A model using a single astrocyte with calcium dynamics

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This script simulates an astrocyte with the model astrocyte_lr_1994, which implements the dynamics in the astrocyte based on [1], [2], and [3]. Recordings are made for two variables in the astrocyte, inositol 1,4,5-trisphosphate (IP3) and cytosolic calcium. The astrocyte is driven by a Poissonian spike train which induces the generation of IP3 in the astrocyte, which in turn influences the calcium dynamics in the astrocyte.

See Also

A tripartite interaction between two neurons and one astrocyte

References

[1]

Li, Y. X., & Rinzel, J. (1994). Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. Journal of theoretical Biology, 166(4), 461-473. DOI: https://doi.org/10.1006/jtbi.1994.1041

[2]

De Young, G. W., & Keizer, J. (1992). A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proceedings of the National Academy of Sciences, 89(20), 9895-9899. DOI: https://doi.org/10.1073/pnas.89.20.9895

[3]

Nadkarni, S., & Jung, P. (2003). Spontaneous oscillations of dressed neurons: a new mechanism for epilepsy?. Physical review letters, 91(26), 268101. DOI: https://doi.org/10.1103/PhysRevLett.91.268101

Import all necessary modules for simulation and plotting.

import matplotlib.pyplot as plt
import nest

Set parameters for the simulation.

# simulation time
sim_time = 60000
# astrocyte parameters
params_astro = {"IP3_0": 0.16}
# Poisson input for the astrocyte
poisson_rate = 1.0
poisson_weight = 0.1

Create astrocyte and devices and connect them.

astrocyte = nest.Create("astrocyte_lr_1994", params=params_astro)
ps_astro = nest.Create("poisson_generator", params={"rate": poisson_rate})
mm_astro = nest.Create("multimeter", params={"record_from": ["IP3", "Ca_astro"]})
nest.Connect(ps_astro, astrocyte, syn_spec={"weight": poisson_weight})
nest.Connect(mm_astro, astrocyte)

Run simulation and get results.

nest.Simulate(sim_time)
data = mm_astro.events

Create and show plots.

fig, axes = plt.subplots(2, 1, sharex=True, figsize=(6.4, 4.8), dpi=100)
axes[0].plot(data["times"], data["IP3"])
axes[1].plot(data["times"], data["Ca_astro"])
axes[0].set_ylabel(r"[IP$_{3}$] ($\mu$M)")
axes[1].set_ylabel(r"[Ca$^{2+}$] ($\mu$M)")
axes[1].set_xlabel("Time (ms)")
plt.tight_layout()
plt.show()
plt.close()