Emilio Kropff - Academia.edu (original) (raw)

Papers by Emilio Kropff

Journal of Statistical Mechanics: Theory and Experiment, 2013

What sort of grid cells do we expect to see in rodents who have spent their developmental period ... more What sort of grid cells do we expect to see in rodents who have spent their developmental period inside a large spherical cage? Or, in a different experimental paradigm, toddling on a revolving ball, with virtual reality simulating a coherently revolving surround? We consider a simple model of grid firing map formation, based on firing rate adaptation, that we have earlier analyzed when playing out on a flat environment. The model predicts that whether experienced on the outside or inside, a spherical environment induces one of a succession of grid maps realized as combinations of spherical harmonics, depending on the relation of the radius to the preferred grid spacing, itself related to the parameters of firing rate adaptation. Numerical simulations concur with analytical predictions.

Biological Cybernetics, 2012

The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cor... more 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 singleunit 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

Behavioral and Brain Sciences, 2013

We show that, given extensive exploration of a three-dimensional volume, grid units can form with... more We show that, given extensive exploration of a three-dimensional volume, grid units can form with the approximate periodicity of a face-centered cubic crystal, as the spontaneous product of a self-organizing process at the single unit level, driven solely by firing rate adaptation.

HFSP Journal, 2007

Autoassociative networks were proposed in the 80's as simplified models of memory function in the... more Autoassociative networks were proposed in the 80's 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.

Hippocampus, 2008

Individual medial entorhinal cortex (mEC) 'grid' cells provide a representation of space that app... more 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. V

New Journal of Physics, 2008

Potts networks, in certain conditions, hop spontaneously from one discrete attractor state to ano... more 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.

Natural Computing, 2007

We study latching dynamics, i.e. the ability of a network to hop spontaneously from one discrete ... more 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.

Journal of Statistical Mechanics: Theory and Experiment, 2005

Journal of Statistical Mechanics: Theory and Experiment, 2013

What sort of grid cells do we expect to see in rodents who have spent their developmental period ... more What sort of grid cells do we expect to see in rodents who have spent their developmental period inside a large spherical cage? Or, in a different experimental paradigm, toddling on a revolving ball, with virtual reality simulating a coherently revolving surround? We consider a simple model of grid firing map formation, based on firing rate adaptation, that we have earlier analyzed when playing out on a flat environment. The model predicts that whether experienced on the outside or inside, a spherical environment induces one of a succession of grid maps realized as combinations of spherical harmonics, depending on the relation of the radius to the preferred grid spacing, itself related to the parameters of firing rate adaptation. Numerical simulations concur with analytical predictions.

Individual medial entorhinal cortex (mEC) 'grid' cells provide a representation of space that app... more 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. lf this is the case, then the topology of the environment in which the development takes place should affect the way the grid final configuration appears.

Biological Cybernetics, 2012

The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cor... more 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 singleunit 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

Behavioral and Brain Sciences, 2013

We show that, given extensive exploration of a three-dimensional volume, grid units can form with... more We show that, given extensive exploration of a three-dimensional volume, grid units can form with the approximate periodicity of a face-centered cubic crystal, as the spontaneous product of a self-organizing process at the single unit level, driven solely by firing rate adaptation.

ABSTRACT The parallel distributed processing (PDP) perspective brings forward the important point... more ABSTRACT The parallel distributed processing (PDP) perspective brings forward the important point that all semantic phenomena are based on analog underlying mechanisms, involving the weighted summation of multiple inputs by individual neurons. It falls short of indicating, however, how the essentially discrete nature of semantic processing may emerge at the cognitive level. Bridging this gap probably requires attractor networks.

Annual Review of Neuroscience, 2008

More than three decades of research have demonstrated a role for hippocampal place cells in repre... more 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.

Neuron, 2015

Developing granule cells (GCs) of the adult dentate gyrus undergo a critical period of enhanced a... more Developing granule cells (GCs) of the adult dentate gyrus undergo a critical period of enhanced activity and synaptic plasticity before becoming mature. The impact of developing GCs on the activity of preexisting dentate circuits remains unknown. Here we combine optogenetics, acute slice electrophysiology, and in vivo chemogenetics to activate GCs at different stages of maturation to study the recruitment of local target networks. We show that immature (4-week-old) GCs can efficiently drive distal CA3 targets but poorly activate proximal interneurons responsible for feedback inhibition (FBI). As new GCs transition toward maturity, they reliably recruit GABAergic feedback loops that restrict spiking of neighbor GCs, a mechanism that would promote sparse coding. Such inhibitory loop impinges only weakly in new cohorts of young GCs. A computational model reveals that the delayed coupling of new GCs to FBI could be crucial to achieve a fine-grain representation of novel inputs in the dentate gyrus.

Science, 2008

We report the existence of an entorhinal cell type that fires when an animal is close to the bord... more 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.

