Development of MD Engine: High-speed accelerator with parallel processor design for molecular dynamics simulations

Computer simulation of molecular recognition in biomolecular system: from in silico screening to generalized ensembles

Prediction of ligand-receptor complex structure is important in both the basic science and the industry such as drug discovery. We report various computation molecular docking methods: fundamental in silico (virtual) screening, ensemble docking, enhanced sampling (generalized ensemble) methods, and other methods to improve the accuracy of the complex structure. We explain not only the merits of these methods but also their limits of application and discuss some interaction terms which are not considered in the in silico methods. In silico screening and ensemble docking are useful when one focuses on obtaining the native complex structure (the most thermodynamically stable complex). Generalized ensemble method provides a free-energy landscape, which shows the distribution of the most stable complex structure and semi-stable ones in a conformational space. Also, barriers separating those stable structures are identified. A researcher should select one of the methods according to the research aim and depending on complexity of the molecular system to be studied.

Stochastic Lag Time Parameterization for Markov State Models of Protein Dynamics

Markov state models (MSMs) play a key role in studying protein conformational dynamics. A sliding count window with a fixed lag time is widely used to sample sub-trajectories for transition counting and MSM construction. However, sub-trajectories sampled with a fixed lag time may not perform well under different selections of lag time, which requires strong prior practice and leads to less robust estimation. To alleviate it, we propose a novel stochastic method from a Poisson process to generate perturbative lag time for sub-trajectory sampling and utilize it to construct a Markov chain. Comprehensive evaluations on the double-well system, WW domain, BPTI, and RBD-ACE2 complex of SARS-CoV-2 reveal that our algorithm significantly increases the robustness and power of a constructed MSM without disturbing the Markovian properties. Furthermore, the superiority of our algorithm is amplified for slow dynamic modes in complex biological processes.

Review of Electrostatic Force Calculation Methods and Their Acceleration in Molecular Dynamics Packages Using Graphics Processors

Molecular dynamics (MD) simulations probe the conformational repertoire of macromolecular systems using Newtonian dynamic equations. The time scales of MD simulations allow the exploration of biologically relevant phenomena and can elucidate spatial and temporal properties of the building blocks of life, such as deoxyribonucleic acid (DNA) and protein, across microsecond (μs) time scales using femtosecond (fs) time steps. A principal bottleneck toward extending MD calculations to larger time scales is the long-range electrostatic force measuring component of the naive nonbonded force computation algorithm, which scales with a complexity of (N, number of atoms). In this review, we present various methods to determine electrostatic interactions in often-used open-source MD packages as well as the implementation details that facilitate acceleration of the electrostatic interaction calculation.

Accelerators for Classical Molecular Dynamics Simulations of Biomolecules

Atomistic Molecular Dynamics (MD) simulations provide researchers the ability to model biomolecular structures such as proteins and their interactions with drug-like small molecules with greater spatiotemporal resolution than is otherwise possible using experimental methods. MD simulations are notoriously expensive computational endeavors that have traditionally required massive investment in specialized hardware to access biologically relevant spatiotemporal scales. Our goal is to summarize the fundamental algorithms that are employed in the literature to then highlight the challenges that have affected accelerator implementations in practice. We consider three broad categories of accelerators: Graphics Processing Units (GPUs), Field-Programmable Gate Arrays (FPGAs), and Application Specific Integrated Circuits (ASICs). These categories are comparatively studied to facilitate discussion of their relative trade-offs and to gain context for the current state of the art. We conclude by providing insights into the potential of emerging hardware platforms and algorithms for MD.

Perspective: Computer simulations of long time dynamics

Atomically detailed computer simulations of complex molecular events attracted the imagination of many researchers in the field as providing comprehensive information on chemical, biological, and physical processes. However, one of the greatest limitations of these simulations is of time scales. The physical time scales accessible to straightforward simulations are too short to address many interesting and important molecular events. In the last decade significant advances were made in different directions (theory, software, and hardware) that significantly expand the capabilities and accuracies of these techniques. This perspective describes and critically examines some of these advances.

