The Attributed Pi Calculus with Priorities

International audienceWe present the attributed $\pi$-calculus for modeling concurrent systems with interaction constraints depending on the values of attributes of processes. The $\pi$-calculus serves as a constraint language underlying the $\pi$-calculus. Interaction constraints subsume priorities, by which to express global aspects of populations. We present a nondeterministic and a stochastic semantics for the attributed $\pi$-calculus. We show how to encode the $\pi$-calculus with priorities and polyadic synchronization $\pi$@ and thus dynamic compartments, as well as the stochastic $\pi$-calculus with concurrent objects spico. We illustrate the usefulness of the attributed $\pi$-calculus for modeling biological systems at two particular examples: Euglena’s spatial movement in phototaxis, and cooperative protein binding in gene regulation of bacteriophage lambda. Furthermore, population-based model is supported beside individual-based modeling. A stochastic simulation algorithm for the attributed $\pi$-calculus is derived from its stochastic semantics. We have implemented a simulator and present experimental results, that confirm the practical relevance of our approach

The Attributed Pi Calculus

International audienceThe attributed pi calculus (pi(L)) forms an extension of the pi calculus with attributed processes and attribute dependent synchronization. To ensure flexibility, the calculus is parametrized with the language L which defines possible values of attributes. pi(L) can express polyadic synchronization as in pi@ and thus diverse compartment organizations. A non-deterministic and a stochastic semantics, where rates may depend on attribute values, is introduced. The stochastic semantics is based on continuous time Markov chains. A simulation algorithm is developed which is firmly rooted in this stochastic semantics. Two examples, the movement processes in the phototaxis of Euglena and the cooperative binding in the gene regulation of the lambda Phage, underline the applicability of pi(L) to systems biology

Imaging biological water permeability barriers using CARS microscopy

Alterations in the water permeability of the vasculature are attributed to several disease processes including atherosclerosis, reperfusion injury, diabetes mellitus, aging, chronic inflammation, and cancer. While vascular permeability has been extensively studied throughout the years, many of these studies have been limited by their invasiveness, specificity and spatial resolution. Coherent anti-Stokes Raman scattering (CARS) microscopy, offers a means to visualize the water permeability barrier of biological structures at high resolution within intact systems. In this thesis, water CARS imaging was characterized for determining water permeability in both dynamic and steady state conditions in model hydrogel systems. Computational models of water transport were used to validate the accuracy of water-CARS permeability mapping within these systems. This technique was then applied to the first CARS examination of water permeability in the cerebral artery and blood brain barrier. The vessels of mice deficient in the water channel protein aquaporin 1 (AQP1) were examined to evaluate the role of AQP1 in vascular water permeability. A layered hydrogel imaging phantom was constructed from poly(ethylene glycol) diacrylate (PEGDA) to validate ability of water-CARS microscopy to determine the relative permeability differences of adjacent material layers. By imaging the dynamic and steady-state H2O and D2O exchange across the uniform and layered composite hydrogel structures, it was indeed possible to measure the relative permeability differences between individual material layers and to determine the location of material interfaces from analysis of the water-CARS image profile. CARS imaging of intact biological samples poses many significant challenges. Microvessel microfluidic systems have the possibility to facilitate microscopy studies of vascular barrier function due to their flexibility of design, relative ease of preparation, and relative simplicity. In this thesis, the fabrication process of a human umbilical vein endothelial cell (HUVEC) microvessel microfluidic was investigated and optimized for future studies of vascular permeability and physiology. Several factors in the device assembly process were identified and optimized to improve the repeatability and reliability of the microvessel microfluidic fabrication protocol. CARS imaging of the mouse cerebral artery water transport produced higher quality images than what had previously been achieved in the rat mesenteric artery, likely due to their reduced wall thickness. Permeability mapping of these arteries localized the water permeability barrier to the endothelial basolateral membrane, a result consistent with previous measurements performed in the rat mesenteric arteries. Previous work by the Laboratory of Cardiac Energetics has suggested that the exclusively apical expression of the channel protein aquaporin 1 (AQP1) may account for the increase in observed permeability of the apical endothelial cell membrane. To test this hypothesis, water-CARS imaging of H2O/D2O exchange across cerebral arteries of wild type and AQP1 knockout (KO) mice was performed. No significant difference in the location of the water permeability barrier was observed. These findings indicate that AQP1 may not, in fact, be rate limiting for water transport across the apical endothelial membrane, and that it may play some other role in the physiology of the endothelial cell.This project was supported by the NIH Oxford Cambridge Scholars Progra

