Self-Organization of Enzyme-Catalyzed Reactions Studied by the Maximum Entropy Production Principle.

The self-organization of open reaction systems is closely related to specific mechanisms that allow the export of internally generated entropy from systems to their environment. According to the second law of thermodynamics, systems with effective entropy export to the environment are better internally organized. Therefore, they are in thermodynamic states with low entropy. In this context, we study how self-organization in enzymatic reactions depends on their kinetic reaction mechanisms. Enzymatic reactions in an open system are considered to operate in a non-equilibrium steady state, which is achieved by satisfying the principle of maximum entropy production (MEPP). The latter is a general theoretical framework for our theoretical analysis. Detailed theoretical studies and comparisons of the linear irreversible kinetic schemes of an enzyme reaction in two and three states are performed. In both cases, in the optimal and statistically most probable thermodynamic steady state, a diffusion-limited flux is predicted by MEPP. Several thermodynamic quantities and enzymatic kinetic parameters, such as the entropy production rate, the Shannon information entropy, reaction stability, sensitivity, and specificity constants, are predicted. Our results show that the optimal enzyme performance may strongly depend on the number of reaction steps when linear reaction mechanisms are considered. Simple reaction mechanisms with a smaller number of intermediate reaction steps could be better organized internally and could allow fast and stable catalysis. These could be features of the evolutionary mechanisms of highly specialized enzymes.

Modelling of energy-driven switch for glucagon and insulin secretion.

We present a mathematical model of the energy-driven metabolic switch for glucagon and insulin secretion from pancreatic alpha and beta cells, respectively. The energy status related to hormone secretion is studied for various glucose concentrations. Additionally, the physiological response is studied with regards to the presence of other metabolites, particularly the free-fatty acids. At low glucose, the ATP production in alpha cells is high due to free-fatty acids oxidation in mitochondria, which enables glucagon secretion. When the glucose concentration is elevated above the threshold value, the glucagon secretion is switched off due to the contribution of glycolytic ATP production, representing an "anaerobic switch". On the other hand, during hypoglycemia, the ATP production in beta cells is low, reflecting a "waiting state" for glucose as the main metabolite. When glucose is elevated above the threshold value, the oxidative fate of glucose in mitochondria is the main source of energy required for effective insulin secretion, i.e. the "aerobic switch". Our results show the importance of well-regulated and fine-tuned energetic processes in pancreatic alpha and beta cells required for efficient hormone secretion and hence effective blood glucose regulation. These energetic processes have to be appropriately switched on and off based on the sensing of different metabolites by alpha and beta cells. Our computational results indicate that disturbances in cell energetics (e.g. mitochondrial dysfunction), and dysfunctional metabolite sensing and distribution throughout the cell might be related to pathologies such as metabolic syndrome and diabetes.

The relationship between node degree and dissipation rate in networks of diffusively coupled oscillators and its significance for pancreatic beta cells.

Self-sustained oscillatory dynamics is a motion along a stable limit cycle in the phase space, and it arises in a wide variety of mechanical, electrical, and biological systems. Typically, oscillations are due to a balance between energy dissipation and generation. Their stability depends on the properties of the attractor, in particular, its dissipative characteristics, which in turn determine the flexibility of a given dynamical system. In a network of oscillators, the coupling additionally contributes to the dissipation, and hence affects the robustness of the oscillatory solution. Here, we therefore investigate how a heterogeneous network structure affects the dissipation rate of individual oscillators. First, we show that in a network of diffusively coupled oscillators, the dissipation is a linearly decreasing function of the node degree, and we demonstrate this numerically by calculating the average divergence of coupled Hopf oscillators. Subsequently, we use recordings of intracellular calcium dynamics in pancreatic beta cells in mouse acute tissue slices and the corresponding functional connectivity networks for an experimental verification of the presented theory. We use methods of nonlinear time series analysis to reconstruct the phase space and calculate the sum of Lyapunov exponents. Our analysis reveals a clear tendency of cells with a higher degree, that is, more interconnected cells, having more negative values of divergence, thus confirming our theoretical predictions. We discuss these findings in the context of energetic aspects of signaling in beta cells and potential risks for pathological changes in the tissue.

