Weighted histogram technique

The energy landscape approach can elucidate such general properties of molecular recognition as the nature of the thermodynamic phases and barriers on the ligand-protein association pathway [127,128]. This method evaluates equilibrium thermodynamic properties of the system from Monte Carlo simulations of the system at a broad temperature range with the aid of the optimized data analysis and the weighted histogram analysis technique [148-153],... 

The techniques (e.g., weighted histogram analysis, equal weight rule, etc.) utilized for one-component systems or incompressible binary mixtures can be readily carried over to compressible systems. Since the system is described by two order parameters one monitors the joint probability distribution of... 

B polysaccharide using the more refined histogram technique, and secondly, present our polydispersity analysis in terms of distributions of molecular weight. 

Thus, the question is whether the combination of Metropolis data obtained in simulations at different temperatures can yield an improved estimate g E). This is indeed possible by means of the multiple-histogram reweighting method [86], sometimes also called weighted histogram analysis method (WHAM) [87]. Even though the general idea is simple, the actual implementation is not trivial. The reason is that conventional Monte Carlo simulation techniques such as the Metropolis method cannot yield absolute estimates for the partition sum Z T)= g E) i. e., estimates for the density of states at differ-... 

Not surprisingly, the essential component of flat-histogram algorithms is the determination of the weights, r/, or the thermodynamic potential, e.g., / or /. There exist a number of techniques for accomplishing this task. The remainder of this section is dedicated to reviewing a small but instructive subset of these methods, the multicanonical, Wang-Landau, and transition-matrix approaches. We subsequently discuss their common and sometimes subtle implementation issues, which become of practical importance in any simulation. 

We believe the most feasible explanation of the bimodal behavior in linewidth to be two distinct molecular weight fractions. The inability to separate the two may be due to an equilibrium between them, or unknown inadequacies in the gel filtration techniques used. The B-polysaccharide sample which we passed through an analytical column (l cm x 90 cm packed with sepharose liB) was diluted to the extent that the precise data required for a histogram analysis was difficult to obtain. 

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