Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Spatial gradients and multidimensional dynamics in a neural integrator circuit

Abstract

In a neural integrator, the variability and topographical organization of neuronal firing-rate persistence can provide information about the circuit's functional architecture. We used optical recording to measure the time constant of decay of persistent firing (persistence time) across a population of neurons comprising the larval zebrafish oculomotor velocity-to-position neural integrator. We found extensive persistence time variation (tenfold; coefficients of variation = 0.58–1.20) across cells in individual larvae. We also found that the similarity in firing between two neurons decreased as the distance between them increased and that a gradient in persistence time was mapped along the rostrocaudal and dorsoventral axes. This topography is consistent with the emergence of persistence time heterogeneity from a circuit architecture in which nearby neurons are more strongly interconnected than distant ones. Integrator circuit models characterized by multiple dimensions of slow firing-rate dynamics can account for our results.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Potential dynamical and spatial structure among hVPNI neurons.
Figure 2: Saccade-related calcium fluctuations in optically identified hindbrain somata.
Figure 3: NpHR-mediated silencing of the caudal hindbrain reduces eye position stability.
Figure 4: The distribution of persistence time ranges in individual larvae.
Figure 5: Agreement between electrical and optical recording–based parameterizations of saccade-related activity.
Figure 6: Activity correlations between cells depend on their pairwise distance.
Figure 7: Persistence time and response index similarity depend on pairwise distance along spatial dimensions.
Figure 8: Mechanistic implications of heterogeneity in dynamics.

References

  1. 1

    Robinson, D.A. Integrating with neurons. Annu. Rev. Neurosci. 12, 33–45 (1989).

    CAS  Article  Google Scholar 

  2. 2

    Oestreich, J., Dembrow, N.C., George, A.A. & Zakon, H.H. A “sample-and-hold” pulse-counting integrator as a mechanism for graded memory underlying sensorimotor adaptation. Neuron 49, 577–588 (2006).

    CAS  Article  Google Scholar 

  3. 3

    Huk, A.C. & Shadlen, M.N. Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making. J. Neurosci. 25, 10420–10436 (2005).

    CAS  Article  Google Scholar 

  4. 4

    Taube, J.S. & Bassett, J.P. Persistent neural activity in head direction cells. Cereb. Cortex 13, 1162–1172 (2003).

    Article  Google Scholar 

  5. 5

    Cohen, B. & Komatsuzaki, A. Eye movements induced by stimulation of the pontine reticular formation: evidence for integration in oculomotor pathways. Exp. Neurol. 36, 101–117 (1972).

    CAS  Article  Google Scholar 

  6. 6

    Skavenski, A.A. & Robinson, D.A. Role of abducens neurons in vestibuloocular reflex. J. Neurophysiol. 36, 724–738 (1973).

    CAS  Article  Google Scholar 

  7. 7

    Major, G. & Tank, D. Persistent neural activity: prevalence and mechanisms. Curr. Opin. Neurobiol. 14, 675–684 (2004).

    CAS  Article  Google Scholar 

  8. 8

    Lopez-Barneo, J., Darlot, C., Berthoz, A. & Baker, R. Neuronal activity in prepositus nucleus correlated with eye movement in the alert cat. J. Neurophysiol. 47, 329–352 (1982).

    CAS  Article  Google Scholar 

  9. 9

    McFarland, J.L. & Fuchs, A.F. Discharge patterns in nucleus prepositus hypoglossi and adjacent medial vestibular nucleus during horizontal eye movement in behaving macaques. J. Neurophysiol. 68, 319–332 (1992).

    CAS  Article  Google Scholar 

  10. 10

    Aksay, E., Baker, R., Seung, H.S. & Tank, D.W. Anatomy and discharge properties of pre-motor neurons in the goldfish medulla that have eye-position signals during fixations. J. Neurophysiol. 84, 1035–1049 (2000).

    CAS  Article  Google Scholar 

  11. 11

    Seung, H.S. How the brain keeps the eyes still. Proc. Natl. Acad. Sci. USA 93, 13339–13344 (1996).

    CAS  Article  Google Scholar 

  12. 12

    Machens, C.K., Romo, R. & Brody, C.D. Flexible control of mutual inhibition: a neural model of two-interval discrimination. Science 307, 1121–1124 (2005).

    CAS  Article  Google Scholar 

  13. 13

    Singh, R. & Eliasmith, C. Higher-dimensional neurons explain the tuning and dynamics of working memory cells. J. Neurosci. 26, 3667–3678 (2006).

    CAS  Article  Google Scholar 

  14. 14

    Seung, H.S., Lee, D.D., Reis, B.Y. & Tank, D.W. Stability of the memory of eye position in a recurrent network of conductance-based model neurons. Neuron 26, 259–271 (2000).

    CAS  Article  Google Scholar 

  15. 15

    Koulakov, A.A., Raghavachari, S., Kepecs, A. & Lisman, J.E. Model for a robust neural integrator. Nat. Neurosci. 5, 775–782 (2002).

    CAS  Article  Google Scholar 

  16. 16

    Goldman, M.S., Levine, J.H., Major, G., Tank, D.W. & Seung, H.S. Robust persistent neural activity in a model integrator with multiple hysteretic dendrites per neuron. Cereb. Cortex 13, 1185–1195 (2003).

    Article  Google Scholar 

  17. 17

    Anastasio, T.J. The fractional-order dynamics of brainstem vestibulo-oculomotor neurons. Biol. Cybern. 72, 69–79 (1994).

    CAS  Article  Google Scholar 

  18. 18

    Major, G., Baker, R., Aksay, E., Seung, H.S. & Tank, D.W. Plasticity and tuning of the time course of analog persistent firing in a neural integrator. Proc. Natl. Acad. Sci. USA 101, 7745–7750 (2004).

    CAS  Article  Google Scholar 

  19. 19

    Maass, W., Joshi, P. & Sontag, E.D. Computational aspects of feedback in neural circuits. PLOS Comput. Biol. 3, e165 (2007).

    Article  Google Scholar 

  20. 20

    Aksay, E. et al. Functional dissection of circuitry in a neural integrator. Nat. Neurosci. 10, 494–504 (2007).

    CAS  Article  Google Scholar 

  21. 21

    Cannon, S.C., Robinson, D.A. & Shamma, S. A proposed neural network for the integrator of the oculomotor system. Biol. Cybern. 49, 127–136 (1983).

    CAS  Article  Google Scholar 

  22. 22

    Goldman, M.S. Memory without feedback in a neural network. Neuron 61, 621–634 (2009).

    CAS  Article  Google Scholar 

  23. 23

    Miri, A., Daie, K., Burdine, R.D., Aksay, E. & Tank, D.W. Regression-based identification of behavior-encoding neurons during large-scale optical imaging of neural activity at cellular resolution. J. Neurophysiol. 105, 964–980 (2011).

    Article  Google Scholar 

  24. 24

    McLean, D.L., Fan, J., Higashijima, S., Hale, M.E. & Fetcho, J.R. A topographic map of recruitment in spinal cord. Nature 446, 71–75 (2007).

    CAS  Article  Google Scholar 

  25. 25

    Weiler, N., Wood, L., Yu, J., Solla, S.A. & Shepherd, G.M. Top-down laminar organization of the excitatory network in motor cortex. Nat. Neurosci. 11, 360–366 (2008).

    CAS  Article  Google Scholar 

  26. 26

    Higashijima, S., Mandel, G. & Fetcho, J.R. Distribution of prospective glutamatergic, glycinergic and GABAergic neurons in embryonic and larval zebrafish. J. Comp. Neurol. 480, 1–18 (2004).

    CAS  Article  Google Scholar 

  27. 27

    Dasen, J.S. & Jessell, T.M. Hox networks and the origins of motor neuron diversity. Curr. Top. Dev. Biol. 88, 169–200 (2009).

    CAS  Article  Google Scholar 

  28. 28

    Pastor, A.M., de La Cruz, R.R. & Baker, R. Eye position and eye velocity integrators reside in separate brainstem nuclei. Proc. Natl. Acad. Sci. USA 91, 807–811 (1994).

    CAS  Article  Google Scholar 

  29. 29

    Arrenberg, A.B., Del Bene, F. & Baier, H. Optical control of zebrafish behavior with halorhodopsin. Proc. Natl. Acad. Sci. USA 106, 17968–17973 (2009).

    CAS  Article  Google Scholar 

  30. 30

    Schoonheim, P.J., Arrenberg, A.B., Del Bene, F. & Baier, H. Optogenetic localization and genetic perturbation of saccade-generating neurons in zebrafish. J. Neurosci. 30, 7111–7120 (2010).

    CAS  Article  Google Scholar 

  31. 31

    Escudero, M., de la Cruz, R.R. & Delgado-Garcia, J.M. A physiological study of vestibular and prepositus hypoglossi neurones projecting to the abducens nucleus in the alert cat. J. Physiol. (Lond.) 458, 539–560 (1992).

    CAS  Article  Google Scholar 

  32. 32

    Aksay, E., Baker, R., Seung, H.S. & Tank, D.W. Correlated discharge among cell pairs within the oculomotor horizontal velocity-to-position integrator. J. Neurosci. 23, 10852–10858 (2003).

    CAS  Article  Google Scholar 

  33. 33

    Shinoda, Y. & Yoshida, K. Dynamic characteristics of responses to horizontal head angular acceleration in vestibuloocular pathway in the cat. J. Neurophysiol. 37, 653–673 (1974).

    CAS  Article  Google Scholar 

  34. 34

    Anastasio, T.J. Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior. Biol. Cybern. 79, 377–391 (1998).

    CAS  Article  Google Scholar 

  35. 35

    Aksay, E. et al. History dependence of rate covariation between neurons during persistent activity in an oculomotor integrator. Cereb. Cortex 13, 1173–1184 (2003).

    Article  Google Scholar 

  36. 36

    Debowy, O. & Baker, R. Encoding of eye position in the goldfish horizontal oculomotor neural integrator. J. Neurophysiol. 105, 896–909 (2011).

