Medial reticular formation of the brainstem: anatomy and dynamics (Humphries et al. 2006, 2007)

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Accession:128816
A set of models to study the medial reticular formation (mRF) of the brainstem. We developed a collection of algorithms to derive the adult-state wiring of the model: one set a stochastic model; the other set mimicking the developmental process. We found that the anatomical models had small-world properties, irrespective of the choice of algorithm; and that the cluster-like organisation of the mRF may have arisen to minimise wiring costs. (The model code includes options to be run as dynamic models; papers examining these dynamics are included in the .zip file).
Reference:
1 . Humphries MD, Gurney K, Prescott TJ (2006) The brainstem reticular formation is a small-world, not scale-free, network. Proc Biol Sci 273:503-11 [PubMed]
2 . Humphries MD, Gurney K, Prescott TJ (2007) Is there a brainstem substrate for action selection? Philos Trans R Soc Lond B Biol Sci 362:1627-39 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB;
Model Concept(s): Activity Patterns; Action Selection/Decision Making; Connectivity matrix; Development; Sensory processing;
Implementer(s): Humphries, Mark D [m.d.humphries at shef.ac.uk];
%   for MNAS book chapter (Humphries et al, 2010); Fig 5c,d
%   script to test relationship between input-output patterns in mRF model: 
%   Inputs: vectors of cluster-input
%   Outputs: all projection neuron outputs; total cluster output
%   Matches: correlation between input-output orthogonality
%
%   Mark Humphries 30/4/2009

clear all
cl_fig

n_ins = 50;    % number of input vectors....

%%%%%%%%%%%% define general structural model parameters %%%%%%%%%%%
% Inter-cluster
Nc = 8;            % number of clusters
Pp = 0.1;           % probability of cluster-unit connection for long-range input 
Pc = 0.25;              % power-law exponent for inter-cluster connection probability (or P(c) for spatially uniform model) 

% Intra-cluster
n = 50;             % number of units per cluster
rho = 0.8;          % proportion of projection units per cluster
Pl = 0.25;           % 0.1..probability of connection for each local interneuron
rho_s = 1;             % all projection neurons receive sensory input
lambda_s = 0;           % proportion of interneurons receiving sensory input
rho_i = 0;             % proportion of inhibitory projection neurons
lambda_i = 1;             % proportion of inhibitory interneurons

%%%%%%%%%%% parameters for full model   %%%%%%%%%%%%%%%%%%%%%%%%%
% simulation parameters
con = 1e-6;         % convergence criteria
max_steps = 10e3;            % maximum number of time-steps
%max_steps = 1;              % set to 1 to get structure only   
theta = -0.05;          % unit threshold
slope = 1;                  % output slope
seed = 1;                   % random number generator seed

flag = 'if';         % flag for options - see DISCRETE_CLUSTER1 help

% set weights...
W = 0.1;    % low weight (0.1) for stable attractor

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Run sims
S = zeros(Nc,n_ins);            % storage for input vectors
Pout = zeros(Nc*n*rho,n_ins);   % storage for output vectors    
Cout = zeros(Nc,n_ins);   % storage for output vectors    
converged = zeros(n_ins,1);

for loop = 1:n_ins
    %%%%%%%%%%%%%%%% input parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %rand('state',3)
    % input to single clusters
    %S(3) = 0.4;
    % S(4) = 0.3; % competing cluster inputs
    % 
    % % random input to each cluster
    rand('state',loop);
    S(:,loop) = rand(Nc,1); % each column is one input vector

    % random inputs to all projection units...
    %flag = [flag 'p'];
    %S = exprnd(0.05,Nc*n,1); % most get small, some get large

    %%%%%%%%%%%%%%% RUN FULL MODEL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % sets seed, so should build same model every time, just changes input...
    [clust_out,clust_act,Proj_units,steps_elapsed,Clust_con,S_clust,proj_out,samp,t_samp,this_model] =...
        discrete_cluster1(Nc,n,Pl,Pp,rho_s,lambda_s,rho,rho_i,lambda_i,Pc,con,max_steps,theta,S(:,loop),seed,flag,[],[],W);
    %converged?
    converged(loop) = real(steps_elapsed < max_steps);
    
    Pout(:,loop) = proj_out(:);     % vector of all projection neuron outputs
    Cout(:,loop) = sum(proj_out)';  % vectors of all cluster outputs
end

%% compute "distances" between inputs

% Eucledian distance between vectors
in_dist = pdist(S'); % Eucledian distance 
Cout_dist = pdist(Cout');
Pout_dist = pdist(Pout');
[BdistC,BINT,R,RINT,STATSdistC] = regress(Cout_dist',[ones(numel(in_dist),1) in_dist']);
[BdistP,BINT,R,RINT,STATSdistP] = regress(Pout_dist',[ones(numel(in_dist),1) in_dist']);

