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Mathematical Models of Neuromodulation and Implications for Neurology and Psychiatry

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Computational Neurology and Psychiatry

Part of the book series: Springer Series in Bio-/Neuroinformatics ((SSBN,volume 6))

Abstract

We use mathematical modeling to study how the electrophysiology and the pharmacology of the brain affect each other and brain function. Necessarily, this involves understanding volume transmission by which neurons in a brain nucleus project to distant nuclei and change the local biochemistry there. Examples include the serotonergic projection from the dorsal raphe nucleus to the striatum and the dopaminergic projection from the substantial nigra pars compacta to the striatum. The serotonin concentration in the striatum affects dopamine release in the striatum through receptors on the dopamine terminals. The concept of volume transmission is discussed and other examples of volume transmission are given. We describe how we construct our mathematical models based on known physiology and biochemistry. We describe model results that show how autoreceptors buffer the serotonin system against genetic polymorphisms and we explain why the brain serotonin concentration depends on diet but the dopamine concentration does not. We discuss the traditional hypotheses about the mechanism of action of selective sserotonin reuptake inhibitors (SSRIs), and introduce a new hypothesis about the mechanisms of SSRIs. We explain why the serotonin system has a large effect on the efficacy of levodopa treatment for Parkinson’s disease and why dyskinesias occur as the disease progresses. Finally, we study various aspects of the homeostasis of dopamine in the striatum. Volume transmission raises many new, interesting questions for the mathematical neuroscience community.

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Acknowledgements

The authors would like to thank Professor Parry Hashemi for stimulating and useful discussions. This work was supported in part by NSF grant EF-1038593 (HFN, MCR), the Mathematical Biosciences Institute and the NSF under grant DMS-0931642 (JAB, MCR), and an NSF CAREER Award DMS-0956057 (JAB).

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  1. The Ohio State University, Columbus, Ohio, 43210, USA

    Janet A. Best

  2. Duke University, Durham, North Carolina, 27708, USA

    H. Frederik Nijhout & Michael C. Reed

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  1. Janet A. Best
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  2. H. Frederik Nijhout
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Correspondence to Janet A. Best .

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  1. Department of Physics, Kalamazoo College, Kalamazoo, Michigan, USA

    Péter Érdi

  2. School of Engineering, University of Lincoln, Lincoln, United Kingdom

    Basabdatta Sen Bhattacharya

  3. Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA

    Amy L. Cochran

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Best, J.A., Frederik Nijhout, H., Reed, M.C. (2017). Mathematical Models of Neuromodulation and Implications for Neurology and Psychiatry. In: Érdi, P., Sen Bhattacharya, B., Cochran, A. (eds) Computational Neurology and Psychiatry. Springer Series in Bio-/Neuroinformatics, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-49959-8_8

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