Structure and input-to-state stability for composable computations in chemical reaction networks

TL;DR

This work tackles the problem of composability for MAS-based molecular computations in chemical reaction networks (CRNs). It introduces a structure-based criterion based on reduced-system analysis and ISS-Lyapunov theory to guarantee dynamic composability, requiring the reduced system $\tilde{\mathscr{C}}^{2}$ to be weakly reversible, have a single linkage class, zero deficiency, and be mass-conservative. The authors show that these structural properties yield an ISS-Lyapunov function, enabling composability without analyzing the full coupled dynamics, and illustrate the approach with a concrete two-stage example that computes a composite function $\sigma_2\circ\sigma_1$. This framework supports direct, topology-driven verification of composability and motivates building a library of composable elementary msCRCs for scalable molecular computation.

Abstract

In the field of molecular computation based on chemical reaction networks (CRNs), leveraging parallelism to enable coupled mass-action systems (MASs) to retain predefined computational functionality has been a research focus. MASs exhibiting this property are termed composable. This paper investigates the structural conditions under which two MASs are composable. By leveraging input-to-state stability (ISS) property, we identify a specific class of CRN architectures that guarantee composability with other networks. A concrete example demonstrates the validity of this conclusion and illustrates the application of composability in computing composite functions.

Figures (1)

• Figure 1: The computation results of the function (\ref{['fun_composite']})