Mathematical Modeling of Biological Processes at the Cellular, Tissue, and System Levels

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  • March 20, 2019
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  • Wessler, Timothy
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • In this work, mathematical modeling is used in conjunction with in vivo and in vitro experiments to investigate disparate biological phenomena at various scales, including cell rounding, virus trapping, and drug delivery. First, a rapid change in cell morphology from a spread to a rounded state is modeled. This transition reveals a several-fold greater cell surface than is required to enclose a perfectly round object of the same volume, and an open question is how this extra surface is stored. A Hamiltonian model, where the energy cost is minimized, is used to address this question and reproduce statistics of the surface morphology. Next, antibody attachments and detachments to pathogens moving through a biological environment are modeled. Experiments demonstrate that a pathogen with absolutely no affinity to mucus can become trapped in a mucus network in the presence of antibodies. Antibodies and mucus work cooperatively to trap pathogens by tethering the pathogen to the mucus via the antibody. Both a continuum reaction-diffusion model and a stochastic model are used to simulate the pathogen and antibody movement and binding kinetics. This work generates many important insights into the design of antibodies that use trapping to protect against foreign pathogens infecting underlying tissue. Finally, the movement of a nanoparticle drug from organ to organ throughout the body is modeled. Covalently attaching polyethylene glycol (PEG) to a drug helps maintain an adequately high concentration in the blood. However, the anti-PEG antibodies increasingly common throughout the population attach to PEG and accelerate the elimination of PEGylated drugs. A possible strategy to temporarily lower the concentration of free anti-PEG antibodies is to introduce free PEG that will bind to free anti-PEG antibodies, thus depleting their numbers before the PEGylated drug treatment begins. This work uses a compartment model with local dynamics at different scales within different compartments to model the organ-specific changes in concentrations of the PEGylated drug, the free PEG, and the anti-PEG antibodies, as well as the binding kinetics. The results lay out guidelines for a nanoparticle PEGylated drug therapy.
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  • In Copyright
Advisor
  • Lai, Samuel
  • Newhall, Katherine
  • Forest, Mark
  • Griffith, Boyce
  • Adalsteinsson, David
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2017
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