A theoratical cooperative system. (a) The ratio \(\epsilon\) (equation \ref{815146}) as a function of the number of polymer units (amino acids) in a bivalent linker with the following set of parameters (dashed line highlights unity): \(\eta_1=\ \eta_2=10^{-2};\ \ \ \ x_1=\ x_2\simeq2.5\times10^{-3};\ \ \ \ C_{\infty}=9;\ \ \ \ l=3.8\)Å
The curves are for different values of (see equation (5)). The above dimensionless parameters correspond to the physical values:
\(c_{AL}=1mM;\ \ \ \ r_{AB}=r_{BX}=10\)\(Å\)
A system with an additional, identical binding site at the edge of a linker 5-amino-acids long, may exhibit over 3-fold improvement in binding to the original site (left arrow highlights the difference between unity and the curve for \(\nu=1/2\)). A system may undergo a switch between uncooperative to cooperative behavior by changes to the properties of the solvent (right arrow connecting between different curves of highlights this behavior). (b) Since a power law relates between the number of polymer units, the linker mean square end-to-end distance and the effective concentration (or, equivalently, \(\tilde{c}\)), one may draw the logarithmically-scaled horizontal axis in (a) according to these variables. The parameter \(\nu\) affects the scaling; here the axes are shown to match the graph for \(v=1/2\). As \(c_{AL}=1\text{mM}\), one may read the axis c as the effective concentration in mM.