Neocort. pyramidal cells subthreshold somatic voltage controls spike propagation (Munro Kopell 2012)

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There is suggestive evidence that pyramidal cell axons in neocortex may be coupled by gap junctions into an ``axonal plexus" capable of generating Very Fast Oscillations (VFOs) with frequencies exceeding 80 Hz. It is not obvious, however, how a pyramidal cell in such a network could control its output when action potentials are free to propagate from the axons of other pyramidal cells into its own axon. We address this problem by means of simulations based on 3D reconstructions of pyramidal cells from rat somatosensory cortex. We show that somatic depolarization enables propagation via gap junctions into the initial segment and main axon, while somatic hyperpolarization disables it. We show further that somatic voltage cannot effectively control action potential propagation through gap junctions on minor collaterals; action potentials may therefore propagate freely from such collaterals regardless of somatic voltage. In previous work, VFOs are all but abolished during the hyperpolarization phase of slow-oscillations induced by anesthesia in vivo. This finding constrains the density of gap junctions on collaterals in our model and suggests that axonal sprouting due to cortical lesions may result in abnormally high gap junction density on collaterals, leading in turn to excessive VFO activity and hence to epilepsy via kindling.
1 . Munro E, Kopell N (2012) Subthreshold somatic voltage in neocortical pyramidal cells can control whether spikes propagate from the axonal plexus to axon terminals: a model study. J Neurophysiol 107:2833-52 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network; Neuron or other electrically excitable cell; Axon;
Brain Region(s)/Organism: Neocortex;
Cell Type(s): Neocortex L5/6 pyramidal GLU cell; Neocortex U1 L2/6 pyramidal intratelencephalic GLU cell;
Channel(s): I Na,t; I K; I Sodium; I Potassium;
Gap Junctions: Gap junctions;
Simulation Environment: NEURON; MATLAB;
Model Concept(s): Oscillations; Detailed Neuronal Models; Axonal Action Potentials; Epilepsy;
Implementer(s): Munro, Erin [ecmun at];
Search NeuronDB for information about:  Neocortex L5/6 pyramidal GLU cell; Neocortex U1 L2/6 pyramidal intratelencephalic GLU cell; I Na,t; I K; I Sodium; I Potassium;
function cycles = find_cycles(conn,node,cycles_through_node)
% give histogram of cycle length
% cycles is a list where each row gives
% [cycle_length #cycles_with_that_length]
% if cycles_through_node==1, only list cycles through node
% Note: lists cycles twice. If cycles go through node, the cycle is 
% counted for each outgoing neighbor. If the cycle does not go through
% node, it is counted on branch where cycle is found twice.
% Note: this assumes that node has more than one connection!!

lc = length(conn);

% Make a spanning tree centered around node
% where each vertex in the tree is placed so that
% its shortest distance in graph is its distance to node.
% Keep previous vertex
% Keep address for each vertex based on branch points.
% Keep distance from each vertex to closest branch point.
% Flag for branch when just AFTER branch node to tell
%    which direction to go from tree

E_tree = []; % edges in tree
E_cycle = []; % edges that make a cycle
% 1st_address1 1st_address2 cell1 cell2

rank_tree = struct('prev',cell(lc,1),'address',cell(lc,1),...

S = []; % searched
R= node; %reached
rank_tree(node) = struct('prev',0,'address',[],....

