% % ESTIMATION OF CONDUCTANCES % 2 DIMENSIONAL CONDUCTANCE-BASED MODELS OF QUADRATIC TYPE % % This program estimates conductances in the subthreshold regime under the % presence of subthreshold-activated ionic currents. The method is % presented at: C.Vich, A.Guillamon (2015), preprint accepted to Journal % of Computational Neuroscience. % % The estimation can be done in models that exhibit a parabolic nullcline % for the voltage and a linear nullcline for the recovery gating variable, % i.e. the resonant currents (e.g slow potassium) and amplifying currents % (e.g., persistent sodium). % % CELL TYPE: medial entorhinal cortex layer II stellate cells and CA1 % pyramidal cells. % % % Model needs to be quadratized (see Horacio G. Rotstein (2015) for more % details about the quadratization procedure), that is, it has to be % written as: % % dv/dt = a*v^2 ? w + Isyn(t) + Iapp % dw/dt = eps*( alpha*v ? lambda - w) % % such that % 'v' stands for the membrane potential. % 'w' stands for the set of gating variables. % 'a' controls the curvature of the v-nullcline. % 'alpha' controls the slope of the w-nullcline. % 'eps' stands for the time scale separation between v and w, % which tends to be small. % 'lambda'controls the relative displacement between the two % nullclines (the v one and the w one). % ESTIMATION PROCEDURE - Required information % % We assume to have a quadratic approximation of a conductance-based neuron   %   model, as in H.Rotstein (2015). Given the resulting membrane potential   %   (v) and the course of the gating variable (w), this program estimates %   the synaptic current that the neuron is receiving at each time.  %   Moreover, given the voltage traces for two different applied (steady) %   currents and the excitatory and inhibitory reversal potentials, the %   program estimates the excitatory and inhibitory conductances separately. %   Finally, the program gives the option of estimating the synaptic %   conductance. This conductance can be estimated in two different ways: % (1)if only one voltage trace is given, the synaptic conductance %   is estimated using the synaptic reversal potential; % (2) however, if two voltage traces are given (for two different applied %   currents), then the synaptic conductance can be either estimated using % the synaptic reversal potential or the leak conductance. % INPUTS AND OUTPUTS % % * Input parameters: % % --> Write on the command window: % % main_Estimation_Conductances(t,v,w,Iapplied) % % Such that: % % t: vector of length m containing the discretization of the time % sample. % % v: m x n matrix containing n different samples of membrane % potential corresponding at n different values of applied % current. % % w: m x n matrix containing n different samples of the set of % gating variables corresponding at n different values of applied % current. % % Iapplied: vector of length n containing the different values of applied % current. If its length is greater than or equal to 2, method % discerns between the excitatory and the inhibitory conductances. % % % % * Required parameters which are asked while running: % % a: parameter that controls the curvature of the v-nullcline. % alpha: parameter that controls the slope of the w-nullcline. % lambda: parameter that controls the relative displacement between the % two nullclines (the v one and the w one). % vE: excitatory reversal potential (if the Iapplied vector has % length greater than or equal to 2). % vI: inhibitory reversal potential (if the Iapplied vector has % length greater than or equal to 2). % % and, if you want to estimate the synaptic conductance, % either % vsyn: synaptic reversal potential. % or % gL: synaptic conductance (only if the Iapplied vector has % length greater than or equal to 2). % % % * Output parameters: % % The output parameters are given inside a .mat file called 'estimation.mat' % such that % % Isyn: an m x n matrix containing