The Wnt/ß-catenin/TCF/Sp5/Zic4 Gene Network That Regulates Head Organizer Activity in Hydra Is Differentially Regulated in Epidermis and Gastrodermis.

Hydra head formation depends on an organizing center in which Wnt/ß-catenin signaling, that plays an inductive role, positively regulates Sp5 and Zic4, with Sp5 limiting Wnt3/ß-catenin expression and Zic4 triggering tentacle formation. Using transgenic lines in which the HySp5 promoter drives eGFP expression in either the epidermis or gastrodermis, we show that Sp5 promoter activity is differentially regulated in each epithelial layer. In intact animals, epidermal HySp5:GFP activity is strong apically and weak along the body column, while in the gastrodermis, it is maximal in the tentacle ring region and maintained at a high level along the upper body column. During apical regeneration, HySp5:GFP is activated early in the gastrodermis and later in the epidermis. Alsterpaullone treatment induces a shift in apical HySp5:GFP expression towards the body column where it forms transient circular figures in the epidermis. Upon ß-catenin(RNAi), HySp5:GFP activity is down-regulated in the epidermis while bud-like structures expressing HySp5:GFP in the gastrodermis develop. Sp5(RNAi) reveals a negative Sp5 autoregulation in the epidermis, but not in the gastrodermis. These differential regulations in the epidermis and gastrodermis highlight the distinct architectures of the Wnt/ß-catenin/TCF/Sp5/Zic4 network in the hypostome, tentacle base and body column of intact animals, as well as in the buds and apical and basal regenerating tips.

The transcription factor Zic4 promotes tentacle formation and prevents epithelial transdifferentiation in Hydra.

The molecular mechanisms that maintain cellular identities and prevent dedifferentiation or transdifferentiation remain mysterious. However, both processes are transiently used during animal regeneration. Therefore, organisms that regenerate their organs, appendages, or even their whole body offer a fruitful paradigm to investigate the regulation of cell fate stability. Here, we used Hydra as a model system and show that Zic4, whose expression is controlled by Wnt3/ß-catenin signaling and the Sp5 transcription factor, plays a key role in tentacle formation and tentacle maintenance. Reducing Zic4 expression suffices to induce transdifferentiation of tentacle epithelial cells into foot epithelial cells. This switch requires the reentry of tentacle battery cells into the cell cycle without cell division and is accompanied by degeneration of nematocytes embedded in these cells. These results indicate that maintenance of cell fate by a Wnt-controlled mechanism is a key process both during homeostasis and during regeneration.

Arnold tongue entrainment reveals dynamical principles of the embryonic segmentation clock.

Living systems exhibit an unmatched complexity, due to countless, entangled interactions across scales. Here, we aim to understand a complex system, that is, segmentation timing in mouse embryos, without a reference to these detailed interactions. To this end, we develop a coarse-grained approach, in which theory guides the experimental identification of the segmentation clock entrainment responses. We demonstrate period- and phase-locking of the segmentation clock across a wide range of entrainment parameters, including higher-order coupling. These quantifications allow to derive the phase response curve (PRC) and Arnold tongues of the segmentation clock, revealing its essential dynamical properties. Our results indicate that the somite segmentation clock has characteristics reminiscent of a highly non-linear oscillator close to an infinite period bifurcation and suggests the presence of long-term feedbacks. Combined, this coarse-grained theoretical-experimental approach reveals how we can derive simple, essential features of a highly complex dynamical system, providing precise experimental control over the pace and rhythm of the somite segmentation clock.

Multispectral Imaging Flow Cytometry with Spatially and Spectrally Resolving Snapshot-Mosaic Cameras for the Characterization and Classification of Bioparticles.

In the development and optimization of biotechnological cultivation processes the continuous monitoring through the acquisition and interpretation of spectral and morphological properties of bioparticles are challenging. There is therefore a need for the parallel acquisition and interpretation of spatially and spectrally resolved measurements with which particles can be characterized and classified in-flow with high throughput. Therefore, in this paper we investigated the scientific and technological connectivity of standard imaging flow cytometry (IFC) with filter-on-chip based spatially and spectrally resolving snapshot-mosaic cameras for photonic sensing and control in a smart and innovative microfluidic device. For the investigations presented here we used the microalgae Haematococcus pluvialis (HP). These microalgae are used commercially to produce the antioxidant keto-carotenoid astaxanthin. Therefore, HP is relevant to practically demonstrate the usability of the developed system for Multispectral Imaging Flow Cytometry (MIFC) platform. The extension of standard IFC with snapshot-mosaic cameras and multivariate data processing is an innovative approach for the in-flow characterization and derived classification of bioparticles. Finally, the multispectral data acquisition and the therefore developed methodology is generalizable and enables further applications far beyond the here characterized population of HP cells.

