Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation

The equation ∂tu = u∂xx2u − (c − 1)(∂xu)2 is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self-similar solutions to this equation is constructed. Numerical investigation of the evolution of non-self-similar solutions to the Cauchy problems having compactly supported initial conditions is performed. Numerical experiments indicate that the self-similar solutions obtained represent intermediate asymptotics of a wider class of solutions when the influence of details of the initial conditions disappears but the solution is still far from the ultimate state: identical zero. An open problem caused by the nonuniqueness of the solution of the Cauchy problem is discussed.

Reverse two-hybrid and one-hybrid systems to detect dissociation of protein-protein and DNA-protein interactions.

Macromolecular interactions define many biological phenomena. Although genetic methods are available to identify novel protein-protein and DNA-protein interactions, no genetic system has thus far been described to identify molecules or mutations that dissociate known interactions. Herein, we describe genetic systems that detect such events in the yeast Saccharomyces cerevisiae. We have engineered yeast strains in which the interaction of two proteins expressed in the context of the two-hybrid system or the interaction between a DNA-binding protein and its binding site in the context of the one-hybrid system is deleterious to growth. Under these conditions, dissociation of the interaction provides a selective growth advantage, thereby facilitating detection. These methods referred to as the "reverse two-hybrid system" and "reverse one-hybrid system" facilitate the study of the structure-function relationships and regulation of protein-protein and DNA-protein interactions. They should also facilitate the selection of dissociator molecules that could be used as therapeutic agents.

Insight into the evolution of the Solanaceae from the parental genomes of Petunia hybrida

Petunia hybrida is a popular bedding plant that has a long history as a genetic model system. We report the whole-genome sequencing and assembly of inbred derivatives of its two wild parents, P. axillaris N and P. inflata S6. The assemblies include 91.3% and 90.2% coverage of their diploid genomes (1.4 Gb; 2n = 14) containing 32,928 and 36,697 protein-coding genes, respectively. The genomes reveal that the Petunia lineage has experienced at least two rounds of hexaploidization: the older gamma event, which is shared with most Eudicots, and a more recent Solanaceae event that is shared with tomato and other solanaceous species. Transcription factors involved in the shift from bee to moth pollination reside in particularly dynamic regions of the genome, which may have been key to the remarkable diversity of floral colour patterns and pollination systems. The high-quality genome sequences will enhance the value of Petunia as a model system for research on unique biological phenomena such as small RNAs, symbiosis, self-incompatibility and circadian rhythms.

Denkschriften der Kaiserlichen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Classe.

Title varies slightly.

A mathematical model of integrin-mediated haptotactic cell migration

Haptotactic cell migration, a directed response to gradients of cell—extracellular matrix adhesion, is an important process in a number of biological phenomena such as wound healing and tumour cell invasion. Previously, mathematical models of haptotaxis have been developed on the premise that cells migrate in response to gradients in the density of the extracellular matrix. In this paper, we develop a novel mathematical model of haptotaxis which includes the adhesion receptors known as integrins and a description of their functional activation, local recruitment and protrusion as part of lamellipodia. Through the inclusion of integrins, the modelled cell matter is able to respond to a true gradient of cell–matrix adhesion, represented by functionally active integrins. We also show that previous matrix-mediated models are in fact a subset of the novel integrin-mediated models, characterised by specific choices of diffusion and haptotaxis coefficients in their model equations. Numerical solutions suggest the existence of travelling waves of cell migration that are confirmed via a phase plane analysis of a simplified model.

PPD v1.0 - an integrated, web-accessible database of experimentally determined protein pKa values

The Protein pKa Database (PPD) v1.0 provides a compendium of protein residue-specific ionization equilibria (pKa values), as collated from the primary literature, in the form of a web-accessible postgreSQL relational database. Ionizable residues play key roles in the molecular mechanisms that underlie many biological phenomena, including protein folding and enzyme catalysis. The PPD serves as a general protein pKa archive and as a source of data that allows for the development and improvement of pKa prediction systems. The database is accessed through an HTML interface, which offers two fast, efficient search methods: an amino acid-based query and a Basic Local Alignment Search Tool search. Entries also give details of experimental techniques and links to other key databases, such as National Center for Biotechnology Information and the Protein Data Bank, providing the user with considerable background information.

