Exact density of states and thermodynamics

In order to study energetic thermodynamic quantities such as mean energy and specific heat, we can determine from the conformations of an HP protein with a given sequence the density of states g E) that conveniently enables the calculation of the partition sum 

Z(T)= Y2 g(E)exp(—E/kBT) and the moments E )t= E S E)exp —E/kBT)/Z, where the subscript T indicates the difference of calculating thermal mean values based on the Boltzmann probability from averages previously introduced in this section. Then, the specific heat as a function of temperature is given by the fluctuation formula 

Obviously this is not the case for the sequences we identified as nondesigning. In fact, the uniqueness of the ground states of designing sequences is a remarkable property as there are not less than 10 possible conformations of HP lattice proteins with 18 monomers. As we also see in Fig. 3.7, the ratio of the density of the first excited state (E= — 8) for the 

The complexity of minimalistic lattice models for protein folding 

Enumeration is a powerful method for the investigation of some interesting features of heteropolymer folding in an evolutionary context, because it creates exact data. However, it is obviously only applicable to small lattice systems. The investigation of longer chains and more specific models requires more sophisticated stochastic approaches, which unfortunately can only generate approximate results. We will introduce some of the standard methods in the following chapter, before we return to the discussion of structural properties of polymers and proteins. 

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