The main objective of this thesis is to develop and analyze mathematical models of cellular
decisions. This work focuses on understanding the mechanisms involved in specific
cellular processes such as immune response in the vascular system, and those involved in
apoptosis, or programmed cellular death.
A series of simple ordinary differential equation (ODE) models are constructed describing
the macrophage response to hemoglobin:haptoglobin (Hb:Hp) complexes that
may be present in vascular inflammation. The models proposed a positive feedback loop
between the CD163 macrophage receptor and anti-inflammatory cytokine interleukin-10
(IL-10) and bifurcation analysis predicted the existence of a cellular phenotypic switch
which was experimentally verified. Moreover, these models are extended to include the
intracellular mediator heme oxygenase-1 (HO-1). Analysis of the proposed models find a
positive feedback mechanism between IL-10 and HO-1. This model also predicts cellular
response of heme and IL-10 stimuli.
For the apoptotic (cell suicide) system, a modularized model is constructed encompassing
the extrinsic and intrinsic signaling pathways. Model reduction is performed
by abstracting the dynamics of complexes (oligomers) at a steady-state. This simplified
model is analyzed, revealing different kinetic properties between type I and type
II cells, and reduced models verify results. The second model of apoptosis proposes
a novel mechanism of apoptosis activation through receptor-ligand clustering, yielding
robust bistability and hysteresis. Using techniques from algebraic geometry, a model selection
criterion is provided between the proposed and existing model as experimental
data becomes available to verify the mechanism.
The models developed throughout this thesis reveal important and relevant mechanisms
specific to cellular response; specifically, interactions necessary for an organism
to maintain homeostasis are identified. This work enables a deeper understanding of the
biological interactions and dynamics of vascular inflammation and apoptosis. The results
of these models provide predictions which may motivate further experimental work and
theoretical study
