Does Optic Flow Explain the Firing of Grid Cells?

*Problem.* Various cues such as vestibular, sensorimotor, or visual information can lead to the firing of grid cells recorded in entorhinal cortex of rats. A recent model uses boundary vector cells to provide information about the 2D spatial position (Barry et al., Review Neuroscience, 17, 2006). However, boundary vector cells need to know the angle and distance of the boundary wall. In contrast we study the estimation of 2D velocity and change of heading of the rat from optic flow and if this information can lead to grid cell firing.
*Approach.* A simple circular cage is modeled as a 3D world and trajectories of a rat’s movement are simulated. Optic flow for a spherical camera model is calculated for regularly sampled locations on the ground of the cage. This flow information is used in a template model to estimate the rat’s 2D linear velocity and yaw rotational velocity. 2D linear velocities are integrated into the velocity controlled oscillator (VCO) model (Burgess, Hippocampus, 18, 2008) while spatial locations are taken from the original trajectory.
*Result and Conclusion.* If velocity estimates are temporally integrated over ~20min the error summation by path integration prevents generation of a clear grid cell firing pattern by the VCO model. However, for short durations velocity estimates and path integration are accurate. If we assume a reset mechanism that recalibrates the spatial location of the rat grid cell firing can be achieved. Different reset intervals were simulated and the grid score for the firing pattern was calculated. For a reset interval longer than one minute this grid score decreases rapidly. We conclude that grid cell firing is not generated only by optic flow, but that a recalibration of the spatial position using cues other than optic flow occurs at least every minute.
Supported by CELEST (NSF SMA-0835976)

Sparse Coding Predicts Optic Flow Specificities of Zebrafish Pretectal Neurons

Zebrafish pretectal neurons exhibit specificities for large-field optic flow patterns associated with rotatory or translatory body motion. We investigate the hypothesis that these specificities reflect the input statistics of natural optic flow. Realistic motion sequences were generated using computer graphics simulating self-motion in an underwater scene. Local retinal motion was estimated with a motion detector and encoded in four populations of directionally tuned retinal ganglion cells, represented as two signed input variables. This activity was then used as input into one of two learning networks: a sparse coding network (competitive learning) and backpropagation network (supervised learning). Both simulations develop specificities for optic flow which are comparable to those found in a neurophysiological study (Kubo et al. 2014), and relative frequencies of the various neuronal responses are best modeled by the sparse coding approach. We conclude that the optic flow neurons in the zebrafish pretectum do reflect the optic flow statistics. The predicted vectorial receptive fields show typical optic flow fields but also "Gabor" and dipole-shaped patterns that likely reflect difference fields needed for reconstruction by linear superposition.Comment: Published Conference Paper from ICANN 2018, Rhode

Context-dependent spatially periodic activity in the human entorhinal cortex

The spatially periodic activity of grid cells in the entorhinal cortex (EC) of the rodent, primate, and human provides a coordinate system that, together with the hippocampus, informs an individual of its location relative to the environment and encodes the memory of that location. Among the most defining features of grid-cell activity are the 60 degrees rotational symmetry of grids and preservation of grid scale across environments. Grid cells, however, do display a limited degree of adaptation to environments. It remains unclear if this level of environment invariance generalizes to human grid-cell analogs, where the relative contribution of visual input to the multimodal sensory input of the EC is significantly larger than in rodents. Patients diagnosed with nontractable epilepsy who were implanted with entorhinal cortical electrodes performing virtual navigation tasks to memorized locations enabled us to investigate associations between grid-like patterns and environment. Here, we report that the activity of human entorhinal cortical neurons exhibits adaptive scaling in grid period, grid orientation, and rotational symmetry in close association with changes in environment size, shape, and visual cues, suggesting scale invariance of the frequency, rather than the wavelength, of spatially periodic activity. Our results demonstrate that neurons in the human EC represent space with an enhanced flexibility relative to neurons in rodents because they are endowed with adaptive scalability and context dependency

Replay as wavefronts and theta sequences as bump oscillations in a grid cell attractor network.

