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

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Accession:189344
" ...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. ..."
Reference:
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;
Gene(s):
Transmitter(s):
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;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Copyright: Marsa Taheri and Gregory Handy, 2016
% This code was used to simulate the mathematical model of Astrocyte 
% IP3-dependent Ca responses in 2 papers submitted in Nov 2016.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Finds the IP3 transient given the following parameters 
% d_rise is the time rising
% d_decay is the time spent decaying
% r_rise is rate of rise
% amp is the maximum IP3 level
% stim_time is the time of the stimulus
% t is the time vector
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [ ip_value ] = ip_function_TH(d_rise, d_decay, r_rise, amp, stim_time, t)

% calculate the max that will be achieved
s_0=amp/(1-exp(-r_rise*(d_rise)));

% calculate the needed r_deg for d_decay to be achieved 
% checks to make sure max_ip is at least 0.005
if amp>0.005
    r_deg=-1/d_decay*log(0.005/amp);
else
    r_deg=-1/d_decay*log(0.005);
end


% either calculate ip3 at a specific time or for a range of times
if length(t)==1
    if t<stim_time
        ip_value=0;
    elseif t>=stim_time && t <= (stim_time + d_rise)
        ip_value=s_0*(1-exp(-r_rise*(t-stim_time)));
    else
        ip_value=amp*exp(-r_deg*(t-stim_time-d_rise));
    end
else
    zeros(length(t),1);
    ip_value=zeros(length(t),1);
    temp=find(t>=stim_time & t <= (stim_time +d_rise));
    ip_value(temp)=s_0*(1-exp(-r_rise*(t(temp)-stim_time)));
    temp=find(t > (stim_time +d_rise));
    ip_value(temp)=amp*exp(-r_deg*(t(temp)-stim_time-d_rise));
end

end

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