Analytically tractable model of synaptic crowding explains emergent small-world structure and network dynamics.

Area of Science:

• Computational Neuroscience
• Systems Neuroscience
• Developmental Neuroscience

Background:

• Neural circuits require balancing local connection constraints with global integration needs.
• Understanding the principles governing neural wiring is crucial for deciphering brain function.

Purpose of the Study:

• To introduce a minimal wiring rule based on synaptic crowding to explain neural network organization.
• To analyze the consequences of this rule on network connectivity, structure, and dynamics.

Main Methods:

• Developed a single-parameter model based on synaptic crowding.
• Derived exact solutions for in-degree distribution and scaling laws.
• Analyzed connection length distributions and small-world network properties.
• Investigated the impact of network statistics on attractor dynamics.

Main Results:

• Synaptic crowding leads to logarithmic growth in mean connectivity and bounded variance, suggesting homeostatic regulation.
• The rule generates power-law distributed connection lengths and small-world networks when combined with spatial proximity and rewiring.
• Network degree statistics significantly influence attractor basin boundaries in dynamic models.

Conclusions:

• A minimal synaptic crowding rule can explain emergent macroscopic network organization and dynamics.
• This model links local developmental constraints to global network properties.
• The findings offer testable predictions for neural circuit development and function.