Multidimensional Pattern Formation Has an Infinite Number of Constants of Motion

Extending our previous work on 2D growth for the Laplace equation we study here {\it multidimensional} growth for {\it arbitrary elliptic} equations, describing inhomogeneous and anisotropic pattern formations processes. We find that these nonlinear processes are governed by an infinite number of conservation laws. Moreover, in many cases {\it all dynamics of the interface can be reduced to the linear time--dependence of only one ``moment" $M_0$} which corresponds to the changing volume while {\it all higher moments, $M_l$, are constant in time. These moments have a purely geometrical nature}, and thus carry information about the moving shape. These conserved quantities (eqs.~(7) and (8) of this article) are interpreted as coefficients of the multipole expansion of the Newtonian potential created by the mass uniformly occupying the domain enclosing the moving interface. Thus the question of how to recover the moving shape using these conserved quantities is reduced to the classical inverse potential problem of reconstructing the shape of a body from its exterior gravitational potential. Our results also suggest the possibility of controlling a moving interface by appropriate varying the location and strength of sources and sinks.Comment: CYCLER Paper 93feb00

Harmonic moment dynamics in Laplacian growth

Harmonic moments are integrals of integer powers of z = x+iy over a domain. Here the domain is an exterior of a bubble of air growing in an oil layer between two horizontal closely spaced plates. Harmonic moments are a natural basis for such Laplacian growth phenomena because, unlike other representations, these moments linearize the zero surface tension problem (Richardson, 1972), so that all moments except the lowest one are conserved in time. For non-zero surface tension, we show that the the harmonic moments decay in time rather than exhibiting the divergences of other representations. Our laboratory observations confirm the theoretical predictions and demonstrate that an interface dynamics description in terms of harmonic moments is physically realizable and robust. In addition, by extending the theory to include surface tension, we obtain from measurements of the time evolution of the harmonic moments a value for the surface tension that is within 20% of the accepted value.Comment: 10 pages, 7 figure

Functional and Biogenetical Heterogeneity of the Inner Membrane of Rat-Liver Mitochondria

Rat liver mitochondria were fragmented by a combined technique of swelling, shrinking, and sonication. Fragments of inner membrane were separated by density gradient centrifugation. They differed in several respects: electronmicroscopic appearance, phospholipid and cytochrome contents, electrophoretic behaviour of proteins and enzymatic activities. Three types of inner membrane fractions were isolated. The first type is characterized by a high activity of metal chelatase, low activities of succinate-cytochrome c reductase and of glycerolphosphate dehydrogenase, as well as by a high phospholipid content and low contents of cytochromes aa3 and b. The second type displays maximal activities of glycerolphosphate dehydrogenase and metal chelatase, but contains relatively little cytochromes and has low succinate-cytochrome c reductase activity. The third type exhibits highest succinate-cytochrome c reductase activity, a high metal chelatase activity and highest cytochrome contents. However, this fraction was low in both glycerolphosphate dehydrogenase activity and phospholipid content. This fraction was also richest in the following enzyme activities: cytochrome oxidase, oligomycin-sensitive ATPase, proline oxidase, 3-hydroxybutyrate dehydrogenase and rotenone-sensitive NADH-cytochrome c reductase. Amino acid incorporation in vitro and in vivo in the presence of cycloheximide occurs predominantly into inner membrane fractions from the second type. These data suggest that the inner membrane is composed of differently organized parts, and that polypeptides synthesized by mitochondrial ribosomes are integrated into specific parts of the inner membrane

Random Matrices in 2D, Laplacian Growth and Operator Theory

Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of theoretical physics, from condensed matter to high energy. The fundamental results obtained so far rely mostly on the theory of random matrices in one dimension (the dimensionality of the spectrum, or equilibrium probability density). In the last few years, this theory has been extended to the case where the spectrum is two-dimensional, or even fractal, with dimensions between 1 and 2. In this article, we review these recent developments and indicate some physical problems where the theory can be applied.Comment: 88 pages, 8 figure

Estimation of Relevant Variables on High-Dimensional Biological Patterns Using Iterated Weighted Kernel Functions

BACKGROUND The analysis of complex proteomic and genomic profiles involves the identification of significant markers within a set of hundreds or even thousands of variables that represent a high-dimensional problem space. The occurrence of noise, redundancy or combinatorial interactions in the profile makes the selection of relevant variables harder. METHODOLOGY/PRINCIPAL FINDINGS Here we propose a method to select variables based on estimated relevance to hidden patterns. Our method combines a weighted-kernel discriminant with an iterative stochastic probability estimation algorithm to discover the relevance distribution over the set of variables. We verified the ability of our method to select predefined relevant variables in synthetic proteome-like data and then assessed its performance on biological high-dimensional problems. Experiments were run on serum proteomic datasets of infectious diseases. The resulting variable subsets achieved classification accuracies of 99% on Human African Trypanosomiasis, 91% on Tuberculosis, and 91% on Malaria serum proteomic profiles with fewer than 20% of variables selected. Our method scaled-up to dimensionalities of much higher orders of magnitude as shown with gene expression microarray datasets in which we obtained classification accuracies close to 90% with fewer than 1% of the total number of variables. CONCLUSIONS Our method consistently found relevant variables attaining high classification accuracies across synthetic and biological datasets. Notably, it yielded very compact subsets compared to the original number of variables, which should simplify downstream biological experimentation

