A bifurcation analysis of calcium buffering

Area of Science:

• Biophysics
• Mathematical Biology
• Calcium Signaling

Background:

• Mathematical models of calcium oscillations often use a rapid buffering approximation.
• This approximation assumes buffer reactions are much faster than other calcium fluxes.
• However, buffer reactions are not always rapid, necessitating investigation into slower buffer dynamics.

Purpose of the Study:

• To investigate the validity of the rapid buffering approximation for slower buffers in mathematical models of calcium oscillations.
• To determine if using this approximation for slower buffers introduces artifacts or alters the model's bifurcation structure.
• To identify parameter regions where the rapid buffering approximation, no buffering, or a transition zone is appropriate.

Main Methods:

• Simulated calcium oscillations using mathematical models with varying buffer reaction speeds.
• Compared model dynamics and bifurcation structures under rapid buffering approximation versus explicit buffering.
• Analyzed parameter spaces to delineate regions for different buffering assumptions.

Main Results:

• The rapid buffering approximation did not introduce qualitative differences in bifurcation structure or dynamics, even with slower buffers.
• Distinct regions of buffer parameters were identified where either the rapid buffering approximation or a no-buffering assumption is suitable.
• A small transition region exists where careful consideration of buffer modeling is required.

Conclusions:

• The rapid buffering approximation is robust for modeling calcium oscillations, even when buffer reactions are not significantly faster than other fluxes.
• Modelers can confidently use the rapid buffering approximation across a wide range of buffer parameters without introducing significant artifacts.
• Understanding distinct parameter regions aids in selecting the most appropriate buffering model for calcium oscillation studies.