An exa-scale high-performance molecular dynamics simulation program: MODYLAS.

A new version of the highly parallelized general-purpose molecular dynamics (MD) simulation program MODYLAS with high performance on the Fugaku computer was developed. A benchmark test using Fugaku indicated highly efficient communication, single instruction, multiple data (SIMD) processing, and on-cache arithmetic operations. The system's performance deteriorated only slightly, even under high parallelization. In particular, a newly developed minimum transferred data method, requiring a significantly lower amount of data transfer compared to conventional communications, showed significantly high performance. The coordinates and forces of 101 810 176 atoms and the multipole coefficients of the subcells could be distributed to the 32 768 nodes (1 572 864 cores) in 2.3 ms during one MD step calculation. The SIMD effective instruction rates for floating-point arithmetic operations in direct force and fast multipole method (FMM) calculations measured on Fugaku were 78.7% and 31.5%, respectively. The development of a data reuse algorithm enhanced the on-cache processing; the cache miss rate for direct force and FMM calculations was only 2.74% and 1.43%, respectively, on the L1 cache and 0.08% and 0.60%, respectively, on the L2 cache. The modified MODYLAS could complete one MD single time-step calculation within 8.5 ms for the aforementioned large system. Additionally, the program contains numerous functions for material research that enable free energy calculations, along with the generation of various ensembles and molecular constraints.

Binding Kinetics Toolkit for Analyzing Transient Molecular Conformations and Computing Free Energy Landscapes.

Understanding ligand binding kinetics and thermodynamics, which involves investigating the free, transient, and final complex conformations, is important in fundamental studies and applications for chemical and biomedical systems. Examining the important but transient ligand-protein-bound conformations, in addition to experimentally determined structures, also provides a more accurate estimation for drug efficacy and selectivity. Moreover, obtaining the entire picture of the free energy landscape during ligand binding/unbinding processes is critical in understanding binding mechanisms. Here, we present a Binding Kinetics Toolkit (BKiT) that includes several utilities to analyze trajectories and compute a free energy and kinetics profile. BKiT uses principal component space to generate approximated unbinding or conformational transition coordinates for accurately describing and easily visualizing the molecular motions. We implemented a new partitioning approach to assign indexes along the approximated coordinates that can be used as milestones or microstates. The program can generate input files to run many short classical molecular dynamics simulations and uses milestoning theory to construct the free energy profile and estimate binding residence time. We first validated the method with a host-guest system, aspirin unbinding from ß-cyclodextrin, and then applied the protocol to pyrazolourea compounds and cyclin-dependent kinase 8 and cyclin C complexes, a kinase system of pharmacological interest. Overall, our approaches yielded good agreement with published results and suggest ligand design strategies. The computed unbinding free energy landscape also provides a more complete picture of ligand-receptor binding barriers and stable local minima for deepening our understanding of molecular recognition. BKiT is easy to use and has extensible features for future expansion of utilities for postanalysis and calculations.

Transient States and Barriers from Molecular Simulations and the Milestoning Theory: Kinetics in Ligand-Protein Recognition and Compound Design.

This study presents a novel computational approach to study molecular recognition and binding kinetics for drug-like compounds dissociating from a flexible protein system. The intermediates and their free energy profile during ligand association and dissociation processes control ligand-protein binding kinetics and bring a more complete picture of ligand-protein binding. The method applied the milestoning theory to extract kinetics and thermodynamics information from running short classical molecular dynamics (MD) simulations for frames from a given dissociation path. High-dimensional ligand-protein motions (3N-6 degrees of freedom) during ligand dissociation were reduced by use of principal component modes for assigning more than 100 milestones, and classical MD runs were allowed to travel multiple milestones to efficiently obtain ensemble distribution of initial structures for MD simulations and estimate the transition time and rate during ligand traveling between milestones. We used five pyrazolourea ligands and cyclin-dependent kinase 8 with cyclin C (CDK8/CycC) as our model system as well as metadynamics and a pathway search method to sample dissociation pathways. With our strategy, we constructed the free energy profile for highly mobile biomolecular systems. The computed binding free energy and residence time correctly ranked the pyrazolourea ligand series, in agreement with experimental data. Guided by a barrier of a ligand passing an αC helix and activation loop, we introduced one hydroxyl group to parent compounds to design our ligands with increased residence time and validated our prediction by experiments. This work provides a novel and robust approach to investigate dissociation kinetics of large and flexible systems for understanding unbinding mechanisms and designing new small-molecule drugs with desired binding kinetics.

Potential Mean Force from Umbrella Sampling Simulations: What Can We Learn and What Is Missed?

