Molecular dynamics simulation algorithms

Lamoureux G, Roux B (2003) Modeling induced polarization with classical Drude oscillators theory and molecular dynamics simulation algorithm. J Chem Phys 119(6) 3025-3039... 

When the CPU requests a data item from main memory, the memory subsystem will check to see if it can be found in cache. If the data is not in cache, a cache miss occurs. When this happens the data item will be searched for at lower levels of the memory system and when it is eventually found it is brought into the cache. Data are fetched from memory in units of a cache line. This kind of memory organization is motivated by the observation that data that is used often should be accessible as quickly as possible and when a data is accessed it is also very likely that data items located close to it in memory will also be accessed soon. So memory access patterns which are local in space and time will be quickly serviced. Molecular Dynamics simulation algorithms often have a quite a lot of potential for memory access patterns that are local both in time and space. How well this can be exploited is very much dependent on the data-structures that are used in implementations. Which, of all possible data-structures, are optimal for MD is currently an open question. 

The theory for various molecular dynamics simulation algorithms for the calculation of transport coefficients of liquid crystals is presented. We show in particular how the thermal conductivity and the viscosity are obtained. The viscosity of a nematic liquid crystal has seven independent components because of the lower symmetry. We present numerical results for various phases of the Gay-Berne fluid even though the theory is completely general and applicable to more realistic model systems. 

An examination of the validity of nonequflibrium molecular-dynamics simulation algorithms for arbitrary steady-state flows. J. Chem, Phys., 123,... 

Berendsen. H.J.C., Van Gunsteren, W.F. Practical algorithms for dynamic simulations, in Molecular Dynamics Simulations of Statistical Mechanical Systems, G. Ciccotti, ed., Soc. Italiana di Fisica, Bologna (1987) 43-65. 

Helmut Grubmuller, Helmut Heller, Andreas Windemuth, and Klaus Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Mol. Sim., 6 121-142, 1991. 

Andreas Windemuth. Advanced Algorithms for Molecular Dynamics Simulation The Program PMD. ACS Books, 1995. 

M. Eichinger, H. Grubmiiller, H. Heller, and P. Tavan. FAMUSAMM An algorithm for rapid evaluation of electrostatic interaction in molecular dynamics simulations. J. Comp. Chem., 18 1729-1749, 1997. 

D. Janezid and F. Merzel. An efficient symplectic integration algorithm for molecular dynamics simulations. J. Chem. Info. Comp. Set, 35 321-326, 1995. 

Extending time scales of Molecular Dynamics simulations is therefore one of the prime challenges of computational biophysics and attracted considerable attention [2-5]. Most efforts focus on improving algorithms for solving the initial value differential equations, which are in many cases, the Newton s equations of motion. 

Janezic, D., Merzel, F. An Efficient Symplectic Integration Algorithm for Molecular Dynamics Simulations. J. Chem. Inf. Comput. Sci. 35 (1995) 321-326... 

Grubmiiller, H., Heller, H., Windemuth, A., Schulten, K. Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with Long-range Interactions. Molecular Simulation 6 (1991) 121-142... 

R. Murty and D. Okunbor, Efficient parallel algorithms for molecular dynamics simulations , submitted to Parallel Computing. 

A. Windemuth, Advanced algorithms for molecular dynamics simulations The program PMD , ACS Symposium Series 592, 151-69, 1995. 

To have an overview of the algorithms and basic concepts used to perform molecular dynamics simulations... 

A molecular dynamics simulation samples the phase space of a molecule (defined by the position of the atoms and their velocities) by integrating Newton s equations of motion. Because MD accounts for thermal motion, the molecules simulated may possess enough thermal energy to overcome potential barriers, which makes the technique suitable in principle for conformational analysis of especially large molecules. In the case of small molecules, other techniques such as systematic, random. Genetic Algorithm-based, or Monte Carlo searches may be better suited for effectively sampling conformational space. 

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 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 ... 

Prepare a molecule for a molecular dynamics simulation. If the forces on atoms are too large, the integration algorithm may fail during a molecular dynamics calculation. 

During a molecular dynamics simulation, HyperChem stores the current positions, Tj (t), and the mid-step velocities, Vj (t - 1/2 At). Since the algorithm provides mid-step velocities, but not velocities, Vj (t), for the positions at time t, HyperChem calculates approximate values of Ej-qt (O- This results in slightly larger fluctuations in Ej-ot (t) than an algorithm that calculates exact values of... 

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. 

For 25 years, molecular dynamics simulations of proteins have provided detailed insights into the role of dynamics in biological activity and function [1-3]. The earliest simulations of proteins probed fast vibrational dynamics on a picosecond time scale. Fifteen years later, it proved possible to simulate protein dynamics on a nanosecond time scale. At present it is possible to simulate the dynamics of a solvated protein on the microsecond time scale [4]. These gains have been made through a combination of improved computer processing (Moore s law) and clever computational algorithms [5]. 

To overcome the limitations of the database search methods, conformational search methods were developed [95,96,109]. There are many such methods, exploiting different protein representations, objective function tenns, and optimization or enumeration algorithms. The search algorithms include the minimum perturbation method [97], molecular dynamics simulations [92,110,111], genetic algorithms [112], Monte Carlo and simulated annealing [113,114], multiple copy simultaneous search [115-117], self-consistent field optimization [118], and an enumeration based on the graph theory [119]. 

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