1
|
Redman WT, Acosta-Mendoza S, Wei XX, Goard MJ. Robust variability of grid cell properties within individual grid modules enhances encoding of local space. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.02.27.582373. [PMID: 38915504 PMCID: PMC11195105 DOI: 10.1101/2024.02.27.582373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/26/2024]
Abstract
Although grid cells are one of the most well studied functional classes of neurons in the mammalian brain, the assumption that there is a single grid orientation and spacing per grid module has not been carefully tested. We investigate and analyze a recent large-scale recording of medial entorhinal cortex to characterize the presence and degree of heterogeneity of grid properties within individual modules. We find evidence for small, but robust, variability and hypothesize that this property of the grid code could enhance the ability of encoding local spatial information. Performing analysis on synthetic populations of grid cells, where we have complete control over the amount heterogeneity in grid properties, we demonstrate that variability, of a similar magnitude to the analyzed data, leads to significantly decreased decoding error, even when restricted to activity from a single module. Our results highlight how the heterogeneity of the neural response properties may benefit coding and opens new directions for theoretical and experimental analysis of grid cells.
Collapse
Affiliation(s)
- William T Redman
- Interdepartmental Graduate Program in Dynamical Neuroscience, University of California, Santa Barbara
- Intelligent Systems Center, Johns Hopkins University Applied Physics Lab
| | - Santiago Acosta-Mendoza
- Interdepartmental Graduate Program in Dynamical Neuroscience, University of California, Santa Barbara
| | - Xue-Xin Wei
- Department of Neuroscience, The University of Texas at Austin
- Department of Psychology, The University of Texas at Austin
- Center for Perceptual Systems, The University of Texas at Austin
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin
| | - Michael J Goard
- Department of Psychological and Brain Sciences, University of California, Santa Barbara
- Department of Molecular, Cellular, and Developmental Biology, University of California, Santa Barbara
- Neuroscience Research Institute, University of California Santa Barbara
| |
Collapse
|
2
|
Ingrosso A, Panizon E. Machine learning at the mesoscale: A computation-dissipation bottleneck. Phys Rev E 2024; 109:014132. [PMID: 38366483 DOI: 10.1103/physreve.109.014132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 12/05/2023] [Indexed: 02/18/2024]
Abstract
The cost of information processing in physical systems calls for a trade-off between performance and energetic expenditure. Here we formulate and study a computation-dissipation bottleneck in mesoscopic systems used as input-output devices. Using both real data sets and synthetic tasks, we show how nonequilibrium leads to enhanced performance. Our framework sheds light on a crucial compromise between information compression, input-output computation and dynamic irreversibility induced by nonreciprocal interactions.
Collapse
Affiliation(s)
- Alessandro Ingrosso
- Quantitative Life Sciences, Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, Italy
| | - Emanuele Panizon
- Quantitative Life Sciences, Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, Italy
| |
Collapse
|
3
|
Nardin M, Csicsvari J, Tkačik G, Savin C. The Structure of Hippocampal CA1 Interactions Optimizes Spatial Coding across Experience. J Neurosci 2023; 43:8140-8156. [PMID: 37758476 PMCID: PMC10697404 DOI: 10.1523/jneurosci.0194-23.2023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Revised: 09/11/2023] [Accepted: 09/14/2023] [Indexed: 10/03/2023] Open
Abstract
Although much is known about how single neurons in the hippocampus represent an animal's position, how circuit interactions contribute to spatial coding is less well understood. Using a novel statistical estimator and theoretical modeling, both developed in the framework of maximum entropy models, we reveal highly structured CA1 cell-cell interactions in male rats during open field exploration. The statistics of these interactions depend on whether the animal is in a familiar or novel environment. In both conditions the circuit interactions optimize the encoding of spatial information, but for regimes that differ in the informativeness of their spatial inputs. This structure facilitates linear decodability, making the information easy to read out by downstream circuits. Overall, our findings suggest that the efficient coding hypothesis is not only applicable to individual neuron properties in the sensory periphery, but also to neural interactions in the central brain.SIGNIFICANCE STATEMENT Local circuit interactions play a key role in neural computation and are dynamically shaped by experience. However, measuring and assessing their effects during behavior remains a challenge. Here, we combine techniques from statistical physics and machine learning to develop new tools for determining the effects of local network interactions on neural population activity. This approach reveals highly structured local interactions between hippocampal neurons, which make the neural code more precise and easier to read out by downstream circuits, across different levels of experience. More generally, the novel combination of theory and data analysis in the framework of maximum entropy models enables traditional neural coding questions to be asked in naturalistic settings.
Collapse
Affiliation(s)
- Michele Nardin
- Institute of Science and Technology Austria, Klosterneuburg AT-3400, Austria
- Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, Virginia 20147
| | - Jozsef Csicsvari
- Institute of Science and Technology Austria, Klosterneuburg AT-3400, Austria
| | - Gašper Tkačik
- Institute of Science and Technology Austria, Klosterneuburg AT-3400, Austria
| | - Cristina Savin
- Center for Neural Science, New York University, New York, New York 10003
- Center for Data Science, New York University, New York, New York 10011
| |
Collapse
|
4
|
Guardamagna M, Stella F, Battaglia FP. Heterogeneity of network and coding states in mouse CA1 place cells. Cell Rep 2023; 42:112022. [PMID: 36709427 DOI: 10.1016/j.celrep.2023.112022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Revised: 10/20/2022] [Accepted: 01/06/2023] [Indexed: 01/29/2023] Open
Abstract
Theta sequences and phase precession shape hippocampal activity and are considered key underpinnings of memory formation. Theta sequences are sweeps of spikes from multiple cells, tracing trajectories from past to future. Phase precession is the correlation between theta firing phase and animal position. Here, we reconsider these temporal processes in CA1 and the computational principles that they are thought to obey. We find stronger heterogeneity than previously described: we identify cells that do not phase precess but reliably express theta sequences. Other cells phase precess only when medium gamma (linked to entorhinal inputs) is strongest. The same cells express more sequences, but not precession, when slow gamma (linked to CA3 inputs) dominates. Moreover, sequences occur independently in distinct cell groups. Our results challenge the view that phase precession is the mechanism underlying the emergence of theta sequences, suggesting a role for CA1 cells in multiplexing diverse computational processes.
