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;
# General tools, Tuomo Maki-Marttunen 2013-2017 (CC-BY 4.0)

import math
import copy
import pylab

def spike_times(time,vrec,V_min_peak=-20,V_max_valley=0):
  valley_reached = 1
  sptime = []  
  for j in range(1,len(time)-1):
    if valley_reached and vrec[j] >= V_min_peak and vrec[j] > vrec[j-1] and vrec[j] >= vrec[j+1]:
      valley_reached = 0
      sptime.append(time[j])
    elif valley_reached==False and vrec[j] <= V_max_valley:
      valley_reached = 1
  return sptime  

#membpotderivs(time,vrec): Given the membrane potentials (vrec) at time points time[0],time[1],...,time[N-1],
#return the derivatives at time points time[1],time[2],...,time[N-3]
def membpotderivs(time,vrec):
  N = len(time)
  tdiff = [x-y for x,y in zip(time[1:N-1],time[0:N-2])]
  vdiff = [x-y for x,y in zip(vrec[1:N-1],vrec[0:N-2])]
  mderiv = [x/y for x,y in zip(vdiff,tdiff)]
  return [0.5*(x+y) for x,y in zip(mderiv[1:N-2],mderiv[0:N-3])]

#limitcyclescaledv(v1,dv1,v2,dv2): Give the coefficient for memb. pot. derivative that one has to use in order to make
#the difference on the derivative axis as significant as the difference on the memb. pot. axis
def limitcyclescaledv(v1,dv1,v2,dv2):
  maxv = max(max(v1),max(v2))
  minv = min(min(v1),min(v2))
  maxdv = max(max(dv1),max(dv2))
  mindv = min(min(dv1),min(dv2))
  return 1.0*(maxv-minv)/(maxdv-mindv)

def limitcyclediff(v1,dv1,v2,dv2,dvcoeff=0.1):
  N1 = len(v1)
  N2 = len(v2)
  dv1 = [dvcoeff*x for x in dv1]
  dv2 = [dvcoeff*x for x in dv2]
  Dmin = N1*[0]
  for i in range(0,N1):
    Dmin[i] = math.sqrt(min([(x-v1[i])**2+(y-dv1[i])**2 for x,y in zip(v2,dv2)]))
  vdiff = [x-y for x,y in zip(v1[1:N1],v1[0:N1-1])] 
  dvdiff = [x-y for x,y in zip(dv1[1:N1],dv1[0:N1-1])] 
  h = [math.sqrt(x**2+y**2) for x,y in zip(vdiff,dvdiff)]
  #use the trapezoid rule for integration:
  Dminmean = [(x+y)/2.0 for x,y in zip(Dmin[1:N1],Dmin[0:N1-1])]
  print "hsum="+str(sum(h))
  return sum([x*y for x,y in zip(Dminmean,h)])
  

def interpolate(tref,vref,tint): #Assumes that the trefs come sorted!
  vint = len(tint)*[0.0]
  addedOne = False
  #print tref
  #print tint
  #if tref[len(tref)-1] == tint[len(tint)-1]:
  #  tref.append(tref[len(tref)-1]+0.0001)
  #  vref.append(vref[len(tref)-1])
  #  addedOne = True
  if tref[0] > tint[0] or tref[len(tref)-1] < tint[len(tint)-1]:
    print "Extrapolation needed!"
    return len(tint)*[-1]
  indvrecnow = 0  
  for j in range(0,len(tint)):
    while tref[indvrecnow+1] <= tint[j]:
      indvrecnow = indvrecnow + 1
      if indvrecnow == len(tref)-1: # It must be the last index if this happens
        vint[j:len(tint)] = [vref[indvrecnow]]*(len(tint)-j)
        return vint
    vint[j] = vref[indvrecnow] + 1.0*(tint[j]-tref[indvrecnow])/(tref[indvrecnow+1]-tref[indvrecnow])*(vref[indvrecnow+1]-vref[indvrecnow])
  return vint

def interpolate_extrapolate_constant(tref,vref,tint): #Assumes that the trefs come sorted!
  vint = len(tint)*[0.0]
  addedOne = False
  #print tref
  #print tint
  #if tref[len(tref)-1] == tint[len(tint)-1]:
  #  tref.append(tref[len(tref)-1]+0.0001)
  #  vref.append(vref[len(tref)-1])
  #  addedOne = True

  indvrecnow = 0  
  for j in range(0,len(tint)):
    if tint[j] < tref[0]:
      vint[j] = vref[0]
      continue
    if indvrecnow >= len(tref) - 1:
      vint[j] = vref[-1]
    while tref[indvrecnow+1] <= tint[j]:
      indvrecnow = indvrecnow + 1
      if indvrecnow == len(tref)-1: # It must be the last index if this happens
        vint[j:len(tint)] = [vref[indvrecnow]]*(len(tint)-j)
        return vint
    vint[j] = vref[indvrecnow] + 1.0*(tint[j]-tref[indvrecnow])/(tref[indvrecnow+1]-tref[indvrecnow])*(vref[indvrecnow+1]-vref[indvrecnow])
  return vint

