Cerebellar granule cell (Masoli et al 2020)

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Accession:265584
"The cerebellar granule cells (GrCs) are classically described as a homogeneous neuronal population discharging regularly without adaptation. We show that GrCs in fact generate diverse response patterns to current injection and synaptic activation, ranging from adaptation to acceleration of firing. Adaptation was predicted by parameter optimization in detailed computational models based on available knowledge on GrC ionic channels. The models also predicted that acceleration required additional mechanisms. We found that yet unrecognized TRPM4 currents specifically accounted for firing acceleration and that adapting GrCs outperformed accelerating GrCs in transmitting high-frequency mossy fiber (MF) bursts over a background discharge. This implied that GrC subtypes identified by their electroresponsiveness corresponded to specific neurotransmitter release probability values. Simulations showed that fine-tuning of pre- and post-synaptic parameters generated effective MF-GrC transmission channels, which could enrich the processing of input spike patterns and enhance spatio-temporal recoding at the cerebellar input stage."
Reference:
1 . Masoli S, Tognolina M, Laforenza U, Moccia F, D'Angelo E (2020) Parameter tuning differentiates granule cell subtypes enriching transmission properties at the cerebellum input stage. Commun Biol 3:222 [PubMed]
Citations  Citation Browser
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 interneuron granule GLU cell;
Channel(s): Ca pump; I Na, leak; I Calcium;
Gap Junctions:
Receptor(s): AMPA; NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON; Python;
Model Concept(s): Action Potentials; Calcium dynamics; Synaptic Integration;
Implementer(s): Masoli, Stefano [stefano.masoli at unipv.it];
Search NeuronDB for information about:  Cerebellum interneuron granule GLU cell; AMPA; NMDA; I Calcium; I Na, leak; Ca pump;
/
Granule_cell_2020
04_GrC_2020_accelerating
mod_files
cdp5_CR_CAM.mod
GRANULE_Ampa_det_vi.mod *
GRANULE_Nmda_det_vi.mod *
GRC_CA.mod *
GRC_KM.mod *
GRC_NA.mod *
GRC_NA_FHF.mod *
Kca11.mod *
Kca22.mod *
Kir23.mod *
Kv11.mod *
Kv15.mod *
Kv22.mod *
Kv34.mod *
Kv43.mod *
Leak.mod *
UBC_TRP.mod
                            
: Calcium ion accumulation with endogenous buffers, DCM and pump

COMMENT

The basic code of Example 9.8 and Example 9.9 from NEURON book was adapted as:

1) Extended using parameters from Schmidt et al. 2003.
2) Pump rate was tuned according to data from Maeda et al. 1999
3) DCM was introduced and tuned to approximate the effect of radial diffusion

Reference: Anwar H, Hong S, De Schutter E (2010) Controlling Ca2+-activated K+ channels with models of Ca2+ buffering in Purkinje cell. Cerebellum*

*Article available as Open Access

PubMed link: http://www.ncbi.nlm.nih.gov/pubmed/20981513

Written by Haroon Anwar, Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 2010.
Contact: Haroon Anwar (anwar@oist.jp)

Modified by Stefano Masoli, Department Brain and Behavioral Sciences, University of Pavia, 2015

1) Buffer for Granule cell model 2015, without Parvalbumin and Calretinin instead of Calbindin.

ENDCOMMENT


NEURON {
  SUFFIX cdp5_CR_CAM
  USEION ca READ cao, cai, ica WRITE cai
  USEION nr2a WRITE nr2ai VALENCE 1
  USEION nr2c WRITE nr2ci VALENCE 1
  USEION con_2c WRITE con_2ci VALENCE 1
  RANGE ica_pmp
  RANGE Nannuli, Buffnull2, rf3, rf4, vrat, cainull, CR, CR_1C_0N, CR_2C_2N, CR_1V, CRnull
  RANGE CAM0, CAM1C, CAM2C, CAM1N2C, CAM1N, CAM2N, CAM2N1C, CAM1C1N, CAM4
  RANGE TotalPump

}


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

PARAMETER {
	Nannuli = 10.9495 (1)
	celsius (degC)
        
	cainull = 45e-6 (mM)
        mginull =.59    (mM)

