A Nonlinear Delay Model for Metabolic Oscillations in Yeast Cells

Metabolic oscillations in yeast have been observed in laboratory settings, but the mechanisms driving these oscillations remain unclear. Prior research has shown that resource allocation plays a role in cellular metabolism, but the specific impact of shared resources on oscillatory behavior has not been fully explored. This gap motivated the development of models to test the hypothesis that limited ribosome availability affects metabolic dynamics. Existing models often assume constant resource availability, which may not reflect real cellular conditions. The study builds on previous work by incorporating time delays and variable resource constraints. Experimental data suggests that ribosome availability influences protein synthesis rates. However, no prior work had resolved how shared resources interact with time delays to produce oscillations. This paper introduces a new approach to model these interactions computationally.

The study aims to investigate how shared resources and time delays contribute to metabolic oscillations in yeast cells. The researchers propose a hypothesis that limited ribosome availability leads to oscillatory behavior through resource competition. They use time-delay models to simulate the dynamics of protein synthesis. The models incorporate a constraint on the total number of available ribosomes. The study compares single- and multi-protein systems to assess the impact of resource sharing. The researchers aim to identify parameter combinations that produce oscillations. Their approach includes numerical methods to detect and analyze these oscillations. The study seeks to provide insights into the mechanisms of metabolic regulation and resource allocation.

The researchers developed two time-delay models to simulate metabolic oscillations. The first model includes a single protein and a constraint on total ribosome availability. The second model extends this to three proteins sharing the same resource pool. They used a spectral element method to approximate the system as a discrete map. This method allowed them to evaluate the stability of the system's equilibria. The researchers then plotted amplitudes of simulation trajectories in 2D parameter space. They used a history function consistent with experimental data to generate oscillations. A boundary value problem was formulated to find approximate periodic solutions. The models were tested under constant delay conditions to detect oscillatory behavior.

The study found that specific combinations of total resource availability and time delay produce oscillations. The oscillation region in parameter space lies between regions with zero and constant production. The single-protein model showed that resource limits and delays interact to generate oscillations. The three-protein model revealed similar behavior when all proteins required the same production time. The researchers observed a shift in protein production rate peaks at low resource availability. This shift suggests the model captures shared resource dynamics. The spectral element method confirmed the presence of periodic solutions. The boundary value problem approach validated the oscillatory behavior in the models.

The authors conclude that shared resource limitations and time delays can lead to metabolic oscillations in yeast cells. Their models suggest that ribosome availability influences oscillatory behavior through resource competition. The study supports the hypothesis that limited resources contribute to oscillations. The results indicate that the oscillation region in parameter space is bounded by steady-state regions. The three-protein model showed similar behavior to the single-protein model. The shift in protein production peaks at low resource availability supports the model's validity. The researchers propose that the models capture key aspects of resource dynamics. Their findings suggest that time-delay models can help explain metabolic oscillations.