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Aghili Yajadda MM, Robinson PA, Henderson JA. Generalized neural field theory of cortical plasticity illustrated by an application to the linear phase of ocular dominance column formation in primary visual cortex. BIOLOGICAL CYBERNETICS 2022; 116:33-52. [PMID: 34773503 DOI: 10.1007/s00422-021-00901-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
Physiologically based neural field theory (NFT) is extended to encompass cortical plasticity dynamics. An illustrative application is provided which treats the evolution of the connectivity of left- and right-eye visual stimuli to neuronal populations in the primary visual cortex (V1), and the initial, linear phase of formation of approximately one-dimensional (1D) ocular dominance columns (ODCs) that sets their transverse spatial scale. This links V1 activity, structure, and physiology within a single theory that already accounts for a range of other brain activity and connectivity phenomena, thereby enabling ODC formation and many other phenomena to be interrelated and cortical parameters to be constrained across multiple domains. The results accord with experimental ODC widths for realistic cortical parameters and are based directly on a unified description of the neuronal populations involved, their connection strengths, and the neuronal activity they support. Other key results include simple analytic approximations for ODC widths and the parameters of maximum growth rate, constraints on cortical excitatory and inhibitory gains, elucidation of the roles of specific poles of the V1 response function, and the fact that ODCs are not formed when input stimuli are fully correlated between eyes. This work provides a basis for further generalization of NFT to model other plasticity phenomena, thereby linking them to the range multiscale phenomena accounted for by NFT.
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Affiliation(s)
- M M Aghili Yajadda
- School of Physics, University of Sydney, Sydney, NSW, 2006, Australia
- Center for Integrative Brain Function, University of Sydney, Sydney, NSW, 2006, Australia
| | - P A Robinson
- School of Physics, University of Sydney, Sydney, NSW, 2006, Australia
- Center for Integrative Brain Function, University of Sydney, Sydney, NSW, 2006, Australia
| | - J A Henderson
- School of Physics, University of Sydney, Sydney, NSW, 2006, Australia.
- Center for Integrative Brain Function, University of Sydney, Sydney, NSW, 2006, Australia.
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Romagnoni A, Ribot J, Bennequin D, Touboul J. Parsimony, Exhaustivity and Balanced Detection in Neocortex. PLoS Comput Biol 2015; 11:e1004623. [PMID: 26587664 PMCID: PMC4654526 DOI: 10.1371/journal.pcbi.1004623] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2015] [Accepted: 10/23/2015] [Indexed: 11/18/2022] Open
Abstract
The layout of sensory brain areas is thought to subtend perception. The principles shaping these architectures and their role in information processing are still poorly understood. We investigate mathematically and computationally the representation of orientation and spatial frequency in cat primary visual cortex. We prove that two natural principles, local exhaustivity and parsimony of representation, would constrain the orientation and spatial frequency maps to display a very specific pinwheel-dipole singularity. This is particularly interesting since recent experimental evidences show a dipolar structures of the spatial frequency map co-localized with pinwheels in cat. These structures have important properties on information processing capabilities. In particular, we show using a computational model of visual information processing that this architecture allows a trade-off in the local detection of orientation and spatial frequency, but this property occurs for spatial frequency selectivity sharper than reported in the literature. We validated this sharpening on high-resolution optical imaging experimental data. These results shed new light on the principles at play in the emergence of functional architecture of cortical maps, as well as their potential role in processing information.
