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;
% maybe want some optional inputs as for makeCell routines

function fitCell_1act1pas(id,IV_data,pas_param,act_props,sim_param)

% OPTIONS: save_b, save_A, save_XY, plot_XY, test

output = []; % output string
% diary([id,'.txt'])
disp(' '); disp(['running fitCell_1act1pas at ',date]); disp(' ')
output = [output,id,'.txt, '];

%% load data from file
warning off MATLAB:load:variableNotFound
disp(['loading ',IV_data,'.mat'])
disp(['loading ',pas_param,'.mat'])
disp(['loading ',act_props,'.mat'])
disp(['loading ',sim_param,'.mat'])

% optional arguments
if ~exist('option','var'); option = ''; end
[id_path,id_name] = fileparts(id); 
nodir = ~exist('dir_sim','var'); if nodir; dir_sim = ['output/output_',id_name]; end
dir_model = fileparts(mfilename('fullpath')); 
if ~exist('dt_sim','var'); dt_sim = tinj(2)-tinj(1); end
if ~exist('chan_sc','var'); chan_sc = []; end
if ~exist('Vhalf','var'); Vhalf = []; end
dir_chans = fileparts(mfilename('fullpath')); 

% ensure voltage trace starts at time zero
ntinj = size(tinj,1); nt = size(t,1); t0 = t(1,:);
tinj = tinj - repmat(t0,[ntinj,1]); t = t - repmat(t0,[nt,1]);

% interpolate data
t_data = t(1):dt_sim:t(end); t_data = t_data(:);
Vs_data = interp1(t,Vs,t_data,'spline'); 
Iinj_data = interp1(t,Iinj,t_data,'spline'); 
nt_data = length(t_data); nsim = size(Vs_data,2);

% ensure chan_sc and Vhalf have nchan elements
nchan = length(chan_list); nsc = size(chan_sc,1); nVh = size(Vhalf,1);
if nsc>nchan; chan_sc(nchan+1:end,:) = []; nsc = nchan; end
chan_sc = [chan_sc; repmat([0,1,1,0,1,1],[nchan-nsc,1])];
if nVh>nchan; Vhalf(nchan+1:end,:) = []; nVh = nchan; end
Vhalf = [Vhalf; repmat([0,0],[nchan-nVh,1])];
for i = 1:nchan; if isempty(fileparts(chan_list{i})); chan_list{i} = [dir_chans,'/',chan_list{i}]; end; end

%% run fitting method

% compensate for trunc in run_fit
rt = 1:nt_data-1; 

% simulate channels & load A_k (split to save memory) 
for k = 1:nchan
    for j = 1:nsim
        dir_chan{j,k} = [dir_sim,'/output_chan',num2str(k),'_sim',num2str(j)];
        simChan(id, t_data,Vs_data(:,j), chan_list{k},chan_sc(k,:),Vhalf(k,:), dir_chan{j,k},dir_model)
        [t1_data,A_k(:,j,k)] = load_Ak(dir_chan{j,k},rt);

% simulate dendrite & load Vd
for j = 1:nsim
    dir_dend{j} = [dir_sim,'/output_dend_sim',num2str(j)];
    simDend_1act1pas(id, t_data,Vs_data(:,j), CM,RM,RA,Em,len,dia, dir_dend{j},dir_model)
    [t2_data,Vd_sim(:,j)] = load_Vd(dir_dend{j},rt); 

% truncate data to same size as A_k
t_data = t1_data; clear t1_data t2_data
nt_data = length(t_data); rt = rt(1:nt_data); 
Vs_data = Vs_data(rt,:); Iinj_data = Iinj_data(rt,:); 
Vd_sim = Vd_sim(rt,:);

% find b current
SA = pi*len.*dia; XA = pi*dia.^2/4; 
IC = CM*SA(1)*deriv(Vs_data,t_data,'Df1'); IC(1,:) = []; IC = [IC; IC(end,:)];
Is = (Em-Vs_data)/(RM/SA(1)); clear Vs
Id = (Vd_sim-Vs_data)/(len(2)*RA/XA(2)); clear Vd_sim
b = IC - Is - Id - Iinj_data;

% find exact solution
A1 = reshape(A_k,nt_data*nsim,nchan); 
b1 = reshape(b,nt_data*nsim,1); % clear A_k
g = pinv(A1)*b1; g = g.*(g>0); G_opt = g'/SA(1); 

% residual current error
I_res = A1*g - b1; e2_res = mean(I_res.^2)/mean(b1.^2); 

%% report, save and clean up

% message
disp(' ')
disp(['G_opt = ',num2str(G_opt)]);
disp(['e^2_res = ',num2str(e2_res)]);
disp(' ')

% save active parameters (option: save_b, save_A, save_XY)
G = G_opt; e2 = e2_res; t = t_data; Ires = I_res;
disp(['saving results: ',id,'.mat'])
if strfind(option,'save_b'); save(id,'t','b','Ires','-append'); disp('option: save t b Ires'); end 
if strfind(option,'save_A'); save(id,'t','A_k','-append'); disp('option: save t A_k'); end
if strfind(option,'save_XY'); save_XY(id,dir_chan); end
output = [output,id,'.mat, '];

% option: plot channel kinetics
if strfind(option,'plot_XY'); plot_XY(id,dir_chan); output = [output,id,'_XY.jpg, ']; end

% clean up
if isempty(strfind(option,'test')); rmdir(dir_sim,'s'); end

% CARMEN output
disp(' ')
diary off


%% derivative function
function dVdt = deriv(V,t,method)

t = repmat(t,[1,size(V,2)]);

function d = Df(V,i); d = V(1+i:end,:)-V(1:end-i,:); d = [d; repmat(d(end,:),[i,1])]; end
function d = Db(V,i); d = V(1+i:end,:)-V(1:end-i,:); d = [repmat(d(end,:),[i,1]); d]; end
function d = Dc(V,i); d = V(1+i:end,:)-V(1:end-i,:); d = [repmat(d(end,:),[i/2,1]); d; repmat(d(end,:),[i/2,1]);]; end
if     strcmp(method,'Df1'); dVdt = Df(V,1)./Df(t,1); 
elseif strcmp(method,'Df2'); dVdt = 2*Df(V,1)./Df(t,1) - Df(V,2)./Df(t,2); 
elseif strcmp(method,'Db1'); dVdt = Db(V,1)./Db(t,1); 
elseif strcmp(method,'Db2'); dVdt = 2*Db(V,1)./Db(t,1) - Db(V,2)./Db(t,2); 
elseif strcmp(method,'Dc2'); dVdt = Dc(V,2)./Dc(t,2); 
elseif strcmp(method,'Dc4'); dVdt = 4/3*Dc(V,2)./Dc(t,2) - 1/3*Dc(V,4)./Dc(t,4); 
end; clear t V


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