Engineered microfluidic platforms for microenvironment control and cell culture

The aim of this thesis is to overcome present limitations in mimicking the in vivo cellular microenvironments with novel in vitro cell culture systems. Since microtechnologies and microfluidics, in particular, provide the tools to reproduce in vivo-like cellular microenvironments in vitro, current relevant research is presented and areas where more research is needed in characterizing the in vitro microenvironment are outlined. 2D and 3D dynamic cell-culture models have recently garnered great attention because they often promote levels of cell differentiation and tissue organization not possible in conventional 2D static culture systems. In this work we developed new microfabrication approaches to reproduce cell-culture microenvironments that both support tissue differentiation and recapitulate the tissue–tissue interfaces, spatiotemporal chemical gradients, and mechanical microenvironments of living systems. These ‘tissues-on-chips’ permit the study of human physiology in physiological contest, enable development of novel in vitro disease models, and could potentially serve as replacement for animals used in drug development and toxin testing. To this aim, a blood brain barrier (BBB) microfluidic device was designed based on a transparent polyester porous membrane sandwiched between a top and a bottom overlying channel made of PMMA. According to our results, the PMMA is the most suitable biocompatible material for the porous membrane integration between two layers, compared to other materials, such as PDMS, commonly used to fabricate similar devices. We faced its permeability issue by engineering the proposed device with a collecting chamber, in the top part, to ensure the oxygen provision. In order to verify the efficacy of this microfluidic system, we tested the passage of BSA and nanoparticles compared to blank porous filter. Afterwards, in order to better mimic the blood-brain barrier and its circular shape we developed an innovative method to fabricate miniaturized circular microchannels from square geometry. A wide range of perfusable microvessel models have been developed, exploiting advances in microfabrication, microfluidics, biomaterials, stem cell technology, and tissue engineering. These models vary in complexity and physiological relevance, but provide a diverse tool kit for the study of vascular phenomena and methods to vascularize artificial organs. Here we developed a fast, cheap and reproducible method to fabricate circular microchannels by coupling spin coating with micromilled square microchannels. In order to validate our approach, an endothelial cell layer was formed by culturing brain endothelial bEnd.3 cells inside the proposed circular microchannels. In addition, considering that the diameter of blood vessels, in humans, spans more than four orders of magnitude, from about 8 μm in capillaries to more than 1 cm in large elastic arteries, we developed a low cost approach, using gelatin dehydration as intermediate, to fabricate microchannels of 5-8 microns in width, in order to mimic smaller capillaries. We are currently exploring the possibility to apply our approaches to fabricate a 3D microvessel model, totally in gelatin, to better mimic the extracellular matrix and the endothelium. In parallel, associated with the development of the above described devices, we proposed practical tips to the miniaturization community, developing innovative techniques that offer a solution to commonly encountered problems in the microfabrication field, or improvements (e.g. a simplification) on existing techniques. Thanks to their cost and technical advantages these microfluidic platforms may have extensive applications for neurobiology, cancer biology and for studying the cell-biomaterial interaction

Peptide processing via silk-inspired spinning enables assembly of multifunctional protein alloy fibers

Diverse fiber-forming proteins are found in nature that accomplish a wide range of functions including signaling, cell adhesion, and mechanical support. Unique sequence characteristics of these proteins often lead to their specialized roles. However, these proteins also share a common organizational hierarchy in primary and secondary structures that strongly influence both their intramolecular folding and intermolecular interactions. Based on what is known regarding protein fiber assembly of silk peptides, shear-induced elongation of the molecular strands drives interchain secondary structure crystallization via anisotropic alignment, which creates a molecular superstructure that forms the basis a fiber network. In this work, the hypothesis is this type of protein fiber assembly is not unique to silk sequences and that other proteins can be spun into fibers in similar fashion while maintaining unique functionality given by their specialized amino acid sequences such as RGD, GX1X2, and so forth. This was investigated by modeling the manner in which hydrophobic and hydrophilic blocks of amino acids create interacting secondary structures at the chain level when exposed to shear. It was determined computationally and then verified experimentally that fiber spinning success is most likely to occur after shear processing if the protein sequence exhibits a balance of hydrophobic and hydrophilic content and has sufficient length. Applied to the biological scale, both pure and mixed solutions of proteins such as fibronectin, laminin, and silk fibroin were spun into fibers. In particular, alloy protein fibers of silk fibroin mixed with fibronectin exhibited the characteristic mechanical integrity of silk and the bioactivity of fibronectin. This simple method of creating protein fibers with hybrid characteristics is significantly faster, less expensive, and less technically intensive than chimeric protein production, which purports to do the same. This finding also provides insight into a fundamental means by which protein fibers may be assembled in vivo by taking advantage of the thermodynamically favorable assembly of peptide sequences at the chain level under proper molecular orientation. Taken together, a high throughput means of producing a wide-range of pure and hybrid protein fibers has been developed for various biological applications and research investigations into the fibrous elements of biology

