Benjamin Dunn

Grid cells require excitatory drive from the hippocampus

To determine how hippocampal backprojections influence spatially periodic firing in grid cells, we recorded neural activity in the medial entorhinal cortex (MEC) of rats after temporary inactivation of the hippocampus. We report two major changes in entorhinal grid cells. First, hippocampal inactivation gradually and selectively extinguished the grid pattern. Second, the same grid cells that lost their grid fields acquired substantial tuning to the direction of the rats head. This transition in firing properties was contingent on a drop in the average firing rate of the grid cells and could be replicated by the removal of an external excitatory drive in an attractor network model in which grid structure emerges by velocity-dependent translation of activity across a network with inhibitory connections. These results point to excitatory drive from the hippocampus, and possibly other regions, as one prerequisite for the formation and translocation of grid patterns in the MEC.

Recurrent inhibitory circuitry as a mechanism for grid formation

Grid cells in layer II of the medial entorhinal cortex form a principal component of the mammalian neural representation of space. The firing pattern of a single grid cell has been hypothesized to be generated through attractor dynamics in a network with a specific local connectivity including both excitatory and inhibitory connections. However, experimental evidence supporting the presence of such connectivity among grid cells in layer II is limited. Here we report recordings from more than 600 neuron pairs in rat entorhinal slices, demonstrating that stellate cells, the principal cell type in the layer II grid network, are mainly interconnected via inhibitory interneurons. Using a model attractor network, we demonstrate that stable grid firing can emerge from a simple recurrent inhibitory network. Our findings thus suggest that the observed inhibitory microcircuitry between stellate cells is sufficient to generate grid-cell firing patterns in layer II of the medial entorhinal cortex.

Correlations and Functional Connections in a Population of Grid Cells

We study the statistics of spike trains of simultaneously recorded grid cells in freely behaving rats. We evaluate pairwise correlations between these cells and, using a maximum entropy kinetic pairwise model (kinetic Ising model), study their functional connectivity. Even when we account for the covariations in firing rates due to overlapping fields, both the pairwise correlations and functional connections decay as a function of the shortest distance between the vertices of the spatial firing pattern of pairs of grid cells, i.e. their phase difference. They take positive values between cells with nearby phases and approach zero or negative values for larger phase differences. We find similar results also when, in addition to correlations due to overlapping fields, we account for correlations due to theta oscillations and head directional inputs. The inferred connections between neurons in the same module and those from different modules can be both negative and positive, with a mean close to zero, but with the strongest inferred connections found between cells of the same module. Taken together, our results suggest that grid cells in the same module do indeed form a local network of interconnected neurons with a functional connectivity that supports a role for attractor dynamics in the generation of grid pattern.

Multi-neuronal activity and functional connectivity in cell assemblies

Our ability to collect large amounts of data from many cells has been paralleled by the development of powerful statistical models for extracting information from this data. Here we discuss how the activity of cell assemblies can be analyzed using these models, focusing on the generalized linear models and the maximum entropy models and describing a number of recent studies that employ these tools for analyzing multi-neuronal activity. We show results from simulations comparing inferred functional connectivity, pairwise correlations and the real synaptic connections in simulated networks demonstrating the power of statistical models in inferring functional connectivity. Further development of network reconstruction techniques based on statistical models should lead to more powerful methods of understanding functional anatomy of cell assemblies.

Learning and inference in a nonequilibrium Ising model with hidden nodes.

We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations of the hidden ones. This, as we show, can be represented as a path integral. Using this representation, we demonstrate that systematic approximate inference and learning rules can be derived using dynamical mean-field theory. Although naive mean-field theory leads to an unstable learning rule, taking into account Gaussian corrections allows learning the couplings involving hidden nodes. It also improves learning of the couplings between the observed nodes compared to when hidden nodes are ignored.

Grid cells show field-to-field variability and this explains the aperiodic response of inhibitory interneurons

Research on network mechanisms and coding properties of grid cells assume that the firing rate of a grid cell in each of its fields is the same. Furthermore, proposed network models predict spatial regularities in the firing of inhibitory interneurons that are inconsistent with experimental data. In this paper, by analyzing the response of grid cells recorded from rats during free navigation, we first show that there are strong variations in the mean firing rate of the fields of individual grid cells and thus show that the data is inconsistent with the theoretical models that predict similar peak magnitudes. We then build a two population excitatory-inhibitory network model in which sparse spatially selective input to the excitatory cells, presumed to arise from e.g. salient external stimuli, hippocampus or a combination of both, leads to the variability in the firing field amplitudes of grid cells. We show that, when combined with appropriate connectivity between the excitatory and inhibitory neurons, the variability in the firing field amplitudes of grid cells results in inhibitory neurons that do not exhibit regular spatial firing, consistent with experimental data. Finally, we show that even if the spatial positions of the fields are maintained, variations in the firing rates of the fields of grid cells are enough to cause remapping of hippocampal cells.

Efficient cortical coding of 3D posture in freely behaving rats

In order to meet physical and behavioral demands of their environments animals constantly update their body posture, but little is known about the neural signals on which this ability depends. To better understand the role of cortex in coordinating natural pose and movement, we tracked the heads and backs of freely foraging rats in 3D while recording simultaneously from posterior parietal cortex (PPC) and frontal motor cortex (M2), areas critical for spatial movement planning and navigation. Single units in both regions were tuned mainly to postural features of the head, back and neck, and much less so to their movement. Representations of the head and back were organized topographically across PPC and M2, and the tuning peaks of the cells were distributed in an efficient manner, where substantially fewer cells encoded postures that occurred more often. Postural signals in both areas were sufficiently robust to allow reconstruction of ongoing behavior with 90% accuracy. Together, these findings demonstrate that both parietal and frontal motor cortices maintain an efficient, organized representation of 3D posture during unrestrained behavior.

Decoding of neural data using cohomological learning

We introduce a novel data-driven approach to discover and decode features in the neural code coming from large population neural recordings with minimal assumptions, using cohomological learning. We apply our approach to neural recordings of mice moving freely in a box, where we find a circular feature. We then observe that the decoded value corresponds well to the head direction of the mouse. Thus we capture head direction cells and decode the head direction from the neural population activity without having to process the behaviour of the mouse. Interestingly, the decoded values convey more information about the neural activity than the tracked head direction does, with differences that have some spatial organization. Finally, we note that the residual population activity, after the head direction has been accounted for, retains some low-dimensional structure which is correlated with the speed of the mouse.

The appropriateness of ignorance in the inverse kinetic Ising model

We develop efficient ways to consider and correct for the effects of hidden units for the paradigmatic case of the inverse kinetic Ising model with fully asymmetric couplings. We identify two sources of error in reconstructing the connectivity among the observed units while ignoring part of the network. One leads to a systematic bias in the inferred parameters, whereas the other involves correlations between the visible and hidden populations and has a magnitude that depends on the coupling strength. We estimate these two terms using a mean field approach and derive self-consistent equations for the couplings accounting for the systematic bias. Through application of these methods on simple networks of varying relative population size and connectivity strength, we assess how and under what conditions the hidden portion can influence inference and to what degree it can be crudely estimated. We find that for weak to moderately coupled systems, the effects of the hidden units is a simple rotation that can be easily corrected for. For strongly coupled systems, the non-systematic term becomes large and can no longer be safely ignored, further highlighting the importance of understanding the average strength of couplings for a given system of interest.