3.2 Iterative Manual Searches

3.3 Sensitivity Testing & "Sensible" fitting

3.4 Numerical Accuracy

A truly professional approach to simulations involves

- a knowledge of the strengths and limits of one's tools - Fitting algorithms, for example
- a knowledge of and skill in manual iterative fit to multiple records
- an ability to fit multiple types of data
- applying sensitivity tests or "Simulation controls"
- testing numerical accuracy
- an ability to make the most sensible fit in the face of moderate or poor data

- 1. a
delayed, sigmoid onset following depolarization but

2. a "fall with no appreciable inflexion" upon repolarization.

This formulation was so powerful and accurate that it is still - some four decades later - the most widely used set of equations (expressions) for describing the ionic channels in nerve cells. That this is true in spite of the fact that other models have been developed which give better fits to other data observed later is truly remarkable and enviable.

This work must be the supreme example of craftsmanship in the field and, while every effort should be made to emulate it with each new system simulated, it may well be that no one else will be able to approach it's completeness.

Another example of where multiple data sets were employed to achieve a "reasonable" representation of neuronal function comes from the work of Fred Dodge on a model of the spinal motoneuron of the cat. He took a Rallian electro-morphological description for soma and dendrites of this cell. From the work of Coombs, Curtis, & Eccles (1957) he postulated that the threshold in the axon was lower than that in the soma and adjusted the rate constants in the HH equations to model this. Furthermore he took voltage clamp data on this motoneuron to set the densities of the HH channels and sought credibility for this model by demonstrating that several independent experimental observations of antidromic and orthodromic propagation were reproduced by the simulations.

Traub (1977) also has employed a variety of types of experimental data to set the density and types of channels in a model of the motorneuron: (a) firing frequency vs current injected into the soma, (b) the shape of the interspike voltage trajectory, (c) afterhyperpolarizations, antidromic spike invasion properties, etc.

In unpublished simulations of a stylized motorneuron, I have adjusted the location and density of HH channels to fit experimental observations: (a) current observed during voltage clamp of the soma, and (b) the shapes and amplitudes of orthodromically generated spikes. In order to match the data on antidromic impulse invasion I had to search for the appropriate first internodal distance. However changes in the assignment of this parameter degraded the quality of fit to (a) or (b) or both. In order to achieve a reasonable fit to all experimental observations I had to iterate the parameter search cycle several times.

- (1) a fitting algorithm which finds the correct values for known generating curves
- (2) a good of fit of a model to experimental data, BUT ALSO
- (3) a knowledge that the structure of the model is isomorphic with the system.

The praxis fitting algorithm has been used to demonstrate this problem. The accuracy of this algorithm is demonstrated by using it in a NEURON application program to find the parameters for a curve generated by a pair of known exponentials. Here it finds both the amplitudes and time constants precisely.

** However** when the
number of states in a model differs from
that in the biological system, one can be
deluded very easily into thinking that one
has a good fit to data. In fact, there may
be NO relation between the model
parameters and those in the system. This
is demonstrated in the figure below where data
points taken from a decay curve
generated by the sum of 3 exponentials is
overlaid by the curve resulting from
forcing a model having only 2
exponentials to fit those data.
Here the
three components generating the data
points have equal amplitudes of 1 and
decay time constants which increase in
the ratios of 1: 3: 9. The "fitted" components have amplitudes (Amp1=1.23 &
Amp2=1.56)
and time constants (tau1=6.77 & tau2=0.37) as seen in the
output panel below. These
"fitted" parameters have no relation to the data values. Nevertheless the
fact that the model curve overlays the data points so well often provokes an
inappropriate
confidence in one's knowledge of the properties of the data.

Only when the ratio between the time constants is increased to 10-fold does the lack of quality in fitting become apparent. This 10-fold difference in the taus strains the algorithm and reveals the poor quality of the parameters found.

A copy of this program is available and one may run it with one's own choices to examine the effect of) changes in relative amplitude and time constants, etc., of the generating function.

Simulations were obviously required and showed up the flaws and possible misinterpretations immediately. Early in the 1960's I ran analog computer simulations on a patch of HH membrane in order to examine the quality of the ramp clamp to generate realistic sodium current patterns. For other rates however, the shape of the curves deviated sharply because both the sdium and potassium conductances vary with time as well as voltage and BOTH contributed to the current observed at any time. I found the distortions so great and the confusing mixture of contributions of potassium to the "sodium" current that I did not judge it worth while to write a paper on a technique which I felt was completely useless.

This is an example of where the verisimilitude of a hoped for match to data could give unwarrented confidence in a completely erroneous interpretation. Nonetheless the ramp clamp was later rediscovered and proposed as a useful way to record data very quickly because the output traces resembled the conventional peak and steady state plots of the step voltage clamp. Because of this I deem it necessary to show figures from ramp clamp simulations.Because my previous analog simulations were unpublished, a colleague, Kevin Martin, used NEURON to recreate them for me and are are shown here. A particular rate of voltage sweep (2mSec for -70mV to +70mV) was chosen to yield a plot resembling the sodium current. Of course for other rates, the shape of the curves deviated sharply because both the sodium and potassium conductances vary with time as well as voltage and BOTH contributed to the current observed at any time.

The most obvious failing with the ramp clamp showed up when the sodium conductance had been completely blocked by application of tetrodotoxin (TTX). While the inward current disappeared for a fast ramp, an outward current persisted at voltages above the sodium equilibrium potential! Having done the original voltage clamp experiments showing that TTX blocked the sodium current in both directions, I knew that this outward current masquerading as Na current was specious. Simulations of this condition showed similar plots and revealed that the apparent "outward sodium current" was actually carried by potassium!

Forward to: 3.2 Manual Iterative Searches

Forward to: 3.3 Sensitivity Testing

Forward to: 3.4 Numerical Accuracy