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

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

Transcriptional Infidelity Promotes Heritable Phenotypic Change in a Bistable Gene Network

Bistable epigenetic switches are fundamental for cell fate determination in unicellular and multicellular organisms. Regulatory proteins associated with bistable switches are often present in low numbers and subject to molecular noise. It is becoming clear that noise in gene expression can influence cell fate. Although the origins and consequences of noise have been studied, the stochastic and transient nature of RNA errors during transcription has not been considered in the origin or modeling of noise nor has the capacity for such transient errors in information transfer to generate heritable phenotypic change been discussed. We used a classic bistable memory module to monitor and capture transient RNA errors: the lac operon of Escherichia coli comprises an autocatalytic positive feedback loop producing a heritable all-or-none epigenetic switch that is sensitive to molecular noise. Using single-cell analysis, we show that the frequency of epigenetic switching from one expression state to the other is increased when the fidelity of RNA transcription is decreased due to error-prone RNA polymerases or to the absence of auxiliary RNA fidelity factors GreA and GreB (functional analogues of eukaryotic TFIIS). Therefore, transcription infidelity contributes to molecular noise and can effect heritable phenotypic change in genetically identical cells in the same environment. Whereas DNA errors allow genetic space to be explored, RNA errors may allow epigenetic or expression space to be sampled. Thus, RNA infidelity should also be considered in the heritable origin of altered or aberrant cell behaviour

Drosophila errantiviruses

Retroelements with long-terminal repeats (LTRs) inhabit nearly all eukaryotic genomes. During the time of their rich evolutionary history they have developed highly diverse forms, ranging from ordinary retrotransposons to complex pathogenic retroviruses such as HIV-I. Errantiviruses are a group of insect endogenous LTR elements that share structural and functional features with vertebrate endogenous retroviruses. The errantiviruses illustrate one of the evolutionary strategies of retrotransposons to become infective, which together with their similarities to vertebrate retroviruses make them an attractive object of research promising to shed more light on the evolution of retroviruses

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

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

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

Spatial abundance and clustering of Culicoides (Diptera: Ceratopogonidae) on a local scale

BACKGROUND: Biting midges, Culicoides, of the Obsoletus group and the Pulicaris group have been involved in recent outbreaks of bluetongue virus and the former was also involved in the Schmallenberg virus outbreak in northern Europe. METHODS: For the first time, here we investigate the local abundance pattern of these two species groups in the field by intensive sampling with a grid of light traps on 16 catch nights. Neighboring trap catches can be spatially dependent on each other, hence we developed a conditional autoregressive (CAR) model framework to test a number of spatial and non-spatial covariates expected to affect Culicoides abundance. RESULTS: The distance to sheep penned in the corner of the study field significantly increased the abundance level up to 200 meters away from the sheep. Spatial clustering was found to be significant but could not be explained by any known factors, and cluster locations shifted between catch nights. No significant temporal autocorrelation was detected. CAR models for both species groups identified a significant positive impact of humidity and significant negative impacts of precipitation and wind turbulence. Temperature was also found to be significant with a peak at just below 16 degrees Celcius. Surprisingly, there was a significant positive impact of wind speed. The CAR model for the Pulicaris group also identified a significant attraction to the smaller groups of sheep placed in the field. Furthermore, a large number of spatial covariates which were incorrectly found to be significant in ordinary regression models were not significant in the CAR models. The 95% C.I. on the prediction estimates ranged from 20.4% to 304.8%, underlining the difficulties of predicting the abundance of Culicoides. CONCLUSIONS: We found that significant spatial clusters of Culicoides moved around in a dynamic pattern varying between catch nights. This conforms with the modeling but was not explained by any of the tested covariates. The mean abundance within these clusters was up to 11 times higher for the Obsoletus group and 4 times higher for the Pulicaris group compared to the rest of the field

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

Transcriptional analysis of the HeT-A retrotransposon in mutant and wild type stocks reveals high sequence variability at Drosophila telomeres and other unusual features

<p>Abstract</p> <p>Background</p> <p>Telomere replication in Drosophila depends on the transposition of a domesticated retroelement, the <it>HeT-A </it>retrotransposon. The sequence of the <it>HeT-A </it>retrotransposon changes rapidly resulting in differentiated subfamilies. This pattern of sequence change contrasts with the essential function with which the <it>HeT-A </it>is entrusted and brings about questions concerning the extent of sequence variability, the telomere contribution of different subfamilies, and whether wild type and mutant Drosophila stocks show different <it>HeT-A </it>scenarios.</p> <p>Results</p> <p>A detailed study on the variability of <it>HeT-A </it>reveals that both the level of variability and the number of subfamilies are higher than previously reported. Comparisons between GIII, a strain with longer telomeres, and its parental strain Oregon-R indicate that both strains have the same set of <it>HeT-A </it>subfamilies. Finally, the presence of a highly conserved splicing pattern only in its antisense transcripts indicates a putative regulatory, functional or structural role for the <it>HeT-A </it>RNA. Interestingly, our results also suggest that most <it>HeT-A </it>copies are actively expressed regardless of which telomere and where in the telomere they are located.</p> <p>Conclusions</p> <p>Our study demonstrates how the <it>HeT-A </it>sequence changes much faster than previously reported resulting in at least nine different subfamilies most of which could actively contribute to telomere extension in Drosophila. Interestingly, the only significant difference observed between Oregon-R and GIII resides in the nature and proportion of the antisense transcripts, suggesting a possible mechanism that would in part explain the longer telomeres of the GIII stock.</p