Math Bio Seminar

Speaker: Adittya Chaudhuri, Indian Statistical Institute, Kolkata
Emergent Feedback Loops from Crosstalk in Directed Labeled Graphs
We study emergent feedback loops: loops that appear only when two signed directed graphs are glued along shared vertices, with neither graph containing them individually. Our motivation comes from crosstalk between cellular signalling pathways, which rarely operate in isolation. When distinct modules share components or cross-regulate, new feedback loops can emerge in the combined network, with significant consequences for sustained signalling, growth control, developmental patterning, and disease progression. We study feedback loops using a generalisation of graph homology with coefficients in a commutative monoid, and describe the emergence of new loops under composition of open graphs via a variant of the Mayer-Vietoris exact sequence in this setting. We quantify the degree of emergence of a feedback loop via a monoid-grading on the free category generated by graphs. This talk is based on my joint work with Prof. John C. Baez (University of California, Riverside, USA). The preprint of this work is available at https://arxiv.org/abs/2506.23375