Computation and analysis of time-dependent sensitivities in Generalized Mass Action systems

Understanding biochemical system dynamics is becoming increasingly important for insights into the functioning of organisms and for biotechnological manipulations, and additional techniques and methods are needed to facilitate investigations of dynamical properties of systems. Extensions to the method of Ingalls and Sauro, addressing time-dependent sensitivity analysis, provide a new tool for executing such investigations. We present here the results of sample analyses using time-dependent sensitivities for three model systems taken from the literature, namely an anaerobic fermentation pathway in yeast, a negative feedback oscillator modeling cell-cycle phenomena, and the Mitogen Activated Protein (MAP) kinase cascade. The power of time-dependent sensitivities is particularly evident in the case of the MAPK cascade. In this example it is possible to identify the emergence of a concentration of MAPKK that provides the best response with respect to rapid and efficient activation of the cascade, while over- and under-expression of MAPKK relative to this concentration have qualitatively different effects on the transient response of the cascade. Also of interest is the quite general observation that phase-plane representations of sensitivities in oscillating systems provide insights into the manner with which perturbations in the envelope of the oscillation result from small changes in initial concentrations of components of the oscillator. In addition to these applied analyses, we present an algorithm for the efficient computation of time-dependent sensitivities for Generalized Mass Action (GMA) systems, the most general of the canonical system representations of Biochemical Systems Theory (BST). The algorithm is shown to be comparable to, or better than, other methods of solution, as exemplified with three biochemical systems taken from the literature.