20,577 research outputs found
Spatial heterogeneity enhances and modulates excitability in a mathematical model of the myometrium
The muscular layer of the uterus (myometrium) undergoes profound changes in global excitability prior to parturition. Here, a mathematical model of the myocyte network is developed to investigate the hypothesis that spatial heterogeneity is essential to the transition from local to global excitation which the myometrium undergoes just prior to birth. Each myometrial smooth muscle cell is represented by an element with FitzHugh–Nagumo dynamics. The cells are coupled through resistors that represent gap junctions. Spatial heterogeneity is introduced by means of stochastic variation in coupling strengths, with parameters derived from physiological data. Numerical simulations indicate that even modest increases in the heterogeneity of the system can amplify the ability of locally applied stimuli to elicit global excitation. Moreover, in networks driven by a pacemaker cell, global oscillations of excitation are impeded in fully connected and strongly coupled networks. The ability of a locally stimulated cell or pacemaker cell to excite the network is shown to be strongly dependent on the local spatial correlation structure of the couplings. In summary, spatial heterogeneity is a key factor in enhancing and modulating global excitability
Molecular motors robustly drive active gels to a critically connected state
Living systems often exhibit internal driving: active, molecular processes
drive nonequilibrium phenomena such as metabolism or migration. Active gels
constitute a fascinating class of internally driven matter, where molecular
motors exert localized stresses inside polymer networks. There is evidence that
network crosslinking is required to allow motors to induce macroscopic
contraction. Yet a quantitative understanding of how network connectivity
enables contraction is lacking. Here we show experimentally that myosin motors
contract crosslinked actin polymer networks to clusters with a scale-free size
distribution. This critical behavior occurs over an unexpectedly broad range of
crosslink concentrations. To understand this robustness, we develop a
quantitative model of contractile networks that takes into account network
restructuring: motors reduce connectivity by forcing crosslinks to unbind.
Paradoxically, to coordinate global contractions, motor activity should be low.
Otherwise, motors drive initially well-connected networks to a critical state
where ruptures form across the entire network.Comment: Main text: 21 pages, 5 figures. Supplementary Information: 13 pages,
8 figure
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions
Neural connectivity at the cellular and mesoscopic level appears very
specific and is presumed to arise from highly specific developmental
mechanisms. However, there are general shared features of connectivity in
systems as different as the networks formed by individual neurons in
Caenorhabditis elegans or in rat visual cortex and the mesoscopic circuitry of
cortical areas in the mouse, macaque, and human brain. In all these systems,
connection length distributions have very similar shapes, with an initial large
peak and a long flat tail representing the admixture of long-distance
connections to mostly short-distance connections. Furthermore, not all
potentially possible synapses are formed, and only a fraction of axons (called
filling fraction) establish synapses with spatially neighboring neurons. We
explored what aspects of these connectivity patterns can be explained simply by
random axonal outgrowth. We found that random axonal growth away from the soma
can already reproduce the known distance distribution of connections. We also
observed that experimentally observed filling fractions can be generated by
competition for available space at the target neurons--a model markedly
different from previous explanations. These findings may serve as a baseline
model for the development of connectivity that can be further refined by more
specific mechanisms.Comment: 31 pages (incl. supplementary information); Cerebral Cortex Advance
Access published online on May 12, 200
Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops
We consider the role of network geometry in two types of diffusion processes:
transport of constant-density information packets with queuing on nodes, and
constant voltage-driven tunneling of electrons. The underlying network is a
homogeneous graph with scale-free distribution of loops, which is constrained
to a planar geometry and fixed node connectivity . We determine properties
of noise, flow and return-times statistics for both processes on this graph and
relate the observed differences to the microscopic process details. Our main
findings are: (i) Through the local interaction between packets queuing at the
same node, long-range correlations build up in traffic streams, which are
practically absent in the case of electron transport; (ii) Noise fluctuations
in the number of packets and in the number of tunnelings recorded at each node
appear to obey the scaling laws in two distinct universality classes; (iii) The
topological inhomogeneity of betweenness plays the key role in the occurrence
of broad distributions of return times and in the dynamic flow. The
maximum-flow spanning trees are characteristic for each process type.Comment: 14 pages, 5 figure
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