2019/08/15 by Dimitri Loutchko, Loutchko, Dimitri
Biochemistry, Genetics and Molecular Biology · Engineering · #20M35 #Biological Physics (physics.bio-ph) #Cell Image Analysis Techniques #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #Molecular Networks (q-bio.MN) #Slime Mold and Myxomycetes Research
paper · pdf · doi:10.48550/arxiv.1908.05483
openalex publication_date 2019/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive coarse-graining operations through quotients of the algebra. Thereby, the class of model is retained and all possible coarse-graining operations are encoded in the lattice of congruences of the model. We analyze a class of algebraic models generated by the subsequent and simultaneous catalytic functions of chemicals within a reaction network. Our ansatz yields coarse-graining operations that cover the network with local functional patches and delete the information about the environment, and complementary operations that resolve only the large-scale functional structure of the network. Finally, we present a geometric interpretation of the algebraic models through an analogy with classical models on vector fields. We then use the geometric framework to show how a coarse-graining of the algebraic model naturally leads to a coarse-graining of the state-space. The framework developed here is aimed at the study of the functional structure of cellular reaction networks spanning a wide range of scales.