Nontrivial amplification below the threshold for excitable cell signaling.

Abstract

In many asymptotically stable fluid systems, arbitrarily small fluctuations can grow by orders of magnitude before eventually decaying, dramatically enhancing the fluctuation variance beyond the minimum predicted by linear stability theory. Here using influential quantitative models drawn from the mathematical biology literature, we establish that dramatic amplification of arbitrarily small fluctuations is found in excitable cell signaling systems as well. Our analysis highlights how positive and negative feedback, proximity to bifurcations, and strong separation of timescales can generate nontrivial fluctuations without nudging these systems across their excitation thresholds. These insights, in turn, are relevant for a broader range of related oscillatory, bistable, and pattern-forming systems that share these features. The common thread connecting all of these systems with fluid dynamical examples of noise amplification is non-normality.