Journal of Statistical Mechanics: Theory and Experiment, 2013

What sort of grid cells do we expect to see in rodents who have spent their developmental period ... more What sort of grid cells do we expect to see in rodents who have spent their developmental period inside a large spherical cage? Or, in a different experimental paradigm, toddling on a revolving ball, with virtual reality simulating a coherently revolving surround? We consider a simple model of grid firing map formation, based on firing rate adaptation, that we have earlier analyzed when playing out on a flat environment. The model predicts that whether experienced on the outside or inside, a spherical environment induces one of a succession of grid maps realized as combinations of spherical harmonics, depending on the relation of the radius to the preferred grid spacing, itself related to the parameters of firing rate adaptation. Numerical simulations concur with analytical predictions.

Biological Cybernetics, 2012

The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cor... more 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 singleunit 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

Behavioral and Brain Sciences, 2013

We show that, given extensive exploration of a three-dimensional volume, grid units can form with... more We show that, given extensive exploration of a three-dimensional volume, grid units can form with the approximate periodicity of a face-centered cubic crystal, as the spontaneous product of a self-organizing process at the single unit level, driven solely by firing rate adaptation.

HFSP Journal, 2007

Autoassociative networks were proposed in the 80's as simplified models of memory function in the... more Autoassociative networks were proposed in the 80's 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.

Hippocampus, 2008

Individual medial entorhinal cortex (mEC) 'grid' cells provide a representation of space that app... more 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. V

New Journal of Physics, 2008

Potts networks, in certain conditions, hop spontaneously from one discrete attractor state to ano... more 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.

Natural Computing, 2007

We study latching dynamics, i.e. the ability of a network to hop spontaneously from one discrete ... more 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.

Journal of Statistical Mechanics: Theory and Experiment, 2005

Journal of Statistical Mechanics: Theory and Experiment, 2013

What sort of grid cells do we expect to see in rodents who have spent their developmental period ... more What sort of grid cells do we expect to see in rodents who have spent their developmental period inside a large spherical cage? Or, in a different experimental paradigm, toddling on a revolving ball, with virtual reality simulating a coherently revolving surround? We consider a simple model of grid firing map formation, based on firing rate adaptation, that we have earlier analyzed when playing out on a flat environment. The model predicts that whether experienced on the outside or inside, a spherical environment induces one of a succession of grid maps realized as combinations of spherical harmonics, depending on the relation of the radius to the preferred grid spacing, itself related to the parameters of firing rate adaptation. Numerical simulations concur with analytical predictions.

Individual medial entorhinal cortex (mEC) 'grid' cells provide a representation of space that app... more 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. lf this is the case, then the topology of the environment in which the development takes place should affect the way the grid final configuration appears.

Biological Cybernetics, 2012

The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cor... more 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 singleunit 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

Behavioral and Brain Sciences, 2013

We show that, given extensive exploration of a three-dimensional volume, grid units can form with... more We show that, given extensive exploration of a three-dimensional volume, grid units can form with the approximate periodicity of a face-centered cubic crystal, as the spontaneous product of a self-organizing process at the single unit level, driven solely by firing rate adaptation.

ABSTRACT The parallel distributed processing (PDP) perspective brings forward the important point... more ABSTRACT The parallel distributed processing (PDP) perspective brings forward the important point that all semantic phenomena are based on analog underlying mechanisms, involving the weighted summation of multiple inputs by individual neurons. It falls short of indicating, however, how the essentially discrete nature of semantic processing may emerge at the cognitive level. Bridging this gap probably requires attractor networks.

Annual Review of Neuroscience, 2008

More than three decades of research have demonstrated a role for hippocampal place cells in repre... more 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.

Neuron, 2015

Developing granule cells (GCs) of the adult dentate gyrus undergo a critical period of enhanced a... more Developing granule cells (GCs) of the adult dentate gyrus undergo a critical period of enhanced activity and synaptic plasticity before becoming mature. The impact of developing GCs on the activity of preexisting dentate circuits remains unknown. Here we combine optogenetics, acute slice electrophysiology, and in vivo chemogenetics to activate GCs at different stages of maturation to study the recruitment of local target networks. We show that immature (4-week-old) GCs can efficiently drive distal CA3 targets but poorly activate proximal interneurons responsible for feedback inhibition (FBI). As new GCs transition toward maturity, they reliably recruit GABAergic feedback loops that restrict spiking of neighbor GCs, a mechanism that would promote sparse coding. Such inhibitory loop impinges only weakly in new cohorts of young GCs. A computational model reveals that the delayed coupling of new GCs to FBI could be crucial to achieve a fine-grain representation of novel inputs in the dentate gyrus.

Science, 2008

We report the existence of an entorhinal cell type that fires when an animal is close to the bord... more 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.