Mapping parameter spaces of biological switches
Abstract
Since the seminal 1961 paper of Monod and Jacob, mathematical models of biomolecular circuits have guided our understanding of cell regulation. Model-based exploration of the functional capabilities of any given circuit requires systematic mapping of multidimensional spaces of model parameters. Despite significant advances in computational dynamical systems approaches, this analysis remains a nontrivial task. Here, we use a nonlinear system of ordinary differential equations to model oocyte selection inDrosophila, a robust symmetry-breaking event that relies on autoregulatory localization of oocyte-specification factors. By applying an algorithmic approach that implements symbolic computation and topological methods, we enumerate all phase portraits of stable steady states in the limit when nonlinear regulatory interactions become discrete switches. Leveraging this initial exact partitioning and further using numerical exploration, we locate parameter regions that are dense in purely asymmetric steady states when the nonlinearities are not infinitely sharp, enabling systematic identification of parameter regions that correspond to robust oocyte selection. This framework can be generalized to map the full parameter spaces in a broad class of models involving biological switches.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 08, 2021
- Source ID
- 10.1371/journal.pcbi.1008711
Entities
People
- Jasmin Imran Alsous
- Justinn Barr
- Konstantin Mischaikow
- Lun Zhang
- Marcio Gameiro
- Paul Schedl
- Rocky Diegmiller
- Stanislav Y Shvartsman
Organizations
- Defense Advanced Research Projects Agency
- National Council for Scientific and Technological Development
- National Institutes of Health
- National Science Foundation
- São Paulo Research Foundation