Skip to main content
SpringerLink
Log in

Attentional modulation of firing rate and synchrony in a model cortical network

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

The response of a neuron in the visual cortex to stimuli of different contrast placed in its receptive field is commonly characterized using the contrast response curve. When attention is directed into the receptive field of a V4 neuron, its contrast response curve is shifted to lower contrast values (Reynolds et al., 2000). The neuron will thus be able to respond to weaker stimuli than it responded to without attention. Attention also increases the coherence between neurons responding to the same stimulus (Fries et al., 2001). We studied how the firing rate and synchrony of a densely interconnected cortical network varied with contrast and how they were modulated by attention. The changes in contrast and attention were modeled as changes in driving current to the network neurons.

We found that an increased driving current to the excitatory neurons increased the overall firing rate of the network, whereas variation of the driving current to inhibitory neurons modulated the synchrony of the network. We explain the synchrony modulation in terms of a locking phenomenon during which the ratio of excitatory to inhibitory firing rates is approximately constant for a range of driving current values.

We explored the hypothesis that contrast is represented primarily as a drive to the excitatory neurons, whereas attention corresponds to a reduction in driving current to the inhibitory neurons. Using this hypothesis, the model reproduces the following experimental observations: (1) the firing rate of the excitatory neurons increases with contrast; (2) for high contrast stimuli, the firing rate saturates and the network synchronizes; (3) attention shifts the contrast response curve to lower contrast values; (4) attention leads to stronger synchronization that starts at a lower value of the contrast compared with the attend-away condition. In addition, it predicts that attention increases the delay between the inhibitory and excitatory synchronous volleys produced by the network, allowing the stimulus to recruit more downstream neurons.

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

Access this article

Log in via an institution

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

  • Albrecht DG, Hamilton DB (1982) Striate cortex of monkey and cat: contrast response function. J. Neurophysiol. 48: 217–237.

    CAS  PubMed  Google Scholar 

  • Albrecht DG, Geisler WS, Frazor RA, Crane AM (2002) Visual cortex neurons of monkeys and cats: Temporal dynamics of the contrast response function. J. Neurophysiol. 88: 888–913.

    PubMed  Google Scholar 

  • Alitto HJ, Usrey WM (2004) Influence of contrast on orientation and temporal frequency tuning in ferret primary visual cortex. J. Neurophysiol. 91: 2797–2808.

    Article  PubMed  Google Scholar 

  • Aradi I, Soltesz I (2002) Modulation of network behaviour by changes in variance in interneuronal properties. J. Physiol. 538: 220–251.

    Article  Google Scholar 

  • Bartos M, Vida I, Frotscher M, Geiger JR, Jonas P (2001) Rapid signaling at inhibitory synapses in a dentate gyrus interneuron network. J. Neurosci. 21: 2687–2698.

    CAS  PubMed  Google Scholar 

  • Bartos M, Vida I, Frotscher M, Meyer A, Monyer H, Geiger JR, Jonas P (2002) Fast synaptic inhibition promotes synchronized gamma oscillations in hippocampal interneuron networks. Proc. Natl. Acad. Sci. USA 99: 13222–13227.

    Article  CAS  PubMed  Google Scholar 

  • Beierlein M, Gibson JR, Connors BW (2003) Two dynamically distinct inhibitory networks in layer 4 of the neocortex. J. Neurophysiol. 90: 2987–3000.

    PubMed  Google Scholar 

  • Bichot NP, Rossi AF, Desimone R (2005) Parallel and serial neural mechanisms for visual search in macaque area V4. Science 308: 529–534.

    Article  CAS  PubMed  Google Scholar 

  • Binzegger T, Douglas RJ, Martin KA (2004) A quantitative map of the circuit of cat primary visual cortex. J. Neurosci. 24: 8441–8453.

    Article  CAS  PubMed  Google Scholar 

  • Blasdel GG (1992a) Differential imaging of ocular dominance and orientation selectivity in monkey striate cortex. J. Neurosci. 12: 3115–3138.

