Neural Systems Under Change of Scale

Area of Science:

• Theoretical physics
• Computational neuroscience
• Complex systems analysis

Background:

• Dynamic Causal Modelling (DCM) traditionally characterizes system dynamics.
• Distinguishing between scalable and scale-free systems requires novel theoretical approaches.
• Understanding scale-invariant properties is crucial in various scientific domains.

Purpose of the Study:

• To develop a unified theoretical construct for characterizing scalable and scale-free systems within the DCM framework.
• To demonstrate the utility of this construct in empirical and simulated settings.
• To investigate the neural correlates of scale-free dynamics in the brain.

Main Methods:

• Derivation of a theoretical framework for system characterization.
• Simulation of planetary orbits to test scalability analysis.
• Application of the framework to calcium imaging data from murine cortex for scale-free analysis.
• Estimation of the dynamical critical exponent using renormalization group theory principles.

Main Results:

• Successfully recovered Kepler's third law from simulated planetary orbit timeseries, validating the scalable system analysis.
• Empirically estimated the dynamical critical exponent in a biological system (murine cortex).
• Observed distinct patterns of dynamical critical exponents in task-relevant vs. task-irrelevant cortical regions during different behavioral states.

Conclusions:

• The proposed theoretical construct effectively characterizes both scalable and scale-free dynamical systems.
• The methodology provides a novel approach for analyzing complex systems in physics and neuroscience.
• Findings suggest that scale-free dynamics in the cortex are modulated by task engagement and region specificity.