Speaker
Description
For a biochemical reaction network, the sparsest steady-state relations (that is, steady-state relations involving fewest chemical complexes) reveal the most direct dependencies in the system, and are closely connected to robustness properties. We may ask, what are the sparsest steady-state relations obtainable from all possible linear combinations of the rate equations, and what features of the network structure explain and govern their complexity? It turns out that matroid theory provides a natural answer to this question through two dual perspectives. From an algorithmic side, we characterise all sparsest generators within the linear span of the rate equations through a procedure which — as it requires no assumption on kinetics — applies beyond the mass-action setting. The complementary structural perspective elucidates the ‘why’; the complexity of steady-state relations is controlled precisely by the interlinking pattern of network cycles, which may be studied in-depth using graph-theoretic and topological methods (particularly for large and complex networks with unknown kinetics). I will illustrate our analysis on several biological examples, including multisite phosphorylation, the EnvZ-OmpR signalling network, and the bifunctional enzyme system PFK-2/FBPase-2. This talk is based on joint work with R.P. Araujo and A. Mokhtar.