    CAS  PubMed  Google Scholar 

  • Blasdel GG (1992b) Orientation selectivity, preference, and continuity in monkey striate cortex. J. Neurosci. 12: 3139–3161.

    CAS  PubMed  Google Scholar 

  • Borgers C, Kopell N (2003) Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity. Neural. Comput. 15: 509–538.

    Article  PubMed  Google Scholar 

  • Borgers C, Kopell N (2005) Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons. Neural. Comput. 17: 557–608.

    Article  PubMed  Google Scholar 

  • Borgers C, Epstein S, Kopell NJ (2005) Background gamma rhythmicity and attention in cortical local circuits: A computational study. Proc. Natl. Acad. Sci. USA 102: 7002–7007.

    Article  PubMed  CAS  Google Scholar 

  • Brunel N, Hakim V (1999) Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural. Comput. 11: 1621–1671.

    Article  CAS  PubMed  Google Scholar 

  • Brunel N, Wang XJ (2003) What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance. J. Neurophysiol 90: 415–430.

    PubMed  Google Scholar 

  • Bush P, Sejnowski T (1996) Inhibition synchronizes sparsely connected cortical neurons within and between columns in realistic network models. J. Comput. Neurosci. 3: 91–110.

    Article  CAS  PubMed  Google Scholar 

  • Callaway EM (1998) Local circuits in primary visual cortex of the macaque monkey. Annu. Rev. Neurosci. 21: 47–74.

    Article  CAS  PubMed  Google Scholar 

  • Chance FS, Abbott LF, Reyes AD (2002) Gain modulation from background synaptic input. Neuron 35: 773–782.

    Article  CAS  PubMed  Google Scholar 

  • Constantinidis C, Goldman-Rakic PS (2002) Correlated discharges among putative pyramidal neurons and interneurons in the primate prefrontal cortex. J. Neurophysiol. 88: 3487–3497.

    PubMed  Google Scholar 

  • Cooper JR, Bloom FE, Roth RH (1996) The Biochemical Basis of Neuropharmacology, 7th Edition. Oxford: Oxford University Press.

  • Coull JT (2005) Psychopharmacology of human attention. In: Neurobiology of Attention (L Itti, G Rees, JK Tsotsos, eds.), 50–56.: Elsevier Academic Press, San Diego.

  • Desimone R, Duncan J (1995) Neural mechanisms of selective visual attention. Annu. Rev. Neurosci. 18: 193–222.

    Article  CAS  PubMed  Google Scholar 

  • Douglas RJ, Martin KA (2004) Neuronal circuits of the neocortex. Annu. Rev. Neurosci. 27: 419–451.

    Article  CAS  PubMed  Google Scholar 

  • Feldman RS, Meyer JS, Quenzer LF (1997) Principles of Neuropsychopharmacology.: Sinauer Associates, Sunderland, Massachusetts

  • Fellous JM, Rudolph M, Destexhe A, Sejnowski TJ (2003) Synaptic background noise controls the input/output characteristics of single cells in anin vitro model ofin vivo activity. Neuroscience 122: 811–829.

    Article  CAS  PubMed  Google Scholar 

  • Fries P, Reynolds JH, Rorie AE, Desimone R (2001) Modulation of oscillatory neuronal synchronization by selective visual attention. Science 291: 1560–1563.

    Article  CAS  PubMed  Google Scholar 

  • Geisler C, Brunel N, Wang XJ (2005) Contributions of intrinsic membrane dynamics to fast network oscillations with irregular neuronal discharges. J. Neurophysiol 94: 4344–4361.

    Google Scholar 

  • Gerald CF, Wheatley PO (1999) Applied Numerical Analysis, 6th ed.: Addison-Wesley, Reading, California.

  • Ghose GM, Ts’o DY (1997) Form processing modules in primate area V4. J. Neurophysiol. 77: 2191–2196.

    CAS  PubMed  Google Scholar 

  • Golomb D, Amitai Y (1997) Propagating neuronal discharges in neocortical slices: Computational and experimental study. J. Neurophysiol. 78: 1199–1211.

    CAS  PubMed  Google Scholar 

  • Golomb D, Hansel D (2000) The number of synaptic inputs and the synchrony of large, sparse neuronal networks. Neural. Comput. 12: 1095–1139.

    Article  CAS  PubMed  Google Scholar 

  • Gray CM, Viana Di Prisco G (1997) Stimulus-dependent neuronal oscillations and local synchronization in striate cortex of the alert cat. J. Neurosci. 17: 3239–3253.

    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 

  • Hansel D, van Vreeswijk C (2002) How noise contributes to contrast invariance of orientation tuning in cat visual cortex. J. Neurosci. 22: 5118–5128.

    CAS  PubMed  Google Scholar 

  • Hansel D, Mato G (2003) Asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons. Neural. Comput. 15: 1–56.

    Article  CAS  PubMed  Google Scholar 

  • Hasselmo ME, McGaughy J (2004) High acetylcholine levels set circuit dynamics for attention and encoding and low acetylcholine levels set dynamics for consolidation. Prog. Brain Res. 145: 207–231.

    CAS  PubMed  Google Scholar 

  • Hasselmo ME, Schnell E, Barkai E (1995) Dynamics of learning and recall at excitatory recurrent synapses and cholinergic modulation in rat hippocampal region CA3. J. Neurosci. 15: 5249–5262.

    CAS  PubMed  Google Scholar 

  • Henrie JA, Shapley R (2005) LFP power spectra in V1 cortex: the graded effect of stimulus contrast. J. Neurophysiol 94: 479–490.

    Google Scholar 

  • Hubel DH (1959) Single unit activity in striate cortex of unrestrained cats. J. Physiol. 147: 226–238.

    CAS  PubMed  Google Scholar 

  • Hubel DH, Wiesel TN (1959) Receptive fields of single neurones in the cat’s striate cortex. J. Physiol. 148: 574–591.

    CAS  PubMed  Google Scholar 

  • Hubel DH, Wiesel TN (1962) Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physiol. 160: 106–154.

    CAS  PubMed  Google Scholar 

  • Kayser C, Konig P (2004) Stimulus locking and feature selectivity prevail in complementary frequency ranges of V1 local field potentials. Eur. J. Neurosci. 19: 485–489.

    Article  PubMed  Google Scholar 

  • Kohn A, Smith MA (2005) Stimulus dependence of neuronal correlation in primary visual cortex of the macaque. J. Neurosci. 25: 3661–3673.

    Article  CAS  PubMed  Google Scholar 

  • Krnjevic K (1993) Central cholinergic mechanisms and function. Prog. Brain Res. 98: 285–292.

    Article  CAS  PubMed  Google Scholar 

  • Luck SJ, Chelazzi L, Hillyard SA, Desimone R (1997) Neural mechanisms of spatial selective attention in areas V1, V2, and V4 of macaque visual cortex. J. Neurophysiol. 77: 24–42.

    CAS  PubMed  Google Scholar 

  • Markram H, Toledo-Rodriguez M, Wang Y, Gupta A, Silberberg G, Wu C (2004) Interneurons of the neocortical inhibitory system. Nat. Rev. Neurosci. 5: 793–807.

    Article  CAS  PubMed  Google Scholar 

  • McAdams CJ, Maunsell JH (1999) Effects of attention on orientation-tuning functions of single neurons in macaque cortical area V4. J. Neurosci. 19: 431–441.

    CAS  PubMed  Google Scholar 

  • Miller KD, Troyer TW (2002) Neural noise can explain expansive, power-law nonlinearities in neural response functions. J. Neurophysiol. 87: 653–659.

    PubMed  Google Scholar 

  • Milstein JA, Dalley JW, Robbins TW (2005) Neuropharmacology of Attention. In L. Itti, G. Rees, JK. Tsotsos, (eds), Neurobiology of Attention, pp.57–62. San Diego: Elsevier Academic Press.

