Paradoxical effect of fAHP amplitude on gain in dentate gyrus granule cells (Jaffe & Brenner 2018)

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Accession:235052
The afterhyperpolarization (AHP) is canonically viewed as a major factor underlying the refractory period, serving to limit neuronal firing rate. We recently reported (Wang et al, J. Neurophys. 116:456, 2016) that enhancing the amplitude of the fast AHP in a relatively slowly firing neuron (versus fast spiking neurons), augments neuronal excitability in dentate gyrus granule neurons expressing gain-of-function BK channels. Here we present a novel, quantitative hypothesis for how varying the amplitude of the fast AHP (fAHP) can, paradoxically, influence a subsequent spike tens of milliseconds later.
Reference:
1 . Jaffe DB, Brenner R (2018) A computational model for how the fast afterhyperpolarization paradoxically increases gain in regularly firing neurons. J Neurophysiol 119:1506-1520 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type:
Brain Region(s)/Organism: Dentate gyrus;
Cell Type(s): Dentate gyrus granule GLU cell;
Channel(s): I K,Ca; I T low threshold; I Na,p;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Action Potentials;
Implementer(s): Jaffe, David B [david.jaffe at utsa.edu];
Search NeuronDB for information about:  Dentate gyrus granule GLU cell; I Na,p; I T low threshold; I K,Ca;
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601886b.nrn
Fig2.hoc
PlotFig2.py
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//////////////////////////////////////////////////////////////////////////////////////////////////////////////
//
//		Figure 2 from Jaffe and Brenner, J. Neurophys., 2017 (in press)
//   	Dentate gyrus granule cell model: paradoxical effect of varying AHP amplitude on firing rate
// 		
//
//////////////////////////////////////////////////////////////////////////////////////////////////////////////

celsius = 25					// temperature
VREST = -80					    //resting potential

//  Independent Parameters List ------------------------------------------------------------------------

// Passive properties

RM = 38000					//membrane resistivity
RI = 200					//input resistance
CM = 1						//membrane conductivity

// Controls

ISTEP = .065				//step amplitude in nA
IDUR = 2000					//duration of the current step

TSTOP = 2000				//duration of the simulation

//  Geometry of the cell ------------------------------------------------------------------------

ropen("601886b.nrn")		// Claiborne DG granule cell

ncompartments=fscan()		// Number of compartments

// arrays

double comp[ncompartments],par[ncompartments],x[ncompartments],y[ncompartments],z[ncompartments]
double len[ncompartments],d[ncompartments]

for i=0,ncompartments-1 {			/* read in dendritic parameters */
	comp[i] = fscan()				// compartment number
	par[i] = fscan()				// parent compartment
	x[i] = fscan()					// x coordinate
	y[i] = fscan()					// y coordinate
	z[i] = fscan()					// z coordinate
	len[i] = fscan()				// compartment length
	d[i] = fscan()					// compartment diameter
}

create cell[ncompartments], hillock, mfiber		/* creates the major regions */

cell[0] {nseg=1 L=len[0] diam = d[0]}			/* soma dimensions */

dredux = .64		      				// Rescale all dendrites by this factor

for i=1,ncompartments-1 {				/* all other soma/dendritic compartments */
cell[i] {nseg=1 pt3dadd(x[par[i]],y[par[i]],z[par[i]],d[par[i]]*dredux) pt3dadd(x[i],y[i],z[i],d[i]*dredux)}
}

for i=1,ncompartments-1 {				/* connect the soma/dendrites */
	cell[par[i]] connect cell[i](0),1    
}  

// AXON and AIS

hillock { L=100 diam(0:1)=1.4:0.5 nseg = 50}  		// Axon initial segment

mfiber { L=1000 diam=0.5 nseg = 100}  				// Axon proper

cell[0] connect hillock(0),0  						// connect the soma ot the AIS to the axon
hillock connect mfiber(0),1

proxlimit = 80									// maximum limit in microns of the proximal region

objref AIS, prox, stim, dend, axon, ahp			// Create objects for subsections

proc subsets() { local i      	    			// procedure defines subsections

    // three subsections: soma/prox region, dendrites, AIS, and axon
	// AIS and axon are only here for future extensibility and serve no function

	objref AIS, prox, stim, dend, axon, ahp			// Create objects

	prox = new SectionList()	
	dend = new SectionList()
	
	access cell[0]
	distance()
	for i=0,ncompartments-1 {					// define which dendrites are proximal
		 access cell[i]
		 howfar = distance(1)
		 if (howfar < proxlimit) cell[i]  prox.append()
		 if (howfar >=proxlimit) cell[i]  dend.append()
	}
								
	AIS = new SectionList()
	axon = new SectionList()

	hillock AIS.append()						// the hillock is the AIS			   mfiber axon.append()						   // mfiber is the axon

}
subsets()						// run the procedure


//  Parameter initialization ------------------------------------------------------------------------

forsec prox {						// Somatic conductances

	insert NaM99SL					// Lazarewicz, Migliore, and Ascoli (2002) Na channel
	gbar_NaM99SL = .035				// g_Na
	
	insert fKDR						// Aradi and Holmes (1999) fast and slow KDR channels
	gbar_fKDR = .003				// g_fKDR
	
	insert sKDR
	gbar_sKDR = .03					// g_fKDR

	// T-channel 

	insert DGCaT					// Huguenard and McCormick (1992); Mainen and Sejnowski (1996)
	gcat_DGCaT = .0035	 			// g_CaT
	mshift_DGCaT = 15				// + valuies shift m in positive direction
	hshift_DGCaT = -10  			// + values shifts h in negative direction