Cardiovascular Comorbidities in COVID-19: Comprehensive Analysis of Key Topics.

BACKGROUND: The interrelation between COVID-19 and various cardiovascular and metabolic disorders has been a critical area of study. There is a growing need to understand how comorbidities such as cardiovascular diseases (CVDs) and metabolic disorders affect the risk and severity of COVID-19. OBJECTIVE: The objective of this study is to systematically analyze the association between COVID-19 and cardiovascular and metabolic disorders. The focus is on comorbidity, examining the roles of CVDs such as embolism, thrombosis, hypertension, and heart failure, as well as metabolic disorders such as disorders of glucose and iron metabolism. METHODS: Our study involved a systematic search in PubMed for literature published from 2000 to 2022. We established 2 databases: one for COVID-19-related articles and another for CVD-related articles, ensuring all were peer-reviewed. In terms of data analysis, statistical methods were applied to compare the frequency and relevance of MeSH (Medical Subject Headings) terms between the 2 databases. This involved analyzing the differences and ratios in the usage of these terms and employing statistical tests to determine their significance in relation to key CVDs within the COVID-19 research context. RESULTS: The study revealed that "Cardiovascular Diseases" and "Nutritional and Metabolic Diseases" were highly relevant as level 1 Medical Subject Headings descriptors in COVID-19 comorbidity research. Detailed analysis at level 2 and level 3 showed "Vascular Disease" and "Heart Disease" as prominent descriptors under CVDs. Significantly, "Glucose Metabolism Disorders" were frequently associated with COVID-19 comorbidities such as embolism, thrombosis, and heart failure. Furthermore, iron deficiency (ID) was notably different in its occurrence between COVID-19 and CVD articles, underlining its significance in the context of COVID-19 comorbidities. Statistical analysis underscored these differences, highlighting the importance of both glucose and iron metabolism disorders in COVID-19 research. CONCLUSIONS: This work lays the foundation for future research that utilizes a knowledge-based approach to elucidate the intricate relationships between these conditions, aiming to develop more effective health care strategies and interventions in the face of ongoing pandemic challenges.

Profiling of patients with type 2 diabetes based on medication adherence data.

Introduction: Type 2 diabetes mellitus (T2DM) is a complex, chronic disease affecting multiple organs with varying symptoms and comorbidities. Profiling patients helps identify those with unfavorable disease progression, allowing for tailored therapy and addressing special needs. This study aims to uncover different T2DM profiles based on medication intake records and laboratory measurements, with a focus on how individuals with diabetes move through disease phases. Methods: We use medical records from databases of the last 20 years from the Department of Endocrinology and Diabetology of the University Medical Center in Maribor. Using the standard ATC medication classification system, we created a patient-specific drug profile, created using advanced natural language processing methods combined with data mining and hierarchical clustering. Results: Our results show a well-structured profile distribution characterizing different age groups of individuals with diabetes. Interestingly, only two main profiles characterize the early 40-50 age group, and the same is true for the last 80+ age group. One of these profiles includes individuals with diabetes with very low use of various medications, while the other profile includes individuals with diabetes with much higher use. The number in both groups is reciprocal. Conversely, the middle-aged groups are characterized by several distinct profiles with a wide range of medications that are associated with the distinct concomitant complications of T2DM. It is intuitive that the number of profiles increases in the later age groups, but it is not obvious why it is reduced later in the 80+ age group. In this context, further studies are needed to evaluate the contributions of a range of factors, such as drug development, drug adoption, and the impact of mortality associated with all T2DM-related diseases, which characterize these middle-aged groups, particularly those aged 55-75. Conclusion: Our approach aligns with existing studies and can be widely implemented without complex or expensive analyses. Treatment and drug use data are readily available in healthcare facilities worldwide, allowing for profiling insights into individuals with diabetes. Integrating data from other departments, such as cardiology and renal disease, may provide a more sophisticated understanding of T2DM patient profiles.