Engineering complex communities by directed evolution.

Directed evolution has been used for decades to engineer biological systems at or below the organismal level. Above the organismal level, a small number of studies have attempted to artificially select microbial ecosystems, with uneven and generally modest success. Our theoretical understanding of artificial ecosystem selection is limited, particularly for large assemblages of asexual organisms, and we know little about designing efficient methods to direct their evolution. Here, we have developed a flexible modelling framework that allows us to systematically probe any arbitrary selection strategy on any arbitrary set of communities and selected functions. By artificially selecting hundreds of in silico microbial metacommunities under identical conditions, we first show that the main breeding methods used to date, which do not necessarily let communities reach their ecological equilibrium, are outperformed by a simple screen of sufficiently mature communities. We then identify a range of alternative directed evolution strategies that, particularly when applied in combination, are well suited for the top-down engineering of large, diverse and stable microbial consortia. Our results emphasize that directed evolution allows an ecological structure-function landscape to be navigated in search of dynamically stable and ecologically resilient communities with desired quantitative attributes.

Regional Striatal Cholinergic Involvement in Human Behavioral Flexibility.

Animal studies have shown that the striatal cholinergic system plays a role in behavioral flexibility but, until recently, this system could not be studied in humans due to a lack of appropriate noninvasive techniques. Using proton magnetic resonance spectroscopy, we recently showed that the concentration of dorsal striatal choline (an acetylcholine precursor) changes during reversal learning (a measure of behavioral flexibility) in humans. The aim of the present study was to examine whether regional average striatal choline was associated with reversal learning. A total of 22 participants (mean age = 25.2 years, range = 18-32 years, 13 female) reached learning criterion in a probabilistic learning task with a reversal component. We measured choline at rest in both the dorsal and ventral striatum using magnetic resonance spectroscopy. Task performance was described using a simple reinforcement learning model that dissociates the contributions of positive and negative prediction errors to learning. Average levels of choline in the dorsal striatum were associated with performance during reversal, but not during initial learning. Specifically, lower levels of choline in the dorsal striatum were associated with a lower number of perseverative trials. Moreover, choline levels explained interindividual variance in perseveration over and above that explained by learning from negative prediction errors. These findings suggest that the dorsal striatal cholinergic system plays an important role in behavioral flexibility, in line with evidence from the animal literature and our previous work in humans. Additionally, this work provides further support for the idea of measuring choline with magnetic resonance spectroscopy as a noninvasive way of studying human cholinergic neurochemistry.SIGNIFICANCE STATEMENT Behavioral flexibility is a crucial component of adaptation and survival. Evidence from the animal literature shows that the striatal cholinergic system is fundamental to reversal learning, a key paradigm for studying behavioral flexibility, but this system remains understudied in humans. Using proton magnetic resonance spectroscopy, we showed that choline levels at rest in the dorsal striatum are associated with performance specifically during reversal learning. These novel findings help to bridge the gap between animal and human studies by demonstrating the importance of cholinergic function in the dorsal striatum in human behavioral flexibility. Importantly, the methods described here cannot only be applied to furthering our understanding of healthy human neurochemistry, but also to extending our understanding of cholinergic disorders.

Functional neurochemical imaging of the human striatal cholinergic system during reversal learning.

Animal studies have shown that acetylcholine (ACh) levels in the dorsal striatum play a role in reversal learning. However, this has not been studied in humans due to a lack of appropriate non-invasive techniques. Proton magnetic resonance spectroscopy (1 H-MRS) can be used to measure metabolite levels in humans in vivo. Although it cannot be used to study ACh directly, 1 H-MRS can be used to study choline, an ACh precursor, which is linked to activity-dependent ACh release. The aim of this study was to use functional-1 H-MRS (fMRS) to measure changes in choline levels in the human dorsal striatum during performance of a probabilistic reversal learning task. We demonstrate a task-dependent decrease in choline, specifically during reversal, but not initial, learning. We interpret this to reflect a sustained increase in ACh levels, which is in line with findings from the animal literature. This task-dependent change was specific to choline and was not observed in control metabolites. These findings provide support for the use of fMRS in the in vivo study of the human cholinergic system.

