The affinity of U2B″ for SLII is also enhanced by the presence of U2A′; however, the cooperativity parameter is smaller than that for the SLIV interaction by a factor of ∼10 (α = 15).
Consider that SNF (S) is the macromolecule that can bind two ligands, each of which binds at a single site, in the thermodynamic cycle shown in Figure 3. Conservation of energy requires that KR,U = α KR and KU,R = α KU, where α is the cooperativity parameter and describes the extent to which binding by one ligand affects binding of the second ligand.
We used this value for fitting the cooperativity parameter α for the U2A′/U1A/SLII titrations; all of the binding parameters associated with U1A are summarized in Table 1.
All binding data were globally fit to eqs 1– 4 to obtain the two bimolecular association constants KR and KU, as well as α, the cooperativity parameter.
Strikingly, transcription factor scaling factors are far more sensitive than the cooperativity parameters for almost every enhancer structure tested.
Thus the cooperativity parameters would be present only in the numerator of the expression function, increasing their sensitivity, possibly to levels comparable to quenching parameters.
Any of these factors may have led to insensitivity in the cooperativity parameters, and should be addressed before trying to improve upon the model or its biological interpretations.
However, cooperativity between two transcription factors can be represented as a post-binding event, by constructing the model in such a way that all states of the enhancer are considered, then weighted by a cooperativity parameter.
With the parameter β = 1, and the average ligand concentration Lmid = 1, we varied the slope of the gradient (Lslope) for four different values of the Hill cooperativity parameter q.
Importantly, this formulation includes the nearest neighbor cooperativity parameter (ω, embedded within ff), which describes cooperative protein assembly on the duplex.
