The zero-multipole summation method for estimating electrostatic interactions in molecular dynamics: analysis of the accuracy and application to liquid systems

A cutoff-based method with charge-distribution-data driven pair potentials for efficiently estimating electrostatic interactions in molecular systems

We introduce a simple cutoff-based method for precise electrostatic energy calculations in the molecular dynamics (MD) simulations of point-particle systems. Our method employs a theoretically derived smooth pair potential function to define electrostatic energy, offering stability and computational efficiency in MD simulations. Instead of imposing specific physical conditions, such as dielectric environments or charge neutrality, we focus on the relationship represented by a single summation formula of charge-weighted pair potentials. This approach allows an accurate energy approximation for each particle, enabling a straightforward error analysis. The resulting particle-dependent pair potential captures the charge distribution information, making it suitable for heterogeneous systems and ensuring an enhanced accuracy through distant information inclusion. Numerical investigations of the Madelung constants of crystalline systems validate the method's accuracy.

Non-Ewald methods for evaluating the electrostatic interactions of charge systems: similarity and difference

In molecular simulations, it is essential to properly calculate the electrostatic interactions of particles in the physical system of interest. Here we consider a method called the non-Ewald method, which does not rely on the standard Ewald method with periodic boundary conditions, but instead relies on the cutoff-based techniques. We focus on the physicochemical and mathematical conceptual aspects of the method in order to gain a deeper understanding of the simulation methodology. In particular, we take into account the reaction field (RF) method, the isotropic periodic sum (IPS) method, and the zero-multipole summation method (ZMM). These cutoff-based methods are based on different physical ideas and are completely distinguishable in their underlying concepts. The RF and IPS methods are "additive" methods that incorporate information outside the cutoff region, via dielectric medium and isotropic boundary condition, respectively. In contrast, the ZMM is a "subtraction" method that tries to remove the artificial effects, generated near the boundary, from the cutoff sphere. Nonetheless, we find physical and/or mathematical similarities between these methods. In particular, the modified RF method can be derived by the principle of neutralization utilized in the ZMM, and we also found a direct relationship between IPS and ZMM.

Reaction-field electrostatics in molecular dynamics simulations: development of a conservative scheme compatible with an atomic cutoff

Shifting and switching schemes are developed to enable strict energy conservation in molecular dynamics simulations relying on reaction-field electrostatic (as well as Lennard-Jones) interactions with an atom-based cutoff truncation.

Effects of number of parallel runs and frequency of bias-strength replacement in generalized ensemble molecular dynamics simulations

Background

The generalized ensemble approach with the molecular dynamics (MD) method has been widely utilized. This approach usually has two features. (i) A bias potential, whose strength is replaced during a simulation, is applied. (ii) Sampling can be performed by many parallel runs of simulations. Although the frequency of the bias-strength replacement and the number of parallel runs can be adjusted, the effects of these settings on the resultant ensemble remain unclear.

Method

In this study, we performed multicanonical MD simulations for a foldable mini-protein (Trp-cage) and two unstructured peptides (8- and 20-residue poly-glutamic acids) with various settings.

Results

As a result, running many short simulations yielded robust results for the Trp-cage model. Regarding the frequency of the bias-potential replacement, although using a high frequency enhanced the traversals in the potential energy space, it did not promote conformational changes in all the systems.

Studies on Molecular Dynamics of Intrinsically Disordered Proteins and Their Fuzzy Complexes: A Mini-Review

The molecular dynamics (MD) method is a promising approach toward elucidating the molecular mechanisms of intrinsically disordered regions (IDRs) of proteins and their fuzzy complexes. This mini-review introduces recent studies that apply MD simulations to investigate the molecular recognition of IDRs. Firstly, methodological issues by which MD simulations treat IDRs, such as developing force fields, treating periodic boundary conditions, and enhanced sampling approaches, are discussed. Then, several examples of the applications of MD to investigate molecular interactions of IDRs in terms of the two kinds of complex formations; coupled-folding and binding and fuzzy complex. MD simulations provide insight into the molecular mechanisms of these binding processes by sampling conformational ensembles of flexible IDRs. In particular, we focused on all-atom explicit-solvent MD simulations except for studies of higher-order assembly of IDRs. Recent advances in MD methods, and computational power make it possible to dissect the molecular details of realistic molecular systems involving the dynamic behavior of IDRs.