Collapse
Affiliation(s)
- Matteo Guardamagna
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway
| | - Federico Stella
- Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, the Netherlands
| | - Francesco P Battaglia
- Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, the Netherlands.
| |
Collapse
|
5
|
Morris G, Derdikman D. The chicken and egg problem of grid cells and place cells. Trends Cogn Sci 2023; 27:125-138. [PMID: 36437188 DOI: 10.1016/j.tics.2022.11.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Revised: 11/02/2022] [Accepted: 11/02/2022] [Indexed: 11/26/2022]
Abstract
Place cells and grid cells are major building blocks of the hippocampal cognitive map. The prominent forward model postulates that grid-cell modules are generated by a continuous attractor network; that a velocity signal evoked during locomotion moves entorhinal activity bumps; and that place-cell activity constitutes summation of entorhinal grid-cell modules. Experimental data support the first postulate, but not the latter two. Several families of solutions that depart from these postulates have been put forward. We suggest a modified model (spatial modulation continuous attractor network; SCAN), whereby place cells are generated from spatially selective nongrid cells. Locomotion causes these cells to move the hippocampal activity bump, leading to movement of the entorhinal manifolds. Such inversion accords with the shift of hippocampal thought from navigation to more abstract functions.
Collapse
Affiliation(s)
- Genela Morris
- Department of Neuroscience, Rappaport Faculty of Medicine and Research Institute, Technion - Israel Institute of Technology, Haifa, Israel; Tel Aviv Sourasky Medical Center, Tel Aviv, Israel.
| | - Dori Derdikman
- Department of Neuroscience, Rappaport Faculty of Medicine and Research Institute, Technion - Israel Institute of Technology, Haifa, Israel.
| |
Collapse
|
6
|
Tukker JJ, Beed P, Brecht M, Kempter R, Moser EI, Schmitz D. Microcircuits for spatial coding in the medial entorhinal cortex. Physiol Rev 2022; 102:653-688. [PMID: 34254836 PMCID: PMC8759973 DOI: 10.1152/physrev.00042.2020] [Citation(s) in RCA: 23] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
The hippocampal formation is critically involved in learning and memory and contains a large proportion of neurons encoding aspects of the organism's spatial surroundings. In the medial entorhinal cortex (MEC), this includes grid cells with their distinctive hexagonal firing fields as well as a host of other functionally defined cell types including head direction cells, speed cells, border cells, and object-vector cells. Such spatial coding emerges from the processing of external inputs by local microcircuits. However, it remains unclear exactly how local microcircuits and their dynamics within the MEC contribute to spatial discharge patterns. In this review we focus on recent investigations of intrinsic MEC connectivity, which have started to describe and quantify both excitatory and inhibitory wiring in the superficial layers of the MEC. Although the picture is far from complete, it appears that these layers contain robust recurrent connectivity that could sustain the attractor dynamics posited to underlie grid pattern formation. These findings pave the way to a deeper understanding of the mechanisms underlying spatial navigation and memory.
Collapse
Affiliation(s)
- John J Tukker
- German Center for Neurodegenerative Diseases (DZNE) Berlin, Berlin, Germany
| | - Prateep Beed
- Neuroscience Research Center, Charité-Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humbold-Universität zu Berlin, Berlin, Germany
- Berlin Institute of Health at Charité-Universitätsmedizin Berlin, Berlin, Germany
| | - Michael Brecht
- Bernstein Center for Computational Neuroscience, Humboldt-Universität zu Berlin, Berlin, Germany
- Neurocure Cluster of Excellence, Charité-Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
- Einstein Center for Neurosciences Berlin, Charité-Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
| | - Richard Kempter
- Institute for Theoretical Biology, Humboldt-Universität zu Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience, Humboldt-Universität zu Berlin, Berlin, Germany
- Einstein Center for Neurosciences Berlin, Charité-Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
| | - Edvard I Moser
- Einstein Center for Neurosciences Berlin, Charité-Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway
| | - Dietmar Schmitz
- German Center for Neurodegenerative Diseases (DZNE) Berlin, Berlin, Germany
- Neuroscience Research Center, Charité-Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humbold-Universität zu Berlin, Berlin, Germany
- Berlin Institute of Health at Charité-Universitätsmedizin Berlin, Berlin, Germany
- Neurocure Cluster of Excellence, Charité-Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
- Einstein Center for Neurosciences Berlin, Charité-Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
| |
Collapse
|
7
|
Hurwitz C, Kudryashova N, Onken A, Hennig MH. Building population models for large-scale neural recordings: Opportunities and pitfalls. Curr Opin Neurobiol 2021; 70:64-73. [PMID: 34411907 DOI: 10.1016/j.conb.2021.07.003] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Revised: 06/11/2021] [Accepted: 07/14/2021] [Indexed: 11/15/2022]
Abstract
Modern recording technologies now enable simultaneous recording from large numbers of neurons. This has driven the development of new statistical models for analyzing and interpreting neural population activity. Here, we provide a broad overview of recent developments in this area. We compare and contrast different approaches, highlight strengths and limitations, and discuss biological and mechanistic insights that these methods provide.
Collapse
Affiliation(s)
- Cole Hurwitz
- University of Edinburgh, Institute for Adaptive and Neural Computation Edinburgh, EH8 9AB, United Kingdom
| | - Nina Kudryashova
- University of Edinburgh, Institute for Adaptive and Neural Computation Edinburgh, EH8 9AB, United Kingdom
| | - Arno Onken
- University of Edinburgh, Institute for Adaptive and Neural Computation Edinburgh, EH8 9AB, United Kingdom
| | - Matthias H Hennig
- University of Edinburgh, Institute for Adaptive and Neural Computation Edinburgh, EH8 9AB, United Kingdom.
| |
Collapse
|
8
|
D'Albis T, Kempter R. Recurrent amplification of grid-cell activity. Hippocampus 2020; 30:1268-1297. [PMID: 33022854 DOI: 10.1002/hipo.23254] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2019] [Revised: 06/18/2020] [Accepted: 07/25/2020] [Indexed: 11/07/2022]
Abstract
High-level cognitive abilities such as navigation and spatial memory are thought to rely on the activity of grid cells in the medial entorhinal cortex (MEC), which encode the animal's position in space with periodic triangular patterns. Yet the neural mechanisms that underlie grid-cell activity are still unknown. Recent in vitro and in vivo experiments indicate that grid cells are embedded in highly structured recurrent networks. But how could recurrent connectivity become structured during development? And what is the functional role of these connections? With mathematical modeling and simulations, we show that recurrent circuits in the MEC could emerge under the supervision of weakly grid-tuned feedforward inputs. We demonstrate that a learned excitatory connectivity could amplify grid patterns when the feedforward sensory inputs are available and sustain attractor states when the sensory cues are lost. Finally, we propose a Fourier-based measure to quantify the spatial periodicity of grid patterns: the grid-tuning index.
