Parameter estimation for Hodgkin-Huxley based models of cortical neurons (Lepora et al. 2011)

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Simulation and fitting of two-compartment (active soma, passive dendrite) for different classes of cortical neurons. The fitting technique indirectly matches neuronal currents derived from somatic membrane potential data rather than fitting the voltage traces directly. The method uses an analytic solution for the somatic ion channel maximal conductances given approximate models of the channel kinetics, membrane dynamics and dendrite. This approach is tested on model-derived data for various cortical neurons.
1 . Lepora NF, Overton PG, Gurney K (2012) Efficient fitting of conductance-based model neurons from somatic current clamp. J Comput Neurosci 32:1-24 [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): Neocortex V1 L6 pyramidal corticothalamic GLU cell; Neocortex V1 L2/6 pyramidal intratelencephalic GLU cell; Neocortex fast spiking (FS) interneuron; Neocortex spiking regular (RS) neuron; Neocortex spiking low threshold (LTS) neuron;
Channel(s): I Na,t; I L high threshold; I T low threshold; I K; I M;
Gap Junctions:
Simulation Environment: GENESIS; MATLAB;
Model Concept(s): Parameter Fitting; Simplified Models; Parameter sensitivity;
Implementer(s): Lepora, Nathan [n.lepora at];
Search NeuronDB for information about:  Neocortex V1 L6 pyramidal corticothalamic GLU cell; Neocortex V1 L2/6 pyramidal intratelencephalic GLU cell; I Na,t; I L high threshold; I T low threshold; I K; I M;
%% ============================
% plot XY kinetics 
function plot_XY(id,dir_output)

% make useable for single/multiple outputs
if ~iscell(dir_output), dir_output = {dir_output}; end
ndir = length(dir_output); rdir = 1:ndir;

% read XY data in A, B format
data_XY = []; 
for i = rdir
    data_XY = [data_XY; load([dir_output{i},'/data_XY.dat'])];

% extract
V = data_XY(:,1); 
tau_X = 1./data_XY(:,3); tau_Y = 1./data_XY(:,5);
X_inf = data_XY(:,2)./data_XY(:,3); Y_inf = data_XY(:,4)./data_XY(:,5);

% individual channels
n = [1; 1+find(diff(V)<0); length(V)+1]; nchan = length(n)-1; rchan = 1:nchan;

% channel props (single/multiple outputs)
if ndir==1
    [ig chan ig ig ig ig ig mpower ig npower] = ...
else for i = rdir
    [ig chan{i} ig ig ig ig ig mpower(i) ig npower(i)] = ...
if iscell(chan{1}); for k = rchan; chan{k} = chan{k}{1}; end; end
for k = rchan; chan{k}(1:end+1-strfind(chan{k}(end:-1:1),'/')) = []; end

% plot results
figure(2); clf
for k = rchan
    % channel properties
    rV = n(k):n(k+1)-1;
    [ig,iXhalf] = min(abs(X_inf(rV)-0.5)); iXhalf = n(k) + iXhalf - 1; 
    [ig,iYhalf] = min(abs(Y_inf(rV)-0.5)); iYhalf = n(k) + iYhalf - 1;  
    if iXhalf==1; iXhalf = 6; end, if iYhalf==1; iYhalf = 6; end % hack if no gate 
    [mtauX,itauX] = max(tau_X(rV)); itauX = n(k) + itauX - 1; 
    [mtauY,itauY] = max(tau_Y(rV)); itauY = n(k) + itauY - 1;
    dXdV = diff(X_inf)./diff(V); dXdVhalf = mean(dXdV(iXhalf+[-5:5])); % scaletabchan issue
    tangX = dXdVhalf*(V(rV)-V(iXhalf)) + 0.5; kX = 0.25/dXdVhalf;
    dYdV = diff(Y_inf)./diff(V); dYdVhalf = mean(dYdV(iYhalf+[-5:5])); % scaletabchan issue
    tangY = dYdVhalf*(V(rV)-V(iYhalf)) + 0.5; kY = 0.25/dYdVhalf;
    % plots
    subplot(2,nchan,k); hold on; grid; box;
    plot(1e3*V(rV),X_inf(rV).^mpower(k).*Y_inf(rV).^npower(k),'k', 'LineWidth',2)
    plot(1e3*V(rV),X_inf(rV),'g', 1e3*V(iXhalf)*[1,1],[0,1.1],'--g',...
        1e3*V(rV),Y_inf(rV),'r', 1e3*V(iYhalf)*[1,1],[0,1.1],'--r', 'LineWidth',2)
    plot(1e3*V(rV),tangX,'--g', 1e3*V(rV),tangY,'--r', 'LineWidth',1)
    axis([-100,50,0,1.1]); title([texlabel(chan{k},'literal'),...
        ' (p,q=',num2str([mpower(k) npower(k)],'%3.0f'),')'],'Fontsize',8);  
    if k==1; ylabel('{\color{green} X_{\infty}}, {\color{red} Y_{\infty}}, {\color{black} X_{\infty}^pY^q_{\infty}}','Fontsize',8); end
    subplot(2,nchan,k+nchan); hold on; grid; box;
    plot(1e3*V(rV),1e3*tau_X(rV),'g', 1e3*V(itauX)*[1,1],[0,1e6],'--g',... 
        1e3*V(rV),1e3*tau_Y(rV),'r', 1e3*V(itauY)*[1,1],[0,1e6],'--r', 'LineWidth',2);
    title({['{\color{green}X_{1/2}}=',num2str(1e3*V(iXhalf),'%3.0f'),' {\color{red}Y_{1/2}}=',num2str(1e3*V(iYhalf),'%3.0f'),...
        ' {\color{green}k_X}=',num2str(1e3*kX,'%3.0f'),' {\color{red}k_Y}=',num2str(1e3*kY,'%3.0f')],...
        ['{\color{green}V_X}=',num2str(1e3*V(itauX),'%3.0f'),' {\color{red}V_Y}=',num2str(1e3*V(itauY),'%3.0f'),...
        '  {\color{green}\tau_X}=',num2str(1e3*mtauX,'%3.1f'),' {\color{red}\tau_Y}=',num2str(1e3*mtauY,'%3.1f')]},'Fontsize',8,'FontWeight','bold');
    axis([-100,50,-1e-10,1.1*1e3*max([mtauX mtauY])]); 
    if k==1; ylabel('{\color{green} \tau_X}, {\color{red} \tau_Y} (msec)','Fontsize',8); end        

% output plot
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 12 8]);
% saveas(gcf,[id,'_XY'])
% close all

% message
disp(['option: plot XY: ',id,'_XY','.jpg']);


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