Potential conformers probability distribution

Here p (I) is the distribution of conformational states that arises from a simulation using the biased potential. The tricky point with this method comes from the fact that we ultimately need to integrate the work function over a series of windows, and the integration constant for each window is undefined. In practice, this problem is addressed using clever approaches that attempt to match up the probability distributions on consecutive intervals. 

The next step is to generate all possible and allowed conformations, which leads to the full probability distribution F). The normalisation of this distribution gives the number of molecules of type i in conformation c, and from this it is trivial to extract the volume fraction profiles for all the molecules in the system. With these density distributions, one can subsequently compute the distribution of charges in the system. The charges should be consistent with the electrostatic potentials, according to the Poisson equation ... 

Dihedral angle distribution functions for the various models are shown in figure 5. Models using the Bartell and BHS intramolecular potential functions show a clear bimodal distribution. The former shows a zero intensity near 9 = 0°. The latter shows a small non-zero intensity near 9 = 0°. The Haigh potential shows a distribution which may be described as lying somewhere between bimodal and monomodal. Both the WW and KK models show a monomodal function with a maximum near 9 = 0°, suggesting the most probable conformation is the planar conformation in the room temperature solid phase. The RDFs for these two models show well defined features which seem to be correlated with the monomodal S(9) exhibited by them. 

Using 112 nodes of the Earth Simulator, we performed a REMD simulation of this system with 224 replicas. The REMD simulation was successful in the sense that we observed a random walk in potential energy space, which suggests that a wide conformational space was sampled. In Fig. 4.10 we show the canonical probability distributions of the total potential energy at the corresponding 224 temperatures ranging from 250 to 700 K. 

First, the current state of affairs is remarkably similar to that of the field of computational molecular dynamics 40 years ago. While the basic equations are known in principle (as we shall see), the large number of unknown parameters makes realistic simulations essentially impossible. The parameters in molecular dynamics represent the force field to which Newton s equation is applied the parameters in the CME are the rate constants. (Accepted sets of parameters for molecular dynamics are based on many years of continuous development and checking predictions with experimental measurements.) In current applications molecular dynamics is used to identify functional conformational states of macromolecules, i.e., free energy minima, from the entire ensemble of possible molecular structures. Similarly, one of the important goals of analyzing the CME is to identify functional states of areaction network from the entire ensemble of potential concentration states. These functional states are associated with the maxima in the steady state probability distribution function p(n i, no, , hn). In both the cases of molecular dynamics and the CME applied to non-trivial systems it is rarely feasible to enumerate all possible states to choose the most probable. Instead, simulations are used to intelligently and realistically sample the state space. 

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