The Cerebellum

, Volume 16, Issue 1, pp 15–25 | Cite as

Computational Architecture of the Granular Layer of Cerebellum-Like Structures

Original Paper

Abstract

In the adaptive filter model of the cerebellum, the granular layer performs a recoding which expands incoming mossy fibre signals into a temporally diverse set of basis signals. The underlying neural mechanism is not well understood, although various mechanisms have been proposed, including delay lines, spectral timing and echo state networks. Here, we develop a computational simulation based on a network of leaky integrator neurons, and an adaptive filter performance measure, which allows candidate mechanisms to be compared. We demonstrate that increasing the circuit complexity improves adaptive filter performance, and relate this to evolutionary innovations in the cerebellum and cerebellum-like structures in sharks and electric fish. We show how recurrence enables an increase in basis signal duration, which suggest a possible explanation for the explosion in granule cell numbers in the mammalian cerebellum.

Keywords

Cerebellum Adaptive filter Granular layer Neural network Computational simulation Cerebellum-like 

Notes

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

References

  1. 1.
    Dean P, Porrill J, Ekerot CF, Jörntell H. The cerebellar microcircuit as an adaptive filter: experimental and computational evidence. Nat Rev Neurosci 2010;11(1):30–43.CrossRefPubMedGoogle Scholar
  2. 2.
    Fujita M. Adaptive filter model of the cerebellum. Biol Cybern 1982;45(3):195–206.CrossRefPubMedGoogle Scholar
  3. 3.
    Sejnowski TJ. Storing covariance with nonlinearly interacting neurons. J Math Biol 1977;4(4):303–21.CrossRefPubMedGoogle Scholar
  4. 4.
    Bell CC, Han V, Sawtell NB. Cerebellum-like structures and their implications for cerebellar function. Annu Rev Neurosci 2008;31:1–24.CrossRefPubMedGoogle Scholar
  5. 5.
    Montgomery J, Coombs S, Conley R, Bodznick D. Hindbrain sensory processing in lateral line, electrosensory, and auditory systems: a comparative overview of anatomical and functional similarities. Aud Neurosci 1995;1:207–31.Google Scholar
  6. 6.
    Bastian J. Pyramidal-cell plasticity in weakly electric fish: a mechanism for attenuating responses to reafferent electrosensory inputs. J Comp Physiol A 1995;176(1):63–78.CrossRefPubMedGoogle Scholar
  7. 7.
    Bell CC. An efference copy which is modified by reafferent input. Science 1981;214(4519):450–3.CrossRefPubMedGoogle Scholar
  8. 8.
    Montgomery J, Bodznick D. An adaptive filter that cancels self-induced noise in the electrosensory and lateral line mechanosensory systems of fish. Neurosci Lett 1994;174(2):145–8.CrossRefPubMedGoogle Scholar
  9. 9.
    Wolpert DM, Miall RC, Kawato M. Internal models in the cerebellum. Trends Cogn Sci 1998;2(9):338–47.CrossRefPubMedGoogle Scholar
  10. 10.
    Bell C, Russell C. Effect of electric organ discharge on ampullary receptors in a mormyrid. Brain Res 1978; 145(1):85–96.CrossRefPubMedGoogle Scholar
  11. 11.
    Kennedy A, Wayne G, Kaifosh P, Alviña K, Abbott L, Sawtell NB. A temporal basis for predicting the sensory consequences of motor commands in an electric fish. Nat Neurosci 2014.Google Scholar
  12. 12.
    Bell CC, Grant K, Serrier J. Sensory processing and corollary discharge effects in the mormyromast regions of the mormyrid electrosensory lobe. i. field potentials, cellular activity in associated structures. J Neurophys 1992;68(3):843–58.Google Scholar
  13. 13.
    Bell C, Bodznick D, Montgomery J, Bastian J. The generation and subtraction of sensory expectations within cerebellum-like structures. Brain Behav Evol 1997;50(Suppl. 1):17–31.PubMedGoogle Scholar
  14. 14.
    Bodznick D, Boord R. Electroreception in chondrichthyes: central anatomy and physiology. Electroreception 1986;8:225–56.Google Scholar
  15. 15.
    Bratby P, Montgomery J, Sneyd J. A biophysical model of adaptive noise filtering in the shark brain. Bull Math Biol 2014;76(2):455–75.CrossRefPubMedGoogle Scholar
  16. 16.