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Affiliation(s)
- Alberto Romagnoni
- Mathematical Neuroscience Team, CIRB—Collège de France (CNRS UMR 7241, INSERM U1050, Labex MEMOLIFE), PSL, Paris, France
- Group for Neural Theory, Laboratoire des Neurosciences Cognitives, INSERM Unité 960, Département d’Études Cognitives, École Normale Supérieure, PSL, Paris, France
- * E-mail:
| | - Jérôme Ribot
- Mathematical Neuroscience Team, CIRB—Collège de France (CNRS UMR 7241, INSERM U1050, Labex MEMOLIFE), PSL, Paris, France
| | - Daniel Bennequin
- Géométrie et dynamique, Université Paris Diderot (Paris VII), Paris, France
| | - Jonathan Touboul
- Mathematical Neuroscience Team, CIRB—Collège de France (CNRS UMR 7241, INSERM U1050, Labex MEMOLIFE), PSL, Paris, France
- INRIA Mycenae Team, Paris-Rocquencourt, France
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Schottdorf M, Keil W, Coppola D, White LE, Wolf F. Random Wiring, Ganglion Cell Mosaics, and the Functional Architecture of the Visual Cortex. PLoS Comput Biol 2015; 11:e1004602. [PMID: 26575467 PMCID: PMC4648540 DOI: 10.1371/journal.pcbi.1004602] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2015] [Accepted: 10/14/2015] [Indexed: 12/11/2022] Open
Abstract
The architecture of iso-orientation domains in the primary visual cortex (V1) of placental carnivores and primates apparently follows species invariant quantitative laws. Dynamical optimization models assuming that neurons coordinate their stimulus preferences throughout cortical circuits linking millions of cells specifically predict these invariants. This might indicate that V1's intrinsic connectome and its functional architecture adhere to a single optimization principle with high precision and robustness. To validate this hypothesis, it is critical to closely examine the quantitative predictions of alternative candidate theories. Random feedforward wiring within the retino-cortical pathway represents a conceptually appealing alternative to dynamical circuit optimization because random dimension-expanding projections are believed to generically exhibit computationally favorable properties for stimulus representations. Here, we ask whether the quantitative invariants of V1 architecture can be explained as a generic emergent property of random wiring. We generalize and examine the stochastic wiring model proposed by Ringach and coworkers, in which iso-orientation domains in the visual cortex arise through random feedforward connections between semi-regular mosaics of retinal ganglion cells (RGCs) and visual cortical neurons. We derive closed-form expressions for cortical receptive fields and domain layouts predicted by the model for perfectly hexagonal RGC mosaics. Including spatial disorder in the RGC positions considerably changes the domain layout properties as a function of disorder parameters such as position scatter and its correlations across the retina. However, independent of parameter choice, we find that the model predictions substantially deviate from the layout laws of iso-orientation domains observed experimentally. Considering random wiring with the currently most realistic model of RGC mosaic layouts, a pairwise interacting point process, the predicted layouts remain distinct from experimental observations and resemble Gaussian random fields. We conclude that V1 layout invariants are specific quantitative signatures of visual cortical optimization, which cannot be explained by generic random feedforward-wiring models.
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Affiliation(s)
- Manuel Schottdorf
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- Bernstein Focus for Neurotechnology, Göttingen, Germany
- Faculty of Physics, University of Göttingen, Göttingen, Germany
- Institute for Theoretical Physics, University of Würzburg, Würzburg, Germany
| | - Wolfgang Keil
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- Bernstein Focus for Neurotechnology, Göttingen, Germany
- Faculty of Physics, University of Göttingen, Göttingen, Germany
- Center for Studies in Physics and Biology, The Rockefeller University, New York, New York, United States of America
| | - David Coppola
- Department of Biology, Randolph-Macon College, Ashland, Virginia, United States of America
| | - Leonard E. White
- Department of Orthopaedic Surgery, Duke Institute for Brain Sciences, Duke University, Durham, North Carolina, United States of America
| | - Fred Wolf
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- Bernstein Focus for Neurotechnology, Göttingen, Germany
- Faculty of Physics, University of Göttingen, Göttingen, Germany
- Kavli Institute for Theoretical Physics, Santa Barbara, California, United States of America
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Afgoustidis A. Monochromaticity of orientation maps in v1 implies minimum variance for hypercolumn size. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2015; 5:10. [PMID: 25859421 PMCID: PMC4388110 DOI: 10.1186/s13408-015-0022-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/13/2014] [Accepted: 03/17/2015] [Indexed: 06/04/2023]
Abstract
In the primary visual cortex of many mammals, the processing of sensory information involves recognizing stimuli orientations. The repartition of preferred orientations of neurons in some areas is remarkable: a repetitive, non-periodic, layout. This repetitive pattern is understood to be fundamental for basic non-local aspects of vision, like the perception of contours, but important questions remain about its development and function. We focus here on Gaussian Random Fields, which provide a good description of the initial stage of orientation map development and, in spite of shortcomings we will recall, a computable framework for discussing general principles underlying the geometry of mature maps. We discuss the relationship between the notion of column spacing and the structure of correlation spectra; we prove formulas for the mean value and variance of column spacing, and we use numerical analysis of exact analytic formulae to study the variance. Referring to studies by Wolf, Geisel, Kaschube, Schnabel, and coworkers, we also show that spectral thinness is not an essential ingredient to obtain a pinwheel density of π, whereas it appears as a signature of Euclidean symmetry. The minimum variance property associated to thin spectra could be useful for information processing, provide optimal modularity for V1 hypercolumns, and be a first step toward a mathematical definition of hypercolumns. A measurement of this property in real maps is in principle possible, and comparison with the results in our paper could help establish the role of our minimum variance hypothesis in the development process.
