Capturing intracellular pH dynamics by coupling its molecular mechanisms within a fully tractable mathematical model

Area of Science:

• Cellular Biology
• Biophysics
• Mathematical Modeling

Background:

• Intracellular pH is a critical parameter for cellular function.
• Existing models often rely on heuristic approaches with limitations.
• Accurate modeling of intracellular pH is essential for understanding cellular regulation.

Purpose of the Study:

• To develop a fully tractable mathematical model for intracellular pH in eukaryotic cells.
• To couple kinetic equations of molecular mechanisms with cellular parameters.
• To provide analytical solutions for steady-state pH and pH regulation.

Main Methods:

• Coupling differential equations for slow processes with steady-state equations for fast reactions.
• Developing a novel algebraic method for integrating kinetic and steady-state equations.
• Creating a modular model structure for integrating additional mechanisms.

Main Results:

• The model accurately calculates intracellular pH, membrane potential, and cytosolic ionic composition.
• Achieved significant improvements over classical heuristic approaches.
• Established the first analytical solutions for steady-state pH and a reduced differential equation for pH regulation.
• Demonstrated consistency with extensive experimental data across various cell types.

Conclusions:

• The developed mathematical model offers a self-consistent and versatile tool for studying intracellular pH.
• Provides new mathematical insights into cellular regulatory phenomena.
• Represents a significant advancement in the quantitative understanding of cellular homeostasis.