In vivo functional neurochemistry of human cortical cholinergic function during visuospatial attention.

Cortical acetylcholine is involved in key cognitive processes such as visuospatial attention. Dysfunction in the cholinergic system has been described in a number of neuropsychiatric disorders. Levels of brain acetylcholine can be pharmacologically manipulated, but it is not possible to directly measure it in vivo in humans. However, key parts of its biochemical cascade in neural tissue, such as choline, can be measured using magnetic resonance spectroscopy (MRS). There is evidence that levels of choline may be an indirect but proportional measure of acetylcholine availability in brain tissue. In this study, we measured relative choline levels in the parietal cortex using functional (event-related) MRS (fMRS) during performance of a visuospatial attention task, with a modelling approach verified using simulated data. We describe a task-driven interaction effect on choline concentration, specifically driven by contralateral attention shifts. Our results suggest that choline MRS has the potential to serve as a proxy of brain acetylcholine function in humans.

Catastrophic cascade of failures in interdependent networks.

Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network. Modern systems are coupled together and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures ('concurrent malfunction') is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations. Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks.

Finding a better immunization strategy.

The problem of finding the best strategy to immunize a population or a computer network with a minimal number of immunization doses is of current interest. It has been accepted that the targeted strategies on most central nodes are most efficient for model and real networks. We present a newly developed graph-partitioning strategy which requires 5% to 50% fewer immunization doses compared to the targeted strategy and achieves the same degree of immunization of the network. We explicitly demonstrate the effectiveness of our proposed strategy on several model networks and also on real networks.

Comparative reliability of proton spectroscopy techniques designed to improve detection of J-coupled metabolites.

Improved detection of J-coupled neurometabolites through the use of modified proton magnetic resonance spectroscopy (1H-MRS) techniques has recently been reported. TE-averaged point-resolved spectroscopy (PRESS) uses the J modulation effects by averaging FIDs with differing echo times to improve detection of glutamate, while standard PRESS detection of glutamate can be improved by using an appropriate single echo determined from J-modulation simulations. In the present study, the reliabilities of TE-averaged PRESS, standard PRESS with TE = 40 ms, and standard PRESS with TE = 30 ms in detecting metabolite levels in the cingulate gyrus of the human brain at 3T were compared in six subjects. TE-averaged PRESS measures showed a mean variability of 9% for N-acetyl aspartate, choline, and creatine, compared with < 4% for the 30- and 40-ms PRESS techniques. The coefficients of variation for glutamate were 10%, 7%, and 5% for TE-averaged, 30-ms, and 40-ms PRESS, respectively. PRESS with a TE of 40 ms also demonstrated improved reliability for GABA and glutamine concentrations. These results show that with the appropriate selection of echo time standard PRESS can be a reliable (1)H-MRS technique for the measurement of J-coupled neurometabolites in the human brain and, moreover, compares favorably with at least one J-edited technique.

Graph partitioning induced phase transitions.

We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree k. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any partitioning process (even if nonoptimal) that partitions the graph into essentially equal sized connected components (clusters), the system undergoes a percolation phase transition at f = fc = 1-2/k where f is the fraction of edges removed to partition the graph. For optimal partitioning, at the percolation threshold, we find S approximately N 0.4 where S is the size of the clusters and l approximately N 0.25 where l is their diameter. Also, we find that S undergoes multiple nonpercolation transitions for f

Betweenness centrality of fractal and nonfractal scale-free model networks and tests on real networks.

We study the betweenness centrality of fractal and nonfractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to nonfractal models. We also show that nodes of both fractal and nonfractal scale-free networks have power-law betweenness centrality distribution P(C) approximately C(-delta). We find that for nonfractal scale-free networks delta=2, and for fractal scale-free networks delta=2-1/dB, where dB is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network at the autonomous system level (N=20566), where N is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to nonfractal networks upon adding random edges to a fractal network. We show that the crossover length l*, separating fractal and nonfractal regimes, scales with dimension dB of the network as p(-1/dB), where p is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with p.

Percolation theory applied to measures of fragmentation in social networks.

