Goldfish Mauthner cell (Medan et al 2017)

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Accession:189308
" ...In fish, evasion of a diving bird that breaks the water surface depends on integrating visual and auditory stimuli with very different characteristics. How do neurons process such differential sensory inputs at the dendritic level? For that we studied the Mauthner-cells (M-cells) in the goldfish startle circuit, which receive visual and auditory inputs via two separate dendrites, both accessible for in vivo recordings. We asked if electrophysiological membrane properties and dendrite morphology, studied in vivo, play a role in selective sensory processing in the M-cell. Our results show that anatomical and electrophysiological differences between the dendrites combine to produce stronger attenuation of visually evoked post synaptic potentials (PSPs) than to auditory evoked PSPs. Interestingly, our recordings showed also cross-modal dendritic interaction, as auditory evoked PSPs invade the ventral dendrite (VD) as well as the opposite, visual PSPs invade the lateral dendrite (LD). However, these interactions were asymmetrical with auditory PSPs being more prominent in the VD than visual PSPs in the LD. Modelling experiments imply that this asymmetry is caused by active conductances expressed in the proximal segments of the VD. ..."
Reference:
1 . Medan V, Mäki-Marttunen T, Sztarker J, Preuss T (2018) Differential processing in modality-specific Mauthner cell dendrites. J Physiol 596:667-689 [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: Goldfish;
Cell Type(s): Mauthner cell;
Channel(s): I Sodium; I Potassium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON; Python;
Model Concept(s): Sensory processing;
Implementer(s): Maki-Marttunen, Tuomo [tuomo.maki-marttunen at tut.fi];
Search NeuronDB for information about:  I Sodium; I Potassium;
# A script that runs the simulations with the dendritic stimulations (active dendrites) using
# various values for active conductances, fits the maximal membrane potential along the dendrites
# to an exponential decay and analyzes the results. Only ventral dendrite is set active, but the
# values of active conductances along the dendrite are controlled by two parameters: mean and
# gradient, such that the difference between two successive compartments along the main branch
# of the ventral dendrite is the gradient (unless either would be less than zero) and the average
# value of the active conductances along the dendrite is the given mean.
# The script plots two figures:
# decays_robustness.eps:
#   Plots the obtained exponential decay constants for each mean and gradient conductance value.
#   These data were not plotted in the paper but may help to understand the results.
# decay_orders_robustness.eps
#   Plots the order of decay constants between the two cases (orthodromic vs antidromic).
#   Corresponds to Figure 9A.
# Tuomo Maki-Marttunen, 2013-2017 (CC-BY 4.0)

import mcell_activedend_varycoeffs as mcell
from pylab import *
from neuron import h
import numpy.matlib
import pickle
import time
from os.path import exists

params = [ 0.008692502978958,  9.033350623275275,  4.380690156620405, -83.399741825852217,  0.000204081169084, -55.832300314690642, -67.436819173866425,  8.100021281440229,  9.559735981936562,  0.020391367006446,  1.412486203424452, -63.999689527874885,  6.046642114148621,  0.170597469041809 ] #(THE BEST ONE FOR ACTIVE VENTRAL DENDRITE)

stimbranches = ['lateral','ventral']
close("all")
f,axarr = subplots(1,2)
cols = ['#800000','#000080'][::-1]
linecols = ['#FF0000','#0000FF'][::-1]

# The variables 'cond_gradients' and 'cond_means' define the parameter space where the effect of the values of active conductances along the ventral dendrite is analyzed.
# The variable 'coeffs' will determine the active conductances at the ventral dendrite. The first compartment ("dend[20]", i.e. previously passive AIS between soma and active AIS) is set
# the conductances such that Na+ channel conductance is coeffs[0]*(Na+ conductance at active AIS) and K+ channel conductance is coeffs[0]*(K+ conductance at active AIS). In a similar
# manner, the following compartments along the main branch until the end of the ventral dendrite ("soma", "dend[21]", "dend[25]", "dend[27]", "dend[29]") receive values that are scaled
# by coeffs[1-5] from the values at active AIS. The values of 'coeffs' is gradually increasing or decreasing depending on the value of cond_gradients, but the last compartment is passive.
cond_gradients = [-0.01+0.0005*i for i in range(0,41)] 
cond_means = [0.0+0.0025*i for i in range(0,51)]
amps = [0.5,1,1.5,2,2.5,3,4,5]

if exists('activedend_decays_varyconds.sav'): # If the result file already exists, use it.
 unpicklefile = open('activedend_decays_varyconds.sav', 'r')
 unpickledlist = pickle.load(unpicklefile)
 unpicklefile.close()
 cond_gradients = unpickledlist[0]
 cond_means = unpickledlist[1]
 cMs_all = unpickledlist[2]
 maxVs_all = unpickledlist[3]
 cMsA_all = unpickledlist[4]
 maxVsA_all = unpickledlist[5]
else: # Simulate the model for all combinations of the cond_means and cond_gradients and save the data in the result file
 cMs_all = []
 maxVs_all = []
 for icond_grad in range(0,len(cond_gradients)):
  cMs_thiscond_grad = []
  maxVs_thiscond_grad = []
  print "ORTHO: icond_grad = "+str(icond_grad)+"/"+str(len(cond_gradients))
  for icond_mean in range(0,len(cond_means)):
   cMs_thiscond_mean = []
   maxVs_thiscond_mean = []
   for ibranch in range(0,len(stimbranches)):
     branch = stimbranches[ibranch]

