Mathematical Modeling in Neuroscience: Neuronal Activity and Its Modulation by Astrocytes.

Vladimir Parpura,Manoj K Gottipati,Shivendra G Tewari

doi:10.3389/fnint.2016.00003

Abstract

Mathematical Modeling in Neuroscience: Neuronal Activity and Its Modulation by Astrocytes.

Highlights

Research in neuroscience has come a long way since it was first hypothesized, in the early twentieth century, that dynamic changes in ion permeability underlie an event termed as action potential (Bernstein, 1912)
Research along the same lines in the 1950s by Hodgkin and Huxley (1952) elucidated the dependence of action potential on the permeability of potassium and sodium ions— a theory achieved using quantitative analysis of potassium, sodium, and leak currents. They suggested that potassium and sodium conduits exist in distinct states during an action potential; this was at a time when the composition of excitable membrane was largely unknown
It is worth mentioning that the model described above involves only 897 ordinary differential equations, which is far less than the number of equations in a model accommodating all the neurons in the CA3CA1 region [estimated to be ∼20 × 106 (West and Gundersen, 1990)]; the amount of redundancy in the latter model could be overwhelming and pruning the less significant proteins would aide in generating a region specific or whole-brain simulation

Summary

Introduction

Research in neuroscience has come a long way since it was first hypothesized, in the early twentieth century, that dynamic changes in ion permeability underlie an event termed as action potential (Bernstein, 1912). It has been demonstrated that the astrocytes can: (1) facilitate or depress synaptic plasticity (De Pittà et al, 2015), (2) synchronize CA1 neuronal firing (Fellin et al, 2004), (3) modulate extracellular field potentials (Lee et al, 2014), (4) repair damaged synapses (Wade et al, 2012), Mathematical Modeling in Neuroscience and/or (5) initiate epileptic discharges (Reato et al, 2012; Tewari and Parpura, 2013).

Results

Conclusion