Correlation Function and Cooperativity

The correlation function was defined in Section 4.2 for any two events. In particular, if the events are site one is occupied and site two is occupied, then the ( -dependent) correlation function is 

Note that here F(l 1) is the probability of finding the two sites occupied (independently of the states of the subunits) and P(l) is the probability of finding a specific site (say, the Ihs in Fig. 4.18) occupied (independently of the state of the subunits and of the occupational state of the second site) P(l) = P(l ) = P( 1). 

As in Sections 4.2 and 4.5, we need only the X. — 0 limit of this correlation function, which is the quantity defined in Eq. (4.7.22), to which we refer as the correlation function between the two events. For these particular events we also say that whenever there exists correlation [i.e., g(l, 1) 1)], the two ligands cooperate hence there exists cooperativity between the ligands, or simply, the system is cooperative. 

We now focus on the indirect correlation. To do so, we can either factor S from g( 1,1), or simply assume that S = 1 and examine the remaining correlation, denoted by y(l, 1). Using the notations (4.7.14) and (4.7.15), and K = QhIQl - Qhh Qll always appear together. Hence, we set 

The second form on the rhs of this equation is very convenient for examining the condition under which indirect correlation exists. In Eq. (4.7.26) and in the following section, we put ri = 

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