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

Exact phase diagram of quasispecies model with mutation rate modifier

We consider an infinite asexual population with a mutator allele which can elevate mutation rates. With probability $f$, a transition from nonmutator to mutator state occurs but the reverse transition is forbidden. We find that at $f=0$, the population is in the state with minimum mutation rate and at $f=f_c$, a phase transition occurs between a mixed phase with both nonmutators and mutators and a pure mutator phase. We calculate the critical probability $f_c$ and the total mutator fraction $Q$ in the mixed phase exactly. Our predictions for $Q$ are in agreement with those seen in microbial populations in static environments.Comment: Revised versio

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

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 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

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

Regional Decline of Coral Cover in the Indo-Pacific: Timing, Extent, and Subregional Comparisons

A number of factors have recently caused mass coral mortality events in all of the world's tropical oceans. However, little is known about the timing, rate or spatial variability of the loss of reef-building corals, especially in the Indo-Pacific, which contains 75% of the world's coral reefs.We compiled and analyzed a coral cover database of 6001 quantitative surveys of 2667 Indo-Pacific coral reefs performed between 1968 and 2004. Surveys conducted during 2003 indicated that coral cover averaged only 22.1% (95% CI: 20.7, 23.4) and just 7 of 390 reefs surveyed that year had coral cover >60%. Estimated yearly coral cover loss based on annually pooled survey data was approximately 1% over the last twenty years and 2% between 1997 and 2003 (or 3,168 km(2) per year). The annual loss based on repeated measures regression analysis of a subset of reefs that were monitored for multiple years from 1997 to 2004 was 0.72 % (n = 476 reefs, 95% CI: 0.36, 1.08).The rate and extent of coral loss in the Indo-Pacific are greater than expected. Coral cover was also surprisingly uniform among subregions and declined decades earlier than previously assumed, even on some of the Pacific's most intensely managed reefs. These results have significant implications for policy makers and resource managers as they search for successful models to reverse coral loss

PLA2G10 Gene Variants, sPLA2 Activity, and Coronary Heart Disease Risk.

Observational studies report that secretory phospholipase A2 (sPLA2) activity is a marker for coronary heart disease (CHD) risk, and activity measures are thought to represent the composite activity of sPLA2-IIA, -V, and -X. The aim of this study was to use genetic variants of PLA2G10, encoding sPLA2-X, to investigate the contribution of sPLA2-X to the measure of sPLA2 activity and coronary heart disease (CHD) risk traits and outcome