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Affiliation(s)
- Alexandre Afgoustidis
- Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris 7 Denis Diderot, 75013 Paris, France
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Wilson SP, Bednar JA. What, if anything, are topological maps for? Dev Neurobiol 2015; 75:667-81. [PMID: 25683193 DOI: 10.1002/dneu.22281] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2014] [Revised: 02/06/2015] [Accepted: 02/10/2015] [Indexed: 11/10/2022]
Abstract
What, if anything, is the functional significance of spatial patterning in cortical feature maps? We ask this question of four major theories of cortical map formation: self-organizing maps, wiring optimization, place coding, and reaction-diffusion. We argue that (i) self-organizing maps yield spatial patterning only as a by-product of efficient mechanisms for developing environmentally appropriate distributions of feature preferences, (ii) wiring optimization assumes rather than explains a map-like organization, (iii) place-coding mechanisms can at best explain only a subset of maps in functional terms, and (iv) reaction-diffusion models suggest two factors in the evolution of maps, the first based on efficient development of feature distributions, and the second based on generating feature-specific long-range recurrent cortical circuitry. None of these explanations for the existence of topological maps requires spatial patterning in maps to be useful. Thus despite these useful frameworks for understanding how maps form and how they are wired, the possibility that patterns are merely epiphenomena in the evolution of mammalian neocortex cannot be rejected. The article is intended as a nontechnical introduction to the assumptions and predictions of these four important classes of models, along with other possible functional explanations for maps.
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Affiliation(s)
- Stuart P Wilson
- Adaptive Behaviour Research Group, Department of Psychology, The University of Sheffield, Sheffield, S10 2TP, United Kingdom
| | - James A Bednar
- Institute for Adaptive & Neural Computation, School of Informatics, The University of Edinburgh, Edinburgh, EH8 9AB, United Kingdom
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Kaschube M. Neural maps versus salt-and-pepper organization in visual cortex. Curr Opin Neurobiol 2013; 24:95-102. [PMID: 24492085 DOI: 10.1016/j.conb.2013.08.017] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2013] [Revised: 08/19/2013] [Accepted: 08/24/2013] [Indexed: 10/26/2022]
Abstract
Theoretical neuroscientists have long been intrigued by the spatial patterns of neuronal selectivities observed in the visual cortices of many mammals, including primates. While theoretical studies have contributed significantly to our understanding of how the brain learns to see, recent experimental discoveries of the spatial irregularity of visual response properties in the rodent visual cortex have prompted new questions about the origin and functional significance of cortical maps. Characterizing the marked differences of cortical design principles among species and comparing them may provide us with a deeper understanding of primate and non-primate vision.
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Affiliation(s)
- Matthias Kaschube
- Frankfurt Institute for Advanced Studies, Faculty of Computer Science and Mathematics, Goethe University, Frankfurt am Main, Germany.
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Reichl L, Heide D, Löwel S, Crowley JC, Kaschube M, Wolf F. Coordinated optimization of visual cortical maps (I) symmetry-based analysis. PLoS Comput Biol 2012; 8:e1002466. [PMID: 23144599 PMCID: PMC3493482 DOI: 10.1371/journal.pcbi.1002466] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2011] [Accepted: 02/24/2012] [Indexed: 11/18/2022] Open
Abstract
In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps.
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Affiliation(s)
- Lars Reichl
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- Bernstein Focus Neurotechnology, Göttingen, Germany
- Faculty of Physics, Georg-August University, Göttingen, Germany
- * E-mail: (LR); (FW)
| | - Dominik Heide
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
- Frankfurt Institute of Advanced Studies, Frankfurt, Germany
| | - Siegrid Löwel
- Bernstein Focus Neurotechnology, Göttingen, Germany
- School of Biology, Georg-August University, Göttingen, Germany
| | - Justin C. Crowley
- Carnegie Mellon University, Department of Biological Sciences, Pittsburgh, Pennsylvania, United States of America
| | - Matthias Kaschube
- Frankfurt Institute of Advanced Studies, Frankfurt, Germany
- Physics Department and Lewis-Sigler Institute, Princeton University, Princeton, New Jersey, United States of America
| | - Fred Wolf
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- Bernstein Focus Neurotechnology, Göttingen, Germany
- Faculty of Physics, Georg-August University, Göttingen, Germany
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California, United States of America
- * E-mail: (LR); (FW)
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