1. S. Wang, J.-R. Lin, E.D. Sontag, and P.K. Sorger. Inferring reaction network structure from single-cell, multiplex data, using toric systems theory. PLoS Computational Biology, 15:e1007311, 2019. [WWW] [PDF] Keyword(s): reaction networks, reaction networks, stoichiometry, complex balancing, toric varieties, systems biology. 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. This paper introduces the concept of effective stoichiometric space (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.

1. Eduardo D. Sontag. Dynamics of binding three independent ligands to a single scaffold, 2025. [WWW] Keyword(s): bispecific antibodies, synthetic biology, immunology, dCAs9, CRISPR, CRN, chemical reaction networks, complex balanced, detail balanced. Abstract:

   This note considers a system in which three ligands can independently bind to a scaffold. Such systems arise in diverse applications, including immunotherapy and synthetic biology. It is shown that there are unique steady states in each conservation class, and these are asymptotically stable. The dependency of the steady-state amount of fully bound complex, as a function of total scaffold, is analyzed as well.

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