Catalyzing Inquiry at the Interface of Computing and Biology

178 CATALYZING INQUIRY

specified conductances and synapses enables researchers to test their intuitions regarding how these
networks function. Simulations also lead to predictions of the effects of neuromodulators and disorders
that affect the electrical excitability of the systems. Nonetheless, simulation alone is not sufficient to
determine the information we would like to extract from these models. The models have large numbers
of parameters, many of which are difficult or impossible to measure, and the goal is to determine how
the system behavior depends on the values of all of these parameters.
Dynamical systems theory provides a conceptual framework for characterizing rhythms. This theory
explains why there are only a small number of dynamical mechanisms that initiate or terminate bursts
of action potentials, and it provides the foundations for algorithms that compute parameter space maps
delineating regions with different dynamical behaviors. The presence of multiple time scales is an
important ingredient of this analysis because the rates at which different families of channels respond to
changes in membrane potential or ligand concentration vary over several orders of magnitude.
Figure 5.16 illustrates this type of analysis using a model for bursting in the pre-Bötzinger complex,
a neural network in the brain stem that controls respiration. The first panel shows voltage recordings
from intracellular recordings of a medullar slice from neonatal rats. Butera and colleagues measured
conductances in this preparation and constructed a model for this system.^104 Simulations of the burst-

a b

d c

f

e

g

k

x T

R

A=T⊗R

h i

A*

V

l j

n m

R ́⊗A*

A•A *

ε=<V,A•A*>

FIGURE 5.15 System for learning and performing deductive reasoning. The graphic describes the proposed sys-
tem used during solution of the Wason card selection task; see P.C. Wason and P.N. Johnson-Laird, Psychology of
Reasoning: Structure and Content, Harvard University Press, Cambridge, MA, 1972. This task requires determining
when a logical rule is valid or invalid, and so is a form of deductive reasoning. Humans perform notoriously badly
on many versions of this task, but well on other versions. This kind of context/content sensitivity is captured by
this model; see C. Eliasmith, “Learning Context Sensitive Logical Inference in a Neurobiolobical Simulation,” pp.
17-19 in Compositional Connectionism in Cognitive Science: Papers from the AAAI Fall Symposium, S.D. Levy and R.
Gayler, Program Co-chairs, October 21-24, 2004, The AAAI Press, Arlington, VA, Technical Report FS-04-03, 2004.
The depicted large-scale circuit consists of 14 neural subsystems, distributed across frontal and ventral areas of the
brain. This is a good example of the degree of complexity that can be built into a neurally realistic simulation using
these new techniques. Populations a-d learn and apply the appropriate context for interpretation of the rule (R)
encoded by population e. Populations f and g apply the relevant transformation (T) to the rule, giving the current
answer (A). Populations h, k, and l determine the degree of correctness or incorrectness of the suggested answer
(either given the correct answer, or given a reward or punishment signal), resulting in an error signal e. Popula-
tions m and n provide a guess at the best possible transformation. This guess and the error signal are integrated
into the learning algorithm. SOURCE: Courtesy of Chris Eliasmith, University of Waterloo.

(^104) 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.