The epicycle model

[EN] The solutions of the equations of motion for a point mass particle under a conservative force field are generally constrained by a basic set of integrals of motion, which depend on the knowledge about the potential function and on time and space properties and symmetries satisfied by the dynamical system. The epicycle approximation is a particular case of integration of the equations of motion under a minimum set of hypotheses, such as symmetry plane and axial symmetry, allowing to obtain solutions for nearly circular orbits in the three dimensional space. Under this approach, any orbit projected onto the symmetry plane describes an ellipse with origin at a guiding centre or epicentre, which moves uniformly in a circular orbit around the centre of the system. The approach is easy to model and allows to visualise the contribution of several parameters to the shape of the orbits, being an excellent example of how education and learning of science can take profit of mathematical modelling.[ES] Las soluciones de las ecuaciones del movimiento para una partícula de masa puntual bajo un campo de fuerzas conservativo están generalmente ligadas a un conjunto básico de integrales del movimiento, que dependen del conocimiento que se tiene de la función potencial y de las simetrías y propiedades espaciales y temporales satisfechas por el sistema dinámico. La aproximación epicíclica es un caso particular de integración de las ecuaciones del movimiento bajo un conjunto mínimo de hipótesis, como son plano de simetría y simetría axial, que permite obtener soluciones para órbitas casi circulares en el espacio tridimensional. Bajo esta proximación, cualquier órbita proyectada sobre el plano de simetría describe una elipse con origen en un centro guía o epicentro, en movimiento circular uniforme alrededor del centro del sistema. La aproximación es fácil de modelar y permite visualizar la contribución de varios parámetros a la forma de las órbitas, siendo un excelente ejemplo de cómo la enseñanza y el aprendizaje de las ciencias pueden beneficiarse de la modelización matemática.Cubarsi, R. (2013). The epicycle model. Modelling in Science Education and Learning. 6(2):171-183. doi:10.4995/msel.2013.1944SWORD17118362Arnold, V. I. (1989). Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics. doi:10.1007/978-1-4757-2063-1J. Binney, S. Tremaine. In Galactic Dynamics. Princeton University Press, Princeton (1987).G. Gilmre, I. King, P. v. d. Kruit. In The Milky Way as a Galaxy. Buser R., King I. Eds. Publ. Geneva Observatory, Geneva Sala F. 1990, A&A, 235, 85 (1989)

Fine architecture of bacterial inclusion bodies

AbstractThe molecular organisation of protein aggregates, formed under physiological conditions, has been explored by in vitro trypsin treatment and electron microscopy analysis of bacterially produced inclusion bodies (IBs). The kinetic modelling of protein digestion has revealed variable proteolysis rates during protease exposure that are not compatible with a surface-restricted erosion of body particles but with a hyper-surfaced disintegration by selective enzymatic attack. In addition, differently resistant species of the IB proteins coexist within the particles, with half-lives that differ among them up to 50-fold. During in vivo protein incorporation throughout IB growth, a progressive increase of proteolytic resistance in all these species is observed, indicative of folding transitions and dynamic reorganisations of the body structure. Both the heterogeneity of the folding state and the time-dependent folding transitions undergone by the aggregated polypeptides indicate that IBs are not mere deposits of collapsed, inert molecules but plastic reservoirs of misfolded proteins that would allow, at least up to a certain extent, their in vivo recovery and transference to the soluble cell fraction

Thick disk kinematics from RAVE and the solar motion

Radial velocity surveys such as the Radial Velocity Experiment (RAVE) provide us with measurements of hundreds of thousands of nearby stars most of which belong to the Galactic thin, thick disk or halo. Ideally, to study the Galactic disks (both thin and thick) one should make use of the multi-dimensional phase-space and the whole pattern of chemical abundances of their stellar populations. In this paper, with the aid of the RAVE Survey, we study the thin and thick disks of the Milky Way, focusing on the latter. We present a technique to disentangle the stellar content of the two disks based on the kinematics and other stellar parameters such as the surface gravity of the stars. Using the Padova Galaxy Model, we checked the ability of our method to correctly isolate the thick disk component from the Galaxy mixture of stellar populations. We introduce selection criteria in order to clean the observed radial velocities from the Galactic differential rotation and to take into account the partial sky coverage of RAVE. We developed a numerical technique to statistically disentangle thin and thick disks from their mixture. We deduce the components of the solar motion relative to the Local Standard of Rest (LSR) in the radial and vertical direction, the rotational lag of the thick disk component relative to the LSR, and the square root of the absolute value of the velocity dispersion tensor for the thick disk alone. The analysis of the thin disk is presented in another paper. We find good agreement with previous independent parameter determinations. In our analysis we used photometrically determined distances. In the Appendix we show that similar values can be found for the thick disk alone as derived in the main sections of our paper even without the knowledge of photometric distances.Comment: accepted on A&A, please see companion paper "THIN disk kinem...

