979 resultados para Microscopic analysis


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Glucocorticoids (GC) are successfully applied in neonatology to improve lung maturation in preterm born babies. Animal studies show that GC can also impair lung development. In this investigation, we used a new approach based on digital image analysis. Microscopic images of lung parenchyma were skeletonised and the geometrical properties of the septal network characterised by analysing the 'skeletal' parameters. Inhibition of the process of alveolarisation after extensive administration of small doses of GC in newborn rats was confirmed by significant changes in the 'skeletal' parameters. The induced structural changes in the lung parenchyma were still present after 60 days in adult rats, clearly indicating a long lasting or even definitive impairment of lung development and maturation caused by GC. Conclusion: digital image analysis and skeletonisation proved to be a highly suited approach to assess structural changes in lung parenchyma.

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Effects of protein deficiency during the whole period of postnatal development and intensive growth were studied in the rat lung parenchyma. Dams received a low protein diet as follows: early restriction, 8% casein diet from parturition, and delayed restriction, 12% then 8% casein diet from lactation d 8. After weaning (d 21), early restriction and delayed restriction group rats were maintained on the 8% casein diet until d 49, wherefore they were returned to normal food (18% casein) for 11 wk. Lungs were processed for light and electron microscopic morphometry on d 21, 49, and 126. The diffusion capacity of the lung for O2 (DLO2) was also determined from the morphologic parameters. Volume and surface densities of the parenchymal components of malnourished rats did not consistently differ from controls. Because of lower lung volumes, absolute values, including DLO2, were all significantly decreased. Further, although lung volume growth was less impaired than body growth and thus deviated from the normal allometric relationship, most morphometric parameters paralleled body weight changes. Visually, we detected minor morphologic alterations at d 21 and 49, not necessarily reflected by morphometric data. But, importantly, lung parenchyma appeared mature at weaning despite the growth retardation. Normal refeeding resulted in a striking regrowth of the lung parenchyma. Although early restriction rats did not fully catch up in lung volume, most parenchymal parameters and DLO2 were largely restored in both refed groups.

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Calmodulin (CaM) is a ubiquitous Ca(2+) buffer and second messenger that affects cellular function as diverse as cardiac excitability, synaptic plasticity, and gene transcription. In CA1 pyramidal neurons, CaM regulates two opposing Ca(2+)-dependent processes that underlie memory formation: long-term potentiation (LTP) and long-term depression (LTD). Induction of LTP and LTD require activation of Ca(2+)-CaM-dependent enzymes: Ca(2+)/CaM-dependent kinase II (CaMKII) and calcineurin, respectively. Yet, it remains unclear as to how Ca(2+) and CaM produce these two opposing effects, LTP and LTD. CaM binds 4 Ca(2+) ions: two in its N-terminal lobe and two in its C-terminal lobe. Experimental studies have shown that the N- and C-terminal lobes of CaM have different binding kinetics toward Ca(2+) and its downstream targets. This may suggest that each lobe of CaM differentially responds to Ca(2+) signal patterns. Here, we use a novel event-driven particle-based Monte Carlo simulation and statistical point pattern analysis to explore the spatial and temporal dynamics of lobe-specific Ca(2+)-CaM interaction at the single molecule level. We show that the N-lobe of CaM, but not the C-lobe, exhibits a nano-scale domain of activation that is highly sensitive to the location of Ca(2+) channels, and to the microscopic injection rate of Ca(2+) ions. We also demonstrate that Ca(2+) saturation takes place via two different pathways depending on the Ca(2+) injection rate, one dominated by the N-terminal lobe, and the other one by the C-terminal lobe. Taken together, these results suggest that the two lobes of CaM function as distinct Ca(2+) sensors that can differentially transduce Ca(2+) influx to downstream targets. We discuss a possible role of the N-terminal lobe-specific Ca(2+)-CaM nano-domain in CaMKII activation required for the induction of synaptic plasticity.

