Entropy-enthalpy transduction caused by conformational shifts can obscure the forces driving protein-ligand binding.

Molecular dynamics simulations of unprecedented duration now can provide new insights into biomolecular mechanisms. Analysis of a 1-ms molecular dynamics simulation of the small protein bovine pancreatic trypsin inhibitor reveals that its main conformations have different thermodynamic profiles and that perturbation of a single geometric variable, such as a torsion angle or interresidue distance, can select for occupancy of one or another conformational state. These results establish the basis for a mechanism that we term entropy-enthalpy transduction (EET), in which the thermodynamic character of a local perturbation, such as enthalpic binding of a small molecule, is camouflaged by the thermodynamics of a global conformational change induced by the perturbation, such as a switch into a high-entropy conformational state. It is noted that EET could occur in many systems, making measured entropies and enthalpies of folding and binding unreliable indicators of actual thermodynamic driving forces. The same mechanism might also account for the high experimental variance of measured enthalpies and entropies relative to free energies in some calorimetric studies. Finally, EET may be the physical mechanism underlying many cases of entropy-enthalpy compensation.

The SAMPL4 host-guest blind prediction challenge: an overview.

Prospective validation of methods for computing binding affinities can help assess their predictive power and thus set reasonable expectations for their performance in drug design applications. Supramolecular host-guest systems are excellent model systems for testing such affinity prediction methods, because their small size and limited conformational flexibility, relative to proteins, allows higher throughput and better numerical convergence. The SAMPL4 prediction challenge therefore included a series of host-guest systems, based on two hosts, cucurbit[7]uril and octa-acid. Binding affinities in aqueous solution were measured experimentally for a total of 23 guest molecules. Participants submitted 35 sets of computational predictions for these host-guest systems, based on methods ranging from simple docking, to extensive free energy simulations, to quantum mechanical calculations. Over half of the predictions provided better correlations with experiment than two simple null models, but most methods underperformed the null models in terms of root mean squared error and linear regression slope. Interestingly, the overall performance across all SAMPL4 submissions was similar to that for the prior SAMPL3 host-guest challenge, although the experimentalists took steps to simplify the current challenge. While some methods performed fairly consistently across both hosts, no single approach emerged as consistent top performer, and the nonsystematic nature of the various submissions made it impossible to draw definitive conclusions regarding the best choices of energy models or sampling algorithms. Salt effects emerged as an issue in the calculation of absolute binding affinities of cucurbit[7]uril-guest systems, but were not expected to affect the relative affinities significantly. Useful directions for future rounds of the challenge might involve encouraging participants to carry out some calculations that replicate each others' studies, and to systematically explore parameter options.

The SAMPL4 hydration challenge: evaluation of partial charge sets with explicit-water molecular dynamics simulations.

We used blind predictions of the 47 hydration free energies in the SAMPL4 challenge to test multiple partial charge models in the context of explicit solvent free energy simulations with the general AMBER force field. One of the partial charge models, IPolQ-Mod, is a fast continuum solvent-based implementation of the IPolQ approach. The AM1-BCC, restrained electrostatic potential (RESP) and IpolQ-Mod approaches all perform reasonably well (R(2) > 0.8), while VCharge, though faster, gives less accurate results (R(2) of 0.5). The AM1-BCC results are more accurate than those of RESP for tertiary amines and nitrates, but the overall difference in accuracy between these methods is not statistically significant. Interestingly, the IPolQ-Mod method is found to yield partial charges in very close agreement with RESP. This observation suggests that the success of RESP may be attributed to its fortuitously approximating the arguably more rigorous IPolQ approach.

Blind prediction of SAMPL4 cucurbit[7]uril binding affinities with the mining minima method.

