How Xenopus laevis embryos replicate reliably: investigating the random-completion problem

TL;DR

This paper models DNA replication timing in Xenopus embryos, showing that stochastic origin activation with increasing initiation rate effectively ensures reliable completion within cell cycle constraints, aligning with experimental observations.

Contribution

The study introduces a phase transition-based model and extreme-value statistics to explain how stochastic origin activation controls replication timing, supporting the biological solution of increasing initiation rate.

Findings

Stochastic origin activation with increasing rate matches experimental replication times.

Spatial regularity in origin placement is not essential for timing control.

The model nearly optimizes the use of replicative proteins.

Abstract

DNA synthesis in \textit{Xenopus} frog embryos initiates stochastically in time at many sites (origins) along the chromosome. Stochastic initiation implies fluctuations in the time to complete and may lead to cell death if replication takes longer than the cell cycle time ($\approx 25$ min). Surprisingly, although the typical replication time is about 20 min, \textit{in vivo} experiments show that replication fails to complete only about 1 in 300 times. How is replication timing accurately controlled despite the stochasticity? Biologists have proposed two solutions to this "random-completion problem." The first solution uses randomly located origins but increases their rate of initiation as S phase proceeds, while the second uses regularly spaced origins. In this paper, we investigate the random-completion problem using a type of model first developed to describe the kinetics of first-order phase transitions. Using methods from the field of extreme-value statistics, we derive the distribution of replication-completion times for a finite genome. We then argue that the biologists' first solution to the problem is not only consistent with experiment but also nearly optimizes the use of replicative proteins. We also show that spatial regularity in origin placement does not alter significantly the distribution of replication times and, thus, is not needed for the control of replication timing.