Rene Markovic

We study the functional connectivity patterns between beta cells in islets of Langerhans from mouse pancreas tissue slices. We build up the functional networks on the basis of correlations between calcium dynamics of individual cells, which were recorded by means of confocal laser-scanning calcium imaging. The extracted patterns of pairwise interactions between network cells, i.e. functional connections, are then scrutinized with conventional tools for network analysis. By calculating the network metrics of interest we can characterize the nature of functional connectivity patterns. Here we focus on the functional organization of the beta cell syncytium at different levels of stimulation with glucose. We show that under low glucose concentrations the networks are very sparse and segregated, whereas higher stimulation levels lead to denser and more efficient networks, which however are still quite modular. The proposed methods provide novel insights into the functional mechanisms and...

Epithelial tissues are structured and highly organized monolayers of cells with many different tissue-specific functions. Ordering of epithelium cells in living tissues relies on spatially and temporally regulated cell behavior and is of vital importance for their functioning. The underlying mechanisms that govern the development of the tissue architecture and morphogenesis rely on planar cell polarity signaling pathways. Mutations and other disruptions of these pathways were found to cause developmental defects, leading to failures in lung branching or kidney development, for example, and are also involved in cancer cell migration. Here, we investigate how these defects affect the spatial arrangement and orientation of epithelium cells, giving special attention to tissue reorganization during development. For the characterization of the resulting polarized cytoarchitectures, we make use of methods developed in the field of liquid crystal (LC) research. In fact, epithelial tissues possess typical features of liquid crystalline systems albeit exhibiting a different local symmetry. Therefore, tools developed in the LC research community can be successfully applied for the description of the overall epithelial tissue topology and its orientational order. We additionally discuss and hypothesize the possibilities of using nanoparticles for structural defect stabilization and its application.

The discovery of small-world and scale-free properties of many man-made and natural complex networks has attracted increasing attention. Of particular interest is how the structural properties of a network facilitate and constrain its dynamical behavior. In this paper we study the synchronization of weakly coupled limit-cycle oscillators in dependence on the network topology as well as the dynamical features of individual oscillators. We show that flexible oscillators, characterized by near zero values of divergence, express maximal correlation in broad-scale small-world networks, whereas the non-flexible (rigid) oscillators are best correlated in more heterogeneous scale-free networks. We found that the synchronization behavior is governed by the interplay between the networks global efficiency and the mutual frequency adaptation. The latter differs for flexible and rigid oscillators. The results are discussed in terms of evolutionary advantages of broad-scale small-world networks in biological systems.

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. B eta cells secrete insulin in response to stimulation by energy rich molecules in a regulated manner and play a central role in whole-body energy homeostasis 1. In vivo, beta cells are organized into microorgans called islets of Langerhans. All beta cells of an islet of Langerhans are coupled into a single functional unit by means of the gap junction protein Connexin 36 (Cx36) that allows for electrical coupling and exchange of small signaling molecules between physically adjacent cells. One of these small signaling molecules being calcium ions 2. In this way, a coordinated activity in a large number of cells can be established, thereby leading to a regulated exocytosis of insulin 3,4. The mechanisms that govern insulin secretion at the single-cell level have been studied extensively. An increase in extracellular glucose concentration leads to an increased entry of glucose into the beta cell, an increased metabolic production of ATP and a decrease in the open probability of ATP-sensitive potassium ion channels. Consequently, the beta cell depolarizes and the voltage-sensitive calcium ion channels open to increase the intracellular calcium concentration ([Ca 21 ] i) that triggers the calcium-sensitive exocytosis of insulin granules. This calcium-induced exocytosis is believed to be augmented via a less well known amplifying pathway 5. The changes in membrane potential, [Ca 21 ] i as well as exocytosis occur in the form of synchronous oscillations 6–10. Insulin acting on different target cells in the body subsequently reduces glucose concentration to stop the stimulation of insulin release and prevent hypoglycemia by means of a negative feedback loop. At the tissue level however, the relationship between the collective activity of cell populations and hormone release is not completely understood 11. This is mainly due to the fact that until recently, our ability to study the physiology of many cells simultaneously had largely been limited by the existing experimental methods 12. The investigations of the intercellular communication between beta cells had mostly relied on imaging changes in

