A detailed algorithmic explanation is required for how a network of chemical reactions can generate the sophisticated behavior displayed by living cells. Though several previous works have shown that reaction networks are computationally universal and can in principle implement any algorithm, there is scope for constructions that map well onto biological reality, make efficient use of the computational potential of the native dynamics of reaction networks, and make contact with statistical mechanics. We describe a new reaction network scheme for solving a large class of statistical problems. Specifically we show how reaction networks can implement information projection, and consequently a generalized Expectation-Maximization algorithm, to solve maximum likelihood estimation problems in partially-observed exponential families on categorical data. Our scheme can be thought of as an algorithmic interpretation of E. T. Jaynes’s vision of statistical mechanics as statistical inference.
There is a rich history of theoretical and empirical results showing that reaction networks can perform computations @cite_36 @cite_21 @cite_31 @cite_24 @cite_32 @cite_15 @cite_18 @cite_11 @cite_37 @cite_1 . Typically these results take a known algorithm, and show how to implement it with chemical reaction networks. In contrast, we have obtained what appears to be a new algorithm within the broad class of generalized EM algorithms. Our algorithm is natural in the sense that it was suggested by the mathematical structure of reaction network dynamics itself, so that analysis of our scheme proceeds from insights about reaction network kinetics rather than from insights about the behavior of some existing classical algorithm.
@cite_18 @cite_37 @cite_15 @cite_36 @cite_21 @cite_1 @cite_32 @cite_24 @cite_31 @cite_11
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Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems of polynomial ordinary differential equations. The steady states of these mass action systems have been analyzed via a variety of techniques, including stoichiometric network analysis, deficiency theory, and algebraic techniques (e.g., Grobner bases). In this paper, we present a novel method for characterizing the steady states of mass action systems. Our method explicitly links a network’s capacity to permit a particular class of steady states, called toric steady states, to topological properties of a generalized network called a translated chemical reaction network. These networks share their reaction vectors with their source network but are permitted to have different complex stoichiometries and different network topologies. We apply the results to examples drawn from the biochemical literature. The discovery of chemical reactions is an inherently unpredictable and time-consuming process1. An attractive alternative is to predict reactivity, although relevant approaches, such as computer-aided reaction design, are still in their infancy2. Reaction prediction based on high-level quantum chemical methods is complex3, even for simple molecules. Although machine learning is powerful for data analysis4,5, its applications in chemistry are still being developed6. Inspired by strategies based on chemists’ intuition7, we propose that a reaction system controlled by a machine learning algorithm may be able to explore the space of chemical reactions quickly, especially if trained by an expert8. Here we present an organic synthesis robot that can perform chemical reactions and analysis faster than they can be performed manually, as well as predict the reactivity of possible reagent combinations after conducting a small number of experiments, thus effectively navigating chemical reaction space. By using machine learning for decision making, enabled by binary encoding of the chemical inputs, the reactions can be assessed in real time using nuclear magnetic resonance and infrared spectroscopy. The machine learning system was able to predict the reactivity of about 1,000 reaction combinations with accuracy greater than 80 per cent after considering the outcomes of slightly over 10 per cent of the dataset. This approach was also used to calculate the reactivity of published datasets. Further, by using real-time data from our robot, these predictions were followed up manually by a chemist, leading to the discovery of four reactions. Generating novel graph structures that optimize given objectives while obeying some given underlying rules is fundamental for chemistry, biology and social science research. This is especially important in the task of molecular graph generation, whose goal is to discover novel molecules with desired properties such as drug-likeness and synthetic accessibility, while obeying physical laws such as chemical valency. However, designing models to find molecules that optimize desired properties while incorporating highly complex and non-differentiable rules remains to be a challenging task. Here we propose Graph Convolutional Policy Network (GCPN), a general graph convolutional network based model for goal-directed graph generation through reinforcement learning. The model is trained to optimize domain-specific rewards and adversarial loss through policy gradient, and acts in an environment that incorporates domain-specific rules. Experimental results show that GCPN can achieve 61 improvement on chemical property optimization over state-of-the-art baselines while resembling known molecules, and achieve 184 improvement on the constrained property optimization task. In biological organisms, networks of chemical reactions control the processing of information in a cell. A general approach to study the behavior of these networks is to analyze common modules. Instead of this analytical approach to study signaling networks, we construct functional motifs from the bottom up. We formulate conceptual networks of biochemical reactions that implement elementary algebraic operations over the domain and range of positive real numbers. We discuss how the steady state behavior relates to algebraic functions, and study the stability of the networks' fixed points. The primitive networks are then combined in feed-forward networks, allowing us to compute a diverse range of algebraic functions, such as polynomials. With this systematic approach, we explore the range of mathematical functions that can be constructed with these networks.