while ~isempty(R)
  %fprintf(1,'current cell: %d\n',R(1));
  nc = length(conn{R(1)});
  % decide if we are at branching point,
  % make note to add address if we are
  if nc-length(intersect([R S],conn{R(1)}))>=2
    branch_node = 1;
    branch_node = 0;
  for k=1:length(conn{R(1)})
    if isempty(find([R S]==conn{R(1)}(k),1))
      %fprintf(1,'not reached yet: %d\n',conn{R(1)}(k));
      R = [R conn{R(1)}(k)];
      rank_tree(conn{R(1)}(k)).prev = R(1);
      % is R(1) part of the address, 
      % i.e. branch of previous branch point?
      if rank_tree(R(1)).branch
        rank_tree(conn{R(1)}(k)).dist = 1;
        rank_tree(conn{R(1)}(k)).address = ...
            [rank_tree(R(1)).address R(1)];
        rank_tree(conn{R(1)}(k)).dist = ...
            rank_tree(R(1)).dist + 1;
        rank_tree(conn{R(1)}(k)).address = ...
      if branch_node
        rank_tree(conn{R(1)}(k)).branch = 1;
        rank_tree(conn{R(1)}(k)).branch = 0;
    elseif conn{R(1)}(k) ~= rank_tree(R(1)).prev
      %fprintf(1,'already in tree: %d\n',conn{R(1)}(k));
      % Neighbor is already in tree, so add edge to E_cycle if it's not
      % already there. Add edges listing lower node first so that 
      % they're easier to find.
      if R(1)<=conn{R(1)}(k) 
        %fprintf(1,'%d <= %d\n',R(1),conn{R(1)}(k));
        if isempty(E_cycle) || ...
              ~any(E_cycle(:,3)==R(1) & E_cycle(:,4)==conn{R(1)}(k))
          % edge not in E_cycle yet
          E_cycle = [E_cycle; branch(R(1),rank_tree)...
                     R(1) conn{R(1)}(k)];
          % fprintf(1,'1 - added cycle edge: %d %d %d %d\n',...
          % branch(R(1),rank_tree),...
          % branch(conn{R(1)}(k),rank_tree),...
          % R(1), conn{R(1)}(k));
      else % R(1) > conn{R(1)}(k)
           %fprintf(1,'%d > %d\n',R(1),conn{R(1)}(k));
        if isempty(E_cycle) || ...
              ~any(E_cycle(:,4)==R(1) &	E_cycle(:,3)==conn{R(1)}(k))
          % edge not in E_cycle yet
          E_cycle = [E_cycle; ...
                     conn{R(1)}(k) R(1)];
          % fprintf(1,'2 - added cycle edge: %d %d %d %d\n',...
          % branch(conn{R(1)}(k),rank_tree),...
          % branch(R(1),rank_tree),...
          % conn{R(1)}(k),R(1));
  S = [S R(1)];
  R = R(2:length(R));

% for i=1:length(conn)
% 	fprintf(1,'%d: address=[',i)
% 	for j=1:length(rank_tree(i).address)
% 		fprintf(1,'%d ',rank_tree(i).address(j))
% 	end
% 	fprintf(1,'], dist=%d\n',rank_tree(i).dist);
% end
% Cycles going through node are made from combinations
% of edges in E_cycle. First, compute cycles with 
% one extra edge
%fprintf(1,'length E_cycle = %d\n',length(E_cycle(:,1)));
n_branches = length(conn{node});
sE = size(E_cycle);
cycles = cell(n_branches,1);
%E = E_cycle;

for i=1:sE(1)
  dist = zeros(4,1);
  if ~cycles_through_node && E_cycle(i,1)==E_cycle(i,2)
    % cycle is on same branch, doesn't go through node
    %fprintf(1,'edge is on single branch: %d %d %d %d\n',E_cycle(i,1),...
    %	E_cycle(i,2),E_cycle(i,3),E_cycle(i,4));
    merge_ind = length(intersect(rank_tree(E_cycle(i,3)).address,...
                                 rank_tree(E_cycle(i,4)).address)) + 1;
    for j=3:4
      if merge_ind<=length(rank_tree(E_cycle(i,j)).address)
        dist(j) = rank_tree(E_cycle(i,j)).dist;
        dist(j) = 0;
      %fprintf(1,'node dist = %d\n',dist(j));
      for k=(merge_ind+1):length(rank_tree(E_cycle(i,j)).address)
        stop = rank_tree(E_cycle(i,j)).address(k);
        dist(j) = dist(j) + rank_tree(stop).dist;
        %fprintf(1,'%d dist = %d\n',stop,rank_tree(stop).dist);
    cycle_length = sum(dist) + 3;
  elseif E_cycle(i,1) ~= E_cycle(i,2)
    for j=3:4
      dist(j) = rank_tree(E_cycle(i,j)).dist;
      for k=1:length(rank_tree(E_cycle(i,j)).address);
        stop = rank_tree(E_cycle(i,j)).address(k);
        dist(j) = dist(j)+rank_tree(stop).dist;
    cycle_length = sum(dist)+1;
  else % cycles_through_node==1
  for j=1:2
    %fprintf('starting branch for E_cycle is %d\n',E_cycle(i,j))
    branch_ind = find(conn{node}==E_cycle(i,j),1);
    sc = size(cycles{branch_ind});
    if sc(1)>0
      cycle_ind = find(cycles{branch_ind}(:,1)...
      % cycle_ind could be empty if no cycles of this length yet
      cycle_ind = [];
    if isempty(cycle_ind)
      cycles{branch_ind} = [cycles{branch_ind};...
                          cycle_length 1];
      cycles{branch_ind}(cycle_ind,2) = ...
  end %j=1:2
end %i=1:sE(1)

% subfunctions --------------------------------------------

function b=branch(cell,rank_tree)
% give branch of cell based on address

if isempty(rank_tree(cell).address)
	b = cell;

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