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Register a new userDynamic self-organized error-correction of grid cells by border cells
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Added by
Vijay Balasubramanian
Publication date
2018
fields
Biology
and research's language is
English
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Grid cells in the entorhinal cortex are believed to establish their regular, spatially correlated firing patterns by path integration of the animals motion. Mechanisms for path integration, e.g. in attractor network models, predict stochastic drift of grid responses, which is not observed experimentally. We demonstrate a biologically plausible mechanism of dynamic self-organization by which border cells, which fire at environmental boundaries, can correct such drift in grid cells. In our model, experience-dependent Hebbian plasticity during exploration allows border cells to learn connectivity to grid cells. Border cells in this learned network reset the phase of drifting grids. This error-correction mechanism is robust to environmental shape and complexity, including enclosures with interior barriers, and makes distinctive predictions for environmental deformation experiments. Our work demonstrates how diverse cell types in the entorhinal cortex could interact dynamically and adaptively to achieve robust path integration.
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Understanding how grid cells perform path integration calculations remains a fundamental problem. In this paper, we conduct theoretical analysis of a general representation model of path integration by grid cells, where the 2D self-position is encoded as a higher dimensional vector, and the 2D self-motion is represented by a general transformation of the vector. We identify two conditions on the transformation. One is a group representation condition that is necessary for path integration. The other is an isotropic scaling condition that ensures locally conformal embedding, so that the error in the vector representation translates proportionally to the error in the 2D self-position. Then we investigate the simplest transformation, i.e., the linear transformation, uncover its explicit algebraic and geometric structure as matrix Lie group of rotation, and establish the connection between the isotropic scaling condition and hexagon grid patterns of grid cells under the linear transformation. Finally, with our optimization-based approach, we manage to learn hexagon grid patterns that share similar properties of the grid cells in the rodent brain. The learned model is capable of accurate long distance path integration.
Place cells in the hippocampus are active when an animal visits a certain location (referred to as a place field) within an environment. Grid cells in the medial entorhinal cortex (MEC) respond at multiple locations, with firing fields that form a periodic and hexagonal tiling of the environment. The joint activity of grid and place cell populations, as a function of location, forms a neural code for space. An ensemble of codes is generated by varying grid and place cell population parameters. For each code in this ensemble, codewords are generated by stimulating a network with a discrete set of locations. In this manuscript, we develop an understanding of the relationships between coding theoretic properties of these combined populations and code construction parameters. These relationships are revisited by measuring the performances of biologically realizable algorithms implemented by networks of place and grid cell populations, as well as constraint neurons, which perform de-noising operations. Objectives of this work include the investigation of coding theoretic limitations of the mammalian neural code for location and how communication between grid and place cell networks may improve the accuracy of each populations representation. Simulations demonstrate that de-noising mechanisms analyzed here can significantly improve fidelity of this neural representation of space. Further, patterns observed in connectivity of each population of simulated cells suggest that inter-hippocampal-medial-entorhinal-cortical connectivity decreases downward along the dorsoventral axis.
It is largely believed that complex cognitive phenomena require the perfect orchestrated collaboration of many neurons. However, this is not what converging experimental evidence suggests. Single neurons, the so-called concept cells, may be responsible for complex tasks performed by an individual. Here, starting from a few first principles, we layout physical foundations showing that concept cells are not only possible but highly likely, given that neurons work in a high dimensional space.
Random measurements have been shown to induce a phase transition in an extended quantum system evolving under chaotic unitary dynamics, when the strength of measurements exceeds a threshold value. Below this threshold, a steady state with a sub-thermal volume law entanglement emerges, which is resistant to the disentangling action of measurements, suggesting a connection to quantum error-correcting codes. Here we quantify these notions by identifying a universal, subleading logarithmic contribution to the volume law entanglement entropy: $S^{(2)}(A)=kappa L_A+frac{3}{2}log L_A$ which bounds the mutual information between a qudit inside region $A$ and the rest of the system. Specifically, we find the power law decay of the mutual information $I({x}:bar{A})propto x^{-3/2}$ with distance $x$ from the regions boundary, which implies that measuring a qudit deep inside $A$ will have negligible effect on the entanglement of $A$. We obtain these results by mapping the entanglement dynamics to the imaginary time evolution of an Ising model, to which we can apply field-theoretic and matrix-product-state techniques. Finally, exploiting the error-correction viewpoint, we assume that the volume-law state is an encoding of a Page state in a quantum error-correcting code to obtain a bound on the critical measurement strength $p_{c}$ as a function of the qudit dimension $d$: $p_{c}log[(d^{2}-1)({p_{c}^{-1}-1})]le log[(1-p_{c})d]$. The bound is saturated at $p_c(drightarrowinfty)=1/2$ and provides a reasonable estimate for the qubit transition: $p_c(d=2) le 0.1893$.
Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For the last two decades, considerable experimental evidence accumulated that the mammalian cortex with its diversity in cell types and connections might exhibit SOC. Here we review experimental findings of isolated, layered cortex preparations to self-organize towards four dynamical motifs identified in the cortex in vivo: up-states, oscillations, neuronal avalanches, and coherence potentials. During up-states, the synchronization observed for nested theta/gamma-oscillations embeds scale-invariant neuronal avalanches that exhibit robust power law scaling in size with a slope of -3/2 and a critical branching parameter of 1. This dynamical coordination, tracked in the local field potential (nLFP) and pyramidal neuron activity using 2-photon imaging, emerges autonomously in superficial layers of organotypic cortex cultures and acute cortex slices, is homeostatically regulated, displays separation of time scales, and reveals unique size vs. quiet time dependencies. A threshold operation identifies coherence potentials; avalanches that in addition maintain the precise time course of propagated synchrony. Avalanches emerge under conditions of external driving. Control parameters are established by the balance of excitation and inhibition (E/I) and the neuromodulator dopamine. This rich dynamical repertoire is not observed in dissociated cortex cultures, which lack cortical layers and exhibit dynamics similar to a 1st-order phase transition. The precise interactions between up-states, nested oscillations, avalanches, and coherence potentials in superficial cortical layers provide compelling evidence for SOC in the brain.
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