Skip to main content
Log in

Minimal Hodgkin–Huxley type models for different classes of cortical and thalamic neurons

  • Prospects
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

We review here the development of Hodgkin–Huxley (HH) type models of cerebral cortex and thalamic neurons for network simulations. The intrinsic electrophysiological properties of cortical neurons were analyzed from several preparations, and we selected the four most prominent electrophysiological classes of neurons. These four classes are “fast spiking” “regular spiking” “intrinsically bursting” and “low-threshold spike” cells. For each class, we fit “minimal” HH type models to experimental data. The models contain the minimal set of voltage-dependent currents to account for the data. To obtain models as generic as possible, we used data from different preparations in vivo and in vitro, such as rat somatosensory cortex and thalamus, guinea-pig visual and frontal cortex, ferret visual cortex, cat visual cortex and cat association cortex. For two cell classes, we used automatic fitting procedures applied to several cells, which revealed substantial cell-to-cell variability within each class. The selection of such cellular models constitutes a necessary step towards building network simulations of the thalamocortical system with realistic cellular dynamical properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Achard P, De Schutter E (2006) Complex parameter landscape for a complex neuron model. PLoS Comput Biol 2: e94

    Article  PubMed  CAS  Google Scholar 

  • Baldi P, Vanier MC, Bower JM (1998) On the use of Bayesian methods for evaluating compartmental neural models. J Comput Neurosci 5: 285–314

    Article  CAS  PubMed  Google Scholar 

  • Bhalla US, Bower JM (1993) Exploring parameter space in detailed single neuron models: simulations of the mitral and granule cells of the olfactory bulb. J Neurophysiol 69: 1948–1965

    CAS  PubMed  Google Scholar 

  • Brette R, Gerstner W (2005) Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. J Neurophysiol 94: 3637–3642

    Article  PubMed  Google Scholar 

  • Cauller LJ, Connors BW (1992) Functions of very distal dendrites: experimental and computational studies of Layer I synapses on neocortical pyramidal cells. In: McKenna T, Davis J, Zornetzer SF (eds) Single neuron computation. Academic Press, Boston

    Google Scholar 

  • Connors BW, Gutnick MJ (1990) Intrinsic firing patterns of diverse neocortical neurons. Trends Neurosci 13: 99–104

    Article  CAS  PubMed  Google Scholar 

  • Contreras D, Steriade M (1995) Cellular basis of EEG slow rhythms: a study of dynamic corticothalamic relationships. J Neurosci 15: 604–622

    CAS  PubMed  Google Scholar 

  • de la Peña E, Geijo-Barrientos E (1996) Laminar organization, morphology and physiological properties of pyramidal neurons that have the low-threshold calcium current in the guinea-pig frontal cortex. J Neurosci 16: 5301–5311

    PubMed  Google Scholar 

  • Destexhe A (2001) Simplified models of neocortical pyramidal cells preserving somatodendritic voltage attenuation. Neurocomputing 38: 167–173

    Article  Google Scholar 

  • Destexhe A, Bal T, McCormick DA, Sejnowski TJ (1996) Ionic mechanisms underlying synchronized oscillations and propagating waves in a model of ferret thalamic slices. J Neurophysiol 76: 2049–2070

    CAS  PubMed  Google Scholar 

  • Destexhe A, Contreras D, Steriade M, Sejnowski TJ, Huguenard JR (1996) In vivo, in vitro and computational analysis of dendritic calcium currents in thalamic reticular neurons. J Neurosci 16: 169–185

    CAS  PubMed  Google Scholar 

  • Destexhe A, Neubig M, Ulrich D, Huguenard JR (1998) Dendritic low-threshold calcium currents in thalamic relay cells. J Neurosci 18: 3574–3588

    CAS  PubMed  Google Scholar 

  • Destexhe A, Contreras D, Steriade M (2001) LTS cells in cerebral cortex and their role in generating spike-and-wave oscillations. Neurocomputing 38: 555–563

    Article  Google Scholar 

  • Druckmann S, Banitt Y, Gidon A, Schurmann F, Markram H, Segev I (2007) A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data. Front Neurosci 1: 7–18

    Article  PubMed  Google Scholar 

  • Eichler-West R, Wilcox G (1997) Robust parameter selection for compartmental models of neurons using evolutionary algorithms. In: Bower JM (eds) Computational neuroscience: trends in research 1997. Plenum Press, New York, pp 75–80

    Google Scholar 

  • Foster WR, Ungar LH, Schwaber JS (1993) Significance of conductances in Hodgkin–Huxley models. J Neurophysiol 70: 2502–2518