Accurate methods for predicting protein-ligand binding affinities are of central interest to computer-aided drug design for hit identification and lead optimization. Here, we used the mining minima (M2) method to predict cucurbit[7]uril binding affinities from the SAMPL4 blind prediction challenge. We tested two different energy models, an empirical classical force field, CHARMm with VCharge charges, and the Poisson-Boltzmann surface area solvation model; and a semiempirical quantum mechanical (QM) Hamiltonian, PM6-DH+, coupled with the COSMO solvation model and a surface area term for nonpolar solvation free energy. Binding affinities based on the classical force field correlated strongly with the experiments with a correlation coefficient (R(2)) of 0.74. On the other hand, binding affinities based on the QM energy model correlated poorly with experiments (R(2) = 0.24), due largely to two major outliers. As we used extensive conformational search methods, these results point to possible inaccuracies in the PM6-DH+ energy model or the COSMO solvation model. Furthermore, the different binding free energy components, solute energy, solvation free energy, and configurational entropy showed significant deviations between the classical M2 and quantum M2 calculations. Comparison of different classical M2 free energy components to experiments show that the change in the total energy, i.e. the solute energy plus the solvation free energy, is the key driving force for binding, with a reasonable correlation to experiment (R(2) = 0.56); however, accounting for configurational entropy further improves the correlation.

The electrostatic response of water to neutral polar solutes: implications for continuum solvent modeling.

Continuum solvation models are widely used to estimate the hydration free energies of small molecules and proteins, in applications ranging from drug design to protein engineering, and most such models are based on the approximation of a linear dielectric response by the solvent. We used explicit-water molecular dynamics simulations with the TIP3P water model to probe this linear response approximation in the case of neutral polar molecules, using miniature cucurbituril and cyclodextrin receptors and protein side-chain analogs as model systems. We observe supralinear electrostatic solvent responses, and this nonlinearity is found to result primarily from waters' being drawn closer and closer to the solutes with increased solute-solvent electrostatic interactions; i.e., from solute electrostriction. Dielectric saturation and changes in the water-water hydrogen bonding network, on the other hand, play little role. Thus, accounting for solute electrostriction may be a productive approach to improving the accuracy of continuum solvation models.

The carmaphycins: new proteasome inhibitors exhibiting an α,ß-epoxyketone warhead from a marine cyanobacterium.

Two new peptidic proteasome inhibitors were isolated as trace components from a Curaçao collection of the marine cyanobacterium Symploca sp. Carmaphycin A (1) and carmaphycin B (2) feature a leucine-derived α,ß-epoxyketone warhead directly connected to either methionine sulfoxide or methionine sulfone. Their structures were elucidated on the basis of extensive NMR and MS analyses and confirmed by total synthesis, which in turn provided more material for further biological evaluations. Pure carmaphycins A and B were found to inhibit the ß5 subunit (chymotrypsin-like activity) of the S. cerevisiae 20S proteasome in the low nanomolar range. Additionally, they exhibited strong cytotoxicity to lung and colon cancer cell lines, as well as exquisite antiproliferative effects in the NCI60 cell-line panel. These assay results as well as initial structural biology studies suggest a distinctive binding mode for these new inhibitors.

Connecting protein and mRNA burst distributions for stochastic models of gene expression.

The intrinsic stochasticity of gene expression can lead to large variability in protein levels for genetically identical cells. Such variability in protein levels can arise from infrequent synthesis of mRNAs which in turn give rise to bursts of protein expression. Protein expression occurring in bursts has indeed been observed experimentally and recent studies have also found evidence for transcriptional bursting, i.e. production of mRNAs in bursts. Given that there are distinct experimental techniques for quantifying the noise at different stages of gene expression, it is of interest to derive analytical results connecting experimental observations at different levels. In this work, we consider stochastic models of gene expression for which mRNA and protein production occurs in independent bursts. For such models, we derive analytical expressions connecting protein and mRNA burst distributions which show how the functional form of the mRNA burst distribution can be inferred from the protein burst distribution. Additionally, if gene expression is repressed such that observed protein bursts arise only from single mRNAs, we show how observations of protein burst distributions (repressed and unrepressed) can be used to completely determine the mRNA burst distribution. Assuming independent contributions from individual bursts, we derive analytical expressions connecting means and variances for burst and steady-state protein distributions. Finally, we validate our general analytical results by considering a specific reaction scheme involving regulation of protein bursts by small RNAs. For a range of parameters, we derive analytical expressions for regulated protein distributions that are validated using stochastic simulations. The analytical results obtained in this work can thus serve as useful inputs for a broad range of studies focusing on stochasticity in gene expression.

Computational modeling of differences in the quorum sensing induced luminescence phenotypes of Vibrio harveyi and Vibrio cholerae.

