Multilevel summation for periodic electrostatics using B-splines.

Fast methods for calculating two-body interactions have many applications, and for molecular science and cosmology, it is common to employ periodic boundary conditions. However, for the 1/r potential, the energy and forces are ill-defined. Adopted here is the model given by the classic Ewald sum.

Scalable molecular dynamics on CPU and GPU architectures with NAMD.

NAMDis a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures.

A minimization principle for transition paths of maximum flux for collective variables.

Considered is the construction of transition paths of conformational changes for proteins and other macromolecules, using methods that do not require the generation of dynamics trajectories. Special attention is given to the use of a reduced set of collective variables for describing such paths. A favored way to define transition paths is to seek channels through the transition state having cross sections with a high reactive flux (density of last hitting points of reactive trajectories).

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations.

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients.

Multilevel summation method for electrostatic force evaluation.

The multilevel summation method (MSM) offers an efficient algorithm utilizing convolution for evaluating long-range forces arising in molecular dynamics simulations. Shifting the balance of computation and communication, MSM provides key advantages over the ubiquitous particle–mesh Ewald (PME) method, offering better scaling on parallel computers and permitting more modeling flexibility, with support for periodic systems as does PME but also for semiperiodic and nonperiodic systems. The version of MSM available in the simulation program NAMD is described, and its performance and accuracy are compared with the PME method.

Compressible generalized hybrid Monte Carlo.

One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a Markov chain Monte Carlo method, which converges only in the limit to the prescribed distribution. Such methods typically inch through configuration space step by step, with acceptance of a step based on a Metropolis(-Hastings) criterion.

αC helix as a switch in the conformational transition of Src/CDK-like kinase domains.

One mechanism of regulating the catalytic activity of protein kinases is through conformational transitions. Despite great diversity in the structural changes involved in the transitions, a certain set of changes within the kinase domain (KD) has been observed for many kinases including Src and CDK2. We investigated this conformational transition computationally to identify the topological features that are energetically critical to the transition.

Dual role of protein phosphorylation in DNA activator/coactivator binding.

Binding free energies are calculated for the phosphorylated and unphosphorylated complexes between the kinase inducible domain (KID) of the DNA transcriptional activator cAMP response element binding (CREB) protein and the KIX domain of its coactivator, CREB-binding protein (CBP). To our knowledge, this is the first application of a method based on a potential of mean force (PMF) with restraining potentials to compute the binding free energy of protein-protein complexes. The KID:KIX complexes are chosen here because of their biological relevance to the DNA transcription process and their relatively small size (81 residues for the KIX domain of CBP, and 28 residues for KID).

Maximum Flux Transition Paths of Conformational Change.

Given two metastable states A and B of a biomolecular system, the problem is to calculate the likely paths of the transition from A to B. Such a calculation is more informative and more manageable if done for a reduced set of collective variables chosen so that paths cluster in collective variable space. The computational task becomes that of computing the "center" of such a cluster.

ON ENERGY CONSERVATION OF THE SIMPLIFIED TAKAHASHI-IMADA METHOD.

In long-time numerical integration of Hamiltonian systems, and especially in molecular dynamics simulation, it is important that the energy is well conserved. For symplectic integrators applied with sufficiently small step size, this is guaranteed by the existence of a modified Hamiltonian that is exactly conserved up to exponentially small terms. This article is concerned with the simplified Takahashi-Imada method, which is a modification of the Störmer-Verlet method that is as easy to implement but has improved accuracy.

WHAT MAKES MOLECULAR DYNAMICS WORK?

The equations of motion for deterministic molecular dynamics (MD) are chaotic, creating problems for their numerical treatment due to the exponential growth of error with time. Indeed, modeling and computational errors overwhelm numerical trajectories in typical simulations. Consequently, accuracy is expected only in a statistical sense, based on random initial conditions.

A separable shadow Hamiltonian hybrid Monte Carlo method.

Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator.

Fast evaluation of polarizable forces.

Polarizability is considered to be the single most significant development in the next generation of force fields for biomolecular simulations. However, the self-consistent computation of induced atomic dipoles in a polarizable force field is expensive due to the cost of solving a large dense linear system at each step of a simulation. This article introduces methods that reduce the cost of computing the electrostatic energy and force of a polarizable model from about 7.

Scalable molecular dynamics with NAMD.

NAMD is a parallel molecular dynamics code designed for high-performance simulation of large biomolecular systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats.

Robust biased Brownian dynamics for rate constant calculation.

A reaction probability is required to calculate the rate constant of a diffusion-dominated reaction. Due to the complicated geometry and potentially high dimension of the reaction probability problem, it is usually solved by a Brownian dynamics simulation, also known as a random walk or path integral method, instead of solving the equivalent partial differential equation by a discretization method. Building on earlier work, this article completes the development of a robust importance sampling algorithm for Brownian dynamics-i.

Multiple grid methods for classical molecular dynamics.

Presented in the context of classical molecular mechanics and dynamics are multilevel summation methods for the fast calculation of energies/forces for pairwise interactions, which are based on the hierarchical interpolation of interaction potentials on multiple grids. The concepts and details underlying multigrid interpolation are described. For integration of molecular dynamics the use of different time steps for different interactions allows longer time steps for many of the interactions, and this can be combined with multiple grids in space.