Evolving Chemical Reaction Networks

International audienceOne goal of synthetic biology is to implement useful functions with biochemical reactions, either by reprogramming living cells or programming artificial vesicles. In this perspective, we consider Chemical Reaction Networks (CRNs) as a programming language. Recent work has shown that continuous CRNs with their dynamics described by ordinary differential equations are Turing complete. That means that any function over the reals that is computable by a Turing machine in arbitrary precision, can be computed by a CRN over a finite set of molecular species. The proof uses an algorithm which, given a computable function presented as the solution of a PIVP (Polynomial Initial Values Problem), generates a finite CRN to implement it. In the generated CRNs, the molecular concentrations play the role of information carriers, similarly to proteins in cells. In this Master’s Thesis, we investigate an approach based on an evolutionary algorithm to build a continuous CRN that approximates a real function given a finite set of the values of the function. The idea is to use a two-level parallel genetic algorithm. A first algorithm is used to evolve the structure of the network, while the other one enables us to optimize the parameters of the CRNs at each step. We compare the CRNs generated by our method on different functions. The CRNs found by evolution often give good results with quite unexpected solutions

Graphical Conditions for Rate Independence in Chemical Reaction Networks

Chemical Reaction Networks (CRNs) provide a useful abstraction of molecular interaction networks in which molecular structures as well as mass conservation principles are abstracted away to focus on the main dynamical properties of the network structure. In their interpretation by ordinary differential equations, we say that a CRN with distinguished input and output species computes a positive real function $f : R+$\rightarrow$R+$, if for any initial concentration x of the input species, the concentration of the output molecular species stabilizes at concentration f (x). The Turing-completeness of that notion of chemical analog computation has been established by proving that any computable real function can be computed by a CRN over a finite set of molecular species. Rate-independent CRNs form a restricted class of CRNs of high practical value since they enjoy a form of absolute robustness in the sense that the result is completely independent of the reaction rates and depends solely on the input concentrations. The functions computed by rate-independent CRNs have been characterized mathematically as the set of piecewise linear functions from input species. However, this does not provide a mean to decide whether a given CRN is rate-independent. In this paper, we provide graphical conditions on the Petri Net structure of a CRN which entail the rate-independence property either for all species or for some output species. We show that in the curated part of the Biomodels repository, among the 590 reaction models tested, 2 reaction graphs were found to satisfy our rate-independence conditions for all species, 94 for some output species, among which 29 for some non-trivial output species. Our graphical conditions are based on a non-standard use of the Petri net notions of place-invariants and siphons which are computed by constraint programming techniques for efficiency reasons

Graphical Conditions for Rate Independence in Chemical Reaction Networks

International audienceChemical Reaction Networks (CRNs) provide a useful abstraction of molecular interaction networks in which molecular structures as well as mass conservation principles are abstracted away to focus on the main dynamical properties of the network structure. In their interpretation by ordinary differential equations, we say that a CRN with distinguished input and output species computes a positive real function $f : R+ → R+$, if for any initial concentration x of the input species, the concentration of the output molecular species stabilizes at concentration f (x). The Turing-completeness of that notion of chemical analog computation has been established by proving that any computable real function can be computed by a CRN over a finite set of molecular species. Rate-independent CRNs form a restricted class of CRNs of high practical value since they enjoy a form of absolute robustness in the sense that the result is completely independent of the reaction rates and depends solely on the input concentrations. The functions computed by rate-independent CRNs have been characterized mathematically as the set of piecewise linear functions from input species. However, this does not provide a mean to decide whether a given CRN is rate-independent. In this paper, we provide graphical conditions on the Petri Net structure of a CRN which entail the rate-independence property either for all species or for some output species. We show that in the curated part of the Biomodels repository, among the 590 reaction models tested, 2 reaction graphs were found to satisfy our rate-independence conditions for all species, 94 for some output species, among which 29 for some non-trivial output species. Our graphical conditions are based on a non-standard use of the Petri net notions of place-invariants and siphons which are computed by constraint programming techniques for efficiency reasons

