James Andrew McCammon

Activation and dynamic network of the M2 muscarinic receptor

G-protein-coupled receptors (GPCRs) mediate cellular responses to various hormones and neurotransmitters and are important targets for treating a wide spectrum of diseases. Although significant advances have been made in structural studies of GPCRs, details of their activation mechanism remain unclear. The X-ray crystal structure of the M2 muscarinic receptor, a key GPCR that regulates human heart rate and contractile forces of cardiomyocytes, was determined recently in an inactive antagonist-bound state. Here, activation of the M2 receptor is directly observed via accelerated molecular dynamics simulation, in contrast to previous microsecond-timescale conventional molecular dynamics simulations in which the receptor remained inactive. Receptor activation is characterized by formation of a Tyr2065.58–Tyr4407.53 hydrogen bond and ∼6-Å outward tilting of the cytoplasmic end of transmembrane α-helix 6, preceded by relocation of Trp4006.48 toward Phe1955.47 and Val1995.51 and flipping of Tyr4307.43 away from the ligand-binding cavity. Network analysis reveals that communication in the intracellular domains is greatly weakened during activation of the receptor. Together with the finding that residue motions in the ligand-binding and G-protein-coupling sites of the apo receptor are correlated, this result highlights a dynamic network for allosteric regulation of the M2 receptor activation.

The adaptive multilevel finite element solution of the Poisson-Boltzmann equation on massively parallel computers

By using new methods for the parallel solution of elliptic partial differential equations, the teraflops computing power of massively parallel computers can be leveraged to perform electrostatic calculations on large biological systems. This paper describes the adaptive multilevel finite element solution of the Poisson-Boltzmann equation for a microtubule on the NPACI Blue Horizon--a massively parallel IBM RS/6000® SP with eight POWER3 SMP nodes. The microtubule system is 40 nm in length and 24 nm in diameter, consists of roughly 600000 atoms, and has a net charge of -1800 e. Poisson-Boltzmann calculations are performed for several processor configurations, and the algorithm used shows excellent parallel scaling.

Coupling nonpolar and polar solvation free energies in implicit solvent models

Recent studies on the solvation of atomistic and nanoscale solutes indicate that a strong coupling exists between the hydrophobic, dispersion, and electrostatic contributions to the solvation free energy, a facet not considered in current implicit solvent models. We suggest a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy of the solvent with respect to a solvent volume exclusion function. The resulting differential equation is similar to the Laplace-Young equation for the geometrical description of capillary interfaces but is extended to microscopic scales by explicitly considering curvature corrections as well as dispersion and electrostatic contributions. Unlike existing implicit solvent approaches, the solvent accessible surface is an output of our model. The presented formalism is illustrated on spherically or cylindrically symmetrical systems of neutral or charged solutes on different length scales. The results are in agreement with computer simulations and, most importantly, demonstrate that our method captures the strong sensitivity of solvent expulsion and dewetting to the particular form of the solvent-solute interactions.

Improved Reweighting of Accelerated Molecular Dynamics Simulations for Free Energy Calculation.

Accelerated molecular dynamics (aMD) simulations greatly improve the efficiency of conventional molecular dynamics (cMD) for sampling biomolecular conformations, but they require proper reweighting for free energy calculation. In this work, we systematically compare the accuracy of different reweighting algorithms including the exponential average, Maclaurin series, and cumulant expansion on three model systems: alanine dipeptide, chignolin, and Trp-cage. Exponential average reweighting can recover the original free energy profiles easily only when the distribution of the boost potential is narrow (e.g., the range ≤20kBT) as found in dihedral-boost aMD simulation of alanine dipeptide. In dual-boost aMD simulations of the studied systems, exponential average generally leads to high energetic fluctuations, largely due to the fact that the Boltzmann reweighting factors are dominated by a very few high boost potential frames. In comparison, reweighting based on Maclaurin series expansion (equivalent to cumulant expansion on the first order) greatly suppresses the energetic noise but often gives incorrect energy minimum positions and significant errors at the energy barriers (∼2–3kBT). Finally, reweighting using cumulant expansion to the second order is able to recover the most accurate free energy profiles within statistical errors of ∼kBT, particularly when the distribution of the boost potential exhibits low anharmonicity (i.e., near-Gaussian distribution), and should be of wide applicability. A toolkit of Python scripts for aMD reweighting “PyReweighting” is distributed free of charge at http://mccammon.ucsd.edu/computing/amdReweighting/.

Electrostatic and hydrodynamic orientational steering effects in enzyme-substrate association.

Diffusional encounters between a dumbbell model of a cleft enzyme and a dumbbell model of an elongated ligand are simulated by Brownian dynamics. The simulations take into account electrostatic and hydrodynamic interactions between the molecules. It is shown that the primary effect of inclusion of hydrodynamic interactions into the simulation is an overall decrease in the rate constant. Hydrodynamic orientational effects are of modest size for the systems considered here. They are manifested when changes in the rate constants for diffusional encounters favored by hydrodynamic interactions are compared with those favored by electrostatic interactions as functions of the overall strength of electrostatic interactions. The electrostatic interactions modify the hydrodynamic torques by modifying the drift velocity of the substrate toward the enzyme. We conclude that simulations referring only to electrostatic interactions between an enzyme and its ligand may yield rate constants that are somewhat (e.g., 20%) too high, but provide realistic descriptions of the orientational steering effects in the enzyme-ligand encounters.

