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Feedback-induced gain control in stochastic spiking networks

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Abstract

The joint influence of recurrent feedback and noise on gain control in a network of globally coupled spiking leaky integrate-and-fire neurons is studied theoretically and numerically. The context of our work is the origin of divisive versus subtractive gain control, as mixtures of these effects are seen in a variety of experimental systems. We focus on changes in the slope of the mean firing frequency-versus-input bias (f –I) curve when the gain control signal to the cells comes from the cells’ output spikes. Feedback spikes are modeled as alpha functions that produce an additive current in the current balance equation. For generality, they occur after a fixed minimum delay. We show that purely divisive gain control, i.e. changes in the slope of the f –I curve, arises naturally with this additive negative or positive feedback, due to a linearizing actions of feedback. Negative feedback alone lowers the gain, accounting in particular for gain changes in weakly electric fish upon pharmacological opening of the feedback loop as reported by Bastian (J Neurosci 6:553–562, 1986). When negative feedback is sufficiently strong it further causes oscillatory firing patterns which produce irregularities in the f –I curve. Small positive feedback alone increases the gain, but larger amounts cause abrupt jumps to higher firing frequencies. On the other hand, noise alone in open loop linearizes the f –I curve around threshold, and produces mixtures of divisive and subtractive gain control. With both noise and feedback, the combined gain control schemes produce a primarily divisive gain control shift, indicating the robustness of feedback gain control in stochastic networks. Similar results are found when the “input” parameter is the contrast of a time-varying signal rather than the bias current. Theoretical results are derived relating the slope of the f –I curve to feedback gain and noise strength. Good agreement with simulation results are found for inhibitory and excitatory feedback. Finally, divisive feedback is also found for conductance-based feedback (shunting or excitatory) with and without noise.

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References

  • 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 

  • Andersen RA, Mountcastle VB (1983) The influence of the angle of gaze upon the excitability of the light-sensitive neurons of the posterior parietal cortex. J Neurosci 3: 532–48

    PubMed  CAS  Google Scholar 

  • Anderson JS, Lampl I, Gillespie DC, Ferster D (2000) The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. Science 290: 1968–1972

    Article  PubMed  CAS  Google Scholar 

  • Arevian AC, Kapoor V, Urban NN (2007) Activity-dependent gating of lateral inhibition in the mouse olfactory bulb. Nat Neurosci 11: 80–87

    Article  PubMed  CAS  Google Scholar 

  • Arsiero M, Luscher HR, Lundstrom BN, Giugliano M (2007) The impact of input fluctuations on the frequency–current relationships of layer 5 pyramidal neurons in the rat medial prefrontal cortex. J Neurosci 27: 3274–3284

    Article  PubMed  CAS  Google Scholar 

  • Bacci A, Huguenard JR, Prince DA (2003) Functional autaptic neurotransmission in fast-spiking interneurons: a novel form of feedback inhibition in the neocortex. J Neurosci 23: 859–866

    PubMed  CAS  Google Scholar 

  • Baca SM, Marin-Burgin A, Wagenaar DA, Kristan WB (2008) Widespread inhibition proportional to excitation controls the gain of a leech behavioral circuit. Neuron 57: 276–289

    Article  PubMed  CAS  Google Scholar 

  • Bastian J (1986) Gain control in the electrosensory system mediated by descending inputs to the electrosensory lateral line lobe. J Neurosci 6: 553–562

    PubMed  CAS  Google Scholar 

  • Bastian J, Chacron MJ, Maler L (2004) Plastic and non-plastic pyramidal cells perform unique roles in a network capable of adaptive redundancy reduction. Neuron 41: 767–779

    Article  PubMed  CAS  Google Scholar 

  • Bell CC, Han V, Sugawara Y, Grant K (1997) Synaptic plasticity in a cerebellum-like structure depends on temporal order. Nature 387: 278–281

    Article  PubMed  CAS  Google Scholar 

  • Berman NJ, Maler L (1999) Neural architecture of the electrosensory lateral line lobe: adaptations for coincidence detection, a sensory searchlight and frequency-dependent adaptive filtering. J Exp Biol 202: 243–1253

    Google Scholar 

  • Brandt SF, Wessel R (2007) Winner-take-all selection in a neural system with delayed feedback. Biol Cybern 97: 221–228

    Article  PubMed  Google Scholar 

  • Brown DA, Adams PR (1980) Muscarinic supression of a novel voltagesensitive K+ current in a vertebrate neuron. Nature 183: 673–676

    Article  Google Scholar 

  • Burkitt AN, Meffin H, Grayden DB (2003) Study of neuronal gain in conductance-based leaky integrate and fire neuron model with balanced excitatory and inhibitory synaptic input. Biol Cybern 89: 119–125