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Charcoal analysis was conducted on sediment cores from three lakes to assess the relationship between the area and number of charcoal particles. Three charcoal-size parameters (maximum breadth, maximum length and area) were measured on sediment samples representing various vegetation types, including shrub tundra, boreal forest and temperate forest. These parameters and charcoal size-class distributions do not differ statistically between two sites where the same preparation technique (glycerine pollen slides) was used, but they differ for the same core when different techniques were applied. Results suggest that differences in charcoal size and size-class distribution are mainly caused by different preparation techniques and are not related to vegetation-type variation. At all three sites, the area and number concentrations of charcoal particles are highly correlated in standard pollen slides; 82–83% of the variability of the charcoal-area concentration can be explained by the particle-number concentration. Comparisons between predicted and measured area concentrations show that regression equations linking charcoal number and area concentrations can be used across sites as long as the same pollen-preparation technique is used. Thus it is concluded that it is unnecessary to measure charcoal areas in standard pollen slides – a time-consuming and tedious process.

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BACKGROUND White matter (WM) fibers connect different brain regions and are critical for proper brain function. However, little is known about the cerebral blood flow in WM and its relation to WM microstructure. Recent improvements in measuring cerebral blood flow (CBF) by means of arterial spin labeling (ASL) suggest that the signal in white matter may be detected. Its implications for physiology needs to be extensively explored. For this purpose, CBF and its relation to anisotropic diffusion was analyzed across subjects on a voxel-wise basis with tract-based spatial statistics (TBSS) and also across white matter tracts within subjects. METHODS Diffusion tensor imaging and ASL were acquired in 43 healthy subjects (mean age = 26.3 years). RESULTS CBF in WM was observed to correlate positively with fractional anisotropy across subjects in parts of the splenium of corpus callosum, the right posterior thalamic radiation (including the optic radiation), the forceps major, the right inferior fronto-occipital fasciculus, the right inferior longitudinal fasciculus and the right superior longitudinal fasciculus. Furthermore, radial diffusivity correlated negatively with CBF across subjects in similar regions. Moreover, CBF and FA correlated positively across white matter tracts within subjects. CONCLUSION The currently observed findings on a macroscopic level might reflect the metabolic demand of white matter on a microscopic level involving myelination processes or axonal function. However, the exact underlying physiological mechanism of this relationship needs further evaluation.

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Organic petrologic and geochemical analyses were performed on modern and Quaternary organic carbon-poor deep sea sediments from the Equatorial Atlantic. The study area covers depositional settings from the West African margin (ODP Site 959) through the Equatorial Divergence (ODP Site 663) to the pelagic Equatorial Atlantic. Response of organic matter (OM) deposition to Quaternary climatic cycles is discussed for ODP Sites 959 and 663. The results are finally compared to a concept established for fossil deep sea environments [Littke and Sachsenhofer, 1994 doi:10.1021/ef00048a041]. Organic geochemical results obtained from Equatorial Atlantic deep sea deposits provide new aspects on the distribution of sedimentary OM in response to continental distance, atmospheric and oceanographic circulation, and depositional processes controlling sedimentation under modern and past glacial-interglacial conditions. The inventory of macerals in deep sea deposits is limited due to mechanical breakdown of particles, degree of oxidation, and selective remineralization of labile (mostly marine) OM. Nevertheless, organic petrology has a great potential for paleoenvironmental studies, especially as a proxy to assess quantitative information on the relative abundance of marine vs. terrigenous OM. Discrepancies between quantitative data obtained from microscopic and isotopic (delta13Corg) analyses were observed depending on the stratigraphic level and depositional setting. Strongest offset between both records was found close to the continent and during glacial periods, suggesting a coupling with wind-born terrigenous OM from central Africa. Since African dust source areas are covered by C4 grass plants, supply of isotopically heavy OM is assumed to have caused the difference between microscopic and isotopic records.