Modeling the Amino Acid Effect on Glucagon Secretion from Pancreatic Alpha Cells.

Type 2 Diabetes Mellitus (T2DM) is a burdensome problem in modern society, and intensive research is focused on better understanding the underlying cellular mechanisms of hormone secretion for blood glucose regulation. T2DM is a bi-hormonal disease, and in addition to 100 years of increasing knowledge about the importance of insulin, the second hormone glucagon, secreted by pancreatic alpha cells, is becoming increasingly important. We have developed a mathematical model for glucagon secretion that incorporates all major metabolic processes of glucose, fatty acids, and glutamine as the most abundant postprandial amino acid in blood. In addition, we consider cAMP signaling in alpha cells. The model predictions quantitatively estimate the relative importance of specific metabolic and signaling pathways and particularly emphasize the important role of glutamine in promoting glucagon secretion, which is in good agreement with known experimental data.

Age-Related Changes in Lipid and Glucose Levels Associated with Drug Use and Mortality: An Observational Study.

BACKGROUND: The pathogenesis of type 2 diabetes mellitus is complex and still unclear in some details. The main feature of diabetes mellitus is high serum glucose, and the question arises of whether there are other statistically observable dysregulations in laboratory measurements before the state of hyperglycemia becomes severe. In the present study, we aim to examine glucose and lipid profiles in the context of age, sex, medication use, and mortality. METHODS: We conducted an observational study by analyzing laboratory data from 506,083 anonymized laboratory tests from 63,606 different patients performed by a regional laboratory in Slovenia between 2008 and 2019. Laboratory data-based results were evaluated in the context of medication use and mortality. The medication use database contains anonymized records of 1,632,441 patients from 2013 to 2018, and mortality data were obtained for the entire Slovenian population. RESULTS: We show that the highest percentage of the population with elevated glucose levels occurs approximately 20 years later than the highest percentage with lipid dysregulation. Remarkably, two distinct inflection points were observed in these laboratory results. The first inflection point occurs at ages 55 to 59 years, corresponding to the greatest increase in medication use, and the second coincides with the sharp increase in mortality at ages 75 to 79 years. CONCLUSIONS: Our results suggest that medications and mortality are important factors affecting population statistics and must be considered when studying metabolic disorders such as dyslipidemia and hyperglycemia using laboratory data.

From Isles of Königsberg to Islets of Langerhans: Examining the Function of the Endocrine Pancreas Through Network Science.

Islets of Langerhans are multicellular microorgans located in the pancreas that play a central role in whole-body energy homeostasis. Through secretion of insulin and other hormones they regulate postprandial storage and interprandial usage of energy-rich nutrients. In these clusters of hormone-secreting endocrine cells, intricate cell-cell communication is essential for proper function. Electrical coupling between the insulin-secreting beta cells through gap junctions composed of connexin36 is particularly important, as it provides the required, most important, basis for coordinated responses of the beta cell population. The increasing evidence that gap-junctional communication and its modulation are vital to well-regulated secretion of insulin has stimulated immense interest in how subpopulations of heterogeneous beta cells are functionally arranged throughout the islets and how they mediate intercellular signals. In the last decade, several novel techniques have been proposed to assess cooperation between cells in islets, including the prosperous combination of multicellular imaging and network science. In the present contribution, we review recent advances related to the application of complex network approaches to uncover the functional connectivity patterns among cells within the islets. We first provide an accessible introduction to the basic principles of network theory, enumerating the measures characterizing the intercellular interactions and quantifying the functional integration and segregation of a multicellular system. Then we describe methodological approaches to construct functional beta cell networks, point out possible pitfalls, and specify the functional implications of beta cell network examinations. We continue by highlighting the recent findings obtained through advanced multicellular imaging techniques supported by network-based analyses, giving special emphasis to the current developments in both mouse and human islets, as well as outlining challenges offered by the multilayer network formalism in exploring the collective activity of islet cell populations. Finally, we emphasize that the combination of these imaging techniques and network-based analyses does not only represent an innovative concept that can be used to describe and interpret the physiology of islets, but also provides fertile ground for delineating normal from pathological function and for quantifying the changes in islet communication networks associated with the development of diabetes mellitus.