    Article  PubMed  CAS  Google Scholar 

  • Carandini M, Heeger DJ (1994) Summation and division by neurons in primate visual cortex. Science 264: 1333–1336

    Article  PubMed  CAS  Google Scholar 

  • Cardin JA, Palmer LA, Contreras D (2008) Cellular mechanisms underlying stimulus-dependent gain modulation in primary visual cortex neurons in vivo. Neuron 59: 150–160

    Article  PubMed  CAS  Google Scholar 

  • Chacron MJ, Longtin A, Maler L (2005) Delayed excitatory and inhibitory feedback shape neural information transmission. Phys Rev E 72: 051917

    Article  CAS  Google Scholar 

  • Chance FS, Abbott LF (2000) Divisive inhibition in recurrent networks. Netw Comput Neural Syst 11: 119–129

    Article  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • Diez-Martinez O, Segundo JP (1983) Behaviour of a single neuron in a recurrent excitatory loop. Biol Cybern 47: 33–41

    Article  PubMed  CAS  Google Scholar 

  • Doiron B, Longtin A, Berman N, Maler L (2001) Subtractive and divisive inhibition: effect of voltage-dependent inhibitory conductances and noise. Neural Comput 13: 227–248

    Article  PubMed  CAS  Google Scholar 

  • Doiron B, Chacron MJ, Maler L, Longtin A, Bastian J (2003) Inhibitory feedback required for network oscillatory responses to communication but not prey stimuli. Nature 421: 539–543

    Article  PubMed  CAS  Google Scholar 

  • Doiron B, Lindner B, Longtin A, Maler L, Bastian J (2004) Oscillatory activity in electrosensory neurons increases with the spatial correlation of the stochastic input stimulus. Phys Rev Lett 93: 048101

    Article  PubMed  CAS  Google Scholar 

  • Douglas RJ, Koch C, Mahowald M, Martin KAC, van Vreeswijk C (1995) Recurrent excitation in neocortical circuits. Science 269: 981–985

    Article  PubMed  CAS  Google Scholar 

  • Ermentrout GB (1998) Linearization of F–I curves by adaptation. Neural Comput 10: 1721–1729

    Article  PubMed  CAS  Google Scholar 

  • Ferster D, Miller KD (2000) Neural mechanisms of orientation selectivity in the visual cortex. Ann Rev Neurosci 23: 441–471

    Article  PubMed  CAS  Google Scholar 

  • French AS, Holden AV, Stein RB (1972) The estimation of the frequency response function of a mechanoreceptor. Kybernetik 11: 15–23

    Article  PubMed  CAS  Google Scholar 

  • Gabbiani F, Krapp HG, Koch C, Laurent G (2002) Multiplicative computation in a visual neuron sensitive to looming. Nature 420: 320–324

    Article  PubMed  CAS  Google Scholar 

  • Grant K, Bell CC, Han V (1996) Sensory expectations and anti-Hebbian synaptic plasticity in cerebellum-like structures. J. Physiol. (Paris) 90: 233–237

    Article  CAS  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

    PubMed  CAS  Google Scholar 

  • Higgs M, Slee SJ, Spain WJ (2007) Diversity of gain modulation by noise in neocortical neurons: regulation by the slow afterhyperpolarization conductance. J Neurosci 26: 8787–8799

    Article  CAS  Google Scholar 

  • Holt GR, Koch C (1997) Shunting inhibition does not have a divisive effect on firing rates. Neural Comput 9: 1001–1013

    Article  PubMed  CAS  Google Scholar 

  • Knight BW (1972) Dynamics of encoding in a population of neurons. J Gen Physiol 59: 734–766

    Article  PubMed  CAS  Google Scholar 

  • Koch C (1999) Biophysics of computation. Oxford University Press, New York

    Google Scholar 

  • Larkum ME, Senn W, Luscher HR (2004) Top-down dendritic input increases the gain of layer 5 pyramidal neurons. Cereb Cortex 14: 1059–1070

    Article  PubMed  Google Scholar 

  • Laing CR, Longtin A (2003) Dynamics of deterministic and stochastic paired excitatory-inhibitory delayed feedback. Neural Comput 15: 2779–2822

    Article  PubMed  Google Scholar 

  • Le Masson G, Renaud-Le Masson, Debay D, Bal T (2002) Feedback inhibition controls spike transfer in hybrid thalamic circuits. Nature 417: 854–858

    Article  PubMed  CAS  Google Scholar 

  • Lindner B, Longtin A, Bulsara AR (2003) Analytical expressions for rate and CV of a Type I neuron driven by Gaussian white noise. Neural Comput 15: 1761–1788

    Article  Google Scholar 

  • Lindner B, García-Ojalvo J, Neiman A, Schimansky-Geier L (2004) Effects of noise in excitable systems. Phys Rep 392: 321–427

