Abstract
The inner workings of a biological cell or a chemical reactor can be rationalized by the network of reactions, whose structure reveals the most important functional mechanisms. For complex systems, these reaction networks are not known a priori and cannot be efficiently computed with ab initio methods; therefore, an important goal is to estimate effective reaction networks from observations, such as time series of the main species. Reaction networks estimated with standard machine learning techniques such as least-squares regression may fit the observations but will typically contain spurious reactions. Here we extend the sparse identification of nonlinear dynamics (SINDy) method to vector-valued ansatz functions, each describing a particular reaction process. The resulting sparse tensor regression method "reactive SINDy" is able to estimate a parsimonious reaction network. We illustrate that a gene regulation network can be correctly estimated from observed time series.
Highlights
Mapping out the reaction networks behind biological processes, such as gene regulation in cancer [1], is paramount to understanding the mechanisms of life and disease
We formulate the problem as data-driven identification of a dynamical system, which renders the method consistent with and an extension of the framework of sparse identification of nonlinear dynamics (SINDy) [5]
We demonstrate the method by estimating the reactions of a gene-regulatory network from time series of concentrations of the involved molecules
Summary
Mapping out the reaction networks behind biological processes, such as gene regulation in cancer [1], is paramount to understanding the mechanisms of life and disease. The system’s “combinatorial control” in E. coli cells was quantitatively investigated in [22], in particular studying repression and activation effects These gene regulatory effects often appear in complex networks [35] and there exist databases resolving these for certain types of cells, e.g., E. coli cells [11] and yeast cells [23]. Another example where mapping the active reactions is important is that of chemical reactors [30], where understanding which reactions are accessible for a given set of educts and reaction conditions is important to design synthesis pathways [7, 20]. This formulation calls for a machine learning method that can infer the reaction network underlying the observation data
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