Emilio Kropff

Place Cells, Grid Cells, and the Brain's Spatial Representation System

More than three decades of research have demonstrated a role for hippocampal place cells in representation of the spatial environment in the brain. New studies have shown that place cells are part of a broader circuit for dynamic representation of self-location. A key component of this network is the entorhinal grid cells, which, by virtue of their tessellating firing fields, may provide the elements of a path integration-based neural map. Here we review how place cells and grid cells may form the basis for quantitative spatiotemporal representation of places, routes, and associated experiences during behavior and in memory. Because these cell types have some of the most conspicuous behavioral correlates among neurons in nonsensory cortical systems, and because their spatial firing structure reflects computations internally in the system, studies of entorhinal-hippocampal representations may offer considerable insight into general principles of cortical network dynamics.

Representation of Geometric Borders in the Entorhinal Cortex

We report the existence of an entorhinal cell type that fires when an animal is close to the borders of the proximal environment. The orientation-specific edge-apposing activity of these “border cells” is maintained when the environment is stretched and during testing in enclosures of different size and shape in different rooms. Border cells are relatively sparse, making up less than 10% of the local cell population, but can be found in all layers of the medial entorhinal cortex as well as the adjacent parasubiculum, often intermingled with head-direction cells and grid cells. Border cells may be instrumental in planning trajectories and anchoring grid fields and place fields to a geometric reference frame.

Speed cells in the medial entorhinal cortex

Grid cells in the medial entorhinal cortex have spatial firing fields that repeat periodically in a hexagonal pattern. When animals move, activity is translated between grid cells in accordance with the animal’s displacement in the environment. For this translation to occur, grid cells must have continuous access to information about instantaneous running speed. However, a powerful entorhinal speed signal has not been identified. Here we show that running speed is represented in the firing rate of a ubiquitous but functionally dedicated population of entorhinal neurons distinct from other cell populations of the local circuit, such as grid, head-direction and border cells. These ‘speed cells’ are characterized by a context-invariant positive, linear response to running speed, and share with grid cells a prospective bias of ∼50–80 ms. Our observations point to speed cells as a key component of the dynamic representation of self-location in the medial entorhinal cortex.

The emergence of grid cells: Intelligent design or just adaptation?

Individual medial entorhinal cortex (mEC) ‘grid’ cells provide a representation of space that appears to be essentially invariant across environments, modulo simple transformations, in contrast to multiple, rapidly acquired hippocampal maps; it may therefore be established gradually during rodent development. We explore with a simplified mathematical model the possibility that the self‐organization of multiple grid fields into a triangular grid pattern may be a single‐cell process, driven by firing rate adaptation and slowly varying spatial inputs. A simple analytical derivation indicates that triangular grids are favored asymptotic states of the self‐organizing system, and computer simulations confirm that such states are indeed reached during a model learning process, provided it is sufficiently slow to effectively average out fluctuations. The interactions among local ensembles of grid units serve solely to stabilize a common grid orientation. Spatial information, in the real mEC network, may be provided by any combination of feedforward cortical afferents and feedback hippocampal projections from place cells, since either input alone is likely sufficient to yield grid fields.

Grid alignment in entorhinal cortex

The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cortex (mEC) show mutually aligned grid patterns. Recent experimental findings have shown that grids can often be better described as elliptical rather than purely circular and that, beyond the mutual alignment of their grid axes, ellipses tend to also orient their long axis along preferred directions. Are grid alignment and ellipse orientation aspects of the same phenomenon? Does the grid alignment result from single-unit mechanisms or does it require network interactions? We address these issues by refining a single-unit adaptation model of grid formation, to describe specifically the spontaneous emergence of conjunctive grid-by-head-direction cells in layers III, V, and VI of mEC. We find that tight alignment can be produced by recurrent collateral interactions, but this requires head-direction (HD) modulation. Through a competitive learning process driven by spatial inputs, grid fields then form already aligned, and with randomly distributed spatial phases. In addition, we find that the self-organization process is influenced by any anisotropy in the behavior of the simulated rat. The common grid alignment often orients along preferred running directions (RDs), as induced in a square environment. When speed anisotropy is present in exploration behavior, the shape of individual grids is distorted toward an ellipsoid arrangement. Speed anisotropy orients the long ellipse axis along the fast direction. Speed anisotropy on its own also tends to align grids, even without collaterals, but the alignment is seen to be loose. Finally, the alignment of spatial grid fields in multiple environments shows that the network expresses the same set of grid fields across environments, modulo a coherent rotation and translation. Thus, an efficient metric encoding of space may emerge through spontaneous pattern formation at the single-unit level, but it is coherent, hence context-invariant, if aided by collateral interactions.

