Correspondence between geometrical and differential definitions of the sine and cosine functions and connection with kinematics

In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms correspond to two different definitions of trigonometric functions, one geometrical using right triangles and unit circles, and the other employing differential equations. Although the two definitions must be equivalent, this equivalence is not demonstrated in textbooks. In this manuscript, the equivalence between the geometrical and the differential definition is presented assuming no a priori knowledge of the properties of sine and cosine functions. We start with the usual length projections on the unit circle and use elementary geometry and elementary calculus to arrive to harmonic differential equations. This more general and abstract treatment not only reveals the equivalence of the two definitions but also provides an instructive perspective on circular and harmonic motion as studied in kinematics. This exercise can help develop an appreciation of abstract thinking in physics.Comment: 6 pages including 1 figur

Randomized controlled trial of a book-sharing intervention in a deprived South African community: effects on carer-infant interactions, and their relation to infant cognitive and socio-emotional outcome

Background: Consistent with evidence from high income countries, we previously showed that, in an informal peri-urban settlement in a low-middle income country, training parents in book-sharing with their infants benefitted infant language and attention (Vally et al., 2015). Here, we investigated whether these benefits were explained by improvements in carer-infant interactions in both book-sharing and non-book-sharing contexts. We also explored whether infant socio-emotional development benefitted from book-sharing. Methods: We conducted a randomized controlled trial in Khayelitsha, South Africa. Carers of 14-16 month-old infants were randomized to 8 weeks’ training in book-sharing (n = 49) or a wait list control group (n = 42). In addition to the cognitive measures reported previously, independent assessments were made at base line and follow-up of carer-infant interactions during book-sharing and toy play. Assessments were also made, at follow-up only, of infant pro-social behaviour in a ‘help task’, and of infant imitation of doll characters’ non-social actions and an interpersonal interaction. Eighty-two carer-infant pairs (90%) were assessed at follow-up. (Trial registration ISRCTN39953901). Results: Carers who received the training showed significant improvements in book-sharing interactions (sensitivity, elaborations, reciprocity), and, to a smaller extent, in toy-play interactions (sensitivity). Infants in the intervention group showed a significantly higher rate of pro-social behaviour, and tended to show more frequent imitation of the interpersonal interaction. Improvements in carer behaviour during book-sharing, but not during toy play, mediated intervention effects on all infant cognitive outcomes, and tended to mediate intervention effects on infant interpersonal imitation. Conclusions: Training in book sharing, a simple, inexpensive intervention that has been shown to benefit infant cognitive development in a low-middle income country, also shows promise for improving infant socio-emotional outcomes in this context. Benefits are mediated by improvements in carer-infant interactions, particularly in book-sharing contexts

Point Interaction in two and three dimensional Riemannian Manifolds

We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac delta interactions on two and three dimensional Riemannian manifolds using the heat kernel. We formulate the problem in terms of a new operator called the principal or characteristic operator. In order to investigate the problem in more detail, we then restrict the problem to one particle sector. The lower bound of the ground state energy is found for general class of manifolds, e.g., for compact and Cartan-Hadamard manifolds. The estimate of the bound state energies in the tunneling regime is calculated by perturbation theory. Non-degeneracy and uniqueness of the ground state is proven by Perron-Frobenius theorem. Moreover, the pointwise bounds on the wave function is given and all these results are consistent with the one given in standard quantum mechanics. Renormalization procedure does not lead to any radical change in these cases. Finally, renormalization group equations are derived and the beta-function is exactly calculated. This work is a natural continuation of our previous work based on a novel approach to the renormalization of point interactions, developed by S. G. Rajeev.Comment: 43 page

A translocation motif in relaxase TrwC specifically affects recruitment by its conjugative type IV secretion system