:	values for a buffer compensating the diffusion

	Buffnull1 = 0	(mM)
	rf1 = 0.0134329	(/ms mM)
	rf2 = 0.0397469	(/ms)

	Buffnull2 = 60.9091	(mM)
	rf3 = 0.1435	(/ms mM)
	rf4 = 0.0014	(/ms)

:	values for benzothiazole coumarin (BTC)
	BTCnull = 0	(mM)
	b1 = 5.33	(/ms mM)
	b2 = 0.08	(/ms)

:	values for caged compound DMNPE-4
	DMNPEnull = 0	(mM)
	c1 = 5.63	(/ms mM)
	c2 = 0.107e-3	(/ms)

:       values for Calretinin (6 sites but only 5 active) (2*2 cooperative sites and 1 single indipendent site)

        CRnull =	0.9             (mM):0.7-1.2
        nT1   = 1.8            (/ms mM)
        nT2   = 0.053        (/ms)
        nR1   = 310           (/ms mM)
        nR2   = 0.02        (/ms)
        
	nV1   = 7.3            (/ms mM)
        nV2   = 0.24        (/ms)
        
:	Calmodulin concentration
	CAM_start 	= 0.03		(mM) :Pepke 2010

: 	Calmodulin Kinetic parameters. The values are the mean between max and min.
	:C-lobe
	Kd1C = 		0.00965	(mM)						: Kd - Equilibrium binding of 1st Ca2+ to CaM C-terminus 
	K1Coff = 	0.04	(/ms)						: From 0C to 1C with X ions on N-lobe
	K1Con = 	5.4	(/mM ms)					: From 1C to 0C with X ions on N-lobe
	Kd2C = 		0.00105	(mM)						: Kd - Equilibrium binding of 2nd Ca2+ to CaM C-terminus
	K2Coff = 	0.00925	(/ms)						: From 1C to 2C with X ions on N-lobe
	K2Con = 	15	(/mM ms)					: From 2C to 1C with X ions on N-lobe

	:N-lobe
	Kd1N = 		0.0275	(uM)						: Kd - Equilibrium binding of 1st Ca2+ to CaM N-terminus 
	K1Noff = 	2.5	(/ms)						: From 0N to 1N with X ions on C-lobe
	K1Non = 	142.5	(/mM ms)					: From 1N to 0N with X ions on C-lobe
	Kd2N = 		0.00615	(mM)						: Kd - Equilibrium binding of 2nd Ca2+ to CaM N-terminus
	K2Noff = 	0.75	(/ms)						: From 1N to 2N with X ions on C-lobe
	K2Non = 	175	(/mM ms)					: From 2N to 1N with X ions on C-lobe        
        
        :pumps

  	kpmp1    = 3e-3       (/mM-ms)
  	kpmp2    = 1.75e-5   (/ms)
  	kpmp3    = 7.255e-5  (/ms)
	TotalPump = 1e-9	(mol/cm2)	

}

ASSIGNED {
	diam      (um)
	ica       (mA/cm2)
	ica_pmp   (mA/cm2)
	parea     (um)     : pump area per unit length
	parea2	  (um)
	cai       (mM)
	mgi	(mM)
	vrat	(1)	
	nr2ai  (mM)
	nr2ci  (mM)
	con_2ci (mM)
}

CONSTANT { cao = 2	(mM) }

STATE {
	: ca[0] is equivalent to cai
	: ca[] are very small, so specify absolute tolerance
	: let it be ~1.5 - 2 orders of magnitude smaller than baseline level

	ca		(mM)    <1e-3>
	mg		(mM)	<1e-6>
	
	Buff1		(mM)	
	Buff1_ca	(mM)

	Buff2		(mM)
	Buff2_ca	(mM)

	BTC		(mM)
	BTC_ca		(mM)

	DMNPE		(mM)
	DMNPE_ca	(mM)	
        
        :calretinin
        
	CR		(mM)
	
        CR_1C_0N	(mM)
	CR_2C_0N	(mM)  
	CR_2C_1N	(mM)
	
	CR_1C_1N	(mM)

	CR_0C_1N	(mM)
	CR_0C_2N	(mM)
	CR_1C_2N	(mM)
	
	CR_2C_2N	(mM)
	
	CR_1V 		(mM)
	
