Purvis, Jeremy E

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  • Publication
    A Systems Approach to Cellular Signal Transduction
    (2009-08-14) Purvis, Jeremy E
    Vital cellular processes such as growth, gene expression, and homeostasis depend on the correct transmission of molecular signals within and between cells. The vast complexity of these molecular signaling networks has necessitated the use of mathematical methods to model, characterize, and predict cellular responses. The work presented in this dissertation shows how computational methods were used to elucidate two clinically-relevant cellular signaling responses: (i) phosphotyrosine signaling through the epidermal growth factor receptor (EGFR), a receptor tyrosine kinase that is commonly overexpressed or structurally altered in human cancers; and (ii) phosphoinositide and calcium signaling in human platelets---the key cellular mediators of hemostasis and pathological thrombus formation. The kinetic model of EGFR-mediated signaling in wild-type and mutant cells showed how mutant forms of the receptor use an irregular pattern of tyrosine phosphorylation that preferentially activates the survival oncoprotein, Akt. By quantifying the amount of signal flow through diverging pathways downstream of the receptor, our calculations provided a mechanistic explanation for the clinical observation that therapeutic tyrosine kinase inhibitors can control tumor growth in cells bearing certain EGFR mutations. In the second major study, a kinetic model of ADP-stimulated calcium release in human platelets was used to make precise, quantitative predictions about the molecular makeup and structural properties of the platelet. Specifically, we found that the resting structure of platelets places strong restrictions on several biophysical quantities, such as the resting concentration of free inositol 1,4,5-trisphosphate, the ratio of calcium ATPase pumps to release channels, and the size of the calcium storage compartment. Notably, the model also demonstrated that the irregular calcium spiking behavior observed in single ADP-stimulated platelets is due to the extremely small cellular volume. A novel method for constructing kinetic signaling networks, based on restricting the steady-state properties of the model, is also presented. Future applications and extensions of the systems approach to signal transduction modeling are discussed in the final chapter.
  • Publication
    Steady-State Kinetic Modeling Constrains Cellular Resting States and Dynamic Behavior
    (2009-03-06) Purvis, Jeremy E; Radhakrishnan, Ravi; Diamond, Scott L
    A defining characteristic of living cells is the ability to respond dynamically to external stimuli while maintaining homeostasis under resting conditions. Capturing both of these features in a single kinetic model is difficult because the model must be able to reproduce both behaviors using the same set of molecular components. Here, we show how combining small, well-defined steady-state networks provides an efficient means of constructing large-scale kinetic models that exhibit realistic resting and dynamic behaviors. By requiring each kinetic module to be homeostatic (at steady state under resting conditions), the method proceeds by (i) computing steady-state solutions to a system of ordinary differential equations for each module, (ii) applying principal component analysis to each set of solutions to capture the steady-state solution space of each module network, and (iii) combining optimal search directions from all modules to form a global steady-state space that is searched for accurate simulation of the time-dependent behavior of the whole system upon perturbation. Importantly, this stepwise approach retains the nonlinear rate expressions that govern each reaction in the system and enforces constraints on the range of allowable concentration states for the full-scale model. These constraints not only reduce the computational cost of fitting experimental time-series data but can also provide insight into limitations on system concentrations and architecture. To demonstrate application of the method, we show how small kinetic perturbations in a modular model of platelet P2Y(1) signaling can cause widespread compensatory effects on cellular resting states.