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

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A phase plane analysis of a two cell interaction between a thalamocortical neuron (TC) and a thalamic reticularis neuron (RE).
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;
Transmitter(s): Gaba; Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Temporal Pattern Generation; Oscillations; Calcium dynamics;
Implementer(s): Lytton, William [billl at]; Destexhe, Alain [Destexhe at];
Search NeuronDB for information about:  Thalamus geniculate nucleus (lateral) principal neuron; Thalamus reticular nucleus cell; GabaA; Glutamate; I T low threshold; Gaba; Glutamate;
calciumpump_destexhe.mod *
HH_traub.mod *
Ih_old.mod *
presyn.mod *
pulse.mod *
boxes.hoc *
declist.hoc *
decvec.hoc *
default.hoc *
local.hoc *
nrnoc.hoc *
params.hoc * *
simctrl.hoc * * *
: $Id: rand.mod,v 1.4 1995/08/23 18:33:27 billl Exp $
$Header: /usr/local/src/nrniv/local/mod/RCS/rand.mod,v 1.4 1995/08/23 18:33:27 billl Exp $

Author: Stephen Fisher
Date:   December 1992

Misc. random routines:
		- set seed
		- return seed

		- uniform distribution (0.0 <= rand < 1.0)

	fran(low, high)
		- returns random number between low and high

		- uniform distribution (0.0 <= rand <= 1.0)

		- gaussian distribution around 0

		- poisson distribution

		- integer poisson distribution using scop

** Note that with a SUFFIX equal to "nothing" these functions do not
have a suffix in hoc.  Thus to call norm() in hoc use simply type
"norm()" <- without the quotes.

	SUFFIX nothing

#include <stdlib.h>
#include <math.h>
/* #include <values.h> /* contains MAXLONG */
#include <limits.h> /* contains MAXLONG */

/* Michael Hines fix for cygwin on mswin */
#if !defined(MAXLONG)
#include <limits.h>
/* some machines do not have drand48 and srand48 so use the implementation
at the end of this file */
extern double my_drand48();
extern void my_srand48();
#undef drand48
#undef srand48
#define drand48 my_drand48
#define srand48 my_srand48

extern double drand48();
#define random()                drand48()*MAXLONG
#define initstate(c1,c2,c3)     srand48(c1)

static long state2[32] = {
	470594912, 650447616, 310934240, 695012864, 850358912,
61088076, 481306752, 786902080, 224042800, 805177664, 938284096,
145937936, 622867968, 160207584, 977329216, 716234240, 127727624,
415316352, 870137472, 18664444, 330872224, 93728752, 914779200,
736261248, 643647616, 755802688, 213052336, 410240448, 218974736,
109419280, 178026128, 689569664

FUNCTION fseed(seed) {
    initstate((unsigned)_lseed,(char *)state2,32);
	_lfseed = _lseed;

FUNCTION n_rand() { : 0.0 <= n_rand < 1.0
    _ln_rand = ((double)random()) / (((double)MAXLONG) + 1.);

FUNCTION fran(l, h) { : returns random number between low and high
	int low, high;
    double num, imax, *getarg();
	low = (int)_ll;
	high = (int)_lh;
    imax = high-low+1; /* the total number of numbers being used */
    _lfran = (double)(low + (int) (imax*n_rand()));  

FUNCTION u_rand() { : uniform distribution (0.0 <= rand <= 1.0)
    _lu_rand = (((double)random()) / ((double)MAXLONG));

FUNCTION norm() { : gaussian distribution around 0
    static int iset = 0;
    static float gset;
    float fac, r , v1, v2;
    double sqrt();

    if (iset == 0) {
        do {
	    	v1 = 2.0 * n_rand() - 1.0;
		    v2 = 2.0 * n_rand() - 1.0;
		    r = v1 * v1 + v2 * v2;
	    } while (r >= 1.0);

        fac = (float)sqrt(-2.0 * log(r) / r);
        gset = v1 * fac;
        iset = 1;
        _lnorm = v2 * fac;

    } else {
        iset = 0;
        _lnorm = (double)gset;

FUNCTION pois(mean) { : poisson distribution
    _lpois = - _lmean * log(((double)random()+1.) / ((double)MAXLONG+1.));

FUNCTION poisint(mean) {
  poisint = poisrand(mean)

/* */
 Michael Hines removed  all code not used by srand48 and drand48,
 the code handling non-floating point processor machines, and the
 pdp-11 fragment. Global names have my_ prefix added.

/*	@(#)drand48.c	2.2	*/
 *	drand48, etc. pseudo-random number generator
 *	This implementation assumes unsigned short integers of at least
 *	16 bits, long integers of at least 32 bits, and ignores
 *	overflows on adding or multiplying two unsigned integers.
 *	Two's-complement representation is assumed in a few places.
 *	Some extra masking is done if unsigneds are exactly 16 bits
 *	or longs are exactly 32 bits, but so what?
 *	An assembly-language implementation would run significantly faster.
#define N	16
#define MASK	((unsigned)(1 << (N - 1)) + (1 << (N - 1)) - 1)
#define LOW(x)	((unsigned)(x) & MASK)
#define HIGH(x)	LOW((x) >> N)
#define MUL(x, y, z)	{ long l = (long)(x) * (long)(y); \
		(z)[0] = LOW(l); (z)[1] = HIGH(l); }
#define CARRY(x, y)	((long)(x) + (long)(y) > MASK)
#define ADDEQU(x, y, z)	(z = CARRY(x, (y)), x = LOW(x + (y)))
#define X0	0x330E
#define X1	0xABCD
#define X2	0x1234
#define A0	0xE66D
#define A1	0xDEEC
#define A2	0x5
#define C	0xB
#define SET3(x, x0, x1, x2)	((x)[0] = (x0), (x)[1] = (x1), (x)[2] = (x2))
#define SEED(x0, x1, x2) (SET3(x, x0, x1, x2), SET3(a, A0, A1, A2), c = C)

static unsigned x[3] = { X0, X1, X2 }, a[3] = { A0, A1, A2 }, c = C;
static unsigned short lastx[3];
static void next();

	static double two16m = 1.0 / (1L << N);

	return (two16m * (two16m * (two16m * x[0] + x[1]) + x[2]));

static void
	unsigned p[2], q[2], r[2], carry0, carry1;

	MUL(a[0], x[0], p);
	ADDEQU(p[0], c, carry0);
	ADDEQU(p[1], carry0, carry1);
	MUL(a[0], x[1], q);
	ADDEQU(p[1], q[0], carry0);
	MUL(a[1], x[0], r);
	x[2] = LOW(carry0 + carry1 + CARRY(p[1], r[0]) + q[1] + r[1] +
		a[0] * x[2] + a[1] * x[1] + a[2] * x[0]);
	x[1] = LOW(p[1] + r[0]);
	x[0] = LOW(p[0]);

long seedval;
	SEED(X0, LOW(seedval), HIGH(seedval));

#if 0
#ifdef DRIVER
	This should print the sequences of integers in Tables 2
		and 1 of the TM:
	1623, 3442, 1447, 1829, 1305, ...
	657EB7255101, D72A0C966378, 5A743C062A23, ...
#include <stdio.h>

	int i;

	for (i = 0; i < 80; i++) {
		printf("%4d ", (int)(4096 * my_drand48()));
		printf("%.4X%.4X%.4X\n", x[2], x[1], x[0]);

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]

References and models cited by this paper

References and models that cite this paper

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