Separating Signaling Space

Bree Aldridge, Massachusetts Institute of Technology

Computational modeling of cell signaling networks is proving to be helpful toward increased understanding of how cells translate extracellular cues into functional responses. Because the dynamic behavior generated from these models is typically highly complex, mathematical analysis methods for elucidating insights about network operation are important. One especially important goal is parametric analysis — ascertaining how qualitative network dynamics depend upon critical model parameters. For ODE-based models, bifurcation analysis of steady-state properties is often found to be beneficial, but this methodology is limited to systems in which the functional behavior is effectively characterized by different steady states. However, many signaling networks influence ultimate cell behavior during transient conditions well before a steady state is reached, making bifurcation analysis inadequate. In this work, we employ Direct Finite-Time Lyapunov Exponent (DLE) analysis to identify separatrices as phase-space surfaces with sensitive dependence on initial conditions. These separatrices delineate qualitatively different transient behaviors which would be indistinguishable using steady-state bifurcation analysis. As a demonstration of their utility in studying biomolecular signaling networks of current biological importance, we applied these methods to a model of interactions between caspase-3, caspase-8, and XIAP. These proteins act in the final stages of the apoptotic decision network and their transient activities appear to determine cell death-vs-survival fates. DLE analysis enabled identification of a separatrix that quantitatively characterized network behavior by defining initial conditions (i.e., protein expression levels at a specified time point) leading to apoptosis. Moreover, a related analysis using the shortest distance between a transient trajectory and one of the unstable fixed points as an associated metric of network trajectories yielded additional insight into the dynamics underlying the cell decision separatrix. DLE analysis should facilitate theoretical investigation of the decision-making mechanisms in larger signaling networks.

Abstract Author(s): Bree Aldridge, George Haller, Peter Sorger, Douglas Lauffenburger