Changes in free energy provide valuable information for molecular recognition, including both ligand-receptor binding thermodynamics and kinetics. Umbrella sampling (US), a widely used free energy calculation method, has long been used to explore the dissociation process of ligand-receptor systems and compute binding free energy. In existing publications, the binding free energy computed from the potential of mean force (PMF) with US simulation mostly yielded "ball park" values with experimental data. However, the computed PMF values are highly influenced by factors such as initial conformations and/or trajectories provided, the reaction coordinate, and sampling of conformational space in each US window. These critical factors have rarely been carefully studied. Here we used US to study the guest aspirin and 1-butanol dissociation processes of ß-cyclodextrin (ß-CD) and an inhibitor SB2 dissociation from a p38α mitogen-activated protein kinase (MAPK) complex. For ß-CD, we used three different ß-CD conformations to generate the dissociation path with US windows. For p38α, we generated the dissociation pathway by using accelerated molecular dynamics followed by conformational relaxing with short conventional MD, steered MD, and manual pulling. We found that, even for small ß-CD complexes, different ß-CD conformations altered the height of the PMF, but the pattern of PMF was not affected if the MD sampling in each US window was well-converged. Because changing the macrocyclic ring conformation needs to rotate dihedral angles in the ring, a bound ligand largely restrains the motion of cyclodextrin. Therefore, once a guest is in the binding site, cyclodextrin cannot freely change its initial conformation, resulting in different absolute heights of the PMF, which cannot be overcome by running excessively long MD simulations for each US window. Moreover, if the US simulations were not converged, the important barrier and minimum were missed. For ligand-protein systems, our studies also suggest that the dissociation trajectories modeled by an enhanced sampling method must maintain a natural molecular movement to avoid biased PMF plots when using US simulations.

An MM and QM Study of Biomimetic Catalysis of Diels-Alder Reactions Using Cyclodextrins.

We performed a computational investigation of the mechanism by which cyclodextrins (CDs) catalyze Diels-Alder reactions between 9-anthracenemethanol and N-cyclohexylmaleimide. Hydrogen bonds (Hbonds) between N-cyclohexylmaleimide and the hydroxyl groups of cyclodextrins were suggested to play an important role in this catalytic process. However, our free energy calculations and molecular dynamics simulations showed that these Hbonds are not stable, and quantum mechanical calculations suggested that the reaction is not promoted by these Hbonds. The binding of 9-anthracenemethanol and N-cyclohexylmaleimide to cyclodextrins was the key to the catalytic process. Cyclodextrins act as a container to hold the two reactants in the cavity, pre-organize them for the reactions, and thus reduce the entropy penalty to the activation free energy. Dimethyl-ß-CD was a better catalyst for this specific reaction than ß-CD because of its stronger van der Waals interaction with the pre-organized reactants and its better performance in reducing the activation energy. This computational work sheds light on the mechanism of the catalytic reaction by cyclodextrins and introduces new perspectives of supramolecular catalysis.

A molecular dynamics investigation of CDK8/CycC and ligand binding: conformational flexibility and implication in drug discovery.

Abnormal activity of cyclin-dependent kinase 8 (CDK8) along with its partner protein cyclin C (CycC) is a common feature of many diseases including colorectal cancer. Using molecular dynamics (MD) simulations, this study determined the dynamics of the CDK8-CycC system and we obtained detailed breakdowns of binding energy contributions for four type-I and five type-II CDK8 inhibitors. We revealed system motions and conformational changes that will affect ligand binding, confirmed the essentialness of CycC for inclusion in future computational studies, and provide guidance in development of CDK8 binders. We employed unbiased all-atom MD simulations for 500 ns on twelve CDK8-CycC systems, including apoproteins and protein-ligand complexes, then performed principal component analysis (PCA) and measured the RMSF of key regions to identify protein dynamics. Binding pocket volume analysis identified conformational changes that accompany ligand binding. Next, H-bond analysis, residue-wise interaction calculations, and MM/PBSA were performed to characterize protein-ligand interactions and find the binding energy. We discovered that CycC is vital for maintaining a proper conformation of CDK8 to facilitate ligand binding and that the system exhibits motion that should be carefully considered in future computational work. Surprisingly, we found that motion of the activation loop did not affect ligand binding. Type-I and type-II ligand binding is driven by van der Waals interactions, but electrostatic energy and entropic penalties affect type-II binding as well. Binding of both ligand types affects protein flexibility. Based on this we provide suggestions for development of tighter-binding CDK8 inhibitors and offer insight that can aid future computational studies.

Binding Thermodynamics and Kinetics Calculations Using Chemical Host and Guest: A Comprehensive Picture of Molecular Recognition.

