Computational Analysis of Ca²⁺ Oscillatory Bio-Signals: Two-Parameter Bifurcation Diagrams

Area of Science:

• Biophysics
• Computational Biology
• Nonlinear Dynamics

Background:

• Cytosolic calcium oscillations are crucial for cellular functions, regulated by complex nonlinear dynamics.
• Understanding the parameter space of these oscillatory systems is essential for deciphering cellular control mechanisms.
• Existing methods for analyzing nonlinear systems may not fully capture the intricate periodic behaviors.

Purpose of the Study:

• To develop and present two novel types of two-parameter bifurcation diagrams for cytosolic calcium nonlinear oscillatory systems.
• To differentiate between periodic and non-periodic (chaotic, unstable) steady-state solutions within the parameter space.
• To complement existing analytical tools for characterizing nonlinear dynamical systems.

Main Methods:

• Numerical solution of a nonlinear dynamical model for cytosolic calcium oscillations using an adaptive step-size solver.
• Generation of two-parameter bifurcation diagrams, including period-n oscillations and frequency distributions.
• Utilization of parallel computations for efficient verification of periodic dynamics across a dense parameter grid.

Main Results:

• Successfully generated two complementary types of bifurcation diagrams, visualizing periodic dynamics in specific parameter regions.
• Identified areas exhibiting periodic, chaotic, and unstable solutions, distinguishing them through a systematic identification process.
• Observed an unusual property where oscillation frequency can vary by several orders of magnitude within the parameter space.

Conclusions:

• The developed bifurcation diagrams provide valuable insights into the parameter-dependent dynamics of cytosolic calcium oscillations.
• These diagrams serve as a powerful tool for identifying and characterizing periodic behaviors in complex nonlinear systems.
• The findings contribute to a deeper understanding of cellular signaling and control mechanisms mediated by calcium dynamics.