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The quantity, type, and maturity of the organic matter in Recent through Upper Jurassic sediments from the Falkland Plateau, DSDP Site 511, have been determined. Sediments were investigated for their hydrocarbon potential by organic carbon and Rock-Eval pyrolysis. Kerogen concentrates were prepared and analyzed in reflected and transmitted light to determine vitrinite reflectance and maceral content. Total extractable organic compounds were analyzed for their elemental composition, and the fraction of the nonaromatic hydrocarbons was determined by capillary column gas chromatography and combined gas chromatography/mass spectrometry. Three main classes of organic matter can be determined at DSDP Site 511 by a qualitative and quantitative evaluation of microscopic and geochemical results. The Upper Jurassic to lower Albian black shales contain high amounts of organic matter of dominantly marine origin. The content of terrigenous organic matter increases at the base of the black shales, whereas the shallowest black shales near the Aptian/Albian boundary are transitional in composition, with increasing amounts of inert, partly oxidized organic matter which is the dominant component in all Albian through Tertiary sediments investigated. The organic matter in the black shales has a low level of maturity and has not yet reached the onset of thermal hydrocarbon generation. This is demonstrated by the low amounts of total extractable organic compounds, low percentages of hydrocarbons, and the pattern and composition of nonaromatic hydrocarbons. The observed reflectance of huminite and vitrinite particles (between 0.4% and 0.5% Ro at bottom-hole depth of 632 m) is consistent with this interpretation. Several geochemical parameters indicate, however, a rapid increase in the maturation of organic matter with depth of burial. This appears to result from the relatively high heat flow observed at Site 511. If we relate the level of maturation of the black shales at the bottom of Hole 511 to their present shallow depth of burial, they appear rather mature. On the basis of comparisons with other sedimentary basins of a known geothermal history, a somewhat higher paleotemperature gradient and/or additional overburden are required to give the observed maturity at shallow depth. A comparison with contemporaneous sediments of DSDP Site 361, Cape Basin, which was the basin adjacent and to the north of the Falkland Plateau during the early stages of the South Atlantic Ocean, demonstrates differences in sedimentological features and in the nature of sedimentary organic matter. We interpret these differences to be the result of the different geological settings for Sites 361 and 511.

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The use of laser beams as excitation sources for the characterization of semiconductor nanowires (NWs) is largely extended. Raman spectroscopy and photoluminescence (PL) are currently applied to the study of NWs. However, NWs are systems with poor thermal conductivity and poor heat dissipation, which result in unintentional heating under the excitation with a focused laser beam with microscopic size, as those usually used in microRaman and microPL experiments. On the other hand, the NWs have subwavelength diameter, which changes the optical absorption with respect to the absorption in bulk materials. Furthermore, the NW diameter is smaller than the laser beam spot, which means that the optical power absorbed by the NW depends on its position inside the laser beam spot. A detailed analysis of the interaction between a microscopic focused laser beam and semiconductor NWs is necessary for the understanding of the experiments involving laser beam excitation of NWs. We present in this work a numerical analysis of the thermal transport in Si NWs, where the heat source is the laser energy locally absorbed by the NW. This analysis takes account of the optical absorption, the thermal conductivity, the dimensions, diameter and length of the NWs, and the immersion medium. Both free standing and heat-sunk NWs are considered. Also, the temperature distribution in ensembles of NWs is discussed. This analysis intends to constitute a tool for the understanding of the thermal phenomena induced by laser beams in semiconductor NWs.

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The plant cuticle has traditionally been conceived as an independent hydrophobic layer that covers the external epidermal cell wall. Due to its complexity, the existing relationship between cuticle chemical composition and ultra-structure remains unclear to date. This study aimed to examine the link between chemical composition and structure of isolated, adaxial leaf cuticles of Eucalyptus camaldulensis and E. globulus by the gradual extraction and identification of lipid constituents (cutin and soluble lipids), coupled to spectroscopic and microscopic analyses. The soluble compounds and cutin monomers identified could not be assigned to a concrete internal cuticle ultra-structure. After cutin depolymerization, a cellulose network resembling the cell wall was observed, with different structural patterns in the regions ascribed to the cuticle proper and cuticular layer, respectively. Our results suggest that the current cuticle model should be revised, stressing the presence and major role of cell wall polysaccharides. It is concluded that the cuticle may be interpreted as a modified cell wall region which contains additional lipids. The major heterogeneity of the plant cuticle makes it difficult to establish a direct link between cuticle chemistry and structure with the existing methodologies.