Performance evaluation of the zero-multipole summation method in modern molecular dynamics software

The zero-multiple summation method (ZMM) is a cutoff-based method for calculating electrostatic interactions in molecular dynamics simulations, utilizing an electrostatic neutralization principle as a physical basis. Since the accuracies of the ZMM have been revealed to be sufficient in previous studies, it is highly desirable to clarify its practical performance. In this paper, the performance of the ZMM is compared with that of the smooth particle mesh Ewald method (SPME), where the both methods are implemented in molecular dynamics software package GROMACS. Extensive performance comparisons against a highly optimized, parameter-tuned SPME implementation are performed for various-sized water systems and two protein-water systems. We analyze in detail the dependence of the performance on the potential parameters and the number of CPU cores. Even though the ZMM uses a larger cutoff distance than the SPME does, the performance of the ZMM is comparable to or better than that of the SPME. This is because the ZMM does not require a time-consuming electrostatic convolution and because the ZMM gains short neighbor-list distances due to the smooth damping feature of the pairwise potential function near the cutoff length. We found, in particular, that the ZMM with quadrupole or octupole cancellation and no damping factor is an excellent candidate for the fast calculation of electrostatic interactions. © 2018 Wiley Periodicals, Inc.

Phosphorylation of an intrinsically disordered region of Ets1 shifts a multi-modal interaction ensemble to an auto-inhibitory state

Multi-modal interactions are frequently observed in intrinsically disordered regions (IDRs) of proteins upon binding to their partners. In many cases, post-translational modifications in IDRs are accompanied by coupled folding and binding. From both molecular simulations and biochemical experiments with mutational studies, we show that the IDR including a Ser rich region (SRR) of the transcription factor Ets1, just before the DNA-binding core domain, undergoes multi-modal interactions when the SRR is not phosphorylated. In the phosphorylated state, the SRR forms a few specific complex structures with the Ets1 core, covering the recognition helix in the core and drastically reducing the DNA binding affinities as the auto-inhibitory state. The binding kinetics of mutated Ets1 indicates that aromatic residues in the SRR can be substituted with other hydrophobic residues for the interactions with the Ets1 core.

Enhanced Sampling of Molecular Dynamics Simulations of a Polyalanine Octapeptide: Effects of the Periodic Boundary Conditions on Peptide Conformation

We investigate the problem of artifacts caused by the periodic boundary conditions (PBC) used in molecular simulation studies. Despite the long history of simulations with PBCs, the existence of measurable artifacts originating from PBCs applied to inherently nonperiodic physical systems remains controversial. Specifically, these artifacts appear as differences between simulations of the same system but with different simulation-cell sizes. Earlier studies have implied that, even in the simple case of a small model peptide in water, sampling inefficiency is a major obstacle to understanding these artifacts. In this study, we have resolved the sampling issue using the replica exchange molecular dynamics (REMD) enhanced-sampling method to explore PBC artifacts. Explicitly solvated zwitterionic polyalanine octapeptides with three different cubic-cells, having dimensions of L = 30, 40, and 50 Å, were investigated to elucidate the differences with 64 replica × 500 ns REMD simulations using the AMBER parm99SB force field. The differences among them were not large overall, and the results for the L = 30 and 40 Å simulations in the conformational free energy landscape were found to be very similar at room temperature. However, a small but statistically significant difference was seen for L = 50 Å. We observed that extended conformations were slightly overstabilized in the smaller systems. The origin of these artifacts is discussed by comparison to an electrostatic calculation method without PBCs.

Molecular mechanisms of cooperative binding of transcription factors Runx1-CBFβ-Ets1 on the TCRα gene enhancer

Ets1 is an essential transcription factor (TF) for several important physiological processes, including cell proliferation and differentiation. Its recognition of the enhancer region of the TCRα gene is enhanced by the cooperative binding of the Runx1–CBFβ heterodimer, with the cancelation of phosphorylation-dependent autoinhibition. The detailed mechanism of this interesting cooperativity between Ets1 and the Runx1–CBFβ heterodimer is still largely unclear. Here, we investigated the molecular mechanisms of this cooperativity, by using molecular dynamics simulations. Consequently, we detected high flexibility of the loop region between the HI2 and H1 helices of Ets1. Upon Runx1–CBFβ heterodimer binding, this loop transiently adopts various sub-stable conformations in its interactions with the DNA. In addition, a network analysis suggested an allosteric pathway in the molecular assembly and identified some key residues that coincide with previous experimental studies. Our simulations suggest that the cooperative binding of Ets1 and the Runx1–CBFβ heterodimer alters the DNA conformation and induces sub-stable conformations of the HI2–H1 loop of Ets1. This phenomenon increases the flexibility of the regulatory module, including the HI2 helix, and destabilizes the inhibitory form of this module. Thus, we hypothesize that this effect facilitates Ets1–DNA binding and prevents the phosphorylation-dependent DNA binding autoinhibition.

Revisiting antibody modeling assessment for CDR-H3 loop

The antigen-binding site of antibodies, also known as complementarity-determining region (CDR), has hypervariable sequence properties. In particular, the third CDR loop of the heavy chain, CDR-H3, has such variability in its sequence, length, and conformation that ordinary modeling techniques cannot build a high-quality structure. At Stage 2 of the Second Antibody Modeling Assessment (AMA-II) held in 2013, the model structures of the CDR-H3 loops were submitted by the seven modelers and were critically assessed. After our participation in AMA-II, we rebuilt one of the long CDR-H3 loops with 13 residues (A52 antibody) by a more precise method, using enhanced conformational sampling with the explicit water model, as compared to our previous method employed at AMA-II. The current stable models obtained from the free energy landscape at 300 K include structures similar to the X-ray crystal structures. Those models were not built in our previous work at AMA-II. The current free energy landscape suggested that the CDR-H3 loop structures in the crystal are not stable in solution, but they are stabilized by the crystal packing effect.

myPresto/omegagene: a GPU-accelerated molecular dynamics simulator tailored for enhanced conformational sampling methods with a non-Ewald electrostatic scheme

Molecular dynamics (MD) is a promising computational approach to investigate dynamical behavior of molecular systems at the atomic level. Here, we present a new MD simulation engine named "myPresto/omegagene" that is tailored for enhanced conformational sampling methods with a non-Ewald electrostatic potential scheme. Our enhanced conformational sampling methods, e.g., the virtual-system-coupled multi-canonical MD (V-McMD) method, replace a multi-process parallelized run with multiple independent runs to avoid inter-node communication overhead. In addition, adopting the non-Ewald-based zero-multipole summation method (ZMM) makes it possible to eliminate the Fourier space calculations altogether. The combination of these state-of-the-art techniques realizes efficient and accurate calculations of the conformational ensemble at an equilibrium state. By taking these advantages, myPresto/omegagene is specialized for the single process execution with Graphics Processing Unit (GPU). We performed benchmark simulations for the 20-mer peptide, Trp-cage, with explicit solvent. One of the most thermodynamically stable conformations generated by the V-McMD simulation is very similar to an experimentally solved native conformation. Furthermore, the computation speed is four-times faster than that of our previous simulation engine, myPresto/psygene-G. The new simulator, myPresto/omegagene, is freely available at the following URLs: http://www.protein.osaka-u.ac.jp/rcsfp/pi/omegagene/ and http://presto.protein.osaka-u.ac.jp/myPresto4/.

Elastic properties of dynein motor domain obtained from all-atom molecular dynamics simulations

Dyneins are large microtubule motor proteins that convert ATP energy to mechanical power. High-resolution crystal structures of ADP-bound cytoplasmic dynein have revealed the organization of the motor domain, comprising the AAA(+) ring, the linker, the stalk/strut and the C sequence. Recently, the ADP.vanadate-bound structure, which is similar to the ATP hydrolysis transition state, revealed how the structure of dynein changes upon ATP binding. Although both the ADP- and ATP-bound state structures have been resolved, the dynamic properties at the atomic level remain unclear. In this work, we built two models named 'the ADP model' and 'the ATP model', where ADP and ATP are bound to AAA1 in the AAA(+) ring, respectively, to observe the initial procedure of the structural change from the unprimed to the primed state. We performed 200-ns molecular dynamics simulations for both models and compared their structures and dynamics. The motions of the stalk, consisting of a long coiled coil with a microtubule-binding domain, significantly differed between the two models. The elastic properties of the stalk were analyzed and compared with the experimental results.