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.

Biomolecular simulation: a computational microscope for molecular biology

Molecular dynamics simulations capture the behavior of biological macromolecules in full atomic detail, but their computational demands, combined with the challenge of appropriately modeling the relevant physics, have historically restricted their length and accuracy. Dramatic recent improvements in achievable simulation speed and the underlying physical models have enabled atomic-level simulations on timescales as long as milliseconds that capture key biochemical processes such as protein folding, drug binding, membrane transport, and the conformational changes critical to protein function. Such simulation may serve as a computational microscope, revealing biomolecular mechanisms at spatial and temporal scales that are difficult to observe experimentally. We describe the rapidly evolving state of the art for atomic-level biomolecular simulation, illustrate the types of biological discoveries that can now be made through simulation, and discuss challenges motivating continued innovation in this field.

Alchemical free energy methods for drug discovery: progress and challenges

Improved rational drug design methods are needed to lower the cost and increase the success rate of drug discovery and development. Alchemical binding free energy calculations, one potential tool for rational design, have progressed rapidly over the past decade, but still fall short of providing robust tools for pharmaceutical engineering. Recent studies, especially on model receptor systems, have clarified many of the challenges that must be overcome for robust predictions of binding affinity to be useful in rational design. In this review, inspired by a recent joint academic/industry meeting organized by the authors, we discuss these challenges and suggest a number of promising approaches for overcoming them.

Crystal structure and molecular dynamics simulation of ubiquitin-like domain of murine parkin

Parkin is the gene product identified as the major cause of autosomal recessive juvenile Parkinsonism (AR-JP). Parkin, a ubiquitin ligase E3, contains a unique ubiquitin-like domain in its N-terminus designated Uld which is assumed to be a interaction domain with the Rpn 10 subunit of 26S proteasome. To elucidate the structural and functional role of Uld in parkin at the atomic level, the X-ray crystal structure of murine Uld was determined and a molecular dynamics simulation of wild Uld and its five mutants (K27N, R33Q, R42P, K48A and V56E) identified from AR-JP patients was performed. Murine Uld consists of two alpha helices [Ile23-Arg33 (alpha1) and Val56-Gln57 (alpha2)] and five beta strands [Met1-Phe7 (beta1), Tyr11-Asp18 (beta2), Leu41-Phe45 (beta3), Lys48-Pro51 (beta4) and Ser65-Arg72 (beta5)] and its overall structure is essentially the same as that of human ubiquitin with a 1.22 A rmsd for the backbone atoms of residues 1-76; however, the sequential identity and similarity between both molecules are 32% and 63%, respectively. This close resemblance is due to the core structure built by same hydrogen bond formations between and within the backbone chains of alpha1 and beta1/2/5 secondary structure elements and by nearly the same hydrophobic interactions formed between the nonpolar amino acids of their secondary structures. The side chain NetaH of Lys27 on the alpha1 helix was crucial to the stabilization of the spatial orientations of beta3 and beta4 strands, possible binding region with Rpn 10 subunit, through three hydrogen bonds. The MD simulations showed the K27N and R33Q mutations increase the structural fluctuation of these beta strands including the alpha1 helix. Reversely, the V56E mutant restricted the spatial flexibility at the periphery of the short alpha2 helix by the interactions between the polar atoms of Glu56 and Ser19 residues. However, a large fluctuation of beta4 strand with respect to beta5 strand was induced in the R42P mutant, because of the impossibility of forming paired hydrogen bonds of Pro for Arg42 in wild Uld. The X-ray structure showed that the side chains of Asp39, Gln40 and Arg42 at the N-terminal periphery of beta3 strand protrude from the molecular surface of Uld and participate in hydrogen bonds with the polar residues of neighboring Ulds. Thus, the MD simulation suggests that the mutation substitution of Pro for Arg42 not only causes the large fluctuation of beta3 strand in the Uld but also leads to the loss of the ability of Uld to trap the Rpn 10 subunit. In contrast, the MD simulation of K48A mutant showed little influence on the beta3-beta4 loop structure, but a large fluctuation of Lys48 side chain, suggesting the importance of flexibility of this side chain for the interaction with the Rpn 10 subunit. The present results would be important in elucidating the impaired proteasomal binding mechanism of parkin in AR-JP.