Potential for Cell-Transplant Therapy with Human Neuronal Precursors to Treat Neuropathic Pain in Models of PNS and CNS Injury: Comparison of hNT2.17 and hNT2.19 Cell Lines

Effective treatment of sensory neuropathies in peripheral neuropathies and spinal cord injury (SCI) is one of the most difficult problems in modern clinical practice. Cell therapy to release antinociceptive agents near the injured spinal cord is a logical next step in the development of treatment modalities. But few clinical trials, especially for chronic pain, have tested the potential of transplant of cells to treat chronic pain. Cell lines derived from the human neuronal NT2 cell line parentage, the hNT2.17 and hNT2.19 lines, which synthesize and release the neurotransmitters gamma-aminobutyric acid (GABA) and serotonin (5HT), respectively, have been used to evaluate the potential of cell-based release of antinociceptive agents near the lumbar dorsal (horn) spinal sensory cell centers to relieve neuropathic pain after PNS (partial nerve and diabetes-related injury) and CNS (spinal cord injury) damage in rat models. Both cell lines transplants potently and permanently reverse behavioral hypersensitivity without inducing tumors or other complications after grafting. Functioning as cellular minipumps for antinociception, human neuronal precursors, like these NT2-derived cell lines, would likely provide a useful adjuvant or replacement for current pharmacological treatments for neuropathic pain.

NOTCH1 Gain of Function in Germ Cells Causes Failure of Spermatogenesis in Male Mice

NOTCH1 is a member of the NOTCH receptor family, a group of single-pass trans-membrane receptors. NOTCH signaling is highly conserved in evolution and mediates communication between adjacent cells. NOTCH receptors have been implicated in cell fate determination, as well as maintenance and differentiation of stem cells. In the mammalian testis expression of NOTCH1 in somatic and germ cells has been demonstrated, however its role in spermatogenesis was not clear. To study the significance of NOTCH1 in germ cells, we applied a cre/loxP approach in mice to induce NOTCH1 gain- or loss-of function specifically in male germ cells. Using a Stra8-icretransgene we produced mice with conditional activation of the NOTCH1 intracellular domain (NICD) in germ cells. Spermatogenesis in these mutants was progressively affected with age, resulting in decreased testis weight and sperm count. Analysis of downstream target genes of NOTCH1 signaling showed an increased expression of Hes5, with a reduction of the spermatogonial differentiation marker, Neurog3 expression in the mutant testis. Apoptosis was significantly increased in mouse germ cells with the corresponding elevation of pro-apoptotic Trp53 and Trp63genes' expression. We also showed that the conditional germ cell-specific ablation of Notch1 had no effect on spermatogenesis or male fertility. Our data suggest the importance of NOTCH signaling regulation in male germ cells for their survival and differentiation.

Specific Increase in MDR1 Mediated Drug-Efflux in Human Brain Endothelial Cells following Co-Exposure to HIV-1 and Saquinavir

Persistence of HIV-1 reservoirs within the Central Nervous System (CNS) remains a significant challenge to the efficacy of potent anti-HIV-1 drugs. The primary human Brain Microvascular Endothelial Cells (HBMVEC) constitutes the Blood Brain Barrier (BBB) which interferes with anti-HIV drug delivery into the CNS. The ATP binding cassette (ABC) transporters expressed on HBMVEC can efflux HIV-1 protease inhibitors (HPI), enabling the persistence of HIV-1 in CNS. Constitutive low level expression of several ABC-transporters, such as MDR1 (a.k.a. P-gp) and MRPs are documented in HBMVEC. Although it is recognized that inflammatory cytokines and exposure to xenobiotic drug substrates (e.g HPI) can augment the expression of these transporters, it is not known whether concomitant exposure to virus and anti-retroviral drugs can increase drug-efflux functions in HBMVEC. Our in vitro studies showed that exposure of HBMVEC to HIV-1 significantly up-regulates both MDR1 gene expression and protein levels; however, no significant increases in either MRP-1 or MRP-2 were observed. Furthermore, calcein-AM dye-efflux assays using HBMVEC showed that, compared to virus exposure alone, the MDR1 mediated drug-efflux function was significantly induced following concomitant exposure to both HIV-1 and saquinavir (SQV). This increase in MDR1 mediated drug-efflux was further substantiated via increased intracellular retention of radiolabeled [3H-] SQV. The crucial role of MDR1 in 3H-SQV efflux from HBMVEC was further confirmed by using both a MDR1 specific blocker (PSC-833) and MDR1 specific siRNAs. Therefore, MDR1 specific drug-efflux function increases in HBMVEC following co-exposure to HIV-1 and SQV which can reduce the penetration of HPIs into the infected brain reservoirs of HIV-1. A targeted suppression of MDR1 in the BBB may thus provide a novel strategy to suppress residual viral replication in the CNS, by augmenting the therapeutic efficacy of HAART drugs.

