Transitions of regular structures two-state models

All-or-none transition is highly cooperative with N being the cooperative length of a transition. 

The expansion of this expression yields the binomial coefficients of the power of s (the degeneracy factors)  

This is the number of ways in which to divide N residues into j in state b and N -y in state a, thus 

The probability of observing any state average across all states Py is 

The fraction in b at each state is the number of b residues, relative to the total number of residues, i.e. fj = 7N. The total fraction of residues as in the system is the average probability of observing b, Pb which is the sum of all the stales having at least one 

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