COMPUTATIONAL MODELING AND SIMULATION AS ENABLERS FOR BIOLOGICAL DISCOVERY 177
priate parameter values, a constant input current larger than a certain critical value and turned on at a
given instant of time results in the potential difference across the membrane taking the form of a regular
spike train—which is reminiscent of how a real neuron fires. More realistic current inputs (e.g., stochas-
tic ones) result in a much more realistic-looking output.
Despite lack of information about much of the cellular and molecular basis of neuronal excitation at
the time, Hodgkin and Huxley were able to provide a relatively accurate quantitative description of
how an action potential was generated by voltage-dependent ionic conductivities. The Hodgkin-Huxley
model provided the basis for research for more than five decades, spinning off a new field of neuro-
physiology: in large part, this field rests on the foundation created by their model. Recent research on
membrane ion channels can be related directly to the seminal ideas and (more importantly) precise
mechanism that their model described.
The “plain vanilla” Hodgkin-Huxley model is still interesting today. For example, a recent study
demonstrated previously unobserved dynamics in the Hodgkin-Huxley model, namely, the existence of
chaotic solutions in the model with its original parameters.^103 The significance of chaos in this context is
that the excitability of a neural membrane with respect to firing is likely to be more complex than can be
explained by a simple sub- or super-threshold potential.
Simulation and mathematical analysis of models have become essential tools in investigations of
the complicated processes underlying rhythm generation in the nervous system. There are many types
of channels and synapses. The number of channels and synapses and their locations distinguish differ-
ent types of neurons from one another. Simulation of networks consisting of model neurons with
FIGURE 5.14 Rodent navigation. These figures depict the behavior of a neurally realistic simulation of the path
integrator in a rat. The simulation was generated by using a single (recurrent) generic neural subsystem. (A) When
the simulation is given random noise, it spontaneously generates a stable, localized bump of neural activity over the
neural sheet, which represents the rat’s current location. This demonstrates that a stable attractor (a widely accepted
model of how the rat’s path integrator is organized) has been implemented. (B) This model also implements control
(i.e., updating of the current location based on the rat’s motion) of the path integrator in a neurally plausible way.
Here, straight-line motion in a rightward direction is shown. (C) The model correctly integrates the circular path of
the rat, demonstrating that it can path integrate in any direction that the rat might move. This simulation has very
little error compared to the simulations of past models. SOURCE: Chris Eliasmith, University of Waterloo, personal
communication, September 7, 2004, and A. Samsonovich and B.L. McNaughton, “Path Integration and Cognitive
Mapping in a Continuous Attractor Model,” Journal of Neuroscience 17(15):5900-5920, 1997.
AB C(^103) J. Guckenheimer and R.A. Oliva, “Chaos in the Hodgkin-Huxley Model,” SIAM Journal on Applied Dynamical Systems 1(1):105-
114, 2002.