Phase transitions in single neurons and neural populations: Critical slowing, anesthesia, and sleep cycles

  • D.A. Steyn-Ross
  • M.L. Steyn-Ross
  • M.T. Wilson
  • J.W. Sleigh
Part of the Springer Series in Computational Neuroscience book series (NEUROSCI, volume 4)


The firing of an action potential by a biological neuron represents a dramatic transition from small-scale linear stochastics (subthreshold voltage fluctuations) to gross-scale nonlinear dynamics (birth of a 1-ms voltage spike). In populations of neurons we see similar, but slower, switch-like there-and-back transitions between low-firing background states and high-firing activated states. These state transitions are controlled by varying levels of input current (single neuron), varying amounts of GABAergic drug (anesthesia), or varying concentrations of neuromodulators and neurotransmitters (natural sleep), and all occur within a milieu of unrelenting biological noise. By tracking the altering responsiveness of the excitable membrane to noisy stimulus, we can infer how close the neuronal system (single unit or entire population) is to switching threshold. We can quantify this “nearness to switching” in terms of the altering eigenvalue structure: the dominant eigenvalue approaches zero, leading to a growth in correlated, low-frequency power, with exaggerated responsiveness to small perturbations, the responses becoming larger and slower as the neural population approaches its critical point–-this is critical slowing. In this chapter we discuss phase-transition predictions for both single-neuron and neural-population models, comparing theory with laboratory and clinical measurement.


subthreshold oscillation critical slowing excitable membrane bifurcation phase transition anesthesia sleep cycles 



This research was supported by the Royal Society of New Zealand Marsden Fund, contract UOW-307. We are grateful for assistance from I.P. Gillies, Yanyang Xu, and J.J. Wright.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • D.A. Steyn-Ross
    • 1
  • M.L. Steyn-Ross
    • 1
  • M.T. Wilson
    • 1
  • J.W. Sleigh
    • 2
  1. 1.Department of EngineeringUniversity of WaikatoHamiltonNew Zealand
  2. 2.Waikato Clinical School, University of Auckland,Waikato HospitalHamiltonNew Zealand

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