State and location dependence of action potential metabolic cost (Hallermann et al., 2012)

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Accession:144526
With this model of a layer 5 pyramidal neuron the state and location dependence of the ATP usage and the metabolic efficiency of action potentials can be analyzed. Model parameters were constrained by direct subcellular recordings at dendritic, somatic and axonal compartments.
Reference:
1 . Hallermann S, de Kock CP, Stuart GJ, Kole MH (2012) State and location dependence of action potential metabolic cost in cortical pyramidal neurons Nat Neurosci. 15(7):1007-14 [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: Neocortex;
Cell Type(s): Neocortex V1 pyramidal corticothalamic L6 cell;
Channel(s): I Na,t; I K;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Action Potential Initiation; Action Potentials;
Implementer(s): Hallermann, Stefan [hallermann at medizin.uni-leipzig.de]; Kole, Maarten [m.kole at nin.knaw.nl];
Search NeuronDB for information about:  Neocortex V1 pyramidal corticothalamic L6 cell; I Na,t; I K;
/
HallermannEtAl2012
readme.txt *
Cad.mod *
CaH.mod *
CaT.mod *
charge.mod *
h.mod *
Kca.mod *
Kv.mod *
Kv1_axonal.mod *
Kv7.mod *
na8st.mod
nax8st.mod
28_04_10_num19.hoc *
all_28_04_10_num19.ses *
Cell parameters.hoc
charge.hoc *
mosinit.hoc *
                            
COMMENT

kv.mod

Potassium channel, Hodgkin-Huxley style kinetics
Kinetic rates based roughly on Sah et al. and Hamill et al. (1991)

Author: Zach Mainen, Salk Institute, 1995, zach@salk.edu
	
ENDCOMMENT

INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}

NEURON {
	SUFFIX Kv
	USEION k READ ek WRITE ik
	RANGE n, gk, gbar
	RANGE ninf, ntau
	GLOBAL Ra, Rb
	GLOBAL q10, temp, tadj, vmin, vmax
}

UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
	(pS) = (picosiemens)
	(um) = (micron)
} 

PARAMETER {
	gbar = 5   	(pS/um2)	: 0.03 mho/cm2
	v 		(mV)
								
	tha  = 25	(mV)		: v 1/2 for inf
	qa   = 9	(mV)		: inf slope		
	
	Ra   = 0.02	(/ms)		: max act rate
	Rb   = 0.002	(/ms)		: max deact rate	

	dt		(ms)
	celsius		(degC)
	temp = 23	(degC)		: original temp 	
	q10  = 2.3			: temperature sensitivity

	vmin = -120	(mV)
	vmax = 100	(mV)
} 


ASSIGNED {
	a		(/ms)
	b		(/ms)
	ik 		(mA/cm2)
	gk		(pS/um2)
	ek		(mV)
	ninf
	ntau (ms)	
	tadj
}
 

STATE { n }

INITIAL { 
	trates(v)
	n = ninf
}

BREAKPOINT {
        SOLVE states
	gk = tadj*gbar*n
	ik = (1e-4) * gk * (v - ek)
} 

LOCAL nexp

PROCEDURE states() {   :Computes state variable n 
        trates(v)      :             at the current v and dt.
        n = n + nexp*(ninf-n)
        VERBATIM
        return 0;
        ENDVERBATIM
}

PROCEDURE trates(v) {  :Computes rate and other constants at current v.
                      :Call once from HOC to initialize inf at resting v.
        LOCAL tinc
        TABLE ninf, nexp
	DEPEND dt, celsius, temp, Ra, Rb, tha, qa
	
	FROM vmin TO vmax WITH 199

	rates(v): not consistently executed from here if usetable_hh == 1

        tadj = q10^((celsius - temp)/10)

        tinc = -dt * tadj
        nexp = 1 - exp(tinc/ntau)
}


PROCEDURE rates(v) {  :Computes rate and other constants at current v.
                      :Call once from HOC to initialize inf at resting v.

        a = Ra * (v - tha) / (1 - exp(-(v - tha)/qa))
        b = -Rb * (v - tha) / (1 - exp((v - tha)/qa))
        ntau = 1/(a+b)
	ninf = a*ntau
}


Hallermann S, de Kock CP, Stuart GJ, Kole MH (2012) State and location dependence of action potential metabolic cost in cortical pyramidal neurons Nat Neurosci. 15(7):1007-14[PubMed]

