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Functional connectivity in islets of Langerhans from mouse pancreas tissue slices.

Stožer A, Gosak M, Dolenšek J, Perc M, Marhl M, Rupnik MS, Korošak D - PLoS Comput. Biol. (2013)

Bottom Line: Moreover, we find that the range of interactions in networks during activity shows a clear dependence on the Euclidean distance, lending support to previous observations that beta cells are synchronized via calcium waves spreading throughout islets.Most interestingly, the functional connectivity patterns between beta cells exhibit small-world properties, suggesting that beta cells do not form a homogeneous geometric network but are connected in a functionally more efficient way.Presented results provide support for the existing knowledge of beta cell physiology from a network perspective and shed important new light on the functional organization of beta cell syncitia whose structural topology is probably not as trivial as believed so far.

View Article: PubMed Central - PubMed

Affiliation: Institute of Physiology, Faculty of Medicine, University of Maribor, Maribor, Slovenia.

ABSTRACT
We propose a network representation of electrically coupled beta cells in islets of Langerhans. Beta cells are functionally connected on the basis of correlations between calcium dynamics of individual cells, obtained by means of confocal laser-scanning calcium imaging in islets from acute mouse pancreas tissue slices. Obtained functional networks are analyzed in the light of known structural and physiological properties of islets. Focusing on the temporal evolution of the network under stimulation with glucose, we show that the dynamics are more correlated under stimulation than under non-stimulated conditions and that the highest overall correlation, largely independent of Euclidean distances between cells, is observed in the activation and deactivation phases when cells are driven by the external stimulus. Moreover, we find that the range of interactions in networks during activity shows a clear dependence on the Euclidean distance, lending support to previous observations that beta cells are synchronized via calcium waves spreading throughout islets. Most interestingly, the functional connectivity patterns between beta cells exhibit small-world properties, suggesting that beta cells do not form a homogeneous geometric network but are connected in a functionally more efficient way. Presented results provide support for the existing knowledge of beta cell physiology from a network perspective and shed important new light on the functional organization of beta cell syncitia whose structural topology is probably not as trivial as believed so far.

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Temporal evolution of the average correlation coefficient, average degree, global network efficiency, and average clustering coefficient under stimulation with glucose.In this figure, temporal changes of the average correlation coefficient (A), average degree (B), the global network efficiency (C) and the average clustering coefficient (D) are presented on a background of the mean-field calcium signal. Parameters calculated for network architectures obtained at different thresholds Rth are color-coded as indicated in the figures. In panels B–D Δτ = 100 s. For this Δτ, the number of degrees of freedom is such that significance at a level of p<0.001 is achieved for all Rij exceeding 0.62. Values of all of the parameters increase during activation and even more so under deactivation. During sustained activity, values are higher than before or after exposure to glucose. During activity, values tend to increase until the solution containing nonstimulatory glucose reaches the cells.
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pcbi-1002923-g004: Temporal evolution of the average correlation coefficient, average degree, global network efficiency, and average clustering coefficient under stimulation with glucose.In this figure, temporal changes of the average correlation coefficient (A), average degree (B), the global network efficiency (C) and the average clustering coefficient (D) are presented on a background of the mean-field calcium signal. Parameters calculated for network architectures obtained at different thresholds Rth are color-coded as indicated in the figures. In panels B–D Δτ = 100 s. For this Δτ, the number of degrees of freedom is such that significance at a level of p<0.001 is achieved for all Rij exceeding 0.62. Values of all of the parameters increase during activation and even more so under deactivation. During sustained activity, values are higher than before or after exposure to glucose. During activity, values tend to increase until the solution containing nonstimulatory glucose reaches the cells.

Mentions: Next we explored how the characteristics of the functional network evolved with time. A visualization of the rewiring process of functional connections within an islet throughout different phases can be found in Video S2. Furthermore, we calculated the evolution of Ravg as well as of several measures for network characterization – the average degree kavg, the global efficiency Eglob, and the average clustering coefficient Cavg, in order to trace the evolution of the functional network structure. For this purpose, we divided the time series of individual cells into intervals of length Δτ and calculated the quantities on given intervals, i.e. sliding windows. Results presented in Figure 4 reveal that Ravg, kavg, Eglob, and Cavg all displayed a similar behaviour, with a peak during activation and deactivation, and with values during activity being higher than during non-stimulatory conditions. The choice of duration of Δτ does not have a significant impact on the calculated Ravg (Figure 4A). Furthermore, it can be noticed that the network measures are qualitatively independent of the chosen threshold Rth, since with increasing Rth only a monotonous decrease of all quantities of interest is observed. To get a more precise insight into the temporal evolution of correlation between cell pairs we additionally calculated the sliding correlation with overlapping intervals. In particular, we calculated the average correlation within a constant interval Δτ = 100 s, whereby the interval was being slided along time series with a step Δτ′ = 20 s. Results showing a more detailed evolution of the average correlation between beta cells are presented in Figure S1.