Anton, a special-purpose machine for molecular dynamics simulation

The ability to perform long, accurate molecular dynamics (MD) simulations involving proteins and other biological macro-molecules could in principle provide answers to some of the most important currently outstanding questions in the fields of biology, chemistry and medicine. A wide range of biologically interesting phenomena, however, occur over time scales on the order of a millisecond--about three orders of magnitude beyond the duration of the longest current MD simulations.

In this paper, we describe a massively parallel machine called Anton, which should be capable of executing millisecond-scale classical MD simulations of such biomolecular systems. The machine, which is scheduled for completion by the end of 2008, is based on 512 identical MD-specific ASICs that interact in a tightly coupled manner using a specialized high-speed communication network. Anton has been designed to use both novel parallel algorithms and special-purpose logic to dramatically accelerate those calculations that dominate the time required for a typical MD simulation. The remainder of the simulation algorithm is executed by a programmable portion of each chip that achieves a substantial degree of parallelism while preserving the flexibility necessary to accommodate anticipated advances in physical models and simulation methods.

Functionally relevant protein motions: Extracting basin-specific collective coordinates from molecular dynamics trajectories

Functionally relevant motion of proteins has been associated with a number of atoms moving in a concerted fashion along so-called "collective coordinates." We present an approach to extract collective coordinates from conformations obtained from molecular dynamics simulations. The power of this technique for differentiating local structural fluctuations between classes of conformers obtained by clustering is illustrated by analyzing nanosecond-long trajectories for the response regulator protein Spo0F of Bacillus subtilis, generated both in vacuo and using an implicit-solvent representation. Conformational clustering is performed using automated histogram filtering of the inter-C(alpha) distances. Orthogonal (varimax) rotation of the vectors obtained by principal component analysis of these interresidue distances for the members of individual clusters is key to the interpretation of collective coordinates dominating each conformational class. The rotated loadings plots isolate significant variation in interresidue distances, and these are associated with entire mobile secondary structure elements. From this we infer concerted motions of these structural elements. For the Spo0F simulations employing an implicit-solvent representation, collective coordinates obtained in this fashion are consistent with the location of the protein's known active sites and experimentally determined mobile regions.

Structural features of human initiation factor 4E, studied by X-ray crystal analyses and molecular dynamics simulations

The structural features of human eIF4E were investigated by X-ray crystal analyses of its cap analog (m(7)GTP and m(7)GpppA) complexes and molecular dynamics (MD) simulations of cap-free and cap-bound eIF4Es, as well as the cap-bound Ser209-phosphorylated eIF4E. Crystal structure analyses at 2.0 A resolution revealed that the molecule forms a temple-bell-shaped surface of eight antiparallel beta-structures, three alpha-helices and ten loop structures, where the N-terminal region corresponds to the handle of the bell. This concave backbone provides a scaffold for the mRNA cap-recognition pocket consisting of three receiving parts for the 5'-terminal m(7)G base, the triphosphate, and the second nucleotide. The m(7)G base is sandwiched between the two aromatic side-chains of Trp102 and Trp56. The two (m(7)G)NH-O (Glu103 carboxy group) hydrogen bonds stabilize the stacking interaction. The basic residues of Arg157 and Lys162 and water molecules construct a binding pocket for the triphosphate moiety, where a universal hydrogen-bonding network is formed. The flexible C-terminal loop region unobserved in the m(7)GTP complex was clearly observed in the m(7)GpppA complex, as a result of the fixation of this loop by the interaction with the adenosine moiety, indicating the function of this loop as a receiving pocket for the second nucleotide. On the other hand, MD simulation in an aqueous solution system revealed that the cap-binding pocket, especially its C-terminal loop structure, is flexible in the cap-free eIF4E, and the entrance of the cap-binding pocket becomes narrow, although the depth is relatively unchanged. SDS-PAGE analyses showed that this structural instability is highly related to the fast degradation of cap-free eIF4E, compared with cap-bound or 4E-BP/cap-bound eIF4E, indicating the conferment of structural stability of eIF4E by the binary or ternary complex formation. MD simulation of m(7)GpppA-bound Ser209-phosphorylated eIF4E showed that the size of the cap-binding entrance is dependent on the ionization state in the Ser209 phosphorylation, which is associated with the regulatory function through the switching on/off of eIF4E phosphorylation.