    CAS  PubMed  Google Scholar 

  • Golowasch J, Goldman MS, Abbott LF, Marder E (2002) Failure of averaging in the construction of a conductance-based neuron model. J Neurophysiol 87: 1129–1131

    PubMed  Google Scholar 

  • Gray CM, McCormick DA (1996) Chattering cells: superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science 274: 109–113

    Article  CAS  PubMed  Google Scholar 

  • Gupta A, Wang Y, Markram H (2000) Organizing principles for a diversity of GABAergic interneurons and synapses in the neocortex. Science 287: 273–278

    Article  CAS  PubMed  Google Scholar 

  • Haufler D, Morinc F, Lacaille JC, Skinner FK (2007) Parameter estimation in single-compartment neuron models using a synchronization-based method. Neurocomputing 70: 1605–1610

    Article  Google Scholar 

  • Hines ML, Carnevale NT (1997) The neuron simulation environment. Neural Comput 9: 1179–1209

    Article  CAS  PubMed  Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117: 500–544

    CAS  PubMed  Google Scholar 

  • Holmes W, Ambros-Ingerson J, Grover L (2006) Fitting experimental data to models that use morphological data from public databases. J Computat Neurosci 20: 349–365

    Article  CAS  Google Scholar 

  • Huguenard JR, McCormick DA (1992) Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons. J Neurophysiol 68: 1373–1383

    CAS  PubMed  Google Scholar 

  • Huguenard JR, Prince DA (1992) A novel T-type current underlies prolonged Ca2+-dependent bursts firing in GABAergic neurons of rat thalamic reticular nucleus. J Neurosci 12: 3804–3817

    CAS  PubMed  Google Scholar 

  • Izhikevich EM (2004) Which model to use for cortical spiking neurons?. IEEE Trans Neural Netw 15: 1063–1070

    Article  PubMed  Google Scholar 

  • Jolivet R, Lewis TJ, Gerstner W (2004) Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. J Neurophysiol 92: 959–976

    Article  PubMed  Google Scholar 

  • LeMasson G, Maex R (2001) Introduction to equation solving and parameter fitting. In: De Schutter E (eds) Computational neuroscience: realistic modeling for experimentalists. CRC Press, Boca Raton, pp 1–22

    Google Scholar 

  • Llinás RR (1988) The intrinsic electrophysiological properties of mammalian neurons: a new insight into CNS function. Science 242: 1654–1664

    Article  PubMed  Google Scholar 

  • Major G, Larkmann AU, Jonas P, Sakmann B, Jack JJB (1994) Detailed passive cable models of whole-cell recorded CA3 pyramidal neurons in rat hippocampal slices. J Neurosci 14: 4613–4638

    CAS  PubMed  Google Scholar 

  • Marder E, Tobin AE, Grashow R (2007) How tightly tuned are network parameters? Insight from computational and experimental studies in small rhythmic motor networks. Prog Brain Res 165: 193–200

    Article  PubMed  Google Scholar 

  • McCormick DA, Connors BW, Lighthall JW, Prince DA (1985) Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. J Neurophysiol 54: 782–806

    CAS  PubMed  Google Scholar 

  • Monier C, Chavane F, Baudot P, Graham LJ, Frégnac Y (2003) Orientation and direction selectivity of synaptic inputs in visual cortical neurons: a diversity of combinations produces spike tuning. Neuron 37: 663–680

    Article  CAS  PubMed  Google Scholar 

  • Press WH, Flannery BP, Teukolsky SA (1992) Numerical recipes in C: The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Rall W, Burke RE, Holmes WR, Jack JJ, Redman SJ, Segev I (1992) Matching dendritic neuron models to experimental data. Physiol Rev 72: S159–S186

    CAS  PubMed  Google Scholar 

  • Rapp M, Segev I, Yarom Y (1994) Physiology, morphology and detailed passive models of guinea-pig cerebellar Purkinje cells. J Physiol 474: 101–118

    CAS  PubMed  Google Scholar 

  • Rauch A, La Camera G, Lüscher H-R, Senn W, Fusi S (2003) Neocortical pyramidal cells respond as integrate-and-fire neurons to in vivo like input currents. J Neurophysiol 90: 1598–1612

    Article  PubMed  Google Scholar 

  • Renaud S, Tomas J, Bornat Y, Daouzli A, Saïghi S (2007) Neuromimetic ICs with analog cores: an alternative for simulating spiking neural networks. In: International symposium on circuits and systems (ISCAS07), New-Orleans, USA, 27–30 May (ISBN 1-4244-0921-1), pp 3355–358

