Chapter 11
Signal Transmission
“Ginny!” said Mr. Weasley, flabbergasted. “Haven’t I taught
you anything? What have I always told you? Never trust
anything that can think for itself if you can’t see where it keeps
its brain?”
(J.K. Rowling, Harry Potter and the Chamber of Secrets)
11.1 Fitzhugh–Nagumo Neuron Model
The previous chapter showed rich dynamics for the case of chemical reactions in
open system. In that chapter, we stressed the sensitivity of system responses to
initial conditions and the role of nonlinearities in determining system behavior. The
model of this chapter captures nonlinearities in the changes of the physical state of a
cell in response to electrical impulses from its surroundings.
Figure 11.1 depicts a neuron or nerve cell. Neurons consist of a cell body,
picking up possible signals from one or all of its several dendritic branches (signals
from other neurons) and transmitting these received (electrical) signals down a
relatively long axon pathway to its terminal. At the terminal the signal is amplified
and transmitted across a synapse to the next nerve cell. The cell remains inactive
until the collective input from the dendrites reaches a critical level whereupon the
cell “fires”—it reacts in such a way as to amplify the collective input signals into a
signal potential at its terminal end. If the collective input signal is not great enough
the signal dies out in the cell due to the action of a recovery mechanism.
The Fitzhugh–Nagumo model is of a nerve cell under special laboratory conditions, where all dendritic receivers are kept at the same potential. The space-change
in potential along the axon and throughout the cell is thus ignored. The only way to
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_11,
© Springer International Publishing Switzerland 2014
91
Signal Transmission
“Ginny!” said Mr. Weasley, flabbergasted. “Haven’t I taught
you anything? What have I always told you? Never trust
anything that can think for itself if you can’t see where it keeps
its brain?”
(J.K. Rowling, Harry Potter and the Chamber of Secrets)
11.1 Fitzhugh–Nagumo Neuron Model
The previous chapter showed rich dynamics for the case of chemical reactions in
open system. In that chapter, we stressed the sensitivity of system responses to
initial conditions and the role of nonlinearities in determining system behavior. The
model of this chapter captures nonlinearities in the changes of the physical state of a
cell in response to electrical impulses from its surroundings.
Figure 11.1 depicts a neuron or nerve cell. Neurons consist of a cell body,
picking up possible signals from one or all of its several dendritic branches (signals
from other neurons) and transmitting these received (electrical) signals down a
relatively long axon pathway to its terminal. At the terminal the signal is amplified
and transmitted across a synapse to the next nerve cell. The cell remains inactive
until the collective input from the dendrites reaches a critical level whereupon the
cell “fires”—it reacts in such a way as to amplify the collective input signals into a
signal potential at its terminal end. If the collective input signal is not great enough
the signal dies out in the cell due to the action of a recovery mechanism.
The Fitzhugh–Nagumo model is of a nerve cell under special laboratory conditions, where all dendritic receivers are kept at the same potential. The space-change
in potential along the axon and throughout the cell is thus ignored. The only way to
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_11,
© Springer International Publishing Switzerland 2014
91