General framework for constraints in molecular dynamics simulations

Journal of …, 1995

In molecular dynamics simulations, the fastest components of the potential eld impose severe restrictions on the stability and hence the speed of computational methods. One possibility for treating this problem is to replace the fastest components with algebraic length constraints. In this paper, the resulting systems of mixed di erential and algebraic equations are studied. Commonly used discretization schemes for constrained Hamiltonian systems are discussed. The form of the nonlinear equations is examined in detail and used to give convergence results for the traditional nonlinear solution technique SHAKE iteration and for a modi cation based on Successive OverRelaxation (SOR). A simple adaptive algorithm for nding the optimal relaxation parameter is presented. Alternative direct methods using sparse matrix techniques are discussed. Numerical results are given for the new techniques, implemented in the molecular modeling software package CHARMM, showing as much as twofold improvement over SHAKE iteration. matrix methods 1. Introduction. In molecular dynamics, the length of timestep for numerically integrating the equations of motion is dictated by the contributions to the force vector which maintain pairs of atoms near some equilibrium distance. The imposition of algebraic constraints that x these lengths removes the associated rapid vibrational modes, enabling the use of longer timesteps without substantially altering important physical characteristics of the motion 1]. Although we treat only length constraints in the present work, constrained techniques are also of interest for conformational search and conformational free energy simulations 2]. In 3] the SHAKE iteration was described for solving the nonlinear equations at each timestep of a constrained version of the Verlet discretization, and a similar scheme was proposed in 4] for use with the RATTLE discretization.

1977

A numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method is applied to a molecular dynamics simulation of a liquid of 64 nbutane molecules and compared to a simulation using generalized coordinates. The method should be useful for molecular dynamics calculations on large molecules with internal degrees of freedom.

In this chapter a summary is given of the key ingredients necessary to carry out a molecular dynamics simulation, with particular emphasis on macromolecular systems. We discuss the form of the intermolecular potential for molecules composed of atoms, and of non-spherical sub-units, giving examples of how to compute the forces and torques. We also describe some of the MD algorithms in current use. Finally, we briefly refer to the factors that influence the size of systems, and length of runs, that are needed to calculate statistical properties.

Computer Physics Reports, 1984

Since its introduction by Alder and Rahman in the 1950's, molecular dynamics simulations of classical fluids have led to a revolution in our understanding of the equilibrium and non-equilibrium properties of fluids. In that time the basic technique has remained plmost unaltered: using an assumed intermolecular potential function one solved Newton's equations of motion ad,, mi,:F.:-I-+ ; d,, for a few hundred to a few thousand molecules subject to periodic boundary conditions. Recently, a number of breakthroughs have resulted in a vast increase in the efficiency and range of applicability of the method. Stimulated by developments in simulating non-equilibrium systems, we now know how to simulate equilibrium systems in ensembles other than the molecular dynamics ensembleconstant mass, momentum, energy and volume, Not surprisingly these new techniques involve the abandonment of Newtonian equations of motion. We are led to consider the motion generated by various synthetic (i.e. not existing in nature) Hamiltonians that are designed to ensure the maintenance of thermodynamic constraints on systems. In many cases (constant temperature systems or heat flow for example) we apparently must abandon motion which may be generated by any Hamiltonian. In these circumstances we simply specify appropriate second order differential equations for the classical trajectory of the N-particle system. The nature of the equations chosen is usually not unique but theory relates the behaviour of the system to the equations chosen and so the simulation provides the required information.

The Journal of chemical physics, 2015

A method which controls momentum evolution in a sub-region within a molecular dynamics simulation is derived from Gauss's principle of least constraint. The technique for localization is founded on the equations by Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] expressed in a weak form according to the control volume (CV) procedure derived by Smith et al. [Phys. Rev. E. 85, 056705 (2012)]. A term for the advection of molecules appears in the derived constraint and is shown to be essential in order to exactly control the time evolution of momentum in the subvolume. The numerical procedure converges the total momentum in the CV to the target value to within machine precision in an iterative manner. The localized momentum constraint can prescribe essentially arbitrary flow fields in non-equilibrium molecular dynamics simulations. The methodology also forms a rigorous mathematical framework for introducing coupling constraints at the boundary between continuum and discrete syst...

This paper reviews the basic concepts needed to understand Molecular Dynamics simulations and will hopefully serve as an introductory guide for the non-expert into this exciting topic.

Proceedings of the National Academy of Sciences, 2020

From the point of view of statistical mechanics, a full characterization of a molecular system requires an accurate determination of its possible states, their populations, and the respective interconversion rates. Toward this goal, well-established methods increase the accuracy of molecular dynamics simulations by incorporating experimental information about states using structural restraints and about populations using thermodynamics restraints. However, it is still unclear how to include experimental knowledge about interconversion rates. Here, we introduce a method of imposing known rate constants as constraints in molecular dynamics simulations, which is based on a combination of the maximum-entropy and maximum-caliber principles. Starting from an existing ensemble of trajectories, obtained from either molecular dynamics or enhanced trajectory sampling, this method provides a minimally perturbed path distribution consistent with the kinetic constraints, as well as modified free...

In this chapter a summary is given of the key ingredients necessary to carry out a molecular dynamics simulation, with particular emphasis on macromolecular systems. We discuss the form of the intermolecular potential for molecules composed of atoms, and of non-spherical sub-units, giving examples of how to compute the forces and torques. We also describe some of the MD algorithms in current use. Finally, we briefly refer to the factors that influence the size of systems, and length of runs, that are needed to calculate statistical properties.

2010

The most important factor for quantitative results in molecular dynamics simulation are well developed force fields and models. In the present work, the development of new models and the usage of force fields from the literature in large systems are presented. Both tasks lead to time consuming simulations that require massively parallel high performance computing. In the present work, new

The Journal of Chemical Physics, 2000

From a specific definition of the roto-translational ͑external͒ and intramolecular ͑internal͒ coordinates, a constrained dynamics algorithm is derived for removing the roto-translational motions during molecular dynamics simulations, within the leap-frog integration scheme. In the paper the theoretical basis of this new method and its statistical mechanical consistency are reported, together with two applications.