A Structural Approach to Identifying Indicator Species in Chemical Reaction Networks

Abstract: Cellular phenotypes display high diversity, reflecting the complex functional states of individual cells. While transcriptomics has traditionally been used to determine these states, recent advances in single-cell technologies are shifting interest toward more detailed classification via metabolomic phenotyping, which directly reflects cellular function. However, the large number of metabolites poses challenges for both measurement and computational clustering in the task of phenotypic classification. A fundamental question therefore arises: which subset of species suffices to represent the system's overall state?

This talk introduces a novel theory that, based solely on the structural information of chemical reaction networks, identifies indicator species—whose concentrations uniquely determine all others and thus distinguish multistable equilibria. An implementing algorithm is applied to biochemical pathway databases. Numerical experiments demonstrate that classification based solely on these indicator species matches or surpasses full-set accuracy, with superior robustness under measurement noise. These results provide a rigorous, topology-based foundation for selecting indicator species, advancing metabolic phenotyping and biomarker discovery.

chemical biologychemical kineticsalgebraic geometrydynamical systemsprobability

Audience: researchers in the topic

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Seminar on the Mathematics of Reaction Networks

Series comments: Subscription link: list.ku.dk/postorius/lists/morn.list.ku.dk/

This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs approximately every other week on Thursdays, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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