Metric connections in projective differential geometry

We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations. Prolonging this system, we may reformulate these equations as defining covariant constant sections of a certain vector bundle with connection. This vector bundle and its connection are derived from the Cartan connection of the underlying projective structure.Comment: 10 page

Basal metabolic rate and the mass of tissues differing in metabolic scope:Migration-related covariation between individual knots<i> Calidris canutus</i>

To examine whether variability in the basal metabolic rate (BMR) of migrant shorebirds is a function of a variably sized metabolic machinery or of temporal changes in metabolic intensities at the tissue level, BMR, body composition and activity of cytochrome-c oxidase (CCO, a marker for maximum tissue respiration) were measured in 14 captive Knots Calidris canutus islandica in late spring, during the period of mass loss after the migratory body mass peak. Although the body mass cycle of captive birds closely followed the changes of free-living conspecifics, their fat-free mass of muscles and organs was somewhat lower and their fat content higher. BMR significantly declined during mass loss, as did the fat-free dry mass. BMR was an allometric function of both body mass (exponent=0.687) and lean dry mass (exponent=1.132). Fat-free dry mass of heart sind flight muscle decreased with the loss of fat. CCO-activity was determined in heart, flight muscle, leg muscle, liver and kidney. It was highest in heart and flight muscle and low in the other tissues. CCO-activity was not correlated with total fat mass. Intraspecific migration-related variation in BMR seems better explained by variation in the mass of organs with a high metabolic scope (as indicated by high CCO-activity), than by variation in the intensity of tissue metabolism

Retention of Conformational Entropy upon Calmodulin Binding to Target Peptides Is Driven by Transient Salt Bridges

AbstractCalmodulin (CaM) is a highly flexible calcium-binding protein that mediates signal transduction through an ability to differentially bind to highly variable binding sequences in target proteins. To identify how binding affects CaM motions, and its relationship to conformational entropy and target peptide sequence, we have employed fully atomistic, explicit solvent molecular dynamics simulations of unbound CaM and CaM bound to five different target peptides. The calculated CaM conformational binding entropies correlate with experimentally derived conformational entropies with a correlation coefficient R2 of 0.95. Selected side-chain interactions with target peptides restrain interhelical loop motions, acting to tune the conformational entropy of the bound complex via widely distributed CaM motions. In the complex with the most conformational entropy retention (CaM in complex with the neuronal nitric oxide synthase binding sequence), Lys-148 at the C-terminus of CaM forms transient salt bridges alternating between Glu side chains in the N-domain, the central linker, and the binding target. Additional analyses of CaM structures, fluctuations, and CaM-target interactions illuminate the interplay between electrostatic, side chain, and backbone properties in the ability of CaM to recognize and discriminate against targets by tuning its conformational entropy, and suggest a need to consider conformational dynamics in optimizing binding affinities

Modellierung von Ladungsträgertransport und Strukturbildung in elektrolumineszierenden ZnS:Mn-Halbleiterbauelementen

Mangandotiertes Zinksulfid (ZnS), das zwischen Isolatoren (IS) eingebettet ist, zeigt in der Elektrolumineszenz (EL) spontane Strukturbildungsprozesse (SP), die durch starke nichtlineare Prozesse (Feldabschirmung durch Raumladung, Stossionisation) verursacht werden. Es wird ein gekoppeltes Drift-Diffusions-Modell für Elektronen, freie und gebundene Löcher diskutiert. Die bekannte EL-Bistabilität kann mit einer Strom-Spannungs-Kennlinie (aus 1D-Simulation) verifiziert werden. Wesentlich ist dabei eine ortsfeste positive Raumladung (OPR), die aus dem Einfang der freien Löcher resultiert. Die Analyse der Kennlinie ist wichtig, da im Experiment nur in einem engen Spannungsbereich (Übergang: schwache -> starke EL) SP auftreten. Entsprechende 2D/3D-Simulationen zeigen Stromfilamente, die durch (de)fokussierende Transportprozesse stabilisiert werden. Die Form wird durch verschiedene Ladungsdichten (an ZnS-IS-Grenzflächen, OPR) sowie weiteren Parametern (z.B. Diffusionskonstanten) bestimmt