Type IV secretion system (T4SS) substrates are recruited through a translocation signal that is poorly defined for conjugative relaxases. The relaxase TrwC of plasmid R388 is translocated by its cognate conjugative T4SS, and it can also be translocated by the VirB/D4 T4SS of Bartonella henselae, causing DNA transfer to human cells. In this work, we constructed a series of TrwC variants and assayed them for DNA transfer to bacteria and human cells to compare recruitment requirements by both T4SSs. Comparison with other reported relaxase translocation signals allowed us to determine two putative translocation sequence (TS) motifs, TS1 and TS2. Mutations affecting TS1 drastically affected conjugation frequencies, while mutations affecting either motif had only a mild effect on DNA transfer rates through the VirB/D4 T4SS of B. henselae. These results indicate that a single substrate can be recruited by two different T4SSs through different signals. The C terminus affected DNA transfer rates through both T4SSs tested, but no specific sequence requirement was detected. The addition of a Bartonella intracellular delivery (BID) domain, the translocation signal for the Bartonella VirB/D4 T4SS, increased DNA transfer up to 4% of infected human cells, providing an excellent tool for DNA delivery to specific cell types. We show that the R388 coupling protein TrwB is also required for this high-efficiency TrwC-BID translocation. Other elements apart from the coupling protein may also be involved in substrate recognition by T4SSs

Aptamer-based multiplexed proteomic technology for biomarker discovery

Interrogation of the human proteome in a highly multiplexed and efficient manner remains a coveted and challenging goal in biology. We present a new aptamer-based proteomic technology for biomarker discovery capable of simultaneously measuring thousands of proteins from small sample volumes (15 [mu]L of serum or plasma). Our current assay allows us to measure ~800 proteins with very low limits of detection (1 pM average), 7 logs of overall dynamic range, and 5% average coefficient of variation. This technology is enabled by a new generation of aptamers that contain chemically modified nucleotides, which greatly expand the physicochemical diversity of the large randomized nucleic acid libraries from which the aptamers are selected. Proteins in complex matrices such as plasma are measured with a process that transforms a signature of protein concentrations into a corresponding DNA aptamer concentration signature, which is then quantified with a DNA microarray. In essence, our assay takes advantage of the dual nature of aptamers as both folded binding entities with defined shapes and unique sequences recognizable by specific hybridization probes. To demonstrate the utility of our proteomics biomarker discovery technology, we applied it to a clinical study of chronic kidney disease (CKD). We identified two well known CKD biomarkers as well as an additional 58 potential CKD biomarkers. These results demonstrate the potential utility of our technology to discover unique protein signatures characteristic of various disease states. More generally, we describe a versatile and powerful tool that allows large-scale comparison of proteome profiles among discrete populations. This unbiased and highly multiplexed search engine will enable the discovery of novel biomarkers in a manner that is unencumbered by our incomplete knowledge of biology, thereby helping to advance the next generation of evidence-based medicine

Conformational Proofreading: The Impact of Conformational Changes on the Specificity of Molecular Recognition

To perform recognition, molecules must locate and specifically bind their targets within a noisy biochemical environment with many look-alikes. Molecular recognition processes, especially the induced-fit mechanism, are known to involve conformational changes. This raises a basic question: Does molecular recognition gain any advantage by such conformational changes? By introducing a simple statistical-mechanics approach, we study the effect of conformation and flexibility on the quality of recognition processes. Our model relates specificity to the conformation of the participant molecules and thus suggests a possible answer: Optimal specificity is achieved when the ligand is slightly off target; that is, a conformational mismatch between the ligand and its main target improves the selectivity of the process. This indicates that deformations upon binding serve as a conformational proofreading mechanism, which may be selected for via evolution

The Legionella effector WipB is a translocated Ser/Thr phosphatase that targets the host lysosomal nutrient sensing machinery

Legionella pneumophila infects human alveolar macrophages and is responsible for Legionnaire’s disease, a severe form of pneumonia. L. pneumophila encodes more than 300 putative effectors, which are translocated into the host cell via the Dot/Icm type IV secretion system. These effectors highjack the host’s cellular processes to allow bacterial intracellular growth and replication. Here we adopted a multidisciplinary approach to investigate WipB, a Dot/Icm effector of unknown function. The crystal structure of the N-terminal domain at 1.7 Å resolution comprising residues 25 to 344 revealed that WipB harbours a Ser/Thr phosphatase domain related to the eukaryotic phospho-protein phosphatase (PPP) family. The C-terminal domain (residues 365–524) is sufficient to pilot the effector to acidified LAMP1-positive lysosomal compartments, where WipB interacts with the v-ATPase and the associated LAMTOR1 phosphoprotein, key components of the lysosomal nutrient sensing (LYNUS) apparatus that controls the mammalian target of rapamycin (mTORC1) kinase complex at the lysosomal surface. We propose that WipB is a lysosome-targeted phosphatase that modulates cellular nutrient sensing and the control of energy metabolism during Legionella infection

