Message Passing Inference with Chemical Reaction Networks

Recent work on molecular programming has explored new possibilities for computational abstractions with biomolecules, including logic gates, neural networks, and linear systems. In the future such abstractions might enable nanoscale devices that can sense and control the world at a molecular scale. Just as in macroscale robotics, it is critical that such devices can learn about their environment and reason under uncertainty. At this small scale, systems are typically modeled as chemical reaction networks. In this work, we develop a procedure that can take arbitrary probabilistic graphical models, represented as factor graphs over discrete random variables, and compile them into chemical reaction networks that implement inference. In particular, we show that marginalization based on sum-product message passing can be implemented in terms of reactions between chemical species whose concentrations represent probabilities. We show algebraically that the steady state concentration of these species correspond to the marginal distributions of the random variables in the graph and validate the results in simulations. As with standard sum-product inference, this procedure yields exact results for tree-structured graphs, and approximate solutions for loopy graphs.Engineering and Applied SciencesOther Research Uni

Experimental Biological Protocols with Formal Semantics

Both experimental and computational biology is becoming increasingly automated. Laboratory experiments are now performed automatically on high-throughput machinery, while computational models are synthesized or inferred automatically from data. However, integration between automated tasks in the process of biological discovery is still lacking, largely due to incompatible or missing formal representations. While theories are expressed formally as computational models, existing languages for encoding and automating experimental protocols often lack formal semantics. This makes it challenging to extract novel understanding by identifying when theory and experimental evidence disagree due to errors in the models or the protocols used to validate them. To address this, we formalize the syntax of a core protocol language, which provides a unified description for the models of biochemical systems being experimented on, together with the discrete events representing the liquid-handling steps of biological protocols. We present both a deterministic and a stochastic semantics to this language, both defined in terms of hybrid processes. In particular, the stochastic semantics captures uncertainties in equipment tolerances, making it a suitable tool for both experimental and computational biologists. We illustrate how the proposed protocol language can be used for automated verification and synthesis of laboratory experiments on case studies from the fields of chemistry and molecular programming

Analysis of Reaction Network Systems Using Tropical Geometry

We discuss a novel analysis method for reaction network systems with polynomial or rational rate functions. This method is based on computing tropical equilibrations defined by the equality of at least two dominant monomials of opposite signs in the differential equations of each dynamic variable. In algebraic geometry, the tropical equilibration problem is tantamount to finding tropical prevarieties, that are finite intersections of tropical hypersurfaces. Tropical equilibrations with the same set of dominant monomials define a branch or equivalence class. Minimal branches are particularly interesting as they describe the simplest states of the reaction network. We provide a method to compute the number of minimal branches and to find representative tropical equilibrations for each branch.Comment: Proceedings Computer Algebra in Scientific Computing CASC 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