2016/08/25 by Mitchell Eithun, Eithun, Mitchell, Anne Shiu +1
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Molecular Junctions and Nanostructures #Molecular Networks (q-bio.MN) #Origins and Evolution of Life #Protein Structure and Dynamics
paper · pdf · doi:10.48550/arxiv.1608.07259
openalex publication_date 2016/08/25 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Phosphorylation, the enzyme-mediated addition of a phosphate group to a\nmolecule, is a ubiquitous chemical mechanism in biology. Multisite\nphosphorylation, the addition of phosphate groups to multiple sites of a single\nmolecule, may be distributive or processive. Distributive systems can be\nbistable, while processive systems were recently shown to be globally stable.\nHowever, this global convergence result was proven only for a specific\nmechanism of processive phosphorylation/dephosphorylation (namely, all\ncatalytic reactions are reversible). Accordingly, we generalize this result to\nallow for processive phosphorylation networks in which each reaction may be\nirreversible, and also to account for possible product inhibition. We\naccomplish this by defining an all-encompassing processive network that\nencapsulates all of these schemes, and then appealing to recent results of\nMarcondes de Freitas, Wiuf, and Feliu that assert global convergence by way of\nmonontone systems theory and network/graph reductions (which correspond to\nremoval of intermediate complexes). Our results form a case study into the\nquestion of when global convergence is preserved when reactions and/or\nintermediate complexes are added to or removed from a network.\n