ANALYTICAL APPROACHES TO BINDING, CONFORMATIONAL AND STRETCHING PROPERTIES OF WEAK POLYELECTROLYTES

Weak polyelectrolytes (PEs) can modulate their charge as a result of external perturbations such as changes in the ionic strength, temperature, solvent, etc., a phenomenon known as Charge Regulation (CR). The paradigmatic mechanism of CR is protonation equilibria, which in turn can be highly coupled to the conformational degrees of freedom: a shift in the ionization state induces changes in the molecular conformation by modifying the electrostatic interactions (EI). EI can be classified as long (SR) and short (LR) range interactions depending whether they are mediated by the macromolecular skeleton (for neighbouring protonating groups) or by the solvent (in case of distant groups).

Our group has developed a variety of analytical techniques to address CR in weak flexible PEs, which can complement computer simulations by facilitating physical insights and providing conformational/binding information in much shorter computer times (from hours/days in molecular simulations to seconds in our analytical theories).

Three approaches are presented here. In the first one, we apply transfer matrices to account for proton and conformation equilibria on the same footing.  We apply this technique to coarse grained models of the type “bead-and-spring”, commonly used in molecular simulation software. We also use this approach to assess the influence of mechanical stretching in macromolecular binding, including possible binding/conformational transitions.

Secondly, since transfer matrices can only be used in absence of LR interactions, we have developed the Local Effective Interaction Parameters (LEIP) technique, which allows to deal with LR interactions by packing them in effective SR interactions using variational principles.

The previously mentioned methods treat both the binding and the conformational states explicitly, a treatment to which we refer as Coupled Conformational Site Binding (CCSB) model.  In the third approach presented, however, the conformational degrees of freedom of the CCSB model are averaged over by using the so-called Conformational Contraction Equations (CCE). The result is an equivalent rigid object, the so-called Site-Binding model. Here the conformations are present only implicitly and the computational times are drastically reduced, which is very useful if the theory needs to be fitted to experimental information such as potentiometric titration curves.