Proteine Bolognese

[EN] The penetration of a modified version of a green fluorescent protein called GFP in the cytoplasm and nucleus of a mammalian cell is modelled. The mathematical model provides a first approach to the experiment, with a progressive decreasing rate of fluorescence as the total luminosity increases until saturation. However, a local deviation from the proposed model is detected, due to a process that takes place in a non-differentiable way. The phenomenon is explained from the sudden entrance of GFP into the cytoplasm and nucleus by the weakening or permeabilization of their membranes, and from the obstruction of GFP flux by the nuclear membrane. Thus, the mathematical model provides relevant information on the deviation from the pattern that has been adopted. To unify the European Higher Education Area (EHEA), and in accordance with the guidelines of the Bologna Process, the subjects of new curricula have under- gone a thorough review of their contents. So the new methodology be fruitful, a highly optimized agenda must be designed by linking every topic with topics from other subjects. The case presented evidences how Mathematical Modelling is useful to implement and review lessons learned in various subjects, from maths and biology in the current case, besides being an effective way to stimulate learning, since it is showing the usefulness of what is studied.[ES] Se modeliza la penetración de una versión modificada de la proteína verde fluorescente llamada GFP en el citoplasma y el núcleo de una célula de mamífero. El modelo matemático proporciona una primera aproximación al experimento, con una disminución progresiva de la tasa de fluorescencia a medida que la luminosidad total va aumentando hasta saturarse. Sin embargo, se detecta una desviación localizada del modelo propuesto, debida a un proceso que no se realiza de forma totalmente diferenciable. El fenómeno es explicable a partir de la irrupción brusca de GFP en el citoplasma y el núcleo por la debilitación o permeabilización de sus membranas, y por la obstrucción del flujo de GFP por la membrana nuclear. El modelo matemático proporciona pues información relevante sobre la desviación del patrón que se ha adoptado. Con la finalidad de unificar del Espacio Europeo de Educación Superior (EEES), y de acuerdo con las directrices del Proceso de Bolonia, las asignaturas de los nuevos planes de estudios han sufrido una re- visión a fondo de sus contenidos. Para que la nueva metodología de sus frutos, es necesario diseñar un temario muy optimizado, en el que cada tema entronque con temas de otras asignaturas. El caso presentado evidencia como la Modelización Matemática es útil para aplicar y revisar los conocimientos adquiridos en diversas asignaturas, de matemáticas y biología en este caso, además de ser una forma eficaz de estimular el aprendizaje, ya que muestra la utilidad de lo que se estudia.Agradecemos el apoyo financiero recibido de MICINN (ACI2009-0919),FISS (PS0900165), AGAUR (2009SGR-108) y el CIBER de Bioingeniería, Biomateriales y Nanomedicina. AV ha sido distinguido con un premio ICREA ACADEMIA.Cubarsi, R.; Vázquez, E.; Villaverde, A. (2011). Proteine Bolognese. Modelling in Science Education and Learning. 4:159-167. https://doi.org/10.4995/msel.2011.3069SWORD1591674Vázquez, E., Cubarsi, R., Unzueta, U., Roldán, M., Domingo-Espín, J., Ferrer-Miralles, N., & Villaverde, A. (2010). Internalization and kinetics of nuclear migration of protein-only, arginine-rich nanoparticles. Biomaterials, 31(35), 9333-9339. doi:10.1016/j.biomaterials.2010.08.06

Endosomal escape of protein nanoparticles engineered through humanized histidine-rich peptides

