A System of m Linearly Arranged Subunits

In previous chapters we developed in several places three levels of complexity of a binding system first, the direct-interaction model second, the model with indirect correlations arising from conformational changes in the entire adsorbent molecule and third, indirect correlations mediated through subunits. 

In this section we omit the second level and extend the model of Section 7.1 to a system of m linearly arranged subunits each of which has a one-binding site. In order to focus on the origin of cooperativity in such a system, we assume that the direct interaction between ligands is negligible. Hence any correlation between ligands is necessarily indirect. This model is essentially the same as that discussed in Sections 4.7, 5.6, and 6.3, but now the number of subunits m is not fixed. 

The formalism is essentially the same as in Sections 7.1 and 7.2, but instead of two states for each site (empty and occupied) we now have four states or four 

the configuration of the entire system is denoted by the m-dimensional 

Although Eq. (7.4.4) looks complicated, it is quite simple. We scan through all the subunits each subunit in state H contributes and, if occupied, also U[j each pair 

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