Abstract
We generalize the Kirkwood-Shumaker theory of protonation fluctuation for an anisotropic distribution of dissociable charges on a globular protein. The fluctuations of the total charge and the total dipole moment, in contrast to their average values, depend on the same proton occupancy correlator, thus exhibiting a similar dependence also on the solution pH. This has important consequences for the Kirkwood-Shumaker interaction and its dependence on the bathing solution conditions.
Highlights
Electrostatic interactions are ubiquitous in proteinaceous systems and make an essential contribution to protein structure, folding, binding, and condensation [1]
We introduce the proton occupancy correlator δqkδqt as the average over fluctuations around the equilibrium value as δqkδqt =
Based upon our previous work [23], we generalized the KS theory of protonisation fluctuation [7] by calculating the electrostatic and charge regulation (CR) free energy contributions due to anisotropic distribution of dissociable charges on a sphere circumscribed to a protein
Summary
Electrostatic interactions are ubiquitous in proteinaceous systems and make an essential contribution to protein structure, folding, binding, and condensation [1]. An important consequence of the CR mechanism is the fact that the charging state of a protein is an annealed variable and can exhibit thermal fluctuations, a theoretical prediction [7] borne out by experiments [16] These thermal protonisation/deprotonisation fluctuations engender fluctuations of both the protein charge as well as the protein dipole moment that in turn lead to capacitance and polarizability of the protein. Upgrading the original KS approach, the fluctuation interactions were cast into a more appropriate theoretical framework of monopole and dipole Casimir-type thermal fluctuation interactions [18, 19] or within the zero frequency Lifshitz term in the general theory of van der Waals interactions [20, 21] Apart from their effect on the interactions, calculations of the protonisation fluctuation contribution to protein capacitance and polarizability are scarce, which is why we embark in this work upon a more detailed analysis of their properties. Our work generalizes some aspects of the seminal approach of Kirkwood and Shumaker [7] and takes explicitly into account the electrostatic interactions on the weak-coupling level in the calculations of the response functions
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