β-cell intrinsic dynamics rather than gap junction structure dictates subpopulations in the islet functional network
- Department of Bioengineering, University of Colorado Anschutz Medical Campus, United States
- Barbara Davis Center for Childhood Diabetes, University of Colorado Anschutz Medical Campus, United States
- Centre for Systems Modelling and Quantitative Biomedicine, University of Birmingham, United Kingdom
- Department of Biomedical Informatics, University of Colorado Anschutz Medical Campus, United States
Figures
Figure 1 with 2 supplements
Analysis of parameters underlying functionally connected cells from the Cha-Noma model, representing fast oscillations.
(a) Schematic of 1000 β-cell computational model, with cells false-colored by heterogeneity in rate of glucokinase, kglyc (left) and gap junction conductance, gcoup (right) parameter values. (b) …
Figure 1—figure supplement 1
Functional network sensitivity to threshold in Cha-Noma model.
(a) Degree distribution of five simulated islets with five different thresholds. (b) kglyc comparing hubs and non-hubs across five different thresholds. (c) gcoup comparing hubs and non-hubs across …
Figure 1—figure supplement 2
Functional network dependence with alternative hub cell definition in Cha-Noma model.
Hubs can be alternatively defined as the 10% of cells with the highest number of functional connections. (a) kglyc comparing alternatively defined hubs and non-hubs. (b) gKATP comparing …
Figure 2 with 2 supplements
Analysis of parameters underlying functionally connected cells from the integrated oscillator model, representing slow oscillations.
(a) Two-dimensional slice of the simulated islet from slow simulation, with lines (edges) representing functional connections between synchronized cells. Hub cells indicated in red. Slice is taken …
Figure 2—figure supplement 1
Functional network sensitivity to threshold in integrated oscillator model (IOM).
(a) Average rate of glucose metabolism (kglyc) values compared between hubs and non-hub in IOM simulated islet determined using threshold 0.999999998. There were on average 18 hubs. This threshold …
Figure 2—figure supplement 2
Functional network dependence with alternative hub cell definition in integrated oscillator model.
Hubs can be alternatively defined as the 10% of cells with the highest number of functional connections. (a) kglyc comparing alternatively defined hubs and non-hubs. (b) gKATP comparing …
Figure 3 with 2 supplements
Experimental comparison between the functional network from slow β-cell oscillations, NAD(P)H activity, and coupling conductance.
(a) Mouse pancreatic islet expressing fluorescent calcium indicator GCaMP6s in β-cells. Glucose level 11 mM. (b) GCamp6s time traces recorded at 2 and 11 mM glucose. Red curves represent dynamics of …
Figure 3—figure supplement 1
Experimental results for fast and mixed oscillations reveal no relationship between gap junction conductance and functional degree.
(a) Recovery rate vs. normalized degree for functional network synchronization threshold 0.85. (b) Recovery rate vs. normalized degree for functional network synchronization threshold 0.95. (c) …
Figure 3—figure supplement 2
Experimental results with alternative hub cell definition.
Hubs can be alternatively defined as the 10% of cells with the highest number of functional connections. (a) Change of the NAD(P)H levels compared between β-cell hubs and non-hubs. Change in NAD(P)H …
Figure 4
Comparison of functional connections, gap junctions, and glucose metabolism in the simulated islet.
(a) Functional connections and structural connections for a representative highly connected β-cell hub, average cell, and low connected cell. Blue cells and edges indicate cells determined as …
Figure 5 with 2 supplements
Comparison of long-range functional synchronization, gap junction network, and glucose metabolism in the simulated islet.
(a) Functional connections and gap junction connections for a representative cell (black). Synchronized cells in blue, gap junction coupled cells in red. Inset shows the entire structural network …
Figure 5—figure supplement 1
Paths that maximized gap junction conductivity.
(a) Cumulative distribution functions of total conductance between two cells from 1 to 12 cells apart. Synchronized CDF is shown in blue, non-synchronized CDF is shown in green. (b) Bar charts …
Figure 5—figure supplement 2
Paths that maximized metabolic rate.
(a) Cumulative distribution functions of total kglyc between two cells from 1 to 12 cells apart. Synchronized CDF is shown in blue, non-synchronized CDF is shown in green. (b) Bar charts comparing …
Figure 6 with 1 supplement
Experimental islet functional networks are influenced by changes in the structural network.
(a) Representative images of Cx36+/+ islet (left), heterozygous Cx36+/- islet (middle), and homozygous islet (right), overlaid with a synchronization network. Dot signifies a cell, blue lines …
Figure 6—figure supplement 1
Alternative network metrics for calcium islets from Cx36KO (Cx36 knockout) mice.
(a) Averaged degree distribution histograms for all islets analyzed. Error bars indicate standard deviation. Purple (top) histogram shows the distribution of connections for wild-type (Cx36+/+) …
Figure 7 with 1 supplement
Simulated islet functional networks are influenced by changes in the structural network.
(a) Functional connections and structural connections in simulated islets of hub cells for high and low gap junction conductance. Blue cells and edges indicate cells determined as ‘synchronized’ via …
Figure 7—figure supplement 1
Alternative network metrics for simulated islet with gap junction coupling change.
(a) Averaged degree distribution histograms for all islets analyzed. Error bars indicate standard deviation. Purple (top) histogram shows the distribution of connections for fully coupled (0.12 nS) …
Figure 8
Graphical summary of results.
Graphical summary of results from data. Inset shows how structural gap junctions are translated to structural network and synchronized calcium oscillations are translated to functional network. To …
Author response image 1
Author response image 2
Tables
Table 1
Essential network statistics and types.
Left: Five network statistics used to quantify the network in this paper. Representative networks show an example of the statistic in red and the rest of the network in blue. Right: Five network …
| Network essentials | |||||
|---|---|---|---|---|---|
| Network statistics | Network types | ||||
| Degree | Number of edges for a given node |  | Regular | A network with ordered connections: high clustering coefficient and long average path length |  |
| Degree distribution | The distribution of the network’s degrees | Small world | A regular network with a few rewired edges: high clustering coefficient and short average path length |  | |
| Clustering coefficient | Likelihood of how often neighbors of a node share connections with each other |  | Random | A network with random connections has low clustering coefficient and short average path length |  |
| Shortest path | Shortest distance between any two nodes |  | Scale-free | A network whose degree distribution follows a power law, such that there are a few very highly connected nodes called hubs |  |
| Efficiency | Inverse of the shortest path | Weighted | A network whose edges are weighted by some edge property |  | |
Author response table 1
| UnpairedP-value | Pairedp-value | Shapiro-Wilk Normality Test (Yes = normally distributed)(Hubs/Non-hubs) | Kolmogorov-Smirnov Normality Test(Yes = normally distributed)(Hubs/Non-hubs) | |
|---|---|---|---|---|
| kglyc | <0.0001 | 0.0001 | Yes/Yes | Yes/Yes |
| gcoup | 0.0180 | 0.0147 | Yes/Yes | Yes/Yes |
| gKATP | 0.1602 | 0.1829 | Yes/No | Yes/Yes |
