Accurate path integration in continuous attractor network models of grid cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ~10–100 meters and ~1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other

Vertical distribution of fish larvae in the Canaries-African coastal transition zone, in summer

13 pages, 6 figures, 2 tables.-- Printed version published Jul 2006.This study reports the vertical distribution of fish larvae during the 1999 summer upwelling season in the Canaries-African Coastal Transition Zone (the Canaries-ACTZ). The transition between the African coastal upwelling and the typical subtropical offshore conditions is a region of intense mesoscale activity that supports a larval fish population dominated by African neritic species. During the study, the thermal stratification extended almost to the surface everywhere, and the surface mixed layer was typically shallow or non-existent. Upwelling occurred on the African shelf in a limited coastal sub-area of our sampling. The vertical distributions of the entire larval fish population, as well as of individual species, were independent of the seasonal thermocline. Fish larvae and mesozooplankton were concentrated at intermediate depths regardless of the thermocline position, probably because of its weak signature and spatial and temporal variability. Day/night vertical distributions suggest that some species did not perform diel vertical migration (DVM), whereas others showed either type I DVM or type II DVM. The opposing DVM patterns of different species compensate for each other resulting in no net DVM for the larval fish population as a whole.Fieldwork was carried out as part of the CANIGO project, funded by the EU, and of the "Pelagic (EU-CICYT 1FD97-1084)" project from the Spanish Ministry of Education and the European Union

Head roll dependent variability of subjective visual vertical and ocular counterroll

We compared the variability of the subjective visual vertical (SVV) and static ocular counterroll (OCR), and hypothesized a correlation between the measurements because of their shared macular input. SVV and OCR were measured simultaneously in various whole-body roll positions [upright, 45 degrees right-ear down (RED), and 75 degrees RED] in six subjects. Gains of OCR were -0.18 (45 degrees RED) and -0.12 (75 degrees RED), whereas gains of compensation for body roll in the SVV task were -1.11 (45 degrees RED) and -0.96 (75 degrees RED). Normalized SVV and OCR variabilities were not significantly different (P > 0.05), i.e., both increased with increasing roll. Moreover, a significant correlation (R (2) = 0.80, slope = 0.29) between SVV and OCR variabilities was found. Whereas the gain of OCR is different from the gain of SVV, trial-to-trial variability of OCR follows the same roll-dependent modulation observed in SVV variability. We propose that the similarities in variability reflect a common otolith input, which, however, is subject to distinct central processing for determining the gain of SVV and OCR