PLoS One

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

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

COMPARISON BETWEEN THE SIGNAL TRANSFER IN BIOLOGICAL AND ELECTRICAL SYSTEMS

V diplomski nalogi primerjamo prenos signalov v bioloških in električnih sistemih. Osredotočili smo se na znotrajcelično signalizacijo, kjer obstajajo signalne poti, sestavljene iz proteinskih kaskad. Z matematičnim modelom smo opravili različne numerične simulacije in analizirali vlogo proteinskih kaskad pri prenosu signala v znotrajceličnem prostoru. Te vloge smo primerjali z različnimi električnimi sistemi, katerih delovanje je dobro znano in ga lahko opišemo matematično. Namen takšnih primerjav je bolje razumeti vloge signalnih poti v znotrajceličnem prostoru. Primerjave temeljijo na numeričnih izračunih in primerjavah diferencialnih enačb, ki tvorijo matematični modeli za opis delovanja določenega sistema. V diplomskem delu je pokazano, da lahko proteinski kaskadi dodelimo lastnosti stikala, ki ojačuje signal in deluje kot nizkofrekvenčno prepustno sito. Pokazali smo tudi, da lahko z uporabo pozitivne povratne zanke aktivnemu stikalu povečamo ojačanje, zmanjšamo mejno frekvenco in povečamo njegovo nestabilnost. Kadar v sistem vključimo negativno povratno zanko, povečamo stabilnost sistema, povečamo mejno frekvenco in zmanjšamo ojačanje. Izdelali smo tudi biološka logična vrata, ki temeljijo na logičnih operacijah v digitalni elektroniki. Z uporabo teh logičnih vrat smo izdelali še spominsko vezje, ki lahko pomni 1 bit podatkov.In this thesis signal transduction pathways in biological and electrical systems are analyzed and compared. The main goal is to analyze intercellular signalization, in particular the pathways consisting of protein cascades. The protein cascades are studied by using mathematical models of signal transduction systems. The biological systems are compared with analogous electrical systems, which are well known and can easily be mathematically described. The main idea of comparing these systems is to gain better knowledge of the functioning of signaling pathways in the intercellular space. The comparison is based on numerical simulations and direct looking for analogies of the differential equations consisting the mathematical models of particular systems. We show that the protein cascades can function as switches that amplify signals and also serve as a low-frequency filter. Furthermore, we show that by introducing a positive feedback loop into an active switch, we can increase its gain, reduce the cutoff frequency and increase the instability of the system. On the other hand, if a negative feedback is applied, the system becomes more stable, the cutoff frequency rises and its gain drops. We also constructed biological logical gates, which are based on logical procedures used in digital electronics. On the basis of these gates, we designed a memory module, which can store 1 bit of information

The influence of topological features of complex networks and dynamical properties of coupled cellular oscillators on collective dynamics

Doktorska disertacija zajema raziskave na področju kolektivne dinamike mrežno sklopljenih oscilatorjev. Razdeljena je na dva dela. V prvem delu analiziramo, kako dinamične lastnosti oscilatorjev in struktura mreže sovisno vplivata na kolektivno dinamiko. Pokažemo, da je kolektivna dinamika fleksibilnih oscilatorjev najbolje koordinirana, ko so oscilatorji povezani v primeru široko skalno mrežo. Oscilatorji z močno disipativno dinamiko, ki implicira rigidnost, pa dosežejo najvišjo raven sinhronizacije v skalno neodvisnih mrežah. Pojav analitično razložimo in rezultate ponazorimo z različnimi matematičnimi modeli, ki vključujejo tako zvezne kakor tudi diskretne oscilatorje, ter izkazujejo različne stopnje dinamične kompleksnosti. Pri analizi kolektivne dinamike upoštevamo tudi hitrost širjenja signalov med vozlišči v mreži. Ugotovimo, da obstaja tako optimalna mrežna topologija kakor tudi optimalna hitrost širjenja signalov med vozlišči mreže, pri kateri je raven kolektivne sinhronizacije najvišja. Ugotovitve in metodologijo iz naših teoretičnih študij v drugem delu disertacije apliciramo na sistem povezanih celic beta v Langerhansovih otočkih trebušne slinavke miši, ki predstavlja z vidika fiziologije metabolnih procesov izredno pomemben predmet preučevanja. Mrežno povezane celice beta, katerih poglavitna naloga je izločanje inzulina in s tem uravnavanje koncentracije glukoze v krvi, analiziramo ob podpori eksperimentalnih podatkov, izmerjenih pri različnih koncentracijah glukoze. Naši rezultati kažejo, da se celice beta povezujejo v lokalne funkcionalne skupnosti. Njihova segregiranost pa se v splošnem manjša z naraščajočo koncentracijo glukoze. S postopnim povečevanjem koncentracije glukoze postanejo v otočku tudi vse bolj izražene lastnosti široko skalnih mrež malega sveta. S tem rezultati doktorske disertacije prispevajo k razlagi fiziološkega pomena učinkovitost mrežne povezanosti celic beta in nakazujejo možnosti patoloških sprememb, ki so posledica sprememb v medcelični komunikaciji.This doctor thesis is both theoretical and applicative. In the theoretical part of the thesis, we examine how the interplay of dynamical features of oscillators and structural properties of complex networks affect the collective behavior of the system. We show, that weakly dissipative and flexible oscillators synchronize best in a broad scale network topology, whereas on the other hand strongly dissipative and rigid oscillators exhibit maximal synchronization in a scale-free network topology. We provide an analytical explanation for this phenomenon and validate it by implementing various continuous as well as discrete mathematical models that exhibit different levels of dynamical complexity. In the continuation, we additionally investigate how speed of signal transmission in the network affects the collective dynamic of the system. Our results show that besides an optimal network topology, also an optimal information transmission speed exists, at which the system reaches the highest degree of global synchronization. In the second part we apply the findings and the methodology from our theoretical studies to the examination of the collective pancreatic beta cell activity in the islets of Langerhans, which represents the main mechanism for the regulation of blood glucose homeostasis by the secretion of the hormone insulin. We show that the beta cells dynamics is not synchronized on the global scale of the whole islets. Instead, the cells form local clusters of synchronized activity which tend to get less segregated under higher stimulatory glucose concentrations. Furthermore, higher glucose concentrations also lead to the presence of broad scale small world connectivity patterns in the functional beta cell network. The main findings thereby shed light on the physiology and collective behavior of the islets of Langerhans and point out the possibilities of pathological changes associated with changes in the intercellular communication pathways

