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

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Accession:128818
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
Reference:
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;
Channel(s):
Gap Junctions:
Receptor(s): D1; D2; GabaA; AMPA; NMDA;
Gene(s):
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 shef.ac.uk];
Search NeuronDB for information about:  Neostriatum medium spiny direct pathway GABA cell; D1; D2; GabaA; AMPA; NMDA; Dopamine;
%%%% script to illustrate exactly what happens during bimodal "jumps"
%%%% induced by large NMDA conductance fluctuations
%%%% Mark Humphries 23/9/2009

clear all

% found values
load fit_model_results_NEWtuning

rand('state',1); randn('state',1);
% -------------------------------------------------------------------------
% Input parameters
% spike-train parameters: start from 500 events/s
% step to range of spike events/s
N_nmda = 84; alpha_nmda = 0;
N_ampa = 84; alpha_ampa = 0;
N_gaba = 84; alpha_gaba = 0; 

%%% the parameter values for the example histogram/spike-trains (though
%%% this spike-train will be different of course]
mNMDA = 100;
r_nmda = 4; 
r_ampa = 4;
r_gaba = 4;

%% or on a huge scale
% mNMDA = 1;
% N_nmda = 10000;
% r_nmda = 1;

% dopamine levels
D1 = 0;
D2 = 0;

% -------------------------------------------------------------------------
% all PSP parameters in saved file
Egaba = -60; 
Enmda = 0;
Eampa = 0;

% these should stay in the same ratio
PSPampa = Xsyn; %% loaded from file...
PSPnmda = PSPampa / ampa_nmda; PSPgaba = PSPampa ./ ampa_gaba;

% 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
vrD1 = vr*(1+D1*KIR);
dD1 = d*(1-D1*LCA);

% D2 - intrinsic
alpha = XD2;
kD2 = k*(1-alpha*D2);

% synaptic
cD1 = Xd1all;
cD2 = Xd2all;

% simulation parameters
T = 1000; % max duration of simulation (milliseconds)
dt = 0.1; % time step 

% init simulation 
t = 0:dt:T;
n = length(t); % number of time points
SynExp_ampa = exp(-dt / ts_ampa);
SynExp_nmda = exp(-dt / ts_nmda);
SynExp_gaba = exp(-dt / ts_gaba);


% scale NMDA conductance
PSPnmda = mNMDA * PSPampa / ampa_nmda;

Ggaba = zeros(1,n); Gampa = zeros(1,n);Gnmda = zeros(1,n);
Igaba = zeros(1,n); Iampa = zeros(1,n); Inmda = zeros(1,n);
BD1all_nmda = zeros(1,n);
vD1all = vr*ones(1,n); uD1all=0*v;

% generate the spike trains
Sampa = spkgen([0:dt:T], N_ampa, r_ampa, alpha_ampa);
Snmda = spkgen([0:dt:T], N_nmda, r_nmda, alpha_nmda);
Sgaba = spkgen([0:dt:T], N_gaba, r_gaba, alpha_gaba);       
S = sum(Sampa + Snmda + Sgaba);   % total spike-events


% do simulation
for i = 1:n-1
    % NMDA gate 
    BD1all_nmda(i+1)  = 1 ./ (1 + (Mg/3.57) * exp(-vD1all(i)*0.062));    % from Moyer et al 
    
    if Snmda(i) >= 1
        i
    end
    % delete events
%     if i == 9709 % 9706
%         Sampa(i) = 0;
%     end
%     if i >= 9650
%         Snmda(i) = 0;
%     end
% 
    Gampa(i+1) = Gampa(i) + (PSPampa .* Sampa(i)./ts_ampa);
    Gampa(i+1) = Gampa(i+1) * SynExp_ampa;

    Gnmda(i+1) = Gnmda(i) + (PSPnmda .* Snmda(i)./ts_nmda);
    Gnmda(i+1) = Gnmda(i+1) * SynExp_nmda;

    Ggaba(i+1) = Ggaba(i) + (PSPgaba .* Sgaba(i)./ ts_gaba); % add the MS PSPs
    Ggaba(i+1) = Ggaba(i+1) * SynExp_gaba;

    % D1 intrinsic + synaptic: 
    
    Iampa(i+1) = (Gampa(i+1) .* (Eampa - vD1all(i)));
    Inmda(i+1) = (1+cD1*D1)*BD1all_nmda(i+1)*(Gnmda(i+1) .* (Enmda - vD1all(i)));
    Igaba(i+1) = (Ggaba(i+1) .* (Egaba - vD1all(i)));
    
    % standard model
    vD1all(i+1) = vD1all(i) + dt*(k*(vD1all(i)-vrD1)*(vD1all(i)-vt)-uD1all(i) + ...
        Iampa(i+1) + Inmda(i+1) + Igaba(i+1))/C;
    uD1all(i+1) = uD1all(i) + dt*a*(b*(vD1all(i)-vrD1)-uD1all(i));
    % spikes?   
    if vD1all(i+1)>=vpeak
        vD1all(i)=vpeak; vD1all(i+1)=c; 
        uD1all(i+1)=uD1all(i+1)+dD1;
    end

end
        

%--------------------------------------------------------------------------
% plot voltage trace 
figure(1); clf
plot(t,vD1all)

spkTs = t(vD1all == vpeak);
%%% pick a first spike to look at... e.g. 975, 1187
tspk = find(spkTs <= 975,1,'last');
ix = spkTs(tspk) / dt;

ix = 9741;

%%% take 100 ms prior to this of v, and all S
seg = 15 / dt; 
vseg = vD1all(ix-seg:ix+1);
Bseg = BD1all_nmda(ix-seg:ix);
Sgaba_seg = Sgaba(ix-seg:ix); gabaix = find(Sgaba_seg >= 1);
Snmda_seg = Snmda(ix-seg:ix); nmdaix = find(Snmda_seg >= 1);
Sampa_seg = Sampa(ix-seg:ix); ampaix = find(Sampa_seg >= 1);
Igaba_seg = Igaba(ix-seg:ix); 
Inmda_seg = Inmda(ix-seg:ix);
Iampa_seg = Iampa(ix-seg:ix);

figure(2); clf
subplot(411), plot(vseg)
subplot(412), plot(Inmda_seg), hold on, plot(nmdaix,ones(numel(nmdaix),1)*300,'r.')
subplot(413), plot(Bseg)

subplot(414), plot(Iampa_seg+Igaba_seg), hold on, plot(ampaix,ones(numel(ampaix),1),'r.'); 
plot(gabaix,ones(numel(gabaix),1),'b.');

% save all 
fname = ['Detailed_single_trial_bimodality_test_D1_' num2str(D1) '.mat'];
save(fname)


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