References and models cited by this paper

References and models that cite this paper

Molecular basis of functional diversity of voltage-gated potassium channels in mammalian brain. EMBO J 8:3235-44 [PubMed]

Aiello L, Wheeler P (1995) The expensive-tissue hypothesis: the brain and the digestive system in human and primate evolution Curr Anthropol 36:199-221

Alle H, Kubota H, Geiger JR (2011) Sparse but highly efficient Kv3 outpace BKCa channels in action potential repolarization at hippocampal mossy fiber boutons. J Neurosci 31:8001-12 [PubMed]

Alle H, Roth A, Geiger JR (2009) Energy-efficient action potentials in hippocampal mossy fibers. Science 325:1405-8 [Journal] [PubMed]

   Action potential reconstitution from measured current waveforms (Alle et al. 2009) [Model]

Attwell D, Laughlin SB (2001) An energy budget for signaling in the grey matter of the brain. J Cereb Blood Flow Metab 21:1133-45 [PubMed]

Awatramani GB, Price GD, Trussell LO (2005) Modulation of transmitter release by presynaptic resting potential and background calcium levels. Neuron 48:109-21 [PubMed]

Bekkers JM, Delaney AJ (2001) Modulation of excitability by alpha-dendrotoxin-sensitive potassium channels in neocortical pyramidal neurons. J Neurosci 21:6553-60 [PubMed]

Braitenberg V, Schuz A (1998) Cortex Statistics and Geometry of Neuronal Connectivity 2nd ed

Carnevale NT, Hines ML (2006) The NEURON Book

Carter BC, Bean BP (2009) Sodium entry during action potentials of mammalian neurons: incomplete inactivation and reduced metabolic efficiency in fast-spiking neurons. Neuron 64:898-909 [PubMed]

Carter BC, Bean BP (2011) Incomplete inactivation and rapid recovery of voltage-dependent sodium channels during high-frequency firing in cerebellar Purkinje neurons. J Neurophysiol 105:860-71 [PubMed]

Christie JM, Chiu DN, Jahr CE (2011) Ca(2+)-dependent enhancement of release by subthreshold somatic depolarization. Nat Neurosci 14:62-8 [PubMed]

Cole KS, Curtis HJ (1939) ELECTRIC IMPEDANCE OF THE SQUID GIANT AXON DURING ACTIVITY. J Gen Physiol 22:649-70 [PubMed]

Crotty P, Sangrey T, Levy WB (2006) Metabolic energy cost of action potential velocity. J Neurophysiol 96:1237-46 [Journal] [PubMed]

de Haas V, Vogel W (1989) Sodium and potassium currents recorded during an action potential. Eur Biophys J 17:49-51 [PubMed]

de Kock CP, Sakmann B (2008) High frequency action potential bursts (>or= 100 Hz) in L2-3 and L5B thick tufted neurons in anaesthetized and awake rat primary somatosensory cortex. J Physiol 586:3353-64 [PubMed]

Engel D, Jonas P (2005) Presynaptic action potential amplification by voltage-gated Na+ channels in hippocampal mossy fiber boutons. Neuron 45:405-17 [PubMed]

Frankenhaeuser B, Huxley AF (1964) The action potential in the myelinated nerve fiber of Xenopus Laevis as computed on the basis of voltage clamp data. J Physiol 171:302-15 [Journal] [PubMed]

   Xenopus Myelinated Neuron (Frankenhaeuser, Huxley 1964) [Model]

Geiger JR, Jonas P (2000) Dynamic control of presynaptic Ca(2+) inflow by fast-inactivating K(+) channels in hippocampal mossy fiber boutons. Neuron 28:927-39 [PubMed]

Gittis AH, Moghadam SH, du Lac S (2010) Mechanisms of sustained high firing rates in two classes of vestibular nucleus neurons: differential contributions of resurgent Na, Kv3, and BK currents. J Neurophysiol 104:1625-34 [PubMed]

Guan D, Tkatch T, Surmeier DJ, Armstrong WE, Foehring RC (2007) Kv2 subunits underlie slowly inactivating potassium current in rat neocortical pyramidal neurons. J Physiol 581:941-60 [PubMed]

Hallermann S, Fejtova A, Schmidt H, Weyhersmuller A, Silver RA, Gundelfinger ED, Eilers J (2010) Bassoon speeds vesicle reloading at a central excitatory synapse. Neuron 68:710-23 [PubMed]

