Mathematical Modeling of Microscale Biology: Ion Pairing, Dielectric Decrement, and Born Energy in Glycosaminoglycan Brushes

TL;DR

This paper develops continuum electrostatic models to understand ion interactions and electrostatic properties in glycosaminoglycan brushes, providing insights into biophysical environments relevant to therapeutics.

Contribution

The authors introduce steady state and transient Poisson models that incorporate ion-specific effects like Hofmeister phenomena into glycosaminoglycan brush simulations.

Findings

Electroneutrality achieved through ion electrophoresis and pairing

Quantified electrostatic potential profiles across interfaces

Characterized bound and unbound ion distributions

Abstract

Biological macromolecules including nucleic acids, proteins, and glycosaminoglycans are typically anionic and can span domains of up to hundreds of nanometers and even micron length scales. The structures exist in crowded environments that are dominated by weak multivalent electrostatic interactions that can be modeled using mean field continuum approaches that represent underlying molecular nanoscale biophysics. We develop such models for glycosaminoglycan brushes using both steady state modified Poisson-Boltzmann models and transient Poisson-Nernst-Planck models that incorporate important ion-specific (Hofmeister) effects. The results quantify how electroneutrality is attained through ion electrophoresis, dielectric decrement hydration forces, and ion-specific pairing. Brush-Salt interfacial profiles of the electrostatic potential as well as bound and unbound ions are characterized for imposed jump conditions across the interface. The models should be applicable to many intrinsically-disordered biophysical environments and are anticipated to provide insight into the design and development of therapeutics and drug-delivery vehicles to improve human health.