O paradoxo da superdifusão de uma caminhada aleatória com memória exponencial

The random walk models with temporal correlation (i.e. memory) are of interest in the study of anomalous diffusion phenomena. The random walk and its generalizations are of prominent place in the characterization of various physical, chemical and biological phenomena. The temporal correlation is an essential feature in anomalous diffusion models. These temporal long-range correlation models can be called non-Markovian models, otherwise, the short-range time correlation counterparts are Markovian ones. Within this context, we reviewed the existing models with temporal correlation, i.e. entire memory, the elephant walk model, or partial memory, alzheimer walk model and walk model with a gaussian memory with profile. It is noticed that these models shows superdiffusion with a Hurst exponent H > 1/2. We study in this work a superdiffusive random walk model with exponentially decaying memory. This seems to be a self-contradictory statement, since it is well known that random walks with exponentially decaying temporal correlations can be approximated arbitrarily well by Markov processes and that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. The solution to the apparent paradox is that the model is genuinely non-Markovian, due to a time-dependent decay constant associated with the exponential behavior. In the end, we discuss ideas for future investigations.

Report of the Workshop on Growth-increment Chronologies in Marine Fish: climate-ecosystem interactions in the North Atlantic 2 (WKGIC2). 18-22 April 2016 Esporles, Mallorca, Spain

Over the past several decades, thousands of otoliths, bivalve shells, and scales have been collected for the purposes of age determination and remain archived in European and North American fisheries laboratories. Advances in digital imaging and computer software combined with techniques developed by tree-ring scientists provide a means by which to extract additional levels of information in these calcified structures and generate annually resolved (one value per year), multidecadal time-series of population-level growth anomalies. Chemical and isotopic properties may also be extracted to provide additional information regarding the environmental conditions these organisms experienced.Given that they are exactly placed in time, chronologies can be directly compared to instrumental climate records, chronologies from other regions or species, or time-seriesof other biological phenomena. In this way, chronologies may be used to reconstruct historical ranges of environmental variability, identify climatic drivers of growth, establish linkages within and among species, and generate ecosystem-level indicators. Following the first workshop in Hamburg, Germany, in December 2014, the second workshop on Growth increment Chronologies in Marine Fish: climate-ecosystem interactions in the North Atlantic (WKGIC2) met at the Mediterranean Institute for Advanced Studies headquarters in Esporles, Spain, on 18–22 April 2016, chaired by Bryan Black (USA) and Christoph Stransky (Germany).Thirty-six participants from fifteen different countries attended. Objectives were to i) review the applications of chronologies developed from growth-increment widths in the hard parts (otoliths, shells, scales) of marine fish and bivalve species ii) review the fundamentals of crossdating and chronology development, iii) discuss assumptions and limitations of these approaches, iv) measure otolith growth-increment widths in image analysis software, v) learn software to statistically check increment dating accuracy, vi) generate a growth increment chronology and relate it to climate indices, and vii) initiate cooperative projects or training exercises to commence after the workshop.The workshop began with an overview of tree-ring techniques of chronology development, including a hands-on exercise in cross dating. Next, we discussed the applications of fish and bivalve biochronologies and the range of issues that could be addressed. We then reviewed key assumptions and limitations, especially those associated with short-lived species for which there are numerous and extensive otolith archives in European fisheries labs. Next, participants were provided with images of European plaice otoliths from the North Sea and taught to measure increment widths in image analysis software. Upon completion of measurements, techniques of chronology development were discussed and contrasted to those that have been applied for long-lived species. Plaice growth time-series were then related to environmental variability using the KNMI Climate Explorer. Finally, potential future collaborations and funding opportunities were discussed, and there was a clear desire to meet again to compare various statistical techniques for chronology development using a range existing fish, bivalve, and tree growth-increment datasets. Overall, we hope to increase the use of these techniques, and over the long term, develop networks of biochronologies for integrative analyses of ecosystem functioning and relationships to long-term climate variability and fishing pressure.

Metastability and dynamics of stem cells: from direct observations to inference at the single cell level

Organismal development, homeostasis, and pathology are rooted in inherently probabilistic events. From gene expression to cellular differentiation, rates and likelihoods shape the form and function of biology. Processes ranging from growth to cancer homeostasis to reprogramming of stem cells all require transitions between distinct phenotypic states, and these occur at defined rates. Therefore, measuring the fidelity and dynamics with which such transitions occur is central to understanding natural biological phenomena and is critical for therapeutic interventions.

