Design Principles of Pancreatic Islets: Glucose-Dependent Coordination of Hormone Pulses

Abstract

Pancreatic islets are functional units involved in glucose homeostasis. The multicellular system comprises three main cell types; β and α cells reciprocally decrease and increase blood glucose by producing insulin and glucagon pulses, while the role of δ cells is less clear. Although their spatial organization and the paracrine/autocrine interactions between them have been extensively studied, the functional implications of the design principles are still lacking. In this study, we formulated a mathematical model that integrates the pulsatility of hormone secretion and the interactions and organization of islet cells and examined the effects of different cellular compositions and organizations in mouse and human islets. A common feature of both species was that islet cells produced synchronous hormone pulses under low- and high-glucose conditions, while they produced asynchronous hormone pulses under normal glucose conditions. However, the synchronous coordination of insulin and glucagon pulses at low glucose was more pronounced in human islets that had more α cells. When β cells were selectively removed to mimic diabetic conditions, the anti-synchronicity of insulin and glucagon pulses was deteriorated at high glucose, but it could be partially recovered when the re-aggregation of remaining cells was considered. Finally, the third cell type, δ cells, which introduced additional complexity in the multicellular system, prevented the excessive synchronization of hormone pulses. Our computational study suggests that controllable synchronization is a design principle of pancreatic islets.

Fig 1. Cellular organization and interaction in pancreatic islets.

Endocrine α (red), β (green), and δ cells (blue) generate pulses of glucagon, insulin, and somatostatin, respectively. They positively (red arrows) or negatively affect (blue bar-headed arrows) hormone pulses of neighboring cells.

Fig 2. Snapshots of islet-cell activities.

Sequential phase changes of α (red circle) and β cells (green circle) with time at different glucose conditions: (A) r_β/r_α = 0.1 (low glucose); (B) r_β/r_α = 1 (normal glucose); (C) r_β/r_α = 10 (high glucose). Each cell spontaneously alternates its phase between 0 (light color) and π (dark color), and its neighboring cells perturb the oscillation. Note that cross sections of three-dimensional structures are displayed for clarity.

Fig 3. Glucose-dependent synchronization of islet cells in mouse and human islets.

Cross sections of (A) mouse and (B) human islets with α (red) and β cells (green). Synchronization and phase coordination of islet cells in (C) mouse (n = 29) and (D) human islets (n = 28). Synchronization indices R_α and R_β represent the degrees of synchronization between α cells and between β cells, respectively, and phase index ΔΘ indicates the difference of average phases of α and β cells. Islets are categorized into three groups according to size N: small islets (N < 1000 cells, blue circle); medium islets (1000 < N < 2000, red square); and large islets (N > 2000, orange triangle). Black lines represent average values of corresponding indices of every islet.

Fig 4. Islet structure and synchronization.

(A) Complete sorting (black circle), (B) shell-core sorting (blue square), and (C) mixing (red diamond) structures of α (red) and β cells (green). The total number of cells and the fraction of β cells are fixed as N = 725 and p_β = 0.6, respectively for all three structures. Note that cross-sections of three-dimensional structures are displayed for clarity. (D) Synchronization index R_β of β cells for different glucose conditions.

Fig 5. Cellular composition and synchronization.

Synchronization indices R_α of α cells (red) and R_β of β cells (green) for various cellular compositions in (A) shell-core sorting and (B) mixing structures. The fractions of β cells are p_β = 0.6 (black circle), 0.7 (blue square), 0.8 (red diamond), and 0.9 (green triangle) among N = 725 cells. Note that cross-sections of three-dimensional structures are displayed for clarity.

Fig 6. Cellular interaction and synchronization.

Synchronization indices R_α of α cells (red) and R_β of β cells (green) and the average phase difference ΔΘ between α and β cells are measured for four scenarios of the mutual interaction between α and β cells in (A) mouse and (B) human islets: (i) α cells activate β cells, while β cells suppress α cells (black circle); (ii) opposite interaction to (i) (blue square); (iii) mutual activation (magenta diamond); and (iv) mutual inhibition (red triangle). Note that (i) black line represents the result from the true interaction in natural islets (See Fig 3).

Fig 7. Synchronization of islet-cells under β-cell loss.

(A) To simulate human diabetic islets, β cells were selectively removed randomly from human islets (n = 28): no (black circle), 30% (blue square), 50% (red diamond), 70% (green triangle), and 90% loss of β-cell mass (yellow empty circle). Note that cross-sections of three-dimensional structures are displayed for clarity. (B) Synchronization index R_β of β cells for the loss of β cells. (C) The remaining cells after the removed β cells (50%) were re-aggregated. (D) Synchronization index R_β of β cells with (red diamond, solid line) and without (red diamond, dashed line) the consideration of re-aggregation. The error bars represent standard errors.