We apply percolation theory to a recently proposed measure of fragmentation F for social networks. The measure F is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction q of nodes and the total number of pairs in the original fully connected network. We compare F with the traditional measure used in percolation theory, P(infinity), the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods from percolation, we study Erdos-Rényi and scale-free networks under various types of node removal strategies. The removal strategies are random removal, high degree removal, and high betweenness centrality removal. We find that for a network obtained after removal (all strategies) of a fraction q of nodes above percolation threshold, P(infinity) approximately (1-F)1/2. For fixed P(infinity) and close to percolation threshold (q=qc), we show that 1-F better reflects the actual fragmentation. Close to qc, for a given P(infinity), 1-F has a broad distribution and it is thus possible to improve the fragmentation of the network. We also study and compare the fragmentation measure F and the percolation measure P(infinity) for a real social network of workplaces linked by the households of the employees and find similar results.

Optimization of the robustness of multimodal networks.

We investigate the robustness against both random and targeted node removal of networks in which P(k), the distribution of nodes with degree k, is a multimodal distribution, [formula--see text] with k(i) proportional to b -(i-1) and Dirac's delta function delta (x). We refer to this type of network as a scale-free multimodal network. For m=2, the network is a bimodal network; in the limit m approaches infinity, the network models a scale-free network. We calculate and optimize the robustness for given values of the number of modes m, the total number of nodes N, and the average degree , using analytical formulas for the random and targeted node removal thresholds for network collapse. We find, when N>>1, that (i) the robustness against random and targeted node removal for this multimodal network is controlled by a single combination of variables, N(1/m-1), (ii) the robustness of the multimodal network against targeted node removal decreases rapidly when the number of modes becomes larger than a critical value that is of the order of 1n N, and (iii) the values of exponent lambda(opt) that characterizes the scale-free degree distribution of the multimodal network that maximize the robustness against both random and targeted node removal fall between 2.5 and 3.

Resilience of complex networks to random breakdown.

Using Monte Carlo simulations we calculate fc, the fraction of nodes that are randomly removed before global connectivity is lost, for networks with scale-free and bimodal degree distributions. Our results differ from the results predicted by an equation for fc proposed by Cohen We discuss the reasons for this disagreement and clarify the domain for which the proposed equation is valid.

Fractal dimension of 3-blocks in four-, five-, and six-dimensional percolation systems.

Using Monte Carlo simulations, we study the distributions of the 3-block mass N3 in four-, five-, and six-dimensional percolation systems. Because the probability of creating large 3-blocks in these dimensions is very small, we use a "go with the winners" method of statistical enhancement to simulate configurations having probability as small as 10(-30). In earlier work, the fractal dimensions of 3-blocks, d(3), in 2D (two dimensional) and 3D were found to be 1.20+/-0.1 and 1.15+/-0.1, respectively, consistent with the possibility that the fractal dimension might be the same in all dimensions. We find that the fractal dimension of 3-blocks decreases rapidly in higher dimensions, and estimate d(3)=0.7+/-0.2 (4D) and 0.5+/-0.2 (5D). At the upper critical dimension of percolation, d(c)=6, our simulations are consistent with d(3)=0 with logarithmic corrections to power-law scaling.

The history of external fixation.

Even though external fixation is considered to be a rather "new" trend in orthopedics and traumatology, in fact it has been something used by physicians and surgeons for thousands of years. In the mid 1800's, external fixation would see some substantial growth and evolution, pioneered by physicians and surgeons whose principles are still in use today. Through the 1900's, the indications and usage would continue to expand, not to mention the modernization of the external fixation apparatus. Many surgeons in this era are notable for their work with external fixation, especially Gavriel Ilizarov, considered to be the father of external fixation. Further research and development with external fixation needs to be performed and, with time, will more than likely become fully integrated into modern clinical practice.

Continuum percolation threshold for interpenetrating squares and cubes.

Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose edges are aligned parallel to one another and (ii) randomly oriented objects. For squares whose edges are aligned, the critical area fraction at the percolation threshold phi(c)=0.6666+/-0.0004, while for randomly oriented squares phi(c)=0.6254+/-0.0002, 6% smaller. For cubes whose edges are aligned, the critical volume fraction at the percolation threshold phi(c)=0.2773+/-0.0002, while for randomly oriented cubes phi(c)=0.2168+/-0.0002, 22% smaller.

Fractal behavior of the shortest path between two lines in percolation systems.

Using Monte Carlo simulations, we determine the scaling form for the probability distribution of the shortest path l between two lines in a three-dimensional percolation system at criticality; the two lines can have arbitrary positions, orientations, and lengths. We find that the probability distributions can exhibit up to four distinct power-law regimes (separated by crossover regimes) with exponents depending on the relative orientations of the lines. We explain this rich fractal behavior with scaling arguments.