Thalamic quiescence of spike and wave seizures (Lytton et al 1997)

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Accession:9889
A phase plane analysis of a two cell interaction between a thalamocortical neuron (TC) and a thalamic reticularis neuron (RE).
Reference:
1 . Lytton WW, Contreras D, Destexhe A, Steriade M (1997) Dynamic interactions determine partial thalamic quiescence in a computer network model of spike-and-wave seizures. J Neurophysiol 77:1679-96 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Thalamus;
Cell Type(s): Thalamus geniculate nucleus (lateral) principal neuron; Thalamus reticular nucleus cell;
Channel(s): I T low threshold;
Gap Junctions:
Receptor(s): GabaA; Glutamate;
Gene(s):
Transmitter(s): Gaba; Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Temporal Pattern Generation; Oscillations; Calcium dynamics;
Implementer(s): Lytton, William [billl at neurosim.downstate.edu]; Destexhe, Alain [Destexhe at iaf.cnrs-gif.fr];
Search NeuronDB for information about:  Thalamus geniculate nucleus (lateral) principal neuron; Thalamus reticular nucleus cell; GabaA; Glutamate; I T low threshold; Gaba; Glutamate;
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lytton97
README
AMPA.mod
calciumpump_destexhe.mod *
GABAB1.mod
GABALOW.mod
gen.mod
HH_traub.mod *
IAHP_destexhe.mod
ICAN_destexhe.mod
Ih_old.mod *
IT_wang.mod
IT2_huguenard.mod
nmda.mod
passiv.mod
presyn.mod *
pulse.mod *
rand.mod
boxes.hoc *
declist.hoc *
decvec.hoc *
default.hoc *
directory
fig7.gif
geom.hoc
grvec.hoc
init.hoc
jnphys77_1679.pdf
local.hoc *
mosinit.hoc
network.hoc
nrnoc.hoc *
params.hoc
presyn.inc *
queue.inc *
run.hoc
simctrl.hoc *
snshead.inc *
synq.inc *
xtmp
                            
: $Id: synq.inc,v 1.8 1996/02/14 20:45:23 billl Exp $

COMMENT
Basic synapse routines from Alain Destexhe and Zach Meinen with queue added.

-----------------------------------------------------------------------------
Simple synaptic mechanism derived for first order kinetics of
binding of transmitter to postsynaptic receptors.

A. Destexhe & Z. Mainen, The Salk Institute, March 12, 1993.
Last modif. Sept 8, 1993.

Reference:

Destexhe, A., Mainen, Z. and Sejnowski, T.J.  An efficient method for 
computing synaptic conductances based on a kinetic model of receptor binding.
Neural Computation, 6: 14-18, 1994.
-----------------------------------------------------------------------------

During the arrival of the presynaptic spike (detected by threshold 
crossing), it is assumed that there is a brief pulse (duration=Cdur)
of neurotransmitter C in the synaptic cleft (the maximal concentration
of C is Cmax).  Then, C is assumed to bind to a receptor Rc according 
to the following first-order kinetic scheme:

Rc + C ---(Alpha)--> Ro							(1)
       <--(Beta)--- 

where Rc and Ro are respectively the closed and open form of the 
postsynaptic receptor, Alpha and Beta are the forward and backward
rate constants.  If R represents the fraction of open gates Ro, 
then one can write the following kinetic equation:

dR/dt = Alpha * C * (1-R) - Beta * R					(2)

and the postsynaptic current is given by:

Isyn = gmax * R * (V-Erev)						(3)

where V is the postsynaptic potential, gmax is the maximal conductance 
of the synapse and Erev is the reversal potential.

If C is assumed to occur as a pulse in the synaptic cleft, such as

C     _____ . . . . . . Cmax
      |   |
 _____|   |______ . . . 0 
     t0   t1

then one can solve the kinetic equation exactly, instead of solving
one differential equation for the state variable and for each synapse, 
which would be greatly time consuming...  

Equation (2) can be solved as follows:

1. during the pulse (from t=t0 to t=t1), C = Cmax, which gives:

   R(t-t0) = Rinf + [ R(t0) - Rinf ] * exp (- (t-t0) / Rtau )		(4)

where 
   Rinf = Alpha * Cmax / (Alpha * Cmax + Beta) 
and
   Rtau = 1 / (Alpha * Cmax + Beta)

2. after the pulse (t>t1), C = 0, and one can write:

   R(t-t1) = R(t1) * exp (- Beta * (t-t1) )				(5)

There is a pointer called "pre" which must be set to the variable which
is supposed to trigger synaptic release.  This variable is usually the
presynaptic voltage but it can be the presynaptic calcium concentration, 
or other.  Prethresh is the value of the threshold at which the release is
initiated.

