Date Published: April 5, 2017
Publisher: Public Library of Science
Author(s): Javier Jarillo, José A. Morín, Elena Beltrán-Heredia, Juan P. G. Villaluenga, Borja Ibarra, Francisco J. Cao, Miklos S. Kellermayer.
Ligands binding to polymers regulate polymer functions by changing their physical and chemical properties. This ligand regulation plays a key role in many biological processes. We propose here a model to explain the mechanical, thermodynamic, and kinetic properties of the process of binding of small ligands to long biopolymers. These properties can now be measured at the single molecule level using force spectroscopy techniques. Our model performs an effective decomposition of the ligand-polymer system on its covered and uncovered regions, showing that the elastic properties of the ligand-polymer depend explicitly on the ligand coverage of the polymer (i.e., the fraction of the polymer covered by the ligand). The equilibrium coverage that minimizes the free energy of the ligand-polymer system is computed as a function of the applied force. We show how ligands tune the mechanical properties of a polymer, in particular its length and stiffness, in a force dependent manner. In addition, it is shown how ligand binding can be regulated applying mechanical tension on the polymer. Moreover, the binding kinetics study shows that, in the case where the ligand binds and organizes the polymer in different modes, the binding process can present transient shortening or lengthening of the polymer, caused by changes in the relative coverage by the different ligand modes. Our model will be useful to understand ligand-binding regulation of biological processes, such as the metabolism of nucleic acid. In particular, this model allows estimating the coverage fraction and the ligand mode characteristics from the force extension curves of a ligand-polymer system.
The study of biopolymers interactions with small ligands is an essential topic to many areas of research. Biological systems abound with polymers such as polynucleotides or polysaccharides, and ligands such as proteins, metal ions, antibiotics, drugs, among others. Thus, there are numerous structural, biochemical and thermodynamic studies on the binding of proteins to nucleic acids [1–22]. The binding of multivalent ions, oligolysines or oligopeptides to polynucleotides has also been studied in depth [10,23–29].
In the present study, we introduce a method to model how binding of small ligands to a biopolymer modifies its elastic properties varying the polymer chain extension at a given force depending on the coverage (number of ligands bound to the polymer).
Ligand binding to a polymer proceeds until equilibrium coverage is reached, which may depend on the force applied on the polymer. We assume that the chemical potential of ni disperse ligands bound in mode i to the polymer at zero tension is given by the expression,
where μi* is the chemical potential of a unique ligand bound in mode i to the polymer at zero tension, or alternatively the ligand binding energy ϵib, μi*=−ϵib. The chemical potential corresponding to all the ligands bound to the polymer is assumed to be just the sum of the chemical potential for each binding mode, μ = ∑μi(ni). The Gibbs free energy of the partially covered polymer is then
The interactions between ligands and biopolymers are relevant to fundamental biological processes. For example, ligand binding to a biopolymer can change its mechanical (including polymer extension, or end-to-end distance) and/or chemical properties interfering in this way with its biological functions. Thus, understanding the influence of the binding kinetics on the elastic properties of biopolymers is essential. In this section, we analyze the time evolution of the coverage of a polymer by ligands in two common scenarios: one binding mode and two binding modes. In addition, we discuss the relation between the coverage of the polymer and its extension.
This paper contributes to understand the binding of ligands to long polymers, a common scenario in molecular biology. We have developed an approach to explain the mechanical, thermodynamics, and the chemical kinetics behaviors of the ligands-polymer system.