CNS*2020 Online

Alexey Martyushev, Erik De Schutter

The NEURON software remains the main neural physiology modeling tool for scientists. Its computational methods benefit from deterministic approximations of the cable equation solutions and 1-dimensional radial calcium diffusion in cylindrical neuron morphologies [1]. However, in real neurons ions diffuse in 3-dimensional volumes [2]and membrane channels get activated in a stochastic manner. Furthermore, NEURON does not suit to model nano-sized spine morphology. In contrast, the Stochastic Engine for Pathway Simulation (STEPS) uses fully stochastic 3-dimensional methods in tetrahedral morphologies that can provide realistic modeling of neurons at the nanoscale [3, 4].

In this work, we compare the modeling results between those two environments for the Purkinje cell model developed by Zang et al. [5]. This model considers a variety of calcium, potassium and sodium channels, and the resulting calcium concentrations affecting the membrane potential of a Purkinje cell. The results demonstrate that: (i) the used cylinder light microscopy morphology can not be identically transformed into a 3D mesh; (ii) the effect of stochastic channel activation determines the timing of membrane potential spikes; (iii) the kinetics of calcium activated potassium channels strongly depends on the specified sub-membrane volumes in both environments.

A further step in developing the model will be integration of a digital microscopy reconstruction of spines to the existing 3D tetrahedral mesh.

**References:**

1. Carnevale, N.T. and M.L. Hines, The NEURON Book. 2009: Cambridge University Press.

2. Anwar, H., et al., Dendritic diameters affect the spatial variability of intracellular calcium dynamics in computer models. Front Cell Neurosci, 2014. 8: p. 168.

3. Hepburn, I., et al., STEPS: efficient simulation of stochastic reaction-diffusion models in realistic morphologies. BMC Syst Biol, 2012. 6: p. 36.

4. Chen, W. and E. De Schutter, Time to Bring Single Neuron Modeling into 3D. Neuroinformatics, 2017. 15(1): p. 1-3.

5. Zang, Y., S. Dieudonne, and E. De Schutter, Voltage- and Branch-Specific Climbing Fiber Responses in Purkinje Cells. Cell Rep, 2018. 24(6): p. 1536-1549.