3.3 Sensitivity Testing and "Sensible" fitting
"Simulation Controls"
Testing the sensitivity (steepness) of simulation outputs to perturbations in all
parameters is essential for professional modelers. Such tests can be considered as
equivalent to
controls in experiments where for example, one tries to find flaws in the hypothesis
under
consideration. Their use gives confidence in the validity of conclusions for the model
and enhances
acceptability to the experimental community. I have, on occasion, observed
considerable reluctance
in acceptance of (and even hostility to) the results of simulations presented to
audiences of
experimenters. I believe that much of this comes about from the lack of attention to
appropriate sensitivity testing by the author.
"Sensible" fitting
The meaning of the term "sensible" is rather subjective but Hodgkin and Huxley
give
numerous examples of the high quality of judgement implied therein. One example was
in the
scaling of their data to "correct" for considerable degradation of physiological
condition with
time. Another was to use independent data on the changes in dynamics induced by
heating or
cooling to adjust for the differences in temperature existing among the data sets and
arrive at a
better composite representation of all of their data. Otherwise it may have taken them
another
squid season or two at Plymouth to collect sufficient data under a variety of conditions.
Yet another example was the choice of the 4th power instead of 6th for "n" in their
expression for the potassium conductance. This represented a very sensible balance of
calculation time vs accuracy because the higher power produced a
" better fit"
only at very short
times after the depolarizing step change in voltage. Now, when computers are so fast
that the
use of a higher power for the "n" variable would require and insignificant increase in
computation time, one might consider refitting their potassium conductance data with a
6th or higher power expression. Nevertheless, their equations have been so useful for
so long
that the slight improvement in the match to their experimental data would seem to be of
only
second-order or third-order importance.
Tight coupling between experiment and simulations
Probably a major reason that the contributions of Hodgkin and Huxley are so
remarkable and enduring results
from involvement in the whole process of developing their model:
- experiments,
- data collection, consolidation and analysis,
- the model selection, and
- the calculations.
In such a setting the investigator is aware of the problems and limitations through out
the experiment-simulation
cycle and can arrive at the most "sensible" use of their time and efforts to arrive at an
understanding of the system under investigation.
I have also found that simulations of my instruments individually and coupled to
the
experimental preparation extraordinarily useful. Such simulations of our voltage clamp
experiments:
(a) provided a unique way to evaluate the quality of data which in turn helped in
knowing "sensible" limits of their interpretation,
(b) showed that one should not take for granted the accuracy of the record shown
on an oscilloscope,
(c) showed sources and magnitudes of the errors in those records, and
(d) gave valuable information as to which errors were amenable to compensation or
correction.