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Biological regulatory networks depend upon chemical interactions to process information. Engineering such molecular computing systems is a major challenge for synthetic biology and related fields. The chemical reaction network (CRN) model idealizes chemical interactions, abstracting away specifics of the molecular implementation, and allowing rigorous reasoning about the computational power of chemical kinetics. Here we focus on function computation with CRNs, where we think of the initial concentrations of some species as the input and the eventual steady-state concentration of another species as the output. Specifically, we are concerned with CRNs that are rate-independent (the computation must be correct independent of the reaction rate law) and composable (𝑓∘𝑔 can be computed by concatenating the CRNs computing f and g). Rate independence and composability are important engineering desiderata, permitting implementations that violate mass-action kinetics, or even “well-mixedness”, and allowing the systematic construction of complex computation via modular design. We show that to construct composable rate-independent CRNs, it is necessary and sufficient to ensure that the output species of a module is not a reactant in any reaction within the module. We then exactly characterize the functions computable by such CRNs as superadditive, positive-continuous, and piecewise rational linear. Our results show that composability severely limits rate-independent computation unless more sophisticated input/output encodings are used.
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This content will become publicly available on August 7, 2026
Chemical master equation parameter exploration using DMRG
Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories, there is interest in systematically approximating the joint distribution over the exponentially large number of possible microstates using tensor networks or tensor trains. We exploit the tensor network strategy to determine when the steady state of a seven-species gene toggle switch CRN model supports bistability as a function of two decomposition rates, both parameters of the kinetic model. We highlight how the tensor network solution captures the effects of stochastic fluctuations, going beyond mean field and indeed deviating meaningfully from a mean-field analysis. The work furthermore develops and demonstrates several technical advances that will allow steady-states of broad classes of CRNs to be computed in a manner conducive to parameter exploration. We show that the steady-state distributions can be computed via the ordinary density matrix renormalization group (DMRG) algorithm, despite having a non-Hermitian rate operator with a small spectral gap, we illustrate how that steady-state distribution can be efficiently projected to an order parameter that identifies bimodality, and we employ excited-state DMRG to calculate a relaxation timescale for the bistability.
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- Award ID(s):
- 2239867
- PAR ID:
- 10630264
- Publisher / Repository:
- American Institute of Physics (AIP Publishing)
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 163
- Issue:
- 5
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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