A molecular reconstruction approach to sitebased 3D-RISM and comparison to GIST hydration thermodynamic maps in an enzyme active site

Computed, high-resolution, spatial distributions of solvation energy and entropy can provide detailed information about the role of water in molecular recognition. While grid inhomogeneous solvation theory (GIST) provides rigorous, detailed thermodynamic information from explicit solvent molecular dynamics simulations, recent developments in the 3D reference interaction site model (3D-RISM) theory allow many of the same quantities to be calculated in a fraction of the time. However, 3D-RISM produces atomic-site, rather than molecular, density distributions, which are difficult to extract physical meaning from. To overcome this difficulty, we introduce a method to reconstruct molecular density distributions from atomic site density distributions. Furthermore, we assess the quality of the resulting solvation thermodynamics density distributions by analyzing the binding site of coagulation Factor Xa with both GIST and 3D-RISM. We find good qualitative agreement between the methods for oxygen and hydrogen densities as well as direct solute-solvent energetic interactions. However, 3D-RISM predicts lower energetic and entropic penalties for moving water from the bulk to the binding site

Accelerating the 3D reference interaction site model theory of molecular solvation with treecode summation and cut-offs

The 3D reference interaction site model (3D-RISM) of molecular solvation is a powerful tool for computing the equilibrium thermodynamics and density distributions of solvents, such as water and co-ions, around solute molecules. However, 3D-RISM solutions can be expensive to calculate, especially for proteins and other large molecules where calculating the potential energy between solute and solvent requires more than half the computation time. To address this problem, we have developed and implemented treecode summation for long-range interactions and analytically corrected cut-offs for short-range interactions to accelerate the potential energy and long-range asymptotics calculations in non-periodic 3D-RISM in the AmberTools molecular modeling suite. For the largest single protein considered in this work, tubulin, the total computation time was reduced by a factor of 4. In addition, parallel calculations with these new methods scale almost linearly and the iterative solver remains the largest impediment to parallel scaling. To demonstrate the utility of our approach for large systems, we used 3D-RISM to calculate the solvation thermodynamics and density distribution of 7-ring microtubule, consisting of 910 tubulin dimers, over 1.2 million atoms.The 3D reference interaction site model (3D-RISM) of molecular solvation computes equilibrium thermodynamics and density distributions of solvents around solute molecules. To accelerate 3D-RISM for large biomolecules, we have developed treecode summation and analytically corrected cut-offs for long- and short-range interactions. This reduces the overall computation time by a factor of 4 for the protein tubulin and allowed the calculation of solvation thermodynamics for a 1.2 million atom microtubule.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/172852/1/jcc26889.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/172852/2/jcc26889_am.pd

Identifying Systematic Force Field Errors Using a 3D-RISM Element Counting Correction

Hydration free energies of small molecules are commonly used as benchmarks for solvation models. However, errors in predicting hydration free energies are partially due to the force fields used and not just the solvation model. To address this, we have used the 3D reference interaction site model (3D-RISM) of molecular solvation and existing benchmark explicit solvent calculations with a simple element count correction (ECC) to identify problems with the non-bond parameters in the general AMBER force field (GAFF). 3D-RISM was used to calculate hydration free energies of all 642 molecules in the FreeSolv database, and a partial molar volume correction (PMVC), ECC, and their combination (PMVECC) were applied to the results. The PMVECC produced a mean unsigned error of 1.01±0.04kcal/mol and root mean squared error of 1.44±0.07kcal/mol, better than the benchmark explicit solvent calculations from FreeSolv, and required less than 15 s of computing time per molecule on a single CPU core. Importantly, parameters for PMVECC showed systematic errors for molecules containing Cl, Br, I, and P. Applying ECC to the explicit solvent hydration free energies found the same systematic errors. The results strongly suggest that some small adjustments to the Lennard–Jones parameters for GAFF will lead to improved hydration free energy calculations for all solvent models

Identifying Systematic Force Field Errors Using a 3D-RISM Element Counting Correction

Hydration free energies of small molecules are commonly used as benchmarks for solvation models. However, errors in predicting hydration free energies are partially due to the force fields used and not just the solvation model. To address this, we have used the 3D reference interaction site model (3D-RISM) of molecular solvation and existing benchmark explicit solvent calculations with a simple element count correction (ECC) to identify problems with the non-bond parameters in the general AMBER force field (GAFF). 3D-RISM was used to calculate hydration free energies of all 642 molecules in the FreeSolv database, and a partial molar volume correction (PMVC), ECC, and their combination (PMVECC) were applied to the results. The PMVECC produced a mean unsigned error of 1.01±0.04kcal/mol and root mean squared error of 1.44±0.07kcal/mol, better than the benchmark explicit solvent calculations from FreeSolv, and required less than 15 s of computing time per molecule on a single CPU core. Importantly, parameters for PMVECC showed systematic errors for molecules containing Cl, Br, I, and P. Applying ECC to the explicit solvent hydration free energies found the same systematic errors. The results strongly suggest that some small adjustments to the Lennard–Jones parameters for GAFF will lead to improved hydration free energy calculations for all solvent models

An MM/3D-RISM approach for ligand binding affinities.