Collapse
Affiliation(s)
- Tiziano D'Albis
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Richard Kempter
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Berlin, Germany.,Bernstein Center for Computational Neuroscience, Berlin, Germany.,Einstein Center for Neurosciences, Berlin, Germany
| |
Collapse
|
9
|
Vinepinsky E, Perchik S, Segev R. A Generalized Linear Model of a Navigation Network. Front Neural Circuits 2020; 14:56. [PMID: 33013326 PMCID: PMC7509173 DOI: 10.3389/fncir.2020.00056] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Accepted: 07/28/2020] [Indexed: 11/22/2022] Open
Abstract
Navigation by mammals is believed to rely on a network of neurons in the hippocampal formation, which includes the hippocampus, the medial entorhinal cortex (MEC), and additional nearby regions. Neurons in these regions represent spatial information by tuning to the position, orientation, and speed of the animal in the form of head direction cells, speed cells, grid cells, border cells, and unclassified spatially modulated cells. While the properties of single cells are well studied, little is known about the functional structure of the network in the MEC. Here, we use a generalized linear model to study the network of spatially modulated cells in the MEC. We found connectivity patterns between all spatially encoding cells and not only grid cells. In addition, the neurons’ past activity contributed to the overall activity patterns. Finally, position-modulated cells and head direction cells differed in the dependence of the activity on the history. Our results indicate that MEC neurons form a local interacting network to support spatial information representations and suggest an explanation for their complex temporal properties.
Collapse
Affiliation(s)
- Ehud Vinepinsky
- Department of Life Sciences, Ben Gurion University of the Negev, Beersheba, Israel.,Zlotowski Center for Neuroscience, Ben Gurion University of the Negev, Beersheba, Israel
| | - Shay Perchik
- Zlotowski Center for Neuroscience, Ben Gurion University of the Negev, Beersheba, Israel.,Department of Cognitive and Brain Sciences, Ben Gurion University of the Negev, Beersheba, Israel
| | - Ronen Segev
- Department of Life Sciences, Ben Gurion University of the Negev, Beersheba, Israel.,Zlotowski Center for Neuroscience, Ben Gurion University of the Negev, Beersheba, Israel.,Department of Biomedical Engineering, Ben Gurion University of the Negev, Beersheba, Israel
| |
Collapse
|
10
|
Terada Y, Obuchi T, Isomura T, Kabashima Y. Inferring Neuronal Couplings From Spiking Data Using a Systematic Procedure With a Statistical Criterion. Neural Comput 2020; 32:2187-2211. [PMID: 32946715 DOI: 10.1162/neco_a_01324] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
Recent remarkable advances in experimental techniques have provided a background for inferring neuronal couplings from point process data that include a great number of neurons. Here, we propose a systematic procedure for pre- and postprocessing generic point process data in an objective manner to handle data in the framework of a binary simple statistical model, the Ising or generalized McCulloch-Pitts model. The procedure has two steps: (1) determining time bin size for transforming the point process data into discrete-time binary data and (2) screening relevant couplings from the estimated couplings. For the first step, we decide the optimal time bin size by introducing the null hypothesis that all neurons would fire independently, then choosing a time bin size so that the null hypothesis is rejected with the strict criteria. The likelihood associated with the null hypothesis is analytically evaluated and used for the rejection process. For the second postprocessing step, after a certain estimator of coupling is obtained based on the preprocessed data set (any estimator can be used with the proposed procedure), the estimate is compared with many other estimates derived from data sets obtained by randomizing the original data set in the time direction. We accept the original estimate as relevant only if its absolute value is sufficiently larger than those of randomized data sets. These manipulations suppress false positive couplings induced by statistical noise. We apply this inference procedure to spiking data from synthetic and in vitro neuronal networks. The results show that the proposed procedure identifies the presence or absence of synaptic couplings fairly well, including their signs, for the synthetic and experimental data. In particular, the results support that we can infer the physical connections of underlying systems in favorable situations, even when using a simple statistical model.
Collapse
Affiliation(s)
- Yu Terada
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, Wako, Saitama 351-0198, Japan
| | - Tomoyuki Obuchi
- Department of Systems Science, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | - Takuya Isomura
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, Wako, Saitama 351-0198, Japan
| | - Yoshiyuki Kabashima
- Institute for Physics of Intelligence, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan
| |
Collapse
|
11
|
Nagele J, Herz AVM, Stemmler MB. Untethered firing fields and intermittent silences: Why grid-cell discharge is so variable. Hippocampus 2020; 30:367-383. [PMID: 32045073 DOI: 10.1002/hipo.23191] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2019] [Revised: 12/20/2019] [Accepted: 12/31/2019] [Indexed: 11/07/2022]
Abstract
Grid cells in medial entorhinal cortex are notoriously variable in their responses, despite the striking hexagonal arrangement of their spatial firing fields. Indeed, when the animal moves through a firing field, grid cells often fire much more vigorously than predicted or do not fire at all. The source of this trial-to-trial variability is not completely understood. By analyzing grid-cell spike trains from mice running in open arenas and on linear tracks, we characterize the phenomenon of "missed" firing fields using the statistical theory of zero inflation. We find that one major cause of grid-cell variability lies in the spatial representation itself: firing fields are not as strongly anchored to spatial location as the averaged grid suggests. In addition, grid fields from different cells drift together from trial to trial, regardless of whether the environment is real or virtual, or whether the animal moves in light or darkness. Spatial realignment across trials sharpens the grid representation, yielding firing fields that are more pronounced and significantly narrower. These findings indicate that ensembles of grid cells encode relative position more reliably than absolute position.