    Article  Google Scholar 

  • Longtin A (1993) Stochastic resonance in neuron models. J Stat Phys 70: 309–327

    Article  Google Scholar 

  • Longtin A (2000) Adiabatic and non-adiabatic resonances in excitable systems. In: Stochastic processes in physics, chemistry and biology. Lecture notes in physics, vol 93. Springer, Berlin, pp 172– 181

  • Longtin A, Doiron B, Bulsara AR (2002) Noise-induced divisive gain control in neuron models. BioSystems 67: 147–156

    Article  PubMed  Google Scholar 

  • Ly C, Doiron B (2009) Divisive gain modulation with dynamic stimuli in integrate-and-fire neurons. PLoS Comp Biol (in press)

  • Madison DV, Nicoll RA (1984) Control of the repetitive discharge of rat CA1 pyramidal neurones in vitro. J Physiol 354: 319–331

    PubMed  CAS  Google Scholar 

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

    PubMed  CAS  Google Scholar 

  • McAdams CJ, Reid RC (2005) Attention modulates the responses of simple cells in monkey primary visual cortex. J Neurosci 25: 11023–11033

    Article  PubMed  CAS  Google Scholar 

  • Mehaffey WH, Doiron B, Maler L, Turner RW (2005) Deterministic multiplicative gain control with active dendrites. J Neurosci 25: 9968–9977

    Article  PubMed  CAS  Google Scholar 

  • Mitchell SJ, Silver RA (2003) Shunting inhibition modulates neuronal gain during synaptic excitation. Neuron 38: 433–445

    Article  PubMed  CAS  Google Scholar 

  • Nelson ME (1994) A mechanism for neuronal gain control by descending pathways. Neural Comput 6: 242–254

    Article  Google Scholar 

  • Pauluis Q, Baker SN, Olivier E (1999) Emergent oscillations in a realistic network: The role of inhibition and the effect of the spatiotemporal distribution of the input. J Comput Neurosci 6: 27–48

    Article  PubMed  CAS  Google Scholar 

  • Perkel DP, Schulman J, Bullock TH, Moore GP, Segundo JP (1964) Pacemaker neurons: effects of regularly spaced synaptic input. Science 145: 61–63

    Article  PubMed  CAS  Google Scholar 

  • Prescott SA, De Koninck Y (2003) Gain control of firing rate by shunting inhibition: roles of synaptic noise and dendritic saturation. Proc Natl Acad Sci (USA) 100: 2076

    Article  CAS  Google Scholar 

  • Salinas E, Abbott LF (1996) A model of multiplicative neural responses in parietal cortex. Proc Natl Acad Sci (USA) 93: 11956–11961

    Article  CAS  Google Scholar 

  • Salinas E, Thier P (2000) Gain modulation: a major computation principle of the central nervous system. Neuron 27: 15–21

    Article  PubMed  CAS  Google Scholar 

  • Salinas E, Sejnowski TJ (2001) Gain modulation in the central nervous system: where behavior, neurophysiology, and computation meet. Neuroscientist 7: 430–440

    Article  PubMed  CAS  Google Scholar 

  • Schwabe L, Obermayer K, Angelucci A, Bressloff PC (2006) The role of feedback in shaping the extra-classical receptive field of cortical neurons: a recurrent network model. J Neurosci 26: 9117–9129

    Article  PubMed  CAS  Google Scholar 

  • Segundo JP (1970) Communication and coding by nerve cells. In: Quarton GC, Melnechuk T, Schmitt FO(eds) The neurosciences. Second study program. . Rockefeller University Press, New York, pp 569–586

    Google Scholar 

  • Trotter Y, Celebrini S (1999) Gaze direction controls response gain in primary visual-cortex neurons. Nature 398: 239–242

    Article  PubMed  CAS  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  PubMed  CAS  Google Scholar 

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Authors and Affiliations

  1. Center for Neural Dynamics, University of Ottawa, 150 Louis Pasteur, Ottawa, K1N 6N5, Canada

    Connie Sutherland, Brent Doiron & André Longtin

  2. Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, K1N 6N5, Canada

    Connie Sutherland, Brent Doiron & André Longtin

  3. Department of Mathematics, University of Pittsburgh, Pittsburgh, 15260, USA

    Brent Doiron

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  1. Connie Sutherland
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  2. Brent Doiron
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  3. André Longtin
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Correspondence to André Longtin.

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This article is part of a special issue on Neuronal Dynamics of Sensory Coding.

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Sutherland, C., Doiron, B. & Longtin, A. Feedback-induced gain control in stochastic spiking networks. Biol Cybern 100, 475–489 (2009). https://doi.org/10.1007/s00422-009-0298-5

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