Pitchfork Bifurcation in a Coupled Cell System

Area of Science:

• Systems Biology
• Mathematical Biology
• Theoretical Biology

Background:

• Bifurcation theory explains biological phenomena like cell differentiation and pattern formation.
• Molecular networks with positive feedback and mutual repression drive cell type diversity.
• Existing studies often focus on intracellular bifurcations, neglecting intercellular interactions.

Purpose of the Study:

• To investigate how intercellular coupling affects bifurcation dynamics in an ensemble of cells.
• To compare bifurcation behavior in positively and negatively coupled cell networks.
• To explore the emergence of homogeneous and heterogeneous steady states in coupled cell systems.

Main Methods:

• Mathematical modeling of a ring of identical interacting cells.
• Analytical techniques to study bifurcation phenomena.
• Numerical simulations to explore system dynamics and steady states.

Main Results:

• Positively coupled cells can exhibit a supercritical pitchfork bifurcation, similar to single cells, leading to homogeneous states.
• Negatively coupled cells lose this homogeneous behavior and display more complex dynamics.
• Cell-cell coupling, regardless of sign, can induce heterogeneous steady states with distinct spatial patterns.

Conclusions:

• Intercellular coupling significantly alters bifurcation dynamics compared to isolated cells.
• Positive coupling can preserve single-cell bifurcation properties under specific conditions.
• Negative coupling and coupling in general can drive the system towards complex heterogeneous states and patterns.