Inferring networks of chemical reactions by curvature analysis of kinetic trajectories

Abstract

Quantifying interaction networks of chemical reactions allows description, prediction, and control of a range of phenomena in chemistry and biology. The challenge lies in unambiguously assigning contributions to changes in rates from different interactions. We propose that the curvature change of kinetic trajectories due to a systematic perturbation of a node in a network can identify the coupling strength and topology. Specifically, the coupling strength can be calculated as the ratio of the curvature change measured from the coupled node and the rate change of a perturbed node. We verified the methodology in numerical simulations with a network with complex ordinary differential equations and experiments with electrochemical networks. The experiments show excellent network inference (without false positive or negative links) of various systems with large heterogeneity in local dynamics and network structure without any a priori knowledge of the kinetics. The theory and the experiments also clarify the influence of local perturbations on response amplitude and timing through network-wide up-regulation. A major advantage of our technique is its independence from hidden/unobserved nodes. This makes our method highly suitable for applications with high temporal and low spatial resolution data from interacting chemical and biochemical systems including neuronal activity monitoring with multi-electrode arrays.