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From a physical perspective, a joint experiences fracturing processes that affect the rock at both microscopic and macroscopic levels. The result is a behaviour that follows a fractal structure. In the first place, for saw-tooth roughness profiles, the use of the triadic Koch curve appears to be adequate and by means of known correlations the JRC parameter is obtained from the angle measured on the basis of the height and length of the roughnesses. Therefore, JRC remains related to the geometric pattern that defines roughness by fractal analysis. In the second place, to characterise the geometry of irregularities with softened profiles, consequently, is proposed a characterisation of the fractal dimension of the joints with a circumference arc generator that is dependent on an average contact angle with regard to the mid-plane. The correlation between the JRC and the fractal dimension of the model is established with a defined statistical ratio.

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Ternary MCrO4 (M = Ba, Sr) semiconductors are materials with a variety of photocatalyst and optoelectronic applications. We present detailed microscopic analyses based on first principles of the structure, the electronic properties and the optical absorption in which the difference between symmetrically non-equivalent atoms has been considered. The high absorption coefficients of these materials are split into chemical species contributions in accordance with the symmetry. The high optical absorption in these materials is mainly because of the Cr–O inter-species transitions.

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Los fieltros son una familia de materiales textiles constituidos por una red desordenada de fibras conectadas por medio de enlaces térmicos, químicos o mecánicos. Presentan menor rigidez y resistencia (al igual que un menor coste de procesado) que sus homólogos tejidos, pero mayor deformabilidad y capacidad de absorción de energía. Los fieltros se emplean en diversas aplicaciones en ingeniería tales como aislamiento térmico, geotextiles, láminas ignífugas, filtración y absorción de agua, impacto balístico, etc. En particular, los fieltros punzonados fabricados con fibras de alta resistencia presentan una excelente resistencia frente a impacto balístico, ofreciendo las mismas prestaciones que los materiales tejidos con un tercio de la densidad areal. Sin embargo, se sabe muy poco acerca de los mecanismos de deformación y fallo a nivel microscópico, ni sobre como influyen en las propiedades mecánicas del material. Esta carencia de conocimiento dificulta la optimización del comportamiento mecánico de estos materiales y también limita el desarrollo de modelos constitutivos basados en mecanismos físicos, que puedan ser útiles en el diseño de componentes estructurales. En esta tesis doctoral se ha llevado a cabo un estudio minucioso con el fin de determinar los mecanismos de deformación y las propiedades mecánicas de fieltros punzonados fabricados con fibras de polietileno de ultra alto peso molecular. Los procesos de deformación y disipación de energía se han caracterizado en detalle por medio de una combinación de técnicas experimentales (ensayos mecánicos macroscópicos a velocidades de deformación cuasi-estáticas y dinámicas, impacto balístico, ensayos de extracción de una o múltiples fibras, microscopía óptica, tomografía computarizada de rayos X y difracción de rayos X de gran ángulo) que proporcionan información de los mecanismos dominantes a distintas escalas. Los ensayos mecánicos macroscópicos muestran que el fieltro presenta una resistencia y ductilidad excepcionales. El estado inicial de las fibras es curvado, y la carga se transmite por el fieltro a través de una red aleatoria e isótropa de nudos creada por el proceso de punzonamiento, resultando en la formación de una red activa de fibra. La rotación y el estirado de las fibras activas es seguido por el deslizamiento y extracción de la fibra de los puntos de anclaje mecánico. La mayor parte de la resistencia y la energía disipada es proporcionada por la extracción de las fibras activas de los nudos, y la fractura final tiene lugar como consecuencia del desenredo total de la red en una sección dada donde la deformación macroscópica se localiza. No obstante, aunque la distribución inicial de la orientación de las fibras es isótropa, las propiedades mecánicas resultantes (en términos de rigidez, resistencia y energía absorbida) son muy anisótropas. Los ensayos de extracción de múltiples fibras en diferentes orientaciones muestran que la estructura de los nudos conecta más fibras en la dirección transversal en comparación con la dirección de la máquina. La mejor interconectividad de las fibras a lo largo de la dirección transversal da lugar a una esqueleto activo de fibras más denso, mejorando las propiedades mecánicas. En términos de afinidad, los fieltros deformados a lo largo de la dirección transversal exhiben deformación afín (la deformación macroscópica transfiere directamente a las fibras por el material circundante), mientras que el fieltro deformado a lo largo de la dirección de la máquina presenta deformación no afín, y la mayor parte de la deformación macroscópica no es transmitida a las fibras. A partir de estas observaciones experimentales, se ha desarrollado un modelo constitutivo para fieltros punzonados confinados por enlaces mecánicos. El modelo considera los efectos de la deformación no afín, la conectividad anisótropa inducida durante el punzonamiento, la curvatura y re-orientación de la fibra, así como el desenredo y extracción de la fibra de los nudos. El modelo proporciona la respuesta de un mesodominio del material correspondiente al volumen asociado a un elemento finito, y se divide en dos bloques. El primer bloque representa el comportamiento de la red y establece la relación entre el gradiente de deformación