Synthesis of spatial tuning functions from theta cell spike trains (Welday et al., 2011)

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Accession:129067
A single compartment model reproduces the firing rate maps of place, grid, and boundary cells by receiving inhibitory inputs from theta cells. The theta cell spike trains are modulated by the rat's movement velocity in such a way that phase interference among their burst pattern creates spatial envelope function which simulate the firing rate maps.
Reference:
1 . Welday AC, Shlifer IG, Bloom ML, Zhang K, Blair HT (2011) Cosine directional tuning of theta cell burst frequencies: evidence for spatial coding by oscillatory interference. J Neurosci 31:16157-76 [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): Hippocampus CA1 pyramidal GLU cell; Hippocampus CA3 pyramidal GLU cell; Entorhinal cortex stellate cell;
Channel(s): I Na,p;
Gap Junctions:
Receptor(s): GabaA; AMPA;
Gene(s):
Transmitter(s): Gaba; Glutamate;
Simulation Environment: NEURON; MATLAB;
Model Concept(s): Synchronization; Envelope synthesis; Grid cell; Place cell/field;
Implementer(s): Blair, Hugh T.;
Search NeuronDB for information about:  Hippocampus CA1 pyramidal GLU cell; Hippocampus CA3 pyramidal GLU cell; GabaA; AMPA; I Na,p; Gaba; Glutamate;
clear;

phz=NaN(12,6); %VCO phases are defined by a 12x6 matrix representing the output from a matrix of theta CPGs in Fig. 7C
rotation_angle = 0; %orientation of the tuning function is zero by default
q=0.65; % spike threshold is 0.65 by default

%%  Note that above, the phz matrix is assigned to all NaNs, meaning that the target neuron
%%  receives no input from any ring oscillator. Assigning a value of N=1-12 to an entry of the 
%%  phz matrix causes the target neuron to receive input from the theta cell at the Nth position
%%  in the ring oscillator at the corresponding matrix position. For example, phz(8,4)=10 causes 
%%  the target neuron to receive input from the 10th theta cell in the ring at row 8, column 4.
%%  Note that this scheme only permits the target neuron to receive input from one theta cell 
%%  per ring, and that by default, the weights of all inputs are uniformly equal to one.

%%%1) border cell against bottom edge in square box
 phz(10,:)=[3 4 6 8 12 10];

%%%2) large spacing entorhinal grid cell in square box 
%phz(:,4)=[10 NaN NaN NaN 10 NaN NaN NaN 4 NaN NaN NaN];

%%%3) small spacing entorhinal grid cell in square box 
%phz(:,5)=[NaN 4 NaN NaN NaN 10 NaN NaN NaN 4 NaN NaN];

%%%4) single-field CA3 place cell in square box
% rotation_angle = 8*pi/6; %orientation of the tuning function is zero by default
% phz(:,3)=   [12    12     1     1     1     1     1     1    12    11    11    11];
% phz(:,4)=   [11    12     1     1     1     1     1     1    11    11    11    11];
% phz(:,5)=   [11    12     1     2     3     2     1     1    11    10     9    10];

%%%5) curved edge border cell in cylinder 
%   phz(12,:)=[2 2 3 5 8 2];
%   phz(1,:)=[2 2 3 5 8 2];
%   phz(2,:)=[2 2 3 5 8 2];
%   phz(3,:)=[2 2 3 5 8 2];
%   phz(4,:)=[2 2 3 5 8 2];
%   phz(5,:)=[2 2 3 5 8 2];
%   q=.75

%%%6) lumpy border cell against right edge in square box
% phz(1,:)=[2 3 4 6 9 4];
% phz(3,3:4)=[7 1]

%%%7) multi-field dentate place cell in square box 
%    phz(:,3)=   [ 9     1     2     2     8     5     3     8     9     9     5     3];
%    phz(:,4)=   [ 4     1     4     1     6     1     2     5     6    10    10    12];
%    phz(:,5)=   [ 1     3     3    11     8     1     1     6     7     3     7     5];

 
cells_per_ring = 12; %number of theta cells assumed to reside in each ring oscillator CPG
cell_phases=(0:(cells_per_ring-1))*2*pi/cells_per_ring; %phases for each cell in a VCO ring
phz=(phz./12)*2*pi; %convert phase matrix from cell numbers to VCO phases

figure(3);
clf
nrows=6; %number of rows in the CPG matrix
ncols=12; %number of columns in the CPG matrix
        Nmesh=50;
        MAX=5;
        ss=linspace(-MAX,MAX,Nmesh);
        [xx,yy]=meshgrid(ss,ss);
        
minrho=0.14; %smallest preferred vector length in the VCO matrix

cosnum=1; Esum=[];

for col=1:ncols
    theta(col,1:nrows)=pi+rotation_angle+(((col-1))/12)*2*pi; %assign the orientations of preferred vectors by column
    for row=1:nrows
         rho(col,row)=minrho*(sqrt(3)^(row-1)); 
        if isnan(phz(col,row)); %assign which cell in this ring projects to the target
            weight(col,row)=0; %weighting coefficient is 1 for the projection cell, implicitly 0 for all others
        else
            weight(col,row)=1; %weighting coefficient is 1 for the projection cell, implicitly 0 for all others
            px=cos(-theta(col,row));
            py=sin(-theta(col,row));
            %analytic signal
            s(cosnum,:,:)=exp(i*(rho(col,row)*px*xx + rho(col,row)*py*yy+phz(col,row)));
         if isempty(Esum);
             Esum=squeeze(s(cosnum,:,:));
         else
             Esum=Esum+squeeze(s(cosnum,:,:));
         end        
            cosnum=cosnum+1;
        end
    end
end

  
        Esum=abs(Esum);
  
        subplot(1,2,1);
        imagesc(ss,ss,Esum)
        axis equal
        axis tight
        colormap jet;
        set(gca,'xtick',[],'ytick',[]);
%colorbar;

        subplot(1,2,2);
        Emax=max(Esum(:));
        EE=max(0, Esum-q*Emax);
        EEmax=max(EE(:));

        imagesc(ss,ss,EE/EEmax)
        axis equal
        axis tight
        colormap jet;
        set(gca,'xtick',[],'ytick',[]);

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