Effect of voltage sensitive fluorescent proteins on neuronal excitability (Akemann et al. 2009)

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Accession:123453
"Fluorescent protein voltage sensors are recombinant proteins that are designed as genetically encoded cellular probes of membrane potential using mechanisms of voltage-dependent modulation of fluorescence. Several such proteins, including VSFP2.3 and VSFP3.1, were recently reported with reliable function in mammalian cells. ... Expression of these proteins in cell membranes is accompanied by additional dynamic membrane capacitance, ... We used recordings of sensing currents and fluorescence responses of VSFP2.3 and of VSFP3.1 to derive kinetic models of the voltage-dependent signaling of these proteins. Using computational neuron simulations, we quantitatively investigated the perturbing effects of sensing capacitance on the input/output relationship in two central neuron models, a cerebellar Purkinje and a layer 5 pyramidal neuron. ... ". The Purkinje cell model is included in ModelDB.
Reference:
1 . Akemann W, Lundby A, Mutoh H, Knöpfel T (2009) Effect of voltage sensitive fluorescent proteins on neuronal excitability. Biophys J 96:3959-76 [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: Cerebellum;
Cell Type(s): Cerebellum Purkinje GABA cell;
Channel(s): I Na,t; I A; I K; I h; I K,Ca; I Calcium;
Gap Junctions:
Receptor(s):
Gene(s): Kv1.1 KCNA1; Kv4.3 KCND3; Kv3.3 KCNC3; Kv3.4 KCNC4; HCN1;
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s):
Implementer(s): Akemann, Walther [akemann at brain.riken.jp];
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell; I Na,t; I A; I K; I h; I K,Ca; I Calcium;
TITLE Voltage-gated potassium channel from Kv4 subunits

COMMENT

NEURON implementation of a potassium channel from Kv4
Kinetical Scheme: Hodgkin-Huxley m^4*h

DATA TAKEN FROM:
A-type potassium currents active at subthreshold potentials in mouse cerebellar Purkinje cells
Sacco et Tempia, J Physiol 543: 505-520, 2002

ACTIVATION:
The rate constants of activation and deactivation were approximated by the following formulas

alphan = can * exp(-(v+cvan)/ckan)
betan = cbn * exp(-(v+cvbn)/ckbn)

Parameters can, cvan, ckan, cbn, cvbn, ckbn
were determined from least square-fits to experimental data of G/Gmax(v) and taun(v).
Values are given in the CONSTANT block.

INACTIVATION:
The model includes only the fast component of inactivation
The voltage dependency of the rate constants was approximated by the following formulas

alphah = cah / (1+exp(-(v+cvah)/ckah))
betah = cbh / (1+exp(-(v+cvbh)/ckbh))

Parameters cah, cvah, ckah, cbh, cvbh, ckbh
were determined from least square-fits to experimental data of G/Gmax(v) and tauh(v).:
Values are given in the CONSTANT block.

Model includes calculation of gating current

Reference: Akemann et al., Biophys. J. (2009) 96: 3959-3976

Laboratory for Neuronal Circuit Dynamics
RIKEN Brain Science Institute, Wako City, Japan
http://www.neurodynamics.brain.riken.jp

Date of Implementation: April 2007
Contact: akemann@brain.riken.jp

ENDCOMMENT


NEURON {
	SUFFIX Kv4
	USEION k READ ek WRITE ik
	NONSPECIFIC_CURRENT i
	RANGE gbar, g, ik, i, igate, nc
	GLOBAL ninf, taun, hinf, tauh
	GLOBAL gateCurrent, gunit
}

UNITS {
	(mV) = (millivolt)
	(mA) = (milliamp)
	(nA) = (nanoamp)
	(pA) = (picoamp)
	(S)  = (siemens)
	(nS) = (nanosiemens)
	(pS) = (picosiemens)
	(um) = (micron)
	(molar) = (1/liter)
	(mM) = (millimolar)		
}

CONSTANT {
	e0 = 1.60217646e-19 (coulombs)
	q10 = 2.7

	can = 0.15743 (1/ms)
	cvan = 57 (mV)
	ckan = -32.19976 (mV)
	cbn = 0.15743 (1/ms)
	cvbn = 57 (mV)
	ckbn = 37.51346 (mV)

	cah = 0.01342 (1/ms)
	cvah = 60 (mV)
	ckah = -7.86476 (mV)
	cbh = 0.04477 (1/ms)
	cvbh = 54 (mV)
	ckbh = 11.3615 (mV)

	zn = 1.4736 (1)		: valence of n-gate
	zh = -5.4726 (1)		: valence of h-gate
}

PARAMETER {
	gateCurrent = 0 (1)	: gating currents ON = 1 OFF = 0
	
	gbar = 0.004 (S/cm2)   <0,1e9>
	gunit = 16 (pS)		: unitary conductance
}

ASSIGNED {
	celsius (degC)
	v (mV)

	ik (mA/cm2)
	i (mA/cm2)
	igate (mA/cm2)
 
	ek (mV)
	g (S/cm2)
	nc (1/cm2)			: membrane density of channel 
	qt (1)

	ninf (1)
	taun (ms)
	alphan (1/ms)
	betan (1/ms)

	hinf (1)
	tauh (ms)
	alphah (1/ms)
	betah (1/ms)        
}

STATE { n h }

INITIAL {
	nc = (1e12) * gbar / gunit
	qt = q10^((celsius-22 (degC))/10 (degC))
	rates(v)
	n = ninf
	h = hinf
}

BREAKPOINT {
	SOLVE states METHOD cnexp
      g = gbar * n^4 * h 
	ik = g * (v - ek)
	igate = nc * (1e6) * e0 * ( 4 * zn * ngateFlip() + zh * hgateFlip() )

	if (gateCurrent != 0) { 
		i = igate
	}
}

DERIVATIVE states {
	rates(v)
	n' = (ninf-n)/taun
	h' = (hinf-h)/tauh 
}

PROCEDURE rates(v (mV)) {
	alphan = alphanfkt(v)
	betan = betanfkt(v)
	ninf = alphan / (alphan + betan) 
	taun = 1 / (qt*(alphan + betan))
	alphah = alphahfkt(v)
	betah = betahfkt(v)
	hinf = alphah / (alphah + betah)
	tauh = 1 / (qt*(alphah + betah))       
}

FUNCTION alphanfkt(v (mV)) (1/ms) {
	alphanfkt = can * exp(-(v+cvan)/ckan) 
}

FUNCTION betanfkt(v (mV)) (1/ms) {
	betanfkt = cbn * exp(-(v+cvbn)/ckbn)
}

FUNCTION alphahfkt(v (mV))  (1/ms) {
	alphahfkt = cah / (1+exp(-(v+cvah)/ckah))
}

FUNCTION betahfkt(v (mV))  (1/ms)  {
	betahfkt = cbh / (1+exp(-(v+cvbh)/ckbh))
}

FUNCTION ngateFlip() (1/ms) {
	ngateFlip = (ninf-n)/taun 
}

FUNCTION hgateFlip() (1/ms) {
	hgateFlip = (hinf-h)/tauh 
}

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