Eduardo D. Sontag
Department of Mathematics and Center for Quantitative Biology
Qualitative features of transient responses
A case study: scale-invariance
November 10, 2015
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 prolonged change in their environment. It has been recently observed that some 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.
I 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 I 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. I will conclude by briefly engaging in some wild and irresponsible speculation about the role of the shape of transient responses in immune system self/other recognition and in evaluating the initial effects of immunotherapy.