  Type 2 diabetes (T2D) is a challenging metabolic disorder characterized by a
substantial loss of $\beta$-cell mass via progressive programmed cell death and
alteration of $\beta$-cell function in the islets of Langerhans, disrupting
insulin secretion and glucose homeostasis. The mechanisms for deficiency in
$\beta$-cell mass and function during the hyperglycemia development and T2D
pathogenesis are complex. To study the relative contribution of $\beta$-cell
mass to $\beta$-cell function in T2D, we make use of a comprehensive
electrophysiological model from human $\beta$-cell clusters. We find that
defect in $\beta$-cell mass causes a functional decline in single $\beta$-cell,
impairment in intra-islet synchrony, and changes in the form of oscillatory
patterns of membrane potential and intracellular $\textrm{Ca}^{2+}$
concentration, which can lead to changes in insulin secretion dynamics and in
insulin levels. The model demonstrates good correspondence between suppression
of synchronizing electrical activity and pulsatile insulin release, and
published experimental measurements. We then compare the role of gap
junction-mediated electrical coupling with both $\beta$-cell synchronization
and metabolic coupling in the behavior of $\textrm{Ca}^{2+}$ concentration
dynamics within human islets. Our results indicate that inter-$\beta$-cellular
electrical coupling depicts a more important factor in shaping the
physiological regulation of islet function and in human T2D. We further predict
that varying the conductance gating of delayed rectifier $\textrm{K}^{+}$
channels modifies oscillatory activity patterns of $\beta$-cell population
lacking intercellular coupling, which significantly affect $\textrm{Ca}^{2+}$
concentration and insulin secretion.
