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Abstract: The T-cell antigen-activated signaling pathway is a highly regulated intracellular biochemical system that is crucial for initiating an appropriate adaptive immune response. To improve the understanding of the complex regulatory mechanisms controlling the early events in T-cell signaling, a detailed mathematical model was developed that utilizes ordinary differential equations to describe chemical reactions of the signaling pathway. The model parameter values were constrained by experimental data on the activation of a specific signaling intermediate and indicated an initial rapid cascade of phosphorylation events followed by a comparatively slow signal downregulation. Nonlinear analysis of the model suggested that thresholding and bistability occur as a result of the embedded positive and negative feedback loops within the model. These nonlinear system properties may enhance the T-cell receptor specificity and provide sub-threshold noise filtering with switch-like behavior to ensure proper cell response. Additional analysis using a reduced second-order model led to further understanding of the observed system behavior. Moreover, the interactions between the positive and negative feedback loops enabled the model to exhibit, among a variety of other feasible dynamics, a sustained oscillation that corresponds to a stable limit cycle in the two-dimensional phase plane. Quantitative analysis in this paper has helped identify potential regulatory mechanisms in the early T-cell signaling events. This integrated approach provides a framework to quantify and discover the ensemble of interconnected T-cell antigen-activated signaling pathways from limited experimental data. [Copyright &y& Elsevier]

Abstract: There is a fundamental difference in complexity between signaling initiated by ligands on the surface of one cell binding to receptors on the surface of another cell and ligands in solution binding to these receptors. The fact that two cells must approach each other and form a number of intercellular bonds of different types, all within the restricted geometry of the intercellular contact region, introduces the possibility of complex spatio-temporal dynamics of surface receptors that is not present otherwise. Mathematical modelling of these dynamics is in its early stages. However, useful tools have emerged. The purpose of this paper is to describe some of these mathematical tools, indicating their strengths and shortcomings, and suggest some directions for future theoretical studies. [Copyright &y& Elsevier]