We have modified the popular MM/PBSA or MM/GBSA approaches (molecular mechanics for a biomolecule, combined with a Poisson-Boltzmann or generalized Born electrostatic and surface area nonelectrostatic solvation energy) by employing instead the statistical-mechanical, three-dimensional molecular theory of solvation (also known as 3D reference interaction site model, or 3D-RISM-KH) coupled with molecular mechanics or molecular dynamics ( Blinov , N. ; et al. Biophys. J. 2010 ; Luchko , T. ; et al. J. Chem. Theory Comput. 2010 ). Unlike the PBSA or GBSA semiempirical approaches, the 3D-RISM-KH theory yields a full molecular picture of the solvation structure and thermodynamics from the first principles, with proper account of chemical specificities of both solvent and biomolecules, such as hydrogen bonding, hydrophobic interactions, salt bridges, etc. We test the method on the binding of seven biotin analogues to avidin in aqueous solution and show it to work well in predicting the ligand-binding affinities. We have compared the results of 3D-RISM-KH with four different generalized Born and two Poisson-Boltzmann methods. They give absolute binding energies that differ by up to 208 kJ/mol and mean absolute deviations in the relative affinities of 10-43 kJ/mol

Ion Counting from Explicit-Solvent Simulations and 3D-RISM

AbstractThe ionic atmosphere around nucleic acids remains only partially understood at atomic-level detail. Ion counting (IC) experiments provide a quantitative measure of the ionic atmosphere around nucleic acids and, as such, are a natural route for testing quantitative theoretical approaches. In this article, we replicate IC experiments involving duplex DNA in NaCl(aq) using molecular dynamics (MD) simulation, the three-dimensional reference interaction site model (3D-RISM), and nonlinear Poisson-Boltzmann (NLPB) calculations and test against recent buffer-equilibration atomic emission spectroscopy measurements. Further, we outline the statistical mechanical basis for interpreting IC experiments and clarify the use of specific concentration scales. Near physiological concentrations, MD simulation and 3D-RISM estimates are close to experimental results, but at higher concentrations (>0.7 M), both methods underestimate the number of condensed cations and overestimate the number of excluded anions. The effect of DNA charge on ion and water atmosphere extends 20–25 Å from its surface, yielding layered density profiles. Overall, ion distributions from 3D-RISMs are relatively close to those from corresponding MD simulations, but with less Na+ binding in grooves and tighter binding to phosphates. NLPB calculations, on the other hand, systematically underestimate the number of condensed cations at almost all concentrations and yield nearly structureless ion distributions that are qualitatively distinct from those generated by both MD simulation and 3D-RISM. These results suggest that MD simulation and 3D-RISM may be further developed to provide quantitative insight into the characterization of the ion atmosphere around nucleic acids and their effect on structure and stability

A molecular reconstruction approach to site-based 3D-RISM and comparison to GIST hydration thermodynamic maps in an enzyme active site.

Computed, high-resolution, spatial distributions of solvation energy and entropy can provide detailed information about the role of water in molecular recognition. While grid inhomogeneous solvation theory (GIST) provides rigorous, detailed thermodynamic information from explicit solvent molecular dynamics simulations, recent developments in the 3D reference interaction site model (3D-RISM) theory allow many of the same quantities to be calculated in a fraction of the time. However, 3D-RISM produces atomic-site, rather than molecular, density distributions, which are difficult to extract physical meaning from. To overcome this difficulty, we introduce a method to reconstruct molecular density distributions from atomic-site density distributions. Furthermore, we assess the quality of the resulting solvation thermodynamics density distributions by analyzing the binding site of coagulation Factor Xa with both GIST and 3D-RISM. We find good qualitative agreement between the methods for oxygen and hydrogen densities as well as direct solute-solvent energetic interactions. However, 3D-RISM predicts lower energetic and entropic penalties for moving water from the bulk to the binding site

Conformational Analysis of the Carboxy-Terminal Tails of Human β-Tubulin Isotypes

Several isotypes of the structural protein tubulin have been characterized. Their expression offers a plausible explanation for differences regarding microtubule function. Although sequence variation between tubulin isotypes occurs throughout the entire protein, it is the extreme carboxy-terminal tails (CTTs) that exhibit the greatest concentration of differences. In humans, the CTTs range in length from 9 to 25 residues and because of a considerable number of glutamic acid residues, contain over 1/3 of tubulin's total electrostatic charge. The CTTs are believed to be highly disordered and their precise function has yet to be determined. However, their absence has been shown to result in altered microtubule stability and a reduction in the interaction with several microtubule-associated proteins (MAPs). To characterize the role that CTTs play in microtubule function, we examined the global conformational differences within a set of nine human β-tubulin isotypes using replica exchange molecular dynamics simulations. Through the analysis of the resulting configuration ensembles, we quantified differences such as the CTTs sequence influence on overall flexibility and average secondary structure. Although only minor variations between each CTT were observed, we suggest that these differences may be significant enough to affect interactions with MAPs, thereby influencing important properties such as microtubule assembly and stability