#kronecker product of list A and list B
def kron(A,B):
  C = []
  if type(B[0]) is int or type(B[0]) is float:
    for i in range(0,len(A)):
      for j in range(0,len(B)):
        print "asdf"
        print B[j]
        C.append(A[i]*B[j])
  elif type(B[0][0]) is int or type(B[0][0]) is float:
    for i in range(0,len(A)):
      for j in range(0,len(B)):
        C.append([x*A[i] for x in B[j]])
  return C
  
def cumprod(A):
  B = len(A)*[0]; B[0]=A[0]
  for j in range(1,len(A)):
    B[j] = B[j-1]*A[j]
  return B

def printlistlen(A):
  #TODO: recursive method might work out but needs some thought...
  #toCheck = A
  #lens = [len(x) for x in A]
  #levels = [0 for x in A]
  #while type(toCheck) is list and len(toCheck) > 0:
  #  while type(toCheck[0]) is list and len(toCheck[0]) > 0:
  #    toCheck.append(toCheck[0][0])
  #    lens.append[len
  #    toCheck[0].pop(0)
  nan = -1
  if type(A) is list:
   B = copy.deepcopy(A)
   listFound0 = False
   for i0 in range(0,len(B)):
    if type(B[i0]) is list:
     listFound0 = True
     listFound1 = False
     for i1 in range(0,len(B[i0])):
      if type(B[i0][i1]) is list:
       listFound1 = True
       listFound2 = False
       for i2 in range(0,len(B[i0][i1])):
        if type(B[i0][i1][i2]) is list:
         listFound2 = True
         listFound3 = False
         for i3 in range(0,len(B[i0][i1][i2])):
          if type(B[i0][i1][i2][i3]) is list:
           listFound3 = True
           listFound4 = False
           for i4 in range(0,len(B[i0][i1][i2][i3])):
            if type(B[i0][i1][i2][i3][i4]) is list:
             listFound4 = True
             listFound5 = False
             for i5 in range(0,len(B[i0][i1][i2][i3][i4])):
              if type(B[i0][i1][i2][i3][i4][i5]) is list:
               listFound5 = True
               listFound6 = False               
               for i6 in range(0,len(B[i0][i1][i2][i3][i4][i5])):
                if type(B[i0][i1][i2][i3][i4][i5][i6]) is list:
                  listFound6 = True
                  B[i0][i1][i2][i3][i4][i5][i6] = len(B[i0][i1][i2][i3][i4][i5][i6])
                else:
                  B[i0][i1][i2][i3][i4][i5][i6] = nan
               if not listFound6:
                 B[i0][i1][i2][i3][i4][i5] = len(B[i0][i1][i2][i3][i4][i5])
              else:
                B[i0][i1][i2][i3][i4][i5] = nan
             if not listFound5:
               B[i0][i1][i2][i3][i4] = len(B[i0][i1][i2][i3][i4])
            else:
              B[i0][i1][i2][i3][i4] = nan
           if not listFound4:
             B[i0][i1][i2][i3] = len(B[i0][i1][i2][i3])
          else:
            B[i0][i1][i2][i3] = nan
         if not listFound3:
           B[i0][i1][i2] = len(B[i0][i1][i2])
        else:
          B[i0][i1][i2] = nan
       if not listFound2:
         B[i0][i1] = len(B[i0][i1])
      else:
        B[i0][i1] = nan
     if not listFound1:
       B[i0] = len(B[i0])
    else:
      B[i0] = nan
   if not listFound0:
     B = len(B)
  else:
   B = nan
  print B

def drawarrow(ax,x,y,acoeff=1,prc=0.9,lw=1,lc='#000000'):
  d = [x[1]-x[0], y[1]-y[0]];
  k = pylab.sqrt(d[0]**2 + d[1]**2)
  d = d/k

  dperp = [acoeff*z for z in [-d[1], d[0]]];
  lens = k-k*(1-prc);
  perplen = 0.5*k*(1-prc);

  px = [x[0],x[1],x[0]+lens*d[0]+perplen*dperp[0],x[0]+lens*d[0]-perplen*dperp[0]];
  py = [y[0],y[1],y[0]+lens*d[1]+perplen*dperp[1],y[0]+lens*d[1]-perplen*dperp[1]];

  px = [px[0],px[1],px[2],px[1],px[3]]
  py = [py[0],py[1],py[2],py[1],py[3]]
  #px = reshape([px(:,[1 2 3 2 4]) nan(size(x,1),1)]',size(x,1)*6,1);
  #py = reshape([py(:,[1 2 3 2 4]) nan(size(x,1),1)]',size(x,1)*6,1);
  ax.plot(px,py,'k-',linewidth=lw,color=lc)

