1,428 research outputs found
Coverage, Continuity and Visual Cortical Architecture
The primary visual cortex of many mammals contains a continuous
representation of visual space, with a roughly repetitive aperiodic map of
orientation preferences superimposed. It was recently found that orientation
preference maps (OPMs) obey statistical laws which are apparently invariant
among species widely separated in eutherian evolution. Here, we examine whether
one of the most prominent models for the optimization of cortical maps, the
elastic net (EN) model, can reproduce this common design. The EN model
generates representations which optimally trade of stimulus space coverage and
map continuity. While this model has been used in numerous studies, no
analytical results about the precise layout of the predicted OPMs have been
obtained so far. We present a mathematical approach to analytically calculate
the cortical representations predicted by the EN model for the joint mapping of
stimulus position and orientation. We find that in all previously studied
regimes, predicted OPM layouts are perfectly periodic. An unbiased search
through the EN parameter space identifies a novel regime of aperiodic OPMs with
pinwheel densities lower than found in experiments. In an extreme limit,
aperiodic OPMs quantitatively resembling experimental observations emerge.
Stabilization of these layouts results from strong nonlocal interactions rather
than from a coverage-continuity-compromise. Our results demonstrate that
optimization models for stimulus representations dominated by nonlocal
suppressive interactions are in principle capable of correctly predicting the
common OPM design. They question that visual cortical feature representations
can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure
On the Nature and Shape of Tubulin Trails: Implications on Microtubule Self-Organization
Microtubules, major elements of the cell skeleton are, most of the time, well
organized in vivo, but they can also show self-organizing behaviors in time
and/or space in purified solutions in vitro. Theoretical studies and models
based on the concepts of collective dynamics in complex systems,
reaction-diffusion processes and emergent phenomena were proposed to explain
some of these behaviors. In the particular case of microtubule spatial
self-organization, it has been advanced that microtubules could behave like
ants, self-organizing by 'talking to each other' by way of hypothetic (because
never observed) concentrated chemical trails of tubulin that are expected to be
released by their disassembling ends. Deterministic models based on this idea
yielded indeed like-looking spatio-temporal self-organizing behaviors.
Nevertheless the question remains of whether microscopic tubulin trails
produced by individual or bundles of several microtubules are intense enough to
allow microtubule self-organization at a macroscopic level. In the present
work, by simulating the diffusion of tubulin in microtubule solutions at the
microscopic scale, we measure the shape and intensity of tubulin trails and
discuss about the assumption of microtubule self-organization due to the
production of chemical trails by disassembling microtubules. We show that the
tubulin trails produced by individual microtubules or small microtubule arrays
are very weak and not elongated even at very high reactive rates. Although the
variations of concentration due to such trails are not significant compared to
natural fluctuations of the concentration of tubuline in the chemical
environment, the study shows that heterogeneities of biochemical composition
can form due to microtubule disassembly. They could become significant when
produced by numerous microtubule ends located in the same place. Their possible
formation could play a role in certain conditions of reaction. In particular,
it gives a mesoscopic basis to explain the collective dynamics observed in
excitable microtubule solutions showing the propagation of concentration waves
of microtubules at the millimeter scale, although we doubt that individual
microtubules or bundles can behave like molecular ants
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