  • Moran J, Desimone R (1985) Selective attention gates visual processing in the extrastriate cortex. Science 229: 782–784.

    CAS  PubMed  Google Scholar 

  • Ohzawa I, Sclar G, Freeman RD (1982) Contrast gain control in the cat visual cortex. Nature 298: 266–268.

    Article  CAS  PubMed  Google Scholar 

  • Olufsen MS, Whittington MA, Camperi M, Kopell N (2003) New roles for the gamma rhythm: population tuning and preprocessing for the Beta rhythm. J. Comput. Neurosci. 14: 33–54.

    Article  PubMed  Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes.: Cambridge University Press, Cambridge.

  • Rauch A, La Camera G, Luscher HR, 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.

    PubMed  Google Scholar 

  • Reynolds JH, Desimone R (2003) Interacting roles of attention and visual salience in V4. Neuron 37: 853–863.

    Article  CAS  PubMed  Google Scholar 

  • Reynolds JH, Chelazzi L (2004) Attentional modulation of visual processing. Ann. Rev. of Neurosci. 27: 611–647.

    Article  CAS  PubMed  Google Scholar 

  • Reynolds JH, Pasternak T, Desimone R (2000) Attention increases sensitivity of V4 neurons. Neuron 26: 703–714.

    Article  CAS  PubMed  Google Scholar 

  • Richardson MJ (2004) Effects of synaptic conductance on the voltage distribution and firing rate of spiking neurons. Phys. Rev. E. Stat. Nonlin. Soft. Matter Phys. 69: 051918.

    PubMed  Google Scholar 

  • Rols G, Tallon-Baudry C, Girard P, Bertrand O, Bullier J (2001) Cortical mapping of gamma oscillations in areas V1 and V4 of the macaque monkey. Vis. Neurosci. 18: 527–540.

    Article  CAS  PubMed  Google Scholar 

  • Rudolph M, Destexhe A (2003) The discharge variability of neocortical neurons during high-conductance states. Neuroscience 119: 855–873.

    Article  CAS  PubMed  Google Scholar 

  • Salin PA, Bullier J (1995) Corticocortical connections in the visual system: Structure and function. Physiol. Rev. 75: 107–154.

    CAS  PubMed  Google Scholar 

  • Salinas E, Sejnowski T (2000) Impact of correlated synaptic input on output variability in simple neuronal models. J. Neurosci. 20: 6193–6209.

    CAS  PubMed  Google Scholar 

  • Sarter M, Hasselmo ME, Bruno JP, Givens B (2005) Unraveling the attentional functions of cortical cholinergic inputs: Interactions between signal-driven and cognitive modulation of signal detection. Brain Res. Brain Res. Rev. 48: 98–111.

    Article  CAS  PubMed  Google Scholar 

  • Sclar G, Freeman RD (1982) Orientation selectivity in the cat’s striate cortex is invariant with stimulus contrast. Exp. Brain Res. 46: 457–461.

    Article  CAS  PubMed  Google Scholar 

  • Shepherd GM, Stepanyants A, Bureau I, Chklovskii D, Svoboda K (2005) Geometric and functional organization of cortical circuits. Nat. Neurosci. 8: 782–790.

    Article  CAS  PubMed  Google Scholar 

  • Song S, Sjostrom PJ, Reigl M, Nelson S, Chklovskii DB (2005) Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS. Biol. 3: e68.

    Article  CAS  Google Scholar 

  • Swadlow HA (2003) Fast-spike Interneurons and Feedforward Inhibition in Awake Sensory Neocortex. Cereb. Cortex 13: 25–32.

    Article  PubMed  Google Scholar 

  • Taylor K, Mandon S, Freiwald WA, Kreiter AK (2005) Coherent Oscillatory Activity in Monkey Area V4 Predicts Successful Allocation of Attention. Cereb. Cortex 15: 1424–1437.