}

forsec dend{						// dendritic conductances

    insert NaM99SL
    gbar_NaM99SL = .003				// low Na channel density in dendrites

	insert fKDR   				
	gbar_fKDR = .003

}

access hillock						// AIS conductances

insert NaM99SL
gbar_NaM99SL = .1
	
insert fKDR
gbar_fKDR = .05

access mfiber						// axon channels
insert NaM99SL
gbar_NaM99SL = .1
	
insert fKDR
gbar_fKDR = .1
	

//  Basic parameters for all compartments  ------------------------------------------------------------------------


forall {
    v = VREST

    Ra = RI
    cm = CM
    
    ek = -90
    ena = 60

    insert pas
    g_pas = 1/RM

	e_pas = v 

}

//  Reinitialization procedure  ------------------------------------------------------------------------


proc init() {

forall {
    v = VREST						// all compartments reset Vrest
}

forsec prox {
	v = VREST					// Redundant resetting of Vrest
	
	finitialize(v)					// Initialize all variables to Vrest
	fcurrent()					// Generate currents at Vrest
	
	e_pas = v + (ina + ik + ica)/g_pas		// calculate E_leak for resting currents
}

forsec axon {
	v = VREST					// Redundant resetting of Vrest
	finitialize(v)
	fcurrent()
	e_pas = v + (ina+ik)/g_pas			// E_leak
}


forsec AIS {						// hillock/AIS resetting
	v = VREST

	finitialize(v)
	fcurrent()
	e_pas = v + (ina + ik)/g_pas
}

forsec dend {						// dendrites resetting
	v = VREST

	finitialize(v)
	fcurrent()
	e_pas = v + (ina + ik)/g_pas
}

}							

//  Current step controls  ------------------------------------------------------------------------

init()							// Initialize model

//  Current step controls  ------------------------------------------------------------------------

access cell[0]
stim = new IClamp(.5)
stim.del = 10
stim.dur = IDUR
stim.amp = ISTEP	

//  AHP modifier controls  ------------------------------------------------------------------------

ahp = new AlphaSynapse(.5)
ahp.onset = 5000
ahp.tau = 1
ahp.e = -90
ahp.gmax = 0.07

// Start of the four simulations  ------------------------------------------------------------------------

//////  Simulation 1 - largest AHP /////////

t=0	    	     		  		// reset time

wopen("output1.dat")			// output file

count = -100					// counter that spaces AHP between spikes

while (t<TSTOP){				// simulation loop
      
	if ((cell[0].v > 0) && (count <=0 )){			// Did the cell fire?
		ahp.onset = t + 1.5   	  		        	// start controlling the AHP  in 1.5 milliseconds
		count = 300   								// Reset counter to 300 
	}
	
	count -= 1					// decrement counter
	

	// output parameters you to analyze
	
	fprint("%g %g %g %g %g %g %g %g %g %g %g\n",t,cell[0].v, hillock.v(.5), cell[119].v, ina, m_DGCaT^2,h_DGCaT, ica, m_NaM99SL^3, h_NaM99SL, ik)
	
	fadvance()					// advance simulation one time step
}

//////  Simulation 2 - second to largest AHP /////////

t=0								// reset time

init()							

wopen("output2.dat")			// output file

while (t<TSTOP){				// simulation loop

	if ((cell[0].v > 0) && (count <=0 )){		// Did the cell fire?
		ahp.e = -90								
		ahp.gmax = .005*10*.4
		ahp.tau = 1
		ahp.onset = t + 1.5
		count = 300
	}
	
	count -= 1					// counter

	fprint("%g %g %g %g %g %g %g %g %g %g %g\n",t,cell[0].v, hillock.v(.5), cell[119].v, ina, m_DGCaT^2,h_DGCaT, cell[0].ica, m_NaM99SL^3, h_NaM99SL, ik)


	fadvance()
}

//////  Simulation 3  -  second to smallest AHP /////////

t = 0								// reset time

init()								// initialize state variables

wopen("output3.dat")				// output file

while (t<TSTOP){					// simulation loop

	if ((cell[0].v > 0) && (count <=0 )){	// Did the cell fire?
		ahp.e = -60
		ahp.gmax = .05
		ahp.tau = 2
		ahp.onset = t + 1.5
		count = 300
	}
	
	count -= 1						// counter
	
	// output parameters you to analyze

	fprint("%g %g %g %g %g %g %g %g %g %g %g\n",t,cell[0].v, hillock.v(.5), cell[119].v, ina, m_DGCaT^2,h_DGCaT, cell[0].ica, m_NaM99SL^3, h_NaM99SL, ik)

	fadvance()						// advance simulation one time step
}

//////  Simulation 4 - smallest AHP /////////

t = 0							// reset time

init()							// initialize state variables

wopen("output4.dat")			// output file

while (t<TSTOP){				// simulation loop

	if ((cell[0].v > 0) && (count <=0 )){		// Did the cell fire?
		ahp.e = -50
		ahp.gmax = .1
		ahp.tau = 2
		ahp.onset = t + .2
		count = 300
	}
	
	count -= 1				// counter

	// output parameters you to analyze

	fprint("%g %g %g %g %g %g %g %g %g %g %g\n",t,cell[0].v, hillock.v(.5), cell[119].v, ina, m_DGCaT^2,h_DGCaT, cell[0].ica, m_NaM99SL^3, h_NaM99SL, ik)


	fadvance()			// advance simulation one time step
}





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