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;
function [FP,JA,JB,Ev,VA,VB,class] = basic_model_stability(vr,vt,a,b,k,C,I)

% BASIC_MODEL_STABILITY linear stability analysis of Izhikevich neuron model
% [B,JA,JB,FP,Ev,VA,VB,CL] = BASIC_MODEL_STABILITY(vr,vt,a,b,k,C,I) given standard
% model parameters (vr,vt,b,k,C) and specified injection current I, computes
% the two fixed points FP (in (v,u) pairs per row), corresponding Jacobians
% JA and JB, and their corresponding eigenvalues Ev and eigenvector
% matrices VA, VB; will also classify both fixed points, returning types in
% cell array CL.
% Mark Humphries & Nathan Lepora 27/11/2008

% Report eq 29
B = sqrt((vr+vt+b/k)^2 - 4*(vr*vt+(b*vr+I)/k));

% Report eq 32
JA = [(b+k*B)/C -1/C; a*b -a];
JB = [(b-k*B)/C -1/C; a*b -a];

% fixed points - report eq 28
vA = 0.5*(vr+vt+b/k)+0.5*B; uA = b/2*(-vr+vt+b/k)+0.5*b*B;
vB = 0.5*(vr+vt+b/k)-0.5*B; uB = b/2*(-vr+vt+b/k)-0.5*b*B;
FP = [vA uA; vB uB];

% eigenvalues
[VA,DA] = eig(JA);
[VB,DB] = eig(JB);
eA = diag(DA)';
eB = diag(DB)';

Ev = [eA; eB];
% classify.... if fixed points exist
class{1} = 'No fixed points';
class{2} = 'No fixed points';
if isreal(vA) class{1} = classify(eA); end
if isreal(vB) class{2} = classify(eB); end

function class = classify(ev)
delta = ev(1)*ev(2); tau = ev(1) + ev(2);

if delta < 0
    class = 'saddle';      
elseif delta > 0
    div = tau^2 - 4*delta;
    if tau > 0
        if div > 0
            class = 'unstable node';
        elseif div < 0
            class = 'unstable spiral';
            class = 'stars, degenerate nodes';
    elseif tau < 0
        if div > 0
            class = 'stable node';
        elseif div < 0
            class = 'stable spiral';
            class = 'stars, degenerate nodes';
        class = 'centre';

    class = 'tiled fixed points';

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