A quantitative analysis of excluded-site effects for highly cooperative binding systems

Cooperative ligand binding to a double-stranded Ising lattice-Application to cofilin binding to actin filaments

Cooperative ligand binding to linear polymers is fundamental in many scientific disciplines, particularly biological and chemical physics and engineering. Such ligand binding interactions have been widely modeled using infinite one-dimensional (1D) Ising models even in cases where the linear polymers are more complex (e.g. actin filaments and other double-stranded linear polymers). Here, we use sequence-generating and transfer matrix methods to obtain an analytical method for cooperative equilibrium ligand binding to double-stranded Ising lattices. We use this exact solution to evaluate binding properties and features and analyze experimental binding data of cooperative binding of the regulatory protein, cofilin, to actin filaments. This analysis, with additional experimental information about the observed bound cofilin cluster sizes and filament structure, reveals that a bound cofilin promotes cooperative binding to its longitudinal nearest-neighbors but has very modest effects on lateral nearest-neighbors. The bound cofilin cluster sizes calculated from the best fit parameters from the double-stranded model are considerably larger than when calculated with the 1D model, consistent with experimental observations made by electron microscopy and fluorescence imaging. The exact solution obtained and the method for using the solution developed here can be widely used for analysis of variety of multistranded lattice systems.

Allosteric conformational spread: exact results using a simple transfer matrix method

A transfer matrix method is described for the conformational spread (CS) model of allosteric cooperativity within a one-dimensional arrangement of four-state binding sites. Each such binding site can realize one of two possible conformational states. Each of these states can either bind ligand or not bind ligand. Thus, analytical expressions that are exact within the context of the CS model are derived for the grand partition function, for the mean fraction of binding sites occupied by ligand versus ligand concentration, and for the mean fraction of binding sites in a given allosteric state versus ligand concentration. The utility of our analytical results is demonstrated by least-mean-square fitting of prior experimental results obtained on the bacterial flagellar motor for the fraction of FliM/FliG/FliN complexes with CheY-P bound [V. Sourjik and H. C. Berg, Proc. Natl. Acad. Sci. U.S.A. 99, 12669 (2002)] and for the cw bias [P. Cluzel, Science 287, 1652 (2000)], which plausibly may be identified as the fraction of protomers realizing state 2. Finally, the relationships between our analytical results and the classical Monod-Wyman-Changeaux, Koshland-Nemethy-Filmer, and McGhee-Von Hippel treatments of allosteric cooperativity are elucidated, as is the connection to an earlier approximate analytical treatment of the CS model.

A note on the quantitative properties of McGhee-von Hippel model

Exact closed-form expressions are presented for the properties of the McGhee-von Hippel model of non-specific binding of large ligands to one-dimensional homogeneous lattices. These properties include the midpoint location and the slope at the middle point of the binding isotherms (v varies with ln L plots), the location and magnitude of the maximum, as well as the location of the inflection point, in the Scatchard plots (v/L varies with v plots).

Use of binding site neighbor-effect parameters to evaluate the interactions between adjacent ligands on a linear lattice. Effects on ligand-lattice association

A method using binding site "neighbor-effect" parameters (NEPs) is introduced to evaluate the effects of interaction between adjacent ligands on their binding to an infinite linear lattice. Binding site overlap is also taken into account. This enables the conditional probability approach of McGhee & von Hippel to be extended to more complex situations. The general equation for the isotherm is v/LF = SFKF, where v is the ratio of bound ligands to lattice residues, LF is the free ligand concentration, SF is the fraction of binding sites that are free, and KF is the average association constant of a free site. Solutions are derived for three cases: symmetric ligands, and asymmetric ligands on isotropic or anisotropic lattices. For symmetric ligands there is one NEP, E, which is the ratio of the average binding affinity of a free site if the status of the lattice residue neighboring one end of the site is unspecified (left to chance) to the affinity when this residue is free (holding the other neighbor constant). Thus KF is KE2, where K is the affinity of an isolated site. If a site is n residues long, SF is f ffn-1, where f = 1 - nv is the fraction of residues that are free and ff is the conditional probability that a free residue is bordered on a given side by another free residue. The expression for ff is 1/(1 + x/E), where x is v/f, E is (1 - x + [(1 - x)2 + 4x omega]1/2)/2, and omega is the co-operativity parameter. The binding of asymmetric ligands to an isotropic lattice is described by two NEPs; the last case involves four NEPs and a bound ligand orientation parameter. For each case, the expected length distribution of clusters of bound ligands can be calculated as a function of v. When Scatchard plots with the same intercepts and initial slope are compared, it is found that ligand asymmetry lowers the isotherm (relative to the corresponding symmetric ligand isotherm), whereas lattice anisotrophy raises it.

On the cooperative binding of large ligands to a one-dimensional homogeneous lattice: the generalized three-state lattice model

We present the general secular equation for three-state lattice models for the cooperative binding of large ligands to a one-dimensional lattice. In addition, a closed-form expression for the isotherm is also obtained, that can be used with all values of the cooperativity parameter omega(0 less than omega less than infinity) thus eliminating the need for multiple equations.