def timeseriesmean(times,x):
  return 1.0*sum([(t2-t1)*(x1+x2)/2 for t1,t2,x1,x2 in zip(times[0:-1],times[1:],x[0:-1],x[1:])])/(times[-1]-times[0])

def timeseriessecondmoment(times,x):
  return 1.0*sum([(t2-t1)*(x1**2+x2**2)/2 for t1,t2,x1,x2 in zip(times[0:-1],times[1:],x[0:-1],x[1:])])

def timeseriesstd(times,x,xmean=pylab.nan):
  if pylab.isnan(xmean):
    xmean = timeseriesmean(times,x)
  return pylab.sqrt(1.0*sum([(t2-t1)*((x1-xmean)**2+(x2-xmean)**2)/2 for t1,t2,x1,x2 in zip(times[0:-1],times[1:],x[0:-1],x[1:])])/(times[-1]-times[0]))

def drawdiscontinuity(ax,y,yoffset,x=0,xoffset=0.1,lw=2.0,lw2=1.0):
  thisline = ax.plot([x-xoffset,x+xoffset],[y-yoffset,y],'k-',linewidth=lw2)
  thisline[0].set_clip_on(False)
  thisline = ax.plot([x-xoffset,x+xoffset],[y,y+yoffset],'k-',linewidth=lw2)
  thisline[0].set_clip_on(False)
  thisline = ax.plot([x-xoffset,x+xoffset],[y-0.5*yoffset,y+0.5*yoffset],'k-',color='#FFFFFF',zorder=100,linewidth=lw)
  thisline[0].set_clip_on(False)

def colorsredtolila(N,coeff):
  C = colorsredtolilaint(N)
  C = [(int(c[0]*coeff), int(c[1]*coeff), int(c[2]*coeff)) for c in C]
  hexlist = []
  for j in range(0,N):
    myhex = '#'
    for k in range(0,3):
      if C[j][k] < 16:
        myhex = myhex + '0' + hex(C[j][k])[2]
      else:
        myhex = myhex + hex(C[j][k])[2:4]
    hexlist.append(myhex)
  return hexlist

def colorsredtolilaint(N):

  linchange = [1.0/(N-1)*x for x in range(0,N)]
  linchange_x = [x/0.8 for x in [0.0, 0.36, 0.45, 0.65, 0.7, 0.8]]
  linchange_y = [0.0, 0.29, 0.46, 0.65, 0.75, 0.83]
  for i in range(0,len(linchange)):
    ind = N
    for j in range(0,len(linchange_x)):
      if linchange[i] >= linchange_x[j]:
        ind = j
    if ind < len(linchange_x)-1:
      linchange[i] = linchange_y[ind]+(linchange_y[ind+1]-linchange_y[ind])*(linchange[i]-linchange_x[ind])/(linchange_x[ind+1]-linchange_x[ind])

  C = hsv2rgblist([int(255*x) for x in linchange],[1.0]*N,[1.0]*N);
  return C

def hsv2rgblist(h, s, v):
  hs = []
  ss = []
  vs = []
  for i in range(0,len(h)):
    h1, s1, v1 = hsv2rgb(h[i],s[i],v[i])
    hs.append(h1)
    ss.append(s1)
    vs.append(v1)
  return zip(hs,ss,vs)

def hsv2rgb(h, s, v):
  h = float(h)
  s = float(s)
  v = float(v)
  h60 = h / 60.0
  h60f = math.floor(h60)
  hi = int(h60f) % 6
  f = h60 - h60f
  p = v * (1 - s)
  q = v * (1 - f * s)
  t = v * (1 - (1 - f) * s)
  r, g, b = 0, 0, 0
  if hi == 0: r, g, b = v, t, p
  elif hi == 1: r, g, b = q, v, p
  elif hi == 2: r, g, b = p, v, t
  elif hi == 3: r, g, b = p, q, v
  elif hi == 4: r, g, b = t, p, v
  elif hi == 5: r, g, b = v, p, q
  r, g, b = int(r * 255), int(g * 255), int(b * 255)
  return r, g, b
    
def rgb2hsv(r, g, b):
  r, g, b = r/255.0, g/255.0, b/255.0
  mx = max(r, g, b)
  mn = min(r, g, b)
  df = mx-mn
  if mx == mn:
    h = 0
  elif mx == r:
    h = (60 * ((g-b)/df) + 360) % 360
  elif mx == g:
    h = (60 * ((b-r)/df) + 120) % 360
  elif mx == b:
    h = (60 * ((r-g)/df) + 240) % 360
  if mx == 0:
    s = 0
  else:
    s = df/mx
  v = mx
  return h, s, v