Functional connectivity in islets of Langerhans from mouse pancreas tissue slices.

Stožer A, Gosak M, Dolenšek J, Perc M, Marhl M, Rupnik MS, Korošak D - PLoS Comput. Biol. (2013)

Temporal evolution of the average correlation coefficient, average degree, global network efficiency, and average clustering coefficient under stimulation with glucose.In this figure, temporal changes of the average correlation coefficient (A), average degree (B), the global network efficiency (C) and the average clustering coefficient (D) are presented on a background of the mean-field calcium signal. Parameters calculated for network architectures obtained at different thresholds Rth are color-coded as indicated in the figures. In panels B–D Δτ = 100 s. For this Δτ, the number of degrees of freedom is such that significance at a level of p<0.001 is achieved for all Rij exceeding 0.62. Values of all of the parameters increase during activation and even more so under deactivation. During sustained activity, values are higher than before or after exposure to glucose. During activity, values tend to increase until the solution containing nonstimulatory glucose reaches the cells.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3585390&req=5

pcbi-1002923-g004: Temporal evolution of the average correlation coefficient, average degree, global network efficiency, and average clustering coefficient under stimulation with glucose.In this figure, temporal changes of the average correlation coefficient (A), average degree (B), the global network efficiency (C) and the average clustering coefficient (D) are presented on a background of the mean-field calcium signal. Parameters calculated for network architectures obtained at different thresholds Rth are color-coded as indicated in the figures. In panels B–D Δτ = 100 s. For this Δτ, the number of degrees of freedom is such that significance at a level of p<0.001 is achieved for all Rij exceeding 0.62. Values of all of the parameters increase during activation and even more so under deactivation. During sustained activity, values are higher than before or after exposure to glucose. During activity, values tend to increase until the solution containing nonstimulatory glucose reaches the cells.
Mentions: Next we explored how the characteristics of the functional network evolved with time. A visualization of the rewiring process of functional connections within an islet throughout different phases can be found in Video S2. Furthermore, we calculated the evolution of Ravg as well as of several measures for network characterization – the average degree kavg, the global efficiency Eglob, and the average clustering coefficient Cavg, in order to trace the evolution of the functional network structure. For this purpose, we divided the time series of individual cells into intervals of length Δτ and calculated the quantities on given intervals, i.e. sliding windows. Results presented in Figure 4 reveal that Ravg, kavg, Eglob, and Cavg all displayed a similar behaviour, with a peak during activation and deactivation, and with values during activity being higher than during non-stimulatory conditions. The choice of duration of Δτ does not have a significant impact on the calculated Ravg (Figure 4A). Furthermore, it can be noticed that the network measures are qualitatively independent of the chosen threshold Rth, since with increasing Rth only a monotonous decrease of all quantities of interest is observed. To get a more precise insight into the temporal evolution of correlation between cell pairs we additionally calculated the sliding correlation with overlapping intervals. In particular, we calculated the average correlation within a constant interval Δτ = 100 s, whereby the interval was being slided along time series with a step Δτ′ = 20 s. Results showing a more detailed evolution of the average correlation between beta cells are presented in Figure S1.

Bottom Line: Moreover, we find that the range of interactions in networks during activity shows a clear dependence on the Euclidean distance, lending support to previous observations that beta cells are synchronized via calcium waves spreading throughout islets.Most interestingly, the functional connectivity patterns between beta cells exhibit small-world properties, suggesting that beta cells do not form a homogeneous geometric network but are connected in a functionally more efficient way.Presented results provide support for the existing knowledge of beta cell physiology from a network perspective and shed important new light on the functional organization of beta cell syncitia whose structural topology is probably not as trivial as believed so far.

View Article: PubMed Central - PubMed

Affiliation: Institute of Physiology, Faculty of Medicine, University of Maribor, Maribor, Slovenia.

ABSTRACT
We propose a network representation of electrically coupled beta cells in islets of Langerhans. Beta cells are functionally connected on the basis of correlations between calcium dynamics of individual cells, obtained by means of confocal laser-scanning calcium imaging in islets from acute mouse pancreas tissue slices. Obtained functional networks are analyzed in the light of known structural and physiological properties of islets. Focusing on the temporal evolution of the network under stimulation with glucose, we show that the dynamics are more correlated under stimulation than under non-stimulated conditions and that the highest overall correlation, largely independent of Euclidean distances between cells, is observed in the activation and deactivation phases when cells are driven by the external stimulus. Moreover, we find that the range of interactions in networks during activity shows a clear dependence on the Euclidean distance, lending support to previous observations that beta cells are synchronized via calcium waves spreading throughout islets. Most interestingly, the functional connectivity patterns between beta cells exhibit small-world properties, suggesting that beta cells do not form a homogeneous geometric network but are connected in a functionally more efficient way. Presented results provide support for the existing knowledge of beta cell physiology from a network perspective and shed important new light on the functional organization of beta cell syncitia whose structural topology is probably not as trivial as believed so far.

Show MeSH
Related in: MedlinePlus