Input-to-state stability-based chemical reaction networks composition for molecular computations

TL;DR

This paper develops a systematic framework for composing chemical reaction networks governed by mass-action kinetics, enabling scalable and accurate molecular computations through input-to-state stability principles.

Contribution

It introduces a new composability framework for rate-dependent CRNs using ISS, expanding beyond rate-independent models and improving computational scalability and accuracy.

Findings

Framework supports layer-by-layer computation of complex functions

Proposed method outperforms existing approaches in accuracy

Examples demonstrate efficiency and practical applicability

Abstract

Molecular computation based on chemical reaction networks (CRNs) has emerged as a promising paradigm for designing programmable biochemical systems. However, the implementation of complex computations still requires excessively large and intricate network structures, largely due to the limited understanding of composability, that is, how multiple subsystems can be coupled while preserving computational functionality. Existing composability frameworks primarily focus on rate-independent CRNs, whose computational capabilities are severely restricted. This article aims to establish a systematic framework for composable CRNs governed by mass-action kinetics, a common type of rate-dependent CRNs. Drawing upon the concepts of composable rate-independent CRNs, we introduce the notions of mass-action chemical reaction computers (msCRCs), dynamic computation and dynamic composability to establish a rigorous mathematical framework for composing two or more msCRCs to achieve layer-by-layer computation of composite functions. Further, we derive several sufficient conditions based on the notions of input-to-state stability (ISS) to characterize msCRCs that can be composed to implement desired molecular computations, thereby providing theoretical support for this framework. Some examples are presented to illustrate the efficiency of our method. Finally, comparative results demonstrate that the proposed method exhibits notable advantages in both computational ability and accuracy over the state-of-the-art methods.