Synthesizing and tuning chemical reaction networks with specified behaviours

We consider how to generate chemical reaction networks (CRNs) from functional specifications. We propose a two-stage approach that combines synthesis by satisfiability modulo theories and Markov chain Monte Carlo based optimisation. First, we identify candidate CRNs that have the possibility to produce correct computations for a given finite set of inputs. We then optimise the reaction rates of each CRN using a combination of stochastic search techniques applied to the chemical master equation, simultaneously improving the of correct behaviour and ruling out spurious solutions. In addition, we use techniques from continuous time Markov chain theory to study the expected termination time for each CRN. We illustrate our approach by identifying CRNs for majority decision-making and division computation, which includes the identification of both known and unknown networks.Comment: 17 pages, 6 figures, appeared the proceedings of the 21st conference on DNA Computing and Molecular Programming, 201

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealisations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with MATLAB implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community

Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics

We show how to extend a recently proposed multi-level Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the system to a specified accuracy. The extension is non-trivial, exploiting a coupling of the requisite processes that is easy to simulate while providing a small variance for the estimator. Further, and in a stark departure from other implementations of multi-level Monte Carlo, we show how to produce an unbiased estimator that is significantly less computationally expensive than the usual unbiased estimator arising from exact algorithms in conjunction with crude Monte Carlo. We thereby dramatically improve, in a quantifiable manner, the basic computational complexity of current approaches that have many names and variants across the scientific literature, including the Bortz-Kalos-Lebowitz algorithm, discrete event simulation, dynamic Monte Carlo, kinetic Monte Carlo, the n-fold way, the next reaction method,the residence-time algorithm, the stochastic simulation algorithm, Gillespie's algorithm, and tau-leaping. The new algorithm applies generically, but we also give an example where the coupling idea alone, even without a multi-level discretization, can be used to improve efficiency by exploiting system structure. Stochastically modeled chemical reaction networks provide a very important application for this work. Hence, we use this context for our notation, terminology, natural scalings, and computational examples.Comment: Improved description of the constants in statement of Theorem