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

Abstract

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.

Data-driven network models for genetic circuits from time-series data with incomplete measurements

“…Given a desired network motif and a physical system, we need to use measurements of the system to determine if the actual, active network of the system matches the intended design. There have been many network reconstruction algorithms developed for natural and synthetic biological networks [24,[39][40][41][42][43][44][45]. Historically, the approach to discovering network interactions has involved direct perturbation of biochemical species or components in a network [41,45,46].…”

“…At the single-cell level, the reconstruction problem for biological networks introduces challenges of inferring nonlinear stochastic models from noisy data [44,48,49]. In [48], the authors show that by comparing average abundances, molecule lifetimes, covariances and magnitude of step, they can map pairwise interaction dynamics, even when the rest of the system is completely unspecified.…”

“…Furthermore, Hilfinger et al [49] showed that there are statistical invariants for certain kinds of network interactions, which can be used to evaluate and challenge existing hypotheses of stochastic gene interaction. More recently, Wang et al showed that effective stoichiometric spaces can be used to determine network structure from the covariances of single-cell multiplex data [44]. These studies show that it is possible to infer meaningful structural information about a genetic network, even when only a portion of the network states are observed and the data are fundamentally noisy.…”

Unsupervised logic-based mechanism inference for network-driven biological processes

“…A mechanistic understanding of dynamic cellular processes is at the core of multiple areas of research including molecular cell biology, physiology, biophysics, and bioengineering [1][2][3][4][5][6]. Although analytical tools have improved the breadth and depth with which intra-or extra-cellular biochemical processes are explored [7][8][9], the vast majority of available data is limited to experiments that probe cue-response relationships with a specified set of inputs and outputs.…”

Efficiently and Effectively Recognizing Toricity of Steady State Varieties

“…Based on the above-mentioned linear algebra condition, MESSI systems have been introduced in [54]. Recently, binomiality of steady state ideals was used to infer network structure of chemical reaction networks out of measurement data [67].…”