Spine head calcium in a CA1 pyramidal cell model (Graham et al. 2014)

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Accession:154732
"We use a computational model of a hippocampal CA1 pyramidal cell to demonstrate that spine head calcium provides an instantaneous readout at each synapse of the postsynaptic weighted sum of all presynaptic activity impinging on the cell. The form of the readout is equivalent to the functions of weighted, summed inputs used in neural network learning rules. Within a dendritic layer, peak spine head calcium levels are either a linear or sigmoidal function of the number of coactive synapses, with nonlinearity depending on the ability of voltage spread in the dendrites to reach calcium spike threshold. ..."
Reference:
1 . Graham BP, Saudargiene A, Cobb S (2014) Spine head calcium as a measure of summed postsynaptic activity for driving synaptic plasticity. Neural Comput 26:2194-222 [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: Hippocampus;
Cell Type(s):
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Synaptic Integration;
Implementer(s): Graham, Bruce [B.Graham at cs.stir.ac.uk];
/
GrahamEtAl2014
Cells
Results
readme.html
burststim2.mod *
cad.mod
cagk.mod
carF.mod
distca.mod
distr.mod *
h.mod *
kadist.mod *
kaprox.mod *
kca.mod *
kdrca1.mod *
km.mod
na3n.mod *
naxn.mod *
nmdaca.mod *
burst_cell.hoc *
CA1PC.hoc
mosinit.hoc
randomlocation.hoc
ranstream.hoc *
run_batsyn.hoc
run_PC.hoc
screenshot1.png
screenshot2.png
screenshot3.png
setup_PC.hoc
synstim.ses
                            
// General CA1 pyramidal cell model
//   - with minimal set of ion channels and their distributions
// Morphology of cell n5038804 as used in Migliore et al J Neurophys 94:4145-4155, 2005.
// Based on Migliore et al 2005 - passive properties, Na, Kdr, Ka, Ih 
// and Poirazzi et al Neuron 37:977-987, 2003 - IM, calcium currents (L, T, R), mAHP, sAHP
// Also Holbro et al PNAS 107:15975-15980, 2010 (fast Ca R)

// Geometry files must define the section lists:
// basal_list, apical_list, trunk_list, oblique_list, SR_list, SLM_list
// soma and axon sections must be called "soma" and "axon"
// SLMbr_list is a special list containing the sections in a single SLM branch
// (used for focal stimulation)

// Last update: BPG 2-5-14

begintemplate PyramidalCell
public is_art, totnseg, totarea, Vrest
public gna, NaMULT, arSOMA, arDIST, arMAX, gka, ghd
public init, topol, basic_shape, subsets, geom, biophys, set_dendrite
public pre_list, connect2target
public cell_init, plotvmx, newsyn, showsyn, showlayersyn, plotcamx, plotcamxd, plotcamxt

public soma, soma_list, axon_list, dendrite_list
public basal_list, apical_list, trunk_list, oblique_list
public SR_list, SRbrp_list, SRbrd_list, SRbrt_list, SRbrt2_list, SRbrtc_list
public SRprox_list, SRdist_list
public SLM_list, SLMbr_list, SLMbrt_list
public shead, sneck, spine_list, sneck_list

objref basal_list, apical_list, trunk_list, oblique_list
objref SR_list, SRbrp_list, SRbrd_list, SRbrt_list, SRbrt2_list, SRbrtc_list
objref SRprox_list, SRdist_list
objref SLM_list, SLMbr_list, SLMbrt_list
objref soma_list, axon_list, dendrite_list, pre_list, spine_list, sneck_list


external lambda_f
proc geom_nseg() {
  forall { nseg = int((L/(0.1*lambda_f(freq))+.9)/2)*2 + 1  }
}


xopen("Cells/Mig_sec5038804.hoc")             // Migliore section file


proc init() {

soma_list = new SectionList()
axon_list = new SectionList()
dendrite_list = new SectionList()
basal_list = new SectionList()
apical_list = new SectionList()
trunk_list = new SectionList()
oblique_list = new SectionList()
SR_list = new SectionList()
SRbrp_list = new SectionList()
SRbrd_list = new SectionList()
SRbrt_list = new SectionList()
SRbrt2_list = new SectionList()
SRbrtc_list = new SectionList()
SRprox_list = new SectionList()
SRdist_list = new SectionList()
SLM_list = new SectionList()
SLMbr_list = new SectionList()
SLMbrt_list = new SectionList()
spine_list = new SectionList()
sneck_list = new SectionList()

xopen("Cells/Mig_geo5038804.hoc")             // Migliore geometry file
fix_seg = 0