Continuous image distortion by astrophysical thick lenses

Image distortion due to weak gravitational lensing is examined using a non-perturbative method of integrating the geodesic deviation and optical scalar equations along the null geodesics connecting the observer to a distant source. The method we develop continuously changes the shape of the pencil of rays from the source to the observer with no reference to lens planes in astrophysically relevant scenarios. We compare the projected area and the ratio of semi-major to semi-minor axes of the observed elliptical image shape for circular sources from the continuous, thick-lens method with the commonly assumed thin-lens approximation. We find that for truncated singular isothermal sphere and NFW models of realistic galaxy clusters, the commonly used thin-lens approximation is accurate to better than 1 part in 10^4 in predicting the image area and axes ratios. For asymmetric thick lenses consisting of two massive clusters separated along the line of sight in redshift up to \Delta z = 0.2, we find that modeling the image distortion as two clusters in a single lens plane does not produce relative errors in image area or axes ratio more than 0.5%Comment: accepted to GR

Computational techniques for the assessment of fracture repair

The combination of high-resolution three-dimensional medical imaging, increased computing power, and modern computational methods provide unprecedented capabilities for assessing the repair and healing of fractured bone. Fracture healing is a natural process that restores the mechanical integrity of bone and is greatly influenced by the prevailing mechanical environment. Mechanobiological theories have been proposed to provide greater insight into the relationships between mechanics (stress and strain) and biology. Computational approaches for modelling these relationships have evolved from simple tools to analyze fracture healing at a single point in time to current models that capture complex biological events such as angiogenesis, stochasticity in cellular activities, and cell-phenotype specific activities. The predictive capacity of these models has been established using corroborating physical experiments. For clinical application, mechanobiological models accounting for patient-to-patient variability hold the potential to predict fracture healing and thereby help clinicians to customize treatment. Advanced imaging tools permit patient-specific geometries to be used in such models. Refining the models to study the strain fields within a fracture gap and adapting the models for case-specific simulation may provide more accurate examination of the relationship between strain and fracture healing in actual patients. Medical imaging systems have significantly advanced the capability for less invasive visualization of injured musculoskeletal tissues, but all too often the consideration of these rich datasets has stopped at the level of subjective observation. Computational image analysis methods have not yet been applied to study fracture healing, but two comparable challenges which have been addressed in this general area are the evaluation of fracture severity and of fracture-associated soft tissue injury. CT-based methodologies developed to assess and quantify these factors are described and results presented to show the potential of these analysis methods

Rational design of a (S)-selective-transaminase for asymmetric synthesis of (1S)-1-(1,1′-biphenyl-2-yl)ethanamine

Amine transaminases offer an environmentally sustainable synthesis route for the production of pure chiral amines. However, their catalytic efficiency toward bulky ketone substrates is greatly limited by steric hindrance and therefore presents a great challenge for industrial synthetic applications. We hereby report an example of rational transaminase enzyme design to help alleviate these challenges. Starting from the Vibrio fluvialis amine transaminase that has no detectable catalytic activity toward the bulky aromatic ketone 2-acetylbiphenyl, we employed a rational design strategy combining in silico and in vitro studies to engineer the transaminase enzyme with a minimal number of mutations, achieving an high catalytic activity and high enantioselectivity. We found that, by introducing two mutations W57G/R415A, detectable enzyme activity was achieved. The rationally designed variant, W57F/R88H/V153S/K163F/I259M/R415A/V422A, showed an improvement in reaction rate by more than 1716-fold toward the bulky ketone under study, producing the corresponding enantiomeric pure (S)-amine (enantiomeric excess (ee) value of &gt;99%)