Research over the past few decades has revealed that many cellular processes require levels of accuracy and sensitivity that cannot be reached near equilibrium; living systems must exist far from thermodynamic equilibrium (TDE) in order to achieve the levels of sensitivity that allow them to survive.This grant supports research by Jordon Horowitz, Assistant Professor of Biophysics and Complex Systems at the University of Michigan, to improve our understand of living systems by studying the biochemical networks active within cells through the lens of thermodynamics. Horowitz will study broad classes of biochemical models in an effort to establish quantitative trade-offs (inequalities) between the maximum achievable sensitivity of any biochemical process and the thermodynamics driving that process. If successful, this line of research will improve our understanding of the factors constraining biological function while also revealing how closely living systems operate from the maximum achievable biochemical sensitivity. 'Sensitivity' here is being used as a flexible term intended to capture a range of bio-performance metrics such as the ability to discriminate between binding to chemical A vs chemical B, or the ability to determine whether there are few or many food molecules in the local environment.Horowitz’s research is divided into three sequential aims. In Aim 1, he will perform numerical analyses of comparatively simple models to gain insight into how network structure and thermodynamics constrain performance in simple biochemical networks. These models are too simple to represent actual cellular processes yet simple enough that numerical analysis of the available phase space is practical. Simulations will be used to study networks with varying topological structure and thermodynamic driving force in order to determine the maximum possible sensitivity, along with the model parameters that achieve that sensitivity. These numerical findings will be captured in a 'library of kinetic networks' classified by sensitivity, network topology, and thermodynamics. In Aim 2, Horowitz will attempt to use graphical methods and the Matrix Tree Theorem to mathematically (analytically) prove that these discovered limitations are in fact rigorous bounds. If successful, the result will be a set of mathematical inequalities that quantify fundamental limitations on sensitivity imposed by network structure and thermodynamic drive.In Aim 3, Horowitz will attempt to expand and apply these findings to more complicated models that have been developed to capture actual cellular process, including generalized ‘butterfly’ networks, the ‘ladder’ model of adaptation, and a generalized bacterial-flagellar-motor model.