    Google Scholar 

  • Tiesinga P, Fellous J-M, Salinas E, Jose JV, Sejnowski T (2004) Synchronization as a mechanism for attentional gain modulation. Neurocomputing 58–60: 641–646.

    Article  Google Scholar 

  • Tiesinga P, Fellous J-M, Salinas E, Jose J, Sejnowski T (2005) Inhibitory synchrony as a mechanism for attentional gain modulation. J. Physiol. (Paris) 98: 296–314.

    Google Scholar 

  • Tiesinga PHE, Jose JV (2000) Robust gamma oscillations in networks of inhibitory hippocampal interneurons. Network-Computation in Neural Systems 11: 1–23.

    Article  CAS  Google Scholar 

  • Tiesinga PHE, Sejnowski TJ (2004) Rapid temporal modulation of synchrony by competition in cortical interneuron networks. Neural. Comput. 16: 251–275.

    Article  CAS  PubMed  Google Scholar 

  • Tiesinga PHE, Jose JV, Sejnowski TJ (2000) Comparison of current-driven and conductance-driven neocortical model neurons with Hodgkin-Huxley voltage-gated channels. Physical Review E 62: 8413–8419.

    Article  CAS  Google Scholar 

  • Tiesinga PHE, Fellous JM, Jose JV, Sejnowski TJ (2001) Computational model of carbachol-induced delta, theta, and gamma oscillations in the hippocampus. Hippocampus 11: 251–274.

    Article  CAS  PubMed  Google Scholar 

  • Traub RD, Contreras D, Cunningham MO, Murray H, LeBeau FE, Roopun A, Bibbig A, Wilent WB, Higley MJ, Whittington MA (2005) Single-column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts. J. Neurophysiol. 93: 2194–2232.

    Article  PubMed  Google Scholar 

  • Troyer TW, Krukowski AE, Priebe NJ, Miller KD (1998) Contrast-invariant orientation tuning in cat visual cortex: Thalamocortical input tuning and correlation-based intracortical connectivity. J. Neurosci. 18: 5908–5927.

    CAS  PubMed  Google Scholar 

  • Wang XJ, Buzsaki G (1996) Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J. Neurosci. 16: 6402–6413.

    CAS  PubMed  Google Scholar 

  • Wang XJ, Tegner J, Constantinidis C, Goldman-Rakic PS (2004) Division of labor among distinct subtypes of inhibitory neurons in a cortical microcircuit of working memory. Proc. Natl. Acad. Sci. USA 101:1368–1373.

    Article  CAS  PubMed  Google Scholar 

  • White JA, Chow CC, Ritt J, Soto-Trevino C, Kopell N (1998) Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons. J. Comput. Neurosci. 5: 5–16.

    Article  CAS  PubMed  Google Scholar 

  • Whittington MA, Traub RD, Jefferys JG (1995) Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation. Nature 373: 612–615.

    Article  CAS  PubMed  Google Scholar 

  • Whittington MA, Traub RD, Kopell N, Ermentrout B, Buhl EH (2000) Inhibition-based rhythms: Experimental and mathematical observations on network dynamics. Int. J. Psychophysiol. 38: 315–336.

    Article  CAS  PubMed  Google Scholar 

  • Yoshimura Y, Dantzker JL, Callaway EM (2005) Excitatory cortical neurons form fine-scale functional networks. Nature 433: 868–873.

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computational Neurophysics Laboratory, Department of Physics & Astronomy, University of North Carolina at Chapel Hill, Campus Box 3255, Chapel Hill, North Carolina, 27599

    Calin Buia & Paul Tiesinga

Authors
  1. Calin Buia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul Tiesinga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Calin Buia.

Additional information

Action Editor: David Golomb

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buia, C., Tiesinga, P. Attentional modulation of firing rate and synchrony in a model cortical network. J Comput Neurosci 20, 247–264 (2006). https://doi.org/10.1007/s10827-006-6358-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-006-6358-0

Keywords

Search

Navigation