Collapse
Affiliation(s)
- Johannes Nagele
- Bernstein Center for Computational Neuroscience Munich and Faculty of Biology, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Andreas V M Herz
- Bernstein Center for Computational Neuroscience Munich and Faculty of Biology, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Martin B Stemmler
- Bernstein Center for Computational Neuroscience Munich and Faculty of Biology, Ludwig-Maximilians-Universität München, Munich, Germany
| |
Collapse
|
12
|
Cubero RJ, Marsili M, Roudi Y. Multiscale relevance and informative encoding in neuronal spike trains. J Comput Neurosci 2020; 48:85-102. [PMID: 31993923 PMCID: PMC7035307 DOI: 10.1007/s10827-020-00740-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Revised: 12/20/2019] [Accepted: 01/03/2020] [Indexed: 11/26/2022]
Abstract
Neuronal responses to complex stimuli and tasks can encompass a wide range of time scales. Understanding these responses requires measures that characterize how the information on these response patterns are represented across multiple temporal resolutions. In this paper we propose a metric - which we call multiscale relevance (MSR) - to capture the dynamical variability of the activity of single neurons across different time scales. The MSR is a non-parametric, fully featureless indicator in that it uses only the time stamps of the firing activity without resorting to any a priori covariate or invoking any specific structure in the tuning curve for neural activity. When applied to neural data from the mEC and from the ADn and PoS regions of freely-behaving rodents, we found that neurons having low MSR tend to have low mutual information and low firing sparsity across the correlates that are believed to be encoded by the region of the brain where the recordings were made. In addition, neurons with high MSR contain significant information on spatial navigation and allow to decode spatial position or head direction as efficiently as those neurons whose firing activity has high mutual information with the covariate to be decoded and significantly better than the set of neurons with high local variations in their interspike intervals. Given these results, we propose that the MSR can be used as a measure to rank and select neurons for their information content without the need to appeal to any a priori covariate.
Collapse
Affiliation(s)
- Ryan John Cubero
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology (NTNU), Trondheim, Norway.
- The Abdus Salam International Center for Theoretical Physics, Trieste, Italy.
- Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy.
- IST Austria, Klosterneuburg, Austria.
| | - Matteo Marsili
- The Abdus Salam International Center for Theoretical Physics, Trieste, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, Italy
| | - Yasser Roudi
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| |
Collapse
|
13
|
Peraza-Goicolea JA, Martínez-Montes E, Aubert E, Valdés-Hernández PA, Mulet R. Modeling functional resting-state brain networks through neural message passing on the human connectome. Neural Netw 2019; 123:52-69. [PMID: 31830607 DOI: 10.1016/j.neunet.2019.11.014] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2019] [Revised: 11/13/2019] [Accepted: 11/18/2019] [Indexed: 10/25/2022]
Abstract
In this work, we propose a natural model for information flow in the brain through a neural message-passing dynamics on a structural network of macroscopic regions, such as the human connectome (HC). In our model, each brain region is assumed to have a binary behavior (active or not), the strengths of interactions among them are encoded in the anatomical connectivity matrix defined by the HC, and the dynamics of the system is defined by the Belief Propagation (BP) algorithm, working near the critical point of the network. We show that in the absence of direct external stimuli the BP algorithm converges to a spatial map of activations that is similar to the Default Mode Network (DMN) of the brain, which has been defined from the analysis of functional MRI data. Moreover, we use Susceptibility Propagation (SP) to compute the matrix of long-range correlations between the different regions and show that the modules defined by a clustering of this matrix resemble several Resting State Networks (RSN) determined experimentally. Both results suggest that the functional DMN and RSNs can be seen as simple consequences of the anatomical structure of the brain and a neural message-passing dynamics between macroscopic regions. With the new model, we explore predictions on how functional maps change when the anatomical brain network suffers structural alterations, like in Alzheimer's disease and in lesions of the Corpus Callosum. The implications and novel interpretations suggested by the model, as well as the role of criticality, are discussed.
Collapse
Affiliation(s)
- Julio A Peraza-Goicolea
- Group of Complex Systems and Statistical Physics, Department of Theoretical Physics, University of Havana, Havana, Cuba; Department of Physics, Florida International University, Miami, FL, USA.
| | - Eduardo Martínez-Montes
- Neuroinformatics Department, Cuban Neuroscience Center, Havana, Cuba; Advanced Center for Electrical and Electronic Engineering (AC3E), Universidad Técnica Federico Santa María, Valparaíso, Chile.
| | - Eduardo Aubert
- Neuroinformatics Department, Cuban Neuroscience Center, Havana, Cuba.
| | | | - Roberto Mulet
- Group of Complex Systems and Statistical Physics, Department of Theoretical Physics, University of Havana, Havana, Cuba.
| |
Collapse
|
14
|
Kang L, DeWeese MR. Replay as wavefronts and theta sequences as bump oscillations in a grid cell attractor network. eLife 2019; 8:46351. [PMID: 31736462 PMCID: PMC6901334 DOI: 10.7554/elife.46351] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2019] [Accepted: 11/15/2019] [Indexed: 11/17/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Louis Kang
- Redwood Center for Theoretical Neuroscience, Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States.,Department of Physics, University of California, Berkeley, Berkeley, United States
| | - Michael R DeWeese
- Redwood Center for Theoretical Neuroscience, Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States.,Department of Physics, University of California, Berkeley, Berkeley, United States
| |
Collapse
|
15
|
Monsalve‐Mercado MM, Roudi Y. Hippocampal spike‐time correlations and place field overlaps during open field foraging. Hippocampus 2019; 30:354-366. [DOI: 10.1002/hipo.23173] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Revised: 10/05/2019] [Accepted: 10/08/2019] [Indexed: 11/05/2022]
Affiliation(s)
- Mauro M. Monsalve‐Mercado
- Physik‐Department Technische Universitat Munchen Munich Germany
- Center for Theoretical Neuroscience Zuckerman Institute, Columbia University New York New York
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, NTNU Trondheim Norway
| | - Yasser Roudi
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, NTNU Trondheim Norway
| |
Collapse
|
16
|
Almog N, Tocker G, Bonnevie T, Moser EI, Moser MB, Derdikman D. During hippocampal inactivation, grid cells maintain synchrony, even when the grid pattern is lost. eLife 2019; 8:e47147. [PMID: 31621577 PMCID: PMC6797478 DOI: 10.7554/elife.47147] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2019] [Accepted: 10/03/2019] [Indexed: 11/29/2022] Open
Abstract
The grid cell network in the medial entorhinal cortex (MEC) has been subject to thorough testing and analysis, and many theories for their formation have been suggested. To test some of these theories, we re-analyzed data from Bonnevie et al., 2013, in which the hippocampus was inactivated and grid cells were recorded in the rat MEC. We investigated whether the firing associations of grid cells depend on hippocampal inputs. Specifically, we examined temporal and spatial correlations in the firing times of simultaneously recorded grid cells before and during hippocampal inactivation. Our analysis revealed evidence of network coherence in grid cells even in the absence of hippocampal input to the MEC, both in regular grid cells and in those that became head-direction cells after hippocampal inactivation. This favors models, which suggest that phase relations between grid cells in the MEC are dependent on intrinsic connectivity within the MEC.
