Biased molecular dynamics

Vallverdu G, Demachy I, Ridard J, Levy B (2009) Using biased molecular dynamics and Brownian dynamics in the study of fluorescent proteins. Theochem-J Mol Struct 898 73-81... 

Paci, E. Karplus, M., Forced unfolding of fibronectin type 3 modules. An analysis by biased molecular dynamics simulations, J. Mol. Biol. 1999, 288, 441 —459... 

Guidoni L, Rothlisberger U, Scanning reactive pathways with orbital biased Molecular Dynamics, J Chem Theory Comput, 1, 554-560 (2005)... 

Paci, E., Caflisch, A., Pluckthun, A., 8c Karplus, M. (2001). Forces and energetics of hapten-antibody dissociation A biased molecular dynamics simulation study. Journal of Molecular Biology, 314, 589. 

F. Marinelli, F. Pietrucci, A. Laio, and S. Piana, PLoS Comput. Biol.,5 8), el000452 (2009). A Kinetic Model of Trp-Cage Folding from Multiple Biased Molecular Dynamics Simulations. 

E. Paci and M. Karplus, J. Mol. Biol., 288, 441 (1999). Forced Unfolding of Fibronectin Type 3 Modules An Analysis by Biased Molecular Dynamics Simulations. 

E. Paci, A. Caflisch, A. Pluckthun, and M. Karplus,/. Mo/. Bio/., 314, 589 (2001). Forces and Energetics of Hapten-Antibody Dissociation A Biased Molecular Dynamics Simulation Study. 

P. Chen, C.-L. Evans, J. D. Hirst, and M. S. Searle, Biochemistry, 50,125 (2011). Structural Insights into the Two Sequential Folding Transition States of the PBl Domain of NBRl from Value Analysis and Biased Molecular Dynamics Simulations. 

There are basically two different computer simulation techniques known as molecular dynamics (MD) and Monte Carlo (MC) simulation. In MD molecular trajectories are computed by solving an equation of motion for equilibrium or nonequilibrium situations. Since the MD time scale is a physical one, this method permits investigations of time-dependent phenomena like, for example, transport processes [25,61-63]. In MC, on the other hand, trajectories are generated by a (biased) random walk in configuration space and, therefore, do not per se permit investigations of processes on a physical time scale (with the dynamics of spin lattices as an exception [64]). However, MC has the advantage that it can easily be applied to virtually all statistical-physical ensembles, which is of particular interest in the context of this chapter. On account of limitations of space and because excellent texts exist for the MD method [25,61-63,65], the present discussion will be restricted to the MC technique with particular emphasis on mixed stress-strain ensembles. 

The most intriguing aspect of the self-spreading lipid bilayer is that any molecule in the bilayer can be transported without any external bias. The unique characteristic of the spreading layer offers the chance to manipulate molecules without applying any external biases. This concept leads to a completely non-biased molecular manipulation system in a microfluidic device. For this purpose, the use of nano-space, which occasionally offers the possibility of controlling molecular diffusion dynamics, would be a promising approach. 

These difficulties can be circumvented by using the adaptive biasing force (ABF) method of Darve, Pohorille, and coworkers [18, 28, 29], which is based on unconstrained molecular dynamics simulations. This is a very efficient approach which begins by establishing a simple formula to calculate d,4/d from regular molecular dynamics in which is not constrained. This derivative represents the mean force acting on . Therefore if we remove this force from the system we obtain... 

Mosey NJ, Hu A, Woo TK, Ab initio molecular dynamics simulations with a HOMO-LUMO gap biasing potential to accelerate rare reaction events, Chem Phys Lett, 373, 498—505 (2003)... 

Molecular Dynamics simulation is one of many methods to study the macroscopic behavior of systems by following the evolution at the molecular scale. One way of categorizing these methods is by the degree of determinism used in generating molecular positions [134], On the scale from the completely stochastic method of Metropolis Monte Carlo to the pure deterministic method of Molecular Dynamics, we find a multitude and increasingly diverse number of methods to name just a few examples Force-Biased Monte Carlo, Brownian Dynamics, General Langevin Dynamics [135], Dissipative Particle Dynamics [136,137], Colli-sional Dynamics [138] and Reduced Variable Molecular Dynamics [139]. 

Blumberger, J., Tavernelli, I., Klein, M.L., Sprik, M. Diabatic free energy curves and coordination fluctuations for the aqueous Ag+/Ag2+ redox couple A biased Born-Oppenheimer molecular dynamics investigation. J. Chem. Phys. 2006,124, 064507. 

If we are to run a molecular dynamics simulation with respect to the biased energy landscape, we need a transcription that tells us how to map the elapsed time as measured by our molecular dynamics time step into the time that would have elapsed had we allowed the dynamics to take place on the unbiased landscape. One argument that can be made to assess this transcription is to replace the ensemble average of the mean escape time, given by... 

Fig. 12.15. Illustration of trajectories associated with the same basic periodic potential when considered using both conventional molecular dynamics and hyperdynamics (a) biased potential and unbiased potential and (b) the particle position as a function of elapsed time.

Following the construction of the model is the calculation of a sequence of states (or a trajectory of the system). This step is usually referred to as the actual simulation. Simulations can be stochastic (Monte Carlo) or deterministic (Molecular Dynamics) or they can combine elements of both, like force-biased Monte Carlo, Brownian dynamics or general Langevin dynamics (see Ref. 16 for a discussion). It is usually assumed that the physical system can be adequately described by the laws of classical mechanics. This assumption will alsq be made throughout the present work. 

Watanabe, Y.S., Kim, J.G., Fukunishi, Y., Nakamura, H. Free energy landscapes of small peptides in an implicit solvent model determined by force-biased multicanonical molecular dynamics simulation. Chem. Phys. Lett. 2004,400,258-63. 

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