Signaling Pathways Dynamics and Cancer Treatment

The rapid development of the biological research techniques in recent years provides more and more high quality data. Current technology allows to observe not only the whole body, tissue, or cell but also what happens inside the single cell, for example the time change (dynamics) of the number and location of biomolecules such as proteins, and their properties such as phosphorylation. With this knowledge it becomes obvious that the intracellular interactions between various molecules are not straightforward but complex with many mutual dependencies and Feedback feedback loops. It becomes clear that for a better understanding of the networks and their dynamics a complex approach is required. This approach can be based on the methodology of system engineering. It involves construction of mathematical models of observed phenomena and then their analysis. Mathematical models may be deterministic, based on ordinary differential equations (ODEs) or stochastic based on reaction propensities. They cover the network of interactions of intracellular species called the signaling pathways. In this chapter we define signaling pathways, describe main reaction types and corresponding equations, describe the main numerical methods for simulation of deterministic and stochastic models, and discuss the basics of the signaling pathways model analysis including stability, sensitivity, and bifurcation analysis. At the end we present an example of the p53 signaling pathway model and discuss possible anticancer therapies using available control signals.