Date of Award


Degree Type

Open Access Dissertation

Degree Name

Mathematics, PhD


Institute of Mathematical Sciences

Advisor/Supervisor/Committee Chair

Yun Lyna Luo

Dissertation or Thesis Committee Member

Marina Chugunova

Dissertation or Thesis Committee Member

Ali Nadim

Dissertation or Thesis Committee Member

James Sterling

Terms of Use & License Information

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

Rights Information

© 2024 William J Ceely


Glycosaminoglycans, Mathematical modeling, Poisson-Boltzmann, Poisson-Nernst-Planck, Polyelectrolyte brushes

Subject Categories

Applied Mathematics | Biophysics | Structural Biology


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 multivalent electrostatic interactions that can be modeled using mean-field continuum approaches that represent underlying molecular nanoscale biophysics. In this thesis, we develop such models for polyelectrolyte brushes using both steady state modified Poisson-Boltzmann models and transient modified Poisson-Nernst-Planck models that incorporate important ion-specific (Hofmeister) effects. The transient model enables observation of the relative physical effects as an initial non-equilibrium state relaxes to the steady state. The results quantify how electroneutrality is attained through diffusion, ion electrophoresis, spatially-varying permittivity 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.