Imaging and imagination: understanding the endo-lysosomal system

Lysosomes are specialized compartments for the degradation of endocytosed and intracellular material and essential regulators of cellular homeostasis. The importance of lysosomes is illustrated by the rapidly growing number of human disorders related to a defect in lysosomal functioning. Here, we review current insights in the mechanisms of lysosome biogenesis and protein sorting within the endo-lysosomal system. We present increasing evidence for the existence of parallel pathways for the delivery of newly synthesized lysosomal proteins directly from the trans-Golgi network (TGN) to the endo-lysosomal system. These pathways are either dependent or independent of mannose 6-phosphate receptors and likely involve multiple exits for lysosomal proteins from the TGN. In addition, we discuss the different endosomal intermediates and subdomains that are involved in sorting of endocytosed cargo. Throughout our review, we highlight some examples in the literature showing how imaging, especially electron microscopy, has made major contributions to our understanding of the endo-lysosomal system today

The peroxisome: still a mysterious organelle

More than half a century of research on peroxisomes has revealed unique features of this ubiquitous subcellular organelle, which have often been in disagreement with existing dogmas in cell biology. About 50 peroxisomal enzymes have so far been identified, which contribute to several crucial metabolic processes such as β-oxidation of fatty acids, biosynthesis of ether phospholipids and metabolism of reactive oxygen species, and render peroxisomes indispensable for human health and development. It became obvious that peroxisomes are highly dynamic organelles that rapidly assemble, multiply and degrade in response to metabolic needs. However, many aspects of peroxisome biology are still mysterious. This review addresses recent exciting discoveries on the biogenesis, formation and degradation of peroxisomes, on peroxisomal dynamics and division, as well as on the interaction and cross talk of peroxisomes with other subcellular compartments. Furthermore, recent advances on the role of peroxisomes in medicine and in the identification of novel peroxisomal proteins are discussed

Levosimendan Administration in Limb Ischemia: Multicomponent Signaling Serving Kidney Protection

AIMS AND OBJECTIVES: Acute renal failure is a severe complication of lower extremity major arterial reconstructions, which could even be fatal. Levosimendan is a dual-acting positive inotropic and vasodilatory agent, which is suspected to have protective effects against cardiac ischemia. However, there is no data available on lower limb or remote organ ischemic injuries therefore the aim of the study was to investigate the effect of levosimendan on lower limb ischemia-reperfusion injury and the corollary renal dysfunction. METHODS: Male Wistar rats underwent 180 min bilateral lower limb ischemia followed by 4 or 24 hours of reperfusion. Intravenous Levosimendan was administered continuously (0.2mug/bwkg/min) throughout the whole course of ischemia and the first 3h of reperfusion. Results were compared with sham-operated and ischemia-reperfusion groups. Hemodynamic monitoring was performed by invasive arterial blood pressure measurement. Kidney and lower limb muscle microcirculation was registered by a laser Doppler flowmeter. After 4h and 24h of reperfusion, serum, urine and histological samples were collected. RESULTS: Systemic hemodynamic parameters and microcirculation of kidney and the lower limb significantly improved in the Levosimendan treated group. Muscle viability was significantly preserved 4 and 24 hours after reperfusion. At the same time, renal functional laboratory tests and kidney histology demonstrated significantly less expressive kidney injury in Levosimendan groups. TNF-alpha levels were significantly less elevated in the Levosimendan group 4 hours after reperfusion. CONCLUSION: The results claim a protective role for Levosimendan administration during major vascular surgeries to prevent renal complications

Endothelial Differentiation of Human Stem Cells Seeded onto Electrospun Polyhydroxybutyrate/Polyhydroxybutyrate-Co-Hydroxyvalerate Fiber Mesh

Tissue engineering is based on the association of cultured cells with structural matrices and the incorporation of signaling molecules for inducing tissue regeneration. Despite its enormous potential, tissue engineering faces a major challenge concerning the maintenance of cell viability after the implantation of the constructs. The lack of a functional vasculature within the implant compromises the delivery of nutrients to and removal of metabolites from the cells, which can lead to implant failure. In this sense, our investigation aims to develop a new strategy for enhancing vascularization in tissue engineering constructs. This study's aim was to establish a culture of human adipose tissue-derived stem cells (hASCs) to evaluate the biocompatibility of electrospun fiber mesh made of polyhydroxybutyrate (PHB) and its copolymer poly-3-hydroxybutyrate-co-3-hydroxyvalerate (PHB-HV) and to promote the differentiation of hASCs into the endothelial lineage. Fiber mesh was produced by blending 30% PHB with 70% PHB-HV and its physical characterization was conducted using scanning electron microscopy analysis (SEM). Using electrospinning, fiber mesh was obtained with diameters ranging 300 nm to 1.3 µm. To assess the biological performance, hASCs were extracted, cultured, characterized by flow cytometry, expanded and seeded onto electrospun PHB/PHB-HV fiber mesh. Various aspects of the cells were analyzed in vitro using SEM, MTT assay and Calcein-AM staining. The in vitro evaluation demonstrated good adhesion and a normal morphology of the hASCs. After 7, 14 and 21 days of seeding hASCs onto electrospun PHB/PHB-HV fiber mesh, the cells remained viable and proliferative. Moreover, when cultured with endothelial differentiation medium (i.e., medium containing VEGF and bFGF), the hASCs expressed endothelial markers such as VE-Cadherin and the vWF factor. Therefore, the electrospun PHB/PHB-HV fiber mesh appears to be a suitable material that can be used in combination with endothelial-differentiated cells to improve vascularization in engineered bone tissues

Lipid droplets: a classic organelle with new outfits

Lipid droplets are depots of neutral lipids that exist virtually in any kind of cell. Recent studies have revealed that the lipid droplet is not a mere lipid blob, but a major contributor not only to lipid homeostasis but also to diverse cellular functions. Because of the unique structure as well as the functional importance in relation to obesity, steatosis, and other prevailing diseases, the lipid droplet is now reborn as a brand new organelle, attracting interests from researchers of many disciplines