182 CATALYZING INQUIRY
PANEL 3
FIGURE 5.16 Continued
Panel 3: Projection of trajectory onto fixed points of fast subsystem. The axes are v: membrane potential; h: inacti-
vation of the HH sodium channel (there is also a persistent sodium channel in the model); and n: activation of the
HH “delayed rectifier” potassium channel. The voltage traces show the changes of voltage as a function of time.
The values of h and n also change with time. Think of v, n, h as the three coordinates of a point moving through
space. This plot depicts the path taken by this point in a bursting oscillation of the model. The curves are states at
which the motion through this space is particularly slow, becoming zero in the limit so that the slower currents in
the model are not allowed to change at all. SOURCE: Derived from Figure 4, Panel A3, in R.J. Butera Jr., J. Rinzel,
and J.C. Smith, “Models of Respiratory Rhythm Generation in the Pre-Bötzinger Complex. I. Bursting Pacemaker
Neurons,” Journal of Neurophysiology 82(1):382-397, 1999. Copyright 1999 American Physiological Society. Used by
permission.
What has been missing is an appropriate set of tools for acquiring, building, simulating, and analyz-
ing biophysically realistic models of subcellular microdomains. Coggan et al. have developed and used
a suite of such computational tools to build a realistic computational model of nicotinic synaptic trans-
mission based on serial electron tomograms of a chick ciliary ganglion somatic spine mat.^105
The chick ciliary ganglion somatic spine mat is a complex system with more than one type of
neurotransmitter receptor, possible alternative locations for transmitter release, and a tortuous synaptic
geometry that includes a spine mat and calyx-type nerve terminal. Highly accurate models of the
synaptic ultrastructure are obtained through large-scale, high-resolution electron tomography; com-
(^105) J.S. Coggan, T.M. Bartol, E. Esquenazi, J.R. Stiles, S. Lamont, M.E. Martone, D.K. Berg, M.H. Ellisman, and T.J. Sejnowski,
“Evidence for Ectopic Neurotransmission at a Neuronal Synapse,” Science 309(5733):446-451, 2005.