Role of cAMP in Double Switch of Glucagon Secretion.

Glucose metabolism plays a crucial role in modulating glucagon secretion in pancreatic alpha cells. However, the downstream effects of glucose metabolism and the activated signaling pathways influencing glucagon granule exocytosis are still obscure. We developed a computational alpha cell model, implementing metabolic pathways of glucose and free fatty acids (FFA) catabolism and an intrinsically activated cAMP signaling pathway. According to the model predictions, increased catabolic activity is able to suppress the cAMP signaling pathway, reducing exocytosis in a Ca2+-dependent and Ca2+ independent manner. The effect is synergistic to the pathway involving ATP-dependent closure of KATP channels and consequent reduction of Ca2+. We analyze the contribution of each pathway to glucagon secretion and show that both play decisive roles, providing a kind of "secure double switch". The cAMP-driven signaling switch plays a dominant role, while the ATP-driven metabolic switch is less favored. The ratio is approximately 60:40, according to the most recent experimental evidence.

Socio-demographic and health factors drive the epidemic progression and should guide vaccination strategies for best COVID-19 containment.

We propose and study an epidemiological model on a social network that takes into account heterogeneity of the population and different vaccination strategies. In particular, we study how the COVID-19 epidemics evolves and how it is contained by different vaccination scenarios by taking into account data showing that older people, as well as individuals with comorbidities and poor metabolic health, and people coming from economically depressed areas with lower quality of life in general, are more likely to develop severe COVID-19 symptoms, and quicker loss of immunity and are therefore more prone to reinfection. Our results reveal that the structure and the spatial arrangement of subpopulations are important epidemiological determinants. In a healthier society the disease spreads more rapidly but the consequences are less disastrous as in a society with more prevalent chronic comorbidities. If individuals with poor health are segregated within one community, the epidemic outcome is less favorable. Moreover, we show that, contrary to currently widely adopted vaccination policies, prioritizing elderly and other higher-risk groups is beneficial only if the supply of vaccine is high. If, however, the vaccination availability is limited, and if the demographic distribution across the social network is homogeneous, better epidemic outcomes are achieved if healthy people are vaccinated first. Only when higher-risk groups are segregated, like in elderly homes, their prioritization will lead to lower COVID-19 related deaths. Accordingly, young and healthy individuals should view vaccine uptake as not only protecting them, but perhaps even more so protecting the more vulnerable socio-demographic groups.

Flexibility of enzymatic transitions as a hallmark of optimized enzyme steady-state kinetics and thermodynamics.

We investigate the relations between the enzyme kinetic flexibility, the rate of entropy production, and the Shannon information entropy in a steady-state enzyme reaction. All these quantities are maximized with respect to enzyme rate constants. We show that the steady-state, which is characterized by the most flexible enzymatic transitions between the enzyme conformational states, coincides with the global maxima of the Shannon information entropy and the rate of entropy production. This steady-state of an enzyme is referred to as globally optimal. This theoretical approach is then used for the analysis of the kinetic and the thermodynamic performance of the enzyme triose-phosphate isomerase. The analysis reveals that there exist well-defined maxima of the kinetic flexibility, the rate of entropy production, and the Shannon information entropy with respect to any arbitrarily chosen rate constant of the enzyme and that these maxima, calculated from the measured kinetic rate constants for the triose-phosphate isomerase are lower, however of the same order of magnitude, as the maxima of the globally optimal state of the enzyme. This suggests that the triose-phosphate isomerase could be a well, but not fully evolved enzyme, as it was previously claimed. Herein presented theoretical investigations also provide clear evidence that the flexibility of enzymatic transitions between the enzyme conformational states is a requirement for the maximal Shannon information entropy and the maximal rate of entropy production.