     coeffs = [max(0,cond_means[icond_mean]+i*cond_gradients[icond_grad]) for i in range(-2,3)]+[0.0]
     data = mcell.run_model_dendritic_stims(params, branch, 5, 50.0, amps, [16, 29], [1.0, 1.0], 15, ["dend[20]", "soma", "dend[21]", "dend[25]", "dend[27]", "dend[29]"], coeffs) 

     times = data[0]
     Vrecs = data[1]
     dists = data[2]
     branches = data[3]

     cMs = []
     print "coeffs = "+str(coeffs)
     for iamp in range(0,len(amps)):
       XL = array([dists[iloc] for iloc in range(0,len(dists)) if dists[iloc] < 400 and branches[iloc]==ibranch or branches[iloc]==-1])
       XM = matrix(c_[np.matlib.repmat(XL,1,1).T, kron([1],ones([len(XL),])).T])
       YL = [array([max(Vrecs[iamp][iloc]) for iloc in range(0,len(dists)) if dists[iloc] < 400 and branches[iloc]==ibranch or branches[iloc]==-1])]
       YM = matrix(concatenate(YL)).T
       thiserr = inf
   
       Vappr = params[3]
 
       cM = inv(XM.T*XM)*XM.T*(log(YM-Vappr))
       thiserr = sum(sum(abs(YM-Vappr-exp(XM*cM))))
       cMs.append(cM[:])
     cMs_thiscond_mean.append(cMs[:])
     maxVs_thiscond_mean.append([max(Vrecs[i][30]) for i in range(0,len(amps))])
   cMs_thiscond_grad.append(cMs_thiscond_mean[:])
   maxVs_thiscond_grad.append(maxVs_thiscond_mean[:])
  cMs_all.append(cMs_thiscond_grad[:])
  maxVs_all.append(maxVs_thiscond_grad[:])

 cMsA_all = []
 maxVsA_all = []
 for icond_grad in range(0,len(cond_gradients)):
  cMsA_thiscond_grad = []
  maxVsA_thiscond_grad = []
  print "ANTI: icond_grad = "+str(icond_grad)+"/"+str(len(cond_gradients))
  for icond_mean in range(0,len(cond_means)):
   cMsA_thiscond_mean = []
   maxVsA_thiscond_mean = []

   stim = []
   for i in range(0,len(amps)):
     stim.append([5,55,amps[i]])
   coeffs = [max(0,cond_means[icond_mean]+i*cond_gradients[icond_grad]) for i in range(-2,3)]+[0.0]
   data = mcell.run_model_somatic_stims(params, stim,[5.0, 10.0, 0], True,  ["dend[20]", "soma", "dend[21]", "dend[25]", "dend[27]", "dend[29]"], coeffs)

   times = data[0]
   Vrecs = data[1]
   VrecsDend = data[2]
   dists = data[3]
   branches = data[4]

   print "coeffs = "+str(coeffs)
   for ibranch in range(0,2):
     cMs = []
     for iamp in range(0,len(amps)):
       XL = array([dists[iloc] for iloc in range(0,len(dists)) if dists[iloc] < 400 and branches[iloc]==ibranch or branches[iloc]==-1])
       XM = matrix(c_[np.matlib.repmat(XL,1,1).T, kron([1],ones([len(XL),])).T])
       YL = [array([max(VrecsDend[iamp][iloc]) for iloc in range(0,len(dists)) if dists[iloc] < 400 and branches[iloc]==ibranch or branches[iloc]==-1])]
       YM = matrix(concatenate(YL)).T
       thiserr = inf
   
       Vappr = params[3] 
 
       cM = inv(XM.T*XM)*XM.T*(log(YM-Vappr))
       thiserr = sum(sum(abs(YM-Vappr-exp(XM*cM))))
       cM = cM
       cMs.append(cM[:])
       if icond_grad == 4 and icond_mean == 3:
         print str(cM)
     cMsA_thiscond_mean.append(cMs[:])
   maxVsA_thiscond_grad.append([max(VrecsDend[i][30]) for i in range(0,len(amps))])
   cMsA_thiscond_grad.append(cMsA_thiscond_mean[:])
  cMsA_all.append(cMsA_thiscond_grad[:])
  maxVsA_all.append(maxVsA_thiscond_grad[:])

 picklelist = [cond_gradients, cond_means, cMs_all, maxVs_all, cMsA_all, maxVsA_all]
 file = open('activedend_decays_varyconds.sav', 'w')
 pickle.dump(picklelist,file)
 file.close()