Grid cells fire in sequences that represent rapid trajectories in space. During locomotion, theta sequences encode sweeps in position starting slightly behind the animal and ending ahead of it. During quiescence and slow wave sleep, bouts of synchronized activity represent long trajectories called replays, which are well-established in place cells and have been recently reported in grid cells. Theta sequences and replay are hypothesized to facilitate many cognitive functions, but their underlying mechanisms are unknown. One mechanism proposed for grid cell formation is the continuous attractor network. We demonstrate that this established architecture naturally produces theta sequences and replay as distinct consequences of modulating external input. Driving inhibitory interneurons at the theta frequency causes attractor bumps to oscillate in speed and size, which gives rise to theta sequences and phase precession, respectively. Decreasing input drive to all neurons produces traveling wavefronts of activity that are decoded as replays

Modeling Boundary Vector Cell Firing Given Optic Flow as a Cue

Boundary vector cells in entorhinal cortex fire when a rat is in locations at a specific distance from walls of an environment. This firing may originate from memory of the barrier location combined with path integration, or the firing may depend upon the apparent visual input image stream. The modeling work presented here investigates the role of optic flow, the apparent change of patterns of light on the retina, as input for boundary vector cell firing. Analytical spherical flow is used by a template model to segment walls from the ground, to estimate self-motion and the distance and allocentric direction of walls, and to detect drop-offs. Distance estimates of walls in an empty circular or rectangular box have a mean error of less than or equal to two centimeters. Integrating these estimates into a visually driven boundary vector cell model leads to the firing patterns characteristic for boundary vector cells. This suggests that optic flow can influence the firing of boundary vector cells

An analysis of waves underlying grid cell firing in the medial enthorinal cortex

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an I_h current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo [2013 Neuronal rebound spiking, resonance frequency and theta cycle skipping may contribute to grid cell firing in medial entorhinal cortex. Phil. Trans. R. Soc. B 369: 20120523] showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the I_h current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in I_h resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the I_h current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions

Combining Feature Selection and Integration—A Neural Model for MT Motion Selectivity

Background: The computation of pattern motion in visual area MT based on motion input from area V1 has been investigated in many experiments and models attempting to replicate the main mechanisms. Two different core conceptual approaches were developed to explain the findings. In integrationist models the key mechanism to achieve pattern selectivity is the nonlinear integration of V1 motion activity. In contrast, selectionist models focus on the motion computation at positions with 2D features. Methodology/Principal Findings: Recent experiments revealed that neither of the two concepts alone is sufficient to explain all experimental data and that most of the existing models cannot account for the complex behaviour found. MT pattern selectivity changes over time for stimuli like type II plaids from vector average to the direction computed with an intersection of constraint rule or by feature tracking. Also, the spatial arrangement of the stimulus within the receptive field of a MT cell plays a crucial role. We propose a recurrent neural model showing how feature integration and selection can be combined into one common architecture to explain these findings. The key features of the model are the computation of 1D and 2D motion in model area V1 subpopulations that are integrated in model MT cells using feedforward and feedback processing. Our results are also in line with findings concerning the solution of the aperture problem. Conclusions/Significance: We propose a new neural model for MT pattern computation and motion disambiguation that i

Encoding of 3D head direction information in the human brain

Head direction cells are critical for navigation because they convey information about which direction an animal is facing within an environment. To date, most studies on head direction encoding have been conducted on a horizontal two-dimensional (2D) plane, and little is known about how three-dimensional (3D) direction information is encoded in the brain despite humans and other animals living in a 3D world. Here, we investigated head direction encoding in the human brain while participants moved within a virtual 3D "spaceship" environment. Movement was not constrained to planes and instead participants could move along all three axes in volumetric space as if in zero gravity. Using functional magnetic resonance imaging (fMRI) multivoxel pattern similarity analysis, we found evidence that the thalamus, particularly the anterior portion, and the subiculum encoded the horizontal component of 3D head direction (azimuth). In contrast, the retrosplenial cortex was significantly more sensitive to the vertical direction (pitch) than to the azimuth. Our results also indicated that vertical direction information in the retrosplenial cortex was significantly correlated with behavioral performance during a direction judgment task. Our findings represent the first evidence showing that the "classic" head direction system that has been identified on a horizontal 2D plane also seems to encode vertical and horizontal heading in 3D space in the human brain