The Evolution of Nervous Systems: From Nerve Nets to Tripartite Synapses - A Mathematical and Biophysical Analysis

The evolution of nervous systems represents one of the most remarkable achievements in biological complexity, spanning from simple nerve nets in early metazoans to the sophisticated neural architectures observed in contemporary organisms. This comprehensive review examines the evolutionary trajectory of nervous systems, beginning with the fundamental origins of neurons and progressing through the development of centralised neural networks. We explore the biophysical mechanisms underlying neuronal communication, including the establishment and maintenance of membrane potentials, the generation and propagation of action potentials, and the diverse forms of synaptic transmission. Particular attention is devoted to the mathematical frameworks that describe these processes, notably the Hodgkin-Huxley model and its derivatives, which provide quantitative insights into neural dynamics. The article further investigates the distinction between chemical and electrical synapses, their respective roles in neural computation, and their evolutionary significance. A central focus is placed upon the concept of the tripartite synapse, which incorporates glial cells as active participants in synaptic function, fundamentally altering our understanding of neural communication from a bipartite to a tripartite model. Through mathematical modelling and computational analysis, we demonstrate the functional implications of these evolutionary developments and their contribution to the remarkable diversity of neural processing capabilities observed across the animal kingdom. The findings presented herein illuminate the progressive sophistication of neural systems and provide a foundation for understanding the mechanistic basis of neurological function and dysfunction.