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The fitness F of a model M to the target data was calculated from the following equation:
EMBED Equation.3, (P SEQ Peq \* MERGEFORMAT \* MERGEFORMAT 1)
where the summation over p represents a sum of this fitness function over two current injection protocols [0, 100 pA]. The three error terms EAP,p, EFR(Slope),p and EFR(Area),p were the error in AP shape ADDIN EN.CITE Weaver200616716716717Weaver, C. M.Wearne, S. L.The role of action potential shape and parameter constraints in optimization of compartment models.Neurocomputing1053-1057692006[42], firing rate area, and firing rate slope between model and target data. The general error term
EMBED Equation.3 (P SEQ Peq \* MERGEFORMAT \* MERGEFORMAT 2)
improved optimization performance by penalizing bursting, firing delay and silent models. Appropriate weights for each term in Equations P1 ((, (, () and P2 (si, i=1,..,3) were chosen heuristically and are given below. The computation of each error term for a given protocol p is described briefly below.
Action potential shape error, EAP
The average shape error EAP was calculated from the individual shape errors EAP(i) between the ith target and model APs within a time window W. The ith target AP and the ith model AP were shifted in time to align their peaks, and the root mean squared (RMS) difference between them, within the window W, was calculated (Fig. S8A). The total AP shape error EAP was the mean of these individual shape errors. We used W = [-5,45] ms relative to each AP, and (=2 in Eq. P1. When there were more model than target APs, the shape of each extra model AP was compared against the last target AP.
Firing rate slope error, EFR(Slope)
The instantaneous firing rate, defined as the reciprocal of each interspike interval, was computed between successive spikes of all model and target data. Fitting a straight line to the instantaneous firing rates versus time, FR(t) = mt + b, for the model and target data separately gave slopes mM and mT and intercepts bM and bT for model and target data respectively (Fig. S8B). Then
EMBED Equation.3, (P SEQ Peq \* MERGEFORMAT \* MERGEFORMAT 3)
with the weight (=1000 in Eq. P1.
Firing rate area error, EFR(Area)
The area between the model and target firing rate versus time curves was computed using the best fit lines defined by (bM, mM) and (bT, mT) above. Let {ti , i=1,..., NT} be the times of the target APs. Taking the RMS difference between the model and target lines over each of these times gave
EMBED Equation.3, (P SEQ Peq \* MERGEFORMAT \* MERGEFORMAT 4)
using the weight (=0.3 in Eq. P1 above. This error is represented by the shading in Figure S8B.
Burst penalty, EBurst
The total number of interspike intervals shorter than a user-defined minimum B ms. Here, B=20, s1 =10.
Firing delay penalty, EDelay
This function penalized the difference between the timing of the first target and first model AP. The penalty was defined by
EMBED Equation.3 , (P seq Peq \* MERGEFORMAT \* MERGEFORMAT 5)
where T1 was the time of first target AP, M1 the time of the first model AP, and ISIT the mean interspike interval of the target data. The parameter s2 = 0.3.
Silent slope penalty, ESilent
An additional penalty, proportional to the area between firing rate curves defined above, was applied to any model that does not fire any APs:
EMBED Equation.3, (P SEQ Peq \* MERGEFORMAT \* MERGEFORMAT 6)
with s3 = 2.
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