Membrane potential changes in dendritic spines during APs and synaptic input (Palmer & Stuart 2009)

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" ... Finally, we used simulations of our experimental observations in morphologically realistic models to estimate spine neck resistance. These simulations indicated that spine neck resistance ranges up to ~500 M Ohm. Spine neck resistances of this magnitude reduce somatic EPSPs by ~15%, indicating that the spine neck is unlikely to act as a physical device to significantly modify synaptic strength."
1 . Palmer LM, Stuart GJ (2009) Membrane potential changes in dendritic spines during action potentials and synaptic input. J Neurosci 29:6897-903 [PubMed]
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:
Cell Type(s):
Gap Junctions:
Simulation Environment: NEURON;
Model Concept(s): Active Dendrites; Influence of Dendritic Geometry; Synaptic Integration;
Implementer(s): Morse, Tom [Tom.Morse at]; Stuart, Greg J. [greg.stuart at];
// fig5.hoc

objref soma_v_vec, dend_v_vec, spine_v_vec,t_vec

soma_v_vec = new Vector()
dend_v_vec = new Vector()
spine_v_vec = new Vector()
t_vec = new Vector()


proc fig5b() {
/* Documention on EPSP stimulus setup:

One of the key observations in the paper was that a spine neck resistance of
approximately 500 MOhm neck was required to reproduce our experimental
findings (Fig.5b). The spine neck resistance in this model is 514 MOhm (diameter
0.051 um), and reproduces both Fig.5B in the paper and the experimental data
in Fig.5A.

It uses a 500 pS "AMPA" conductance at spine_head[0]. Activation of this
input alone gives an EPSP in the dendritic shaft, at dend1[881](0.5), of
~1.5 mV. This is similar to that observed experimentally for quantal,
putative single spine, events in these dendrites, but much smaller than the
dendritic EPSP we observed experimentally during synaptic stimulation. We
concluded from this that our synaptic stimulation activating multiple
surrounding inputs which sum together to increase the amplitude of the
recorded dendritic EPSP. Consistent with this idea the EPSP recorded at the
soma in these experiments was large (~ 5mV), and much larger than one would
predict if only a single spine was activated.

As stated in the Methods to mimic this "background" input "we placed
additional synaptic inputs onto the same dendrite as that with the
reconstructed spine. The number of additional inputs on the same dendrite
was adjusted to match the amplitude of the "background" depolarization
observed in experimental responses in spines and the adjacent dendrite.

What is not stated in the Methods is actually how we did this. This was
done by adding a synapse halfway along compartment
dend1[879], a slightly more proximal dendritic compartment on the same
dendritic branch as the spine. A synapse with conductance of 10.5 nS seems
to do the trick.
  tstop = 30
  dt = 0.01 // turn off variable step method
  step_per_ms = 100
  IClamp[0].amp=0   // make sure the hyper-pol. current is off
  syn[3].gmax = 0.0105  // 10.5 nS EPSP producing conductance
  spine_neck[0] diam = 0.051 // Rneck = 514 M Ohm
  syn[0].onset= 5
  syn[0].gmax = 0.0005 // on spine_head[0]
  syn[1].gmax = 0.0   // on spine_head[1]
  syn[2].gmax = 0.0   // on spine_head[2]
  {init() run()}
  {spine_v_vec.resize(0) dend_v_vec.resize(0)}
  g.exec_menu("View = plot")  // fig 5b shares same graph with fig. 2c

objref fig5c_g, fig5d_g
objref soma_v_vecs[7], t_vecs[7], EPSP_size_vec, neck_resistance_vec
EPSP_size_vec = new Vector()
neck_resistance_vec = new Vector()

proc fig5cd() {
  tstop = 80
  dt= 0.05
  CVode[0].active(0) // switch to fixed time step to match paper result
  EPSP_size_vec.resize(0)  // set to empty in case run multiple times
  print "Calculating fig5c, 5d"
  spine_neck[0].diam(0.5)=diam_of_Rn(514e6)  // value from paper
  print "Calculating fig 5c with spine neck diam ",spine_neck[0].diam(0.5)
  syn[0].onset = 20 
  syn[3].gmax = 0.0
  fig5c_g = new Graph()
  fig5d_g = new Graph()
  num_points = 5
  for (iter=0; iter<num_points+1; iter+=1) {
    t_vecs[iter] = new Vector()
    epsilon = 1e-4  // helps not crash when Ra  0
    spine_neck[0].Ra = 105 *( (iter+epsilon)/num_points )
    print "iter: ",iter,"/",num_points," neck axial resistance = ", \
      spine_neck[0].Ra," total neck resistance = ",         \
      Rn(spine_neck[0].diam(0.5))*(iter+epsilon)/(num_points*1e6)," MOhms"
    {init() run()}
  fig5c_g.exec_menu("Keep Lines")
  for iter=0,num_points {
//    soma_v_vecs[iter].line(fig5c_g,t_vecs[iter],1,iter+1)
  fig5c_g.exec_menu("View = plot")
  fig5c_g.label(0.47,0.9,"Fig. 5c")
  CVode[0].active(1) // turn on variable time step for other figures
  EPSP_size_vec.div(normalize).mul(100)  // change to percentage of first
  EPSP_size_vec.line(fig5d_g, neck_resistance_vec)
  EPSP_size_vec.mark(fig5d_g, neck_resistance_vec,"o")
  fig5d_g.label(0.47,0.9,"Fig. 5d")

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