Interactions, molecular dynamics

Yan, C., Yersin, A., Afrin, R., Sekiguchi, H., and ikai, A. 2009. Single molecular dynamic interactions between glycophorin A and lectin as probed by atomic force microscopy, Biophys Chem 144, 72-77. 

The theoretical treatments of Section III-2B have been used to calculate interfacial tensions of solutions using suitable interaction potential functions. Thus Gubbins and co-workers [88] report a molecular dynamics calculation of the surface tension of a solution of A and B molecules obeying Eq. III-46 with o,bb/ o,aa = 0.4 and... 

Because of limitations of space, this section concentrates very little on rotational motion and its interaction with the vibrations of a molecule. However, this is an extremely important aspect of molecular dynamics of long-standing interest, and with development of new methods it is the focus of mtense investigation [18, 19, 20. 21. 22 and 23]. One very interesting aspect of rotation-vibration dynamics involving geometric phases is addressed in section A1.2.20. 

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

Ultimately we may want to make direct comparisons with experimental measurements made on specific materials, in which case a good model of molecular interactions is essential. The aim of so-called ab initio molecular dynamics is to reduce the amount of fitting and guesswork in this process to a minimum. On the other hand, we may be interested in phenomena of a rather generic nature, or we may simply want to discriminate between good and bad theories. When it comes to aims of this kind, it is not necessary to have a perfectly realistic molecular model one that contains the essential physics may be quite suitable. 

Molecular dynamics consists of the brute-force solution of Newton s equations of motion. It is necessary to encode in the program the potential energy and force law of interaction between molecules the equations of motion are solved numerically, by finite difference techniques. The system evolution corresponds closely to what happens in real life and allows us to calculate dynamical properties, as well as thennodynamic and structural fiinctions. For a range of molecular models, packaged routines are available, either connnercially or tlirough the academic conmuinity. 

Procacci P, Darden T A, Paci E and Marchi M 1997 ORAC a molecular dynamics program to simulate complex molecular systems with realistic electrostatic interactions J. Comput. Chem. 18 1848-62... 

Finally, Sections B3.4.10. touches on the application of quantum molecular dynamics to a very exciting field laser interactions with molecules. This field presents, in principle, the opportunity to influence chemistry by lasers rather than to simply observe it. 

The scope of this section restricts the discussion. One omitted topic is the collision and interaction of molecules with surfaces (see [20, 21] and section A3.9). This topic coimects quantum molecular dynamics in gas and condensed phases. Depending on the time scales of the interaction of a molecule witli a surface, the... 

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

The most important molecular interactions of all are those that take place in liquid water. For many years, chemists have worked to model liquid water, using molecular dynamics and Monte Carlo simulations. Until relatively recently, however, all such work was done using effective potentials [4T], designed to reproduce the condensed-phase properties but with no serious claim to represent the tme interactions between a pair of water molecules. 

In favourable contrast to molecular dynamics, BD allows molecular movements of realistically long duration to be simulated. Nevertheless, the practical number of protein molecules which can be simulated is only two since collective phenomena are often of crucial importance in detennining the course of interaction events, other simulation teclmiques, such as cellular automata [115], need to be used to capture the behaviour of large numbers of particles. 

The method of molecular dynamics (MD), described earlier in this book, is a powerful approach for simulating the dynamics and predicting the rates of chemical reactions. In the MD approach most commonly used, the potential of interaction is specified between atoms participating in the reaction, and the time evolution of their positions is obtained by solving Hamilton s equations for the classical motions of the nuclei. Because MD simulations of etching reactions must include a significant number of atoms from the substrate as well as the gaseous etchant species, the calculations become computationally intensive, and the time scale of the simulation is limited to the... 

Procacci, P., Darden, T., Marchi, M., A very fast molecular dynamics method to simulate biomolecular systems with realistic electrostatic interactions. J. Phys. Chem. 100 (1996) 10464-10468. 

Tasaki, K., McDonald, S., Brady, J.W. Observations concerning the treatment of long range interactions in molecular dynamics simulations. J. Comput. Chem. 14 (1993) 278-284. 

Belhadj,M., Alper, H.A., Levy, R.M. Molecular dynamics simulations of wa ter with Ewald summation for the long-range electrostatic interactions. Chem. Phys. Lett. 179 (1991) 13-20. 

The simulations also revealed that flapping motions of one of the loops of the avidin monomer play a crucial role in the mechanism of the unbinding of biotin. The fluctuation time for this loop as well as the relaxation time for many of the processes in proteins can be on the order of microseconds and longer (Eaton et al., 1997). The loop has enough time to fluctuate into an open state on experimental time scales (1 ms), but the fluctuation time is too long for this event to take place on the nanosecond time scale of simulations. To facilitate the exit of biotin from its binding pocket, the conformation of this loop was altered (Izrailev et al., 1997) using the interactive molecular dynamics features of MDScope (Nelson et al., 1995 Nelson et al., 1996 Humphrey et al., 1996). 

Abstract. Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FA-MUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales. 

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. 

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. 

S. Miyamoto and P. A. Kollman. Absolute and relative binding free energy calculations of the interaction of biotin and its analogs with streptavidin using molecular dynamics/free energy perturbation approaches. Proteins, 16 226-245, 1993. 

Ligand-Protein Interactions The energy of formation of ligand-protein contacts can be computed as a sum of non-bonded (Lennard-Jones and electrostatic) terms similar to those used in a molecular dynamics simulation. 

Fig. 5. To generate an ensemble using Molecular Dynamics or Monte-Carlo simulation techniques the interaction between all pairs of atoms within a given cutoff radius must be considered. In contrast, to estimate changes in free energy using a stored trajectory only those interactions which are perturbed need be determined making the approach highly efficient.

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