# Figure 3- Effects of Polarization Induced by Non-Weak Electric Fields on the Excitability of Elongated Neurons With Active Dendrites

RIR July 8, 2015 Weak and Intermediate polarization With Linear Fit. Assumes four panels each with a different pair of M and E_{K} Default: Ek={-25,-45} mV X M = {0.3,0.8} \muA/(cm^{2} s) Ramp current injection protocol RIR July 5, 2015

## Contents

- Dependencies
- User Supplied Inputs

## Dependencies

1. IniPR_db
2. NumerEquilPR_db
3. SingIntegODE23PRWithInjCurr_db

## User Supplied Inputs

1. Specify range of V_{ds}^{out} by MaxVdsOut, DeltaVdsOut, and NumVdsOut
2. Ms: The slope of the injected current in

    MaxVdsOut=10; %Default: 10 mV
    DeltaVdsOut=0.5; %Default: 0.5 mV
    NumVdsOut=51;   %Default: 51
    Ms=[0.8,0.3];
    Eks=[-45,-25];
    guessVsVd=[0,0];
    SomaInj=true;
    VsThresh=30;
    %delay =500;
    delay=40; %prior to this model neuron should be at rest with VdsOut. Provides a good sanity check clear before and after, just remember to subtract delay from spike time to get TTFS
    Tend=17500;
    termaftevent=true;
    Isinj=-0.5;
    smp=[15,47];
    f1=figure();
    for i=1:2
        tmpM=Ms(i);
        tmpuAmpsPermsecCm2=tmpM*1e-3;
        for j=1:2
           tmpEk=Eks(j);
           tmpPR=IniPR_db(Isinj,tmpEk);
           for k=1:NumVdsOut
               tmpVdsOut=MaxVdsOut-(k-1)*DeltaVdsOut;
               [tmpnumSSPR,diffProjFullEq,Jacob,eigJacob,nzeig] = NumerEquilPR_db(tmpPR,guessVsVd,tmpVdsOut);
               tmpPR.SS.NumSS=tmpnumSSPR;
               tmpSingPR = SingIntegODE23PRWithInjCurr_db(tmpPR,tmpuAmpsPermsecCm2,delay,Tend,tmpVdsOut,VsThresh,SomaInj,termaftevent);
               subsample=100;
               extr=1:subsample:size(tmpSingPR.T,1);
               VsVdTrace(i,j).T(k).T=tmpSingPR.T(extr);
               VsVdTrace(i,j).Vs(k).Vs=tmpSingPR.YMultcol(extr,1);
               VsVdTrace(i,j).Vd(k).Vd=tmpSingPR.YMultcol(extr,2);
               VsVdTrace(i,j).VdsOut(k)=tmpVdsOut;
               VsVdTrace(i,j).TTFS(k)=tmpSingPR.te-tmpSingPR.delay;
               VsVdTrace(i,j).M=tmpM;
               VsVdTrace(i,j).Ek=tmpEk;
           end
           idx=2*(i-1)+j;
           subplot(2,2,idx)
           def=linspace(1,NumVdsOut,NumVdsOut);
           nosubidx=find(def~=smp(1,1) & def ~= smp(1,2));
           plot(VsVdTrace(i,j).VdsOut(nosubidx),VsVdTrace(i,j).TTFS(nosubidx),'ok','MarkerFaceColor','k','MarkerSize',2)
           hold on;
           plot(VsVdTrace(i,j).VdsOut(smp(1)),VsVdTrace(i,j).TTFS(smp(1)),'ok','MarkerFaceColor','w','MarkerSize',4)
           hold on;
           plot(VsVdTrace(i,j).VdsOut(smp(2)),VsVdTrace(i,j).TTFS(smp(2)),'+k','MarkerSize',6)
           title({['m = ', num2str(tmpM),' \muA/(cm^{2} s)',' Ek= ',num2str(tmpEk),' mV']},'FontSize',10)
           ax1=gca();
           set(ax1,'FontSize',8)
           hold off;

           if idx==1
           axes('Position',[.38 .8 .1 .1])
           elseif idx==2
           axes('Position',[.88 .8 .1 .1])
           elseif idx==3
           axes('Position',[.38 .3 .1 .1])
           elseif idx==4
           axes('Position',[.88 .3 .1 .1])
           end
           box on
           plot(VsVdTrace(i,j).T(smp(1)).T,VsVdTrace(i,j).Vs(smp(1)).Vs,'ok','MarkerFaceColor','w','MarkerSize',2,'MarkerEdgeColor','w')
           hold on;
           plot(VsVdTrace(i,j).T(smp(2)).T,VsVdTrace(i,j).Vs(smp(2)).Vs,'+k','MarkerSize',2)
           ylabel('V_{s} (mV)','FontSize',8)
           xlabel('Time (ms)','FontSize',8)
           ax3=gca();
           set(ax3,'FontSize',8)
        end
    end

    % aPR=IniPR_db(Isinj,Ek,varargin);
    % [numSSPR,diffProjFullEq,Jacob,eigJacob,nzeig] = NumerEquilPR_db(aPR,guessVsVd,tmpVdsOut);
    %
    % tmpSingPR = SingIntegODE23PRWithInjCurr_db(aPR,uAmpsPermsecCm2,delay,Tend,VdsOut,VsThresh,SomaInj,termaftevent,varargin);