Collapse
Affiliation(s)
- Noam Almog
- Rappaport Faculty of Medicine and Research InstituteTechnion – Israel Institute of TechnologyHaifaIsrael
| | - Gilad Tocker
- Rappaport Faculty of Medicine and Research InstituteTechnion – Israel Institute of TechnologyHaifaIsrael
- Gonda Multidisciplinary Brain Research CenterBar Ilan UniversityRamat GanIsrael
| | - Tora Bonnevie
- Kavli Institute for Systems Neuroscience and Centre for Neural ComputationNorwegian University of Science and TechnologyTrondheimNorway
| | - Edvard I Moser
- Kavli Institute for Systems Neuroscience and Centre for Neural ComputationNorwegian University of Science and TechnologyTrondheimNorway
| | - May-Britt Moser
- Kavli Institute for Systems Neuroscience and Centre for Neural ComputationNorwegian University of Science and TechnologyTrondheimNorway
| | - Dori Derdikman
- Rappaport Faculty of Medicine and Research InstituteTechnion – Israel Institute of TechnologyHaifaIsrael
| |
Collapse
|
17
|
Kang L, Balasubramanian V. A geometric attractor mechanism for self-organization of entorhinal grid modules. eLife 2019; 8:46687. [PMID: 31373556 PMCID: PMC6776444 DOI: 10.7554/elife.46687] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2019] [Accepted: 08/01/2019] [Indexed: 11/13/2022] Open
Abstract
Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of 'grid fields' in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4-1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.
Collapse
Affiliation(s)
- Louis Kang
- David Rittenhouse Laboratories, University of Pennsylvania, Philadelphia, United States.,Redwood Center for Theoretical Neuroscience, University of California, Berkeley, Berkeley, United States
| | - Vijay Balasubramanian
- David Rittenhouse Laboratories, University of Pennsylvania, Philadelphia, United States
| |
Collapse
|
18
|
Abstract
We investigate the complexity of logistic regression models, which is defined by counting the number of indistinguishable distributions that the model can represent (Balasubramanian, 1997). We find that the complexity of logistic models with binary inputs depends not only on the number of parameters but also on the distribution of inputs in a nontrivial way that standard treatments of complexity do not address. In particular, we observe that correlations among inputs induce effective dependencies among parameters, thus constraining the model and, consequently, reducing its complexity. We derive simple relations for the upper and lower bounds of the complexity. Furthermore, we show analytically that defining the model parameters on a finite support rather than the entire axis decreases the complexity in a manner that critically depends on the size of the domain. Based on our findings, we propose a novel model selection criterion that takes into account the entropy of the input distribution. We test our proposal on the problem of selecting the input variables of a logistic regression model in a Bayesian model selection framework. In our numerical tests, we find that while the reconstruction errors of standard model selection approaches (AIC, BIC, ℓ1 regularization) strongly depend on the sparsity of the ground truth, the reconstruction error of our method is always close to the minimum in all conditions of sparsity, data size, and strength of input correlations. Finally, we observe that when considering categorical instead of binary inputs, in a simple and mathematically tractable case, the contribution of the alphabet size to the complexity is very small compared to that of parameter space dimension. We further explore the issue by analyzing the data set of the "13 keys to the White House," a method for forecasting the outcomes of US presidential elections.
Collapse
Affiliation(s)
- Nicola Bulso
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Matteo Marsili
- The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy
| | - Yasser Roudi
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| |
Collapse
|
19
|
Liu H, Bridges D, Randall C, Solla SA, Wu B, Hansma P, Yan X, Kosik KS, Bouchard K. In vitro validation of in silico identified inhibitory interactions. J Neurosci Methods 2019; 321:39-48. [PMID: 30965073 DOI: 10.1016/j.jneumeth.2019.04.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2019] [Accepted: 04/01/2019] [Indexed: 10/27/2022]
Abstract
BACKGROUND Understanding how neuronal signals propagate in local network is an important step in understanding information processing. As a result, spike trains recorded with multi-electrode arrays (MEAs) have been widely used to study the function of neural networks. Studying the dynamics of neuronal networks requires the identification of both excitatory and inhibitory connections. The detection of excitatory relationships can robustly be inferred by characterizing the statistical relationships of neural spike trains. However, the identification of inhibitory relationships is more difficult: distinguishing endogenous low firing rates from active inhibition is not obvious. NEW METHOD In this paper, we propose an in silico interventional procedure that makes predictions about the effect of stimulating or inhibiting single neurons on other neurons, and thereby gives the ability to accurately identify inhibitory effects. COMPARISON To experimentally test these predictions, we have developed a Neural Circuit Probe (NCP) that delivers drugs transiently and reversibly on individually identified neurons to assess their contributions to the neural circuit behavior. RESULTS Using the NCP, putative inhibitory connections identified by the in silico procedure were validated through in vitro interventional experiments. CONCLUSIONS Together, these results demonstrate how detailed microcircuitry can be inferred from statistical models derived from neurophysiology data.
Collapse
Affiliation(s)
- Honglei Liu
- Department of Computer Science, University of California, Santa Barbara, CA, USA
| | - Daniel Bridges
- Department of Physics, University of California, Santa Barbara, CA, USA
| | - Connor Randall
- Department of Physics, University of California, Santa Barbara, CA, USA
| | - Sara A Solla
- Department of Physiology, Northwestern University, Chicago, IL, USA
| | - Bian Wu
- Neuroscience Research Institute, University of California, Santa Barbara, CA, USA; Department of Molecular Cellular and Developmental Biology, University of California, Santa Barbara, CA, USA
| | - Paul Hansma
- Department of Physics, University of California, Santa Barbara, CA, USA
| | - Xifeng Yan
- Department of Computer Science, University of California, Santa Barbara, CA, USA
| | - Kenneth S Kosik
- Neuroscience Research Institute, University of California, Santa Barbara, CA, USA.
| | - Kristofer Bouchard
- Biological Systems and Engineering Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA; Helen Wills Neuroscience Institute and Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA, USA.
| |
Collapse
|
20
|
Xu ZQJ, Crodelle J, Zhou D, Cai D. Maximum entropy principle analysis in network systems with short-time recordings. Phys Rev E 2019; 99:022409. [PMID: 30934291 DOI: 10.1103/physreve.99.022409] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2018] [Indexed: 11/07/2022]
Abstract
In many realistic systems, maximum entropy principle (MEP) analysis provides an effective characterization of the probability distribution of network states. However, to implement the MEP analysis, a sufficiently long-time data recording in general is often required, e.g., hours of spiking recordings of neurons in neuronal networks. The issue of whether the MEP analysis can be successfully applied to network systems with data from short-time recordings has yet to be fully addressed. In this work, we investigate relationships underlying the probability distributions, moments, and effective interactions in the MEP analysis and then show that, with short-time recordings of network dynamics, the MEP analysis can be applied to reconstructing probability distributions of network states that is much more accurate than the one directly measured from the short-time recording. Using spike trains obtained from both Hodgkin-Huxley neuronal networks and electrophysiological experiments, we verify our results and demonstrate that MEP analysis provides a tool to investigate the neuronal population coding properties for short-time recordings.
