A Developmental Model of Ocular Dominance Column Formation on a Growing Cortex

Oster, Andrew M.; Bressloff, Paul C.

doi:10.1007/s11538-005-9055-7

Cited by 11 publications

(7 citation statements)

References 22 publications

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“…It does not require rotation symmetry of the instability mechanism. A recent onedimensional cortical growth study focused on the Eckhaus instability [40]. However, in our simulations, we did not observe an Eckhaus instability, even in the case of large instantaneous increase or decrease of area size.…”

Section: B Eckhaus Instabilitycontrasting

confidence: 66%

“…Consistent with the present study, the average spacings in V1 and V2 remained largely constant over this period. A theoretical study [40] of a onedimensional model of OD development during cortical growth predicts a splitting of OD stripes analogous to the Eckhaus instability (SI Appendix ). As we show here, two-dimensional models exhibit a much richer dynamics and behave qualitatively different.…”

Section: Relation To Previous Workmentioning

confidence: 99%

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Reorganization of columnar architecture in the growing visual cortex

Keil

Schmidt

Löwel

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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Many cortical areas increase in size considerably during postnatal development, progressively displacing neuronal cell bodies from each other. At present, little is known about how cortical growth affects the development of neuronal circuits. Here, in acute and chronic experiments, we study the layout of ocular dominance (OD) columns in cat primary visual cortex during a period of substantial postnatal growth. We find that despite a considerable size increase of primary visual cortext, the spacing between columns is largely preserved. In contrast, their spatial arrangement changes systematically over this period. Whereas in young animals columns are more band-like, layouts become more isotropic in mature animals. We propose a novel mechanism of growth-induced reorganization that is based on the "zigzag instability," a dynamical instability observed in several inanimate pattern forming systems. We argue that this mechanism is inherent to a wide class of models for the activity-dependent formation of OD columns. Analyzing one representative of this class, the Elastic Network model, we show that this mechanism can account for the preservation of column spacing and the specific mode of reorganization of OD columns that we observe. We conclude that column width is preserved by systematic reorganization of neuronal selectivities during cortical expansion and that this reorganization is well described by the zigzag instability. Our work suggests that cortical circuits may remain plastic for an extended period in development to facilitate the modification of neuronal circuits to adjust for cortical growth.cortical growth | ocular dominance columns | postnatal development | critical period | zigzag instability

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Section: B Eckhaus Instabilitycontrasting

confidence: 66%

Section: Relation To Previous Workmentioning

confidence: 99%

Reorganization of columnar architecture in the growing visual cortex

Keil

Schmidt

Löwel

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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“…The proposed antenatal self-organization of cortical synapses leads to the creation of a tabula rasa on which homeomorphic maps, in a form disguised by the Möbius-strip-like folding of connections, occur in lateral connections at the millimetric scale, embedding the statistics of spatial organization of the sensory world to first approximation, before any detailed sensory inputs are received. The assumptions and findings of the model overlap with, and although not necessarily contradictory to, are not identical to, those of other models (Erwin and Miller, 1998; Wolf and Geisel, 1998; Kang et al, 2003; Oster and Bressloff, 2006). Distinguishing features include the explanation of the relationship of superficial patch connections to macrocolumn centers, and their hexagonal rotational symmetry, and crucially, the findings of Basole et al (2003), which cannot be explained by any model dependent on “like-to-like” connections between feature-specific neurons.…”

Section: Resultsmentioning

confidence: 48%

“…Measurements of the average distance of separation of OP singularities (the singularity taken as demarcating the center of a macrocolumn) show this distance to be relatively constant over a 40-fold variation of body size, and related size of V1 (Kaschube et al, 2010; Keil et al, 2012). Models using symmetry arguments indicate that macrocolumns must undergo divisions during cortical development to maintain uniform surface density of singularities (Wolf and Geisel, 1998; Oster and Bressloff, 2006). Kaschube and colleagues conclude that self-organization has canalized the evolution of the underlying OP maps into a single common design—subject to the proviso that, from further symmetry arguments, this can only be the case where long-range interactions between developing macrocolumns, suppressing some possible connections, can take place.…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of cortical development: synchrony and synaptic self-organization

Wright

Bourke

2013

Front. Comput. Neurosci.

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We describe a model for cortical development that resolves long-standing difficulties of earlier models. It is proposed that, during embryonic development, synchronous firing of neurons and their competition for limited metabolic resources leads to selection of an array of neurons with ultra-small-world characteristics. Consequently, in the visual cortex, macrocolumns linked by superficial patchy connections emerge in anatomically realistic patterns, with an ante-natal arrangement which projects signals from the surrounding cortex onto each macrocolumn in a form analogous to the projection of a Euclidean plane onto a Möbius strip. This configuration reproduces typical cortical response maps, and simulations of signal flow explain cortical responses to moving lines as functions of stimulus velocity, length, and orientation. With the introduction of direct visual inputs, under the operation of Hebbian learning, development of mature selective response “tuning” to stimuli of given orientation, spatial frequency, and temporal frequency would then take place, overwriting the earlier ante-natal configuration. The model is provisionally extended to hierarchical interactions of the visual cortex with higher centers, and a general principle for cortical processing of spatio-temporal images is sketched.

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“…New white stripes are inserted between the existing older stripes, resulting in a doubling of the number of stripes each time the fish doubles in size. Stripe insertion has also been modeled within the context of ocular dominance columns within developing cortex [23]. In the case of synaptogenesis in C. elegans, maintenance of synaptic density could be analogous to a stripe insertion mechanism and is something we hope to explore in future work.…”

Section: Discussionmentioning

confidence: 99%

A Mechanism for Turing Pattern Formation with Active and Passive Transport

Brooks

Bressloff²

2016

SIAM J. Appl. Dyn. Syst.

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We propose a novel mechanism for Turing pattern formation that provides a possible explanation for the regular spacing of synaptic puncta along the ventral cord of C. elegans during development. The model consists of two interacting chemical species, where one is passively diffusing and the other is actively trafficked by molecular motors. We identify the former as the kinase CaMKII and the latter as the glutamate receptor GLR-1. We focus on a one-dimensional model in which the motor-driven chemical switches between forward and backward moving states with identical speeds. We use linear stability analysis to derive conditions on the associated nonlinear interaction functions for which a Turing instability can occur. We find that the dimensionless quantity γ = αd/v 2 has to be sufficiently small for patterns to emerge, where α is the switching rate between motor states, v is the motor speed, and d is the passive diffusion coefficient. One consequence is that patterns emerge outside the parameter regime of fast switching where the model effectively reduces to a twocomponent reaction-diffusion system. Numerical simulations of the model using experimentally based parameter values generates patterns with a wavelength consistent with the synaptic spacing found in C. elegans. Finally, in the case of biased transport, we show that the system supports spatially periodic patterns in the presence of boundary forcing, analogous to flow distributed structures in reaction-diffusion-advection systems. Such forcing could represent the insertion of new motor-bound GLR-1 from the soma of ventral cord neurons.

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A Developmental Model of Ocular Dominance Column Formation on a Growing Cortex

Cited by 11 publications

References 22 publications

Reorganization of columnar architecture in the growing visual cortex

Reorganization of columnar architecture in the growing visual cortex

On the dynamics of cortical development: synchrony and synaptic self-organization

A Mechanism for Turing Pattern Formation with Active and Passive Transport

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