Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Self-Organization and optimization in the evolution of visual cortical circuits

Response characteristics of orientation-tuned neurons in the visual cortex appear to be similar in mammalian lineages widely separated in evolution.  The spatial arrangement of preferences across the cortex, however, shows fundamental differences.  While in primates and carnivores orientation preferences form orientation maps, in rodents they are spatially interspersed.  The developmental processes and evolutionary origins of these two opposite layout-types remain enigmatic.  We discovered that columnar orientation maps realize an apparently quantitatively universal, common design [1, 2, 3, 4] that naturally emerges by activity-dependent self-organization of large scale neuronal circuits when orientation selective long-range interactions are present [1, 6, 7, 8, 9].  In particular we performed comparative studies of visual cortical orientation columns and pinwheels in mammalian species whose evolutionary paths separated more than 65 million years ago [1, 3].  We found that statistical measures characterizing the spatial layout of pinwheels from the scale of hundreds of microns to the entire primary visual cortex (V1) were virtually identical, agreeing with an accuracy of a few percent.  To understand how distinct evolutionary lineages can independently evolve this common design, we examined a broad set of mathematical models for the developmental self-organization of orientation columns [1, 6, 7, 8, 9].  We found that models from a symmetry-defined class, exhibiting a universal (i.e., model-independent) solution set, robustly and specifically predict every aspect of the common design when suppressive long-range interactions are dominant [1, 8] (see [1, 5] for evidence that the developmental reorganization orientation columns depend on long-range interactions).  This suggests that developmental network self-organization has canalized the evolution of neuronal circuitry underlying orientation maps in these species into the common design that was not present in their last common ancestor.  A predicted signature of this mechanism is a pinwheel density close to the mathematical constant pi.  Confirming this prediction, we found that mean pinwheel density was indeed statistically indistinguishable from the predicted value with a potential deviation of only up to 2%.

Fig. 1:  Self-Organization in the Evolution of Visual Cortical Architecture.  (A) Overview of the evolutionary invention of neocortex and its likely transformation during the evolution of modern mammals.  Primates and rodents differ fundamentally in the layout of orientation selective neurons in their primary visual cortex.  In primates neurons are arranged in columns and maps.  Rodents show an interspersed layout without any discernible spatial organization.  As mesozoic mammals were small brained and nocturnal they presumably lacked orientation columns as do all small brained modern mammals.  Neocortical tissue receiving ascending thalamic afferent innervation presumably originated with the invention of the neocortex in the first mammals about 200 million years ago.  (B) Schematic representation of key processes during the self-organization of orientation selective cortical circuitry.  Individual neurons can dynamically reorganize their orientation selectivity but do so under the influence of the extensive cortical circuit in which they are embedded.  (C) Different types of intracortical interactions lead to qualitatively distinct types of emerging spatial arrangements of orientation selective neurons.


To understand the origin of the qualitative difference between the two design types found in primates and in rodents, we then investigated whether cortical circuit self-organization can also explain the rodent layout type in a unified model.  We demonstrate a direct transition from quasi-periodic arrays of orientation columns to interspersed organization.  An interspersed organization is actively generated when local circuits are predominantly suppressive.  Numerical simulations show that the final arrangement of orientations shows a weak negative correlation between nearest neighbours and that it suffers from a substantial dynamical lability of neuronal selectivities compared to columnar architectures.  Interspersed layouts in general exhibit superior stimulus coverage but cause  higher wiring costs to maintain a selective like-to-like connectivity.  We thus examined models in which cortical organization is assumed to optimize a composite cost function that penalizes reductions in stimulus coverage and excessive wiring length depending on cortex size.  In these models we found a transition from interspersed layouts to columnar architecture above a critical area size.  Our results suggest that neuronal circuit self-organization played a critical role in the evolution of cortical functional organization and that the invention of orientation columns was driven by the emergence of large brains.


[1] Kaschube, Schnabel, Coppola, Löwel, White, and Wolf, Science 330:1113 (2010).
[2] Kaschube, Coppola, Schnabel, Löwel, White, and Wolf, Science doi: 10.1126/science.1194869 (2011).
[3] Keil, Kaschube, Schnabel, Kisvarday, Löwel, Coppola, White, and Wolf, Science 336:6080, (2012).
[4] Greifzu, Wolf, and Löwel, Network influences on cortical plasticity, e-Neuroforum. 302: 41, (2012).
[5] Kaschube, Schnabel, Wolf, and Lowel, Proc. Natl. Acad. Sci. USA 106: 17205-17210 (2009).
[6] Reichl, Heide, Löwel, Crowley, Kaschube, and Wolf, PLoS Comput Biol. 8(11): e1002466 (2012).
[7] Reichl, Heide, Löwel, Crowley, Kaschube, and Wolf, PLoS Comput Biol. 8(11): e1002756 (2012).
[8] Keil and Wolf, Neural & Systems Circuits, doi: 10.1186/2042-1001-1-17 (2011).
[9] Schottdorf, Eglen, Wolf, and Keil, in revision, arXiv: 1306.2808.

Contact:  Fred Wolf 

Members working within this Project:

 Fred Wolf 
 Manuel Schottdorf 
 Juan Daniel Flórez Weidinger 

Former Members:

 Wolfgang Keil 
 Lars Reichl 

Selected Publications:

M. Schottdorf, W. Keil, D. Coppola, L.E. White, and F. Wolf (2015).
Random Wiring, Ganglion Cell Mosaics, and the Functional Architecture of the Visual Cortex
PLoS Computational Biology 11(11): e1004602.

M. Schottdorf, S.J. Eglen, F. Wolf, and W. Keil (2014).
Can Retinal Ganglion Cell Dipoles Seed Iso-Orientation Domains in the Visual Cortex?
PLoS ONE 9(1): e86139.

F. Greifzu, F. Wolf, and S. Löwel (2012).
Network influences on cortical plasticity
e-Neuroforum 3:41--48. download file

L. Reichl, D. Heide, S. Löwel, J.C. Crowley, M. Kaschube, and F. Wolf (2012).
Coordinated Optimization of Visual Cortical Maps (I) Symmetry-based Analysis
PLoS Comput. Biol. 8(11). download file

L. Reichl, D. Heide, S. Löwel, J.C. Crowley, M. Kaschube, and F. Wolf (2012).
Coordinated Optimization of Visual Cortical Maps (II) Numerical Studies
PLoS Comput. Biol. 8(11). download file

W. Keil, M. Kaschube, M. Schnabel, Z.F. Kisvárday, S. Löwel, D.M. Coppola, L.E. White, and F. Wolf (2012).
Response to Comment on "Universality in the Evolution of Orientation Columns in the Visual Cortex"
Science 336(6080):413. download file

W. Keil, and F. Wolf (2011).
Coverage, continuity and visual cortical architecture
Neural Systems and Circuits 1(17):doi:10.1186/2042-1001-1-17. download file

M. Kaschube, M. Schnabel, S. Loewel, D.M. Coppola, L.E. White, and F. Wolf (2010).
Universality in the Evolution of Orientation Columns in the Visual Cortex
Science 330:1113--1116. download file

M. Kaschube, M. Schnabel, F. Wolf, and S. Löwel (2009).
Inter-areal coordination of columnar architectures during visual cortical development
Proceedings of the National Academy of Sciences 106(40):17205–17210.