Utveckling av kemiska reaktionsnätverk

One goal of synthetic biology is to implement useful functions with biochemical reactions, either by reprogramming living cells or programming artificial vesicles. In this perspective, we consider Chemical Reaction Networks (CRNs) as a programming language. Recent work has shown that continuous CRNs with their dynamics described by ordinary differential equations are Turing complete. That means that any function over the reals that is computable by a Turing machine in arbitrary precision, can be computed by a CRN over a finite set of molecular species. The proof uses an algorithm which, given a computable function presented as the solution of a PIVP (PolynomialInitial Values Problem), generates a finite CRN to implement it. In the generated CRNs, the molecular concentrations play the role of information carriers, similarly to proteins in cells. In this Master’s Thesis, we investigate an approach based on an evolutionary algorithm to build a continuous CRN that approximates a real function given a finite set of the values of the function. The idea is to use a two-level parallel genetic algorithm. A first algorithm is used to evolve the structure of the network, while the other one enables us to optimize the parameters of the CRNs at each step. We compare the CRNs generated by our method on different functions. The CRNs found by evolution often give good results with quite unexpected solutions.Ett mål med syntetisk biologi är att genomföra användbara funktioner med biokemiska reaktioner, antingen genom omprogrammering av levande celler eller programmering av artificiella vesiklar. I detta perspektiv anser vi Chemical Reaction Networks (CRNs) som ett programmeringsspråk. Det senaste arbetet har visat att kontinuerliga CRNs med dynamik som beskrivs av vanliga differentialekvationer är Turingkompletta. Det betyder att en funktion över de realla talen som kan beräknas av en Turing-maskin i godtycklig precision, kan beräknas av en CRN över en ändlig uppsättning molekylära arter. Beviset använder en algoritm som, givet en beräkningsbar funktion som presenteras som lösningen av ett PIVP (Polynomial Initial Values Problem), genererar en ändlig CRN för att implementera den. I de genererade CRN:erna spelar molekylkoncentrationerna rollen som informationsbärare, på samma sätt som proteiner i celler. I detta examensarbete undersöker vi ett tillvägagångssätt baserat på en evolutionär algoritm för att bygga en kontinuerlig CRN som approximerar en verklig funktion med en ändlig uppsättning av värden för funktionen. Tanken är att använda parallell genetisk algoritm i två nivåer. En första algoritm används för att utveckla nätets struktur, medan den andra möjliggör att optimera parametrarna för CRN:erna vid varje steg. Vi jämför de CRN som genereras av vår metod på olika funktioner. De CRN som hittas av evolutionen ger ofta bra resultat med ganska oväntade lösningar

Utveckling av kemiska reaktionsnätverk

One goal of synthetic biology is to implement useful functions with biochemical reactions, either by reprogramming living cells or programming artificial vesicles. In this perspective, we consider Chemical Reaction Networks (CRNs) as a programming language. Recent work has shown that continuous CRNs with their dynamics described by ordinary differential equations are Turing complete. That means that any function over the reals that is computable by a Turing machine in arbitrary precision, can be computed by a CRN over a finite set of molecular species. The proof uses an algorithm which, given a computable function presented as the solution of a PIVP (PolynomialInitial Values Problem), generates a finite CRN to implement it. In the generated CRNs, the molecular concentrations play the role of information carriers, similarly to proteins in cells. In this Master’s Thesis, we investigate an approach based on an evolutionary algorithm to build a continuous CRN that approximates a real function given a finite set of the values of the function. The idea is to use a two-level parallel genetic algorithm. A first algorithm is used to evolve the structure of the network, while the other one enables us to optimize the parameters of the CRNs at each step. We compare the CRNs generated by our method on different functions. The CRNs found by evolution often give good results with quite unexpected solutions.Ett mål med syntetisk biologi är att genomföra användbara funktioner med biokemiska reaktioner, antingen genom omprogrammering av levande celler eller programmering av artificiella vesiklar. I detta perspektiv anser vi Chemical Reaction Networks (CRNs) som ett programmeringsspråk. Det senaste arbetet har visat att kontinuerliga CRNs med dynamik som beskrivs av vanliga differentialekvationer är Turingkompletta. Det betyder att en funktion över de realla talen som kan beräknas av en Turing-maskin i godtycklig precision, kan beräknas av en CRN över en ändlig uppsättning molekylära arter. Beviset använder en algoritm som, givet en beräkningsbar funktion som presenteras som lösningen av ett PIVP (Polynomial Initial Values Problem), genererar en ändlig CRN för att implementera den. I de genererade CRN:erna spelar molekylkoncentrationerna rollen som informationsbärare, på samma sätt som proteiner i celler. I detta examensarbete undersöker vi ett tillvägagångssätt baserat på en evolutionär algoritm för att bygga en kontinuerlig CRN som approximerar en verklig funktion med en ändlig uppsättning av värden för funktionen. Tanken är att använda parallell genetisk algoritm i två nivåer. En första algoritm används för att utveckla nätets struktur, medan den andra möjliggör att optimera parametrarna för CRN:erna vid varje steg. Vi jämför de CRN som genereras av vår metod på olika funktioner. De CRN som hittas av evolutionen ger ofta bra resultat med ganska oväntade lösningar

On Chemical Reaction Network Design by a Nested Evolution Algorithm

International audienceOne goal of synthetic biology is to implement useful functions with biochemical reactions, either by reprogramming living cells or programming artificial vesicles. In this perspective, we consider Chemical Reaction Networks (CRN) as a programming language, and investigate the CRN program synthesis problem. Recent work has shown that CRN interpreted by differential equations are Turing-complete and can be seen as analog computers where the molecular concentrations play the role of information carriers. Any real function that is computable by a Turing machine in arbitrary precision can thus be computed by a CRN over a finite set of molecular species. The proof of this result gives a numerical method to generate a finite CRN for implementing a real function presented as the solution of a Polynomial Initial Values Problem (PIVP). In this paper, we study an alternative method based on artificial evolution to build a CRN that approximates a real function given on finite sets of input values. We present a nested search algorithm that evolves the structure of the CRN and optimizes the kinetic parameters at each generation. We evaluate this algorithm on the Heaviside and Cosine functions both as functions of time and functions of input molecular species. We then compare the CRN obtained by artificial evolution both to the CRN generated by the numerical method from a PIVP definition of the function, and to the natural CRN found in the BioModels repository for switches and oscillators