:State for the Calmodulin      

	CAM0		(mM)

	:C-lobe mainly
	CAM1C		(mM)
	CAM2C		(mM)
	CAM1N2C		(mM)
	
	:N-Lobe Mainly
	CAM1N		(mM)
	CAM2N		(mM)
	CAM2N1C		(mM)

	:One ion on C-lobe and one on N-lobe
	CAM1C1N		(mM)

	:CaM complete
	CAM4		(mM)	
	

	:pumps
	
	pump		(mol/cm2) <1e-15>
	pumpca		(mol/cm2) <1e-15>

}

BREAKPOINT {
	SOLVE state METHOD sparse
}

LOCAL factors_done

INITIAL {
		factors()

		ca = cainull
		mg = mginull
		
		Buff1 = ssBuff1()
		Buff1_ca = ssBuff1ca()

		Buff2 = ssBuff2()
		Buff2_ca = ssBuff2ca()

		BTC = ssBTC()
		BTC_ca = ssBTCca()		

		DMNPE = ssDMNPE()
		DMNPE_ca = ssDMNPEca()
		
  	:to calculate the steady state of each protein at starting point
		
		CR 	= CRnull		
		
		CR_1C_0N = 0
		CR_2C_0N = 0	 
		CR_2C_1N = 0	
		
		CR_1C_1N = 0

		CR_0C_1N = 0
		CR_0C_2N = 0	
		CR_1C_2N = 0
		
		CR_2C_2N = 0	
		
		CR_1V 	= 0	

        :Calmodulin
	CAM0	= CAM_start		
	CAM1C	= 0
	CAM2C	= 0
	CAM1N2C = 0
	CAM1N   = 0
	CAM2N	= 0
	CAM2N1C = 0
	CAM1C1N = 0
	CAM4	= 0
		


		
  	parea = PI*diam
	parea2 = PI*(diam-0.2)
	ica = 0
	ica_pmp = 0
:	ica_pmp_last = 0
	pump = TotalPump
	pumpca = 0
	
	cai = ca
	
}

PROCEDURE factors() {
        LOCAL r, dr2
        r = 1/2                : starts at edge (half diam)
        dr2 = r/(Nannuli-1)/2  : full thickness of outermost annulus,
        vrat = PI*(r-dr2/2)*2*dr2  : interior half
        r = r - dr2
}


LOCAL dsq, dsqvol  : can't define local variable in KINETIC block
                   :   or use in COMPARTMENT statement

KINETIC state {
  COMPARTMENT diam*diam*vrat {ca mg Buff1 Buff1_ca Buff2 Buff2_ca BTC BTC_ca DMNPE DMNPE_ca CR CR_1C_0N CR_2C_0N CR_2C_1N CR_0C_1N CR_0C_2N CR_1C_2N CR_1C_1N CR_2C_1N CR_1C_2N CR_2C_2N}
  COMPARTMENT (1e10)*parea {pump pumpca}


	:pump
	~ ca + pump <-> pumpca  (kpmp1*parea*(1e10), kpmp2*parea*(1e10))
	~ pumpca <-> pump   (kpmp3*parea*(1e10), 0)
  	CONSERVE pump + pumpca = TotalPump * parea * (1e10)
	
	ica_pmp = 2*FARADAY*(f_flux - b_flux)/parea	
	: all currents except pump
	: ica is Ca efflux
	~ ca << (-ica*PI*diam/(2*FARADAY))

	:RADIAL DIFFUSION OF ca, mg and mobile buffers

	dsq = diam*diam
		dsqvol = dsq*vrat
		~ ca + Buff1 <-> Buff1_ca (rf1*dsqvol, rf2*dsqvol)
		~ ca + Buff2 <-> Buff2_ca (rf3*dsqvol, rf4*dsqvol)
		~ ca + BTC <-> BTC_ca (b1*dsqvol, b2*dsqvol)
		~ ca + DMNPE <-> DMNPE_ca (c1*dsqvol, c2*dsqvol)
        	
        	:Calretinin
        	:Slow state
		~ ca + CR <-> CR_1C_0N (nT1*dsqvol, nT2*dsqvol)
	       	~ ca + CR_1C_0N <-> CR_2C_0N (nR1*dsqvol, nR2*dsqvol)
	       	~ ca + CR_2C_0N <-> CR_2C_1N (nT1*dsqvol, nT2*dsqvol)
	       	