Vibrio harveyi and Vibrio cholerae have quorum sensing pathways with similar design and highly homologous components including multiple small RNAs (sRNAs). However, the associated luminescence phenotypes of strains with sRNA deletions differ dramatically: in V. harveyi, the sRNAs act additively; however, in V. cholerae, the sRNAs act redundantly. Furthermore, there are striking differences in the luminescence phenotypes for different pathway mutants in V. harveyi and V. cholerae. However, these differences have not been connected with the observed differences for the sRNA deletion strains in these bacteria. In this work, we present a model for quorum sensing induced luminescence phenotypes focusing on the interactions of multiple sRNAs with target mRNA. Within our model, we find that one key parameter - the fold-change in protein concentration necessary for luminescence activation - can control whether the sRNAs appear to act additively or redundantly. For specific parameter choices, we find that differences in this key parameter can also explain hitherto unconnected luminescence phenotypes differences for various pathway mutants in V. harveyi and V. cholerae. The model can thus provide a unifying explanation for observed differences in luminescence phenotypes and can also be used to make testable predictions for future experiments.

Charge state of the globular histone core controls stability of the nucleosome.

Presented here is a quantitative model of the wrapping and unwrapping of the DNA around the histone core of the nucleosome that suggests a mechanism by which this transition can be controlled: alteration of the charge state of the globular histone core. The mechanism is relevant to several classes of posttranslational modifications such as histone acetylation and phosphorylation; several specific scenarios consistent with recent in vivo experiments are considered. The model integrates a description based on an idealized geometry with one based on the atomistic structure of the nucleosome, and the model consistently accounts for both the electrostatic and nonelectrostatic contributions to the nucleosome free energy. Under physiological conditions, isolated nucleosomes are predicted to be very stable (38 +/- 7 kcal/mol). However, a decrease in the charge of the globular histone core by one unit charge, for example due to acetylation of a single lysine residue, can lead to a significant decrease in the strength of association with its DNA. In contrast to the globular histone core, comparable changes in the charge state of the histone tail regions have relatively little effect on the nucleosome's stability. The combination of high stability and sensitivity explains how the nucleosome is able to satisfy the seemingly contradictory requirements for thermodynamic stability while allowing quick access to its DNA informational content when needed by specific cellular processes such as transcription.

A model for signal transduction during quorum sensing in Vibrio harveyi.

We present a framework for analyzing luminescence regulation during quorum sensing in the bioluminescent bacterium Vibrio harveyi. Using a simplified model for signal transduction in the quorum sensing pathway, we identify key dimensionless parameters that control the system's response. These parameters are estimated using experimental data on luminescence phenotypes for different mutant strains. The corresponding model predictions are consistent with results from other experiments which did not serve as input for determining model parameters. Furthermore, the proposed framework leads to novel testable predictions for luminescence phenotypes and for responses of the network to different perturbations.

Systems biology of microbial communities.

Microbes exist naturally in a wide range of environments in communities where their interactions are significant, spanning the extremes of high acidity and high temperature environments to soil and the ocean. We present a practical discussion of three different approaches for modeling microbial communities: rate equations, individual-based modeling, and population dynamics. We illustrate the approaches with detailed examples. Each approach is best fit to different levels of system representation, and they have different needs for detailed biological input. Thus, this set of approaches is able to address the operation and function of microbial communities on a wide range of organizational levels.

An analytical approach to computing biomolecular electrostatic potential. I. Derivation and analysis.

Analytical approximations to fundamental equations of continuum electrostatics on simple shapes can lead to computationally inexpensive prescriptions for calculating electrostatic properties of realistic molecules. Here, we derive a closed-form analytical approximation to the Poisson equation for an arbitrary distribution of point charges and a spherical dielectric boundary. The simple, parameter-free formula defines continuous electrostatic potential everywhere in space and is obtained from the exact infinite-series (Kirkwood) solution by an approximate summation method that avoids truncating the infinite series. We show that keeping all the terms proves critical for the accuracy of this approximation, which is fully controllable for the sphere. The accuracy is assessed by comparisons with the exact solution for two unit charges placed inside a spherical boundary separating the solute of dielectric 1 and the solvent of dielectric 80. The largest errors occur when the source charges are closest to the dielectric boundary and the test charge is closest to either of the sources. For the source charges placed within 2 A from the boundary, and the test surface located on the boundary, the root-mean-square error of the approximate potential is less than 0.1 kcal/mol/mid R:emid R: (per unit test charge). The maximum error is 0.4 kcal/mol/mid R:emid R:. These results correspond to the simplest first-order formula. A strategy for adopting the proposed method for realistic biomolecular shapes is detailed. An extensive testing and performance analysis on real molecular structures are described in Part II that immediately follows this work as a separate publication. Part II also contains an application example.

