Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations.

Area of Science:

• Computational Biology
• Mathematical Biology
• Systems Biology

Background:

• Boolean delay equations (BDEs) are established modeling tools in fields like climate dynamics.
• Previous applications of BDEs in biology were limited to molecular-level processes.
• Hormonal regulation, such as the bovine estrous cycle, involves complex oscillatory dynamics.

Purpose of the Study:

• To derive and present novel BDE models for hormonal oscillators.
• To adapt BDEs for modeling the bovine estrous cycle, extending their biological application.
• To validate the developed BDE models against established ordinary differential equation (ODE) models and experimental scenarios.

Main Methods:

• Derivation of two BDE models from an existing ODE model of the bovine estrous cycle.
• Simulation and comparison of BDE model outputs with ODE model trajectories.
• Numerical validation through parameter-induced switches in oscillatory patterns and simulation of hormonal administration.

Main Results:

• The derived BDE models successfully simulate the bovine estrous cycle dynamics.
• BDE models demonstrated accurate prediction of oscillatory pattern shifts upon parameter changes.
• Simulations of hormone administration using BDEs showed expected shifts in the estrous cycle timing.

Conclusions:

• The study presents the first BDE models for hormonal oscillators and drug administration.
• BDEs offer a viable framework for systematic modeling of complex biological oscillators.
• Further research is needed to address challenges in automatic parameter estimation for BDEs.