A Characterization of Scale Invariant Responses in Enzymatic Networks

TL;DR

This paper investigates the conditions under which enzymatic networks exhibit scale-invariant responses, discovering a new property called ULFO that is both necessary and sufficient for this behavior, supported by computational and mathematical analysis.

Contribution

It introduces the ULFO property as a key criterion for scale invariance in enzymatic networks, providing a unified theoretical framework.

Findings

ULFO is necessary and sufficient for scale invariance

Computational study reveals the simplicity and generality of ULFO

Mathematical explanation links ULFO to scale-invariant behavior

Abstract

An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately) the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO), whose validity we show is both necessary and sufficient for scale invariance of enzymatic networks. Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions.