Figure 1.
oscillations from
-cells in intact islets. Islets are perfused with a solution containing 0.5 mM glucose for the first 10 minutes, and then, solution is changed to one containing 11 mM glucose for the following 15 minutes. Oscillations, triggered by low glucose concentrations, are highly irregular. The level of
is indicated in arbitrary fluorescence units.
Figure 2.
Stages proposed for glucagon secretion.
Granules coming from the Reserve pool () resupply the Primed pool (
) and then, upon binding 3
ions, granules become Fused (pool
). The Releasable stage includes all primed granules with 0 to 3 bound
.
and
are the forward and backward resupply rates, respectively.
and
are the binding and unbinding rates, respectively, associated to the
-sensor.
stands for the fusion rate that manages the last non-reversible step of exocytosis.
and
represent the rates of granules formation and granule release, respectively.
Table 1.
Parameters to estimate membrane concentration.
Table 2.
Parameters used to simulate secretion dynamics.
Figure 3.
and secretion dynamics in a 20-minute period, going from low (
) to high glucose (
). The
time-series are shown in arbitrary units (top), while simulated individual (middle) and average (bottom) secretion rates are in fg per cell per minute. Secretion is computed as the numerical integral of
, taking into account that 1 granule corresponds to 2 fg of glucagon. Notice that individual and average secretory responses have the same trends. All individual responses to low and high glucose are summarized in Figure 4.
Figure 4.
Individual cell secretion rates induced by
oscillations (A), and by constant
levels (B). The constant levels used for simulations correspond to the individual mean values of
oscillations. Secretion rates in pg per cell per hour predicted at
(dots) and
(triangles) are shown. Secretion in one hour is computed as the numerical integral of
, taking into account that 1 granule corresponds to 2 fg of glucagon. Lines indicate average secretion rates of the ensemble at low (blue) and high glucose (red). In agreement with experimental measurements, the model predicts that mean glucagon secretion is reduced at high glucose.
Table 3.
Distribution of individual -cell secretion.
Figure 5.
Cell secretion rates as a function of individual mean
level. Secretion rates are plotted against the mean
level of each cell, for different experimental and simulated conditions (see plot legend). Secretion in one hour is computed as the numerical integral of
, taking into account that 1 granule corresponds to 2 fg of glucagon. Best-fit curves for data sets are power functions with correlation coefficients
0.9. Notice that for a given value of individual mean
, the presence of low glucose (dots) induces a lower secretion rate than the high glucose (triangles), because of the glucose-dependence of granule resupply. The inset shows the behaviour of secretion rates at the lowest
range, indicating that for a mean
level of 0.1
M, the model predicts a basal rate about 0.1 pg/cell/hr (20–40 pg/islet/hr) in agreement with experimental observations [7]–[10].
Figure 6.
and secretion dynamics in a 20-minute period at low glucose (
), before and after the addition of 4 nM insulin. The
time-series in arbitrary units (top), as well as the simulated individual (middle) and average (bottom) secretion rates are shown in fg per cell per minute. Secretion is computed as the numerical integral of
, taking into account that 1 granule corresponds to 2 fg of glucagon. Notice that individual and average secretory responses have the same trends.
Figure 7.
Effect of insulin and high glucose on mean
level and glucagon secretion for the six studied islets. (A) Reduction of the mean
level due to the elevation of glucose in islets 1–3 (blue and red bars in the left), compared to the reduction induced by insulin at low glucose in islets 4–6 (blue and green bars in the right). Average
levels are indicated with dashed lines. (B) Glucagon inhibition induced by increasing extracellular glucose in islets 1–3 (blue and red bars in the left), compared to the inhibition induced by the presence of insulin in islets 4–6 (blue and green bars in the right). Secretion is normalized to the largest value to emphasize differences. Average secretions are marked with dashed lines.