Free association transitions in models of cortical latching dynamics

Potts networks, in certain conditions, hop spontaneously from one discrete attractor state to another, a process we have called latching dynamics. When continuing indefinitely, latching can serve as a model of infinite recursion, which is nontrivial if the matrix of transition probabilities presents a structure, i.e. a rudimentary grammar. We show here, with computer simulations, that latching transitions cluster in a number of distinct classes: effectively random transitions between weakly correlated attractors; structured, history-dependent transitions between attractors with intermediate correlations; and oscillations between pairs of closely overlapping attractors. Each type can be described by a reduced set of equations of motion, which, once numerically integrated, matches simulations results. We propose that the analysis of such equations may offer clues on how to embed meaningful grammatical structures into more realistic models of specific recursive processes.

Dynamic role of adult-born dentate granule cells in memory processing.

Throughout the adult life of all mammals including humans, new neurons are incorporated to the dentate gyrus of the hippocampus. During a critical window that lasts about two weeks, adult-born immature neurons are more excitable and plastic than mature ones, and they respond to a wider range of inputs. In apparent contradiction, new neurons have been shown to be crucial to solve behavioral tasks that involve the discrimination of very similar situations, which would instead require high input specificity. We propose that immature neurons are initially unspecific because their task is to identify novel elements inside a high dimensional input space. With maturation, they would specialize to represent details of these novel inputs, favoring discrimination.

The storage capacity of Potts models for semantic memory retrieval

We introduce and analyse a minimal network model of semantic memory in the human brain. The model is a global associative memory structured as a collection of N local modules, each coding a feature, which can take S possible values, with a global sparseness a (the average fraction of features describing a concept). We show that, under optimal conditions, the number cM of modules connected on average to a module can range widely between very sparse connectivity (high dilution, ) and full connectivity (), maintaining a global network storage capacity (the maximum number pc of stored and retrievable concepts) that scales like pc~cMS2/a, with logarithmic corrections consistent with the constraint that each synapse may store up to a fraction of a bit.

The complexity of latching transitions in large scale cortical networks

We study latching dynamics, i.e. the ability of a network to hop spontaneously from one discrete attractor state to another, which has been proposed as a model of an infinitely recursive process in large scale cortical networks, perhaps associated with higher cortical functions, such as language. We show that latching dynamics can span the range from deterministic to random under the control of a threshold parameter U. In particular, the interesting intermediate case is characterized by an asymmetric and complex set of transitions. We also indicate how finite latching sequences can become infinite, depending on the properties of the transition probability matrix and of its eigenvalues.

Uninformative memories will prevail: the storage of correlated representations and its consequences.

Autoassociative networks were proposed in the 80s as simplified models of memory function in the brain, using recurrent connectivity with Hebbian plasticity to store patterns of neural activity that can be later recalled. This type of computation has been suggested to take place in the CA3 region of the hippocampus and at several levels in the cortex. One of the weaknesses of these models is their apparent inability to store correlated patterns of activity. We show, however, that a small and biologically plausible modification in the “learning rule” (associating to each neuron a plasticity threshold that reflects its popularity) enables the network to handle correlations. We study the stability properties of the resulting memories (in terms of their resistance to the damage of neurons or synapses), finding a novel property of autoassociative networks: not all memories are equally robust, and the most informative are also the most sensitive to damage. We relate these results to category‐specific effects in semantic memory patients, where concepts related to “non‐living things” are usually more resistant to brain damage than those related to “living things,” a phenomenon suspected to be rooted in the correlation between representations of concepts in the cortex.