Neuroscience and Math


Due to unforeseen circumstances, our science advent has taken a bit of a break, but we’re back and ready to talk about the eleventh prompt, if and how math helps us in neuroscience.

Well, as a computational neuroscientist, my entire job is basically about math, physics, and programming. In general, to put it simply, computational neuroscience involves writing down equations which describe the behaviour of individual neurons or of groups of neurons, then solving them so we can understand the systems we’re studying.

Some examples of such models include:

  • the model of the action potential created by Hodgkin and Huxley. This was one of the first computational models and it not only contributed to establishing computational neuroscience as a research field, but it also led to numerous new experiments;
  • Hopfield networks (a type of recurrent neural networks capable of memory storage) as models of Hebbian plasticity (neurons that fire together, wire together). This contributed to our understanding of memory consolidation during sleep;
  • modelling how microscopic changes (increased self-inhibition of a type of neurons called pyramidal cells) lead to changes in the EEG of schizophrenic patients. Part of a new subfield called computational psychiatry, this model, together with similar approaches, aim to bridge the gap between microscopic changes in the brain and macroscopic neural and behavioural changes.

There are other math-intensive subfields of neuroscience, such as neuroengineering and neurorobotics. But, while some of the other subfields use less math, you still need at least a basic understanding of mathematical concepts.

Still, if you feel that you don’t have the “talent” for it, don’t let that discourage you. You can always learn math. As one of my computational neuroscience professors used to say: “you wouldn’t claim that you can’t do push-ups because your grandma couldn’t do push-ups. You’d just get on with your training. It’s the same with math.”

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Further reading

Adams, R. A., Pinotsis, D., Tsirlis, K., Unruh, L., Mahajan, A., Horas, A. M., … & Anticevic, A. (2022). Computational modeling of electroencephalography and functional magnetic resonance imaging paradigms indicates a consistent loss of pyramidal cell synaptic gain in schizophrenia. Biological psychiatry91(2), 202-215.

Häusser, M. (2000). The Hodgkin-Huxley theory of the action potential. Nature neuroscience3(11), 1165-1165.

Walker, R., & Russo, V. (2004). Memory consolidation and forgetting during sleep: A neural network model. Neural processing letters19(2), 147-156.

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