Models of Electrical Activity: Calibration and Prediction Testing on the Same Cell  Maurizio Tomaiuolo, Richard Bertram, Gareth Leng, Joël Tabak  Biophysical Journal  Volume 103, Issue 9, Pages 2021-2032 (November 2012) DOI: 10.1016/j.bpj.2012.09.034 Copyright © 2012 Biophysical Society Terms and Conditions

Figure 1 Model calibration is important for reliable predictions. Three different combinations of the conductances gCa, gK, gSK, gBK, and gleak are used in the model (Table 2), with each combination producing tonic spiking. With the first parameter set (model A), increasing gCa (Ab) or gBK (Ac) by 1 nS does not affect the tonic spiking. With the second parameter set (model B), increasing gBK (Bc) results in a transition to bursting, but increasing gCa (Bb) does not. Using the third parameter set (model C), an increase in gCa (Cb) results in a transition to bursting, but an increase in gBK (Cc) does not. Biophysical Journal 2012 103, 2021-2032DOI: (10.1016/j.bpj.2012.09.034) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 2 Current and new strategies for model calibration and predictions testing. (A) With the current strategy, a model is tested on cells other than those used for calibration. (B) With the new strategy, the model is tested on the cell used to calibrate it. Biophysical Journal 2012 103, 2021-2032DOI: (10.1016/j.bpj.2012.09.034) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 3 Calibration on synthetic data. (A and D) Target trace (solid line) and corresponding fit (open triangles) for tonic spiking (A) and bursting (D). (B and E) Target voltage-clamp currents (solid lines) and corresponding fits (open triangles) for tonic spiking (B) and bursting (E). (C and F) Parameter distances for spiking (C) and bursting (F). Biophysical Journal 2012 103, 2021-2032DOI: (10.1016/j.bpj.2012.09.034) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 4 Accuracy of calibration depends on the data used and the number of fitting parameters. Each column represents the average of 10 fits. (A) Average fitness score for fits to tonic spiking, bursting, spiking using voltage-clamp (VC) data, and bursting using voltage-clamp data. (B) The average parameter distance (sum of the absolute distances for the five fitting parameters) is greatly reduced when voltage-clamp data are used in the fitting process. (C and D) Fitness and parameter accuracy decline as the number of free parameters is increased. For all fits, we used bursting with voltage-clamp data. Each data point represents the mean of 10 fits, with randomly chosen parameters to be estimated. For each parameter we created a uniform distribution within ±90% of its default value. (C) Fitness decreases as the number of parameters increases. (D) Accuracy of parameter estimation decays (absolute parameter distance increases) as the number of parameters to be estimated increases. Biophysical Journal 2012 103, 2021-2032DOI: (10.1016/j.bpj.2012.09.034) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 5 Predictions using different calibration scenarios. The vertical axis shows the fraction of models with ≥2 (black), ≥4 (gray), and 6 (white bars) of 6 correct predictions. (A) First set of bars (CTRL) is for the case where no calibration was used. Second set of bars (Calibration) shows the case where the calibration process was used to fit five parameters. Third set of bars (Missing Current) refers to the case where calibration was used to fit five parameters but a current was missing from the model. (B) CTRL bars refer to no calibration, and all parameters were different from the target. Second set of bars (Incorrect Parameters) refers to the case where the calibration procedure was used to fit five parameters. Biophysical Journal 2012 103, 2021-2032DOI: (10.1016/j.bpj.2012.09.034) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 6 Testing model predictions: bursting from spiking and vice versa via BK modulation. (A and B) Voltage-clamp and voltage-trace model fits. (C) Testing the model prediction (dashed line) that adding 1 nS of BK conductance should convert spiking to bursting. Tested on the same cell used for calibration (solid line). (D) Testing the model prediction that a further increase in BK conductance will increase the duration of the burst active phase. (E and F) Voltage-clamp and voltage-trace model fits. (G) Testing the model prediction that removal of BK conductance should convert bursting to spiking. Biophysical Journal 2012 103, 2021-2032DOI: (10.1016/j.bpj.2012.09.034) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 7 The model was calibrated to a spiking cell and then several predictions were made and tested with dynamic clamp on the same cell. Prediction 1 was that spikes would convert to bursting when gBK = 1 nS is added. Prediction 2 was that broadening of the active phase and reduction of amplitude would occur when gBK is 10 nS and τBK is increased to 10 ms. Prediction 3was that there would be no conversion to bursting when τBK is 12 ms or more in the added current. The dashed lines indicate breaks in time. Biophysical Journal 2012 103, 2021-2032DOI: (10.1016/j.bpj.2012.09.034) Copyright © 2012 Biophysical Society Terms and Conditions