Stefan Boresch

Rationalization of the dielectric properties of common three-site water models in terms of their force field parameters

The dielectric properties (static dielectric constant e0, Debye relaxation time τD and distance dependent Kirkwood G-factor Gk(R)) of commonly used three-site water models (the “simple point charge” models SPC and SPC/E, as well as the “transferable intermolecular potentials with three point charges” TIP3P and its CHARMM modified variant TIP3Pmod) were evaluated from 2 ns molecular dynamics simulations using the Ewald summation method to compute the electrostatic interactions. The results for SPC (e0=65±5, τD=7.6±0.8 ps) and SPC/E (e0=68±6, τD=12.1±1.3 ps) are in good agreement with the literature; for TIP3P (TIP3Pmod) we obtained a dielectric constant e0=97±7 (97±6) and a Debye relaxation time τD=7.3±0.7 ps (6.9±0.6 ps). The surprisingly large differences in e0 were rationalized by an investigation of the relationship between the force field parameters and the dielectric properties. Based on simulations of hybrid SPC/TIP3P models, the HOH bond angle was identified as the determining factor of the dielect...

Simulation studies of the protein-water interface. II. Properties at the mesoscopic resolution.

We report molecular dynamics simulations of three globular proteins: ubiquitin, apo-calbindin D(9K), and the C-terminal SH2 domain of phospholipase C-gamma1 in explicit water. The proteins differ in their overall charge and fold type and were chosen to represent to some degree the structural variability found in medium-sized proteins. The length of each simulation was at least 15 ns, and larger than usual solvent boxes were used. We computed radial distribution functions, as well as orientational correlation functions about the surface residues. Two solvent shells could be clearly discerned about charged and polar amino acids. Near apolar amino acids the water density near such residues was almost devoid of structure. The mean residence time of water molecules was determined for water shells about the full protein, as well as for water layers about individual amino acids. In the dynamic properties, two solvent shells could be characterized as well. However, by comparison to simulations of pure water it could be shown that the influence of the protein reaches beyond 6 A, i.e., beyond the first two shells. In the first shell (r < or =3.5 A), the structural and dynamical properties of solvent waters varied considerably and depended primarily on the physicochemical properties of the closest amino acid side chain, with which the waters interact. By contrast, the solvent properties seem not to depend on the specifics of the protein studied (such as the net charge) or on the secondary structure element in which an amino acid is located. While differing considerably from the neat liquid, the properties of waters in the second solvation shell (3.5< r < or =6 A) are rather uniform; a direct influence from surface amino acids are already mostly shielded.

Efficiency of alchemical free energy simulations. I. A practical comparison of the exponential formula, thermodynamic integration, and Bennett's acceptance ratio method.

We investigate the relative efficiency of thermodynamic integration, three variants of the exponential formula, also referred to as thermodynamic perturbation, and Bennetts acceptance ratio method to compute relative and absolute solvation free energy differences. Our primary goal is the development of efficient protocols that are robust in practice. We focus on minimizing the number of unphysical intermediate states (λ‐states) required for the computation of accurate and precise free energy differences. Several indicators are presented which help decide when additional λ‐states are necessary. In all tests Bennetts acceptance ratio method required the least number of λ‐states, closely followed by the “double‐wide” variant of the exponential formula. Use of the exponential formula in only strict “forward” or “backward” mode was not found to be competitive. Similarly, the performance of thermodynamic integration in terms of efficiency was rather poor. We show that this is caused by the use of the trapezoidal rule as method of numerical quadrature. A systematic study focusing on the optimization of thermodynamic integration is presented in a companion paper.

Multiscale Free Energy Simulations: An Efficient Method for Connecting Classical MD Simulations to QM or QM/MM Free Energies Using Non-Boltzmann Bennett Reweighting Schemes.

The reliability of free energy simulations (FES) is limited by two factors: (a) the need for correct sampling and (b) the accuracy of the computational method employed. Classical methods (e.g., force fields) are typically used for FES and present a myriad of challenges, with parametrization being a principle one. On the other hand, parameter-free quantum mechanical (QM) methods tend to be too computationally expensive for adequate sampling. One widely used approach is a combination of methods, where the free energy difference between the two end states is computed by, e.g., molecular mechanics (MM), and the end states are corrected by more accurate methods, such as QM or hybrid QM/MM techniques. Here we report two new approaches that significantly improve the aforementioned scheme; with a focus on how to compute corrections between, e.g., the MM and the more accurate QM calculations. First, a molecular dynamics trajectory that properly samples relevant conformational degrees of freedom is generated. Next, potential energies of each trajectory frame are generated with a QM or QM/MM Hamiltonian. Free energy differences are then calculated based on the QM or QM/MM energies using either a non-Boltzmann Bennett approach (QM-NBB) or non-Boltzmann free energy perturbation (NB-FEP). Both approaches are applied to calculate relative and absolute solvation free energies in explicit and implicit solvent environments. Solvation free energy differences (relative and absolute) between ethane and methanol in explicit solvent are used as the initial test case for QM-NBB. Next, implicit solvent methods are employed in conjunction with both QM-NBB and NB-FEP to compute absolute solvation free energies for 21 compounds. These compounds range from small molecules such as ethane and methanol to fairly large, flexible solutes, such as triacetyl glycerol. Several technical aspects were investigated. Ultimately some best practices are suggested for improving methods that seek to connect MM to QM (or QM/MM) levels of theory in FES.

