The Integrated Alpha-
Cell Regulation Model

We can now construct a model that considers both the glucose-dependent response and the nonglycemic regulation by multiplying the two models.  First, we use the glucose concentration in the glycemic model to calculate a preliminary glucagon concentration.  Then, we multiply this preliminary glucagon concentration by the adjustment factor in the nonglycemic model at each point in time post-meal to generate a predicted glucagon concentration.

This combination of models is termed the “Integrated Alpha-Cell Regulation Model.” (The “integrated model.”)

In Exhibit 30 we compare for nondiabetics the actual glucagon concentrations to those predicted by the integrated model.

Exhibit 30.jpg

The fit is quite good, as shown in Exhibit 31 which compares the integrated model predictions of circulating glucagon to the measured levels.

Exhibit 31.jpg

The slope is close to 1.0 with an intercept of 6 pg/ml, and the R-squared is 0.93; thus, the integrated model accounts for over 90% of the variation in glucagon for this study, a level similar to the R-squared value for the insulin model (Exhibit 10).

We expected that the integrated model would do a good job of predicting the data from which it was derived.  To test the general applicability of the model, we used the integrated model to predict glucagon levels for the simple carb study and correlated the predicted values with actual simple carb results as shown in Exhibit 31.  The R-squared was 0.88; however, the slope of that linear correlation equation was 0.66, and the intercept was 33 pg/ml.  Presumably this deviation from a slope of 1.0 and an intercept of 0.0 reflects the slight differences in the dose-response curves shown in Exhibit 17.

To determine whether the nonglycemic effects on glucagon secretion differed between studies, we used the glycemic equations in Exhibit 17 to calculate the deviations from the glucose correlation equations.  The simple carb deviations mimicked the breakfast deviations in the diurnal study, as shown in Exhibit 32.

  • The basal fasting deviation of the simple carb study is almost three times as deep as that of the diurnal study glycemic model prediction.  As shown in Exhibit 26, the breakfast deviation for the diurnal study was 30%, which is similar to the simple carb study in Exhibit 28.

  • The two studies show similar four-phase patterns of nonglycemic variations.

  • However, Phase 2 of the simple carb study is shorter, reaching bottom about 30 minutes earlier than the diurnal study.   The simple carb study also showed a deeper deviation below the glycemic prediction at the end of Phase 2.

Exhibit 32.jpg

We then applied the integrated model to analyzing the degree and timing of hyperglucagonemia in the T1D population.  Exhibit 33 compares the actual diurnal glucagon profile of the T1D subjects to the profile predicted by the Integrated Model.

Exhibit 33.jpg

At the start of mealtimes, T1D glucagon levels are briefly in the “normal” zone for the relevant glucose levels and prandial timing, but between meals T1D glucagon levels are excessive, with a total daily over-exposure of about 35% based on AUCs.

Since T1D patients have lost the glucose-driven regulatory mechanism, their pattern of postprandial glucagon variations could be expected to mimic those predicted by the nonglycemic model, if the non-glucose forcings on alpha-cells are relatively normal in T1D.  To test this idea, for each of the three diurnal study meal periods for T1D subjects, we calculated the five-hour glucagon average concentrations, then calculated for each meal period the percentage deviations of actual glucagon levels from these averages (Actual / Projected – 1), and finally averaged the three deviations for each time reading.  This index is equivalent to assuming that circulating glucose has no effect on circulating glucagon in T1D.

As shown in Exhibit 34, the T1D deviation from average pattern is remarkably similar to the nonglycemic model for healthy subjects.

Exhibit 34.jpg

Following are the differences between nonglycemic-driven glucagon in healthy vs. T1D subjects by phases of the nonglycemic model:

  • Phase 1:  The T1D rate of increase is the same as the healthy rate, except that the T1D rise peaks at about the average concentration.

  • Phase 2:  Both T1D and healthy deviations decline to about the same level, except that the T1D nadir is reached about 30 minutes earlier.

  • Phase 3:  Again, the T1D rate of increase is about the same as the healthy rate, except that the peak is reached about 60 minutes earlier.

  • Phase 4:  Both T1D and healthy glucagon deviations have converged at just over 10% by five hours.

It appears from the profiles in Exhibit 34 that, while T1D subjects have lost glycemic regulation of alpha-cells, that the nonglycemic regulatory mechanisms remain largely intact.  This also suggests that the nondiabetic deviations from the glycemic model are not caused by time lags in alpha-cell response to circulating glucose levels.