Understanding the fine balance between changes of entropy and enthalpy and the competition between a guest and water molecules in molecular binding is crucial in fundamental studies and practical applications. Experiments provide measurements. However, illustrating the binding/unbinding processes gives a complete picture of molecular recognition not directly available from experiments, and computational methods bridge the gaps. Here, we investigated guest association/dissociation with ß-cyclodextrin (ß-CD) by using microsecond-time-scale molecular dynamics (MD) simulations, postanalysis and numerical calculations. We computed association and dissociation rate constants, enthalpy, and solvent and solute entropy of binding. All the computed values of kon, koff, ΔH, ΔS, and ΔG using GAFF-CD and q4MD-CD force fields for ß-CD could be compared with experimental data directly and agreed reasonably with experiment findings. In addition, our study further interprets experiments. Both force fields resulted in similar computed ΔG from independently computed kinetics rates, ΔG = -RT ln(kon·C0/koff), and thermodynamics properties, ΔG = ΔH - TΔS. The water entropy calculations show that the entropy gain of desolvating water molecules are a major driving force, and both force fields have the same strength of nonpolar attractions between solutes and ß-CD as well. Water molecules play a crucial role in guest binding to ß-CD. However, collective water/ß-CD motions could contribute to different computed kon and ΔH values by different force fields, mainly because the parameters of ß-CD provide different motions of ß-CD, hydrogen-bond networks of water molecules in the cavity of free ß-CD, and strength of desolvation penalty. As a result, q4MD-CD suggests that guest binding is mostly driven by enthalpy, while GAFF-CD shows that gaining entropy is the major driving force of binding. The study deepens our understanding of ligand-receptor recognition and suggests strategies for force field parametrization for accurately modeling molecular systems.

Systematic Dissociation Pathway Searches Guided by Principal Component Modes.

We introduce a novel method, Pathway Search guided by Internal Motions (PSIM), that efficiently finds molecular dissociation pathways of a ligand-receptor system with guidance from principal component (PC) modes obtained from molecular dynamics (MD) simulations. Modeling ligand-receptor dissociation pathways can provide insights into molecular recognition and has practical applications, including understanding kinetic mechanisms and barriers to binding/unbinding as well as design of drugs with desired kinetic properties. PSIM uses PC modes in multilayer internal coordinates to identify natural molecular motions that guide the search for conformational switches and unbinding pathways. The new multilayer internal coordinates overcome problems with Cartesian and classical internal coordinates that fail to smoothly present dihedral rotation or generate nonphysical distortions. We used HIV-1 protease, which has large-scale flap motions, as an example protein to demonstrate use of the multilayer internal coordinates. We provide examples of algorithms and implementation of PSIM with alanine dipeptide and chemical host-guest systems, 2-naphthyl ethanol-ß-cyclodextrin and tetramethylammonium-cryptophane complexes. Tetramethylammonium-cryptophane has slow binding/unbinding kinetics. Its residence time, the length to dissociate tetramethylammonium from the host, is ∼14 s from experiments, and PSIM revealed 4 dissociation pathways in approximately 150 CPU h. We also searched the releasing pathways for the product glyceraldehyde-3-phosphate from tryptophan synthase, and one complete dissociation pathway was constructed after running multiple search iterations in approximately 300 CPU h. With guidance by internal PC modes from MD simulations, the PSIM method has advantages over simulation-based methods to search for dissociation pathways of molecular systems with slow noncovalent kinetic behavior.

Adaptation of a Genetic Screen Reveals an Inhibitor for Mitochondrial Protein Import Component Tim44.

Diverse protein import pathways into mitochondria use translocons on the outer membrane (TOM) and inner membrane (TIM). We adapted a genetic screen, based on Ura3 mistargeting from mitochondria to the cytosol, to identify small molecules that attenuated protein import. Small molecule mitochondrial import blockers of the Carla Koehler laboratory (MB)-10 inhibited import of substrates that require the TIM23 translocon. Mutational analysis coupled with molecular docking and molecular dynamics modeling revealed that MB-10 binds to a specific pocket in the C-terminal domain of Tim44 of the protein-associated motor (PAM) complex. This region was proposed to anchor Tim44 to the membrane, but biochemical studies with MB-10 show that this region is required for binding to the translocating precursor and binding to mtHsp70 in low ATP conditions. This study also supports a direct role for the PAM complex in the import of substrates that are laterally sorted to the inner membrane, as well as the mitochondrial matrix. Thus, MB-10 is the first small molecule modulator to attenuate PAM complex activity, likely through binding to the C-terminal region of Tim44.

Understanding ligand-receptor non-covalent binding kinetics using molecular modeling.

Kinetic properties may serve as critical differentiators and predictors of drug efficacy and safety, in addition to the traditionally focused binding affinity. However the quantitative structure-kinetics relationship (QSKR) for modeling and ligand design is still poorly understood. This review provides an introduction to the kinetics of drug binding from a fundamental chemistry perspective. We focus on recent developments of computational tools and their applications to non-covalent binding kinetics.