Dentate gyrus network model pattern separation and granule cell scaling in epilepsy (Yim et al 2015)

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The dentate gyrus (DG) is thought to enable efficient hippocampal memory acquisition via pattern separation. With patterns defined as spatiotemporally distributed action potential sequences, the principal DG output neurons (granule cells, GCs), presumably sparsen and separate similar input patterns from the perforant path (PP). In electrophysiological experiments, we have demonstrated that during temporal lobe epilepsy (TLE), GCs downscale their excitability by transcriptional upregulation of ‘leak’ channels. Here we studied whether this cell type-specific intrinsic plasticity is in a position to homeostatically adjust DG network function. We modified an established conductance-based computer model of the DG network such that it realizes a spatiotemporal pattern separation task, and quantified its performance with and without the experimentally constrained leaky GC phenotype. ...
1 . Yim MY, Hanuschkin A, Wolfart J (2015) Intrinsic rescaling of granule cells restores pattern separation ability of a dentate gyrus network model during epileptic hyperexcitability. Hippocampus 25:297-308 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network; Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Dentate gyrus;
Cell Type(s): Dentate gyrus granule GLU cell; Dentate gyrus mossy cell; Dentate gyrus basket cell; Dentate gyrus hilar cell; Dentate gyrus MOPP cell;
Channel(s): I Chloride; I K,leak; I Cl, leak; Kir; Kir2 leak;
Gap Junctions:
Receptor(s): GabaA; AMPA;
Gene(s): IRK; Kir2.1 KCNJ2; Kir2.2 KCNJ12; Kir2.3 KCNJ4; Kir2.4 KCNJ14;
Transmitter(s): Gaba; Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Activity Patterns; Spatio-temporal Activity Patterns; Intrinsic plasticity; Pathophysiology; Epilepsy; Homeostasis; Pattern Separation;
Implementer(s): Yim, Man Yi [manyi.yim at]; Hanuschkin, Alexander ; Wolfart, Jakob ;
Search NeuronDB for information about:  Dentate gyrus granule GLU cell; GabaA; AMPA; I Chloride; I K,leak; I Cl, leak; Kir; Kir2 leak; Gaba; Glutamate;
TITLE ichan2.mod combination of Nav and Kv channels for Hodgin-Huxely-type action potential mechanism

Original Mod File:
Original name 'ichan2.mod'
Santhakumar V, Aradi I, Soltesz I (2005) J Neurophysiol 93:437-53
Morgan RJ, Soltesz I (2008) Proc Natl Acad Sci U S A 105:6179-84
Morgan RJ, Santhakumar V, Soltesz I (2007) Prog Brain Res 163:639-58
Cutsuridis V, Cobb S, Graham BP (2009) Hippocampus 20(3):423-46 

Current version by A. Hanuschkin <AH, 2011> for:
Yim MY, Hanuschkin A, Wolfart J (2015) Hippocampus 25:297-308.

Changes in current versus original version:
 - added a tonic (leak) GABAA conductance to be modified during epilepsy (see Young CC, Stegen M, Bernard R, Muller M, Bischofberger J, Veh RW, Haas CA, Wolfart J (2009) J Physiol 587:4213-4233)
 - checked, simplified (reduced to single k Ion, Ekf=Eks=Ek) & commented by A. Hanuschkin 2011,2012

Mod File history:
I_Na: (equivalent to Santhakumar et al 2005)
* modified parameters (shifted voltage dependence by 68mV) 
  Aradi I and Soltesz I (2002) J Physiol. 538(Pt 1):227-51.
* dynamics (NOTE in this paper (at least) sign error in alpha_m, beta_m and alpha_n! (1-exp()) -> should be (exp()-1) <ah>)
Aradi and Soltesz (2002)
* modified from 
  Yuen GL, Durand D, (1991) Neuroscience 41(2-3):411-23.
* Aradi and Soltesz (2002) parameters =  
  Aradi I, Holmes WR (1999) J Comput Neurosci 6:215-35
parameters = 
  Yuen and Durand (1991) parameters + V shift of 16mV