    Ivry RB, Keele SW. Timing functions of the cerebellum. J Cogn Neurosci 1989;1(2):136–52.CrossRefPubMedGoogle Scholar
  17. 17.
    Gao Z, van Beugen BJ, De Zeeuw CI. Distributed synergistic plasticity and cerebellar learning. Nat Rev Neurosci 2012;13(9):619–35.CrossRefPubMedGoogle Scholar
  18. 18.
    Itō M. The cerebellum and neural control. Raven Pr 1984.Google Scholar
  19. 19.
    Moore J, Desmond J, Berthier N. Adaptively timed conditioned responses and the cerebellum: a neural network approach. Biol Cybern 1989;62(1):17–28.CrossRefPubMedGoogle Scholar
  20. 20.
    Lukoṡeviċius M. A practical guide to applying echo state networks. Neural networks: tricks of the trade. Springer; 2012. p. 659–86.Google Scholar
  21. 21.
    Maex R, De Schutter E. Oscillations in the cerebellar cortex: a prediction of their frequency bands. Prog Brain Res 2005;148:181–8.CrossRefPubMedGoogle Scholar
  22. 22.
    Medina JF, Garcia KS, Nores WL, Taylor NM, Mauk MD. Timing mechanisms in the cerebellum: testing predictions of a large-scale computer simulation. J Neurosci 2000;20(14):5516–25.PubMedGoogle Scholar
  23. 23.
    Yamazaki T, Tanaka S. The cerebellum as a liquid state machine. Neural Netw 2007;20(3):290–7.CrossRefPubMedGoogle Scholar
  24. 24.
    Bullock D, Fiala JC, Grossberg S. A neural model of timed response learning in the cerebellum. Neural Netw 1994;7(6):1101–14.CrossRefGoogle Scholar
  25. 25.
    Mugnaini E, Sekerková G, Martina M. The unipolar brush cell: a remarkable neuron finally receiving deserved attention. Brain Res Rev 2011;66(1):220–45.CrossRefPubMedGoogle Scholar
  26. 26.
    Widrow B, Stearns SD, Vol. 491. Adaptive signal processing. Englewood Cliffs: Prentice-Hall, Inc; 1985, p. 1.Google Scholar
  27. 27.
    Jaeger H. The “echo state” approach to analysing and training recurrent neural networks-with an erratum note. Bonn, Germany: German National Research Center for Information Technology GMD Technical Report 2001;148:34.Google Scholar
  28. 28.
    Maass W, Natschläger T, Markram H. Real-time computing without stable states: a new framework for neural computation based on perturbations. Neural Comput 2002;14(11):2531–60.CrossRefPubMedGoogle Scholar
  29. 29.
    Sussillo D, Abbott LF. Generating coherent patternsof activity from chaotic neural networks. Neuron 2009; 63(4):544–57.CrossRefPubMedPubMedCentralGoogle Scholar
  30. 30.
    Lepora NF, Porrill J, Yeo CH, Dean P. Sensory prediction or motor control? Application of marr–albus type models of cerebellar function to classical conditioning. Front Comput Neurosci 2010:4.Google Scholar
  31. 31.
    Voogd J, Glickstein M. The anatomy of the cerebellum. Trends Cogn Sci 1998;2(9):307–13.CrossRefPubMedGoogle Scholar
  32. 32.
    Rössert C, Dean P, Porrill J. At the edge of chaos: Howcerebellar granular layer network dynamics can provide the basis for temporal filters. PLoS Comput Biol 2015;11(10):e1004,515.CrossRefGoogle Scholar
  33. 33.
    Johansson F, Jirenhed DA, Rasmussen A, Zucca R, Hesslow G. Memory trace and timing mechanism localized to cerebellar purkinje cells. Proc Natl Acad Sci 2014;111(41):14,930–4.CrossRefGoogle Scholar
  34. 34.
    Boyden ES, Katoh A, Raymond JL. Cerebellum-dependent learning: the role of multiple plasticity mechanisms. Neuroscience 2004:27.Google Scholar
  35. 35.
    Sawtell NB. Multimodal integration in granule cells as a basis for associative plasticity and sensory prediction in a cerebellum-like circuit. Neuron 2010;66(4):573–84.CrossRefPubMedGoogle Scholar
  36. 36.
    Chabrol FP, Arenz A, Wiechert MT, Margrie TW, DiGregorio DA. Synaptic diversity enables temporal codingof coincident multisensory inputs in single neurons. Nat Neurosci 2015;18(5):718–27.CrossRefPubMedPubMedCentralGoogle Scholar
  37. 37.
    Ermentrout GB, Terman DH, Vol. 35. Mathematical foundations of neuroscience: Springer Science & Business Media; 2010.Google Scholar
  38. 38.
    Rasmussen CE. 2006. Gaussian processes for machine learning.Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AucklandAucklandNew Zealand
  2. 2.School of Biological SciencesUniversity of AucklandAucklandNew Zealand

Personalised recommendations