Reaction-diffusion systems for spatio-temporal intracellular protein networks: A beginner's guide with two examples

Area of Science:

• Biochemistry
• Systems Biology
• Computational Biology

Background:

• Protein spatio-temporal dynamics are crucial for cellular signaling pathways.
• Post-translational modifications significantly impact protein stability and activity.
• Existing models often simplify spatial aspects of cellular environments.

Purpose of the Study:

• To extend traditional kinetic models (Michaelis-Menten, Hill) into partial differential equations.
• To incorporate a more realistic spatial representation of the cell, including nucleus and cytoplasm.
• To model passive transport across the nuclear membrane using Kedem-Katchalsky conditions.

Main Methods:

• Developed a nonlinear partial differential equation framework for intracellular reactions.
• Modeled the cell as two compartments (nucleus, cytoplasm) separated by a nuclear membrane.
• Employed the semi-implicit Rothe method for solving the nonlinear partial differential equations.
• Utilized Kedem-Katchalsky boundary conditions to simulate species migration.

Main Results:

• Successfully extended ordinary differential equation models to partial differential equations for improved spatial accuracy.
• Demonstrated the model's capability to represent spatial oscillators.
• Illustrated the model with two examples: FRQ protein circadian rhythm and p53 protein dynamics post-DNA damage.

Conclusions:

• The developed partial differential equation framework provides a more realistic approach to modeling protein dynamics within cellular compartments.
• This enhanced modeling approach accurately captures complex spatio-temporal behaviors, including biological oscillations.
• The methodology is applicable to studying various signaling pathways and protein regulatory networks.