// Spine dimesions (if spines used)
// approximate Grunditz et al model
//sneck_diam = 0.04 /* um (high resistance) */
sneck_diam = 0.125 /* um (low resistance) */
sneck_len = 1.0 /* um */
shead_diam = 0.5 /* um */
shead_len = 0.5 /* um */

// Passive properties from Migliore 2005
Vrest = -65
celsius = 35.0  

Rm = 28000	// Migliore
//Rm = 200000	// Poirazi soma (cf Kali 300000)
RmDend = Rm
RmSoma = Rm
RmAx = Rm

Cm    = 1
CmSoma= Cm
CmAx  = Cm
CmDend = Cm

//RaAll= 50	// low Ra
//RaSoma=50  
//RaAx = 50
//RaSpine = 50
RaAll= 150	// Migliore 2005
RaSoma=150  
RaAx = 150
RaSpine = 150

gna =  0.025	// Migliore 2005
AXONM = 5
NaMULT = 0.015/0.025	// scale Na in dendrites (=1 for Migliore)
arSOMA = 1.0	// slow inactivation at soma (1=none; 0=max) (BPG)
arMAX = 0.5	// slow inact at distance (BPG)
arDIST = 350	// distance at which inactivation saturates (BPG)

gkdr = 0.01

gka = 0.03	// standard high KA
//gka = 0.01	// suitably reduced: low KA
KMULT =  gka
KMULTP = gka

ghd=0.00005
//ghd=0.0001	// doubled Ih

soma_km = 0.06	// not used (BPG)

soma_caR = 0.03 
soma_sAHP = 0.001
soma_mAHP = 0.001

caR_init = 0.03 
sAHP_init = 0.001
mAHP_init = 0.001
caR_spine = 0.03 
sAHP_spine = 0.001
mAHP_spine = 0.001
caR_vact = -30	// make half-activation point more hyperpolarised
caR_tinact = 20	// make inactivation faster


forsec axon_list {insert pas e_pas=Vrest g_pas = 1/RmAx Ra=RaAx cm=CmAx}
forsec soma_list {insert pas e_pas=Vrest g_pas = 1/RmSoma Ra=RaSoma cm=CmSoma}
forsec dendrite_list {insert pas e_pas=Vrest g_pas = 1/RmDend Ra=RaAll cm=CmDend}

access soma
freq=50
if (!fix_seg) {geom_nseg()}	// adjust segment number in each section
totnseg=0
forall {totnseg=totnseg+nseg}
totarea=0
forall {for (x) totarea=totarea+area(x)}
access soma
distance()

forsec axon_list {   
                insert nax gbar_nax=gna*AXONM
                insert kdr gkdrbar_kdr=gkdr
                insert kap gkabar_kap = KMULTP
}

forsec soma_list {   
		insert hd ghdbar_hd=ghd	vhalfl_hd=-73
                insert na3 gbar_na3=gna ar_na3=arSOMA
                insert kdr gkdrbar_kdr=gkdr
                insert kap gkabar_kap = KMULTP
       		//insert km gbar_km=soma_km
            	insert carF gcabar_carF = soma_caR vha_carF=caR_vact ti_carF=caR_tinact           
            	//insert kca gbar_kca = soma_sAHP  // sAHP       
            	insert kmAHP gkbar_kmAHP = soma_mAHP  // mAHP      
       		insert cad    // calcium pump/buffering mechanism
}

forsec dendrite_list {
		insert hd ghdbar_hd=ghd
                insert na3 gbar_na3=gna*NaMULT
                insert kdr gkdrbar_kdr=gkdr
		insert kap gkabar_kap=0
		insert kad gkabar_kad=0
       		//insert km gbar_km=soma_km
            	insert carF gcabar_carF = caR_init vha_carF=caR_vact ti_carF=caR_tinact            
            	//insert kca gbar_kca = sAHP_init  // sAHP       
            	insert kmAHP gkbar_kmAHP = mAHP_init  // mAHP      
       		insert cad    // calcium pump/buffering mechanism
       		insert ds
       		insert dca

		for (x) if (x>0 && x<1) { xdist = distance(x)
		
			// Na slow inactivation saturates at 350um (BPG)
			if (xdist < arDIST) {
                	  ar_na3(x) = arSOMA-(arSOMA-arMAX)*(xdist/arDIST)
                	} else {
                	  ar_na3(x) = arMAX
                	}

			// Ih saturates at 350um (BPG)
			if (xdist < 350) {
                	  ghdbar_hd(x) = ghd*(1+3*xdist/100)
                	} else {
                	  ghdbar_hd(x) = ghd*(1+3*350/100)
                	}
                	
