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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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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
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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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
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 17 (11 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
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 16 (11 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
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 14 (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.
Negative Interactions in Irreversible SelfAssembly ∗
"... This paper explores the use of negative (i.e., repulsive) interactions in the abstract Tile Assembly Model defined by Winfree. Winfree in his Ph.D. thesis postulated negative interactions to be physically plausible, and Reif, Sahu, and Yin studied them in the context of reversible attachment operati ..."
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This paper explores the use of negative (i.e., repulsive) interactions in the abstract Tile Assembly Model defined by Winfree. Winfree in his Ph.D. thesis postulated negative interactions to be physically plausible, and Reif, Sahu, and Yin studied them in the context of reversible attachment operations. We investigate the power of negative interactions with irreversible attachments, and we achieve two main results. Our first result is an impossibility theorem: after t steps of assembly, Ω(t) tiles will be forever bound to an assembly, unable to detach. Thus negative glue strengths do not afford unlimited power to reuse tiles. Our second result is a positive one: we construct a set of tiles that can simulate an sspacebounded, ttimebounded Turing machine, while ensuring that no intermediate assembly grows larger than O(s), rather than O(s · t) as required by the standard Turing machine simulation with tiles. 1
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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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
Turing Universality of the Biochemical Ground Form
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2009
"... 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, ..."
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Cited by 6 (2 self)
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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 wellknown 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.
Strand Algebras for DNA Computing
"... 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. 1 ..."
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Cited by 6 (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. 1
RATEINDEPENDENT CONSTRUCTS FOR CHEMICAL COMPUTATION ∗
"... This paper presents a collection of computational modules implemented with chemical reactions: an inverter, an incrementer, a decrementer, a copier, a comparator, and a multiplier. Unlike previous schemes for chemical computation, ours produces designs that are dependent only on coarse rate categori ..."
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Cited by 5 (0 self)
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This paper presents a collection of computational modules implemented with chemical reactions: an inverter, an incrementer, a decrementer, a copier, a comparator, and a multiplier. Unlike previous schemes for chemical computation, ours produces designs that are dependent only on coarse rate categories for the reactions (“fast ” vs. “slow”). Given such categories, the computation is exact and independent of the specific reaction rates. We validate our designs through stochastic simulations of the chemical kinetics. Although conceptual for the time being, our methodology has potential applications in domains of synthetic biology such as biochemical sensing and drug delivery. We are exploring DNAbased computation via strand displacement as a possible experimental chassis.