Yuhui Cheng

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation

We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a number of molecules are demonstrated, showing that our methods possess several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). We also demonstrate an example of molecular simulation using the finite element method and the meshes generated by our method. The approaches presented and their implementations are also applicable to other types of inputs such as 3D scalar volumes and triangular surface meshes with low quality, and hence can be used for generation/improvement of meshes in a broad range of applications.

How does activation loop phosphorylation modulate catalytic activity in the cAMP‐dependent protein kinase: A theoretical study

Phosphorylation mediates the function of many proteins and enzymes. In the catalytic subunit of cAMP‐dependent protein kinase, phosphorylation of Thr 197 in the activation loop strongly influences its catalytic activity. In order to provide theoretical understanding about this important regulatory process, classical molecular dynamics simulations and ab initio QM/MM calculations have been carried out on the wild‐type PKA–Mg2 ATP–substrate complex and its dephosphorylated mutant, T197A. It was found that pThr 197 not only facilitates the phosphoryl transfer reaction by stabilizing the transition state through electrostatic interactions but also strongly affects its essential protein dynamics as well as the active site conformation.

A dynamic model of HIV integrase inhibition and drug resistance.

Human immunodeficiency virus type 1 (HIV-1) integrase is one of three virally encoded enzymes essential for replication and, therefore, a rational choice as a drug target for the treatment of HIV-1-infected individuals. In 2007, raltegravir became the first integrase inhibitor approved for use in the treatment of HIV-infected patients, more than a decade since the approval of the first protease inhibitor (saquinavir, Hoffman La-Roche, 1995) and two decades since the approval of the first reverse transcriptase inhibitor (retrovir, GlaxoSmithKline, 1987). The slow progress toward a clinically effective HIV-1 integrase inhibitor can at least in part be attributed to a poor structural understanding of this key viral protein. Here we describe the development of a restrained molecular dynamics protocol that produces a more accurate model of the active site of this drug target. This model provides an advance on previously described models as it ensures that the catalytic DDE motif makes correct, monodentate interactions with the two active-site magnesium ions. Dynamic restraints applied to this coordination state create models with the correct solvation sphere for the metal ion complex and highlight the coordination sites available for metal-binding ligands. Application of appropriate dynamic flexibility to the core domain allowed the inclusion of multiple conformational states in subsequent docking studies. These models have allowed us to (1) explore the effects of key drug resistance mutations on the dynamic flexibility and conformational preferences of HIV integrase and to (2) study raltegravir binding in the context of these dynamic models of both wild type and the G140S/Q148H drug-resistant enzyme.

Thioamide Hydroxypyrothiones Supersede Amide Hydroxypyrothiones in Potency Against Anthrax Lethal Factor

Anthrax lethal factor (LF) is a critical virulence factor in the pathogenesis of anthrax. A structure-activity relationship (SAR) of potential lethal factor inhibitors (LFi) is presented in which the zinc-binding group (ZBG), linker, and backbone moieties for a series of hydroxypyrone-based compounds were systematically varied. It was found that hydroxypyrothione ZBGs generate more potent inhibitors than hydroxypyrone ZBGs. Furthermore, coupling the hydroxypyrothione to a backbone group via a thioamide bond improves potency when compared to an amide linker. QM/MM studies show that the thioamide bond in these inhibitors allows for the formation of two additional hydrogen bonds with the protein active site. In both types of hydroxypyrothione compounds, ligand efficiencies of 0.29-0.54 kcal mol(-1) per heavy atom were achieved. The results highlight the need for a better understanding to optimize the interplay between the ZBG, linker, and backbone to get improved LFi.

Numerical analysis of Ca2+ signaling in rat ventricular myocytes with realistic transverse-axial tubular geometry and inhibited sarcoplasmic reticulum.

The t-tubules of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca2+). To investigate how the t-tubule microanatomy and the distribution of membrane Ca2+ flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca2+ signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca2+ signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca2+ flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca2+ buffers, including the Ca2+ indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca2+ transients was found when the Ca2+ flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca2+ signals are predicted. Even at modest elevation of Ca2+, reached during Ca2+ influx, large and steep Ca2+ gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca2+ flux density along the cell membrane support initiation and propagation of Ca2+ waves in rat myocytes.

Diffusional channeling in the sulfate-activating complex: combined continuum modeling and coarse-grained brownian dynamics studies.

Enzymes required for sulfur metabolism have been suggested to gain efficiency by restricted diffusion (i.e., channeling) of an intermediate APS2– between active sites. This article describes modeling of the whole channeling process by numerical solution of the Smoluchowski diffusion equation, as well as by coarse-grained Brownian dynamics. The results suggest that electrostatics plays an essential role in the APS2– channeling. Furthermore, with coarse-grained Brownian dynamics, the substrate channeling process has been studied with reactions in multiple active sites. Our simulations provide a bridge for numerical modeling with Brownian dynamics to simulate the complicated reaction and diffusion and raise important questions relating to the electrostatically mediated substrate channeling in vitro, in situ, and in vivo.

Multi-core CPU or GPU-accelerated Multiscale Modeling for Biomolecular Complexes.