% angle between vectors
in_cos = pdist(S','cosine');
Cout_cos = pdist(Cout','cosine');
Pout_cos = pdist(Pout','cosine');
[BcosC,BINT,R,RINT,STATScosC] = regress(Cout_cos',[ones(numel(in_cos),1) in_cos']);
[BcosP,BINT,R,RINT,STATScosP] = regress(Pout_cos',[ones(numel(in_cos),1) in_cos']);

% correlation between vectors
in_correlation = pdist(S','correlation');
Cout_correlation = pdist(Cout','correlation');
Pout_correlation = pdist(Pout','correlation');
[BcorrelationC,BINT,R,RINT,STATScorrelationC] = regress(Cout_correlation',[ones(numel(in_correlation),1) in_correlation']);
[BcorrelationP,BINT,R,RINT,STATScorrelationP] = regress(Pout_correlation',[ones(numel(in_correlation),1) in_correlation']);

% plot distances....
figure(1); clf
subplot(311),plot(in_dist,Cout_dist,'.'); hold on; plot(in_dist,BdistC(1) + BdistC(2)*in_dist,'k')
xlabel('Input distance'); ylabel('Cluster output distance'); title(['r^2 = ' num2str(STATSdistC(1)) '; p = ' num2str(STATSdistC(3))]); 
subplot(312),plot(in_cos,Cout_cos,'.'); hold on; plot(in_cos,BcosC(1) + BcosC(2)*in_cos,'k')
xlabel('Input angle'); ylabel('Cluster output angle'); title(['r^2 = ' num2str(STATScosC(1)) '; p = ' num2str(STATScosC(3))]); 
subplot(313),plot(in_correlation,Cout_correlation,'.'); hold on; plot(in_correlation,BcorrelationC(1) + BcorrelationC(2)*in_correlation,'k')
xlabel('Input correlation'); ylabel('Cluster output correlation'); title(['r^2 = ' num2str(STATScorrelationC(1)) '; p = ' num2str(STATScorrelationC(3))]); 


figure(2); clf
subplot(311),plot(in_dist,Pout_dist,'.'); hold on; plot(in_dist,BdistP(1) + BdistP(2)*in_dist,'k')
xlabel('Input distance'); ylabel('Projection neuron output distance'); title(['r^2 = ' num2str(STATSdistP(1)) '; p = ' num2str(STATSdistP(3))]); 
subplot(312),plot(in_cos,Pout_cos,'.'); hold on; plot(in_cos,BcosP(1) + BcosP(2)*in_cos,'k')
xlabel('Input angle'); ylabel('Projection neuron output angle'); title(['r^2 = ' num2str(STATScosP(1)) '; p = ' num2str(STATScosP(3))]); 
subplot(313),plot(in_correlation,Pout_correlation,'.'); hold on; plot(in_correlation,BcorrelationP(1) + BcorrelationP(2)*in_correlation,'k')
xlabel('Input correlation'); ylabel('Projection neuron output correlation'); title(['r^2 = ' num2str(STATScorrelationP(1)) '; p = ' num2str(STATScorrelationP(3))]); 

%% look at general properties of sims
totalS = sum(S)';
totalC = sum(Cout)';
[Btot,BINT,R,RINT,STATStot] = regress(totalC,[ones(n_ins,1) totalS]);
figure(3)
plot(totalS,totalC,'.'); hold on; plot(totalS,Btot(1) + Btot(2)*totalS,'k')
xlabel('Total input'); ylabel('Total cluster output'); title(['r^2 = ' num2str(STATStot(1)) '; p = ' num2str(STATStot(3))]); 

% is Eucledian distance metric related to activity levels? NO!
k = 0;
totalInput = zeros(numel(in_dist),1);
totalOutput = zeros(numel(in_dist),1);
for j =1:n_ins
    for i = 1:k
      % distance between (i,j) is...
      ix = (i-1)*(n_ins-i/2)+j-i;   % see Help for pdist
      d = in_dist(ix);
      % these input and output totals should be linearly related of
      % course...
      totalInput(ix) = totalS(i)+totalS(j);
      totalOutput(ix) = totalC(i)+totalC(j);
    end
    k = k+1;
end

figure(4)
subplot(211),plot(totalInput,in_dist,'.');
xlabel('Total input');
subplot(212),plot(totalOutput,in_dist,'.');
    
save cluster_input_IO_results