Computational methods complex system dynamics

The use of computer simulations to study internal motions and thermodynamic properties is receiving increased attention. One important use of the method is to provide a more fundamental understanding of the molecular information contained in various kinds of experiments on these complex systems. In the first part of this paper we review recent work in our laboratory concerned with the use of computer simulations for the interpretation of experimental probes of molecular structure and dynamics of proteins and nucleic acids. The interplay between computer simulations and three experimental techniques is emphasized (1) nuclear magnetic resonance relaxation spectroscopy, (2) refinement of macro-molecular x-ray structures, and (3) vibrational spectroscopy. The treatment of solvent effects in biopolymer simulations is a difficult problem. It is not possible to study systematically the effect of solvent conditions, e.g. added salt concentration, on biopolymer properties by means of simulations alone. In the last part of the paper we review a more analytical approach we have developed to study polyelectrolyte properties of solvated biopolymers. The results are compared with computer simulations. 

In addition to the described above methods, there are computational QM-MM (quantum mechanics-classic mechanics) methods in progress of development. They allow prediction and understanding of solvatochromism and fluorescence characteristics of dyes that are situated in various molecular structures changing electrical properties on nanoscale. Their electronic transitions and according microscopic structures are calculated using QM coupled to the point charges with Coulombic potentials. It is very important that in typical QM-MM simulations, no dielectric constant is involved Orientational dielectric effects come naturally from reorientation and translation of the elements of the system on the pathway of attaining the equilibrium. Dynamics of such complex systems as proteins embedded in natural environment may be revealed with femtosecond time resolution. In more detail, this topic is analyzed in this volume [76]. 

The molecular dynamics unit provides a good example with which to outline the basic approach. One of the most powerful applications of modem computational methods arises from their usefulness in visualizing dynamic molecular processes. Small molecules, solutions, and, more importantly, macromolecules are not static entities. A protein crystal structure or a model of a DNA helix actually provides relatively little information and insight into function as function is an intrinsically dynamic property. In this unit students are led through the basics of a molecular dynamics calculation, the implementation of methods integrating Newton s equations, the visualization of atomic motion controlled by potential energy functions or molecular force fields and onto the modeling and visualization of more complex systems. 

Sn2 reactions of methyl halides with anionic nucleophiles are one of the reactions most frequently studied with computational methods, since they are typical group-transfer reactions whose reaction profiles are simple. Back in 1986, Basilevski and Ryaboy have carried out quantum dynamical calculations for Sn2 reactions of X + CH3Y (X = H, F, OH) with the collinear collision approximation, in which only a pair of vibrations of the three-center system X-CH3-Y were considered as dynamical degrees of freedom and the CH3 fragment was treated as a structureless particle [Equation (11)].30 They observed low efficiency of the gas-phase reactions. The results indicated that the decay rate constants of the reactant complex in the product direction and in the reactant direction did not represent statistical values. This constitutes a... 

Electronic and optical properties of complex systems are now accessible thanks to the impressive development of theoretical approaches and of computer power. Surfaces, nanostructures, and even biological systems can now be studied within ab-initio methods [53,54]. In principle within the Born-Oppenheimer approximation to decouple the ionic and electronic dynamics, the equation that governs the physics of all those systems is the many-body equation ... 

Molecular dynamics (MD) simulations provide a detailed description of complex systems in a wide range of time and spatial scales.138 Simulations involve a statistical uncertainty component as the result of the finite length of the simulation.139 143 MD methods generate a series of time-correlated points in phase space by propagating a suitable starting set of coordinates and velocities according to Newton s second equation. This kind of computational simulations are useful in studies of time evolution of a variety of systems biological molecules, polymers, or catalytic materials, and in a variety of states crystal, aqueous solutions, or in the gas phase. 

The first molecular simulations were performed almost five decades ago by Metropolis et al. (1953) on a system of hard disks by the Monte Carlo (MC) method. Soon after, hard spheres (Rosenbluth and Rosenbluth, 1954) and Lennard-Jones (Wood and Parker, 1957) particles were also studied by both MC and molecular dynamics (MD). Over the years, the simulation techniques have evolved to deal with more complex systems by introducing different sampling or computational algorithms. Molecular simulation studies have been made of molecules ranging from simple systems (e.g., noble gases, small organic molecules) to complex molecules (e.g., polymers, biomolecules). 

Chapter 8—Molecular Interactions Learning from Protein Complexes The spectrum of interactions is critical to comprehending the dynamics of a living system, and understanding it can help to develop methodology for future studies in other systems. Rojas, de Juan, and Valencia review the current state of experimental and computational methods for the study of protein interactions, including prospects for future developments. 

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