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Assembly and Characterization of Biomolecular Memristors Consisting of Ion Channel-doped Lipid Membranes

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Tractable nonlinear memory functions as a tool to capture and explain dynamical behaviors.

Edgar Herrera-Delgado¹, James Briscoe², Peter Sollich³

¹The Francis Crick Institute, 1 Midland Rd., London NW1 1AT, United Kingdom and Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom.

Physical Review Research

|March 1, 2023

Summary

Zwanzig-Mori projection methods simplify complex biological networks by reducing dimensionality while preserving dynamics. This approach offers a powerful tool for understanding multistable dynamical systems, including gene regulatory networks.

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Area of Science:

Dynamical systems theory
Mathematical biology
Systems biology

Background:

Dynamical systems theory is crucial for modeling biological processes like protein interactions and gene regulatory networks.
Increasing network complexity necessitates simplification and coarse-graining techniques for analysis.

Purpose of the Study:

To demonstrate the utility of Zwanzig-Mori projection methods for dimensionality reduction in dynamical networks.
To show that these methods retain essential dynamical properties and provide explicit solutions for memory functions.

Main Methods:

Application of Zwanzig-Mori projection techniques.
Systematic expansion around the quasi-steady-state approximation.
Analysis of dynamical properties including steady states, transients, multistability, and oscillations.

Main Results:

Arbitrary dimensionality reduction of dynamical networks is achievable while preserving dynamics.
Explicit memory functions are derived without prior dynamic knowledge.
The method accurately replicates system transients, steady states, multistability, and oscillatory behaviors.

Conclusions:

Zwanzig-Mori projection methods offer a broadly applicable and efficient approach for analyzing multistable dynamical systems.
The technique successfully identified key regulatory features in a vertebrate neural tube gene network.
This method provides valuable insights into the behavior of complex biological networks.