How optimal synchronization of oscillators depends on the network structure and the individual dynamical properties of the oscillators

The problem of making a network of dynamical systems synchronize onto a common evolution is the subject of much ongoing research in several scientific disciplines. It is nowadays a well-known fact that the synchronization processes are gradually in influenced by the interaction topology between the dynamically interacting units. A complex coupling configuration can significantly affect the synchronization abilities of a networked system. However, the question arises what is the optimal network topology that provides enhancement of the synchronization features under given circumstances. In order to address this issue we make use of a network model in which we can smoothly tune the topology from a highly heterogeneous and efficient scale-free network to a homogeneous and less efficient network. The network is then populated with Poincaré oscillators, a paradigmatic model for limit-cycle oscillations. This oscillator model exhibits a parameter that enables changes of the limit cycle attraction and is thus immediately related to flexibility/rigidity properties of the oscillator. Our results reveal that for weak attractions of the limit cycle, intermediate homogeneous topology ensures maximal synchronization, whereas highly heterogeneous scale-free topology ensures maximal synchronization for strong attractions of the limit cycle. We argue that the flexibility/rigidity of individual nodes of the networks defines the topology, where maximal global coherence is achieved

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

Progressive glucose stimulation of islet beta cells reveals a transition from segregated to integrated modular functional connectivity patterns

Collective beta cell activity in islets of Langerhans is critical for the supply of insulin within an organism. Even though individual beta cells are intrinsically heterogeneous, the presence of intercellular coupling mechanisms ensures coordinated activity and a well-regulated exocytosis of insulin. In order to get a detailed insight into the functional organization of the syncytium, we applied advanced analytical tools from the realm of complex network theory to uncover the functional connectivity pattern among cells composing the intact islet. The procedure is based on the determination of correlations between long temporal traces obtained from confocal functional multicellular calcium imaging of beta cells stimulated in a stepwise manner with a range of physiological glucose concentrations. Our results revealed that the extracted connectivity networks are sparse for low glucose concentrations, whereas for higher stimulatory levels they become more densely connected. Most importantly, for all ranges of glucose concentration beta cells within the islets form locally clustered functional sub-compartments, thereby indicating that their collective activity profiles exhibit a modular nature. Moreover, we show that the observed non-linear functional relationship between different network metrics and glucose concentration represents a well-balanced setup that parallels physiological insulin release

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

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

The analysis of intracellular and intercellular calcium signaling in human anterior lens capsule epithelial cells with regard to different types and stages of the cataract

In this work we investigated how modifications of the Ca2+ homeostasis in anterior lens epithelial cells (LECs) are associated with different types of cataract (cortical or nuclear) and how the progression of the cataract (mild or moderate) affects the Ca2+ signaling. We systematically analyzed different aspects of intra- and inter-cellular Ca2+ signaling in the human LECs, which are attached to surgically isolated lens capsule (LC), obtained during cataract surgery. We monitored the temporal and spatial changes in intracellular Ca2+ concentration after stimulation with acetylcholine by means of Fura-2 fluorescence captured with an inverted microscope. In our analysis we compared the features of Ca2+ signals in individual cells, synchronized activations, spatio-temporal grouping and the nature of intercellular communication between LECs. The latter was assessed by using the methodologies of the complex network theory. Our results point out that at the level of individual cells there are no significant differences when comparing the features of the signals with regard either to the type or the stage of the cataract. On the other hand, noticeable differences are observed at the multicellular level, despite inter-capsule variability. LCs associated with more developed cataracts were found to exhibit a slower collective response to stimulation, a less pronounced spatio-temporal clustering of LECs with similar signaling characteristics. The reconstructed intercellular networks were found to be sparser and more segregated than in LCs associated with mild cataracts. Moreover, we show that spontaneously active LECs often operate in localized groups with quite well aligned Ca2+ activity. The presence of spontaneous activity was also found to affect the stimulated Ca2+ responses of individual cells. Our findings indicate that the cataract progression entails the impairment of intercellular signaling thereby suggesting the functional importance of altered Ca2+ signaling of LECs in cataractogenesis