Assessing Different Temporal Scales of Calcium Dynamics in Networks of Beta Cell Populations.

Beta cells within the pancreatic islets of Langerhans respond to stimulation with coherent oscillations of membrane potential and intracellular calcium concentration that presumably drive the pulsatile exocytosis of insulin. Their rhythmic activity is multimodal, resulting from networked feedback interactions of various oscillatory subsystems, such as the glycolytic, mitochondrial, and electrical/calcium components. How these oscillatory modules interact and affect the collective cellular activity, which is a prerequisite for proper hormone release, is incompletely understood. In the present work, we combined advanced confocal Ca2+ imaging in fresh mouse pancreas tissue slices with time series analysis and network science approaches to unveil the glucose-dependent characteristics of different oscillatory components on both the intra- and inter-cellular level. Our results reveal an interrelationship between the metabolically driven low-frequency component and the electrically driven high-frequency component, with the latter exhibiting the highest bursting rates around the peaks of the slow component and the lowest around the nadirs. Moreover, the activity, as well as the average synchronicity of the fast component, considerably increased with increasing stimulatory glucose concentration, whereas the stimulation level did not affect any of these parameters in the slow component domain. Remarkably, in both dynamical components, the average correlation decreased similarly with intercellular distance, which implies that intercellular communication affects the synchronicity of both types of oscillations. To explore the intra-islet synchronization patterns in more detail, we constructed functional connectivity maps. The subsequent comparison of network characteristics of different oscillatory components showed more locally clustered and segregated networks of fast oscillatory activity, while the slow oscillations were more global, resulting in several long-range connections and a more cohesive structure. Besides the structural differences, we found a relatively weak relationship between the fast and slow network layer, which suggests that different synchronization mechanisms shape the collective cellular activity in islets, a finding which has to be kept in mind in future studies employing different oscillations for constructing networks.

Diabetes and metabolic syndrome as risk factors for COVID-19.

BACKGROUND AND AIMS: Clinical evidence exists that patients with diabetes are at higher risk for Coronavirus disease 2019 (COVID-19). We investigated the physiological origins of this clinical observation linking diabetes with severity and adverse outcome of COVID-19. METHODS: Publication mining was applied to reveal common physiological contexts in which diabetes and COVID-19 have been investigated simultaneously. Overall, we have acquired 1,121,078 publications from PubMed in the time span between 01-01-2000 and 17-04-2020, and extracted knowledge graphs interconnecting the topics related to diabetes and COVID-19. RESULTS: The Data Mining revealed three pathophysiological pathways linking diabetes and COVID-19. The first pathway indicates a higher risk for COVID-19 because of a dysregulation of Angiotensin-converting enzyme 2. The other two important physiological links between diabetes and COVID-19 are liver dysfunction and chronic systemic inflammation. A deep network analysis has suggested clinical biomarkers predicting the higher risk: Hypertension, elevated serum Alanine aminotransferase, high Interleukin-6, and low Lymphocytes count. CONCLUSIONS: The revealed biomarkers can be applied directly in clinical practice. For newly infected patients, the medical history needs to be checked for evidence of a long-term, chronic dysregulation of these biomarkers. In particular, patients with diabetes, but also those with prediabetic state, deserve special attention.

Mitochondrial Dysfunction in Pancreatic Alpha and Beta Cells Associated with Type 2 Diabetes Mellitus.

