Boltzmann distributions simulation techniques

To study protein folding theoretically, simulation methods have proved indispensable. The folding transition is ultimately governed by statistical thermodynamics and hence it is paramount to use sampling methods that are able to reproduce the canonical Boltzmann distribution. Common sampling techniques are molecular dynamics (MD), Langevin or Brownian dynamics (BD) and Monte Carlo (MC). 

Applicable to both of the standard MC and MD methods is the simulated annealing technique. Both MC and MD methods simulate the Boltzmann distribution of the molecular conformations at a given temperature. However, at low temperatures, the sampling is easily trapped in incidental local... 

The difficulties in simulating polymer systems stem from the long relaxation times these systems display. Long runs are needed in order to ensure adequate equilibration. We have employed the method of Wall and Mandel (21) as modified for continuum three dimensional polymers by Webman, Ceperley, Kalos and Lebowitz (22). Each chain is considered in order and one end is chosen randomly as a bead. Suppose the initial chain coordi-nates are C = X, .. Xn A new position of that bead, X, is selected such that X = X + Ax where Xn is the initial head position and Ax is a vector randomly chosen via a rejection technique from the probability distribution exp(-BUfl(AX))(3=l/kBT, kfi Boltzmann s constant, T the temperature) and Ujj is iv< n in Eq. 

The CG force field of the atactic PS should reproduce the same distributions of three bonds and six angles as mentioned above. It should also match to the intra and inter molecular RDFs extracted from the atomistic MD simulation trajectories. In this case, similar approach like PA-66 was adopted to calculate all the bonded and non-bonded potentials. For the bonded potential the bond and angle distributions were fitted to a combination of Gaussians (equation 6) and further Boltzmann inversion was performed. However, for non-bonded interactions the IBI technique was used. 

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