Abstract
We present a model for calculating the net and effective electrical charge of globular macromolecules and linear polyelectrolytes such as proteins and DNA, given the concentration of monovalent salt and pH in solution. The calculation is based on a numerical solution of the non-linear Poisson-Boltzmann equation using a finite element discretized continuum approach. The model simultaneously addresses the phenomena of charge regulation and renormalization, both of which underpin the electrostatics of biomolecules in solution. We show that while charge regulation addresses the true electrical charge of a molecule arising from the acid-base equilibria of its ionizable groups, charge renormalization finds relevance in the context of a molecule’s interaction with another charged entity. Writing this electrostatic interaction free energy in terms of a local electrical potential, we obtain an “interaction charge” for the molecule which we demonstrate agrees closely with the “effective charge” discussed in charge renormalization and counterion-condensation theories. The predictions of this model agree well with direct high-precision measurements of effective electrical charge of polyelectrolytes such as nucleic acids and disordered proteins in solution, without tunable parameters. Including the effective interior dielectric constant for compactly folded molecules as a tunable parameter, the model captures measurements of effective charge as well as published trends of shifts in globular proteins. Our results suggest a straightforward general framework to model electrostatics in biomolecules in solution. In offering a platform that directly links theory and experiment, these calculations could foster a systematic understanding of the interrelationship between molecular 3D structure and conformation, electrical charge and electrostatic interactions in solution. The model could find particular relevance in situations where molecular crystal structures are not available or rapid, reliable predictions are desired.
Highlights
Contrary to the situation in vacuum, the electrical charge of a macromolecule in solution is governed strongly by thermodynamic processes in the electrolyte that render both theoretical predictions and experimental measurements of the quantity non-trivial
In conjunction with interaction free energy calculations, we present a coherent picture of macromolecular electrostatics that includes the effects of both charge regulation and renormalization
Comparing the calculated object-slit interaction free energy, Fos(z∗), with the electrostatic energy of an equivalent charged test object placed at z = z∗ + R, we find that the former is almost always significantly smaller than the latter, in keeping with the expectation created by the charge renormalization concept
Summary
Contrary to the situation in vacuum, the electrical charge of a macromolecule in solution is governed strongly by thermodynamic processes in the electrolyte that render both theoretical predictions and experimental measurements of the quantity non-trivial. Alteration in the charged state of an ionizable group in the context of the molecular environment, while the latter deals with the highly non-linear screening of molecular charge by counterions in the surrounding electrolyte phase Both phenomena generally result in a reduced “effective” charge of an electrically charged object, and have each received extensive theoretical attention, from polyelectrolytes and proteins to colloidal particles and charged surfaces in solution.. Using the effective internal dielectric constant as a tunable parameter, we further demonstrate that the model predicts net charge values that agree well with measurements of globular macromolecules such as the tetrameric protein β-Glucuronidase (Gus β—290 kDa). We consider recent measurements of pKa shifts in variants of SNase containing single amino acid substitutions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
