The World Health Organization declared the coronavirus disease 2019 a pandemic on March 11th, pointing to the over 118,000 cases in over 110 countries and territories around the world at that time. ...At the time of writing this manuscript, the number of confirmed cases has been surging rapidly past the half-million mark, emphasizing the sustained risk of further global spread. Governments around the world are imposing various containment measures while the healthcare system is bracing itself for tsunamis of infected individuals that will seek treatment. It is therefore important to know what to expect in terms of the growth of the number of cases, and to understand what is needed to arrest the very worrying trends. To that effect, we here show forecasts obtained with a simple iteration method that needs only the daily values of confirmed cases as input. The method takes into account expected recoveries and deaths, and it determines maximally allowed daily growth rates that lead away from exponential increase toward stable and declining numbers. Forecasts show that daily growth rates should be kept at least below 5% if we wish to see plateaus any time soon—unfortunately far from reality in most countries to date. We provide an executable as well as the source code for a straightforward application of the method on data from other countries.
Presented with sensory challenges, living cells employ extensive noisy, fluctuating signaling and communication among themselves to compute a physiologically proper response. Using coupled stochastic ...oscillators model, we propose that biological computation mechanism undertaken by insulin secreting beta-cells consists of a combination of dual intracellular Ca
2+
release processes to ensure multilayered exploration contributing to enhanced robustness and sensitivity. The computational output is macroscopically observed as disorder-order phase transition in a collective beta-cell response to increases in nutrient concentrations. Our own experimental data and analogies from previously described examples of biological computation suggest that the initial limited response to nutrients may be followed by an adaptive phase to expand the sensory spectrum and consolidate memory.
Network science is today established as a backbone for description of structure and function of various physical, chemical, biological, technological, and social systems. Here we review recent ...advances in the study of complex biological systems that were inspired and enabled by methods of network science. First, we present research highlights ranging from determination of the molecular interaction network within a cell to studies of architectural and functional properties of brain networks and biological transportation networks. Second, we focus on synergies between network science and data analysis, which enable us to determine functional connectivity patterns in multicellular systems. Until now, this intermediate scale of biological organization received the least attention from the network perspective. As an example, we review the methodology for the extraction of functional beta cell networks in pancreatic islets of Langerhans by means of advanced imaging techniques. Third, we concentrate on the emerging field of multilayer networks and review the first endeavors and novel perspectives offered by this framework in exploring biological complexity. We conclude by outlining challenges and directions for future research that encompass utilization of the multilayer network formalism in exploring intercellular communication patterns in tissues, and we advocate for network science being one of the key pillars for assessing physiological function of complex biological systems—from organelles to organs—in health and disease.
•Network science offers a comprehensive toolset for exploring biological systems.•Intercellular interaction patterns can be successfully studied by network approaches.•The emergent field of multilayer networks is promising for biological data analysis.
Mice remain the most studied animal model in pancreas research. Since the findings of this research are typically extrapolated to humans, it is important to understand both similarities and ...differences between the 2 species. Beside the apparent difference in size and macroscopic organization of the organ in the 2 species, there are a number of less evident and only recently described differences in organization of the acinar and ductal exocrine tissue, as well as in the distribution, composition, and architecture of the endocrine islets of Langerhans. Furthermore, the differences in arterial, venous, and lymphatic vessels, as well as innervation are potentially important. In this article, the structure of the human and the mouse pancreas, together with the similarities and differences between them are reviewed in detail in the light of conceivable repercussions for basic research and clinical application.
Islets of Langerhans operate as multicellular networks in which several hundred β cells work in synchrony to produce secretory pulses of insulin, a hormone crucial for controlling metabolic ...homeostasis. Their collective rhythmic activity is facilitated by gap junctional coupling and affected by their functional heterogeneity, but the details of this robust and coordinated behavior are still not fully understood. Recent advances in multicellular imaging and optogenetic and photopharmacological strategies, as well as in network science, have led to the discovery of specialized β cell subpopulations that were suggested to critically determine the collective dynamics in the islets. In particular hubs, i.e., β cells with many functional connections, are believed to significantly enhance communication capacities of the intercellular network and facilitate an efficient spreading of intercellular Ca2+ waves, whereas wave-initiator cells trigger intercellular signals in their cohorts. Here, we determined Ca2+ signaling characteristics of these two β cell subpopulations and the relationship between them by means of functional multicellular Ca2+ imaging in mouse pancreatic tissue slices in combination with methods of complex network theory. We constructed network layers based on individual Ca2+ waves to identify wave initiators, and functional correlation-based networks to detect hubs. We found that both cell types exhibit a higher-than-average active time under both physiological and supraphysiological glucose concentrations, but also that they differ significantly in many other functional characteristics. Specifically, Ca2+ oscillations in hubs are more regular, and their role appears to be much more stable over time than for initiator cells. Moreover, in contrast to wave initiators, hubs transmit intercellular signals faster than other cells, which implies a stronger intercellular coupling. Our research indicates that hubs and wave-initiator cell subpopulations are both natural features of healthy pancreatic islets, but their functional roles in principle do not overlap and should thus not be considered equal.
In endocrine cells within islets of Langerhans calcium ions couple cell stimulation to hormone secretion. Since the advent of modern fluorimetry, numerous in vitro studies employing primarily ...isolated mouse islets have investigated the effects of various secretagogues on cytoplasmic calcium, predominantly in insulin-secreting beta cells. Due to technical limitations, insights of these studies are inherently limited to a rather small subpopulation of outermost cells. The results also seem to depend on various factors, like culture conditions and duration, and are not always easily reconcilable with findings in vivo. The main controversies regard the types of calcium oscillations, presence of calcium waves, and the level of synchronized activity. Here, we set out to combine the in situ acute mouse pancreas tissue slice preparation with noninvasive fluorescent calcium labeling and subsequent confocal laser scanning microscopy to shed new light on the existing controversies utilizing an innovative approach enabling the characterization of responses in many cells from all layers of islets. Our experiments reproducibly showed stable fast calcium oscillations on a sustained plateau rather than slow oscillations as the predominant type of response in acute tissue slices, and that calcium waves are the mechanistic substrate for synchronization of oscillations. We also found indirect evidence that even a large amplitude calcium signal was not sufficient and that metabolic activation was necessary to ensure cell synchronization upon stimulation with glucose. Our novel method helped resolve existing controversies and showed the potential to help answer important physiological questions, making it one of the methods of choice for the foreseeable future.
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.
Pancreatic islets are highly interconnected structures that produce pulses of insulin and other hormones, maintaining normal homeostasis of glucose and other nutrients. Normal stimulus-secretion and ...intercellular coupling are essential to regulated secretory responses, and these hallmarks are known to be altered in diabetes. In the current study, we used calcium imaging of isolated human islets to assess their collective behavior. The activity occurred in the form of calcium oscillations, was synchronized across different regions of islets through calcium waves, and was glucose dependent: higher glucose enhanced the activity, elicited a greater proportion of global calcium waves, and led to denser and less fragmented functional networks. Hub regions were identified in stimulatory conditions, and they were characterized by long active times. Moreover, calcium waves were found to be initiated in different subregions and the roles of initiators and hubs did not overlap. In type 2 diabetes, glucose dependence was retained, but reduced activity, locally restricted waves, and more segregated networks were detected compared with control islets. Interestingly, hub regions seemed to suffer the most by losing a disproportionately large fraction of connections. These changes affected islets from donors with diabetes in a heterogeneous manner.
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