### BibTeX

@MISC{_generalizedbelief,

author = {},

title = {Generalized Belief Propagation and Free Energy Approximations},

year = {}

}

### OpenURL

### Abstract

In this lecture we talked about graphical models and belief propagation algorithms. As an application, we discussed a generalized belief propagation algorithm for approximating the free energy of a protein structure. 1 Free Energy A general definition for the free energy of a system is “the amount of energy which can be converted into work”. Although there are several types of free energy, the most widely used is probably the Gibbs free energy, which can be defined as the amount of thermodynamic energy which can be converted into work at constant temperature and pressure. Formally, we write: G = H − T · S = (E + P · V) − T · S where G=Gibbs free energy, H=enthalpy (the heat content of the system), S=entropy (a measure of the degree of randomness of the system), E=internal energy, T =temperature, P =pressure and V =volume. The change in the Gibbs free energy of a system is ∆G = (∆E + P · ∆V) − T · ∆S, and since the change in volume is small for nearly all biochemical reactions we can write ∆G = ∆E − T · ∆S. Free energy functions have been successfully used in protein structure prediction, fold recognition, homology modeling, protein design [1]. However, most free energy functions only model the internal energy E using inter- and intramolecular interactions terms (van der Waals, electrostatic, solvent, etc.). The entropy S is usually ignored because it is harder to compute, since it involves summing over an exponential number of terms. Another approach is to compute the free energy using statistical potentials derived from known protein structures (e.g. from PDB). Such methods have the advantage that the derived potentials encode both the entropy S and the internal energy E. But there are several disadvantages, the most important being the fact that the observed interactions are usually not independent [2]. In [3], Kamisetty et al. use a generalized belief propagation algorithm to compute an approximation of the free energy function which includes the entropy term. 2

### Keyphrases

free energy internal energy belief propagation free energy function free energy approximation gibbs free energy generalized belief propagation algorithm protein structure fold recognition statistical potential constant temperature free energy general definition observed interaction several disadvantage exponential number heat content entropy term several type belief propagation algorithm protein structure prediction thermodynamic energy biochemical reaction derived potential homology modeling intramolecular interaction term graphical model van der waals