- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Intricate phase diagram of a prevalent visual circuit reveals universal dynamics, phase transitions, and resonances

Matthew S. Caudill*, Sebastian F. Brandt, Zohar Nussinov, and Ralf Wessel

  • Department of Physics, Washington University, Campus Box 1105, St. Louis, Missouri 63130-4899, USA

  • *mcaudill@physics.wustl.edu
PDF

Phys. Rev. E 80, 051923 – Published 25 November, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.051923

Abstract

Neural feedback-triads consisting of two feedback loops with a nonreciprocal lateral connection from one loop to the other are ubiquitous in the brain. We show analytically that the dynamics of this network topology are determined by algebraic combinations of its five synaptic weights. Exploration of network activity over the parameter space demonstrates the importance of the nonreciprocal lateral connection and reveals intricate behavior involving continuous transitions between qualitatively different activity states. In addition, we show that the response to periodic inputs is narrowly tuned around a center frequency determined by the effective synaptic parameters.

View figure in article

Article Text

References (24)

  1. G. M. Shepherd, The Synaptic Organization of the Brain (Oxford University Press, New York, 2004).
  2. R. Cabeza and A. Kingstone, Handbook of Functional Neuroimaging of Cognition (MIT Press, Cambridge, 2006).
  3. S. Grillner and A. Graybiel, Microcircuits: The Interface Between Neurons and Global Brain Function (MIT Press, Cambridge, 2006).
  4. S. M. Sherman and R. W. Guillery, Exploring the Thalamus and Its Role in Cortical Function (MIT Press, Cambridge, 2006).
  5. A. M. Sillito, J. Cudeiro, and H. E. Jones, Trends Neurosci. 29, 307 (2006).
  6. R. J. Douglas and K. A. C. Martin, Annu. Rev. Neurosci. 27, 419 (2004).
  7. E. R. Gruberg, E. A. Dudkin, Y. Wang, G. Marin, C. Salas, E. Sentis, J. C. Letelier, J. Mpodozis, J. Malpeli, H. Cui et al., J. Neurosci. 26, 10368 (2006).
  8. Y. Wang, D. E. Major, and H. J. Karten, J. Comp. Neurol. 469, 275 (2004).
  9. Y. Wang, H. Luksch, N. Brecha, and H. Karten, J. Comp. Neurol. 494, 7 (2006).
  10. M. I. Sereno and P. S. Ulinski, J. Comp. Neurol. 261, 319 (1987).
  11. A. S. Powers and A. Reiner, Brain Behav. Evol. 41, 326 (1993).
  12. A. C. Tsoi and A. Back, Neurocomputing 15, 183 (1997).
  13. Z. Yi and K. K. Tan, IEEE Trans. Neural Netw. 15, 329 (2004).
  14. R. Haschke and J. Steil, Neurocomputing 64, 25 (2005).
  15. S. M. Sherman and R. W. Guillery, Philos. Trans. R. Soc. London, Ser. B 357, 1695 (2002).
  16. J. Bélair and S. Dofour, Can. Appl. Math. Q. 4, 135 (1996).
  17. C. C. Canavier, D. A. Baxter, J. W. Clark, and J. H. Byrne, J. Neurophysiol. 69, 2252 (1993).
  18. H. R. Wilson and J. D. Cowan, Biophys. J. 12, 1 (1972).
  19. M. Steriade, The Intact and Sliced Brain (MIT Press, Cambridge, 2006).
  20. V. I. Arnol’d, Mathematical Methods of Classical Mechanics (Springer, New York, 1974).
  21. M. H. Jensen, P. Bak, and T. Bohr, Phys. Rev. A 30, 1960 (1984).
  22. U. Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits (CRC, Boca Raton, 2006).
  23. J. A. Papin, J. L. Reed, and B. O. Palsson, Trends Biochem. Sci. 29, 641 (2004).
  24. A. A. Prinz, D. Bucher, and E. Marder, Nat. Neurosci. 7, 1345 (2004).

Outline

Information

Phys. Rev. E 80, 051923– Published 25 November, 2009
  • Received 19 March 2009

© 2009 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation