Mathematical Modeling of Early Embryonic Cell Cycles of Drosophila melanogaster

TL;DR

This paper presents a biochemical-mathematical model of early Drosophila embryonic cell cycles, analyzing oscillations and the impact of CycB synthesis on cycle timing.

Contribution

It introduces a biochemically sound mathematical model that captures cell cycle oscillations and explains cycle period changes through CycB synthesis dynamics.

Findings

Model exhibits oscillations in certain parameter regions.

CycB synthesis influences the period lengthening of cell cycles.

Time-dependent CycB synthesis reproduces experimental cycle timing data.

Abstract

In the early stages of development, Drosophila melanogaster embryos possess very fast and well-coordinated cell cycles. In the cell cycle, CDK activity is essentially regulated by binding CDK and CycB to form an active complex and by phosphorylating CDK via CDC25 and dephosphorylating it via Wee1. We develop a mathematical model for the embryonic cell cycle which is biochemically sound and which can be rigorously analysed after a model reduction. We show that there exists a region in the parameter space where the model describes oscillations. We then focus on the role of two parameters: the CycB synthesis and the activation coefficient of APC. Our main biological hypothesis is that the first one is responsible for the period lengthening over the first 14 cycles which can be experimentally observed and this hypothesis is supported by numerical simulations of our model: if the CycB synthesis is made time-dependent with a prescribed dynamics, then our simulations show qualitatively a very similar behavior to experimental data reported in the literature.