cMsL = [[[log(3.0)/cMs_all[i][j][0][k][0][0,0] for j in range(0,len(cMs_all[i]))] for i in range(0,len(cMs_all))] for k in range(0,len(amps))]
cMsV = [[[log(3.0)/cMs_all[i][j][1][k][0][0,0] for j in range(0,len(cMs_all[i]))] for i in range(0,len(cMs_all))] for k in range(0,len(amps))]
mcMsL = mean(array(cMsL),axis=0)
mcMsV = mean(array(cMsV),axis=0)

cMsAL = [[[-log(3.0)/cMsA_all[i][j][0][k][0][0,0] for j in range(0,len(cMsA_all[i]))] for i in range(0,len(cMsA_all))] for k in range(0,len(amps))]
cMsAV = [[[-log(3.0)/cMsA_all[i][j][1][k][0][0,0] for j in range(0,len(cMsA_all[i]))] for i in range(0,len(cMsA_all))] for k in range(0,len(amps))]
mcMsAL = mean(array(cMsAL),axis=0)
mcMsAV = mean(array(cMsAV),axis=0)

f,axarr = subplots(2,2)
a1 = axarr[0,0].imshow(mcMsL,extent=[min(cond_means),max(cond_means),min(cond_gradients),max(cond_gradients)],interpolation='nearest')
colorbar(a1,ax = axarr[0,0], orientation='horizontal')
axarr[0,0].set_title('Ortho, L')

a2 = axarr[0,1].imshow(mcMsV,extent=[min(cond_means),max(cond_means),min(cond_gradients),max(cond_gradients)],interpolation='nearest')
colorbar(a2,ax = axarr[0,1], orientation='horizontal')
axarr[0,1].set_title('Ortho, C')

a3 = axarr[1,0].imshow(mcMsAL,extent=[min(cond_means),max(cond_means),min(cond_gradients),max(cond_gradients)],interpolation='nearest')
colorbar(a3,ax = axarr[1,0], orientation='horizontal')
axarr[1,0].set_title('Anti, L')

a4 = axarr[1,1].imshow(mcMsAV,extent=[min(cond_means),max(cond_means),min(cond_gradients),max(cond_gradients)],interpolation='nearest')
colorbar(a4,ax = axarr[1,1], orientation='horizontal')
axarr[1,1].set_title('Anti, V')

f.savefig("decays_robustness.eps")

mask_chosen = zeros(array(cMsL[0]).shape)
mask_chosen[find(array(cond_gradients)==0.0)[0],find(array(cond_means)==0.035)[0]] = True
f,axarr = subplots(1,1)

data = (12*logical_and(greater(numpy.min(array(cMsL[1:]),axis=0),numpy.max(array(cMsV[1:]),axis=0)),greater(numpy.min(array(cMsAV[1:-2]),axis=0),numpy.max(array(cMsAL[1:-2]),axis=0))) + \
        7.5*logical_and(greater(numpy.min(array(cMsL[1:]),axis=0),numpy.max(array(cMsV[1:]),axis=0)),logical_not(greater(numpy.min(array(cMsAV[1:-2]),axis=0),numpy.max(array(cMsAL[1:-2]),axis=0)))) + \
        8*logical_and(logical_not(greater(numpy.min(array(cMsL[1:]),axis=0),numpy.max(array(cMsV[1:]),axis=0))),greater(numpy.min(array(cMsAV[1:-2]),axis=0),numpy.max(array(cMsAL[1:-2]),axis=0))) + \
        -0.5*logical_and(greater(numpy.min(array(cMsL[1:]),axis=0),numpy.max(array(cMsV[1:]),axis=0)),less(numpy.max(array(cMsAV[1:-2]),axis=0),numpy.min(array(cMsAL[1:-2]),axis=0))) + \
        0.5*logical_and(less(numpy.max(array(cMsL[1:]),axis=0),numpy.min(array(cMsV[1:]),axis=0)),greater(numpy.min(array(cMsAV[1:-2]),axis=0),numpy.max(array(cMsAL[1:-2]),axis=0))) \
        )*(1-mask_chosen)
data2 = zeros([2*x for x in data.shape])
for i in range(0,data.shape[0]):
  for j in range(0,data.shape[1]):
    if abs(data[i,j]-12) < 1e-7 or abs(data[i,j]-7.0) < 1e-7 or abs(data[i,j]-0) < 1e-7 or abs(data[i,j]-8.5) < 1e-7:
      data2[2*i:2*i+2,2*j:2*j+2] = data[i,j]
    elif abs(data[i,j]-7.5) < 1e-7:
      data2[2*i:2*i+2,2*j:2*j+2] = array([[7,12],[12,7]])
    elif abs(data[i,j]-8.0) < 1e-7:
      data2[2*i:2*i+2,2*j:2*j+2] = array([[12,8],[8,12]])
a3 = axarr.imshow(data2, extent=[min(cond_means),max(cond_means),max(cond_gradients),min(cond_gradients)],interpolation='nearest', cmap="hot")
axarr.set_ylim([-0.01,0.00518])
axarr.set_aspect('auto')
axarr.set_position([0.2,0.33,0.6,0.5])
axarr.set_xlabel('$c_{\mu}$')
myyl = axarr.set_ylabel('$c_{\delta}$')
myyl.set_rotation(0)
f.savefig("decay_orders_robustness.eps")