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Spatial gradients and multidimensional dynamics in a neural integrator circuit


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.

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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.


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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




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.

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The authors declare no competing financial interests.

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Miri, A., Daie, K., Arrenberg, A. et al. Spatial gradients and multidimensional dynamics in a neural integrator circuit. Nat Neurosci 14, 1150–1159 (2011).

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