Mapping parameter spaces of biological switches.

Rocky Diegmiller,Konstantin Mischaikow,Lun Zhang,Marcio Gameiro,Jasmin Imran Alsous,Stanislav Y Shvartsman,Justinn Barr,Paul Schedl,Stacey Finley

doi:10.1371/journal.pcbi.1008711

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 in Drosophila, 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.

Highlights

Clusters of cells interconnected by stable cytoplasmic bridges serve important functions in existing species and are thought to have played a role in the emergence of multicellularity [1]
Identification of qualitatively different regimes in models of biomolecular switches is essential for understanding dynamics of complex biological processes, including symmetry breaking in cells and cell networks
A notable example wherein such cysts arise is animal oogenesis, which includes an obligate stage where the future oocyte develops while connected to auxiliary cells that supply it with molecules and organelles [2,3,4,5,6,7,8]

Summary

Introduction

Clusters of cells interconnected by stable cytoplasmic bridges serve important functions in existing species and are thought to have played a role in the emergence of multicellularity [1]. The developmental unit of Drosophila oogenesis is the egg chamber—a 16-cell germline cyst surrounded by a somatically derived epithelium [3]. This cyst arises from a single stem cell-derived cystoblast (Fig 1A) that undergoes four synchronous divisions, generating the stereotypical network of cells shown in Fig 1B [9]. These divisions are incomplete, leaving cells interconnected by reinforced cytoplasmic bridges called ring canals [10, 11] that allow for transport of proteins, mRNA, and cytoplasmic components between cells. The 15 remaining cells become nurse cells, supplying the oocyte with components required for its growth and development [12]

Methods

Results

Discussion

Conclusion