Harris JJ, Attwell D (2012) The energetics of CNS white matter. J Neurosci 32:356-71 [PubMed]

Hasenstaub A, Otte S, Callaway E, Sejnowski TJ (2010) Metabolic cost as a unifying principle governing neuronal biophysics. Proc Natl Acad Sci U S A 107:12329-34 [PubMed]

Herculano-Houzel S (2011) Scaling of brain metabolism with a fixed energy budget per neuron: implications for neuronal activity, plasticity and evolution. PLoS One 6:e17514 [PubMed]

Hodgkin A (1975) The optimum density of sodium channels in an unmyelinated nerve. Philos Trans R Soc Lond B Biol Sci 270:297-300 [PubMed]

Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-44 [Journal] [PubMed]

   Squid axon (Hodgkin, Huxley 1952) (LabAXON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (NEURON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SNNAP) [Model]
   Squid axon (Hodgkin, Huxley 1952) used in (Chen et al 2010) (R language) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SBML, XPP, other) [Model]

Hopkins WF (1998) Toxin and subunit specificity of blocking affinity of three peptide toxins for heteromultimeric, voltage-gated potassium channels expressed in Xenopus oocytes. J Pharmacol Exp Ther 285:1051-60 [PubMed]

Juusola M, Robinson HP, de Polavieja GG (2007) Coding with spike shapes and graded potentials in cortical networks. Bioessays 29:178-87 [PubMed]

Keren N, Bar-Yehuda D, Korngreen A (2009) Experimentally guided modelling of dendritic excitability in rat neocortical pyramidal neurones. J Physiol 587:1413-37 [PubMed]

Kole MH (2011) First node of Ranvier facilitates high-frequency burst encoding. Neuron 71:671-82 [PubMed]

   [16 reconstructed morphologies on NeuroMorpho.Org]

Kole MH, Hallermann S, Stuart GJ (2006) Single Ih channels in pyramidal neuron dendrites: properties, distribution, and impact on action potential output. J Neurosci 26:1677-87 [Journal] [PubMed]

   [1 reconstructed morphology on NeuroMorpho.Org]
   Stochastic Ih and Na-channels in pyramidal neuron dendrites (Kole et al 2006) [Model]

Kole MH, Ilschner SU, Kampa BM, Williams SR, Ruben PC, Stuart GJ (2008) Action potential generation requires a high sodium channel density in the axon initial segment. Nat Neurosci 11:178-86 [Journal] [PubMed]

   [1 reconstructed morphology on NeuroMorpho.Org]
   Na+ channel dependence of AP initiation in cortical pyramidal neuron (Kole et al. 2008) [Model]

Kole MH, Letzkus JJ, Stuart GJ (2007) Axon initial segment Kv1 channels control axonal action potential waveform and synaptic efficacy. Neuron 55:633-47 [PubMed]

Kole MH, Stuart GJ (2008) Is action potential threshold lowest in the axon? Nat Neurosci 11:1253-5 [PubMed]

Kole MH, Stuart GJ (2012) Signal processing in the axon initial segment. Neuron 73:235-47 [PubMed]

Lennie P (2003) The cost of cortical computation. Curr Biol 13:493-7 [PubMed]

Levy WB, Baxter RA (1996) Energy efficient neural codes. Neural Comput 8:531-43 [PubMed]

Lohmann H, Rörig B (1994) Long-range horizontal connections between supragranular pyramidal cells in the extrastriate visual cortex of the rat. J Comp Neurol 344:543-58 [PubMed]

Lorincz A, Nusser Z (2008) Cell-type-dependent molecular composition of the axon initial segment. J Neurosci 28:14329-40 [PubMed]

Lorincz A, Nusser Z (2010) Molecular identity of dendritic voltage-gated sodium channels. Science 328:906-9 [PubMed]

Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382:363-6 [Journal] [PubMed]

   [2 reconstructed morphologies on NeuroMorpho.Org]
   Pyramidal Neuron Deep, Superficial; Aspiny, Stellate (Mainen and Sejnowski 1996) [Model]

Markram H, Lubke J, Frotscher M, Roth A, Sakmann B (1997) Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. J Physiol 500 ( Pt 2):409-40 [PubMed]

Niven JE, Laughlin SB (2008) Energy limitation as a selective pressure on the evolution of sensory systems. J Exp Biol 211:1792-804 [PubMed]