Accelerated molecular dynamics simulations of ligand binding to a muscarinic G-protein-coupled receptor

Elucidating the detailed process of ligand binding to a receptor is pharmaceutically important for identifying druggable binding sites. With the ability to provide atomistic detail, computational methods are well poised to study these processes. Here, accelerated molecular dynamics (aMD) is proposed to simulate processes of ligand binding to a G-protein-coupled receptor (GPCR), in this case the M3 muscarinic receptor, which is a target for treating many human diseases, including cancer, diabetes and obesity. Long-timescale aMD simulations were performed to observe the binding of three chemically diverse ligand molecules: antagonist tiotropium (TTP), partial agonist arecoline (ARc) and full agonist acetylcholine (ACh). In comparison with earlier microsecond-timescale conventional MD simulations, aMD greatly accelerated the binding of ACh to the receptor orthosteric ligand-binding site and the binding of TTP to an extracellular vestibule. Further aMD simulations also captured binding of ARc to the receptor orthosteric site. Additionally, all three ligands were observed to bind in the extracellular vestibule during their binding pathways, suggesting that it is a metastable binding site. This study demonstrates the applicability of aMD to protein-ligand binding, especially the drug recognition of GPCRs.

Antiinfectives targeting enzymes and the proton motive force

Significance Uncoupling agents might be expected to be generally cytotoxic, but many US Food and Drug Administration (FDA)-approved drugs do have activity as uncouplers, in addition to targeting enzymes. There is therefore interest in the discovery of antibiotics that have such multitarget activity. Here, we show that some FDA-approved drugs, such as clofazimine, clomiphene, and bedaquiline, with antiinfective activity act as uncouplers. Using molecular dynamics-based in silico screening, we also discovered that the brain cancer drug lead vacquinol is an uncoupler that inhibits an enzyme involved in the formation of tuberculosis (TB) virulence factors, in addition to killing TB bacteria. Our results indicate strong drug–membrane interactions, and that screening for combined enzyme inhibition plus uncoupler activity will lead to new antibiotic leads. There is a growing need for new antibiotics. Compounds that target the proton motive force (PMF), uncouplers, represent one possible class of compounds that might be developed because they are already used to treat parasitic infections, and there is interest in their use for the treatment of other diseases, such as diabetes. Here, we tested a series of compounds, most with known antiinfective activity, for uncoupler activity. Many cationic amphiphiles tested positive, and some targeted isoprenoid biosynthesis or affected lipid bilayer structure. As an example, we found that clomiphene, a recently discovered undecaprenyl diphosphate synthase inhibitor active against Staphylococcus aureus, is an uncoupler. Using in silico screening, we then found that the anti-glioblastoma multiforme drug lead vacquinol is an inhibitor of Mycobacterium tuberculosis tuberculosinyl adenosine synthase, as well as being an uncoupler. Because vacquinol is also an inhibitor of M. tuberculosis cell growth, we used similarity searches based on the vacquinol structure, finding analogs with potent (∼0.5–2 μg/mL) activity against M. tuberculosis and S. aureus. Our results give a logical explanation of the observation that most new tuberculosis drug leads discovered by phenotypic screens and genome sequencing are highly lipophilic (logP ∼5.7) bases with membrane targets because such species are expected to partition into hydrophobic membranes, inhibiting membrane proteins, in addition to collapsing the PMF. This multiple targeting is expected to be of importance in overcoming the development of drug resistance because targeting membrane physical properties is expected to be less susceptible to the development of resistance.

Parallelizing molecular dynamics using spatial decomposition

Several algorithms have been used for parallel molecular dynamics, including the replicated algorithm and those based on spatial decompositions. The replicated algorithm stores the entire systems coordinates and forces at each processor, and therefore has a low overhead in maintaining the data distribution. Spatial decompositions distribute the data, providing better locality and scalability with respect to memory and computation. We present EULERGROMOS, a parallelization of the GROMOS molecular dynamics program which is based on a spatial decomposition. EULERGROMOS parallelizes all molecular dynamics phases, with most data structures using O(N/P) memory. The paper focuses on the structure of EULERGROMOS and analyses its performance using molecular systems of current interest in the molecular dynamics community. EULERGROMOS achieves performance increases with as few as twenty atoms per processor. We also compare EULERGROMOS with an earlier parallelization of GROMOS, UHGROMOS, which uses the replicated algorithm.<<ETX>>

Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation

We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L(∞) estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem. The convergence and accuracy of the overall AFEM algorithm is also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein.

Optimizing the Poisson Dielectric Boundary with Explicit Solvent Forces and Energies: Lessons Learned with Atom-Centered Dielectric Functions.

Accurate implicit solvent models require parameters that have been optimized in a system- or atom-specific manner on the basis of experimental data or more rigorous explicit solvent simulations. Models based on the Poisson or Poisson-Boltzmann equation are particularly sensitive to the nature and location of the boundary which separates the low dielectric solute from the high dielectric solvent. Here, we present a novel method for optimizing the solute radii, which define the dielectric boundary, on the basis of forces and energies from explicit solvent simulations. We use this method to optimize radii for protein systems defined by AMBER ff99 partial charges and a spline-smoothed solute surface. The spline-smoothed surface is an atom-centered dielectric function that enables stable and efficient force calculations. We explore the relative performance of radii optimized with forces alone and those optimized with forces and energies. We show that our radii reproduce the explicit solvent forces and energies more accurately than four other parameter sets commonly used in conjunction with the AMBER force field, each of which has been appropriately scaled for spline-smoothed surfaces. Finally, we demonstrate that spline-smoothed surfaces show surprising accuracy for small, compact systems but may have limitations for highly solvated protein systems. The optimization method presented here is efficient and applicable to any system with explicit solvent parameters. It can be used to determine the optimal continuum parameters when experimental solvation energies are unavailable and the computational costs of explicit solvent charging free energies are prohibitive.