    Article  Google Scholar 

  37. 37

    Sklavos, S., Porrill, J., Kaneko, C.R. & Dean, P. Evidence for wide range of time scales in oculomotor plant dynamics: implications for models of eye-movement control. Vision Res. 45, 1525–1542 (2005).

    Article  Google Scholar 

  38. 38

    Kinkhabwala, A. et al. A structural and functional ground plan for neurons in the hindbrain of zebrafish. Proc. Natl. Acad. Sci. USA 108, 1164–1169 (2011).

    CAS  Article  Google Scholar 

  39. 39

    McLean, D.L., Masino, M.A., Koh, I.Y., Lindquist, W.B. & Fetcho, J.R. Continuous shifts in the active set of spinal interneurons during changes in locomotor speed. Nat. Neurosci. 11, 1419–1429 (2008).

    CAS  Article  Google Scholar 

  40. 40

    Goldberg, J.M. & Fernandez, C. Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. I. Resting discharge and response to constant angular acceleration. J. Neurophysiol. 34, 635–660 (1971).

    CAS  Article  Google Scholar 

  41. 41

    Miles, F.A. & Braitman, D.J. Long-term adaptive changes in primate vestibuloocular reflex. II. Electrophysiological observations on semicircular canal primary afferents. J. Neurophysiol. 43, 1426–1436 (1980).

    CAS  Article  Google Scholar 

  42. 42

    Sussillo, D. & Abbott, L.F. Generating coherent patterns of activity from chaotic neural networks. Neuron 63, 544–557 (2009).

    CAS  Article  Google Scholar 

  43. 43

    Helmstaedter, M., Briggman, K.L. & Denk, W. 3D structural imaging of the brain with photons and electrons. Curr. Opin. Neurobiol. 18, 633–641 (2008).

    CAS  Article  Google Scholar 

  44. 44

    Beck, J.C., Rothnie, P., Straka, H., Wearne, S.L. & Baker, R. Precerebellar hindbrain neurons encoding eye velocity during vestibular and optokinetic behavior in the goldfish. J. Neurophysiol. 96, 1370–1382 (2006).

    Article  Google Scholar 

  45. 45

    Ma, L.H., Punnamoottil, B., Rinkwitz, S. & Baker, R. Mosaic hoxb4a neuronal pleiotropism in zebrafish caudal hindbrain. PLoS ONE 4, e5944 (2009).

    Article  Google Scholar 

  46. 46

    Huang, Z. Membrane potential fluctuations in a neural integrator. PhD thesis, Princeton University (2009).

  47. 47

    Aksay, E., Gamkrelidze, G., Seung, H.S., Baker, R. & Tank, D.W. In vivo intracellular recording and perturbation of persistent activity in a neural integrator. Nat. Neurosci. 4, 184–193 (2001).

    CAS  Article  Google Scholar 

  48. 48

    Teramae, J.N. & Fukai, T. A cellular mechanism for graded persistent activity in a model neuron and its implications in working memory. J. Comput. Neurosci. 18, 105–121 (2005).

    Article  Google Scholar 

  49. 49

    Fransén, E., Tahvildari, B., Egorov, A.V., Hasselmo, M.E. & Alonso, A.A. Mechanism of graded persistent cellular activity of entorhinal cortex layer V neurons. Neuron 49, 735–746 (2006).

    Article  Google Scholar 

  50. 50

    Loewenstein, Y. & Sompolinsky, H. Temporal integration by calcium dynamics in a model neuron. Nat. Neurosci. 6, 961–967 (2003).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank D. Dombeck for technical advice, F. Collman for motion-correction software, and M. Goldman, A. Kinkhabwala and P. Bradley for helpful discussions. This work was supported by a National Science Foundation predoctoral fellowship (A.M.), a US National Institutes of Health Training grant (EY007138-16, K.D.), a Krevans fellowship (A.B.A.), a Burroughs Wellcome Career Award at the Scientific Interface, a Searle Scholar award, the Frueauff Foundation (E.A.), the Human Frontier Science Program (H.B.), and US National Institutes of Health grants (R01 MH060651 to D.W.T. and R01 NS053358 to H.B.).

Author information

Affiliations

Authors

Contributions

A.M. collected functional imaging and electrical recording data under the supervision of D.W.T.; A.M., E.A. and D.W.T. developed the preparation, experimental procedures and instrumentation for the imaging and electrophysiological studies; A.M. and K.D. analyzed this data with guidance from E.A. and D.W.T.; A.B.A. and H.B. designed the NpHR study; A.B.A. collected and analyzed the NpHR data; and A.M., K.D., E.A. and D.W.T. wrote the paper.

Corresponding authors

Correspondence to Emre Aksay or David W Tank.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–9 and Supplementary Tables 1 and 2 (PDF 5985 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Miri, A., Daie, K., Arrenberg, A. et al. Spatial gradients and multidimensional dynamics in a neural integrator circuit. Nat Neurosci 14, 1150–1159 (2011). https://doi.org/10.1038/nn.2888

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing