Understanding the Optimal Response Properties of Tricyclic Cascade Networks through Dynamic Optimization

The mitogen-activated protein kinase (MAPK) cascades are ubiquitous in eukaryotic signal transduction, and these pathways are conserved in cells from yeast to mammals. They relay extracellular stimuli from the plasma membrane to targets in the cytoplasm and nucleus, initiating diverse responses involving cell growth, mitogenesis, differentiation and stress responses in mammalian cells. Much effort has been devoted, in recent years, for constructing detailed kinetic models of MAPK networks linking molecular (protein-protein, protein-DNA, and protein-RNA) interactions, gene expression and chemical reactions to cellular behavior. These networks are most naturally described by systems of differential-algebraic equations (DAEs): the ordinary differential equations express the mass-action kinetics, whereas the algebraic equations enforce conservation relations among the constituents. Moreover, these models typically involve a relatively large number of parameters, such as the rate constants and strength of protein- protein interactions, the values of which are not directly accessible in vivo and are subject to large uncertainty. In this presentation, we investigate the application of dynamic optimization techniques to study the relationships between model parameters and functions in signal transduction pathways. Dynamic optimization is ideally suited for studying biochemical networks since it allows dealing with large-scale, nonlinear DAE models and can handle a great variety of objective functions and constraints. Yet, very few applications have been reported in this context to date. We employ dynamic optimization methods to identify ranges of the parameters that confer optimal dynamic response properties in a linear three-kinase model. Our focus is on the duration of the signal, the time from input to output, and the amplitude of the signal, which are important dynamic response properties for MAPK networks. Comparisons of alternative mathematical representations are considered.