Robust control of biochemical reaction networks via stochastic morphing

TL;DR

This paper introduces a stochastic morpher controller for biochemical networks that can shape the entire probability distribution of target species, enabling control over complex distribution features like multi-modality and multi-stability, with proven robustness and practical implementation strategies.

Contribution

It presents the first controller capable of morphing the full probability distribution of biochemical species, extending beyond mean and variance control.

Findings

The stochastic morpher achieves desired distribution shapes under certain conditions.

Properties like robust perfect adaptation and convergence are rigorously proven.

Demonstrations include various biochemical network examples.

Abstract

Synthetic biology is an interdisciplinary field aiming to design biochemical systems with desired behaviors. To this end, molecular controllers have been developed which, when embedded into a pre-existing ambient biochemical network, control the dynamics of the underlying target molecular species. When integrated into smaller compartments, such as biological cells in vivo, or vesicles in vitro, controllers have to be calibrated to factor in the intrinsic noise. In this context, molecular controllers put forward in the literature have focused on manipulating the mean (first moment), and reducing the variance (second moment), of the target species. However, many critical biochemical processes are realized via higher-order moments, particularly the number and configuration of the modes (maxima) of the probability distributions. To bridge the gap, a controller called stochastic morpher is put forward in this paper, inspired by gene-regulatory networks, which, under suitable time-scale separations, morphs the probability distribution of the target species into a desired predefined form. The morphing can be performed at the lower-resolution, allowing one to achieve desired multi-modality/multi-stability, and at the higher-resolution, allowing one to achieve arbitrary probability distributions. Properties of the controller, such as robust perfect adaptation and convergence, are rigorously established, and demonstrated on various examples. Also proposed is a blueprint for an experimental implementation of stochastic morpher.