Inferring reaction network structure from single-cell, multiplex data, using toric systems theory

• Published in: PLoS computational biology Vol. 15; no. 12; p. e1007311
• Main Authors: Wang, Shu, Lin, Jia-Ren, Sontag, Eduardo D., Sorger, Peter K.
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 01.12.2019; Public Library of Science (PLoS)
• Subjects: Biology; Biology and Life Sciences; Cell division; Cell fate; Chemical reactions; Computational Biology; Computer and Information Sciences; Computer Simulation; Covariance; Data acquisition; Data analysis; Dynamical systems; Experimental methods; Flow cytometry; Flow Cytometry - statistics & numerical data; Fluorescence; Gene Regulatory Networks; Immunofluorescence; Kinases; Kinetics; Laboratories; Linear Models; Localization; Mapping; Mathematical models; Medical schools; Metabolic Networks and Pathways; Models, Biological; Multiplexing; Organic chemistry; Pharmacology; Physical Sciences; Research and Analysis Methods; Single-Cell Analysis - statistics & numerical data; Statistical analysis; Statistical methods; Statistical models; Supervision; System theory; Systems Theory; United States > US; Massachusetts
• ISSN: 1553-7358; 1553-734X; 1553-7358
• DOI: 10.1371/journal.pcbi.1007311

The goal of many single-cell studies on eukaryotic cells is to gain insight into the biochemical reactions that control cell fate and state. In this paper we introduce the concept of Effective Stoichiometric Spaces (ESS) to guide the reconstruction of biochemical networks from multiplexed, fixed time-point, single-cell data. In contrast to methods based solely on statistical models of data, the ESS method leverages the power of the geometric theory of toric varieties to begin unraveling the structure of chemical reaction networks (CRN). This application of toric theory enables a data-driven mapping of covariance relationships in single-cell measurements into stoichiometric information, one in which each cell subpopulation has its associated ESS interpreted in terms of CRN theory. In the development of ESS we reframe certain aspects of the theory of CRN to better match data analysis. As an application of our approach we process cytomery- and image-based single-cell datasets and identify differences in cells treated with kinase inhibitors. Our approach is directly applicable to data acquired using readily accessible experimental methods such as Fluorescence Activated Cell Sorting (FACS) and multiplex immunofluorescence.