Abstract
Methods from stochastic dynamical systems theory have been instrumental in understanding the behaviours of chemical reaction networks (CRNs) arising in natural systems. However, considerably less attention has been given to the inverse problem of synthesizing CRNs with a specified behaviour, which is important for the forward engineering of biological systems. Here, we present a method for generating discrete-state stochastic CRNs from functional specifications, which combines synthesis of reactions using satisfiability modulo theories and parameter optimization using Markov chain Monte Carlo. First, we identify candidate CRNs that have the possibility to produce correct computations for a given finite set of inputs. We then optimize the parameters of each CRN, using a combination of stochastic search techniques applied to the chemical master equation, to improve the probability of correct behaviour and rule out spurious solutions. In addition, we use techniques from continuous-time Markov chain theory to analyse the expected termination time for each CRN. We illustrate our approach by synthesizing CRNs for probabilistically computing majority, maximum and division, producing both known and previously unknown networks, including a novel CRN for probabilistically computing the maximum of two species. In future, synthesis techniques such as these could be used to automate the design of engineered biological circuits and chemical systems.
Highlights
A central goal of synthetic biology is to implement specified behaviours in biological systems
The method addresses problem 2.3, allowing us to search for Chemical reaction networks (CRNs) for which there exists a computation path that satisfies the set of path predicates ( problem 2.3(1)), optimize the rate parameters to maximize the probability that the behaviour is satisfied ( problem 2.3(1))
We presented a computational approach for the synthesis and parameter tuning of CRNs, given a specification of the system’s correctness
Summary
A central goal of synthetic biology is to implement specified behaviours in biological systems. Chemical reaction networks (CRNs) have been used extensively to model a broad range of biological systems, gene regulatory networks [1], synthetic logic circuits [2] and molecular programs built from DNA [3]. The computational power of CRNs has been extensively studied [6], and it has been shown that error-free stably computing CRNs [8] compute exactly the class of semi-linear functions [9,10]. Given the expressive power of CRNs and their direct correspondence to biological implementations, we sought to develop a methodology for synthesizing candidate CRNs that exhibit a specified behaviour
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