyses of the models support several experimental observations that indicate the orientation of the α₂ helix is a critical determinant for peptide specificity. The models were also used to predict binding free energies for nine new variants, corresponding to point mutants of the Syndecan1 and Caspr4 peptides. The predictions did not reveal improved binding; however, they suggest that an unnatural amino acid could be used to increase protease resistance and peptide lifetimes in vivo. The overall performance of the model should allow its use in the design of new PDZ ligands in the future.

Predicting Binding Free Energies: Frontiers and Benchmarks

Binding free energy calculations based on molecular simulations provide predicted affinities for biomolecular complexes. These calculations begin with a detailed description of a system, including its chemical composition and the interactions among its components. Simulations of the system are then used to compute thermodynamic information, such as binding affinities. Because of their promise for guiding molecular design, these calculations have recently begun to see widespread applications in early-stage drug discovery. However, many hurdles remain in making them a robust and reliable tool. In this review, we highlight key challenges of these calculations, discuss some examples of these challenges, and call for the designation of standard community benchmark test systems that will help the research community generate and evaluate progress. In our view, progress will require careful assessment and evaluation of new methods, force fields, and modeling innovations on well-characterized benchmark systems, and we lay out our vision for how this can be achieved.

Nonpolar Solvation Free Energy from Proximal Distribution Functions

Using precomputed near neighbor or proximal distribution functions (pDFs) that approximate solvent density about atoms in a chemically bonded context one can estimate the solvation structures around complex solutes and the corresponding solute-solvent energetics. In this contribution, we extend this technique to calculate the solvation free energies (ΔG) of a variety of solutes. In particular we use pDFs computed for small peptide molecules to estimate ΔG for larger peptide systems. We separately compute the non polar (ΔG_vdW) and electrostatic (ΔG_elec) components of the underlying potential model. Here we show how the former can be estimated by thermodynamic integration using pDF-reconstructed solute-solvent interaction energy. The electrostatic component can be approximated with Linear Response theory as half of the electrostatic solute-solvent interaction energy. We test the method by calculating the solvation free energies of butane, propanol, polyalanine, and polyglycine and by comparing with traditional free energy simulations. Results indicate that the pDF-reconstruction algorithm approximately reproduces ΔG_vdW calculated by benchmark free energy simulations to within ∼ kcal/mol accuracy. The use of transferable pDFs for each solute atom allows for a rapid estimation of ΔG for arbitrary molecular systems.

Microscopic mechanisms that govern the titration response and pKa values of buried residues in staphylococcal nuclease mutants

To probe the microscopic mechanisms that govern the titration behavior of buried ionizable groups, microsecond explicit solvent molecular dynamics simulations are carried out for several mutants of Staphylococcal nuclease using both fixed charge and polarizable force fields. While the ionization of Asp 66, Glu 66, and Lys 125 lead to enhanced structural fluctuations and partial unfolding of adjacent α-helical regions, the ionization of Lys 25 causes local unfolding of adjacent β sheets. Using the sampled conformational ensembles, good agreement with experimental pK_a values is obtained with Poisson-Boltzmann calculations using a protein dielectric constant of 2-4 for V66D/E; slightly larger dielectric constants are needed for Lys mutants especially L25K, suggesting that structural responses beyond microseconds are involved in ionization of Lys 25. Overall, the set of unbiased simulations provides insights into the spatial and temporal scales of protein and solvent motions that dictate the diverse titration behaviors of buried protein residues. Proteins 2017; 85:268-281. © 2016 Wiley Periodicals, Inc.