Molecular dynamics simulations of double-stranded DNA in an explicit solvent model with the zero-dipole summation method

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.

Thermal stability of single-domain antibodies estimated by molecular dynamics simulations

Single‐domain antibodies (sdAbs) function like regular antibodies, however, consist of only one domain. Because of their low molecular weight, sdAbs have advantages with respect to production and delivery to their targets and for applications such as antibody drugs and biosensors. Thus, sdAbs with high thermal stability are required. In this work, we chose seven sdAbs, which have a wide range of melting temperature (T_m) values and known structures. We applied molecular dynamics (MD) simulations to estimate their relative stability and compared them with the experimental data. High‐temperature MD simulations at 400 K and 500 K were executed with simulations at 300 K as a control. The fraction of native atomic contacts, Q, measured for the 400 K simulations showed a fairly good correlation with the T_m values. Interestingly, when the residues were classified by their hydrophobicity and size, the Q values of hydrophilic residues exhibited an even better correlation, suggesting that stabilization is correlated with favorable interactions of hydrophilic residues. Measuring the Q value on a per‐residue level enabled us to identify residues that contribute significantly to the instability and thus demonstrating how our analysis can be used in a mutant case study.

Structural Dynamics of the PET-Degrading Cutinase-like Enzyme from Saccharomonospora viridis AHK190 in Substrate-Bound States Elucidates the Ca2+-Driven Catalytic Cycle

A cutinase-type polyesterase from Saccharomonospora viridis AHK190 (Cut190) has been shown to degrade the inner block of polyethylene terephthalate. A unique feature of Cut190 is that its function and stability are regulated by Ca²⁺ binding. Our previous crystal structure analysis of Cut190S226P showed that one Ca²⁺ binds to the enzyme, which induces large conformational changes in several loop regions to stabilize an open conformation [Miyakawa, T., et al. (2015) Appl. Microbiol. Biotechnol. 99, 4297]. In this study, to analyze the substrate recognition mechanism of Cut190, we determined the crystal structure of the inactive form of a Cut190 mutant, Cut190*S176A, in complex with calcium ions and/or substrates. We found that three calcium ions bind to Cut190*S176A, which is supported by analysis using native mass spectrometry experiments and 3D Reference Interaction Site Model calculations. The complex structures with the two substrates, monoethyl succinate and monoethyl adipate (engaged and open forms), presumably correspond to the pre- and post-reaction states, as the ester bond is close to the active site and pointing outward from the active site, respectively, for the two complexes. Ca²⁺ binding induces the pocket to open, enabling the substrate to access the pocket more easily. Molecular dynamics simulations suggest that a post-reaction state in the engaged form presumably exists between the experimentally observed forms, indicating that the substrate would be cleaved in the engaged form and then requires the enzyme to change to the open form to release the product, a process that Ca²⁺ can greatly accelerate.

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.

B-DNA model systems in non-terran bio-solvents: implications for structure, stability and replication

We have computationally analyzed a comprehensive series of Watson–Crick and mismatched B-DNA base pairs, in the gas phase and in several solvents, including toluene, chloroform, ammonia, methanol and water, using dispersion-corrected density functional theory and implicit solvation.

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.

Mathematical and computational modeling in biology at multiple scales

A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields for protein simulations and methods for the calculation of solvation free energies. The utility of quantum mechanical methods in biophysical and biochemical modeling is explored. The field of computational enzymology is examined.

A novel approach of dynamic cross correlation analysis on molecular dynamics simulations and its application to Ets1 dimer-DNA complex

The dynamic cross correlation (DCC) analysis is a popular method for analyzing the trajectories of molecular dynamics (MD) simulations. However, it is difficult to detect correlative motions that appear transiently in only a part of the trajectory, such as atomic contacts between the side-chains of amino acids, which may rapidly flip. In order to capture these multi-modal behaviors of atoms, which often play essential roles, particularly at the interfaces of macromolecules, we have developed the "multi-modal DCC (mDCC)" analysis. The mDCC is an extension of the DCC and it takes advantage of a Bayesian-based pattern recognition technique. We performed MD simulations for molecular systems modeled from the (Ets1)2-DNA complex and analyzed their results with the mDCC method. Ets1 is an essential transcription factor for a variety of physiological processes, such as immunity and cancer development. Although many structural and biochemical studies have so far been performed, its DNA binding properties are still not well characterized. In particular, it is not straightforward to understand the molecular mechanisms how the cooperative binding of two Ets1 molecules facilitates their recognition of Stromelysin-1 gene regulatory elements. A correlation network was constructed among the essential atomic contacts, and the two major pathways by which the two Ets1 molecules communicate were identified. One is a pathway via direct protein-protein interactions and the other is that via the bound DNA intervening two recognition helices. These two pathways intersected at the particular cytosine bases (C110/C11), interacting with the H1, H2, and H3 helices. Furthermore, the mDCC analysis showed that both pathways included the transient interactions at their intermolecular interfaces of Tyr396-C11 and Ala327-Asn380 in multi-modal motions of the amino acid side chains and the nucleotide backbone. Thus, the current mDCC approach is a powerful tool to reveal these complicated behaviors and scrutinize intermolecular communications in a molecular system.

