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 see if increasing NMDA conductance creates
%%%% bimodality within a single trial (cf Durstewitz & Gabriel, 2007) 


clear all

% found values
load fit_model_results_NEWtuning

rand('state',1); randn('state',1);
% -------------------------------------------------------------------------
% Input parameters
% spike-train parameters:
N_nmda = 84; alpha_nmda = 0;
N_ampa = 84; alpha_ampa = 0;
N_gaba = 84; alpha_gaba = 0; 

r_nmda = 1:1:4; 
r_ampa = 4;
r_gaba = 4;

% dopamine levels
D1 = 0;
D2 = 0;

% NMDA multiplier
mNMDA = [50:50:150];
mGABA = 1;   

% or pick single values to look at spike-trains
% mNMDA = 200;
% r_nmda = 4; 
% r_ampa = 4;
% r_gaba = 4;

% -------------------------------------------------------------------------
% 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 = 5000; % 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);

% storage
nHz = numel(r_nmda);
vnospks = cell(nHz,numel(mNMDA));
S = zeros(nHz,numel(mNMDA));    % mean spike-event count for each combo
nspks = zeros(nHz,numel(mNMDA)); 
stbl = zeros(nHz,numel(mNMDA)); 
subsamp = floor(1:1/dt:n);
% run sims...

for j = 1:numel(mNMDA)
    j
    
    PSPnmda = mNMDA(j) * PSPampa / ampa_nmda;
    
    PSPgaba = mGABA * PSPgaba / ampa_gaba;
       
    tic
    for loop = 1:nHz
        loop
        Ggaba = zeros(1,n);
        Gampa = zeros(1,n);
        Gnmda = 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(loop), alpha_nmda);
        Sgaba = spkgen([0:dt:T], N_gaba, r_gaba, alpha_gaba);       
        S(loop,j) = sum(Sampa + Snmda + Sgaba);   % total spike-events


        % do simulation
        for i = 1:n-1
            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
            BD1all_nmda  = 1 ./ (1 + (Mg/3.57) * exp(-vD1all(i)*0.062));    % from Moyer et al 
            
            % standard model
            vD1all(i+1) = vD1all(i) + dt*(k*(vD1all(i)-vrD1)*(vD1all(i)-vt)-uD1all(i) + ...
                    (Gampa(i+1) .* (Eampa - vD1all(i)))+ (1+cD1*D1)*BD1all_nmda*(Gnmda(i+1) .* (Enmda - vD1all(i))) + (Ggaba(i+1) .* (Egaba - vD1all(i))))/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
        
        % record all
        vrecord{loop,j} = vD1all;

        % record spikes
        nspks(loop,j) = sum(vD1all == vpeak);
        
    end
    toc
    
end


%--------------------------------------------------------------------------
% plot results 
figure(1); clf
plot(vD1all)

figure(3); clf
edges = -90:1:-20;
mids = edges(1:end-1) + diff(edges)/2;

counter = 0;
for j = 1:numel(mNMDA)
    for loop = 1:nHz
        counter = counter + 1;
        vsnip = vrecord{loop,j}(t>=1000 & t<=t(end));
        vnospks = vsnip(vsnip < -20);
        N = histc(vnospks,edges)';
        subplot(numel(mNMDA),nHz,counter), bar(edges,N,'histc')
        title(['V for ' num2str(mNMDA(j)) 'xNMDA, r=' num2str(r_nmda(loop)) ' NMDA Hz']);
    end    
end

fname = ['NMDA_NEW_single_trial_bimodality_test_D1_' num2str(D1) '.mat'];

if nHz > 1
    % do not save if just doing single run...
    save(fname)
end

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