Computational Neuroscience – Biophysical Modeling of Neural Systems

Abstract

Only within the past few decades have we had the tools capable of probing the brain to search for the fundamental components of cognition. Modern numerical techniques coupled with the fabrication of precise electronics have allowed us to identify the very substrates of our own minds. The pioneering work of Hodgkin and Huxley provided us with the first biologically validated mathematical model describing the flow of ions across the membranes of giant squid axon. This model demonstrated the fundamental principles underlying how the electrochemical potential difference, maintained across the neuronal membrane, can serve as a medium for signal transmission. This early model has been expanded and improved to include elements not originally described through collaboration between biologists, computer scientists, physicists and mathematicians. Multi-disciplinary efforts are required to understand this system that spans multiple orders of magnitude and involves diverse cellular signaling cascades. The massive amount of data published concerning specific functionality within neural networks is currently one of the major challenges faced in neuroscience. The diverse and sometimes disparate data collected across many laboratories must be collated into the same framework before we can transition to a general theory explaining the brain. Since this broad field would typically be the subject of its own textbook, here we will focus on the fundamental physical relationships that can be used to understand biological processes in the brain.