Type 2 diabetes mellitus is a complex multifactorial disease of epidemic proportions. It involves genetic and lifestyle factors that lead to dysregulations in hormone secretion and metabolic homeostasis. Accumulating evidence indicates that altered mitochondrial structure, function, and particularly bioenergetics of cells in different tissues have a central role in the pathogenesis of type 2 diabetes mellitus. In the present study, we explore how mitochondrial dysfunction impairs the coupling between metabolism and exocytosis in the pancreatic alpha and beta cells. We demonstrate that reduced mitochondrial ATP production is linked with the observed defects in insulin and glucagon secretion by utilizing computational modeling approach. Specifically, a 30-40% reduction in alpha cells' mitochondrial function leads to a pathological shift of glucagon secretion, characterized by oversecretion at high glucose concentrations and insufficient secretion in hypoglycemia. In beta cells, the impaired mitochondrial energy metabolism is accompanied by reduced insulin secretion at all glucose levels, but the differences, compared to a normal beta cell, are the most pronounced in hyperglycemia. These findings improve our understanding of metabolic pathways and mitochondrial bioenergetics in the pathology of type 2 diabetes mellitus and might help drive the development of innovative therapies to treat various metabolic diseases.

Modelling of dysregulated glucagon secretion in type 2 diabetes by considering mitochondrial alterations in pancreatic α-cells.

Type 2 diabetes mellitus (T2DM) has been associated with insulin resistance and the failure of ß-cells to produce and secrete enough insulin as the disease progresses. However, clinical treatments based solely on insulin secretion and action have had limited success. The focus is therefore shifting towards α-cells, in particular to the dysregulated secretion of glucagon. Our qualitative electron-microscopy-based observations gave an indication that mitochondria in α-cells are altered in Western-diet-induced T2DM. In particular, α-cells extracted from mouse pancreatic tissue showed a lower density of mitochondria, a less expressed matrix and a lower number of cristae. These deformities in mitochondrial ultrastructure imply a decreased efficiency in mitochondrial ATP production, which prompted us to theoretically explore and clarify one of the most challenging problems associated with T2DM, namely the lack of glucagon secretion in hypoglycaemia and its oversecretion at high blood glucose concentrations. To this purpose, we constructed a novel computational model that links α-cell metabolism with their electrical activity and glucagon secretion. Our results show that defective mitochondrial metabolism in α-cells can account for dysregulated glucagon secretion in T2DM, thus improving our understanding of T2DM pathophysiology and indicating possibilities for new clinical treatments.

Heterogeneity and Delayed Activation as Hallmarks of Self-Organization and Criticality in Excitable Tissue.

Self-organized critical dynamics is assumed to be an attractive mode of functioning for several real-life systems and entails an emergent activity in which the extent of observables follows a power-law distribution. The hallmarks of criticality have recently been observed in a plethora of biological systems, including beta cell populations within pancreatic islets of Langerhans. In the present study, we systematically explored the mechanisms that drive the critical and supercritical behavior in networks of coupled beta cells under different circumstances by means of experimental and computational approaches. Experimentally, we employed high-speed functional multicellular calcium imaging of fluorescently labeled acute mouse pancreas tissue slices to record calcium signals in a large number of beta cells simultaneously, and with a high spatiotemporal resolution. Our experimental results revealed that the cellular responses to stimulation with glucose are biphasic and glucose-dependent. Under physiological as well as under supraphysiological levels of stimulation, an initial activation phase was followed by a supercritical plateau phase with a high number of global intercellular calcium waves. However, the activation phase displayed fingerprints of critical behavior under lower stimulation levels, with a progressive recruitment of cells and a power-law distribution of calcium wave sizes. On the other hand, the activation phase provoked by pathophysiologically high glucose concentrations, differed considerably and was more rapid, less continuous, and supercritical. To gain a deeper insight into the experimentally observed complex dynamical patterns, we built up a phenomenological model of coupled excitable cells and explored empirically the model's necessities that ensured a good overlap between computational and experimental results. It turned out that such a good agreement between experimental and computational findings was attained when both heterogeneous and stimulus-dependent time lags, variability in excitability levels, as well as a heterogeneous cell-cell coupling were included into the model. Most importantly, since our phenomenological approach involved only a few parameters, it naturally lends itself not only for determining key mechanisms of self-organized criticality at the tissue level, but also points out various features for comprehensive and realistic modeling of different excitable systems in nature.

