Computing the Hessenberg matrix associated with a self-similar measure

We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures. Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix

Precise quantification of silica and ceria nanoparticle uptake revealed by 3D fluorescence microscopy

Particle_in_Cell-3D is a powerful method to quantify the cellular uptake of nanoparticles. It combines the advantages of confocal fluorescence microscopy with fast and precise semi-automatic image analysis. In this work we present how this method was applied to investigate the impact of 310 nm silica nanoparticles on human vascular endothelial cells (HUVEC) in comparison to a cancer cell line derived from the cervix carcinoma (HeLa). The absolute number of intracellular silica nanoparticles within the first 24 h was determined and shown to be cell type-dependent. As a second case study, Particle_in_Cell-3D was used to assess the uptake kinetics of 8 nm and 30 nm ceria nanoparticles interacting with human microvascular endothelial cells (HMEC-1). These small nanoparticles formed agglomerates in biological medium, and the particles that were in effective contact with cells had a mean diameter of 417 nm and 316 nm, respectively. A significant particle size-dependent effect was observed after 48 h of interaction, and the number of intracellular particles was more than four times larger for the 316 nm agglomerates. Interestingly, our results show that for both particle sizes there is a maximum dose of intracellular nanoparticles at about 24 h. One of the causes for such an interesting and unusual uptake behavior could be cell division

Petrology and In Situ Trace Element Chemistry of a Suite of R Chondrites

Rumuruti (R) chondrites are characterized by low chondrule/matrix modal ratios, high oxidation state, small mean chondrule size, abundant sulfides and low metal contents, and are of petrologic types 3 to 6 [1, 2]. LAP 04840 (R5, [3]) and MIL 11207 (R6), contain the high-T hydrous phases amphibole and mica [3, 4]; not all equilibrated R chondrites contain these [2]. R chondrites thus can provide evidence on whether there are compositional effects caused by high-T, high-fluid metamorphism of nebular materials. We are investigating a suite of R chondrites of diverse petrologic grades to further understand the nature of the metamorphic processes that engendered them [5]. We report on our petrological studies, plus preliminary in situ analyses of trace elements in amphibole-bearing R chondrites

Petrology and Cosmochemistry of a Suite of R Chondrites

Chondrites are among the most primitive surviving materials from the early solar system. They are divided into groups based on chemical types defined by mineralogy, bulk composition, and oxygen isotope compositions. Chondrites range in petrographic grade from type 1 to type 7. Type 3 chondrites are the most primitive and are little changed from the nebular solids accreted to form asteroids. They are composed of chondrules, fine-grained matrix, metal and sulfide, plus or minus Ca-Al-rich inclusions. With increasing aqueous alteration at low temperatures, members of some chondrite classes transformed from type 3 towards type 1. With increasing thermal metamorphism and low fluid content, members of other classes changed from type 3 towards type 7. Rumuruti (R) chondrites are a rare group (0.1% of falls) similar to ordinary chondrites in some properties but different in others. They are characterized by low chondrule/matrix modal abundance ratios, high oxidation state, small mean chondrule size, abundant sulfides and low metal contents. R chondrites vary in petrologic type from 3 to 6. They are important objects to study because some of them have undergone metamorphism at high temperatures in the presence of aqueous fluids. In contrast, CM and CI chondrites were heated to low temperatures in the presence of aqueous fluids leading to alteration; they contain low-T hydrous phases (phyllosilicates) and little or no remaining metal. Ordinary chondrites were heated to high temperatures in a low-fluid environment resulting in anhydrous metamorphic rocks. R6 chondrites are highly metamorphosed and some contain the high-T hydrous phases mica and amphibole. R chondrites are thus unique and give us an opportunity to examine whether there are compositional effects caused by high-T, highfluid metamorphism of nebular materials

A surface acoustic wave-driven micropump for particle uptake investigation under physiological flow conditions in very small volumes

Static conditions represent an important shortcoming of many in vitro experiments on the cellular uptake of nanoparticles. Here, we present a versatile microfluidic device based on acoustic streaming induced by surface acoustic waves (SAWs). The device offers a convenient method for introducing fluid motion in standard cell culture chambers and for mimicking capillary blood flow. We show that shear rates over the whole physiological range in sample volumes as small as 200 mu L can be achieved. A precise characterization method for the induced flow profile is presented and the influence of flow on the uptake of Pt-decorated CeO2 particles by endothelial cells (HMEC-1) is demonstrated. Under physiological flow conditions the particle uptake rates for this system are significantly lower than at low shear conditions. This underlines the vital importance of the fluidic environment for cellular uptake mechanisms

Intake of silica nanoparticles by giant lipid vesicles: influence of particle size and thermodynamic membrane state

The uptake of nanoparticles into cells often involves their engulfment by the plasma membrane and a fission of the latter. Understanding the physical mechanisms underlying these uptake processes may be achieved by the investigation of simple model systems that can be compared to theoretical models. Here, we present experiments on a massive uptake of silica nanoparticles by giant unilamellar lipid vesicles (GUVs). We find that this uptake process depends on the size of the particles as well as on the thermodynamic state of the lipid membrane. Our findings are discussed in the light of several theoretical models and indicate that these models have to be extended in order to capture the interaction between nanomaterials and biological membranes correctly

Intake of silica nanoparticles by giant lipid vesicles: influence of particle size and thermodynamic membrane state

The uptake of nanoparticles into cells often involves their engulfment by the plasma membrane and a fission of the latter. Understanding the physical mechanisms underlying these uptake processes may be achieved by the investigation of simple model systems that can be compared to theoretical models. Here, we present experiments on a massive uptake of silica nanoparticles by giant unilamellar lipid vesicles (GUVs). We find that this uptake process depends on the size of the particles as well as on the thermodynamic state of the lipid membrane. Our findings are discussed in the light of several theoretical models and indicate that these models have to be extended in order to capture the interaction between nanomaterials and biological membranes correctly

Mitochondrial metabolism: Yin and Yang for tumor progression

Altered metabolism is a distinct feature of cancer cells. During transformation, the entire metabolic network is rewired to efficiently convert nutrients to biosynthetic precursors to sustain cancer cell growth and proliferation. Whilst the molecular underpinnings of this metabolic reprogramming have been described, its role in tumor progression is still under investigation. Importantly, the mitochondrion is a central actor in many of the metabolic processes that are altered in tumors. Yet, we have only begun to understand the dualities of mitochondrial function during cancer metastasis and therapy resistance. Paradoxically, mitochondrial metabolism can be both advantageous and detrimental to these processes, highlighting the need for a better understanding of the molecular and microenvironmental cues that define the role of this fascinating organelle. In this review article, we present an updated view on the different mitochondrial metabolic strategies adopted by cancer cells to overcome the many hurdles faced during tumor progression.The work of A.C. is supported by the Ramón y Cajal award, the Basque Department of Industry, Tourism and Trade (Etortek) and the Department of Education (IKERTALDE IT1106-16), ISCIII (PI10/01484, PI13/00031), FERO VIII Fellowship, the BBVA Foundation, the MINECO (SAF2016-79381-R), and the European Research Council Starting Grant (336343). The participation of A.C. and V.T. as part of CIBERONC was cofunded with FEDER funds. L.V-J. is supported by Basque Government of Education. V.T. is funded by Fundación Vasca de Innovación e Investigación Sanitarias, BIOEF (BIO15/CA/052), the AECC J.P. Bizkaia, and the Basque Department of Health (2016111109). E.G. and C.F. are supported by the Medical Research Council, core fund to the MRC Cancer Unit SKAG106