An analytical approach to computing biomolecular electrostatic potential. II. Validation and applications.

An ability to efficiently compute the electrostatic potential produced by molecular charge distributions under realistic solvation conditions is essential for a variety of applications. Here, the simple closed-form analytical approximation to the Poisson equation rigorously derived in Part I for idealized spherical geometry is tested on realistic shapes. The effects of mobile ions are included at the Debye-Huckel level. The accuracy of the resulting closed-form expressions for electrostatic potential is assessed through comparisons with numerical Poisson-Boltzmann (NPB) reference solutions on a test set of 580 representative biomolecular structures under typical conditions of aqueous solvation. For each structure, the deviation from the reference is computed for a large number of test points placed near the dielectric boundary (molecular surface). The accuracy of the approximation, averaged over all test points in each structure, is within 0.6 kcal/mol/mid R:emid R: approximately kT per unit charge for all structures in the test set. For 91.5% of the individual test points, the deviation from the NPB potential is within 0.6 kcal/mol/mid R:emid R:. The deviations from the reference decrease with increasing distance from the dielectric boundary: The approximation is asymptotically exact far away from the source charges. Deviation of the overall shape of a structure from ideal spherical does not, by itself, appear to necessitate decreased accuracy of the approximation. The largest deviations from the NPB reference are found inside very deep and narrow indentations that occur on the dielectric boundaries of some structures. The dimensions of these pockets of locally highly negative curvature are comparable to the size of a water molecule; the applicability of a continuum dielectric models in these regions is discussed. The maximum deviations from the NPB are reduced substantially when the boundary is smoothed by using a larger probe radius (3 A) to generate the molecular surface. A detailed accuracy analysis is presented for several proteins of various shapes, including lysozyme whose surface features a functionally relevant region of negative curvature. The proposed analytical model is computationally inexpensive; this strength of the approach is demonstrated by computing and analyzing the electrostatic potential generated by a full capsid of the tobacco ring spot virus at atomic resolution (500 000 atoms). An analysis of the electrostatic potential of the inner surface of the capsid reveals what might be a RNA binding pocket. These results are generated with the modest computational power of a desktop personal computer.

Modulation of nucleosomal DNA accessibility via charge-altering post-translational modifications in histone core.

