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 characterized 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 behavior of GRNs.
(Work in collaboration with Edgar Herrera, James Briscoe & Ruben Perez Carrasco.)
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Peter Sollich (University of Göttingen, Germany) received his Ph.D. in theoretical physics from the University of Edinburgh, for a thesis on the statistical mechanics of neural networks. His postdoctoral work was funded by a Royal Society Dorothy Hodgkin Research Fellowship, and he then moved to King’s College London to take up a permanent appointment. He was Professor of Statistical Mechanics at King’s College from 2004 to 2018, and has recently taken up a chair in Non-Equilibrium Statistical Physics at the Institute for Theoretical Physics at the University of Goettingen. His interests are in non-equilibrium statistical mechanics, often on networks, and he has led both a European Network (NETADIS) and a UK Centre for Doctoral Training (CANES) in this area.
Coffee break: 3:45 pm.