Turing Complete Catalytic Particle Computers

Liekens, Anthony; Fernando, Chrisantha

doi:10.1007/978-3-540-74913-4_120

“…Fig. 6D shows a different style of algorithmic behavior: a state machine (5,6). This state machine increments the number of green spikes between consecutive red spikes by 1 every time.…”

Section: Examplesmentioning

confidence: 99%

DNA as a universal substrate for chemical kinetics

Soloveichik

¹

,

Seelig

²

,

Winfree

³

2010

Proc. Natl. Acad. Sci. U.S.A.

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Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and ever-increasing complexity. A key goal is to develop embedded control circuitry within a chemical system to direct molecular events. Here we show that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions. By using strand displacement reactions as a primitive, we construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into real chemical systems. We illustrate our method on the Lotka-Volterra oscillator, a limit-cycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior. . Whereas the use of mass-action kinetics to describe existing chemical systems is well established, the inverse problem of experimentally implementing a given set of chemical reactions has not been considered in full generality. Here, we ask: Given a set of formal chemical reaction equations, involving formal species X 1 ; X 2 ; …; X n , can we find a set of actual molecules M 1 ; M 2 ; …; M m that interact in an appropriate buffer to approximate the formal system's mass-action kinetics? If this were possible, the formalism of chemical reaction networks (CRNs) could be treated as an effective programming language for the design of complex network behavior (5-9).Unfortunately, a formally expressed system of coupled chemical equations may not have an obvious realization in known chemistry. In a formal system of chemical reactions, a species may participate in multiple reactions, both as a reactant and/or as a product, and these reactions progress at relative rates determined by the corresponding rate constants, all of which imposes formidable constraints on the chemical properties of the species participating in the reactions. For example, it is likely hard to find a physical implementation of arbitrary chemical reaction equations using small molecules, because small molecules have a limited set of reactivities.Thus, formal CRNs may appear to be an unforgiving target for general implementation strategies. Indeed, most experimental work in chemical and biological engineering has started with particular molecular systems-genetic regulatory networks (10), RNA folding and processing (11), metabolic pathways (12), signal transduction pathways (13), cell-free enzyme systems (14, 15), and small molecules (16, 17)-and found ways to modify or rewire the components to achieve particular functions. Attempts to systematically understand what functional behaviors can be obtained by using such components have targeted connections to analog and digital electronic circuits (10,18,19), neural networks (20)(21)(22), and computing machines (...

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“…Here, we ask: Given a set of formal chemical reaction equations, involving formal species X 1 ; X 2 ; …; X n , can we find a set of actual molecules M 1 ; M 2 ; …; M m that interact in an appropriate buffer to approximate the formal system's mass-action kinetics? If this were possible, the formalism of chemical reaction networks (CRNs) could be treated as an effective programming language for the design of complex network behavior (5)(6)(7)(8)(9).…”

mentioning

confidence: 99%

DNA as a Universal Substrate for Chemical Kinetics

Soloveichik

¹

,

Seelig

²

,

Winfree

³

2009

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Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and ever-increasing complexity. A key goal is to develop embedded control circuitry within a chemical system to direct molecular events. Here we show that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions. By using strand displacement reactions as a primitive, we construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into real chemical systems. We illustrate our method on the Lotka-Volterra oscillator, a limit-cycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior. . Whereas the use of mass-action kinetics to describe existing chemical systems is well established, the inverse problem of experimentally implementing a given set of chemical reactions has not been considered in full generality. Here, we ask: Given a set of formal chemical reaction equations, involving formal species X 1 ; X 2 ; …; X n , can we find a set of actual molecules M 1 ; M 2 ; …; M m that interact in an appropriate buffer to approximate the formal system's mass-action kinetics? If this were possible, the formalism of chemical reaction networks (CRNs) could be treated as an effective programming language for the design of complex network behavior (5-9).Unfortunately, a formally expressed system of coupled chemical equations may not have an obvious realization in known chemistry. In a formal system of chemical reactions, a species may participate in multiple reactions, both as a reactant and/or as a product, and these reactions progress at relative rates determined by the corresponding rate constants, all of which imposes formidable constraints on the chemical properties of the species participating in the reactions. For example, it is likely hard to find a physical implementation of arbitrary chemical reaction equations using small molecules, because small molecules have a limited set of reactivities.Thus, formal CRNs may appear to be an unforgiving target for general implementation strategies. Indeed, most experimental work in chemical and biological engineering has started with particular molecular systems-genetic regulatory networks (10), RNA folding and processing (11), metabolic pathways (12), signal transduction pathways (13), cell-free enzyme systems (14, 15), and small molecules (16, 17)-and found ways to modify or rewire the components to achieve particular functions. Attempts to systematically understand what functional behaviors can be obtained by using such components have targeted connections to analog and digital electronic circuits (10,18,19), neural networks (20)(21)(22), and computing machines (...

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“…For instance, work by Liekens and Fernando (Liekens and Fernando 2007) shows how to approximate in a language of discrete chemistry finite computations of Register Machines with an error probability smaller than any given precision δ > 0. Soloveichik et al (Soloveichik et al 2008), besides proving that in notations for discrete chemistry it is not possible to precisely model any Turing powerful formalism, show also how to approximate unbounded computations.…”

Section: Resultsmentioning

confidence: 99%

Turing universality of the Biochemical Ground Form

Cardelli¹,

Zavattaro²

2010

Math. Struct. Comp. Sci.

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We explore the expressive power of languages that naturally model biochemical interactions with relative to languages that naturally model only basic chemical reactions, identifying molecular association as the basic mechanism that distinguishes the former from the latter. We use a process algebra, the Biochemical Ground Form (BGF), which extends with primitives for molecular association CGF, a process algebra proved to be equivalent to the traditional notations for describing basic chemical reactions. We first observe that, differently from CGF, BGF is Turing universal as it supports a finite precise encoding of Random Access Machines, a well-known Turing powerful formalism. Then we prove that the Turing universality of BGF derives from the interplay between the molecular primitives of association and dissociation. In fact, the elimination from BGF of the primitives already present in CGF does not reduce the computational strength of the process algebra, while if either association or dissociation is removed then BGF is no longer Turing complete.

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Turing Complete Catalytic Particle Computers

Cited by 18 publications

References 15 publications

DNA as a universal substrate for chemical kinetics

DNA as a universal substrate for chemical kinetics

DNA as a Universal Substrate for Chemical Kinetics

Turing universality of the Biochemical Ground Form

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