Altres ajuts: EU COST Action CA 17140. AV received an ICREA ACADEMIA awardPoly-histidine peptides such as H6 (HHHHHH) are used in protein biotechnologies as purification tags, protein-assembling agents and endosomal-escape entities. The pleiotropic properties of such peptides make them appealing to design protein-based smart materials or nanoparticles for imaging or drug delivery to be produced in form of recombinant proteins. However, the clinical applicability of H6-tagged proteins is restricted by the potential immunogenicity of these segments. In this study, we have explored several humanized histidine-rich peptides in tumor-targeted modular proteins, which can specifically bind and be internalized by the target cells through the tumoral marker CXCR4. We were particularly interested in exploring how protein purification, self-assembling and endosomal escape perform in proteins containing the variant histidine-rich tags. Among the tested candidates, the peptide H5E (HEHEHEHEH) is promising as a good promoter of endosomal escape of the associated full-length protein upon endosomal internalization. The numerical modelling of cell penetration and endosomal escape of the tested proteins has revealed a negative relationship between the amount of protein internalized into target cells and the efficiency of cytoplasmic release. This fact demonstrates that the His-mediated, proton sponge-based endosomal escape saturates at moderate amounts of internalized protein, a fact that might be critical for the design of protein materials for cytosolic molecular delivery

Bottom-up instructive quality control in the biofabrication of smart protein materials

The impact of cell factory quality control on material properties is a neglected but critical issue in the fabrication of protein biomaterials, which are unique in merging structure and function. The molecular chaperoning of protein conformational status is revealed here as a potent molecular instructor of the macroscopic properties of self-assembling, cell-targeted protein nanoparticles, including biodistribution upon in vivo administration

CXCR4+-targeted protein nanoparticles produced in the food-grade bacterium Lactococcus lactis

Altres ajuts: CIBER de Bioingeniería, Biomateriales y Nanomedicina (project NANOPROTHER). A Villaverde received an ICREA ACADEMIA award. OC Garrido received a PhD fellowship from MECD and EGF a postdoctoral fellowship from INIA (DOC-INIA, INIA, MINECO). Unzueta received a Sara Borrell postdoctoral fellowship from ISCIII.Aim: Lactococcus lactis is a Gram-positive (endotoxin-free) food-grade bacteria exploited as alternative to Escherichia coli for recombinant protein production. We have explored here for the first time the ability of this platform as producer of complex, self-assembling protein materials. Materials & methods: Biophysical properties, cell penetrability and in vivo biodistribution upon systemic administration of tumor-targeted protein nanoparticles produced in L. lactis have been compared with the equivalent material produced in E. coli. Results: Protein nanoparticles have been efficiently produced in L. lactis, showing the desired size, internalization properties and biodistribution. Conclusion: In vitro and in vivo data confirm the potential and robustness of the production platform, pointing out L. lactis as a fascinating cell factory for the biofabrication of protein materials intended for therapeutic applications

Intrinsic functional and architectonic heterogeneity of tumor-targeted protein nanoparticles

Altres ajuts: CIBER de Bioingeniería, Biomateriales y Nanomedicina (project NANOPROTHER) (to AV), Marató de TV3 foundation (TV32013-132031) (TV32013-133930). Protein production has been partially performed by the ICTS "NANBIOSIS", more specifically by the Protein Production Platform of CIBER in Bioengineering, Biomaterials & Nanomedicine (CIBER-BBN)/IBB, at the UAB SepBioES scientific-technical service (http://www.nanbiosis.es/unit/u1-protein-production-platform-ppp/) and DLS measurements have been done at the Biomaterial Processing and Nanostructuring Unit of NANBIOSIS. We are also indebted to Fran Cortés from the Cell Culture and Cytometry Units of the Servei de CultiusCel·lulars, Producciód'AnticossosiCitometria (SCAC), and to the Servei de Microscòpia, both at the UAB. Strain KPM335 was kindly provided by Research Corporation Technologies, Tucson, AZ. AV received an ICREA ACADEMIA award.Self-assembling proteins are gaining attention as building blocks for application-tailored nanoscale materials. This is mostly due to the biocompatibility, biodegradability, and functional versatility of peptide chains. Such a potential for adaptability is particularly high in the case of recombinant proteins, which are produced in living cells and are suitable for genetic engineering. However, how the cell factory itself and the particular protein folding machinery influence the architecture and function of the final material is still poorly explored. In this study we have used diverse analytical approaches, including small-angle X-ray scattering (SAXS) and field emission scanning electron microscopy (FESEM) to determine the fine architecture and geometry of recombinant, tumor-targeted protein nanoparticles of interest as drug carriers, constructed on a GFP-based modular scheme. A set of related oligomers were produced in alternative Escherichia coli strains with variant protein folding networks. This resulted in highly regular populations of morphometric types, ranging from 2.4 to 28 nm and from spherical- to rod-shaped materials. These differential geometric species, whose relative proportions were determined by the features of the producing strain, were found associated with particular fluorescence emission, cell penetrability and receptor specificity profiles. Then, nanoparticles with optimal properties could be analytically identified and further isolated from producing cells for use. The cell's protein folding machinery greatly modulates the final geometry reached by the constructs, which in turn defines the key parameters and biological performance of the material

