Long time windows from theta modulated inhib. in entorhinal–hippo. loop (Cutsuridis & Poirazi 2015)

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Accession:181967
"A recent experimental study (Mizuseki et al., 2009) has shown that the temporal delays between population activities in successive entorhinal and hippocampal anatomical stages are longer (about 70–80 ms) than expected from axon conduction velocities and passive synaptic integration of feed-forward excitatory inputs. We investigate via computer simulations the mechanisms that give rise to such long temporal delays in the hippocampus structures. ... The model shows that the experimentally reported long temporal delays in the DG, CA3 and CA1 hippocampal regions are due to theta modulated somatic and axonic inhibition..."
Reference:
1 . Cutsuridis V, Poirazi P (2015) A computational study on how theta modulated inhibition can account for the long temporal windows in the entorhinal-hippocampal loop. Neurobiol Learn Mem 120:69-83 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism:
Cell Type(s): Dentate gyrus granule cell; Hippocampus CA1 pyramidal cell; Hippocampus CA3 pyramidal cell; Hippocampus CA3 interneuron basket cell; Dentate gyrus mossy cell; Dentate gyrus basket cell; Dentate gyrus hilar cell; Hippocampus CA1 basket cell; Hippocampus CA3 stratum oriens lacunosum-moleculare interneuron; Hippocampus CA1 bistratified cell; Hippocampus CA1 axo-axonic cell; Hippocampus CA3 axo-axonic cells;
Channel(s): I Na,t; I L high threshold; I N; I T low threshold; I A; I K; I M; I h; I K,Ca; I_AHP;
Gap Junctions:
Receptor(s): GabaA; AMPA; NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Pattern Recognition; Temporal Pattern Generation; Spatio-temporal Activity Patterns; Brain Rhythms; Storage/recall;
Implementer(s): Cutsuridis, Vassilis [vcutsuridis at gmail.com];
Search NeuronDB for information about:  Dentate gyrus granule cell; Hippocampus CA1 pyramidal cell; Hippocampus CA3 pyramidal cell; Hippocampus CA3 interneuron basket cell; GabaA; AMPA; NMDA; I Na,t; I L high threshold; I N; I T low threshold; I A; I K; I M; I h; I K,Ca; I_AHP;
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CutsuridisPoirazi2015
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TITLE Calcium ion accumulation and diffusion
: The internal coordinate system is set up in PROCEDURE coord_cadifus()
: and must be executed before computing the concentrations.
: The scale factors set up in this procedure do not have to be recomputed
: when diam or DFree are changed.
: The amount of calcium in an annulus is ca[i]*diam^2*vol[i] with
: ca[0] being the second order correct concentration at the exact edge
: and ca[NANN-1] being the concentration at the exact center

NEURON {
	SUFFIX cadifus
	USEION ca READ cao, cai, ica WRITE cai, ica
	GLOBAL vol, Buffer0
	RANGE ipump
}
DEFINE NANN  4

UNITS {
        (mol)   = (1)
	(molar) = (1/liter)
	(mM)	= (millimolar)
	(um)	= (micron)
	(mA)	= (milliamp)
	FARADAY = (faraday)	 (10000 coulomb)
	PI	= (pi) (1)
}

PARAMETER {
	DFree = .6	(um2/ms)
	diam		(um)
	cao		(mM)
	ica		(mA/cm2)
	k1buf = 500	(/mM-ms)
	k2buf = 0.5	(/ms)
        k1=1.e10            (um3/s)
        k2=50.e7            (/s)	: k1*50.e-3
        k3=1.e10            (/s)	: k1
        k4=5.e6	            (um3/s)	: k1*5.e-4
	area		(um2)
} 
CONSTANT { volo=1  (liter)}

ASSIGNED {
	cai		(mM)
	vol[NANN]	(1)	: gets extra cm2 when multiplied by diam^2
	ipump           (mA/cm2)
	last_ipump           (mA/cm2)

}

STATE {
	ca[NANN]	(mM) <1.e-5> : ca[0] is equivalent to cai
	CaBuffer[NANN]  (mM)
	Buffer[NANN]    (mM)
        pump            (mol/cm2) <1.e-3>
        pumpca          (mol/cm2) <1.e-15>

}

LOCAL totpump, kd,totbuf

INITIAL {
           totpump=0.2
           pump=totpump/(1+1.e-18*k4*cao/k3)
           pumpca=2.e-22
	   ipump=0

           totbuf=1.2
           kd=k2buf/k1buf
           FROM i=0 TO NANN-1 {
                ca[i] = cai
		CaBuffer[i] =(totbuf*ca[i])/(kd+ca[i])
		Buffer[i] = totbuf - CaBuffer[i]
                }

}

BREAKPOINT {
	SOLVE state METHOD sparse
	last_ipump=ipump
	ica = ipump
}

LOCAL coord_done

INITIAL {
	if (coord_done == 0) {
		coord_done = 1
		coord()
	}
	: note Buffer gets set to Buffer0 automatically
	: and CaBuffer gets set to 0 (Default value of CaBuffer0) as well
	FROM i=0 TO NANN-1 {
		ca[i] = cai
	}
}

LOCAL frat[NANN] 	: gets extra cm when multiplied by diam

PROCEDURE coord() {
	LOCAL r, dr2
	: cylindrical coordinate system  with constant annuli thickness to
	: center of cell. Note however that the first annulus is half thickness
	: so that the concentration is second order correct spatially at
	: the membrane or exact edge of the cell.
	: note ca[0] is at edge of cell
	:      ca[NANN-1] is at center of cell
	r = 1/2					:starts at edge (half diam)
	dr2 = r/(NANN-1)/2			:half thickness of annulus
	vol[0] = 0
	frat[0] = 2*r
	FROM i=0 TO NANN-2 {
		vol[i] = vol[i] + PI*(r-dr2/2)*2*dr2	:interior half
		r = r - dr2
		frat[i+1] = 2*PI*r/(2*dr2)	:exterior edge of annulus
					: divided by distance between centers
		r = r - dr2
		vol[i+1] = PI*(r+dr2/2)*2*dr2	:outer half of annulus
	}
}

LOCAL dsq, dsqvol : can't define local variable in KINETIC block or use
		:  in COMPARTMENT
KINETIC state {
	COMPARTMENT i, diam*diam*vol[i]*1(um) {ca CaBuffer Buffer}
        COMPARTMENT (1.e10)*area {pump pumpca}
        COMPARTMENT (1.e15)*volo {cao}

	~ ca[0] << (-(ica-last_ipump)*PI*diam*frat[0]*1(um)/(2*FARADAY))
	FROM i=0 TO NANN-2 {
		~ ca[i] <-> ca[i+1] (DFree*frat[i+1]*1(um), DFree*frat[i+1]*1(um))
	}
	dsq = diam*diam*1(um)
	FROM i=0 TO NANN-1 {
		dsqvol = dsq*vol[i]
		~ ca[i] + Buffer[i] <-> CaBuffer[i] (k1buf*dsqvol,k2buf*dsqvol)
	}
        ~ca[0] + pump <-> pumpca ((1.e-11)*k1*area, (1.e7)*k2*area)
        ~pumpca       <-> pump + cao ((1.e7)*k3*area, (1.e-11)*k4*area)

        ipump = 2*FARADAY*(f_flux-b_flux)/area

	cai = ca[0]
}
	
COMMENT
At this time, conductances (and channel states and currents are
calculated at the midpoint of a dt interval.  Membrane potential and
concentrations are calculated at the edges of a dt interval.  With
secondorder=2 everything turns out to be second order correct.
ENDCOMMENT