BACKGROUND: Controlled modulation of nucleosomal DNA accessibility via post-translational modifications (PTM) is a critical component to many cellular functions. Charge-altering PTMs in the globular histone core-including acetylation, phosphorylation, crotonylation, propionylation, butyrylation, formylation, and citrullination-can alter the strong electrostatic interactions between the oppositely charged nucleosomal DNA and the histone proteins and thus modulate accessibility of the nucleosomal DNA, affecting processes that depend on access to the genetic information, such as transcription. However, direct experimental investigation of the effects of these PTMs is very difficult. Theoretical models can rationalize existing observations, suggest working hypotheses for future experiments, and provide a unifying framework for connecting PTMs with the observed effects. RESULTS: A physics-based framework is proposed that predicts the effect of charge-altering PTMs in the histone core, quantitatively for several types of lysine charge-neutralizing PTMs including acetylation, and qualitatively for all phosphorylations, on the nucleosome stability and subsequent changes in DNA accessibility, making a connection to resulting biological phenotypes. The framework takes into account multiple partially assembled states of the nucleosome at the atomic resolution. The framework is validated against experimentally known nucleosome stability changes due to the acetylation of specific lysines, and their effect on transcription. The predicted effect of charge-altering PTMs on DNA accessibility can vary dramatically, from virtually none to a strong, region-dependent increase in accessibility of the nucleosomal DNA; in some cases, e.g., H4K44, H2AK75, and H2BK57, the effect is significantly stronger than that of the extensively studied acetylation sites such H3K56, H3K115 or H3K122. Proximity to the DNA is suggestive of the strength of the PTM effect, but there are many exceptions. For the vast majority of charge-altering PTMs, the predicted increase in the DNA accessibility should be large enough to result in a measurable modulation of transcription. However, a few possible PTMs, such as acetylation of H4K77, counterintuitively decrease the DNA accessibility, suggestive of the repressed chromatin. A structural explanation for the phenomenon is provided. For the majority of charge-altering PTMs, the effect on DNA accessibility is simply additive (noncooperative), but there are exceptions, e.g., simultaneous acetylation of H4K79 and H3K122, where the combined effect is amplified. The amplification is a direct consequence of the nucleosome-DNA complex having more than two structural states. The effect of individual PTMs is classified based on changes in the accessibility of various regions throughout the nucleosomal DNA. The PTM's resulting imprint on the DNA accessibility, "PTMprint," is used to predict effects of many yet unexplored PTMs. For example, acetylation of H4K44 yields a PTMprint similar to the PTMprint of H3K56, and thus acetylation of H4K44 is predicted to lead to a wide range of strong biological effects. CONCLUSION: Charge-altering post-translational modifications in the relatively unexplored globular histone core may provide a precision mechanism for controlling accessibility to the nucleosomal DNA.

Evaluation of Representations and Response Models for Polarizable Force Fields.

For classical simulations of condensed-phase systems, such as organic liquids and biomolecules, to achieve high accuracy, they will probably need to incorporate an accurate, efficient model of conformation-dependent electronic polarization. Thus, it is of interest to understand what determines the accuracy of a polarizable electrostatics model. This study approaches this problem by breaking polarization models down into two main components: the representation of electronic polarization and the response model used for mapping from an inducing field to the polarization within the chosen representation. Among the most common polarization representations are redistribution of atom-centered charges, such as those used in the fluctuating charge model, and atom-centered point dipoles, such as those used in a number of different polarization models. Each of these representations has been combined with one or more response models. The response model of fluctuating charge, for example, is based on the idea of electronegativity equalization in the context of changing electrostatic potentials (ESPs), whereas point-dipole representations typically use a response model based on point polarizabilities whose induced dipoles are computed based on interaction with other charges and dipoles. Here, we decouple polarization representations from their typical response models to analyze the strengths and weaknesses of various polarization approximations. First, we compare the maximal possible accuracies achievable by the charge redistribution and point-dipole model representations, by testing their ability to replicate quantum mechanical (QM) ESPs around small molecules polarized by external inducing charges. Perhaps not surprisingly, the atom-centered dipole model can yield higher accuracy. Next, we test two of the most commonly used response functions used for the point-dipole representations, self-consistent and direct (or first-order) inducible point polarizabilities, where the polarizabilities are optimized to best fit the full set of polarized QM potentials for each molecule studied. Strikingly, the induced-dipole response model markedly degrades accuracy relative to that obtainable with optimal point dipoles. In fact, the maximal accuracy achievable with this response model is even lower than that afforded by an optimal charge-redistribution representation. This means that, if coupled with a sufficiently accurate response function, the point-charge representation could outperform the standard induced-dipole model. Furthermore, although a key advantage of the point-dipole representation, relative to charge redistribution, is its ability to capture out-of-plane polarization, the inducible dipole response model causes it to be less accurate than optimal charge redistribution for out-of-plane induction of the planar nitrobenzene molecule. Thus, the widely used inducible dipole response function falls short of the full potential accuracy achievable with the point-dipole representation it employs. Additional results reported here bear on the relative accuracy of self-consistent inducible dipoles versus that of the first-order, or direct, approximation and on methods for assigning partial atomic charges for use in conjunction with inducible dipole models. In sum, these results point to the improvement of polarization response models as an important direction for future research aimed at improving the accuracy of molecular simulations.

Computational Calorimetry: High-Precision Calculation of Host-Guest Binding Thermodynamics.