	       	:fast state
		~ ca + CR <-> CR_0C_1N (nT1*dsqvol, nT2*dsqvol)
		~ ca + CR_0C_1N <-> CR_0C_2N (nR1*dsqvol, nR2*dsqvol)
		~ ca + CR_0C_2N <-> CR_1C_2N (nT1*dsqvol, nT2*dsqvol)
		
        	:complete
        	~ ca + CR_2C_1N <-> CR_2C_2N (nR1*dsqvol, nR2*dsqvol)
        	~ ca + CR_1C_2N <-> CR_2C_2N (nR1*dsqvol, nR2*dsqvol)
        	
        	:mixed
        	~ ca + CR_1C_0N <-> CR_1C_1N (nT1*dsqvol, nT2*dsqvol)   
		~ ca + CR_0C_1N <-> CR_1C_1N (nT1*dsqvol, nT2*dsqvol) 
		
		~ ca + CR_1C_1N <-> CR_2C_1N (nR1*dsqvol, nR2*dsqvol)   
		~ ca + CR_1C_1N <-> CR_1C_2N (nR1*dsqvol, nR2*dsqvol) 
        	
        	:Fith site
        	~ ca + CR  <-> CR_1V	     (nV1*dsqvol, nV2*dsqvol)
        
        :Calmodulin
		  :C-lobe
		~ ca + CAM0 <-> CAM1C (K1Con*dsqvol, K1Coff*dsqvol)
		~ ca + CAM1C <-> CAM2C (K2Con*dsqvol, K2Coff*dsqvol)
		~ ca + CAM2C <-> CAM1N2C (K1Non*dsqvol, K1Noff*dsqvol)
		~ ca + CAM1N2C <-> CAM4 (K2Non*dsqvol, K2Noff*dsqvol) 

		  :N-lobe
		~ ca + CAM0 <-> CAM1N (K1Non*dsqvol, K1Noff*dsqvol)
		~ ca + CAM1N <-> CAM2N (K2Non*dsqvol, K2Noff*dsqvol) 
		~ ca + CAM2N <-> CAM2N1C (K1Con*dsqvol, K1Coff*dsqvol)
		~ ca + CAM2N1C <-> CAM4 (K2Con*dsqvol, K2Coff*dsqvol)

		  :Mixed C and N lobes
		~ ca + CAM1C <-> CAM1C1N (K1Non*dsqvol, K1Noff*dsqvol) 
		~ ca + CAM1N <-> CAM1C1N (K1Con*dsqvol, K1Coff*dsqvol)
		~ ca + CAM1C1N <-> CAM1N2C (K2Con*dsqvol, K2Coff*dsqvol)
		~ ca + CAM1C1N <-> CAM2N1C (K2Non*dsqvol, K2Noff*dsqvol) 

        	
  	cai = ca
	mgi = mg
	
        nr2ai = CAM4/2
	nr2ci = CAM4/2
	
	con_2ci = CAM2C
}

FUNCTION ssBuff1() (mM) {
	ssBuff1 = Buffnull1/(1+((rf1/rf2)*cainull))
}
FUNCTION ssBuff1ca() (mM) {
	ssBuff1ca = Buffnull1/(1+(rf2/(rf1*cainull)))
}
FUNCTION ssBuff2() (mM) {
        ssBuff2 = Buffnull2/(1+((rf3/rf4)*cainull))
}
FUNCTION ssBuff2ca() (mM) {
        ssBuff2ca = Buffnull2/(1+(rf4/(rf3*cainull)))
}

FUNCTION ssBTC() (mM) {
	ssBTC = BTCnull/(1+((b1/b2)*cainull))
}

FUNCTION ssBTCca() (mM) {
	ssBTCca = BTCnull/(1+(b2/(b1*cainull)))
}

FUNCTION ssDMNPE() (mM) {
	ssDMNPE = DMNPEnull/(1+((c1/c2)*cainull))
}

FUNCTION ssDMNPEca() (mM) {
	ssDMNPEca = DMNPEnull/(1+(c2/(c1*cainull)))
}