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. V C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4926673] Self-sustained oscillators are models of naturally oscillating objects, and as such they embrace many concepts in physics, biology, and engineering. Stable dissipative oscil-latory dynamics results from the flow of energy or matter through a nonlinear system. If the energy is supplied to the system at a rate at which it is dissipated, ordered, and stable, self-organized oscillations may occur. In general, the stability and robustness of such a dynamical state depend on the dissipative properties of individual oscilla-tors, which in turn determine the important dynamical features, such as synchronization and entraining capability. However, in ensembles of interconnected oscillators, the coupling itself can also significantly affect both robustness and dissipation. Motivated by the fact that many real-life systems are composed of coupled dissipa-tive elements that exhibit complex connectivity patterns, in the present study, we therefore analyze the impact of a heterogeneous network structure on the dissipation rates of oscillators. To this effect, we first examine theoretically and numerically the relationship between node degree and average dissipation of oscillators and show that for networks of diffusively coupled oscillators this relation is linear. Next, we validate this result experimentally by measuring the activity of coupled beta cells within intact mouse pancreatic tissue by means of confocal imaging. On the basis of the measured cellular signals, we extract the intercellular functional connectivity patterns and calculate the average dissipation of individual cells. Our results reveal a clear tendency of cells in the network with a higher node degree having higher dissipation rates, which corroborates and in fact confirms our theoretical predictions. Moreover, our findings point out that the intercellular communication quite noticeably contributes to the energy needs of beta cells, which encompasses important aspects of structural and functional performance of beta cell networks in health and disease.

Modern theory of networks has been recognized as a very successful methodological concept for the description and analysis of complex systems. However, some complex systems are more complex than others. For instance, several real-life systems are constituted by interdependent subsystems and their elements are subjected to different types of interactions that can also change with time. Recently, the multilayer network formalism has been proposed as a general theoretical framework for the description and analysis of such multi-dimensional complex systems and is acquiring more and more prominence in terms of a new research direction. In the present study, we use this methodology for the description of functional connectivity patterns and signal propagation between pancre-atic beta cells in an islet of Langerhans at the levels of membrane potential (MP) and cytosolic calcium concentration ([Ca 2+ ] c) dynamics to study the extent of overlap in the two networks and to clarify whether time lags between the two signals in individual cells are in any way dependent on the role these cells play in the functional networks. The two corresponding network layers are constructed on the basis of signal directions and pair-wise correlations, whereas the interlayer connections represent the time lag between both measured signals. Our results confirm our previous finding that both MP and [Ca 2+ ] c change spread across an islet in the form of a depolarization and a [Ca 2+ ] c wave, respectively. Both types of waves follow nearly the same path and the networks in both layers have a similar but not entirely the same structure. We show that the observed discrepancies are attributed to variability in delays between the depolarization and rise in [Ca 2+ ] c. In particular, high-degree nodes in both layers are found to exhibit a larger time lag between the MP and the [Ca 2+ ] c signal than nodes with less connections. We speculate that this finding reflects a higher activity of endoplasmic reticulum calcium pumps in the most connected cells. Our findings indicate that visualizing and studying the temporal information flow and interaction patterns between beta cells as a multiplex network can provide valuable new insights into the physiology of the complex signaling processes in islets of Langerhans.

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 vas-culature. 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 Funding: Financial support for researchers' mobility: French-Slovenian Hubert-Curien partnership Proteus n˚33325NL Endothelial planar cell polarity and vascular network structure and functionality http://www.campusfrance.org/fr/PHC.

Because of the complexity of processes that govern the regulatory mechanisms which control the cellular functions and dynamic behavior, mathematical models and numerical simulations are needed to fully grasp the mechanisms and functions of biological rhythms. In the last decade the theory of complex networks is frequently applied to address those issues. In the present paper we investigate theoretically the role of the intercellular communication network structure by synchronization of cellular oscillators. Motivated by the fact that in biological systems the interplay between the network structure and the dynamics taking place on it is closely interrelated, we develop a spatial network representation of an ensemble of cells in which we can tune the network organization between a scale-free network with dominating long-range connections and a homogeneous network with mostly adjacent neurons connected. Our results reveal that for noise-induced oscillations in excitable cells and for chaotic bursting oscillations the most synchronized response is obtained for the intermediate regime where long-as well as short-range connections constitute the intercellular network. On the other hand, for periodic oscillations it is found than the scale-free network topology ensures the greatest collective response. We argue that those findings are related to flexibility properties of individual cells.

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 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.

Synchronized neuronal activity has been observed at all levels of human and any other nervous systems and was suggested as particularly relevant in information processing and coding. In the present paper we investigate the synchronization of bursting neuronal activity. Motivated by the fact that in neural systems the interplay between the network structure and the dynamics taking place on it is closely interrelated, we develop a spatial network representation of neural architecture in which we can tune the network organization between a scale-free network with dominating long-range connections and a homogeneous network with mostly adjacent neurons connected. Our results reveal that the most synchronized response is obtained for the intermediate regime where long- as well as short-range connections constitute the neural architecture. Moreover, the optimal response is additionally enhanced when the speed of signal propagation is optimized.