Results 1  10
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53
DNA as a universal substrate for chemical kinetics.
 Proc. Natl Acad. Sci. USA 107,
, 2010
"... Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and everincreasing 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 cons ..."
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Cited by 94 (21 self)
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Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and everincreasing 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 LotkaVolterra oscillator, a limitcycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior. . Whereas the use of massaction 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 massaction 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 (59). 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 systemsgenetic regulatory networks (10), RNA folding and processing (11), metabolic pathways (12), signal transduction pathways (13), cellfree 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 Here we propose a method for compiling an arbitrary CRN into nucleicacidbased chemistry. Given a formal specification of coupled chemical kinetics, we systematically design DNA molecules implementing an approximation of the system scaled to an appropriate temporal and concentration regime. Formal species are identified with certain DNA strands, whose interactions are mediated by a set of auxiliary DNA complexes. Nonconserving CRNs can be implemented because the auxiliary species implicitly supply energy and mass. Conveniently, the base sequence of nucleic acids can determine reactivity not only through direct hybridization of singlestranded species (29) but also through branch migration and strand displacement reaction pathways (3032). These powerful reaction primitives have been used previously for designing nucleicacidbased molecular machines with complex behaviors, such as motors, logic gates, and amplifiers (3337). Here we use these reaction mechanisms as the basis for the implementation of arbitrary CRNs. Our work advances a systematic approach that aims to provide a general mechanism for implementing a wellspecified class of behaviors. Molecular Primitive: Strand Displacement Cascades Because simple hybridization reactions cannot be cascaded, we use the more flexible strand displacement reaction as a molecular primitive. [We use "strand displacement" as a shorthand for toeholdmediated branch migration and strand displacement A preliminary version of this work appeared as ref. 52.
Programmable chemical controllers made from DNA
 Nature Nanotechnology
"... Biological organisms use complex molecular networks to navigate their environment and regulate their internal state. The development of synthetic systems with similar capabilities could lead to applications such as smart therapeutics or fabrication methods based on selforganization. To achieve this ..."
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Cited by 27 (16 self)
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Biological organisms use complex molecular networks to navigate their environment and regulate their internal state. The development of synthetic systems with similar capabilities could lead to applications such as smart therapeutics or fabrication methods based on selforganization. To achieve this, molecular control circuits need to be engineered to perform integrated sensing, computation and actuation. Here we report a DNAbased technology for implementing the computational core of such controllers. We use the formalism of chemical reaction networks as a ’programming language’ and our DNA architecture can, in principle, implement any behaviour that can be mathematically expressed as such. Unlike logic circuits, our formulation naturally allows complex signal processing of intrinsically analogue biological and chemical inputs. Controller components can be derived from biologically synthesized (plasmid) DNA, which reduces errors associated with chemically synthesized DNA. We implement several buildingblock reaction types and then combine them into a network that realizes, at the molecular level, an algorithm used in distributed control systems for achieving consensus between multiple agents. M olecular devices have captured the imagination of chemists and engineers for at least 30 years1. Rationally designed ‘active ’ molecules include nanoparticles for the targeted
Programmability of Chemical Reaction Networks
"... Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard c ..."
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Cited by 25 (6 self)
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Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and
Deterministic Function Computation with Chemical Reaction Networks ∗
"... We study the deterministic computation of functions on tuples of natural numbers by chemical reaction networks (CRNs). CRNs have been shown to be efficiently Turinguniversal when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, ..."
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Cited by 21 (13 self)
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We study the deterministic computation of functions on tuples of natural numbers by chemical reaction networks (CRNs). CRNs have been shown to be efficiently Turinguniversal when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semilinear predicates. We introduce the notion of function, rather than predicate, computation by representing the output of a function f: N k → N l by a count of some molecular species, i.e., if the CRN starts with n1,..., nk molecules of some “input ” species X1,..., Xk, the CRN is guaranteed to converge to having f(n1,..., nk) molecules of the “output ” species Y1,..., Yl. We show that a function f: N k → N l is deterministically computed by a CRN if and only if its graph {(x, y) ∈ N k × N l  f(x) = y} is a semilinear set. Finally, we show that each semilinear function f can be computed on input x in expected time O(polylog ‖x‖1). 1
Efficient Turinguniversal computation with DNA polymers (extended abstract)
"... Abstract. Bennett’s proposed chemical Turing machine is one of the most important thought experiments in the study of the thermodynamics of computation. Yet the sophistication of molecular engineering required to physically construct Bennett’s hypothetical polymer substrate and enzyme has deterred e ..."