Collapse
Affiliation(s)
- Zhi-Qin John Xu
- NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
| | - Jennifer Crodelle
- Courant Institute of Mathematical Sciences, New York University, New York, New York, USA
| | - Douglas Zhou
- School of Mathematical Sciences, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, P.R. China
| | - David Cai
- NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates.,Courant Institute of Mathematical Sciences, New York University, New York, New York, USA.,School of Mathematical Sciences, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, P.R. China.,Center for Neural Science, New York University, New York, New York, USA
| |
Collapse
|
21
|
Hippocampal Reactivation of Random Trajectories Resembling Brownian Diffusion. Neuron 2019; 102:450-461.e7. [DOI: 10.1016/j.neuron.2019.01.052] [Citation(s) in RCA: 65] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2018] [Revised: 12/11/2018] [Accepted: 01/25/2019] [Indexed: 12/25/2022]
|
22
|
Correlation structure of grid cells is preserved during sleep. Nat Neurosci 2019; 22:598-608. [DOI: 10.1038/s41593-019-0360-0] [Citation(s) in RCA: 52] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2017] [Accepted: 02/06/2019] [Indexed: 01/16/2023]
|
23
|
Pastore VP, Massobrio P, Godjoski A, Martinoia S. Identification of excitatory-inhibitory links and network topology in large-scale neuronal assemblies from multi-electrode recordings. PLoS Comput Biol 2018; 14:e1006381. [PMID: 30148879 PMCID: PMC6128636 DOI: 10.1371/journal.pcbi.1006381] [Citation(s) in RCA: 48] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2017] [Revised: 09/07/2018] [Accepted: 07/20/2018] [Indexed: 12/23/2022] Open
Abstract
Functional-effective connectivity and network topology are nowadays key issues for studying brain physiological functions and pathologies. Inferring neuronal connectivity from electrophysiological recordings presents open challenges and unsolved problems. In this work, we present a cross-correlation based method for reliably estimating not only excitatory but also inhibitory links, by analyzing multi-unit spike activity from large-scale neuronal networks. The method is validated by means of realistic simulations of large-scale neuronal populations. New results related to functional connectivity estimation and network topology identification obtained by experimental electrophysiological recordings from high-density and large-scale (i.e., 4096 electrodes) microtransducer arrays coupled to in vitro neural populations are presented. Specifically, we show that: (i) functional inhibitory connections are accurately identified in in vitro cortical networks, providing that a reasonable firing rate and recording length are achieved; (ii) small-world topology, with scale-free and rich-club features are reliably obtained, on condition that a minimum number of active recording sites are available. The method and procedure can be directly extended and applied to in vivo multi-units brain activity recordings. The balance between excitation and inhibition is fundamental for proper brain functions and for this reason is precisely regulated in adult cortices. Impaired excitation/inhibition balance is often associated with several neurological disorders, such as epilepsy, autism and schizophrenia. However, estimating functional inhibitory connections is not an easy task and few methods are available to identify such connections from electrophysiological data. Here we present a cross-correlation based method to identify both excitatory and inhibitory functional connections in large-scale neuronal networks. The method is applicable to both in vitro and in vivo spike data recordings. Once a connectivity map (i.e. a graph) is obtained, we characterized the associated topology by means of classical graph theory metrics to unveil functional architecture. In this work, we analyze in vitro cortical networks probed by means of large-scale microelectrode arrays (i.e., 4096 sensors) and we derive network topologies from spike data. The functional organization found is called “small-world and scale-free” and is the same organization found in cortical in vivo brain regions by means of different experimental methods. We also show that to obtain reliable information about network architecture at least a network with a hundred of nodes-neurons is needed.
Collapse
Affiliation(s)
- Vito Paolo Pastore
- University of Genova, Dept. of Informatics, Bioengineering, Robotics and System Engineering, Genova, Italy
| | - Paolo Massobrio
- University of Genova, Dept. of Informatics, Bioengineering, Robotics and System Engineering, Genova, Italy
| | - Aleksandar Godjoski
- University of Genova, Dept. of Informatics, Bioengineering, Robotics and System Engineering, Genova, Italy
- 3Brain gmbh, Wädenswil, Switzerland
| | - Sergio Martinoia
- University of Genova, Dept. of Informatics, Bioengineering, Robotics and System Engineering, Genova, Italy
- CNR—Institute of Biophysics, Genova, Italy
- * E-mail:
| |
Collapse
|
24
|
Sizochenko N, Mikolajczyk A, Jagiello K, Puzyn T, Leszczynski J, Rasulev B. How the toxicity of nanomaterials towards different species could be simultaneously evaluated: a novel multi-nano-read-across approach. NANOSCALE 2018; 10:582-591. [PMID: 29168526 DOI: 10.1039/c7nr05618d] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Application of predictive modeling approaches can solve the problem of missing data. Numerous studies have investigated the effects of missing values on qualitative or quantitative modeling, but only a few studies have discussed it for the case of applications in nanotechnology-related data. The present study is aimed at the development of a multi-nano-read-across modeling technique that helps in predicting the toxicity of different species such as bacteria, algae, protozoa, and mammalian cell lines. Herein, the experimental toxicity of 184 metal and silica oxide (30 unique chemical types) nanoparticles from 15 datasets is analyzed. A hybrid quantitative multi-nano-read-across approach that combines interspecies correlation analysis and self-organizing map analysis is developed. In the first step, hidden patterns of toxicity among nanoparticles are identified using a combination of methods. Subsequently, the developed model based on categorization of the toxicity of the metal oxide nanoparticle outcomes is evaluated via the combination of supervised and unsupervised machine learning techniques to determine the underlying factors responsible for the toxicity.
