Hodgkin-Huxley model of persistent activity in PFC neurons (Winograd et al. 2008) (NEURON python)

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Accession:144376
The paper demonstrate a form of graded persistent activity activated by hyperpolarization. This phenomenon is modeled based on a slow calcium regulation of Ih, similar to that introduced earlier for thalamic neurons (see Destexhe et al., J Neurophysiol. 1996). The only difference is that the calcium signal is here provided by the high-threshold calcium current (instead of the low-threshold calcium current in thalamic neurons).
Reference:
1 . Winograd M, Destexhe A, Sanchez-Vives MV (2008) Hyperpolarization-activated graded persistent activity in the prefrontal cortex. Proc Natl Acad Sci U S A 105:7298-303 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Channel/Receptor;
Brain Region(s)/Organism: Prefrontal cortex (PFC);
Cell Type(s):
Channel(s): I Na,t; I L high threshold; I K; I M; I h;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Activity Patterns; Ion Channel Kinetics;
Implementer(s): Skolnick, Yosef [yskolnick at gmail.com];
Search NeuronDB for information about:  I Na,t; I L high threshold; I K; I M; I h;
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Skolnik_python_WinogradEtAl2008
readme.txt
APCounter2.mod *
Cadynamics.mod *
HH2.mod *
ICaL.mod *
Ih.mod *
IKM.mod *
ipulse3.mod *
pasi.mod *
demo_HPGA_non_saturating.py
demo_HPGA_non_saturating_noIh.py
demo_HPGA_saturating.py
geoms.py
pyinit.py
simgui.hoc
simgui.py
winograd.py
                            
TITLE Hippocampal HH channels
:
: Fast Na+ and K+ currents responsible for action potentials
: Iterative equations
:
: Equations modified by Traub, for Hippocampal Pyramidal cells, in:
: Traub & Miles, Neuronal Networks of the Hippocampus, Cambridge, 1991
:
: range variable vtraub adjust threshold
:
: Written by Alain Destexhe, Salk Institute, Aug 1992
:
: Modified Oct 96 for compatibility with Windows: trap low values of arguments
:

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

NEURON {
	SUFFIX hh3
	USEION na READ ena WRITE ina
	USEION k READ ek WRITE ik
	RANGE gnabar, gkbar, vtraub
	RANGE m_inf, h_inf, n_inf
	RANGE tau_m, tau_h, tau_n
	RANGE m_exp, h_exp, n_exp
}


UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
}

PARAMETER {
	gnabar  = .1  (mho/cm2)
	gkbar   = .01  (mho/cm2)

	ena     = 50    (mV)
	ek      = -95   (mV)
	celsius = 36    (degC)
	dt              (ms)
	v               (mV)
	vtraub  = -55   (mV)
}

STATE {
	m h n
}

ASSIGNED {
	ina     (mA/cm2)
	ik      (mA/cm2)
	il      (mA/cm2)
	m_inf
	h_inf
	n_inf
	tau_m
	tau_h
	tau_n
	m_exp
	h_exp
	n_exp
	tadj
}


BREAKPOINT {
	SOLVE states
	ina = gnabar * m*m*m*h * (v - ena)
	ik  = gkbar * n*n*n*n * (v - ek)
}


:DERIVATIVE states {   : exact Hodgkin-Huxley equations
:       evaluate_fct(v)
:       m' = (m_inf - m) / tau_m
:       h' = (h_inf - h) / tau_h
:       n' = (n_inf - n) / tau_n
:}

PROCEDURE states() {    : exact when v held constant
	evaluate_fct(v)
	m = m + m_exp * (m_inf - m)
	h = h + h_exp * (h_inf - h)
	n = n + n_exp * (n_inf - n)
	VERBATIM
	return 0;
	ENDVERBATIM
}

UNITSOFF
INITIAL {
:
:  Q10 was assumed to be 3 for both currents
:
	tadj = 3.0 ^ ((celsius-36)/ 10 )

	m = 0
	h = 0
	n = 0
}

PROCEDURE evaluate_fct(v(mV)) { LOCAL a,b,v2

	v2 = v - vtraub : convert to traub convention

	a = 0.32 * vtrap(13-v2, 4)
	b = 0.28 * vtrap(v2-40, 5)
	tau_m = 1 / (a + b) / tadj
	m_inf = a / (a + b)

	a = 0.128 * Exp((17-v2)/18)
	b = 4 / ( 1 + Exp((40-v2)/5) )
	tau_h = 1 / (a + b) / tadj
	h_inf = a / (a + b)

	a = 0.032 * vtrap(15-v2, 5)
	b = 0.5 * Exp((10-v2)/40)
	tau_n = 1 / (a + b) / tadj
	n_inf = a / (a + b)

	m_exp = 1 - Exp(-dt/tau_m)
	h_exp = 1 - Exp(-dt/tau_h)
	n_exp = 1 - Exp(-dt/tau_n)
}
FUNCTION vtrap(x,y) {
	if (fabs(x/y) < 1e-6) {
		vtrap = y*(1 - x/y/2)
	}else{
		vtrap = x/(Exp(x/y)-1)
	}
}

FUNCTION Exp(x) {
	if (x < -100) {
		Exp = 0
	}else{
		Exp = exp(x)
	}
} 

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