Quantifying Dispersal of European Culicoides (Diptera: Ceratopogonidae) Vectors between Farms Using a Novel Mark-Release-Recapture Technique

Studying the dispersal of small flying insects such as Culicoides constitutes a great challenge due to huge population sizes and lack of a method to efficiently mark and objectively detect many specimens at a time. We here describe a novel mark-release-recapture method for Culicoides in the field using fluorescein isothiocyanate (FITC) as marking agent without anaesthesia. Using a plate scanner, this detection technique can be used to analyse thousands of individual Culicoides specimens per day at a reasonable cost. We marked and released an estimated 853 specimens of the Pulicaris group and 607 specimens of the Obsoletus group on a cattle farm in Denmark. An estimated 9,090 (8,918-9,260) Obsoletus group specimens and 14,272 (14,194-14,448) Pulicaris group specimens were captured in the surroundings and subsequently analysed. Two (0.3%) Obsoletus group specimens and 28 (4.6%) Pulicaris group specimens were recaptured. The two recaptured Obsoletus group specimens were caught at the release point on the night following release. Eight (29%) of the recaptured Pulicaris group specimens were caught at a pig farm 1,750 m upwind from the release point. Five of these were recaptured on the night following release and the three other were recaptured on the second night after release. This is the first time that movement of Culicoides vectors between farms in Europe has been directly quantified. The findings suggest an extensive and rapid exchange of disease vectors between farms. Rapid movement of vectors between neighboring farms may explain the the high rate of spatial spread of Schmallenberg and bluetongue virus (BTV) in northern Europe

Type IV Secretion-Dependent Activation of Host MAP Kinases Induces an Increased Proinflammatory Cytokine Response to Legionella pneumophila

The immune system must discriminate between pathogenic and nonpathogenic microbes in order to initiate an appropriate response. Toll-like receptors (TLRs) detect microbial components common to both pathogenic and nonpathogenic bacteria, whereas Nod-like receptors (NLRs) sense microbial components introduced into the host cytosol by the specialized secretion systems or pore-forming toxins of bacterial pathogens. The host signaling pathways that respond to bacterial secretion systems remain poorly understood. Infection with the pathogen Legionella pneumophila, which utilizes a type IV secretion system (T4SS), induced an increased proinflammatory cytokine response compared to avirulent bacteria in which the T4SS was inactivated. This enhanced response involved NF-κB activation by TLR signaling as well as Nod1 and Nod2 detection of type IV secretion. Furthermore, a TLR- and RIP2-independent pathway leading to p38 and SAPK/JNK MAPK activation was found to play an equally important role in the host response to virulent L. pneumophila. Activation of this MAPK pathway was T4SS-dependent and coordinated with TLR signaling to mount a robust proinflammatory cytokine response to virulent L. pneumophila. These findings define a previously uncharacterized host response to bacterial type IV secretion that activates MAPK signaling and demonstrate that coincident detection of multiple bacterial components enables immune discrimination between virulent and avirulent bacteria

A high-throughput synthetic platform enables the discovery of proteomimetic cell penetrating peptides and bioportides

Collectively, cell penetrating peptide (CPP) vectors and intrinsically active bioportides possess tremendous potential for drug delivery applications and the discrete modulation of intracellular targets including the sites of protein–protein interactions (PPIs). Such sequences are usually relatively short (< 25 AA), polycationic in nature and able to access the various intracellular compartments of eukaryotic cells without detrimental influences upon cellular biology. The high-throughput platform for bioportide discovery described herein exploits the discovery that many human proteins are an abundant source of potential CPP sequences which are reliably predicted using QSAR algorithms or other methods. Subsequently, microwave-enhanced solid phase peptides synthesis provides a high-throughput source of novel proteomimetic CPPs for screening purposes. By focussing upon cationic helical domains, often located within the molecular interfaces that facilitate PPIs, bioportides which act by a dominant-negative mechanism at such sites can be reliably identified within small number libraries of CPPs. Protocols that employ fluorescent peptides, routinely prepared by N-terminal acylation with carboxytetramethylrhodamine, further enable both the quantification of cellular uptake kinetics and the identification of specific site(s) of intracellular accretion. Chemical modifications of linear peptides, including strategies to promote and stabilise helicity, are compatible with the synthesis of second-generation bioportides with improved drug-like properties to further exploit the inherent selectivity of biologics