Robust Real-Time Computing with Chemical Reaction Networks

Fletcher, Willem; Klinge, Titus H.; Lathrop, James I.; Nye, Dawn A.; Rayman, Matthew

doi:10.1007/978-3-030-87993-8_3

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…The direct consequence of this remark is that, at least locally around the solution, the convergence toward the stable region is always exponential with a characteristic time of the order of ,0) . A more rigorous proof of this assertion can be found in [16].…”

Section: Proposition 19mentioning

confidence: 87%

“…A recent work by Fletcher & al. presents results very close to ours. In [16], the authors propose a Lyapunov computational framework for computing real numbers with CRNs, and show that the set of numbers that are equilibrium points of such systems is exactly the set of algebraic numbers. An interesting result of this paper is the proof that these equilibrium points are locally exponentially stable, a result we will use in Sec.…”

Section: Related Workmentioning

confidence: 99%

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Algebraic Biochemistry: A Framework for Analog Online Computation in Cells

Hemery

Fages

2022

Lecture Notes in Computer Science

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The Turing completeness of continuous Chemical Reaction Networks (CRNs) states that any computable real function can be computed by a continuous CRN on a finite set of molecular species, possibly restricted to elementary reactions, i.e. with at most two reactants and mass action law kinetics. In this paper, we introduce a more stringent notion of robust online analog computation, and Absolute Functional Robustness (AFR), for the CRNs that stabilize the concentration values of some output species to the result of one function of the input species concentrations, in a perfectly robust manner with respect to perturbations of both intermediate and output species. We prove that the set of real functions stabilized by a CRN with mass action law kinetics is precisely the set of real algebraic functions. Based on this result, we present a compiler which takes as input any algebraic function (defined by one polynomial and one point for selecting one branch of the algebraic curve defined by the polynomial) and generates an abstract CRN to stabilize it. Furthermore, we provide error bounds to estimate and control the error of an unperturbed system, under the assumption that the environment inputs are driven by k-Lipschitz functions.

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Section: Proposition 19mentioning

confidence: 87%

Section: Related Workmentioning

confidence: 99%