macroscópico y la respuesta microscópica, obtenido a partir de la integración de la respuesta de las fibras en el mesodominio. El segundo bloque describe el comportamiento de la fibra, teniendo en cuenta las características de la deformación de cada familia de fibras en el mesodominio, incluyendo deformación no afín, estiramiento, deslizamiento y extracción. En la medida de lo posible, se ha asignado un significado físico claro a los parámetros del modelo, por lo que se pueden identificar por medio de ensayos independientes. Las simulaciones numéricas basadas en el modelo se adecúan a los resultados experimentales de ensayos cuasi-estáticos y balísticos desde el punto de vista de la respuesta mecánica macroscópica y de los micromecanismos de deformación. Además, suministran información adicional sobre la influencia de las características microstructurales (orientación de la fibra, conectividad de la fibra anisótropa, afinidad, etc) en el comportamiento mecánico de los fieltros punzonados. Nonwoven fabrics are a class of textile material made up of a disordered fiber network linked by either thermal, chemical or mechanical bonds. They present lower stiffness and strength (as well as processing cost) than the woven counterparts but much higher deformability and energy absorption capability and are used in many different engineering applications (including thermal insulation, geotextiles, fireproof layers, filtration and water absorption, ballistic impact, etc). In particular, needle-punched nonwoven fabrics manufactured with high strength fibers present an excellent performance for ballistic protection, providing the same ballistic protection with one third of the areal weight as compared to dry woven fabrics. Nevertheless, very little is known about their deformation and fracture micromechanisms at the microscopic level and how they contribute to the macroscopic mechanical properties. This lack of knowledge hinders the optimization of their mechanical performance and also limits the development of physically-based models of the mechanical behavior that can be used in the design of structural components with these materials. In this thesis, a thorough study was carried out to ascertain the micromechanisms of deformation and the mechanical properties of a needle-punched nonwoven fabric made up by ultra high molecular weight polyethylene fibers. The deformation and energy dissipation processes were characterized in detail by a combination of experimental techniques (macroscopic mechanical tests at quasi-static and high strain rates, ballistic impact, single fiber and multi fiber pull-out tests, optical microscopy, X-ray computed tomography and wide angle X-ray diffraction) that provided information of the dominant mechanisms at different length scales. The macroscopic mechanical tests showed that the nonwoven fabric presented an outstanding strength and energy absorption capacity. It was found that fibers were initially curved and the load was transferred within the fabric through the random and isotropic network of knots created by needlepunching, leading to the formation of an active fiber network. Uncurling and stretching of the active fibers was followed by fiber sliding and pull-out from the entanglement points. Most of the strength and energy dissipation was provided by the extraction of the active fibers from the knots and final fracture occurred by the total disentanglement of the fiber network in a given section at which the macroscopic deformation was localized. However, although the initial fiber orientation distribution was isotropic, the mechanical properties (in terms of stiffness, strength and energy absorption) were highly anisotropic. Pull-out tests of multiple fibers at different orientations showed that structure of the knots connected more fibers in the transverse direction as compared with the machine direction. The better fiber interconnection along the transverse direction led to a denser active fiber skeleton, enhancing the mechanical response. In terms of affinity, fabrics deformed along the transverse direction essentially displayed affine deformation {i.e. the macroscopic strain was directly transferred to the fibers by the surrounding fabric, while fabrics deformed along the machine direction underwent non-affine deformation, and most of the macroscopic strain was not transferred to the fibers. Based on these experimental observations, a constitutive model for the mechanical behavior of the mechanically-entangled nonwoven fiber network was developed. The model accounted for the effects of non-affine deformation, anisotropic connectivity induced by the entanglement points, fiber uncurling and re-orientation as well as fiber disentanglement and pull-out from the knots. The model provided the constitutive response for a mesodomain of the fabric corresponding to the volume associated to a finite element and is divided in two blocks. The first one was the network model which established the relationship between the macroscopic deformation gradient and the microscopic response obtained by integrating the response of the fibers in the mesodomain. The second one was the fiber model, which took into account the deformation features of each set of fibers in the mesodomain, including non-affinity, uncurling, pull-out and disentanglement. As far as possible, a clear physical meaning is given to the model parameters, so they can be identified by means of independent tests. The numerical simulations based on the model were in very good agreement with the experimental results of in-plane and ballistic mechanical response of the fabrics in terms of the macroscopic mechanical response and of the micromechanisms of deformation. In addition, it provided additional information about the influence of the microstructural features (fiber orientation, anisotropic fiber connectivity, affinity) on the mechanical performance of mechanically-entangled nonwoven fabrics.

