NONLINEARITY, OSCILLATIONS AND CHAOS
IN PACEMAKER NEURONS
In these studies,
a single compartment mathematical models
of central nervous system neurons of a snail, Helix pomatia, were used.
The models
demonstrated the major experimental observable phenomena in bursting neurons
and allow one to investigate the role of separate components in firing pattern
regulation, in particularly, neuropeptide-modulated currents.
Interspike
intervals (ISI), time courses of the membrane potential and [Ca2+]in
were employed to analyze different regimes in the models.
The model activity
can be silent, beating,
bursting,
and chaotic
depending on physiological significant parameters, initial conditions and
stimuli. Using methods of time series analysis (time series observation,
interspike interval histogram analysis, correlation and spectral analysis) and
quantitative and qualitative analysis of nonlinear dynamic systems (phase plane
trajectories and one-dimensional
return map construction, Lyapunov exponent computation), it was established
that approaches to chaos were generated. Different types of strange attractors
depending on structure and parameters of the models were investigated.
Period-doubling
bifurcation, crisis and fractal features in phase diagrams of initial conditions and bifurcation diagrams,
existence of several stable attractors at single sets of parameters were
revealed.
Fractal dimension (Df)
may be a measure of complexity of the diagram. At least two stable informational
significant modes of electrical activity can be selected from different firing
patterns: bursting and single spiking (beating and chaotic), which correspond
to different levels of
neurotrasmitter secretion. Bursting activity enhances neurotransmitter
release in vivo and an important factor in determining release is the number of
short interspike intervals.
Stable
parameter-independent mode transitions from one type of activity to another
(beating- chaotic-bursting
-silent) were induced by short-lasting membrane polarization and concentration
shifts of intracellular Ca ions. Transient
pulse induced a persistent change in model neuronal activity. These results
indicate that single bursting neuron can act as dynamical switch in neuronal
ensemble; the sensitivity of this switch can be regulated by modulatory
transmitter. The simulations suggest that deterministic chaos may play an
important role in information processing and storage at the level of a single
nerve cell.
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