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Cited by 20 (4 self)
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Abstract. Bennett’s proposed chemical Turing machine is one of the most important thought experiments in the study of the thermodynamics of computation. Yet the sophistication of molecular engineering required to physically construct Bennett’s hypothetical polymer substrate and enzyme has deterred experimental implementations. Here we propose a chemical implementation of stack machines — a Turinguniversal model of computation similar to Turing machines — using strand displacement cascades as the underlying chemical primitive. More specifically, the mechanism described herein is the addition and removal of monomers from the end of a polymer, controlled by strand displacement logic. We capture the motivating feature of Bennett’s scheme — that physical reversibility corresponds to logically reversible computation, and arbitrarily little energy per computation step is required. Further, as a method of embedding logic control into chemical and biological systems, polymerbased chemical computation is significantly more efficient than geometryfree chemical reaction networks. 1
Timing in chemical reaction networks
 In SODA 2014: Proceedings of the 25th Annual ACMSIAM Symposium on Discrete Algorithms
, 2014
"... Chemical reaction networks (CRNs) formally model chemistry in a wellmixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising programming language for the design of ..."
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Cited by 15 (7 self)
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Chemical reaction networks (CRNs) formally model chemistry in a wellmixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising programming language for the design of artificial molecular control circuitry. Due to a formal equivalence between CRNs and a model of distributed computing known as population protocols, results transfer readily between the two models. We show that if a CRN respects finite density (at most O(n) additional molecules can be produced from n initial molecules), then starting from any dense initial configuration (all molecular species initially present have initial count Ω(n), where n is the initial molecular count and volume), every producible species is produced in constant time with high probability. This implies that no CRN obeying the stated constraints can function as a timer, able to produce a molecule, but doing so only after a time that is an unbounded function of the input size. This has consequences regarding an open question of Angluin, Aspnes, and Eisenstat concerning the ability of population protocols to perform fast, reliable leader election and to simulate arbitrary algorithms from a uniform initial state.
Stochastic process semantics for dynamical grammar syntax: an overview. In:
 Ninth International Symposium on Artificial Intelligence and Mathematics,
, 2006
"... Abstract We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is formally mapped to semantics given in terms of a ring of operators ..."
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Cited by 13 (8 self)
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Abstract We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is formally mapped to semantics given in terms of a ring of operators, so that composition of grammars corresponds to operator addition or multiplication. The operators are generators for the timeevolution of stochastic processes. The dynamical evolution occurs in continuous time but is related to a corresponding discretetime dynamics. An expansion of the exponential of such timeevolution operators can be used to derive a variety of simulation algorithms. Within this modeling framework one can express data clustering models, logic programs, ordinary and stochastic differential equations, branching processes, graph grammars, and stochastic chemical reaction kinetics. The mathematical formulation connects these apparently distant fields to one another and to mathematical methods from quantum field theory and operator algebra. Such broad expressiveness makes the framework particularly suitable for applications in machine learning and multiscale scientific modeling.
Strand Algebras for DNA Computing
, 2009
"... We present a process algebra for DNA computing, discussing compilation of other formal systems into the algebra, and compilation of the algebra into DNA structures. ..."
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Cited by 12 (1 self)
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We present a process algebra for DNA computing, discussing compilation of other formal systems into the algebra, and compilation of the algebra into DNA structures.
Morphisms of reaction networks that couple structure to function
 BMC Systems Biology
"... Background: The mechanisms underlying complex biological systems are routinely represented as networks. Network kinetics is widely studied, and so is the connection between network structure and behavior. However, similarity of mechanism is better revealed by relationships between network structures ..."
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Cited by 12 (6 self)
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Background: The mechanisms underlying complex biological systems are routinely represented as networks. Network kinetics is widely studied, and so is the connection between network structure and behavior. However, similarity of mechanism is better revealed by relationships between network structures. Results: We define morphisms (mappings) between reaction networks that establish structural connections between them. Some morphisms imply kinetic similarity, and yet their properties can be checked statically on the structure of the networks. In particular we can determine statically that a complex network will emulate a simpler network: it will reproduce its kinetics for all corresponding choices of reaction rates and initial conditions. We use this property to relate the kinetics of many common biological networks of different sizes, also relating them to a fundamental population algorithm. Conclusions: Structural similarity between reaction networks can be revealed by network morphisms, elucidating mechanistic and functional aspects of complex networks in terms of simpler networks.
Termination problems in chemical kinetics
 of Lecture Notes in Computer Science
, 2008
"... Abstract. We consider nondeterministic and probabilistic termination problems in a process algebra that is equivalent to basic chemistry. We show that the existence of a terminating computation is decidable, but that termination with any probability strictly greater than zero is undecidable. Moreove ..."
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Cited by 10 (1 self)
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Abstract. We consider nondeterministic and probabilistic termination problems in a process algebra that is equivalent to basic chemistry. We show that the existence of a terminating computation is decidable, but that termination with any probability strictly greater than zero is undecidable. Moreover, we show that the fairness intrinsic in stochastic computations implies that termination of all computation paths is undecidable, while it is decidable in a nondeterministic framework. 1