I_Kf: (equivalent to Santhakumar et al 2005)
* modified parameters Aradi and Soltesz (2002)/Aradi & Holmes (1999) (shifted voltage dependence by 65mV) 
* NOTE typo in formular beta_n in Aradi and Soltesz (2002): beta_n = 0.264/exp((v-22)/4) -> should be beta_n = 0.264/exp((v-22)/40) <ah>
* modified parameters from Yuen and Durand (1991)

I_Ks: (equivalent to Santhakumar et al 2005)
* modified parameters Aradi & Holmes (1999) (shifted voltage dependence by 65mV) 

I_leak: (equivalent to Santhakumar et al 2005)

I_GABAA: (tonic GABAA leak (see above), added in Yim et al (2015))
* replicated from I_leak
A. Hanuschkin(c) 2011,2012

        (mA) =(milliamp)
        (mV) =(millivolt)
        (uF) = (microfarad)
	(molar) = (1/liter)
	(nA) = (nanoamp)
	(mM) = (millimolar)
	(um) = (micron)
	FARADAY = 96520 (coul)
	R = 8.3134	(joule/degC)
: "suffix marks the mechanism to be distributed and whose variables & parameters are identified in hoc by a particular suffix" The Neuron Book Chap 9.5
SUFFIX ichan2

: ION usage block
USEION na READ ena WRITE ina VALENCE 1			: Na current
USEION k READ ek WRITE ik  				: K current
NONSPECIFIC_CURRENT il, igabaa 				: leak current

: range variable definition block,
: i.e. variables that might change with space along a compartment / could be declared global in this case
RANGE gnatbar, gkfbar, gksbar				: gbar values for Na, K(slow/fast)
RANGE gl, el, ina, ik, il, ggabaa, igabaa, egabaa	: gbar and reversal poti for leak current	

: The INDEPENDENT statement was omitted; INDEPENDENT statements are irrelevant to NEURON. 
: INDEPENDENT {t FROM 0 TO 100 WITH 100 (ms)}
: Variables whose values are normally specified by the user are parameters, and are declared in a PARAMETER block.
: Variables in the parameter section will have global scope
        :v (mV) 
        :celsius = 6.3 (degC)
        :dt (ms) 

        gnatbar (mho/cm2)   				: Na (gbar and reversal poti)
        ena  	(mV)	
	gkfbar 	(mho/cm2)				: K  (gbar(slow/fast), reversal is ek)
	gksbar = 0 (mho/cm2)	                        : init to 0 (not included in BC, HIPP and MC) <ah>
        ek     	(mV)                      

	gl 	(mho/cm2)    				: leak (gbar and reversal poti)
 	el 	(mV)

	ggabaa 	(mho/cm2)    				: GABAA (gbar and reversal poti)
 	egabaa 	(mV)

: "If a model involves differential equations [..] their dependent variables or unknowns are to be listed in the STATE block" The Neuron Book Chap 9.5
	m h nf ns

: The ASSIGNED block is used to declare two kinds of variables
: 1) those given values outside the mod file (variables potentially available to every mechanism (e.g. v, celsius,t..)
: 2) left hand side of assignment statements (unknowns in set of equations, dependent variables in differential euqtions ...)
: 1)
        v (mV) 
        celsius (degC)
        dt (ms) 
: 2) 
        gna (mho/cm2) 					: Na
        ina (mA/cm2)
        gkf (mho/cm2)					: K
        gks (mho/cm2)
	ik (mA/cm2)

	il (mA/cm2)					: leak 

	igabaa (mA/cm2)					: GABAA 

	minf hinf nfinf nsinf				: left hand side of differential equations
 	mtau (ms) htau (ms) nftau (ms) nstau (ms)	: and other assignment variables
	mexp hexp nfexp nsexp

: This block is evaluated every time step. 
	SOLVE states					: here the state variables are updated 
        gna = gnatbar*m*m*m*h  			: calculated g at timepoint t
        gkf = gkfbar*nf*nf*nf*nf
        gks = gksbar*ns*ns*ns*ns

        ina = gna*(v - ena)				: calculated currents flowing
       	ik = gkf*(v-ek) + gks*(v-ek)
	il = gl*(v-el)
	igabaa = ggabaa*(v-egabaa)
: Called from Neuron during initializing the model
	m = minf
	h = hinf
        nf = nfinf
        ns = nsinf
	return 0;

