biological systems

We consider a general class of translation-invariant systems with a specific category of output nonlinearities motivated by biological sensing. We show that no dynamic output feedback can stabilize this class of systems to an isolated equilibrium point. To overcome this fundamental limitation, we propose a simple control scheme that includes a low-amplitude periodic forcing function akin to so-called "active sensing" in biology, together with nonlinear output feedback. Our analysis shows that this approach leads to the emergence of an exponentially stable limit cycle. These findings offer a provably stable active sensing strategy and may thus help to rationalize the active sensing movements made by animals as they perform certain motor behaviors.

Applying Modular Response Analysis to a synthetic gene circuit, which was introduced in a recent paper by the authors, leads to the inference of a nontrivial "ghost" regulation edge which was not explicitly engineered into the network and which is, in fact, not immediately apparent from experimental measurements. One may thus hypothesize that this ghost regulatory effect is due to competition for resources. A mathematical model is proposed, and analyzed in closed form, that lends validation to this hypothesis.