Phase oscillator models for lamprey central pattern generators (Varkonyi et al. 2008)

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Accession:118392
In our paper, Varkonyi et al. 2008, we derive phase oscillator models for the lamprey central pattern generator from two biophysically based segmental models. We study intersegmental coordination and show how these models can provide stable intersegmental phase lags observed in real animals.
Reference:
1 . Várkonyi PL, Kiemel T, Hoffman K, Cohen AH, Holmes P (2008) On the derivation and tuning of phase oscillator models for lamprey central pattern generators. J Comput Neurosci 25:245-61 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network; Connectionist Network;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB;
Model Concept(s): Temporal Pattern Generation; Oscillations; Spatio-temporal Activity Patterns; Parameter Fitting; Parameter sensitivity; Phase Response Curves;
Implementer(s): Varkonyi, Peter [vpeter at mit.bme.hu];
% This code computes certain properties of a 'network-based' segmental
% oscillator model of the lamprey spinal chord proposed by [Williams, 1990].
%
%The following plots are generated:
% 1. the dynamics of an oscillator (Figure 2, top of paper).
% 
% 2. The PRC of an oscillator for perturbations of E,L, and C cells (Figure
%    2, bottom of paper). The direct method is used, i.e. the effect of small finite
%    perturbations is simulated numerically.
%
% 3. Coupling function of two unidirectionally coupled segmental network-based oscillators (Figure 6 of paper), 
%    This is calculated as the integral of 
%    [presynaptic activity] x [difference between reversion potential and current postsynaptic potential] x [postsynaptic PRC] 
%    over a period summed for all connections, at given phaseshift between the connected oscillators
%
%4. the stable (decreasing) roots of the coupling functions (Figure 7 of paper) 
%
%All calculations are done for several values of tonic drive to E cells,
%which can be specified determined by user.


%levels of tonic drive to E cells
disp('Insert level(s) of tonic drive to E cells ');
disp('please write number in [...] divided by blank spaces');
disp('or press return for default [.005 .0075 .01 .02 .04 .06 .07]');
ves=input('>>>:');
if length(ves)== 0
    ves=[.005 .0075 .01 .02 .04 .06 .07];
    disp(ves);
end
%ve=[.005  .01  .07];


%%%%%%%%%%%%%%%%%%%%%%%%%determination of coupling functions;
%%%%elements of Fig 2 are plotted during evaluation of @couplingfuncion
for i=1:length(ves)
    disp('Current level of tonic drive to E cells is')
    disp(ves(i)); disp('Please wait!');
    disp('****************************');
    [shift{i}, H{i}, fi{i}, PRC{i}, T(i)]=couplingfunction(ves(i),i,length(ves));
    
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%plotting Fig 6
figure(6);
for i=1:length(shift)
    plot(-shift{i},H{i});
    title('***********FIGURE 6*************'); 
   hold on;
end

%%%%%%%%%%%%%%%%%stable zeros of coupling function
disp('calculating roots of copupling functions');
for i=1:length(shift)
    for j=1:length(H{i})-1
        if H{i}(j+1)*H{i}(j)<=0
            if H{i}(j+1)>H{i}(j)
                stab(i)=(shift{i}(j)*H{i}(j+1)-shift{i}(j+1)*H{i}(j))/(H{i}(j+1)-H{i}(j))/2/pi;
            end
        end
    end
end
%%%%%%%%%%%%%%%%%%%%%plotting Fig 7
figure(7);
plot(1./T,-stab,'s-');
title('***********FIGURE 7*************');
disp('Ready!');