: discreticed versions of the differential equations, hence a PROCEDURE and not DERIVATIVE block
PROCEDURE states() {	: Computes state variables m, h, and n 
        trates(v)	: at the current v and dt.
        m = m + mexp*(minf-m)
        h = h + hexp*(hinf-h)
        nf = nf + nfexp*(nfinf-nf)
        ns = ns + nsexp*(nsinf-ns)
        return 0;

: moved this to assign block <ah> 
: LOCAL q10

:Computes rate and other constants at current v.
PROCEDURE rates(v) {  
        LOCAL  alpha, beta, sum
        q10 = 3^((celsius - 6.3)/10)
                :"m" sodium activation system - act and inact cross at -40	: shifted by 68mV compared to in Aradi 1999/2002
	alpha = -0.3*vtrap((v+60-17),-5)		: in Aradi 1999: alpha = -0.3*vtrap((v-25),-5); in Aradi 2002: alpha = 0.3*vtrap((v-25),-5) <ah>
	beta = 0.3*vtrap((v+60-45),5)			: in Aradi 1999: beta = 0.3*vtrap((v-53),5);  in Aradi 2002:  beta = -0.3*vtrap((v-53),5) <ah>
	sum = alpha+beta        
	mtau = 1/sum      minf = alpha/sum
                :"h" sodium inactivation system		: shifted by 68mV compared to in Aradi 1999/2002
	alpha = 0.23/exp((v+60+5)/20)			: in Aradi 1999/2002:  alpha = 0.23/exp((v-3)/20) <ah>
	beta = 3.33/(1+exp((v+60-47.5)/-10))		: in Aradi 1999/2002:  beta = 3.33/(1+exp((v-55.5)/-10)) <ah>
	sum = alpha+beta
	htau = 1/sum 
        hinf = alpha/sum 

             :"ns" sKDR activation system		: shifted by 65mV compared to Aradi 1999 <ah>
        alpha = -0.028*vtrap((v+65-35),-6)		: in Aradi 1999: alpha = -0.028*vtrap((v-35),-6) 
	beta = 0.1056/exp((v+65-10)/40)			: in Aradi 1999: beta = 0.1056/exp((v-10)/40)   
	sum = alpha+beta        			
	nstau = 1/sum      nsinf = alpha/sum		
            :"nf" fKDR activation system		: shifted by 65mV compared to Aradi 1999/2002 <ah>
        alpha = -0.07*vtrap((v+65-47),-6)		: in Aradi 1999: alpha = -0.07*vtrap((v-47),-6); in Aradi 2002: alpha = 0.07*vtrap((v-47),-6) <ah>
	beta = 0.264/exp((v+65-22)/40)			: in Aradi 1999/2002: beta = 0.264/exp((v-22)/40)  // probably typo in Aradi & Soltez 2002 there: beta = 0.264/exp((v-22)/4) <ah>
	sum = alpha+beta        
	nftau = 1/sum      nfinf = alpha/sum

: Computes rate and other constants at current v. 
PROCEDURE trates(v) {  
	LOCAL tinc
        : TABLE minf, mexp, hinf, hexp, nfinf, nfexp, nsinf, nsexp, mtau, htau, nftau, nstau   : <ah>
	: DEPEND dt, celsius FROM -100 TO 100 WITH 200					       : <ah>
	rates(v)	: not consistently executed from here if usetable_hh == 1
			: so don't expect the tau values to be tracking along with
			: the inf values in hoc

        tinc = -dt * q10
        mexp = 1 - exp(tinc/mtau)
        hexp = 1 - exp(tinc/htau)
	nfexp = 1 - exp(tinc/nftau)
	nsexp = 1 - exp(tinc/nstau)

:Traps for 0 in denominator of rate eqns.
FUNCTION vtrap(x,y) {  
        if (fabs(x/y) < 1e-6) {
                vtrap = y*(1 - x/y/2)
                vtrap = x/(exp(x/y) - 1)