Special Functions: Fractional Calculus and the Pathway for Entropy

Historically, the notion of entropy emerged in conceptually very distinct contexts. This book deals with the connection between entropy, probability, and fractional dynamics as they appeared, for example, in solar neutrino astrophysics since the 1970's (Mathai and Rathie 1975, Mathai and Pederzoli 1977, Mathai and Saxena 1978, Mathai, Saxena, and Haubold 2010). The original solar neutrino problem, experimentally and theoretically, was resolved through the discovery of neutrino oscillations and was recently enriched by neutrino entanglement entropy. To reconsider possible new physics of solar neutrinos, diffusion entropy analysis, utilizing Boltzmann entropy, and standard deviation analysis was undertaken with Super-Kamiokande solar neutrino data. This analysis revealed a non-Gaussian signal with harmonic content. The Hurst exponent is different from the scaling exponent of the probability density function and both Hurst exponent and scaling exponent of the Super-Kamiokande data deviate considerably from the value of ½, which indicates that the statistics of the underlying phenomenon is anomalous. Here experiment may provide guidance about the generalization of theory of Boltzmann statistical mechanics. Arguments in the so-called Boltzmann-Planck-Einstein discussion related to Planck's discovery of the black-body radiation law are recapitulated mathematically and statistically and emphasize from this discussion is pursued that a meaningful implementation of the complex ‘entropy-probability-dynamics’ may offer two ways for explaining the results of diffusion entropy analysis and standard deviation analysis. One way is to consider an anomalous diffusion process that needs to use the fractional space-time diffusion equation (Gorenflo and Mainardi) and the other way is to consider a generalized Boltzmann entropy by assuming a power law probability density function. Here new mathematical framework, invented by sheer thought, may provide guidance for the generalization of Boltzmann statistical mechanics. In this book Boltzmann entropy, generalized by Tsallis and Mathai, is considered. The second one contains a varying parameter that is used to construct an entropic pathway covering generalized type-1 beta, type-2 beta, and gamma families of densities. Similarly, pathways for respective distributions and differential equations can be developed. Mathai's entropy is optimized under various conditions reproducing the well-known Boltzmann distribution, Raleigh distribution, and other distributions used in physics. Properties of the entropy measure for the generalized entropy are examined. In this process the role of special functions of mathematical physics, particularly the H-function, is highlighted

Developing a recombinant model of the P2Y1 and P2Y11 receptor interactions mediating relaxation in gut smooth muscle

ATP and ADP mediate gut smooth muscle relaxation through two receptors, P2Y1 and P2Y11. This project aims to investigate the interaction between these two receptors by developing a recombinant model of the P2Y receptors expressed in gut smooth muscle cells (SMCs) by transfecting the human P2Y11 receptor cDNA into CHO-K1 cells, which express an endogenous P2Y1 receptor. Individual clonal cell lines expressing different densities of hP2Y11 were isolated from this stably-transfected CHO-K1:P2Y11 pool and characterized. A clone expressing a “high” density of hP2Y11 (13) and a clone expressing a “low” density of hP2Y11 (6) were selected for further study. Control 1321N1 cell lines expressing each receptor in isolation (1321N1-hP2Y1 and 1321N1-hP2Y11) were used for comparison purposes. The potency (EC50) of eight different nucleotide agonists was determined in calcium assays in the co-expressing cell lines. ADP and 2meSATP responses were biphasic in clone 13 but monophasic in clone 6. To investigate the nature of the two sites of the biphasic curves in clone 13, the effect of MRS 2179, NF 340 and Reactive Red on agonist responses was determined. MRS 2179 antagonized the high affinity site of the biphasic ADP and 2meSATP responses in clone 13 without affecting the low affinity site. NF 340 had no effect on agonist responses in clone 13. Reactive Red antagonized both sites of the biphasic curves in clone 13. These data suggest that the high-affinity site of the biphasic ADP and 2meSATP responses in clone 13 corresponds to P2Y1. The low-affinity site of the 2meSATP curve is most likely P2Y11. The low-affinity site the ADP response displays both P2Y1 and P2Y11-like. The novel ADP site, therefore, is elicited by differences in the expression level of P2Y11 and may correspond to a P2Y1:hP2Y11 receptor heteromer or a macromolecular complex containing both P2Y1 and P2Y11