Once pre has crossed the threshold value given by Prethresh, a pulse
of C is generated for a duration of Cdur, and the synaptic conductances
are calculated accordingly to eqs (4-5).  Another event is not allowed to
occur for Deadtime milliseconds following after pre rises above threshold.

The user specifies the presynaptic location in hoc via the statement
	connect pre_GABA[i] , v.section(x)

where x is the arc length (0 - 1) along the presynaptic section (the currently
specified section), and i is the synapse number (Which is located at the
postsynaptic location in the usual way via
	postsynaptic_section {loc_GABA(i, x)}
Notice that loc_GABA() must be executed first since that function also
allocates space for the synapse.

*****************************************************************************
    NEURON {
      POINT_PROCESS NAME
    }

    PARAMETER {

      Cmax	= 1	(mM)		: max transmitter concentration
      Cdur	= 1.08	(ms)		: transmitter duration (rising phase)
      Alpha	= 1	(/ms mM)	: forward (binding) rate
      Beta	= 0.02	(/ms)		: backward (unbinding) rate
      Erev	= -80	(mV)		: reversal potential
      Prethresh = 0 			: voltage level nec for release
      Deadtime = 1	(ms)		: mimimum time between release events
      gmax		(umho)		: maximum conductance
    }

    
    INCLUDE "synq.inc"
*****************************************************************************

ENDCOMMENT

INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}

NEURON {
  POINTER pre
  RANGE C, R, R0, R1, g, gmax, lastrelease, spk
  NONSPECIFIC_CURRENT i
  GLOBAL Cmax, Cdur, Alpha, Beta, Erev, Prethresh, Deadtime, Rinf, Rtau
}
 
INCLUDE "queue.inc"  : queue routines

UNITS {
  (nA) = (nanoamp)
  (mV) = (millivolt)
  (umho) = (micromho)
  (mM) = (milli/liter)
}

ASSIGNED {
  v		(mV)		: postsynaptic voltage
  i 		(nA)		: current = g*(v - Erev)
  g 		(umho)		: conductance
  C		(mM)		: transmitter concentration
  R				: fraction of open channels
  R0				: open channels at start of release
  R1				: open channels at end of release
  Rinf				: steady state channels open
  Rtau		(ms)		: time constant of channel binding
  pre 				: pointer to presynaptic variable
  spk                           : flag for spk occuring
  lastrelease	(ms)		: time of last spike
}

INITIAL {
  initq()                       : ****

  R = 0
  C = 0
  R0 = 0
  R1 = 0
  Rinf = Cmax*Alpha / (Cmax*Alpha + Beta)
  Rtau = 1 / ((Alpha * Cmax) + Beta)
  lastrelease = -9e4
}

BREAKPOINT {
  SOLVE releaser
  g = gmax * R
  i = g*(v - Erev)
}

PROCEDURE releaser() { LOCAL q
  :will crash if user hasn't set pre with the connect statement 
  
  if (! spk && pre > Prethresh) { : new spike occured?
    spk = 1
    pushq(t+delay) }

  if (spk && pre < Prethresh) { : spike over?
    spk = 0 
  }

  q = ((t - lastrelease) - Cdur) : time since last release ended

  : ready for another release?
  if (q >= Deadtime + dt) {

    if (t >= queu[head]) {      : **** a current spike time
      popq()                    : ****
      C = Cmax			: start new release
      R0 = R
      lastrelease = t
    }
  } else {		: still releasing?

    if (t > queu[head]) { popq() } : **** throw away value from missed spikes

  } 

  if (q < Deadtime && q > 0 && C == Cmax) {	: in dead time after release
    R1 = R
    C = 0.
  }
  
  if (C > 0) {			: transmitter being released?
    
    R = Rinf + (R0 - Rinf) * exptable (- (t - lastrelease) / Rtau)
    
  } else {			: no release occuring
    
    R = R1 * exptable (- Beta * (t - (lastrelease + Cdur)))
  }
  
  VERBATIM
  return 0;
  ENDVERBATIM
}

FUNCTION exptable(x) { 
  TABLE  FROM -10 TO 10 WITH 2000
  
  if ((x > -10) && (x < 10)) {
    exptable = exp(x)
  } else {
    exptable = 0.
  }
}

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