ESTIMATION OF CONDUCTANCES 2 DIMENSIONAL CONDUCTANCE-BASED MODELS OF QUADRATIC TYPEThis program estimates conductances in the subthreshold regime under the presence of subthreshold-activated ionic currents. The method is presented in C.Vich, A.Guillamon (2015), 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 informationWe 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: To run the program, write on the command window the next sentence 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.ADJOINT EXAMPLE presented in C.Vich and A.Guillamon (2015)A Matlab file called StellateModel.mat is added to the folder. This file contains all the needed inputs to simulate an estimation of the synaptic current, excitatory and inhibitory conductances and, giving the leak conductance, also estimate the synaptic conductances. Data comes from a reduced model for medial entorhinal cortex stellate cell given in Rotstein et al (2006) that displays subthreshold oscillations. The only considered activated currents in the model are the persistent sodium (INaP) current and the h-(Ih) current. Detailed Usage (matlab command line excerpt): >> load StellateModel.mat >> [Isyn, gsyn, gE, gI]=main_Estimation_Conductances(t, v, w, Iapplied); ------ ESTIMATION OF CONDUCTANCES ------ Write the parameter that controls the curvature of the v-nullcline a = 0.1 Write the parameter that controls the slope of the w-nullcline. alpha = 0.4 Write the parameter that controls the relative displacement between the two nullclines lambda = -.2 Estimating the synaptic current from v and w... The synaptic current has been estimated. Since the applied current vector has length greater than 1, we are going to estimate the excitatory and inhibitory conductances Write the excitatory reversal potential. vE = 55 Write the inhibitory reversal potential. vI = -25 Estimating the excitatory and inhibitory conductances... Do you want to estimate the synaptic conductance? Yes (Y) or No (N) gSyn estimation = 'Y' Do you want to estimate the synaptic conductance using the synaptic reversal potential (vsyn) or the constant leak conductance (gL) option to estimate the synaptic conductance = 'gL' Write the constant leak conductance gL = 0.5 >> figure(); hold on; plot(t,Isyn(2,:),'-'); axis([0 500 -3 2]); hold off; >> figure(); hold on; plot(t,gsyn,'-'); axis([0 500 0.5 0.8]); hold off; >> figure(); hold on; plot(t,gE,'-'); axis([0 500 -0.02 0.1]); hold off; >> figure(); hold on; plot(t,gI,'-'); axis([0 500 0 0.2]); hold off; These reproduce the dotted black traces in Figure 10A, 11A, 11B, 11C respectively: