Kinetic Diagram Analysis: A Python Library for Calculating Steady-State Observables of Biochemical Systems Analytically

Abstract

Kinetic diagrams are commonly used to represent biochemical systems in order to study phenomena such as free energy transduction and ion selectivity. While numerical methods are commonly used to analyze such kinetic networks, the diagram method by King, Altman and Hill makes it possible to construct exact algebraic expressions for steady-state observables in terms of the rate constants of the kinetic diagram. However, manually obtaining these expressions becomes infeasible for models of even modest complexity as the number of the required intermediate diagrams grows with the factorial of the number of states in the diagram. We developedKinetic Diagram Analysis(KDA), a Python library that programmatically generates the relevant diagrams and expressions from a user-defined kinetic diagram.KDAoutputs symbolic expressions for state probabilities and cycle fluxes at steady-state that can be symbolically manipulated and evaluated to quantify macroscopic system observables. We demonstrate theKDAapproach for examples drawn from the biophysics of active secondary transmembrane transporters. For a generic 6-state antiporter model, we show how the introduction of a single leakage transition reduces transport efficiency by quantifying substrate turnover. We applyKDAto a real-world example, the 8-state free exchange model of the small multidrug resistance transporter EmrE of Hussey et al (J General Physiology152(2020), e201912437), where a change in transporter phenotype is achieved by biasing two different subsets of kinetic rates: alternating access and substrate unbinding rates.KDAis made available as open source software under the GNU General Public License version 3.