Multiple histogram equations

Although these equations are expressions for the density of states as a function of both energy and reaction coordinate, the free energies are identical to those obtained from the standard one-dimensional multiple histogram equation. 

Given a set of histograms, Hi Ej) from multiple temperature sweeps, Eqs. (14-16) can be solved for Wj seif consistently. We initialize Wj at dj and subsequently iterate these equations sequentially until the total change in W is less than a predetermined limit (set at 10 in our calculations). Once solved, the static thermodynamic properties of the system can be determined from Wj. The partition function, internal energy, specific heat, and entropy can be estimated by... 

The shape of the distribution function for the translocation time given by the drift-diffusion equation (Figure 10.11b) is similar to experimentally observed histograms, as long as the multiple peaks of Figure 10.1a are deconvoluted. When the reflecting boundary condition is used at the pore entry, theory yields only one peak in the distribution function of the translocation time. On the other hand, experiments show that there are two peaks, after the first peak corresponding to faster collisions between the polymer and pore is deleted. This feature is particular to the aHL protein pore and ssDNA, and is also based on the way the data are analyzed. 

---