Development of hardware accelerator for molecular dynamics simulations: a computation board that calculates nonbonded interactions in cooperation with fast multipole method

Evaluation of long-range Coulombic interactions still represents a bottleneck in the molecular dynamics (MD) simulations of biological macromolecules. Despite the advent of sophisticated fast algorithms, such as the fast multipole method (FMM), accurate simulations still demand a great amount of computation time due to the accuracy/speed trade-off inherently involved in these algorithms. Unless higher order multipole expansions, which are extremely expensive to evaluate, are employed, a large amount of the execution time is still spent in directly calculating particle-particle interactions within the nearby region of each particle. To reduce this execution time for pair interactions, we developed a computation unit (board), called MD-Engine II, that calculates nonbonded pairwise interactions using a specially designed hardware. Four custom arithmetic-processors and a processor for memory manipulation ("particle processor") are mounted on the computation board. The arithmetic processors are responsible for calculation of the pair interactions. The particle processor plays a central role in realizing efficient cooperation with the FMM. The results of a series of 50-ps MD simulations of a protein-water system (50,764 atoms) indicated that a more stringent setting of accuracy in FMM computation, compared with those previously reported, was required for accurate simulations over long time periods. Such a level of accuracy was efficiently achieved using the cooperative calculations of the FMM and MD-Engine II. On an Alpha 21264 PC, the FMM computation at a moderate but tolerable level of accuracy was accelerated by a factor of 16.0 using three boards. At a high level of accuracy, the cooperative calculation achieved a 22.7-fold acceleration over the corresponding conventional FMM calculation. In the cooperative calculations of the FMM and MD-Engine II, it was possible to achieve more accurate computation at a comparable execution time by incorporating larger nearby regions.

A novel parallel algorithm for large-scale Fock matrix construction with small locally distributed memory architectures: RT parallel algorithm

We developed a novel parallel algorithm for large-scale Fock matrix calculation with small locally distributed memory architectures, and named it the "RT parallel algorithm." The RT parallel algorithm actively involves the concept of integral screening, which is indispensable for reduction of computing times with large-scale biological molecules. The primary characteristic of this algorithm is parallel efficiency, which is achieved by well-balanced reduction of both communicating and computing volume. Only the density matrix data necessary for Fock matrix calculations are communicated, and the data once communicated are reutilized for calculations as many times as possible. The RT parallel algorithm is a scalable method because required memory volume does not depend on the number of basis functions. This algorithm automatically includes a partial summing technique that is indispensable for maintaining computing accuracy, and can also include some conventional methods to reduce calculation times. In our analysis, the RT parallel algorithm had better performance than other methods for massively parallel processors. The RT parallel algorithm is most suitable for massively parallel and distributed Fock matrix calculations for large-scale biological molecules with more than thousands of basis functions.

Molecular dynamics simulations

Molecular dynamics simulations have become a standard tool for the investigation of biomolecules. Simulations are performed of ever bigger systems using more realistic boundary conditions and better sampling due to longer sampling times. Recently, realistic simulations of systems as complex as transmembrane channels have become feasible. Simulations aid our understanding of biochemical processes and give a dynamic dimension to structural data; for example, the transformation of harmless prion protein into the disease-causing agent has been modeled.