Spiral arm kinematics for Milky Way stellar populations

We present a new theoretical population synthesis model (the Galaxy model) to examine and deal with large amounts of data from surveys of the Milky Way and to decipher the present and past structure and history of our own Galaxy. We assume the Galaxy to consist of a superposition of many composite stellar populations belonging to the thin and thick discs, the stellar halo and the bulge, and to be surrounded by a single dark matter halo component. A global model for the Milky Way's gravitational potential is built up self-consistently with the density profiles from the Poisson equation. In turn, these density profiles are used to generate synthetic probability distribution functions (PDFs) for the distribution of stars in colour- magnitude diagrams (CMDs). Finally, the gravitational potential is used to constrain the stellar kinematics by means of the moment method on a (perturbed)-distribution function. Spiral arms perturb the axisymmetric disc distribution functions in the linear response framework of density-wave theory where we present an analytical formula of the so-called 'reduction factor' using hypergeometric functions. Finally, we consider an analytical non-axisymmetric model of extinction and an algorithm based on the concept of probability distribution function to handle CMDs with a large number of stars. A genetic algorithm is presented to investigate both the photometric and kinematic parameter space. This galaxy model represents the natural framework to reconstruct the structure of the Milky Way from the heterogeneous data set of surveys such as Gaia-ESO, SEGUE, APOGEE2, RAVE and the Gaia mission

Detectability of testosterone esters and estradiol benzoate in bovine hair and plasma following pour-on treatment

The abuse of synthetic esters of natural steroids such as testosterone and estradiol in cattle fattening and sports is hard to detect via routine urine testing. The esters are rapidly hydrolysed in vivo into substances which are also endogenously present in urine. An interesting alternative can be provided by the analysis of the administered synthetic steroids themselves, i.e., the analysis of intact steroid esters in hair by liquid chromatography tandem mass spectrometry (LC/MS/MS). However, retrospective estimation of the application date following a non-compliant finding is hindered by the complexity of the kinetics of the incorporation of steroid esters in hair. In this study, the incorporation of intact steroid esters in hair following pour-on treatment has been studied and critically compared with results from intramuscular treatment. To this end animals were pour-on treated with a hormone cocktail containing testosterone cypionate, testosterone decanoate and estradiol benzoate in different carriers. The animals were either treated using injection and pour-on application once or three times having 1 week between treatments using injection and pour-on application. Animals were slaughtered from 10–12 weeks after the last treatment. Both hair and blood plasma samples were collected and analysed by LC/MS/MS. From the results, it is concluded that after single treatment the levels of steroid esters in hair drop to CCβ levels (5–20 µg/kg) after 5–7 weeks. When treatment is repeated two times, the CCβ levels are reached after 9–11 weeks. Furthermore, in plasma, no steroid esters were detected; not even at the low microgramme per litre level but—in contrast with the pour-on application—after i.m. injection, significant increase of 17β-testosterone and 17β-estradiol were observed. These observations suggest that transport of steroid esters after pour-on application is not only performed by blood but also by alternative fluids in the animal so probably the steroid esters are already hydrolysed and epimerized before entering the blood