Memory functions reveal structural properties of gene regulatory networks

Abstract

Gene regulatory networks (GRNs) control cellular function and decision making during tissue development and homeostasis. Mathematical tools based on dynamical systems theory are often used to model these networks, but the size and complexity of these models mean that their behaviour is not always intuitive and the underlying mechanisms can be difficult to decipher. For this reason, methods that simplify and aid exploration of complex networks are necessary. To this end we develop a broadly applicable form of the Zwanzig-Mori projection. By first converting a thermodynamic state ensemble model of gene regulation into mass action reactions we derive a general method that produces a set of time evolution equations for a subset of components of a network. The influence of the rest of the network, the bulk, is captured by memory functions that describe how the subnetwork reacts to its own past state via components in the bulk. These memory functions provide probes of near-steady state dynamics, revealing information not easily accessible otherwise. We illustrate the method on a simple cross-repressive transcriptional motif to show that memory functions not only simplify the analysis of the subnetwork but also have a natural interpretation. We then apply the approach to a GRN from the vertebrate neural tube, a well characterised developmental transcriptional network composed of four interacting transcription factors. The memory functions reveal the function of specific links within the neural tube network and identify features of the regulatory structure that specifically increase the robustness of the network to initial conditions. Taken together, the study provides evidence that Zwanzig-Mori projections offer powerful and effective tools for simplifying and exploring the behaviour of GRNs.

arXiv comment28 pages, 8 figures

References in corpus (5)

• Glassy dynamics of kinetically constrained models
• Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
• Simplifying Biochemical Models With Intermediate Species
• The breakdown of the reaction-diffusion master equation with non-elementary rates
• Michaelis-Menten dynamics in protein subnetworks

Cited by in corpus (5)

• Emergence of molecular friction in liquids: bridging between the atomistic and hydrodynamic pictures
• Tackling the subsampling problem to infer collective properties from limited data
• Tractable nonlinear memory functions as a tool to capture and explain dynamical behaviours
• A deep learning approach to the measurement of long-lived memory kernels from Generalised Langevin Dynamics
• Systematic model reduction captures the dynamics of extrinsic noise in biochemical subnetworks