Abstract Multi-scale modeling plays an important role in understanding the structure and biological functionalities of large biomolecular complexes. In this paper, we present an efficient computational framework to construct multi-scale models from atomic resolution data in the Protein Data Bank (PDB), which is accelerated by multi-core CPU and programmable Graphics Processing Units (GPU). A multi-level summation of Gaussian kernel functions is employed to generate implicit models for biomolecules. The coefficients in the summation are designed as functions of the structure indices, which specify the structures at a certain level and enable a local resolution control on the biomolecular surface. A method called neighboring search is adopted to locate the grid points close to the expected biomolecular surface, and reduce the number of grids to be analyzed. For a specific grid point, a KD-tree or bounding volume hierarchy is applied to search for the atoms contributing to its density computation, and faraway atoms are ignored due to the decay of Gaussian kernel functions. In addition to density map construction, three modes are also employed and compared during mesh generation and quality improvement to generate high quality tetrahedral meshes: CPU sequential, multi-core CPU parallel and GPU parallel. We have applied our algorithm to several large proteins and obtained good results.

Modeling Effects of L-Type Ca2+ Current and Na+-Ca2+ Exchanger on Ca2+ Trigger Flux in Rabbit Myocytes with Realistic T-Tubule Geometries

The transverse tubular system of rabbit ventricular myocytes consists of cell membrane invaginations (t-tubules) that are essential for efficient cardiac excitation-contraction coupling. In this study, we investigate how t-tubule micro-anatomy, L-type Ca2+ channel (LCC) clustering, and allosteric activation of Na+/Ca2+ exchanger by L-type Ca2+ current affects intracellular Ca2+ dynamics. Our model includes a realistic 3D geometry of a single t-tubule and its surrounding half-sarcomeres for rabbit ventricular myocytes. The effects of spatially distributed membrane ion-transporters (LCC, Na+/Ca2+ exchanger, sarcolemmal Ca2+ pump, and sarcolemmal Ca2+ leak), and stationary and mobile Ca2+ buffers (troponin C, ATP, calmodulin, and Fluo-3) are also considered. We used a coupled reaction-diffusion system to describe the spatio-temporal concentration profiles of free and buffered intracellular Ca2+. We obtained parameters from voltage-clamp protocols of L-type Ca2+ current and line-scan recordings of Ca2+ concentration profiles in rabbit cells, in which the sarcoplasmic reticulum is disabled. Our model results agree with experimental measurements of global Ca2+ transient in myocytes loaded with 50 μM Fluo-3. We found that local Ca2+ concentrations within the cytosol and sub-sarcolemma, as well as the local trigger fluxes of Ca2+ crossing the cell membrane, are sensitive to details of t-tubule micro-structure and membrane Ca2+ flux distribution. The model additionally predicts that local Ca2+ trigger fluxes are at least threefold to eightfold higher than the whole-cell Ca2+ trigger flux. We found also that the activation of allosteric Ca2+-binding sites on the Na+/Ca2+ exchanger could provide a mechanism for regulating global and local Ca2+ trigger fluxes in vivo. Our studies indicate that improved structural and functional models could improve our understanding of the contributions of L-type and Na+/Ca2+ exchanger fluxes to intracellular Ca2+ dynamics.

Multiscale modeling in rodent ventricular myocytes

This paper indicates that in ventricular myocytes when the SR (sarcoplasmic reticulum) is pharmacologically inhibited, the intracellular Ca²⁺concentration rapidly increases during Ca²⁺ entrance (0-70 ms), whereas the decay of Ca²⁺ is slow; in the absence of fluorescent dye, large Ca²⁺ concentration gradients might develop near the cell membrane; intracellular Ca²⁺ distribution is tightly regulated by the localization of Ca²⁺transporter proteins along the sarcolemma and strongly relays on the presence of mobile and stationary Ca²⁺ buffers. These studies also imply that in ventricular cells with intact and functional SR, the Ca²⁺ signal most likely would spread faster along the t-tubular system, surface membrane than to the cell interior and that in the absence of Ca²⁺ dye high Ca²⁺ gradients under the surface membrane and more uniform Ca²⁺ distribution in the cell interior might be expected.

Multi-scale continuum modeling of biological processes: from molecular electro-diffusion to sub-cellular signaling transduction

This article provides a brief review of multi-scale modeling at the molecular to cellular scale, with new results for heart muscle cells. A finite element-based simulation package (SMOL) was used to investigate the signaling transduction at molecular and sub-cellular scales (http://mccammon.ucsd.edu/smol/, http://FETK.org) by numerical solution of time-dependent Smoluchowski equations and a reaction-diffusion system. At the molecular scale, SMOL has yielded experimentally-validated estimates of the diffusion-limited association rates for the binding of acetylcholine to mouse acetylcholinesterase using crystallographic structural data. The predicted rate constants exhibit increasingly delayed steady-state times with increasing ionic strength and demonstrate the role of an enzymes electrostatic potential in influencing ligand binding. At the sub-cellular scale, an extension of SMOL solves a non-linear, reaction-diffusion system describing Ca2+ ligand buffering and diffusion in experimentally-derived rodent ventricular myocyte geometries. Results reveal the important role for mobile and stationary Ca2+ buffers, including Ca2+ indicator dye. We found that the alterations in Ca2+-binding and dissociation rates of troponin C (TnC) and total TnC concentration modulate subcellular Ca2+ signals. Model predicts that reduced off-rate in whole troponin complex (TnC, TnI, TnT) versus reconstructed thin filaments (Tn, Tm, actin) alters cytosolic Ca2+ dynamics under control conditions or in disease-linked TnC mutations. The ultimate goal of these studies is to develop scalable methods and theories for integration of molecular-scale information into simulations of cellular-scale systems.