Collapse
Affiliation(s)
- Natalia Sizochenko
- Laboratory of Environmental Chemometrics, Faculty of Chemistry, University of Gdansk, Gdansk, Poland
| | | | | | | | | | | |
Collapse
|
25
|
Abstract
Since the first place cell was recorded and the cognitive-map theory was subsequently formulated, investigation of spatial representation in the hippocampal formation has evolved in stages. Early studies sought to verify the spatial nature of place cell activity and determine its sensory origin. A new epoch started with the discovery of head direction cells and the realization of the importance of angular and linear movement-integration in generating spatial maps. A third epoch began when investigators turned their attention to the entorhinal cortex, which led to the discovery of grid cells and border cells. This review will show how ideas about integration of self-motion cues have shaped our understanding of spatial representation in hippocampal-entorhinal systems from the 1970s until today. It is now possible to investigate how specialized cell types of these systems work together, and spatial mapping may become one of the first cognitive functions to be understood in mechanistic detail.
Collapse
|
26
|
D’Albis T, Kempter R. A single-cell spiking model for the origin of grid-cell patterns. PLoS Comput Biol 2017; 13:e1005782. [PMID: 28968386 PMCID: PMC5638623 DOI: 10.1371/journal.pcbi.1005782] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2017] [Revised: 10/12/2017] [Accepted: 09/18/2017] [Indexed: 11/19/2022] Open
Abstract
Spatial cognition in mammals is thought to rely on the activity of grid cells in the entorhinal cortex, yet the fundamental principles underlying the origin of grid-cell firing are still debated. Grid-like patterns could emerge via Hebbian learning and neuronal adaptation, but current computational models remained too abstract to allow direct confrontation with experimental data. Here, we propose a single-cell spiking model that generates grid firing fields via spike-rate adaptation and spike-timing dependent plasticity. Through rigorous mathematical analysis applicable in the linear limit, we quantitatively predict the requirements for grid-pattern formation, and we establish a direct link to classical pattern-forming systems of the Turing type. Our study lays the groundwork for biophysically-realistic models of grid-cell activity.
Collapse
Affiliation(s)
- Tiziano D’Albis
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Richard Kempter
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
- Einstein Center for Neurosciences Berlin, Berlin, Germany
| |
Collapse
|
27
|
Savin C, Tkačik G. Maximum entropy models as a tool for building precise neural controls. Curr Opin Neurobiol 2017; 46:120-126. [DOI: 10.1016/j.conb.2017.08.001] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2017] [Revised: 07/31/2017] [Accepted: 08/03/2017] [Indexed: 12/27/2022]
|
28
|
Parvalbumin and Somatostatin Interneurons Control Different Space-Coding Networks in the Medial Entorhinal Cortex. Cell 2017; 171:507-521.e17. [PMID: 28965758 PMCID: PMC5651217 DOI: 10.1016/j.cell.2017.08.050] [Citation(s) in RCA: 81] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Key Words] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2017] [Revised: 06/12/2017] [Accepted: 08/28/2017] [Indexed: 11/24/2022]
Abstract
The medial entorhinal cortex (MEC) contains several discrete classes of GABAergic interneurons, but their specific contributions to spatial pattern formation in this area remain elusive. We employed a pharmacogenetic approach to silence either parvalbumin (PV)- or somatostatin (SOM)-expressing interneurons while MEC cells were recorded in freely moving mice. PV-cell silencing antagonized the hexagonally patterned spatial selectivity of grid cells, especially in layer II of MEC. The impairment was accompanied by reduced speed modulation in colocalized speed cells. Silencing SOM cells, in contrast, had no impact on grid cells or speed cells but instead decreased the spatial selectivity of cells with discrete aperiodic firing fields. Border cells and head direction cells were not affected by either intervention. The findings point to distinct roles for PV and SOM interneurons in the local dynamics underlying periodic and aperiodic firing in spatially modulated cells of the MEC. Video Abstract
Parvalbumin (PV) interneurons maintain spatially periodic firing in grid cells PV interneurons are necessary for speed tuning in entorhinal speed cells Somatostatin (SOM) interneurons maintain selectivity of aperiodic spatial cells PV and SOM cells regulate discrete subsets of spatially tuned entorhinal cell types
Collapse
|
29
|
Cocco S, Monasson R, Posani L, Tavoni G. Functional networks from inverse modeling of neural population activity. ACTA ACUST UNITED AC 2017. [DOI: 10.1016/j.coisb.2017.04.017] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
|
30
|
Learning with unknowns: Analyzing biological data in the presence of hidden variables. ACTA ACUST UNITED AC 2017. [DOI: 10.1016/j.coisb.2016.12.010] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
|
31
|
Abstract
The medial entorhinal cortex (MEC) creates a neural representation of space through a set of functionally dedicated cell types: grid cells, border cells, head direction cells, and speed cells. Grid cells, the most abundant functional cell type in the MEC, have hexagonally arranged firing fields that tile the surface of the environment. These cells were discovered only in 2005, but after 10 years of investigation, we are beginning to understand how they are organized in the MEC network, how their periodic firing fields might be generated, how they are shaped by properties of the environment, and how they interact with the rest of the MEC network. The aim of this review is to summarize what we know about grid cells and point out where our knowledge is still incomplete.
Collapse
Affiliation(s)
- David C Rowland
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, 7491 Trondheim, Norway; , , ,
| | - Yasser Roudi
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, 7491 Trondheim, Norway; , , ,
| | - May-Britt Moser
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, 7491 Trondheim, Norway; , , ,
| | - Edvard I Moser
- Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, 7491 Trondheim, Norway; , , ,
| |
Collapse
|
32
|
Stensola T, Moser EI. Grid Cells and Spatial Maps in Entorhinal Cortex and Hippocampus. RESEARCH AND PERSPECTIVES IN NEUROSCIENCES 2016. [DOI: 10.1007/978-3-319-28802-4_5] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
|
33
|
Stemmler M, Mathis A, Herz AVM. Connecting multiple spatial scales to decode the population activity of grid cells. SCIENCE ADVANCES 2015; 1:e1500816. [PMID: 26824061 PMCID: PMC4730856 DOI: 10.1126/science.1500816] [Citation(s) in RCA: 78] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2015] [Accepted: 11/24/2015] [Indexed: 05/27/2023]
Abstract
Mammalian grid cells fire when an animal crosses the points of an imaginary hexagonal grid tessellating the environment. We show how animals can navigate by reading out a simple population vector of grid cell activity across multiple spatial scales, even though neural activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into discrete modules within which all cells have the same lattice scale and orientation. The lattice scale changes from module to module and should form a geometric progression with a scale ratio of around 3/2 to minimize the risk of making large-scale errors in spatial localization. Such errors should also occur if intermediate-scale modules are silenced, whereas knocking out the module at the smallest scale will only affect spatial precision. For goal-directed navigation, the allocentric grid cell representation can be readily transformed into the egocentric goal coordinates needed for planning movements. The goal location is set by nonlinear gain fields that act on goal vector cells. This theory predicts neural and behavioral correlates of grid cell readout that transcend the known link between grid cells of the medial entorhinal cortex and place cells of the hippocampus.