While these processes may produce robust population-level behaviors, decisions are made by individual cells. In certain circumstances, these minuscule computing units effectively roll dice to determine their fate. And while the 'omics' era has provided vast amounts of data on what these populations are doing en masse, the behaviors of the underlying units of these processes get washed out in averages.

Therefore, in order to understand the behavior of a sample of cells, it is critical to reveal how its underlying components, or mixture of cells in distinct states, each contribute to the overall phenotype. As such, we must first define what states exist in the population, determine what controls the stability of these states, and measure in high dimensionality the dynamics with which these cells transition between states.

To address a specific example of this general problem, we investigate the heterogeneity and dynamics of mouse embryonic stem cells (mESCs). While a number of reports have identified particular genes in ES cells that switch between 'high' and 'low' metastable expression states in culture, it remains unclear how levels of many of these regulators combine to form states in transcriptional space. Using a method called single molecule mRNA fluorescent in situ hybridization (smFISH), we quantitatively measure and fit distributions of core pluripotency regulators in single cells, identifying a wide range of variabilities between genes, but each explained by a simple model of bursty transcription. From this data, we also observed that strongly bimodal genes appear to be co-expressed, effectively limiting the occupancy of transcriptional space to two primary states across genes studied here. However, these states also appear punctuated by the conditional expression of the most highly variable genes, potentially defining smaller substates of pluripotency.

Having defined the transcriptional states, we next asked what might control their stability or persistence. Surprisingly, we found that DNA methylation, a mark normally associated with irreversible developmental progression, was itself differentially regulated between these two primary states. Furthermore, both acute or chronic inhibition of DNA methyltransferase activity led to reduced heterogeneity among the population, suggesting that metastability can be modulated by this strong epigenetic mark.

Finally, because understanding the dynamics of state transitions is fundamental to a variety of biological problems, we sought to develop a high-throughput method for the identification of cellular trajectories without the need for cell-line engineering. We achieved this by combining cell-lineage information gathered from time-lapse microscopy with endpoint smFISH for measurements of final expression states. Applying a simple mathematical framework to these lineage-tree associated expression states enables the inference of dynamic transitions. We apply our novel approach in order to infer temporal sequences of events, quantitative switching rates, and network topology among a set of ESC states.

Taken together, we identify distinct expression states in ES cells, gain fundamental insight into how a strong epigenetic modifier enforces the stability of these states, and develop and apply a new method for the identification of cellular trajectories using scalable in situ readouts of cellular state.

Study of biological desalination phenomena: salt transport mechanisms of selective avian salt glands,

Mode of access: Internet.

A software tool for simulating spatial separation and kinetics in biological membranes

Self-segregation and compartimentalisation are observed experimentally to occur spontaneously on live membranes as well as reconstructed model membranes. It is believed that many of these processes are caused or supported by anomalous diffusive behaviours of biomolecules on membranes due to the complex and heterogeneous nature of these environments. These phenomena are on the one hand of great interest in biology, since they may be an important way for biological systems to selectively localize receptors, regulate signaling or modulate kinetics; and on the other, they provide an inspiration for engineering designs that mimick natural systems. We present an interactive software package we are developing for the purpose of simulating such processes numerically using a fundamental Monte Carlo approach. This program includes the ability to simulate kinetics and mass transport in the presence of either mobile or immobile obstacles and other relevant structures such as liquid-ordered lipid microdomains. We also present preliminary simulation results regarding the selective spatial localization and chemical kinetics modulating power of immobile obstacles on the membrane, obtained using the program.

Fractional models for the migration of biological cells in complex spatial domains

Travelling wave phenomena are observed in many biological applications. Mathematical theory of standard reaction-diffusion problems shows that simple partial differential equations exhibit travelling wave solutions with constant wavespeed and such models are used to describe, for example, waves of chemical concentrations, electrical signals, cell migration, waves of epidemics and population dynamics. However, as in the study of cell motion in complex spatial geometries, experimental data are often not consistent with constant wavespeed. Non-local spatial models have successfully been used to model anomalous diffusion and spatial heterogeneity in different physical contexts. In this paper, we develop a fractional model based on the Fisher-Kolmogoroff equation and analyse it for its wavespeed properties, attempting to relate the numerical results obtained from our simulations to experimental data describing enteric neural crest-derived cells migrating along the intact gut of mouse embryos. The model proposed essentially combines fractional and standard diffusion in different regions of the spatial domain and qualitatively reproduces the behaviour of neural crest-derived cells observed in the caecum and the hindgut of mouse embryos during in vivo experiments.