Dopamine-modulated medium spiny neuron, reduced model (Humphries et al. 2009)

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We extended Izhikevich's reduced model of the striatal medium spiny neuron (MSN) to account for dopaminergic modulation of its intrinsic ion channels and synaptic inputs. We tuned our D1 and D2 receptor MSN models using data from a recent (Moyer et al, 2007) large-scale compartmental model. Our new models capture the input-output relationships for both current injection and spiking input with remarkable accuracy, despite the order of magnitude decrease in system size. They also capture the paired pulse facilitation shown by MSNs. Our dopamine models predict that synaptic effects dominate intrinsic effects for all levels of D1 and D2 receptor activation. Our analytical work on these models predicts that the MSN is never bistable. Nonetheless, these MSN models can produce a spontaneously bimodal membrane potential similar to that recently observed in vitro following application of NMDA agonists. We demonstrate that this bimodality is created by modelling the agonist effects as slow, irregular and massive jumps in NMDA conductance and, rather than a form of bistability, is due to the voltage-dependent blockade of NMDA receptors
1 . Humphries MD, Lepora N, Wood R, Gurney K (2009) Capturing dopaminergic modulation and bimodal membrane behaviour of striatal medium spiny neurons in accurate, reduced models. Front Comput Neurosci 3:26 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Neostriatum medium spiny direct pathway GABA cell;
Gap Junctions:
Receptor(s): D1; D2; GabaA; AMPA; NMDA;
Transmitter(s): Dopamine;
Simulation Environment: MATLAB;
Model Concept(s): Action Potential Initiation; Parameter Fitting; Simplified Models; Parkinson's; Bifurcation;
Implementer(s): Humphries, Mark D [m.d.humphries at];
Search NeuronDB for information about:  Neostriatum medium spiny direct pathway GABA cell; D1; D2; GabaA; AMPA; NMDA; Dopamine;
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% effect of changing D1 on current injection response of tuned MSN

% found values
load fit_model_results_NEWtuning

% MS neuron parameters in saved file
k = izipars(1); a = izipars(2); b = izipars(3); c = izipars(4); vr = izipars(5); vpeak = izipars(6);

% found MS parameters: X = [C,vt,d]
C = X(1); vt =X(2); d = X(3);

% extra DA model parameters in saved file
KIR = XD1(1);    % KIR modifier 
LCA = XD1(2);    % LCA modifier

% parameters for this test
I = 200:5:400;
nInj = numel(I);

D1 = 0:0.2:1;

% simulation parameters
T = 5000; % duration of simulation (milliseconds)
dt = 0.1; % time step in ms

% init simulation 
t = 0:dt:T;
n = length(t); % number of time points
f_start = 1000/dt;
f_end = T/dt;
f_time = (f_end - f_start) * 1e-3 * dt;

%% f-I curves
fID1_DA = zeros(numel(D1),nInj);
fI1stD1_DA = zeros(numel(D1),nInj);
for j = 1:numel(D1)
    for loop = 1:nInj
        vD1 = vr*ones(1,n); uD1=0*vD1;
        vrD1 = vr*(1+D1(j)*KIR);
        dD1 = d*(1-D1(j)*LCA);
        for i = 1:n-1
            % D1 model
                vD1(i+1) = vD1(i) + dt*(k*(vD1(i)-vrD1)*(vD1(i)-vt)-uD1(i) + I(loop))/C;

                uD1(i+1) = uD1(i) + dt*a*(b*(vD1(i)-vrD1)-uD1(i));
                % spikes?   
                if vD1(i+1)>=vpeak
                    vD1(i)=vpeak; vD1(i+1)=c; 
        % firing rate at this frequency
        fID1_DA(j,loop) = sum(vD1(f_start:f_end) == vpeak) ./ f_time;
        temp = find(vD1 == vpeak); isis = diff(temp)*dt;
        if isis fI1stD1_DA(j,loop) = 1000./isis(1); else fI1stD1_DA(j,loop) = 0; end

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