the total synaptic current. Each % column corresponds to a different value of applied current. % % gsyn: an m x n matrix containing the total synaptic conductance. % Each column corresponds to a different value of applied % current. % % gE: vector of length m containing the excitatory synaptic % conductance. It is only computed if, at least, 2 applied % currents are considered. % % gI: vector of length m containing the inhibitory synaptic % conductance. It is only computed if, at least, 2 applied % currents are considered. % % function [Isyn,gsyn,gE,gI] = main_Estimation_Conductances (t,v,w,Iapplied) % Checking that the dimensions of the input matrices are consistent [rv,cv]=size(v); [rw,cw]=size(w); [rI,cI]=size(Iapplied); if (rI~=1) && (cI~=1) disp('The applied current must be a vector'); stop; end if (cv~=length(Iapplied)) disp('The number of columns of the voltage matrix has to be equal'); disp('to the length of the applied current vector.'); stop; end if (cw~=length(Iapplied)) disp('The number of columns of the gating variable matrix has to be equal'); disp('to the length of the applied current vector.'); stop; end if (rv~=rw) disp('The size of the gating variable matrix has to be equal'); disp('to the size of the voltage matrix.'); stop; end disp( '------ ESTIMATION OF CONDUCTANCES ------' ); % values for the stellate cell considered in C.Vich and A.Guillamon (2015) % a=0.1; alpha=0.4; lambda=-0.2; disp('Write the parameter that controls the curvature of the v-nullcline'); a = input('a = '); disp('Write the parameter that controls the slope of the w-nullcline.'); alpha = input('alpha = '); disp('Write the parameter that controls the relative displacement between the two nullclines'); lambda = input('lambda = '); disp('Estimating the synaptic current from v and w...'); for i=1:length(Iapplied) % ESTIMATION procedure c1=w(1,i); t=transpose(t); Isyn(i,1)=-a*v(1,i)^2+exp(-t(1))*(c1+exp(t(1)).*(alpha*v(1,i)-lambda)); for j=1:(length(t)-1) s=t(j) - t(j+1); c1e(i,j)=w(j,i)*exp(s); trapezi(i,j)=-s*(exp(s)*(alpha*v(j,i)-lambda) + (alpha*v(j+1,i)-lambda))/2; Isyn(i,j+1)=-a*v(j+1,i)^2+c1e(i,j)+trapezi(i,j); end end disp('The synaptic current has been estimated.'); % Estimate the conductances gE(t) and gI(t). if length(Iapplied)>=2 disp('Since the applied current vector has length greater than 1,'); disp('we are going to estimate the excitatory and inhibitory conductances'); disp('Write the excitatory reversal potential.'); vE = input('vE = '); disp('Write the inhibitory reversal potential.'); vI = input('vI = '); disp('Estimating the excitatory and inhibitory conductances...'); for j=i:length(t) Ivector=[Isyn(1,j)-Iapplied(1); Isyn(2,j)-Iapplied(2)]; Vmatrix=[v(j,1)-vE v(j,1)-vI ; v(j,2)-vE v(j,2)-vI]; G=linsolve(-Vmatrix,Ivector); gE(j,1)=G(1); gI(j,1)=G(2); end else gE=[]; gI=[]; end for i=1:length(Iapplied) Isyn(i,:)=Isyn(i,:)-Iapplied(i); end disp('Do you want to estimate the synaptic conductance? Yes (Y) or No (N)'); conditionGsyn = input('gSyn estimation = '); if strcmp(conditionGsyn,'Y') || strcmp(conditionGsyn,'y') if length(Iapplied)>=2 disp('Do you want to estimate the synaptic conductance using'); disp('the synaptic reversal potential (vsyn) or the constant leak conductance (gL)'); opGsyn = input('option to estimate the synaptic conductance = '); if strcmp(opGsyn,'gL') || strcmp(opGsyn,'gl') disp('Write the constant leak conductance'); GL = input('gL = '); gsyn=gE+gI+GL; end end if (length(Iapplied)==1) || strcmp(opGsyn,'vsyn') disp('Write the synaptic reversal potential'); vsyn = input('vsyn = '); disp('Estimating the synaptic conductance...'); for i=1:length(Iapplied) gsyn(:,i)=transpose(Isyn(i,:))./(v(:,i)-vsyn); end end if strcmp(opGsyn,'gL')==0 && strcmp(opGsyn,'gl')==0 && strcmp(opGsyn,'vsyn')==0 disp('The option to estimate the synaptic conductance is not valid'); stop; end else gsyn=[]; end save('estimation','Isyn', 'gsyn', 'gE', 'gI'); end