                	// KA saturates at 350um (BPG)
                	if (xdist > 100 && xdist < 350) {
				vhalfl_hd=-81
                        	gkabar_kad(x) = KMULT*(1+xdist/100)
                        } else if (xdist >= 350) {
				vhalfl_hd=-81
                        	gkabar_kad(x) = KMULT*(1+350/100)
                	} else {
				vhalfl_hd=-73
                        	gkabar_kap(x) = KMULTP*(1+xdist/100)
               		}
		}
}

cell_init()

pre_list = new List()
//synapses()


} // end init


proc set_dendrite() {
	KMULT =  gka
	KMULTP = gka
	access soma
	distance()
	forsec dendrite_list {
		gbar_na3=gna*NaMULT		
		for (x) if (x>0 && x<1) { xdist = distance(x)
		
			// Na slow inactivation saturates at 350um (BPG)
			if (xdist < arDIST) {
                	  ar_na3(x) = arSOMA-(arSOMA-arMAX)*(xdist/arDIST)
                	} else {
                	  ar_na3(x) = arMAX
                	}

			// Ih saturates at 350um (BPG)
			if (xdist < 350) {
                	  ghdbar_hd(x) = ghd*(1+3*xdist/100)
                	} else {
                	  ghdbar_hd(x) = ghd*(1+3*350/100)
                	}
                	
                	// KA saturates at 350um (BPG)
                	if (xdist > 100 && xdist < 350) {
				vhalfl_hd=-81
                        	gkabar_kad(x) = KMULT*(1+xdist/100)
                        } else if (xdist >= 350) {
				vhalfl_hd=-81
                        	gkabar_kad(x) = KMULT*(1+350/100)
                	} else {
				vhalfl_hd=-73
                        	gkabar_kap(x) = KMULTP*(1+xdist/100)
               		}
		}
	}
	cell_init()
}


proc cell_init() {
	t=0
        forall {
        v=Vrest
        if (ismembrane("nax") || ismembrane("na3")) {ena=55}
        if (ismembrane("kdr") || ismembrane("kap") || ismembrane("kad")) {ek=-90}
        if (ismembrane("hd") ) {ehd_hd=-30}
	}
	finitialize(Vrest)
        fcurrent()

        forall {
	for (x) {
	if (ismembrane("na3")||ismembrane("nax")){e_pas(x)=v(x)+(ina(x)+ik(x))/g_pas(x)}
	if (ismembrane("hd")) {e_pas(x)=e_pas(x)+i_hd(x)/g_pas(x)}
		}
	}
}


objref distrx, distry, c
proc plotvmx() {	// plot max voltage with distance
	c = new Graph()
	c.size(0,1000,0,100)
	c.xaxis(1)
	c.exec_menu("10% Zoom out")
	c.color(1)
	c.label(0.4,0.8," peak AP")

	distrx=new Vector()
	distry=new Vector()
	forsec $o1 {
		for (x) if (x>0 && x<1) {
			if (diam>=0.) {
			distrx.append(distance(x)) 
			distry.append(vmax_ds(x)-Vrest)
			}
		}
	}
	distry.mark(c,distrx,"O",3,3,2)
//	distry.mark(c,distrx,"t",5,1,1) 
	c.flush()
	doNotify()
}


objref cax, cay, cca
proc plotcamx() {local i	// plot max ca across spine heads
	cca = new Graph()
	cca.size(0,$2,0,$3)
	cca.xaxis(1)
	cca.exec_menu("10% Zoom out")
	cca.color(1)
	cca.label(0.4,0.8," peak Ca")

	cax=new Vector()
	cay=new Vector()
	i = 0
	forsec $o1 {
	  i = i+1
	  cax.append(i) 
	  cay.append(camax_dca(0.5))
	}
	cay.mark(cca,cax,"O",3,3,2)
	cca.flush()
	doNotify()
	print cay.mean(), cay.max(), cay.min()
}

objref tcax, tcay, ccat
proc plotcamxt() {local i	// plot max ca against time
	ccat = new Graph()
	ccat.size(0,$2,0,$3)
	ccat.xaxis(1)
	ccat.exec_menu("10% Zoom out")
	ccat.color(1)
	ccat.label(0.4,0.8," peak Ca")

	tcax=new Vector()
	tcay=new Vector()
	i = 0
	forsec $o1 {
	  tcax.append(tmax_dca(0.5)) 
	  tcay.append(camax_dca(0.5))
	}
	tcay.mark(ccat,tcax,"O",3,3,2)
	ccat.flush()
	doNotify()
	print tcay.mean(), tcay.max(), tcay.min()
}

objref dcax, dcay, ccad
proc plotcamxd() {	// plot max calcium with distance
	ccad = new Graph()
	ccad.size(0,1000,0,1)
	ccad.xaxis(1)
	ccad.exec_menu("10% Zoom out")
	ccad.color(1)
	ccad.label(0.4,0.8," peak Ca")

