Inferring a nonlinear biochemical network model from a heterogeneous single-cell time course data

Yuki Shindo,Yohei Kondo,Yasushi Sako

doi:10.1038/s41598-018-25064-w

Yuki Shindo, Yohei Kondo + Show 1 more

Open Access

https://doi.org/10.1038/s41598-018-25064-w

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Abstract

Mathematical modeling and analysis of biochemical reaction networks are key routines in computational systems biology and biophysics; however, it remains difficult to choose the most valid model. Here, we propose a computational framework for data-driven and systematic inference of a nonlinear biochemical network model. The framework is based on the expectation-maximization algorithm combined with particle smoother and sparse regularization techniques. In this method, a “redundant” model consisting of an excessive number of nodes and regulatory paths is iteratively updated by eliminating unnecessary paths, resulting in an inference of the most likely model. Using artificial single-cell time-course data showing heterogeneous oscillatory behaviors, we demonstrated that this algorithm successfully inferred the true network without any prior knowledge of network topology or parameter values. Furthermore, we showed that both the regulatory paths among nodes and the optimal number of nodes in the network could be systematically determined. The method presented in this study provides a general framework for inferring a nonlinear biochemical network model from heterogeneous single-cell time-course data.

Highlights

A biochemical reaction network is a key concept in understanding how higher-order functions in the cell emerge from relatively simple individual elements, such as proteins and metabolites
Because the elemental reaction in our modeling is described by a Hill function commonly used to express various types of biochemical reactions, our method can be directly applied to a wide range of networks, including transcriptional control, signal transduction, and metabolic regulation
We focused on the fact that a regulatory path can be negligible when the association constant in the Hill function describing the path is equal to zero

Summary

Introduction

A biochemical reaction network is a key concept in understanding how higher-order functions in the cell emerge from relatively simple individual elements, such as proteins and metabolites. Mathematical analysis can help to eliminate the nonessential individuality of biological targets and identify core principles that govern the behaviors and function of the system in the cell. Recent advances in experimental methods have made available highly quantitative and time-resolved data at the single-cell level[29], thereby making it desirable for the framework to handle single-cell datasets To address these problems, we developed a method combining an expectation-maximization (EM) algorithm with a particle smoother and sparse regularization. We developed a method combining an expectation-maximization (EM) algorithm with a particle smoother and sparse regularization Using this method, we showed that an oscillatory network model can be systematically inferred based only on single-cell time-course data. We evaluated the performance of the method using artificial time-course data and showed that the algorithm accurately inferred the true network model in a data-driven manner

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