HillTau: A fast, compact abstraction for model reduction in biochemical signaling networks.

Upinder S Bhalla,Joanna Jędrzejewska-Szmek

doi:10.1371/journal.pcbi.1009621

Upinder S Bhalla, Joanna Jędrzejewska-Szmek

Open Access

https://doi.org/10.1371/journal.pcbi.1009621

Copy DOI

Abstract

Signaling networks mediate many aspects of cellular function. The conventional, mechanistically motivated approach to modeling such networks is through mass-action chemistry, which maps directly to biological entities and facilitates experimental tests and predictions. However such models are complex, need many parameters, and are computationally costly. Here we introduce the HillTau form for signaling models. HillTau retains the direct mapping to biological observables, but it uses far fewer parameters, and is 100 to over 1000 times faster than ODE-based methods. In the HillTau formalism, the steady-state concentration of signaling molecules is approximated by the Hill equation, and the dynamics by a time-course tau. We demonstrate its use in implementing several biochemical motifs, including association, inhibition, feedforward and feedback inhibition, bistability, oscillations, and a synaptic switch obeying the BCM rule. The major use-cases for HillTau are system abstraction, model reduction, scaffolds for data-driven optimization, and fast approximations to complex cellular signaling.

Highlights

John von Neumann’s elephant haunts mechanistically detailed models. von Neumann was reported to have claimed that he could fit an elephant with 4 parameters, with the implication that models with many parameters are under-constrained and over-fitted [1]
We introduce HillTau as a simplified way to model complex chemical networks
HillTau models condense multiple reaction steps into single steps defined by a small number of parameters for activation and settling time

Summary

Introduction

John von Neumann’s elephant haunts mechanistically detailed models. von Neumann was reported to have claimed that he could fit an elephant with 4 parameters, with the implication that models with many parameters are under-constrained and over-fitted [1]. John von Neumann’s elephant haunts mechanistically detailed models. Von Neumann was reported to have claimed that he could fit an elephant with 4 parameters, with the implication that models with many parameters are under-constrained and over-fitted [1]. There are two major arguments to exorcise this elephant: that mechanistic detail is needed to address certain kinds of questions; and that in the era of big data it is both easier and less biased to build up detailed models with all the available pieces. There are an estimated 1400 protein species localized to the postsynaptic density alone [2]. These support a range of functions including synaptic transmission, maintenance, plasticity, activity-driven protein synthesis, metabolic control, and traffic [3]

Methods

Results

Discussion

Conclusion