Andrew T. Fenley

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.

Analytical electrostatics for biomolecules: Beyond the generalized Born approximation

The modeling and simulation of macromolecules in solution often benefits from fast analytical approximations for the electrostatic interactions. In our previous work [G. Sigalov et al., J. Chem. Phys. 122, 094511 (2005)], we proposed a method based on an approximate analytical solution of the linearized Poisson-Boltzmann equation for a sphere. In the current work, we extend the method to biomolecules of arbitrary shape and provide computationally efficient algorithms for estimation of the parameters of the model. This approach, which we tentatively call ALPB here, is tested against the standard numerical Poisson-Boltzmann (NPB) treatment on a set of 579 representative proteins, nucleic acids, and small peptides. The tests are performed across a wide range of solvent/solute dielectrics and at biologically relevant salt concentrations. Over the range of the solvent and solute parameters tested, the systematic deviation (from the NPB reference) of solvation energies computed by ALPB is 0.5-3.5 kcal/mol, which is 5-50 times smaller than that of the conventional generalized Born approximation widely used in this context. At the same time, ALPB is equally computationally efficient. The new model is incorporated into the AMBER molecular modeling package and tested on small proteins.

Charge Hydration Asymmetry: The Basic Principle and How to Use It to Test and Improve Water Models

Charge hydration asymmetry (CHA) manifests itself in the experimentally observed strong dependence of free energy of ion hydration on the sign of the ion charge. This asymmetry is not consistently accounted for by popular models of solvation; its magnitude varies greatly between the models. While it is clear that CHA is somehow related to charge distribution within a water molecule, the exact nature of this relationship is unknown. We propose a simple, yet general and rigorous criterion that relates rotational and charge inversion properties of a water molecules charge distribution with its ability to cause CHA. We show which electric multipole components of a water molecule are key to explain its ability for asymmetric charge hydration. We then test several popular water models and explain why specific models show none, little, or strong CHA in simulations. We use the gained insight to derive an analogue of the Born equation that includes the missing physics necessary to account for CHA and does not rely on redefining the continuum dielectric boundary. The proposed formula is as simple as the original, does not contain any fitting parameters, and predicts hydration free energies and entropies of spherical cations and anions within experimental uncertainty. Our findings suggest that the gap between the practical continuum electrostatics framework and the more fundamental explicit solvent treatment may be reduced considerably by explicitly introducing CHA into the existing continuum framework.

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 nucleosomes 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.

The carmaphycins: new proteasome inhibitors exhibiting an α,β-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,β‐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 β5 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.

Bridging Calorimetry and Simulation through Precise Calculations of Cucurbituril-Guest Binding Enthalpies.

We used microsecond time scale molecular dynamics simulations to compute, at high precision, binding enthalpies for cucurbit[7]uril (CB7) with eight guests in aqueous solution. The results correlate well with experimental data from previously published isothermal titration calorimetry studies, and decomposition of the computed binding enthalpies by interaction type provides plausible mechanistic insights. Thus, dispersion interactions appear to play a key role in stabilizing these complexes, due at least in part to the fact that their packing density is greater than that of water. On the other hand, strongly favorable Coulombic interactions between the host and guests are compensated by unfavorable solvent contributions, leaving relatively modest electrostatic contributions to the binding enthalpies. The better steric fit of the aliphatic guests into the circular host appears to explain why their binding enthalpies tend to be more favorable than those of the more planar aromatic guests. The present calculations also bear on the validity of the simulation force field. Somewhat unexpectedly, the TIP3P water yields better agreement with experiment than the TIP4P-Ew water model, although the latter is known to replicate the properties of pure water more accurately. More broadly, the present results demonstrate the potential for computational calorimetry to provide atomistic explanations for thermodynamic observations.

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.

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.

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 β-cyclodextrin (βCD) 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.

Accelerating electrostatic surface potential calculation with multi-scale approximation on graphics processing units

Tools that compute and visualize biomolecular electrostatic surface potential have been used extensively for studying biomolecular function. However, determining the surface potential for large biomolecules on a typical desktop computer can take days or longer using currently available tools and methods. Two commonly used techniques to speed-up these types of electrostatic computations are approximations based on multi-scale coarse-graining and parallelization across multiple processors. This paper demonstrates that for the computation of electrostatic surface potential, these two techniques can be combined to deliver significantly greater speed-up than either one separately, something that is in general not always possible. Specifically, the electrostatic potential computation, using an analytical linearized Poisson-Boltzmann (ALPB) method, is approximated using the hierarchical charge partitioning (HCP) multi-scale method, and parallelized on an ATI Radeon 4870 graphical processing unit (GPU). The implementation delivers a combined 934-fold speed-up for a 476,040 atom viral capsid, compared to an equivalent non-parallel implementation on an Intel E6550 CPU without the approximation. This speed-up is significantly greater than the 42-fold speed-up for the HCP approximation alone or the 182-fold speed-up for the GPU alone.