Oberlaender M, Boudewijns ZS, Kleele T, Mansvelder HD, Sakmann B, de Kock CP (2011) Three-dimensional axon morphologies of individual layer 5 neurons indicate cell type-specific intracortical pathways for whisker motion and touch. Proc Natl Acad Sci U S A 108:4188-93 [PubMed]

Oberlaender M, de Kock CP, Bruno RM, Ramirez A, Meyer HS, Dercksen VJ, Helmstaedter M, Sakman (2012) Cell type-specific three-dimensional structure of thalamocortical circuits in a column of rat vibrissal cortex. Cereb Cortex 22:2375-91 [PubMed]

Ogawa Y, Horresh I, Trimmer JS, Bredt DS, Peles E, Rasband MN (2008) Postsynaptic density-93 clusters Kv1 channels at axon initial segments independently of Caspr2. J Neurosci 28:5731-9 [PubMed]

Popovic MA, Foust AJ, McCormick DA, Zecevic D (2011) The spatio-temporal characteristics of action potential initiation in layer 5 pyramidal neurons: a voltage imaging study. J Physiol 589:4167-87 [PubMed]

Raman IM, Bean BP (1997) Resurgent sodium current and action potential formation in dissociated cerebellar Purkinje neurons. J Neurosci 17:4517-26 [PubMed]

Rhodes KJ, Strassle BW, Monaghan MM, Bekele-Arcuri Z, Matos MF, Trimmer JS (1997) Association and colocalization of the Kvbeta1 and Kvbeta2 beta-subunits with Kv1 alpha-subunits in mammalian brain K+ channel complexes. J Neurosci 17:8246-58 [PubMed]

Schmidt-Hieber C, Bischofberger J (2010) Fast Sodium Channel Gating Supports Localized and Efficient Axonal Action Potential Initiation J. Neurosci. 30(30):10233-10242 [Journal] [PubMed]

   Fast sodium channel gating in mossy fiber axons (Schmidt-Hieber et al. 2010) [Model]

Schoppa NE, Sigworth FJ (1998) Activation of Shaker potassium channels. III. An activation gating model for wild-type and V2 mutant channels. J Gen Physiol 111:313-42 [PubMed]

Sengupta B, Stemmler M, Laughlin SB, Niven JE (2010) Action potential energy efficiency varies among neuron types in vertebrates and invertebrates. PLoS Comput Biol 6:e1000840 [PubMed]

Shu Y, Hasenstaub A, Duque A, Yu Y, McCormick DA (2006) Modulation of intracortical synaptic potentials by presynaptic somatic membrane potential. Nature 441:761-5 [Journal] [PubMed]

   Intracortical synaptic potential modulation by presynaptic somatic potential (Shu et al. 2006, 2007) [Model]

Shu Y, Yu Y, Yang J, McCormick DA (2007) Selective control of cortical axonal spikes by a slowly inactivating K+ current. Proc Natl Acad Sci U S A 104:11453-8 [Journal] [PubMed]

   Selective control of cortical axonal spikes by a slowly inactivating K+ current (Shu et al. 2007) [Model]

Wang H, Kunkel DD, Schwartzkroin PA, Tempel BL (1994) Localization of Kv1.1 and Kv1.2, two K channel proteins, to synaptic terminals, somata, and dendrites in the mouse brain. J Neurosci 14:4588-99 [PubMed]

Wang SS, Shultz JR, Burish MJ, Harrison KH, Hof PR, Towns LC, Wagers MW, Wyatt KD (2008) Functional trade-offs in white matter axonal scaling. J Neurosci 28:4047-56 [PubMed]

Yellen G (2002) The voltage-gated potassium channels and their relatives. Nature 419:35-42 [PubMed]

Zagotta WN, Hoshi T, Aldrich RW (1994) Shaker potassium channel gating. III: Evaluation of kinetic models for activation. J Gen Physiol 103:321-62 [PubMed]

Ben-Shalom R, Keeshen CM,Berrios KN, An JY, Sanders SJ, Bender KJ (2017) Opposing effects on NaV1.2 function underlie differences between SCN2A variants observed in individuals with autism spectrum disorder or infantile seizures Biological Psychiatry, epub before print [Journal]

   Pyramidal neurons with mutated SCN2A gene (Nav1.2) (Ben-Shalom et al 2017) [Model]

Ju H, Hines ML, Yu Y (2016) Cable energy function of cortical axons. Sci Rep 6:29686 [Journal] [PubMed]

(61 refs)