Mathematical Biology Seminar Hwai-Ray Tung, Math Department, U of U, Wednesday, September 13, 2023 1:45pm in LCB 323 Understanding and quantifying network robustness to stochastic inputs Abstract: A variety of biomedical systems are modeled by networks of deterministic differential equations with stochastic inputs. In some cases, the network output is remarkably constant despite a randomly fluctuating input. In the context of biochemistry and cell biology, chemical reaction networks and multistage processes with this property are called robust. Similarly, the notion of a forgiving drug in pharmacology is a medication that maintains therapeutic effect despite lapses in patient adherence to the prescribed regimen. What makes a network robust to stochastic noise? This question is challenging due to the many network parameters (size, topology, rate constants) and possible types of noisy inputs. In this paper, we propose a summary statistic to describe the robustness of a network of linear differential equations (i.e.\ a first-order mass-action system). This statistic describes the variance of a certain conditional last passage time on the network. This statistic can be quickly computed on a modern computer, even for networks with thousands of nodes. Furthermore, we use this statistic to prove theorems about how certain network motifs increase robustness. Importantly, our analysis reveals the essential reason why a network is or is not robust to noise. We illustrate our results in several examples of networks and classes of stochastic inputs. This work is done with Sean Lawley.