Perturbed and Permuted: Signal Integration in Network-Structured Dynamic Systems

TL;DR

This paper introduces structural metrics for complex dynamic systems modeled by sparse differential equations to assess how signals interact and influence each other's effects, with implications for understanding biological responses.

Contribution

It develops novel structural metrics that quantify signal modulation and independence in network-structured dynamic systems, enhancing analysis of multi-signal responses.

Findings

Metrics correlate with signal susceptibility to modulation.

One metric indicates increased independence of signal responses.

Metrics relate to normalized arc density near influential nodes.

Abstract

Biological systems (among others) may respond to a large variety of distinct external stimuli, or signals. These perturbations will generally be presented to the system not singly, but in various combinations, so that a proper understanding of the system response requires assessment of the degree to which the effects of one signal modulate the effects of another. This paper develops a pair of structural metrics for sparse differential equation models of complex dynamic systems and demonstrates that said metrics correlate with proxies of the susceptibility of one signal-response to be altered in the context of a second signal. One of these metrics may be interpreted as a normalized arc density in the neighborhood of certain influential nodes; this metric appears to correlate with increased independence of signal response.