Activated dynamical scaling

Figure 14-1. Left Relative errors (RELE) in the force as a function of radial distance from the center of the active dynamical region for the VEP-RVM charge-scaling method [80] for the solvated hammerhead ribozyme at different discretization levels [151] of die co surface. Right The projected total electrostatic potential due to the fully solvated hammerhead ribozyme projected onto die YEP surface [80]...

All of the simulation approaches, other than harmonic dynamics, include the basic elements that we have outlined. They differ in the equations of motion that are solved (Newton s equations, Langevin equations, etc.), the specific treatment of the solvent, and/or the procedures used to take account of the time scale associated with a particular process of interest (molecular dynamics, activated dynamics, etc.). For example, the first application of molecular dynamics to proteins considered the molecule in vacuum.15 These calculations, while ignoring solvent effects, provided key insights into the important role of flexibility in biological function. Many of the results described in Chapts. VI-VIII were obtained from such vacuum simulations. Because of the importance of the solvent to the structure and other properties of biomolecules, much effort is now concentrated on systems in which the macromolecule is surrounded by solvent or other many-body environments, such as a crystal. 

The motions of sidechains in proteins play an important role in their dynamics. The time scales involved range from picoseconds for local oscillations in a single potential well to milliseconds or longer for some barrier crossings, such as the 180° rotations (ring flips ) of aromatic sidechains. This range of motions makes it necessary to use a variety of theoretical approaches in the analysis of sidechain dynamics they include molecular dynamics, activated dynamics, and stochastic dynamics (see Chapt. IV.). There are a number of well-characterized examples where sidechain motions have been shown to play a specific role in protein function. 

Figure 1- Dynamics of appearance and disappearence of GS synthetases. Key O, growth , GS and A, total GS biosynthetic activity (Synthetase scale).

From stochastic molecnlar dynamics calcnlations on the same system, in the viscosity regime covered by the experiment, it appears that intra- and intennolecnlar energy flow occur on comparable time scales, which leads to the conclnsion that cyclohexane isomerization in liquid CS2 is an activated process [99]. Classical molecnlar dynamics calcnlations [104] also reprodnce the observed non-monotonic viscosity dependence of ic. Furthennore, they also yield a solvent contribntion to the free energy of activation for tlie isomerization reaction which in liquid CS, increases by abont 0.4 kJ moC when the solvent density is increased from 1.3 to 1.5 g cm T Tims the molecnlar dynamics calcnlations support the conclnsion that the high-pressure limit of this unimolecular reaction is not attained in liquid solntion at ambient pressure. It has to be remembered, though, that the analysis of the measnred isomerization rates depends critically on the estimated valne of... 

The second aspect, predicting reaction dynamics, including the quantum behaviour of protons, still has some way to go There are really two separate problems the simulation of a slow activated event, and the quantum-dynamical aspects of a reactive transition. Only fast reactions, occurring on the pico- to nanosecond time scale, can be probed by direct simulation an interesting example is the simulation by ab initio MD of metallocene-catalysed ethylene polymerisation by Meier et al. [93]. 

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]. 

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