Context in Synthetic Biology: Memory Effects of Environments with Mono-molecular Reactions

TL;DR

This paper investigates how environmental memory effects influence synthetic biological circuits, providing exact analytical expressions for these effects when the environment consists of mono-molecular reactions, enhancing predictability of subnetwork dynamics.

Contribution

It introduces a method to derive exact memory functions for small modules coupled with mono-molecular reaction environments, advancing understanding of environmental impacts in synthetic biology.

Findings

Derived exact analytical expressions for environmental memory functions.

Mapped coupled dynamics onto random walks for analytical tractability.

Provided insights into types of memory functions affecting subnetwork behavior.

Abstract

Synthetic biology aims at designing modular genetic circuits that can be assembled according to the desired function. When embedded in a cell, a circuit module becomes a small subnetwork within a larger environmental network, and its dynamics is therefore affected by potentially unknown interactions with the environment. It is well-known that the presence of the environment not only causes extrinsic noise but also memory effects, which means that the dynamics of the subnetwork is affected by its past states via a memory function that is characteristic of the environment. We study several generic scenarios for the coupling between a small module and a larger environment, with the environment consisting of a chain of mono-molecular reactions. By mapping the dynamics of this coupled system onto random walks, we are able to give exact analytical expressions for the arising memory functions. Hence, our results give insights into the possible types of memory functions and thereby help to better predict subnetwork dynamics.