[Paper Review] A globally attractive cycle driven by sequential bifurcations containing ghost effects in a 3-node yeast cell cycle model

Fangting Li, Mingyang Hu+4 more|arXiv (Cornell University)|Dec 18, 2013

Gene Regulatory Network Analysis30 references4 citations

TL;DR

This study proposes a 3-node simplified model of the budding yeast cell cycle that exhibits global robustness and sequential phase transitions driven by saddle-node bifurcations with 'ghost effects.' The ghost effect prolongs event durations and enables modularity in state and parameter space, ensuring stable, irreversible progression through DNA replication and mitosis despite perturbations.

ABSTRACT

Yeast cells produce daughter cells through a DNA replication and mitosis cycle associated with checkpoints and governed by the cell cycle regulatory network. To ensure genome stability and genetic information inheritance, this regulatory network must be dynamically robust against various fluctuations. Here we construct a simplified cell cycle model for a budding yeast to investigate the underlying mechanism that ensures robustness in this process containing sequential tasks (DNA replication and mitosis). We first establish a three-variable model and select a parameter set that qualitatively describes the yeast cell cycle process. Then, through nonlinear dynamic analysis, we demonstrate that the yeast cell cycle process is an excitable system driven by a sequence of saddle-node bifurcations with ghost effects. We further show that the yeast cell cycle trajectory is globally attractive with modularity in both state and parameter space, while the convergent manifold provides a suitable control state for cell cycle checkpoints. These results not only highlight a regulatory mechanism for executing successive cell cycle processes, but also provide a possible strategy for the synthetic network design of sequential-task processes.

Motivation & Objective

• To understand the dynamic mechanisms enabling robust, sequential execution of DNA replication and mitosis in the yeast cell cycle.
• To investigate how regulatory networks maintain stability against intrinsic fluctuations and parameter variations.
• To explore the role of cell cycle checkpoints from a dynamical systems perspective.
• To identify design principles for synthetic networks that execute sequential biological tasks reliably.

Proposed method

• A coarse-grained 3-variable dynamical model is constructed to represent key regulators in the budding yeast cell cycle (G1/S, early M, late M phases).
• Nonlinear dynamic analysis is applied to identify saddle-node bifurcations and their associated ghost effects during phase transitions.
• Perturbation methods are used to analyze the local manifold structure along the cell cycle trajectory.
• The model is tested for global attractivity by simulating trajectories from diverse initial conditions.
• Parameter space modularity is assessed by decoupling kinetic parameters across different phases.
• The convergent manifold is mapped to identify potential checkpoint control points.

Experimental results

Research questions

• RQ1 How does the yeast cell cycle ensure reliable, irreversible progression through sequential phases like DNA replication and mitosis?
• RQ2 What dynamical mechanisms underlie the robustness of the cell cycle against parameter fluctuations and noise?
• RQ3 How do cell cycle checkpoints emerge from the underlying nonlinear dynamics of the regulatory network?
• RQ4 To what extent do ghost effects in saddle-node bifurcations contribute to event duration and modularity?
• RQ5 Can the wave transition 'domino' model be generalized as a design principle for synthetic sequential-task networks?

Key findings

• The yeast cell cycle is an excitable system driven by sequential saddle-node bifurcations with ghost effects, which prolong the duration of each phase.
• The system exhibits global attractivity, meaning all initial conditions converge to the same limit cycle trajectory.
• The convergent manifold along the trajectory corresponds to the functional state of cell cycle checkpoints.
• Modularity in both state and parameter space ensures that small changes in one phase do not disrupt the overall cycle dynamics.
• The wave transition 'domino' model explains how successive events are robustly controlled via feedback-driven bifurcations.
• The ghost effect provides a sufficient mechanism for long event durations and dynamic decoupling between phases.