Real-Time Equivalence of Chemical Reaction Networks and Analog Computers

Huang, Xiang; Klinge, Titus H.; Lathrop, James I.

doi:10.1007/978-3-030-26807-7_3

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…Since species concentrations are non-negative, we encode a real number as the difference between two species. (This is a common technique and was used to show that CRNs are equivalent to the general purpose analog computer (GPAC) [13]). Thus, a real-valued signal x(t) is encoded as x + (t) − x − (t) where X + and X − are two species.…”

Section: Functional Reactive Programmingmentioning

confidence: 99%

Reactamole: functional reactive molecular programming

Klinge,

Lathrop,

Osera

et al. 2024

Nat Comput

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Chemical reaction networks (CRNs) are an important tool for molecular programming, a field that is rapidly expanding our ability to deploy computer programs into biological systems for a variety of applications. However, CRNs are also difficult to work with due to their massively parallel nature, leading to the need for higher-level languages that allow for easier computation with CRNs. Recently, research has been conducted into a variety of higher-level languages for deterministic CRNs but modeling CRN parallelism, managing error accumulation, and finding natural CRN representations are ongoing challenges.We introduce Reactamole, a higher-level language for deterministic CRNs that utilizes the functional reactive programming (FRP) paradigm to represent CRNs as a reactive dataflow network. Reactamole equates a CRN with a functional reactive program, implementing the key primitives of the FRP paradigm directly as CRNs. The functional nature of Reactamole makes reasoning about molecular programs easier, and its strong static typing allows us to ensure that a CRN is well-formed by virtue of being well-typed. In this paper, we describe the design of Reactamole and how we use CRNs to represent the common datatypes and operations found in FRP. We also demonstrate the potential of this functional reactive approach to molecular programming by giving an extended example where a CRN is constructed using FRP to modulate and demodulate an amplitude modulated signal.

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Section: Functional Reactive Programmingmentioning

confidence: 99%

Reactamole: functional reactive molecular programming

Klinge,

Lathrop,

Osera

et al. 2024

Nat Comput

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“…The definition of real-time computable by a CRN used in this paper is given by [12,13]. We repeat the definition here for convenience.…”

Section: Preliminariesmentioning

confidence: 99%

“…Bournez et al introduced the notion of computing a real number in the limit with a general purpose analog computer (GPAC) [2]. To compute α P R "in the limit," a designated variable xptq must satisfy lim tÑ8 xptq " α. Computing real numbers in this way has also been investigated in population protocols [3] and chemical reaction networks (CRNs) [12]. Huang et al defined a number α P R to be real-time computable by chemical reaction networks, written α P R RTCRN , if there exists a CRN with integral rate constants and a designated species X such that, if all species concentrations are initialized to zero, then xptq converges to α exponentially quickly [13].…”

Section: Introductionmentioning

confidence: 99%

Robust Real-time Computing with Chemical Reaction Networks

Fletcher¹,

Klinge²,

Lathrop³

et al. 2021

Preprint

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Recent research into analog computing has introduced new notions of computing real numbers. Huang, Klinge, Lathrop, Li, and Lutz defined a notion of computing real numbers in real-time with chemical reaction networks (CRNs), introducing the classes RLCRN (the class of all Lyapunov CRN-computable real numbers) and RRTCRN (the class of all real-time CRN-computable numbers). In their paper, they show the inclusion of the real algebraic numbers ALG Ď RLCRN Ď RRTCRN and that ALG Ř RRTCRN but leave open where the inclusion is proper. In this paper, we resolve this open problem and show ALG " RLCRN Ř RRTCRN. However, their definition of real-time computation is fragile in the sense that it is sensitive to perturbations in initial conditions. To resolve this flaw, we further require a CRN to withstand these perturbations. In doing so, we arrive at a discrete model of memory. This approach has several benefits. First, a bounded CRN may compute values approximately in finite time. Second, a CRN can tolerate small perturbations of its species' concentrations. Third, taking a measurement of a CRN's state only requires precision proportional to the exactness of these approximations. Lastly, if a CRN requires only finite memory, this model and Turing machines are equivalent under real-time simulations.

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