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;
function f = stagethree(x,pars)

% return fit of tuned Izi MSN basic type neuron to Moyer et al f-f plot data

% approximate r values to get same overall synaptic Hz...
N_ctx = 84; alpha_ctx = 0;  r_ctx = [4:0.5:8]; % r_ctx = 8;  
N_gaba = 84; alpha_gaba = 0; r_gaba = r_ctx; % r_gaba = 8;


% pars = [k,a,b, c, vr, vpeak, T, dt, f_start, f_end, f_time, Istore, C, vt, d];
k = pars(1); a = pars(2); b = pars(3); c = pars(4); vr = pars(5); vpeak = pars(6);
T = pars(7); dt = pars(8); f_start=pars(9); f_end=pars(10); f_time=pars(11); Istore = pars(12);
% newly tuned parameters added to end of pars list
C = pars(13); vt = pars(14); d = pars(15); 

% fitted linear function to Moyer data
B1 = pars(16); B2 = pars(17);

% synaptic parameters
r_ampa_nmda = pars(18);  r_ampa_gaba = pars(19); 
Egaba = pars(20); Enmda = pars(21); Eampa = pars(22); Mg = pars(23);
ts_ampa = pars(24); ts_nmda =pars(25); ts_gaba = pars(26);
 
% set conductances
PSPampa = x(1);
PSPnmda = PSPampa / r_ampa_nmda;
PSPgaba = PSPampa / r_ampa_gaba;

% run simulation
t = 0:dt:T;         
n = length(t); % number of time points
nHz = numel(r_ctx);

SynExp_ampa = exp(-dt / ts_ampa);
SynExp_nmda = exp(-dt / ts_nmda);
SynExp_gaba = exp(-dt / ts_gaba);

for loop = 1:nHz
    v = vr*ones(1,n); u=0*v;
    Ggaba = zeros(1,n);
    Gampa = zeros(1,n);
    Gnmda = zeros(1,n);

    % generate the spike trains
    Sctx = spkgen([0:dt:T], N_ctx, r_ctx(loop), alpha_ctx);
    Sgaba = spkgen([0:dt:T], N_gaba, r_gaba(loop), alpha_gaba);
    S = Sctx + Sgaba;

    for i = 1:n-1
        %%% update synaptic input
        Gampa(i+1) = Gampa(i) + (PSPampa .* Sctx(i)./ts_ampa);
        Gampa(i+1) = Gampa(i+1) * SynExp_ampa;
        Gnmda(i+1) = Gnmda(i) + (PSPnmda .* Sctx(i)./ts_nmda);
        Gnmda(i+1) = Gnmda(i+1) * SynExp_nmda;
        Ggaba(i+1) = Ggaba(i) + (PSPgaba .* Sgaba(i) ./ ts_gaba); 
        Ggaba(i+1) = Ggaba(i+1) * SynExp_gaba;
        
        % update NMDA plug
        B_nmda  = 1 ./ (1 + (Mg/3.57) * exp(-v(i)*0.062)); 
        
        %%% unmodified
        v(i+1) = v(i) + dt*(k*(v(i)-vr)*(v(i)-vt)-u(i) + (Gampa(i+1) .* (Eampa - v(i))) ...
                          + B_nmda*(Gnmda(i+1) .* (Enmda - v(i))) + (Ggaba(i+1) .* (Egaba - v(i))) )/C;
        u(i+1) = u(i) + dt*a*(b*(v(i)-vr)-u(i));
        
        % spikes?   
        if v(i+1)>=vpeak
            v(i)=vpeak; v(i+1)=c; u(i+1)=u(i+1)+d;
        end
    end
    brate(loop) = sum(S) / (T*1e-3);
    ff(loop) = sum(v(f_start:f_end) == vpeak) ./ f_time;
    temp = find(v == vpeak); isis = diff(temp)*dt;
    if isis ffISI(loop) = 1000./mean(isis); else ffISI(loop) = 0; end
end

%-------------- compute fit
% calculate expected value from fitted function
expff = B1 + B2 .* brate;
expff(expff < 0) = 0;   % rectify fit!! 

% f = sum((ff-expff).^2); % SSE

% SRE
norm = expff; norm(norm == 0) = 1;
f = sum(abs(ff-expff)./norm);


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