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

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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.
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]
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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;
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;
function powspect = autopowspect(maxfreq, numfreqs, blocklen, autohisto, speedbins, balcounts)

%% maxfreq -- compute power spectrum from 0 - maxfreq
%% numfreqs -- number of frequency bins in the spectrum
%% blocklen -- length of each data block (in seconds)
%% ratehisto -- rate histogram data in matrix format (each row is the histogram for a movement episode of length blocklen)
%% speedbins -- an ordered list (length is same as number of rows in ratehisto) of which bin of the speed distribution each movement episide falls into
%% balcounts -- the counts for each speed bin in the balanced speed distribution (these define the "speed quotas" for the spectral analysis)

%% returns the power spectrum in 'powspect'

global iterat
f = (numfreqs/blocklen)*(0:(2^18))/2^19;  %frequency bins of the power spectrum
peakwidth = 1.5; %bandwidth (in Hz) on either side of the theta peak across which to intgrate for computing expected frequency value

nonzerobins=find(balcounts>0); %find the speed bin numbers with non-zero quotas

powspect=zeros(1,2^19); %initialize the power spectrum to zero for cumulative averaging
for i=1:100 %we will run the FFT a total of 100 times, randomly refilling the speed quotas each time
    ssignal=[]; %variable for accumulating the speed-balanced rate histogram on each pass through the data
    for j=nonzerobins %loop through the bins of the speed distribution which have nonzero quotas
        %%%first, try to fill the speed quota by sampling rows from the rate histogram WITHOUT replacement
        bsignal=[]; %variable for accumulating the rows of the rate histogram that fall into speed bin j
        thisbinepochs=autohisto(find(speedbins==j),:); %extract the rows of the autocorrelogram with running speeds that fall into speed bin j
        bsignal=[bsignal; thisbinepochs]; %accumulate the rows
        %%%second, if necessary, fill what remains of the speed quota by resampling rows from the rate histogram as little replacement as possible
        while (size(bsignal,1)<balcounts(j)) %while the quota for speed bin j has not yet been filled
            randthisbin=[thisbinepochs rand(size(thisbinepochs,1),1)]; %append a column of random numbers to the accumulated rate histogram
            randthisbin=sortrows(randthisbin,size(randthisbin,2)); %use the random number column to randomly order the rows
            randthisbin=randthisbin(:,1:size(thisbinepochs,2)); %remove he random number column now that its job is done
            if (size(bsignal,1)+size(randthisbin,1))<=balcounts(j) %if we have not yet exceeded our desired speed quota
                bsignal=[bsignal; randthisbin]; %then add all of the randomly ordered autocorrelogram rows to our accumulating total
            else %otherwise
                bsignal=[bsignal; randthisbin(1:(balcounts(j)-size(bsignal,1)),:)]; %add only as many rows as we need to fill the quota and be done
        ssignal=[ssignal; bsignal]; %accumulate the rows from speed bin j into the balanced rate histogram
    Pyy = Y.* conj(Y) / 2^19;      
    powspect = powspect+Pyy/100;