Molecular dynamics, algorithmic methods

Methods of Quantum Pharmacology for Conformational Analysis Monte Carlo Methods, Molecular Dynamics, Genetic Algorithms... 

Methods and algorithms for molecular dynamics simulations of molecular fluids are described. Those techniques are emphasized that in the experience of the authors are reliable and easy to implement. This implies the use of cartesian coordinates throughout, the use of the SHAKE procedure to satisfy constraints and the incorporation of an adjustable coupling to an external bath with constant temperature and pressure. 

Critical to simulating such large systems efficiently and accurately are algorithms for molecular dynamics, Brownian dynamics, and Monte Carlo methods The state of the art... 

Cao, J., Martyna, G.J. Adiabatic path integral molecular dynamics methods. II. Algorithms. J. Chem. Phys. 104 (1996) 2028-2035. 

R. Zhou and B. J. Berne. A new molecular dynamics method combining the reference system propagator algorithm with a fast multipole method for simulating proteins and other complex systems. J. Phys. Chem., 103 9444-9459, 1995. 

Other methods which are applied to conformational analysis and to generating multiple conformations and which can be regarded as random or stochastic techniques, since they explore the conformational space in a non-deterministic fashion, arc genetic algorithms (GA) [137, 1381 simulation methods, such as molecular dynamics (MD) and Monte Carlo (MC) simulations 1139], as well as simulated annealing [140], All of those approaches and their application to generate ensembles of conformations arc discussed in Chapter II, Section 7.2 in the Handbook. 

An important though deman ding book. Topics include statistical mechanics, Monte Carlo sim illation s. et uilibrium and non -ec iiilibrium molecular dynamics, an aly sis of calculation al results, and applications of methods to problems in liquid dynamics. The authors also discuss and compare many algorithms used in force field simulations. Includes a microfiche containing dozens of Fortran-77 subroutines relevant to molecular dynamics and liquid simulations. 

The input to a minimisation program consists of a set of initial coordinates for the system. The initial coordinates may come from a variety of sources. They may be obtained from an experimental technique, such as X-ray crystallography or NMR. In other cases a theoretical method is employed, such as a conformational search algorithm. A combination of experimenfal and theoretical approaches may also be used. For example, to study the behaviour of a protein in water one may take an X-ray structure of the protein and immerse it in a solvent bath, where the coordinates of the solvent molecules have been obtained from a Monte Carlo or molecular dynamics simulation. 

There are many algorithms for integrating the equations of motion using finite difference methods, several of which are commonly used in molecular dynamics calculations. All algorithms assume that the positions and dynamic properties (velocities, accelerations, etc.) can be approximated as Taylor series expansions ... 

There are many variants of the predictor-corrector theme of these, we will only mention the algorithm used by Rahman in the first molecular dynamics simulations with continuous potentials [Rahman 1964]. In this method, the first step is to predict new positions as follows ... 

Zhou R and B J Berne 1995. A New Molecular Dynamics Method Combining the Reference Sys Propagator Algorithm with a Fast Multipole Method for Simulating Proteins and Ol Complex Systems. Journal of Chemical Physics 103 9444-9459. 

The main difference between the force-bias and the smart Monte Carlo methods is that the latter does not impose any limit on the displacement that m atom may undergo. The displacement in the force-bias method is limited to a cube of the appropriate size centred on the atom. However, in practice the two methods are very similar and there is often little to choose between them. In suitable cases they can be much more efficient at covering phase space and are better able to avoid bottlenecks in phase space than the conventional Metropolis Monte Carlo algorithm. The methods significantly enhance the acceptance rate of trial moves, thereby enabling Icirger moves to be made as well as simultaneous moves of more than one particle. However, the need to calculate the forces makes the methods much more elaborate, and comparable in complexity to molecular dynamics. 

PLS (partial least-squares) algorithm used for 3D QSAR calculations PM3 (parameterization method three) a semiempirical method PMF (potential of mean force) a solvation method for molecular dynamics calculations... 

Computational methods have played an exceedingly important role in understanding the fundamental aspects of shock compression and in solving complex shock-wave problems. Major advances in the numerical algorithms used for solving dynamic problems, coupled with the tremendous increase in computational capabilities, have made many problems tractable that only a few years ago could not have been solved. It is now possible to perform two-dimensional molecular dynamics simulations with a high degree of accuracy, and three-dimensional problems can also be solved with moderate accuracy. 

An algorithm for performing a constant-pressure molecular dynamics simulation that resolves some unphysical observations in the extended system (Andersen s) method and Berendsen s methods was developed by Feller et al. [29]. This approach replaces the deterministic equations of motion with the piston degree of freedom added to the Langevin equations of motion. This eliminates the unphysical fluctuation of the volume associated with the piston mass. In addition, Klein and coworkers [30] present an advanced constant-pressure method to overcome an unphysical dependence of the choice of lattice in generated trajectories. 

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