We present a strategy for carrying out high-precision calculations of binding free energy and binding enthalpy values from molecular dynamics simulations with explicit solvent. The approach is used to calculate the thermodynamic profiles for binding of nine small molecule guests to either the cucurbit[7]uril (CB7) or ß-cyclodextrin (ßCD) host. For these systems, calculations using commodity hardware can yield binding free energy and binding enthalpy values with a precision of ∼0.5 kcal/mol (95% CI) in a matter of days. Crucially, the self-consistency of the approach is established by calculating the binding enthalpy directly, via end point potential energy calculations, and indirectly, via the temperature dependence of the binding free energy, i.e., by the van't Hoff equation. Excellent agreement between the direct and van't Hoff methods is demonstrated for both host-guest systems and an ion-pair model system for which particularly well-converged results are attainable. Additionally, we find that hydrogen mass repartitioning allows marked acceleration of the calculations with no discernible cost in precision or accuracy. Finally, we provide guidance for accurately assessing numerical uncertainty of the results in settings where complex correlations in the time series can pose challenges to statistical analysis. The routine nature and high precision of these binding calculations opens the possibility of including measured binding thermodynamics as target data in force field optimization so that simulations may be used to reliably interpret experimental data and guide molecular design.

Toward Improved Force-Field Accuracy through Sensitivity Analysis of Host-Guest Binding Thermodynamics.

Improving the capability of atomistic computer models to predict the thermodynamics of noncovalent binding is critical for successful structure-based drug design, and the accuracy of such calculations remains limited by nonoptimal force field parameters. Ideally, one would incorporate protein-ligand affinity data into force field parametrization, but this would be inefficient and costly. We now demonstrate that sensitivity analysis can be used to efficiently tune Lennard-Jones parameters of aqueous host-guest systems for increasingly accurate calculations of binding enthalpy. These results highlight the promise of a comprehensive use of calorimetric host-guest binding data, along with existing validation data sets, to improve force field parameters for the simulation of noncovalent binding, with the ultimate goal of making protein-ligand modeling more accurate and hence speeding drug discovery.

Binding enthalpy calculations for a neutral host-guest pair yield widely divergent salt effects across water models.

Dissolved salts are a part of the physiological milieu and can significantly influence the kinetics and thermodynamics of various biomolecular processes, such as binding and catalysis; thus, it is important for molecular simulations to reliably describe their effects. The present study uses a simple, nonionized host-guest model system to study the sensitivity of computed binding enthalpies to the choice of water and salt models. Molecular dynamics simulations of a cucurbit[7]uril host with a neutral guest molecule show striking differences in the salt dependency of the binding enthalpy across four water models, TIP3P, SPC/E, TIP4P-Ew, and OPC, with additional sensitivity to the choice of parameters for sodium and chloride. In particular, although all of the models predict that binding will be less exothermic with increasing NaCl concentration, the strength of this effect varies by 7 kcal/mol across models. The differences appear to result primarily from differences in the number of sodium ions displaced from the host upon binding the guest rather than from differences in the enthalpy associated with this displacement, and it is the electrostatic energy that contributes most to the changes in enthalpy with increasing salt concentration. That a high sensitivity of salt affecting the choice of water model, as observed for the present host-guest system despite it being nonionized, raises issues regarding the selection and adjustment of water models for use with biological macromolecules, especially as these typically possess multiple ionized groups that can interact relatively strongly with ions in solution.

Calculation and visualization of atomistic mechanical stresses in nanomaterials and biomolecules.

Many biomolecules have machine-like functions, and accordingly are discussed in terms of mechanical properties like force and motion. However, the concept of stress, a mechanical property that is of fundamental importance in the study of macroscopic mechanics, is not commonly applied in the biomolecular context. We anticipate that microscopical stress analyses of biomolecules and nanomaterials will provide useful mechanistic insights and help guide molecular design. To enable such applications, we have developed Calculator of Atomistic Mechanical Stress (CAMS), an open-source software package for computing atomic resolution stresses from molecular dynamics (MD) simulations. The software also enables decomposition of stress into contributions from bonded, nonbonded and Generalized Born potential terms. CAMS reads GROMACS topology and trajectory files, which are easily generated from AMBER files as well; and time-varying stresses may be animated and visualized in the VMD viewer. Here, we review relevant theory and present illustrative applications.