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Microtubule Instability

Microtubules are hollow cylindrical filaments having a diameter of approximately 25 nm and a length that varies from 200 nm to 25 μm. GTP-bound tubulin subunits form αβ-heterodimers for microtubule assembly. These core building blocks interact longitudinally, polymerizing into protofilaments. The protofilaments then interact with one another through lateral bonding forces to form stable cylindrical microtubules. These cylindrical filaments are dynamic as they undergo repeated assembly and...
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In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
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Controlled Cortical Impact Model for Traumatic Brain Injury
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Published on: August 5, 2014

Critical fluctuations in cortical models near instability.

Matthew J Aburn1, C A Holmes, James A Roberts

  • 1School of Mathematics and Physics, The University of Queensland Brisbane, QLD, Australia.

Frontiers in Physiology
|September 7, 2012
PubMed
Summary

Non-linear dynamics in brain activity, specifically the Jansen-Rit model, show statistical signatures near bifurcations. These indicators, like autocorrelation length, depend on the direction of neural input, impacting electroencephalography (EEG) signal interpretation.

Keywords:
Hopf bifurcationautocorrelationcritical fluctuationsneural mass model

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Area of Science:

  • Computational neuroscience
  • Non-linear dynamical systems
  • Brain activity modeling

Background:

  • Cortical dynamics are often assumed to be linearly stable.
  • Human electroencephalography (EEG) data reveals long-term autocorrelation, suggesting non-linear influences.
  • Statistical properties like power-law scaling and bistable switching may indicate bifurcations in non-linear systems.

Purpose of the Study:

  • To investigate statistical signatures accompanying bifurcations in a computational model of cortical activity (Jansen-Rit model).
  • To understand how non-linear dynamics and input fluctuations affect brain activity patterns.

Main Methods:

  • Studied temporal fluctuations in the Jansen-Rit model of cortical activity.
  • Tuned background excitatory input to approach supercritical Hopf bifurcations.
  • Analyzed autocorrelation length, variance, and power-law scaling of fluctuations.

Main Results:

  • A significant increase in autocorrelation length was observed near Hopf bifurcations.
  • This increase was sensitive to the direction of input fluctuations in phase space.
  • Power-law scaling in fluctuation size and duration was observed over four orders of magnitude at the bifurcation point.

Conclusions:

  • The study demonstrates that statistical indicators of linear instability can be detected in computational models of brain activity.
  • The expression of these indicators is sensitive to the neuronal pathway of incoming fluctuations.
  • These findings have implications for interpreting electroencephalography (EEG) signals and understanding non-linear brain dynamics.