Coupling of Charge Regulation and Conformational Equilibria in Linear Weak Polyelectrolytes: Treatment of Long Range Interactions via Effective Short-Ranged and pH-Dependent Interaction Parameters

Abstract

The classical Rotational Isomeric State (RIS) model, originally proposed by Flory, has been used to rationalize a wide range of physicochemical properties of neutral polymers. However, many weak polyelectrolytes of interest are able to regulate their charge depending on the conformational state of the bonds. Recently, it has been shown that the RIS model can be coupled with the Site Binding (SB) model, for which the ionizable sites can adopt two states: protonated or deprotonated. The resulting combined scheme, the SBRIS model, allows to analyse ionization and conformational equilibria on the same foot. In the present work this approach is extended to include pH-dependent electrostatic Long Range (LR) interactions, ubiquitous in weak polyelectrolytes at moderate and low ionic strengths. With this aim the original LR interactions are taken into account by defining effective Short Range (SR) and pH-dependent parameters, such as effective microscopic protonation constants and rotational bond energies. The new parameters are systematically calculated using variational methods. The machinery of statistical mechanics for SR interactions, including the powerful and fast transfer matrix methods, can then be applied. The resulting technique, to which we will refer as Local Effective Interaction Parameters (LEIP) method, is illustrated with a minimal model of a flexible linear polyelectrolyte containing only one type of rotating bonds. LEIP reproduces very well the pH dependence of the degree of protonation and bond probabilities obtained by semi-grand canonical Monte Carlo simulations, where LR interactions are taken explicitly into account. The reduction in the computational time in several orders of magnitude suggests that the LEIP technique could be useful in a range of areas involving linear weak polyelectrolytes, allowing direct fitting of the relevant physical parameters to the experimental quantities.

Effect of pH on the Supramolecular Structure of Helicobacter pylori Urease by Molecular Dynamics Simulations

“…The SGCMC procedure used to obtain the urease charge distribution seems to be an efficient method to generate different charge states to simulate proteins under a wide range of pH conditions [ 16 , 17 , 18 , 19 ]. This procedure assigns charges to monomers of the protein that are not identical but are statistically compatible with the simulated pH.…”

“…We have designed a homemade c program to calculate the different protonation states of Asp, Glu, Arg, Lys and His residues, and the C- and N- termini for seven pHs (2, 3, 4, 5, 6, 7 and 7.5) using the semi-grand canonical Monte Carlo (SGCMC) ensemble [ 16 , 17 , 18 , 19 , 21 ]. A characteristic feature of semi-grand canonical Monte Carlo (SGCMC) simulations is that the total charge is not constant but it fluctuates as a natural result of the dynamic proton binding/unbinding.…”

“…However, the effect of pH on the mechanism of urease is still not known. For this reason, in this work we determined the different protonation states at seven pHs by semi-grand canonical Monte Carlo (SGCMC) [ 16 , 17 , 18 , 19 ] and the behavior of each system through molecular dynamic simulations.…”

Effect of Charge Regulation and Conformational Equilibria in the Stretching Properties of Weak Polyelectrolytes

“…57 A 171 similar model has been recently proposed to study the role of 172 long-range interactions in the conformational/protonation 173 coupling. 52 Let us assume that the chain is symmetric (i.e., 174 the chain has a plane of symmetry when it is completely 175 elongated), thus avoiding the question of tacticity, and contains a protonating site situated every three chain positions. 177 In Figure 1, inert and protonating sites are depicted in gray and blue, respectively.…”

“…Combining the SB and RIS approaches, we obtain the SBRIS model, which deals with ionization and conformational equilibria simultaneously. 52,56,57 The resulting free energy can be expressed as the sum of five contributions…”