Network science of biological systems at different scales: A review.

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.

Critical and Supercritical Spatiotemporal Calcium Dynamics in Beta Cells.

A coordinated functioning of beta cells within pancreatic islets is mediated by oscillatory membrane depolarization and subsequent changes in cytoplasmic calcium concentration. While gap junctions allow for intraislet information exchange, beta cells within islets form complex syncytia that are intrinsically nonlinear and highly heterogeneous. To study spatiotemporal calcium dynamics within these syncytia, we make use of computational modeling and confocal high-speed functional multicellular imaging. We show that model predictions are in good agreement with experimental data, especially if a high degree of heterogeneity in the intercellular coupling term is assumed. In particular, during the first few minutes after stimulation, the probability distribution of calcium wave sizes is characterized by a power law, thus indicating critical behavior. After this period, the dynamics changes qualitatively such that the number of global intercellular calcium events increases to the point where the behavior becomes supercritical. To better mimic normal in vivo conditions, we compare the described behavior during supraphysiological non-oscillatory stimulation with the behavior during exposure to a slightly lower and oscillatory glucose challenge. In the case of this protocol, we observe only critical behavior in both experiment and model. Our results indicate that the loss of oscillatory changes, along with the rise in plasma glucose observed in diabetes, could be associated with a switch to supercritical calcium dynamics and loss of beta cell functionality.

Planar cell polarity genes frizzled4 and frizzled6 exert patterning influence on arterial vessel morphogenesis.

Quantitative analysis of the vascular network anatomy is critical for the understanding of the vasculature structure and function. In this study, we have combined microcomputed tomography (microCT) and computational analysis to provide quantitative three-dimensional geometrical and topological characterization of the normal kidney vasculature, and to investigate how 2 core genes of the Wnt/planar cell polarity, Frizzled4 and Frizzled6, affect vascular network morphogenesis. Experiments were performed on frizzled4 (Fzd4-/-) and frizzled6 (Fzd6-/-) deleted mice and littermate controls (WT) perfused with a contrast medium after euthanasia and exsanguination. The kidneys were scanned with a high-resolution (16 µm) microCT imaging system, followed by 3D reconstruction of the arterial vasculature. Computational treatment includes decomposition of 3D networks based on Diameter-Defined Strahler Order (DDSO). We have calculated quantitative (i) Global scale parameters, such as the volume of the vasculature and its fractal dimension (ii) Structural parameters depending on the DDSO hierarchical levels such as hierarchical ordering, diameter, length and branching angles of the vessel segments, and (iii) Functional parameters such as estimated resistance to blood flow alongside the vascular tree and average density of terminal arterioles. In normal kidneys, fractal dimension was 2.07±0.11 (n = 7), and was significantly lower in Fzd4-/- (1.71±0.04; n = 4), and Fzd6-/- (1.54±0.09; n = 3) kidneys. The DDSO number was 5 in WT and Fzd4-/-, and only 4 in Fzd6-/-. Scaling characteristics such as diameter and length of vessel segments were altered in mutants, whereas bifurcation angles were not different from WT. Fzd4 and Fzd6 deletion increased vessel resistance, calculated using the Hagen-Poiseuille equation, for each DDSO, and decreased the density and the homogeneity of the distal vessel segments. Our results show that our methodology is suitable for 3D quantitative characterization of vascular networks, and that Fzd4 and Fzd6 genes have a deep patterning effect on arterial vessel morphogenesis that may determine its functional efficiency.