A mathematical model of evoked calcium dynamics in astrocytes (Handy et al 2017)

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" ...Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. ..."
1 . Handy G, Taheri M, White JA, Borisyuk A (2017) Mathematical investigation of IP3-dependent calcium dynamics in astrocytes. J Comput Neurosci 42:257-273 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Glia;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): Ca pump; I_SERCA; I Calcium;
Gap Junctions:
Receptor(s): IP3;
Simulation Environment: MATLAB; XPP;
Model Concept(s): Calcium dynamics; Oscillations; Bifurcation;
Implementer(s): Handy, Gregory [handy at math.utah.edu]; Taheri, Marsa ;
Search NeuronDB for information about:  IP3; I Calcium; I_SERCA; Ca pump;
# XPP code to recreate bifurcation diagrams
# Copyright: Marsa Taheri and Gregory Handy, 2016

# ODEs
c' = (j_ip3r(c)-j_serca(c)+j_leak(c)+(j_in-j_out-j_pmca+j_soc(c,c_t))*delta)
c_t' = ((j_in-j_out-j_pmca+j_soc(c,c_t))*delta)

aux ca_er=(c_t-c)*gamma

# Terms on ER
m_inf = ip/(ip+d_1)
n_inf(c) = c/(c+d_5)
h_inf(c) = q_2/(q_2+c)

q_2 = d_2 *(ip+d_1)/(ip+d_3)
tau_h(c) = 1/(a_2*(q_2+c))

j_ip3r(c) = v_ip3r*m_inf^3*n_inf(c)^3*h^3*((c_t-c)*gamma-c)

j_leak(c) = v_leak*((c_t-c)*gamma-c)

j_serca(c) = v_serca*c^1.75/(c^1.75+k_serca^1.75)

# Terms on plasma membrane
j_in = v_in
j_out = k_out*c

j_pmca=v_pmca*c^2/(k_pmca^2 + c^2)

j_soc(c,c_t) = v_soc*k_soc^4/(k_soc^4+((c_t-c)*gamma)^4)

# Initial Conditions
init c=0.0865415,h=0.6255124
init c_t=36.49084

param ip=0

param gamma=5.4054

# Leak for ER
param v_leak=0.002

# Leak across plasma membrane
param v_in=0.05, k_out=1.2

# IP3R Parameters
param v_ip3r=0.222
param d_1=.13,d_2=1.049,d_3=.9434,d_5=.08234
param a_2=0.04

# PMCA Terms
param v_pmca=10,k_pmca=2.5

# SOC Terms
param v_soc=1.57,k_soc=90

# SERCA Terms
param v_serca=0.9, k_serca=0.1

# Sneyd Parameter
param delta=0.2

@ ylo=0,ds=0.005,dsmin=0.001,dsmax=0.01,nmax=700,npr=700
@ autoymin=0,autoymax=.708,parmax=100,autoxmin=0,autoxmax=.5
@ total=1000,xhi=100,ylo=0,yhi=1.5,nmesh=100

@ bounds=1000


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