Collapse
Affiliation(s)
- Martin Stemmler
- Bernstein Center for Computational Neuroscience Munich and Department of Biology II, Ludwig-Maximilians-Universität München, Grosshadernerstrasse 2, 82152 Planegg-Martinsried, Germany
| | - Alexander Mathis
- Department of Molecular and Cellular Biology and Center for Brain Science, Harvard University, 16 Divinity Avenue, Cambridge, MA 02138, USA
| | - Andreas V. M. Herz
- Bernstein Center for Computational Neuroscience Munich and Department of Biology II, Ludwig-Maximilians-Universität München, Grosshadernerstrasse 2, 82152 Planegg-Martinsried, Germany
| |
Collapse
|
34
|
Wei XX, Prentice J, Balasubramanian V. A principle of economy predicts the functional architecture of grid cells. eLife 2015; 4:e08362. [PMID: 26335200 PMCID: PMC4616244 DOI: 10.7554/elife.08362] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2015] [Accepted: 09/01/2015] [Indexed: 11/13/2022] Open
Abstract
Grid cells in the brain respond when an animal occupies a periodic lattice of ‘grid fields’ during navigation. Grids are organized in modules with different periodicity. We propose that the grid system implements a hierarchical code for space that economizes the number of neurons required to encode location with a given resolution across a range equal to the largest period. This theory predicts that (i) grid fields should lie on a triangular lattice, (ii) grid scales should follow a geometric progression, (iii) the ratio between adjacent grid scales should be √e for idealized neurons, and lie between 1.4 and 1.7 for realistic neurons, (iv) the scale ratio should vary modestly within and between animals. These results explain the measured grid structure in rodents. We also predict optimal organization in one and three dimensions, the number of modules, and, with added assumptions, the ratio between grid periods and field widths. DOI:http://dx.doi.org/10.7554/eLife.08362.001 In the 1930s, neuroscientists studying how rodents find their way through a maze proposed that the animals could construct an internal map of the maze inside their heads. The map was thought to enable the animals to navigate between familiar locations and also to identify shortcuts and alternative routes whenever familiar ones were blocked. In the 1960s, recordings of electrical activity in the rat brain provided the first clues as to which nerve cells form this spatial map. In a region of the brain called the hippocampus, nerve cells called ‘place cells’ are active whenever the rat finds itself in a specific location. However, place cells alone are not able to support all types of navigation. Some spatial tasks also require cells in a region of the brain called the medial entorhinal cortex (MEC), which supplies most of the information that the hippocampus receives. Cells in the MEC called ‘grid cells’ represent two-dimensional space as a repeating grid of triangles. A given grid cell is activated if the animal is located at a particular distance and angle away from the center of any of these triangles. The size of the triangles in these grids varies systematically throughout the MEC. Individual grid cells at one end of the structure encode space in finer detail than grid cells at the opposite end. Wei et al. have now used mathematical modeling to explore how grid cells are organized. The model assumes that the brain seeks to encode space at whatever resolution an animal requires using as few nerve cells as possible. The model successfully reproduces several known features of grid cells, including the triangular shape of the grid, and the fact that the size of the triangles increases in steps of a specific size across the MEC. In addition to providing a mathematical basis for the way that grid cells are organized in the brain, the model makes a number of testable predictions. These include predictions of the number of grid cells in the rat brain, as well as the pattern that grid cells adopt in three-dimensions: a question that is currently being studied in bats. Wei et al.'s findings suggest that the code used by the grid to represent space is an analog of a decimal number system—except that space is not subdivided by factors of 10 to form decimal ‘digits’, but by a quantity related to a famous constant in the field of mathematics called Euler's number. DOI:http://dx.doi.org/10.7554/eLife.08362.002
Collapse
Affiliation(s)
- Xue-Xin Wei
- Department of Psychology, University of Pennsylvania, Philadelphia, United States
| | - Jason Prentice
- Princeton Neuroscience Institute, Princeton University, Princeton, United States
| | - Vijay Balasubramanian
- Department of Physics, University of Pennsylvania, Philadelphia, United States.,Department of Neuroscience, University of Pennsylvania, Philadelphia, United States
| |
Collapse
|
35
|
Tocker G, Barak O, Derdikman D. Grid cells correlation structure suggests organized feedforward projections into superficial layers of the medial entorhinal cortex. Hippocampus 2015; 25:1599-613. [DOI: 10.1002/hipo.22481] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/17/2015] [Indexed: 01/29/2023]
Affiliation(s)
- Gilad Tocker
- Neuroscience Dept., The Rappaport Faculty of Medicine, Technion - Israel Institute of Technology; Bat Galim Haifa 31096 Israel
- Gonda Multidisciplinary Brain Research Center; Bar Ilan University; Ramat-Gan 52900 Israel
- Rappaport Research Institute; Bat Galim; Haifa 31096 Israel
| | - Omri Barak
- Neuroscience Dept., The Rappaport Faculty of Medicine, Technion - Israel Institute of Technology; Bat Galim Haifa 31096 Israel
| | - Dori Derdikman
- Neuroscience Dept., The Rappaport Faculty of Medicine, Technion - Israel Institute of Technology; Bat Galim Haifa 31096 Israel
- Rappaport Research Institute; Bat Galim; Haifa 31096 Israel
| |
Collapse
|
36
|
Abstract
One of the grand challenges in neuroscience is to comprehend neural computation in the association cortices, the parts of the cortex that have shown the largest expansion and differentiation during mammalian evolution and that are thought to contribute profoundly to the emergence of advanced cognition in humans. In this Review, we use grid cells in the medial entorhinal cortex as a gateway to understand network computation at a stage of cortical processing in which firing patterns are shaped not primarily by incoming sensory signals but to a large extent by the intrinsic properties of the local circuit.
Collapse
|