Molecular dynamics simulations of Gly-12-->Val mutant of p21(ras): dynamic inhibition mechanism

The mutant p21(ras) protein is a G protein produced by the point-mutated H-ras gene, and this mutant protein has been shown to cause carcinogenesis due to a reduction in its GTPase activity. However, the mechanism underlying this strange phenomenon has still not been elucidated. In our previous study, we have clarified the mechanism of the GTP-->GDP hydrolysis reaction in the wild-type p21(ras) at the atomic level and concluded that GTPase-activating protein plays a significant role in the supply of H2O molecules for the hydrolysis. The structure of the active site in the mutant is the same as that in the wild type. However, by performing molecular dynamic calculations, we found that the structure of the active site of the enzyme substrate complex in the oncogenic mutant p21(ras) continuously changes, and these continuous changes in the active site would make it difficult for the GTP-->GDP hydrolysis reaction to occur in the mutant. These findings can explain the fact that the GTPase activity in the mutant was only 15% of that in the wild type and the fact that GTPase-activating protein has no reaction-activating effect in the mutant. This is a dynamic inhibition mechanism of a vital reaction that can be explained by considering the molecular dynamics.

Monooxygenation mechanism by cytochrome p-450

The substrate oxygenation mechanism by an ultimate species in monooxygenation by cytochrome P-450 (compound I) was investigated by the density functional theory method. An initial model compound was constructed from a structure obtained by 300-ps molecular dynamics simulation of compound I-formed P-450cam under physiologic conditions, and it consisted of porphine for protoporphyrin IX, S(-)-CH(3) for the side chain of Cys357 of the fifth ligand of heme, a methane molecule for the substrate, a heme iron, and an oxygen atom of the sixth ligand of heme. The results of the calculation revealed that the substrate oxygenation mechanism had four elementary processes, i.e., (1) formation of [FeOH](3+) and a substrate radical by hydrogen atom abstraction from the substrate caused by [FeO](3+), (2) rotation of the OH group of the sixth ligand of [FeOH](3+) produced by process 1, (3) substrate radical binding with the [FeOH](3+), and (4) elimination of the oxygenated substrate formed at the sixth ligand binding site. The rate-determining step is process 1, hydrogen atom abstraction from the substrate, and the activation energy was determined to be about 15 kcal/mol. For this reason, it is thought that this reaction occurs in vivo.

Fast lipid disorientation at the onset of membrane fusion revealed by molecular dynamics simulations

Membrane fusion is a key event in vesicular trafficking in every cell, and many fusion-related proteins have been identified. However, how the actual fusion event occurs has not been elucidated. By using molecular dynamics simulations we found that when even a small region of two membranes is closely apposed such that only a limited number of water molecules remain in the apposed area (e.g., by a fusogenic protein and thermal membrane fluctuations), dramatic lipid disorientation results within 100 ps-2 ns, which might initiate membrane fusion. Up to 12% of phospholipid molecules in the apposing layers had their alkyl chains outside the hydrophobic region, lying almost parallel to the membrane surface or protruding out of the bilayer by 2 ns after two membranes were closely apposed.

Molecular dynamics generation of nonarbitrary membrane models reveals lipid orientational correlations

This report addresses the following problems associated with the generation of computer models of phospholipid bilayer membranes using molecular dynamics simulations: arbitrary initial structures and short equilibration periods, an Ewald-induced strong coupling of phospholipids, uncertainty regarding which value should be used for surface tension to alleviate the problem of the small size of the membrane, and simultaneous realization of both order parameters and the surface area. We generated a computer model of the liquid-crystalline L-alpha-dimyristoylphosphatidylcholine (DMPC) bilayer, starting from a configuration based on a crystal structure (rather than from an arbitrary structure). To break the crystalline structure, a 20-ps high-temperature pulse of 510 K (but not 450 or 480 K) was effective. The system finally obtained is an all-atom model, with Ewald summation to evaluate Coulombic interactions and a constant surface tension of 35 dynes/cm/water-membrane interface, equilibrated for 12 ns (over 50 ns total calculation time), which reproduces all of the experimentally observed parameters examined in this work. Furthermore, this model shows the presence of significant orientational correlations between neighboring alkyl chains and between shoulder vectors (which show the orientations of the lipids about their long axes) of neighboring DMPCs.