	dcax=new Vector()
	dcay=new Vector()
	forsec $o1 {
		for (x) if (x>0 && x<1) {
			if (diam>=0.) {
			dcax.append(distance(x)) 
			dcay.append(camax_dca(x))
			}
		}
	}
	dcay.mark(ccad,dcax,"O",3,3,2)
//	distry.mark(ccad,dcax,"t",5,1,1) 
	ccad.flush()
	doNotify()
	print dcay.mean(), dcay.max(), dcay.min()
}


obfunc connect2target() { localobj nc //$o1 target point process, optional $o2 returned NetCon
  soma nc = new NetCon(&v(1), $o1)
  nc.threshold = -10
  if (numarg() == 2) { $o2 = nc } // for backward compatibility
  return nc
}


// Code to add individual synapses in random locations (BPG 6-2-10)
create shead[1], sneck[1]
spi = 0		// current spine index

proc newsyn() { local i, j localobj syn, rl, syn_list, snr, shr 
// $1 type $2 number $o3 target section list, $o4 uniform random no., $5 flag spines, $6 total spines
  access soma
  rl = new RandomLocation($o3, $o4)
  if ($5 == 1 && spi == 0) {
    create sneck[$6], shead[$6]
  }
  for i=0, $2-1 {
    syn_list = new List()
    if ($1 == 1) {	// AMPA
      soma syn = new Exp2Syn(0.5) pre_list.append(syn)
      syn.tau1 = 0.5
      syn.tau2 = 3
      syn.e = 0
      syn_list.append(syn)
    } else if ($1 == 2) {	// AMPA/NMDA
      soma syn = new Exp2Syn(0.5) pre_list.append(syn)
      syn.tau1 = 0.5	// Spruston JPhysiol 1995
      syn.tau2 = 3	// Spruston JPhysiol 1995
      syn.e = 0
      syn_list.append(syn)
      soma syn = new NMDAca(0.5) pre_list.append(syn)
      syn.fCa = 0.1	// fraction of Ca current (Bloodgood & Sabatini)
      syn.tcon = 3	
      syn.tcoff = 100
      syn.mgconc = 1	// (mM) standard Mg conc
      syn.gamma = 0.08	// Larkum Science 2009 (sharpens voltage curve)
      syn_list.append(syn)
    } else if ($1 == 3) {	// GABAA
      soma syn = new Exp2Syn(0.5) pre_list.append(syn)
      syn.tau1 = 1
      syn.tau2 = 8
      syn.e = -75
      syn_list.append(syn)
    } else if ($1 == 4) {	// GABAB
      soma syn = new Exp2Syn(0.5) pre_list.append(syn)
      syn.tau1 = 35
      syn.tau2 = 100
      syn.e = -75
      syn_list.append(syn)
    }
    if ($5 == 1) {  // spines
      sneck[spi].L = sneck_len
      sneck[spi].diam = sneck_diam
      shead[spi].L = shead_len
      shead[spi].diam = shead_diam
      sneck[spi] {insert pas e_pas=Vrest g_pas=1/RmDend Ra=RaAll cm=CmDend
        insert cad taur_cad=14 insert ds insert dca}
      shead[spi] {insert pas e_pas=Vrest g_pas=1/RmDend Ra=RaAll cm=CmDend
        insert carF gcabar_carF=caR_spine vha_carF=caR_vact ti_carF=caR_tinact
        insert kmAHP gkbar_mAHP = mAHP_spine  // mAHP      
        insert cad taur_cad=14 depth_cad=shead_diam/2
        insert ds insert dca 
        }
      sneck[spi] snr = new SectionRef()
      sneck[spi] sneck_list.append()
      shead[spi] shr = new SectionRef()
      shead[spi] spine_list.append()
      access soma
      rl.locsp(syn_list, snr, shr)
      spi = spi + 1
    } else {	// no spines
      rl.loc(syn_list)
    }
  }
}

objref cell_shape

proc showsyn() { local i
  cell_shape = new Shape()
  for i=0,pre_list.count()-1 {
    cell_shape.point_mark(pre_list.o(i), 3)
  }
}

proc showlayersyn() { local i
  if ($4 == 1) {
    cell_shape = new Shape()
  }
  for i=$1,$2 {
    cell_shape.point_mark(pre_list.o(i), $3)
  }
}


//**********************************************************************

objref syn_
proc synapses() {
  	/* E0 */   	soma syn_ = new Exp2Syn(0.5)  pre_list.append(syn_)
    	syn_.tau1 = 0.5
    	syn_.tau2 = 3
}


func is_art() { return 0 }

endtemplate PyramidalCell

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