Efficiency of alchemical free energy simulations. II. Improvements for thermodynamic integration

We attempt to optimize the efficiency of thermodynamic integration, as defined by the minimal number of unphysical intermediate states required for the computation of accurate and precise free energy differences. The suitability of various numerical quadrature methods is tested. In particular, we compare the trapezoidal rule, Simpsons rule, Gauss‐Legendre, Gauss‐Kronrod‐Patterson, and Clenshaw‐Curtis integration, as well as integration based on a cubic spline approximation of the integrand. We find that Simpsons rule and spline integration are already significantly more efficient that the trapezoidal rule, i.e., correct free energy differences can be obtained using fewer λ‐states. We demonstrate that Simpsons rule can be used advantageously with nonequidistant values of the abscissa, which increases the flexibility of the method. Efficiency is enhanced even further if higher order methods, such as Gauss‐Legendre, Gauss‐Kronrod‐Patterson, or Clenshaw‐Curtis integration, are used; no more than seven λ‐states, which in the case of Clenshaw‐Curtis integration include the physical end states, were required for accurate results in all test problems studied. Thus, the performance of thermodynamic integration can equal that of Bennetts acceptance ratio method. We also show, however, that the high efficiency found here relies on the particular functional form of the soft‐core potential used; overall, thermodynamic integration is more susceptible to the details of the hybrid Hamiltonian used than Bennetts acceptance ratio method. Therefore, we recommend Bennetts acceptance ratio method as the most robust method to compute alchemical free energy differences; nevertheless, scenarios when thermodynamic integration may be preferable are discussed.

Dielectric spectroscopy in aqueous solutions of oligosaccharides: Experiment meets simulation

We report the frequency-dependent complex dielectric permittivity of aqueous solutions of the homologous saccharides D(+)-glucose, maltose, and maltotriose in the frequency range 200 MHz⩽ν⩽20 GHz. For each solute, solutions having concentrations between 0.01 and 1 mol dm−3 were studied. In all measured spectra two dispersion/loss regions could be discerned. With the exception of the two most concentrated maltotriose solutions, a good description of the spectra by the superposition of two Debye processes was possible. The amplitudes and correlation times of the glucose and maltose solutions determined from fits of the experimental data were compared to those obtained in an earlier molecular dynamics study of such systems; the overall agreement between experiment and simulation is quite satisfactory. A dielectric component analysis of the simulation results permitted a more detailed assignment of the relaxation processes occurring on the molecular level. The physical picture emerging from this analysis is c...

Hydration Free Energies of Amino Acids: Why Side Chain Analog Data Are Not Enough

Using molecular dynamics based free energy simulations, we computed relative solvation free energies for pairs of N-acetyl-methylamide amino acids (Ala-Ser, Val-Thr, Phe-Tyr, Val-Ala, Thr-Ser, Phe-Ala, and Tyr-Ser) and compared the results with the relative solvation free energies of the corresponding pairs of side chain analogs. We observed differences in (relative) solvent affinity DeltaDeltaDeltaA between amino acids and side chain analogs of up to 66% or, in absolute numbers, 4.9 kcal/mol (Ala-Ser). To rationalize these findings, we estimated separately contributions from what we refer to as solvent exclusion and self-solvation. While the former accounts for the reduction in solute-solvent interactions as one part of the solute occludes other parts of the solute, the latter turned out to be the determining contribution for small polar amino acids and could be shown to arise from interactions between the polar backbone and the polar functional group of the respective side chain in the gas phase. Consequently, the solvent affinity of small polar amino acids depends strongly on the backbone conformation. Our results indicate that the still widely used group additivity-solvent exclusion assumption to estimate solvation free energies for large(r) molecules (such as peptides and proteins) from model compound data (such as side chain analogs) is insufficient. To illustrate practical consequences, we compare the explicit solvent results with those of implicit solvent models. While approaches based on the generalized Born model give results in (mostly) good agreement with explicit solvent, approaches relying (primarily) on the group additivity-solvent exclusion assumption fail to reproduce DeltaDeltaDeltaA. Finally, we briefly discuss the implications of our results for hydrophobicity scales.

Non‐Boltzmann sampling and Bennett's acceptance ratio method: How to profit from bending the rules

The exact computation of free energy differences requires adequate sampling of all relevant low energy conformations. Especially in systems with rugged energy surfaces, adequate sampling can only be achieved by biasing the exploration process, thus yielding non‐Boltzmann probability distributions. To obtain correct free energy differences from such simulations, it is necessary to account for the effects of the bias in the postproduction analysis. We demonstrate that this can be accomplished quite simply with a slight modification of Bennetts Acceptance Ratio method, referring to this technique as Non‐Boltzmann Bennett. We illustrate the method by several examples and show how a creative choice of the biased state(s) used during sampling can also improve the efficiency of free energy simulations.

Alchemical free energy calculations and multiple conformational substates

Thermodynamic integration (TI) was combined with (adaptive) umbrella sampling to improve the convergence of alchemical free energy simulations in which multiple conformational substates are present. The approach, which we refer to as non-Boltzmann TI (NBTI), was tested by computing the free energy differences between three five-atomic model systems, as well as the free energy difference of solvation between leucine and asparagine. In both cases regular TI failed to give converged results, whereas the NBTI results were free from hysteresis and had standard deviations well below +/-0.7 kcal/mole. We also present theoretical considerations that make it possible to compute free energy differences between simple molecules, such as the five-atomic model systems, by numerical integration of the partition functions at the respective end points.

The Jacobian factor in free energy simulations

The role of Jacobian factors in free energy simulations is described. They provide a simple interpretation of ‘‘moment of inertia correction’’ and ‘‘dynamic stretch free energy’’ terms in such simulations. Since the relevant Jacobian factors can often be evaluated analytically by use of the configurational partition function of a polyatomic molecule, it is possible to subtract them from the simulation results when they make unphysical contributions. An important case arises in alchemical simulations that use a single topology method and introduce dummy particles to have the same number of atoms in the initial and final state. The more general utility of the Jacobian factors for simulations of complex systems is briefly discussed.