Monte Carlo data analysis with the weighted histogram method

Monte-Carlo data analysis with the weighted histogram method 

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], 

Consider N simulations carried at different temperatures with the nth simulation being performed at temperature / and the density of the energies being Wn E). We write the probability distribution as the follows  

The objective of the weighted histogram method is to obtain the best estimate of the density of states W E) at each temperature. This estimate can be written as a weighted sum of the N estimates Wn E) ( n = 1. N) 

Importantly, the weights p E) depend only on E, so a certain confidence level can be incorporated for different simulations that are performed at different temperatures. 

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IV.3. Monte-Carlo data analysis with the weighted histogram method... 

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