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

In the preceding paper [I. Fukuda, J. Chem. Phys. 139, 174107 (2013)], the zero-multipole (ZM) summation method was proposed for efficiently evaluating the electrostatic Coulombic interactions of a classical point charge system. The summation takes a simple pairwise form, but prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large energetic noises and significant artifacts. The purpose of this paper is to judge the ability of the ZM method by investigating the accuracy, parameter dependencies, and stability in applications to liquid systems. To conduct this, first, the energy-functional error was divided into three terms and each term was analyzed by a theoretical error-bound estimation. This estimation gave us a clear basis of the discussions on the numerical investigations. It also gave a new viewpoint between the excess energy error and the damping effect by the damping parameter. Second, with the aid of these analyses, the ZM method was evaluated based on molecular dynamics (MD) simulations of two fundamental liquid systems, a molten sodium-chlorine ion system and a pure water molecule system. In the ion system, the energy accuracy, compared with the Ewald summation, was better for a larger value of multipole moment l currently induced until l ≲ 3 on average. This accuracy improvement with increasing l is due to the enhancement of the excess-energy accuracy. However, this improvement is wholly effective in the total accuracy if the theoretical moment l is smaller than or equal to a system intrinsic moment L. The simulation results thus indicate L ∼ 3 in this system, and we observed less accuracy in l = 4. We demonstrated the origins of parameter dependencies appearing in the crossing behavior and the oscillations of the energy error curves. With raising the moment l we observed, smaller values of the damping parameter provided more accurate results and smoother behaviors with respect to cutoff length were obtained. These features can be explained, on the basis of the theoretical error analyses, such that the excess energy accuracy is improved with increasing l and that the total accuracy improvement within l ⩽ L is facilitated by a small damping parameter. Although the accuracy was fundamentally similar to the ion system, the bulk water system exhibited distinguishable quantitative behaviors. A smaller damping parameter was effective in all the practical cutoff distance, and this fact can be interpreted by the reduction of the excess subset. A lower moment was advantageous in the energy accuracy, where l = 1 was slightly superior to l = 2 in this system. However, the method with l = 2 (viz., the zero-quadrupole sum) gave accurate results for the radial distribution function. We confirmed the stability in the numerical integration for MD simulations employing the ZM scheme. This result is supported by the sufficient smoothness of the energy function. Along with the smoothness, the pairwise feature and the allowance of the atom-based cutoff mode on the energy formula lead to the exact zero total-force, ensuring the total-momentum conservations for typical MD equations of motion.

Structure of the entire stalk region of the Dynein motor domain

Dyneins are large microtubule-based motor complexes that power a range of cellular processes including the transport of organelles, as well as the beating of cilia and flagella. The motor domain is located within the dynein heavy chain and comprises an N-terminal mechanical linker element, a central ring of six AAA+ modules of which four bind or hydrolyze ATP, and a long stalk extending from the AAA+ring with a microtubule-binding domain (MTBD) at its tip. A crucial mechanism underlying the motile activity of cytoskeletal motor proteins is precise coupling between the ATPase and track-binding activities. In dynein, a stalk region consisting of a long (~15nm) antiparallel coiled coil separates these two activities, which must facilitate communication between them. This communication is mediated by a small degree of helix sliding in the coiled coil. However, no high-resolution structure is available of the entire stalk region including the MTBD. Here, we have reported the structure of the entire stalk region of mouse cytoplasmic dynein in a weak microtubule-binding state, which was determined using X-ray crystallography, and have compared it with the dynein motor domain from Dictyostelium discoideum in a strong microtubule-binding state and with a mouse MTBD with its distal portion of the coiled coil fused to seryl-tRNA synthetase from Thermus thermophilus. Our results strongly support the helix-sliding model based on the complete structure of the dynein stalk with a different form of coiled-coil packing. We also propose a plausible mechanism of helix sliding together with further analysis using molecular dynamics simulations. Our results present the importance of conserved proline residues for an elastic motion of stalk coiled coil and imply the manner of change between high-affinity state and low-affinity state of MTBD.

The fuzzy oil drop model, based on hydrophobicity density distribution, generalizes the influence of water environment on protein structure and function

In this paper we show that the fuzzy oil drop model represents a general framework for describing the generation of hydrophobic cores in proteins and thus provides insight into the influence of the water environment upon protein structure and stability. The model has been successfully applied in the study of a wide range of proteins, however this paper focuses specifically on domains representing immunoglobulin-like folds. Here we provide evidence that immunoglobulin-like domains, despite being structurally similar, differ with respect to their participation in the generation of hydrophobic core. It is shown that β-structural fragments in β-barrels participate in hydrophobic core formation in a highly differentiated manner. Quantitatively measured participation in core formation helps explain the variable stability of proteins and is shown to be related to their biological properties. This also includes the known tendency of immunoglobulin domains to form amyloids, as shown using transthyretin to reveal the clear relation between amyloidogenic properties and structural characteristics based on the fuzzy oil drop model.

Molecular Dynamics Simulations Accelerated by GPU for Biological Macromolecules with a Non-Ewald Scheme for Electrostatic Interactions

A molecular dynamics (MD) simulation program for biological macromolecules was implemented with a non-Ewald scheme for long-ranged electrostatic interactions and run on a general purpose graphics processing unit (GPU). We recently developed several non-Ewald methods to compute the electrostatic energies with high precision. In particular, the zero-dipole summation (ZD) method, which takes into account the neutralities of charges and dipoles in a truncated subset, enables the calculation of electrostatic interactions with high accuracy and low computational cost, and its algorithm is simple enough to be implemented in a GPU. We developed an MD program with the space decomposition algorithm, myPresto/psygene, and applied it to several biological macromolecular systems with GPUs implementing the ZD method. Rapid computing performance with high accuracy was obtained.