Dynamic Response Phenotypes As Tools for Model Discrimination in Systems Biology

Abstract

One of the central questions in systems and synthetic biology is that of understanding the roles of signal transduction pathways and feedback loops, from the elucidation of such pathways in natural systems to the engineering design of networks that exhibit a desired behavior. This talk discusses certain types of network qualitative information that can be gleaned from “dynamic phenotypes”, a term that we take as encompassing both the transient characteristics of temporal responses and the use of rich classes of probing signals beyond step inputs. We focus on three examples: fold-change detection, non-monotonic responses, and subharmonic oscillations. An ubiquitous property of sensory systems is “adaptation”: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a pro- longed change in their environment. Certain adapting systems, ranging from bacterial chemotaxis pathways to signal transduction mechanisms in eukaryotes, enjoy a remarkable additional feature: scale invariance or “fold change detection” meaning that the initial, transient behavior remains approximately the same even when the background signal level is scaled (“log sensing”). We will review the biological phenomenon, and formulate a theoretical framework leading to a general theorem characterizing scale invariant behavior by equivariant actions on sets of vector fields that satisfy appropriate Lie-algebraic nondegeneracy conditions. The theorem allows one to make experimentally testable predictions, and the presentation will discuss the validation of these predictions using genetically engineered bacteria and microfluidic devices, as well their use as a “dynamical phenotype” for model invalidation. Systems described by order-preserving dynamics are called “monotone systems”. Such systems can be shown to have monotone response properties when starting from steady states: a nondecreasing input can never give rise to a biphasic response, for example. We briefly review some of this theory and show as an example how this tool can be used to invalidate a published model of M. tuberculosis stress response (hypoxic induction pathway). One challenging question in systems biology is that of comparing different architectures for perfect adaptation. For example both incoherent feedforward loops (IFFLs) and integral feedback systems give rise to perfect adaptation and, in some configurations, scale invariance. Recent work has proposed the use of periodic signals to discriminate between these models. We review a theoretical result showing that feedforward loops and monotone systems both lead to entrainment, but nonlinear feedback architectures (such as nonlinear integral feedback) may lead to period doubling bifurcations and even chaos. This result is illustrated through experimental work with C. elegans AIA interneurons, in which odor-evoked intracellular Ca2+ response signatures, to periodic on-off pulses of diacetyl, display subharmonic behavior at high forcing frequencies. The talk will also include some speculative remarks about the role of the shape of transient responses in immune system self/other recognition.