The statistical-mechanics study for the distribution of water molecules in aquaporin

RISMiCal: A software package to perform fast RISM/3D-RISM calculations

Solvent plays an essential role in a variety of chemical, physical, and biological processes that occur in the solution phase. The reference interaction site model (RISM) and its three-dimensional extension (3D-RISM) serve as powerful computational tools for modeling solvation effects in chemical reactions, biological functions, and structure formations. We present the RISM integrated calculator (RISMiCal) program package, which is based on RISM and 3D-RISM theories with fast GPU code. RISMiCal has been developed as an integrated RISM/3D-RISM program that has interfaces with external programs such as Gaussian16, GAMESS, and Tinker. Fast 3D-RISM programs for single- and multi-GPU codes written in CUDA would enhance the availability of these hybrid methods because they require the performance of many computationally expensive 3D-RISM calculations. We expect that our package can be widely applied for chemical and biological processes in solvent. The RISMiCal package is available at https://rismical-dev.github.io.

Potential of Mean Force Calculations of Solute Permeation Across UT-B and AQP1: A Comparison between Molecular Dynamics and 3D-RISM

Membrane channels facilitate the efficient and selective flux of various solutes across biological membranes. A common approach to investigate the selectivity of a channel has been the calculation of potentials of mean force (PMFs) for solute permeation across the pore. PMFs have been frequently computed from molecular dynamics (MD) simulations, yet the three-dimensional reference interaction site model (3D-RISM) has been suggested as a computationally efficient alternative to MD. Whether the two methods yield comparable PMFs for solute permeation has remained unclear. In this study, we calculated potentials of mean force for water, ammonia, urea, molecular oxygen, and methanol across the urea transporter B (UT-B) and aquaporin-1 (AQP1), using 3D-RISM, as well as using MD simulations and umbrella sampling. To allow direct comparison between the PMFs from 3D-RISM and MD, we ensure that all PMFs refer to a well-defined reference area in the bulk or, equivalently, to a well-defined density of channels in the membrane. For PMFs of water permeation, we found reasonable agreement between the two methods, with differences of ≲3 kJ mol-1. In contrast, we found stark discrepancies for the PMFs for all other solutes. Additional calculations confirm that discrepancies between MD and 3D-RISM are not explained by the choice for the closure relation, the definition the reaction coordinate (center of mass-based versus atomic site-based), details of the molecule force field, or fluctuations of the protein. Comparison of the PMFs suggests that 3D-RISM may underestimate effects from hydrophobic solute-channel interactions, thereby, for instance, missing the urea binding sites in UT-B. Furthermore, we speculate that the orientational averages inherent to 3D-RISM might lead to discrepancies in the narrow channel lumen. These findings suggest that current 3D-RISM solvers provide reasonable estimates for the PMF for water permeation, but that they are not suitable to study the selectivity of membrane channels with respect to uncharged nonwater solutes.

Modified Anderson Method for Accelerating 3D-RISM Calculations Using Graphics Processing Unit

A fast algorithm is proposed to solve the three-dimensional reference interaction site model (3D-RISM) theory on a graphics processing unit (GPU). 3D-RISM theory is a powerful tool for investigating biomolecular processes in solution; however, such calculations are often both memory-intensive and time-consuming. We sought to accelerate these calculations using GPUs, but to work around the problem of limited memory size in GPUs, we modified the less memory-intensive "Anderson method" to give faster convergence to 3D-RISM calculations. Using this method on a Tesla C2070 GPU, we reduced the total computational time by a factor of 8, 1.4 times by the modified Andersen method and 5.7 times by GPU, compared to calculations on an Intel Xeon machine (eight cores, 3.33 GHz) with the conventional method.

Placevent: an algorithm for prediction of explicit solvent atom distribution-application to HIV-1 protease and F-ATP synthase

We have created a simple algorithm for automatically predicting the explicit solvent atom distribution of biomolecules. The explicit distribution is coerced from the three-dimensional (3D) continuous distribution resulting from a 3D reference interaction site model (3D-RISM) calculation. This procedure predicts optimal location of solvent molecules and ions given a rigid biomolecular structure and the solvent composition. We show examples of predicting water molecules near the KNI-272 bound form of HIV-1 protease and predicting both sodium ions and water molecules near the rotor ring of F-adenosine triphosphate (ATP) synthase. Our results give excellent agreement with experimental structure with an average prediction error of 0.39-0.65 Å. Further, unlike experimental methods, this method does not suffer from the partial occupancy limit. Our method can be performed directly on 3D-RISM output within minutes. It is extremely useful for examining multiple specific solvent-solute interactions, as a convenient method for generating initial solvent structures for molecular dynamics calculations, and may assist in refinement of experimental structures. © 2012 Wiley Periodicals, Inc.

A New Approach for Investigating the Molecular Recognition of Protein: Toward Structure-Based Drug Design Based on the 3D-RISM Theory

A new approach to investigate a molecular recognition process of protein is presented based on the three-dimensional reference interaction site model (3D-RISM) theory, a statistical mechanics theory of molecular liquids. Numerical procedure for solving the conventional 3D-RISM equation consists of two steps. In step 1, we solve ordinary RISM (or 1D-RISM) equations for a solvent mixture including target ligands in order to obtain the density pair correlation functions (PCF) among molecules in the solution. Then, we solve the 3D-RISM equation for a solute-solvent system to find three-dimensional density distribution functions (3D-DDF) of solvent species around a protein, using PCF obtained in the first step. A key to the success of the method was to regard a target ligand as one of "solvent" species. However, the success is limited due to a difficulty of solving the 1D-RISM equation for a solvent mixture, including large ligand molecules. In the present paper, we propose a method which eases the limitation concerning solute size in the conventional method. In this approach, we solve a solute-solute 3D-RISM equations for a protein-ligand system in which both proteins and ligands are regarded as "solutes" at infinite dilution. The 3D- and 1D-RISM equations are solved for protein-solvent and ligand-solvent systems, respectively, in order to obtain the 3D- and 1D-DDF of solvent around the solutes, which are required for solving the solute-solute 3D-RISM equation. The method is applied to two practical and noteworthy examples concerning pharmaceutical design. One is an odorant binding protein in the Drosophila melanogaster , which binds an ethanol molecule. The other is phospholipase A2, which is known as a receptor of acetylsalicylic acid or aspirin. The result indicates that the method successfully reproduces the binding mode of the ligand molecules in the binding sites measured by the experiments.

Molecular recognition in biomolecules studied by statistical-mechanical integral-equation theory of liquids

Recent progress in the theory of molecular recognition in biomolecules is reviewed, which has been made based on the statistical mechanics of liquids or the RISM/3D-RISM theory during the last five years in the authors' group. The method requires just the structure of protein and the potential energy parameters for the biomolecules and solutions as inputs. The calculation is carried out in two steps. The first step is to obtain the pair correlation functions for solutions consisting of water and ligands based on the RISM theory. Then, given the pair correlation functions prepared in the first step, we calculate the 3D-distribution functions of water and ligands around and inside protein based on the 3D-RISM theory. The molecular recognition of a ligand by the protein is realized by the 3D-distribution functions: if one finds some conspicuous peaks in the distribution of a ligand inside protein, then the ligand is regarded as "recognized" by the protein. Some biochemical processes are investigated, which are intimately related to the molecular recognition of small ligands including water, noble gases, and ions by a protein.