Excess entropies reveal higher organization levels in developing neuron cultures

Multi-component systems often exhibit dynamics of a high degree of complexity, rendering it difficult to assess whether a proposed model’s description is adequate. For the multitude of systems that allow for a symbolic encoding, we provide a symbolic-dynamics based entropy measure that quantifies the degree of deviation obtained by a systems’s internal dynamics from random dynamics using identical average symbol probabilities. We apply this measure to several well-studied theoretical models and show its ability to characterize differences in internal dynamics, thus providing a means to accurately compare model and experiment. Data from neuronal cultures on a multi-electrode array chip validate the usefulness of our approach, revealing inadequacies of existing models and providing guidelines for their improvement. We propose our measure to be systematically used to develop future models and simulations.