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In this study we demonstrate, at an ultrastructural level, the in situ distribution of heterogeneous nuclear RNA transcription sites after microinjection of 5-bromo-UTP (BrUTP) into the cytoplasm of living cells and subsequent postembedding immunoelectron microscopic visualization after different labeling periods. Moreover, immunocytochemical localization of several pre-mRNA transcription and processing factors has been carried out in the same cells. This high-resolution approach allowed us to reveal perichromatin regions as the most important sites of nucleoplasmic RNA transcription and the perichromatin fibrils (PFs) as in situ forms of nascent transcripts. Furthermore, we show that transcription takes place in a rather diffuse pattern, without notable local accumulation of transcription sites. RNA polymerase II, heterogeneous nuclear ribonucleoprotein (hnRNP) core proteins, general transcription factor TFIIH, poly(A) polymerase, splicing factor SC-35, and Sm complex of small nuclear ribonucleoproteins (snRNPs) are associated with PFs. This strongly supports the idea that PFs are also sites of major pre-mRNA processing events. The absence of nascent transcripts, RNA polymerase II, poly(A) polymerase, and hnRNPs within the clusters of interchromatin granules rules out the possibility that this domain plays a role in pre-mRNA transcription and polyadenylation; however, interchromatin granule-associated zones contain RNA polymerase II, TFIIH, and Sm complex of snRNPs and, after longer periods of BrUTP incubation, also Br-labeled RNA. Their role in nuclear functions still remains enigmatic. In the nucleolus, transcription sites occur in the dense fibrillar component. Our fine structural results show that PFs represent the major nucleoplasmic structural domain involved in active pre-mRNA transcriptional and processing events.

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Buforin II is a 21-aa potent antimicrobial peptide that forms, in a hydrophobic medium, an amphipathic structure consisting of an N-terminal random coil region (residues 1–4), an extended helical region (residues 5–10), a hinge (residue 11), and a C-terminal regular α-helical region (residues 12–21). To elucidate the structural features of buforin II that are required for its potent antimicrobial activity, we synthesized a series of N- and C-terminally truncated or amino acid-substituted synthetic buforin II analogs and examined their antimicrobial activity and mechanism of action. Deletion of the N-terminal random coil region increased the antibacterial activity ≈2-fold, but further N-terminal truncation yielded peptide analogs with progressively decreasing activity. Removal of four amino acids from the C-terminal end of buforin II resulted in a complete loss of antimicrobial activity. The substitution of leucine for the proline hinge decreased significantly the antimicrobial activity. Confocal fluorescence microscopic studies showed that buforin II analogs with a proline hinge penetrated the cell membrane without permeabilization and accumulated in the cytoplasm. However, removal of the proline hinge abrogated the ability of the peptide to enter cells, and buforin II analogs without a proline hinge localized on the cell surface, permeabilizing the cell membrane. In addition, the cell-penetrating efficiency of buforin II and its truncated analogs, which depended on the α-helical content of the peptides, correlated linearly with their antimicrobial potency. Our results demonstrate clearly that the proline hinge is responsible for the cell-penetrating ability of buforin II, and the cell-penetrating efficiency determines the antimicrobial potency of the peptide.

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Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.