  • Reuveni I, Friedman A, Amitai Y, Gutnick MJ (1993) Stepwise repolarization from Ca2+ plateaus in neocortical pyramidal cells: evidence for nonhomogeneous distribution of HVA Ca2+ channels in dendrites. J Neurosci 13: 4609–4621

    CAS  PubMed  Google Scholar 

  • Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. In: Teramoto E, Yamaguti M (eds) Mathematical topics in population biology, morphogenesis and neurosciences. Springer, Berlin, pp 267–281

    Google Scholar 

  • Rinzel J, Ermentrout GB (1989) Analysis of neural excitability and oscillations. In: Koch C, Segev I (eds) Methods in neuronal modeling. MIT press, Cambridge, pp 135–169

    Google Scholar 

  • Rose RM, Hindmarsh JL (1989) The assembly of ionic currents in a thalamic neuron. I. The three-dimensional model. Proc R Soc Lond B Biol Sci 237: 267–288

    Article  CAS  PubMed  Google Scholar 

  • Sayer RJ, Schwindt PC, Crill WE (1990) High- and low-threshold calcium currents in neurons acutely isolated from rat sensorimotor cortex. Neurosci Lett 120: 175–178

    Article  CAS  PubMed  Google Scholar 

  • Shu Y, Hasenstaub A, Badoual M, Bal T, McCormick DA (2003) Barrages of synaptic activity control the gain and sensitivity of cortical neurons. J Neurosci 23: 10388–10401

    CAS  PubMed  Google Scholar 

  • Smith GD, Cox CL, Sherman M, Rinzel J (2000) Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model. J Neurophysiol 83: 588–610

    CAS  PubMed  Google Scholar 

  • Steriade M, Timofeev I, Durmüller N, Grenier F (1998) Dynamic properties of corticothalamic neurons and local cortical interneurons generating fast rhythmic (30–40 Hz) spike bursts. J Neurophysiol 79: 483–490

    CAS  PubMed  Google Scholar 

  • Stratford K, Mason A, Larkman A, Major G, Jack J (1989) The modeling of pyramidal neurones in the visual cortex. In: Durbin A, Miall C, Mitchison G (eds) The computing neuron. Addison-Wesley, Workingham, pp 296–321

    Google Scholar 

  • Stuart G, Spruston N (1998) Determinants of voltage attenuation in neocortical pyramidal neuron dendrites. J Neurosci 18: 3501–3510

    CAS  PubMed  Google Scholar 

  • Tawfik B, Durand DM (1994) Nonlinear parameter-estimation by linear associationapplication to a 5-parameter passive neuron model. IEEE Trans Biomed Eng 41: 461–469

    Article  CAS  PubMed  Google Scholar 

  • Taylor AL, Hickey TJ, Prinz AA, Marder E (2006) Structure and visualization of high-dimensional conductance spaces. J Neurophysiol 96: 891–905

    Article  PubMed  Google Scholar 

  • Tien JH, Guckenheimer J (2008) Parameter estimation for bursting neural models. J Computat Neurosci 24: 358–373

    Article  Google Scholar 

  • Toledo-Rodriguez M, Blumenfeld B, Wu C, Luo J, Attali B, Goodman P, Markram H (2004) Correlation maps allow neuronal electrical properties to be predicted from single-cell gene expression profiles in rat neocortex. Cereb Cortex 14: 1310–1327

    Article  PubMed  Google Scholar 

  • Traub RD, Miles R (1991) Neuronal networks of the Hippocampus. Cambridge University Press, Cambridge

    Google Scholar 

  • Vanier MC, Bower JM (1999) A comparative survey of automated parameter-search methods for compartmental neural models. J Comput Neurosci 7: 149–171

    Article  CAS  PubMed  Google Scholar 

  • Yamada WM, Koch C, Adams PR (1989) Multiple channels and calcium dynamics. In: Koch C, Segev I (eds) Methods in neuronal modeling. MIT press, Cambridge, pp 97–134

    Google Scholar 

  • Zou Q, Bornat Y, Saïghi S, Tomas J, Renaud S, Destexhe A (2006) Analog-digital simulations of full conductance-based networks of spiking neurons with spike timing dependent plasticity. Network 17: 211–233

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alain Destexhe.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pospischil, M., Toledo-Rodriguez, M., Monier, C. et al. Minimal Hodgkin–Huxley type models for different classes of cortical and thalamic neurons. Biol Cybern 99, 427–441 (2008). https://doi.org/10.1007/s00422-008-0263-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-008-0263-8

Keywords

Navigation