Optimal Computation of Avoided Words

The deviation of the observed frequency of a word $w$ from its expected frequency in a given sequence $x$ is used to determine whether or not the word is avoided. This concept is particularly useful in DNA linguistic analysis. The value of the standard deviation of $w$, denoted by $std(w)$, effectively characterises the extent of a word by its edge contrast in the context in which it occurs. A word $w$ of length $k>2$ is a $\rho$-avoided word in $x$ if $std(w) \leq \rho$, for a given threshold $\rho < 0$. Notice that such a word may be completely absent from $x$. Hence computing all such words na\"{\i}vely can be a very time-consuming procedure, in particular for large $k$. In this article, we propose an $O(n)$-time and $O(n)$-space algorithm to compute all $\rho$-avoided words of length $k$ in a given sequence $x$ of length $n$ over a fixed-sized alphabet. We also present a time-optimal $O(\sigma n)$-time and $O(\sigma n)$-space algorithm to compute all $\rho$-avoided words (of any length) in a sequence of length $n$ over an alphabet of size $\sigma$. Furthermore, we provide a tight asymptotic upper bound for the number of $\rho$-avoided words and the expected length of the longest one. We make available an open-source implementation of our algorithm. Experimental results, using both real and synthetic data, show the efficiency of our implementation

Green's Dyadic Approach of the Self-Stress on a Dielectric-Diamagnetic Cylinder with Non-Uniform Speed of Light

We present a Green's dyadic formulation to calculate the Casimir energy for a dielectric-diamagnetic cylinder with the speed of light differing on the inside and outside. Although the result is in general divergent, special cases are meaningful. It is pointed out how the self-stress on a purely dielectric cylinder vanishes through second order in the deviation of the permittivity from its vacuum value, in agreement with the result calculated from the sum of van der Waals forces.Comment: 8 pages, submitted to proceedings of QFEXT0

Effects of common mutations in the SARS-CoV-2 Spike RBD domain and its ligand the human ACE2 receptor on binding affinity and kinetics

The interaction between the SARS-CoV-2 virus Spike protein receptor binding domain (RBD) and the ACE2 cell surface protein is required for viral infection of cells. Mutations in the RBD are present in SARS-CoV-2 variants of concern that have emerged independently worldwide. For example, the B.1.1.7 lineage has a mutation (N501Y) in its Spike RBD that enhances binding to ACE2. There are also ACE2 alleles in humans with mutations in the RBD binding site. Here we perform a detailed affinity and kinetics analysis of the effect of five common RBD mutations (K417N, K417T, N501Y, E484K, and S477N) and two common ACE2 mutations (S19P and K26R) on the RBD/ACE2 interaction. We analysed the effects of individual RBD mutations and combinations found in new SARS-CoV-2 Alpha (B.1.1.7), Beta (B.1.351), and Gamma (P1) variants. Most of these mutations increased the affinity of the RBD/ACE2 interaction. The exceptions were mutations K417N/T, which decreased the affinity. Taken together with other studies, our results suggest that the N501Y and S477N mutations enhance transmission primarily by enhancing binding, the K417N/T mutations facilitate immune escape, and the E484K mutation enhances binding and immune escape

Missense variants in human ACE2 strongly affect binding to SARS-CoV-2 Spike providing a mechanism for ACE2 mediated genetic risk in Covid-19:A case study in affinity predictions of interface variants

SARS-CoV-2 Spike (Spike) binds to human angiotensin-converting enzyme 2 (ACE2) and the strength of this interaction could influence parameters relating to virulence. To explore whether population variants in ACE2 influence Spike binding and hence infection, we selected 10 ACE2 variants based on affinity predictions and prevalence in gnomAD and measured their affinities and kinetics for Spike receptor binding domain through surface plasmon resonance (SPR) at 37°C. We discovered variants that reduce and enhance binding, including three ACE2 variants that strongly inhibited (p.Glu37Lys, ΔΔG = –1.33 ± 0.15 kcal mol(-1) and p.Gly352Val, predicted ΔΔG = –1.17 kcal mol(-1)) or abolished (p.Asp355Asn) binding. We also identified two variants with distinct population distributions that enhanced affinity for Spike. ACE2 p.Ser19Pro (ΔΔG = 0.59 ± 0.08 kcal mol(-1)) is predominant in the gnomAD African cohort (AF = 0.003) whilst p.Lys26Arg (ΔΔG = 0.26 ± 0.09 kcal mol(-1)) is predominant in the Ashkenazi Jewish (AF = 0.01) and European non-Finnish (AF = 0.006) cohorts. We compared ACE2 variant affinities to published SARS-CoV-2 pseudotype infectivity data and confirmed that ACE2 variants with reduced affinity for Spike can protect cells from infection. The effect of variants with enhanced Spike affinity remains unclear, but we propose a mechanism whereby these alleles could cause greater viral spreading across tissues and cell types, as is consistent with emerging understanding regarding the interplay between receptor affinity and cell-surface abundance. Finally, we compared mCSM-PPI2 ΔΔG predictions against our SPR data to assess the utility of predictions in this system. We found that predictions of decreased binding were well-correlated with experiment and could be improved by calibration, but disappointingly, predictions of highly enhanced binding were unreliable. Recalibrated predictions for all possible ACE2 missense variants at the Spike interface were calculated and used to estimate the overall burden of ACE2 variants on Covid-19

Effect of composition on the dielectric relaxation of zeolite-conducting polyaniline blends

The complex permittivity of conducting polyaniline and zeolite - polyaniline blends was measured in the frequency range 0.01 to 2000000 Hz from room temperature to liquid nitrogen temperature. A loss peak is detected for 25, 35 and 50 wt % zeolite blends. Its position in the frequency domain, activation energy and intensity is a function of composition. The experimental results are interpreted through the competing multiple role of zeolite: as being less conducting than polyaniline, it impedes the electric charge flow by dividing large conducting polyaniline regions into smaller pieces, subsequently provides short-range pathways and, moreover, enriches the blend in interfaces separating zeolite from polyaniline.Comment: Accepted for publication in J. Appl. Phy

Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach

A theoretical framework is proposed to derive a dynamic equation motion for rectilinear dislocations within isotropic continuum elastodynamics. The theory relies on a recent dynamic extension of the Peierls-Nabarro equation, so as to account for core-width generalized stacking-fault energy effects. The degrees of freedom of the solution of the latter equation are reduced by means of the collective-variable method, well known in soliton theory, which we reformulate in a way suitable to the problem at hand. Through these means, two coupled governing equations for the dislocation position and core width are obtained, which are combined into one single complex-valued equation of motion, of compact form. The latter equation embodies the history dependence of dislocation inertia. It is employed to investigate the motion of an edge dislocation under uniform time-dependent loading, with focus on the subsonic/transonic transition. Except in the steady-state supersonic range of velocities---which the equation does not address---our results are in good agreement with atomistic simulations on tungsten. In particular, we provide an explanation for the transition, showing that it is governed by a loading-dependent dynamic critical stress. The transition has the character of a delayed bifurcation. Moreover, various quantitative predictions are made, that could be tested in atomistic simulations. Overall, this work demonstrates the crucial role played by core-width variations in dynamic dislocation motion.Comment: v1: 11 pages, 4 figures. v2: title changed, extensive rewriting, and new material added; 19 pages, 12 figures (content as published

Casimir energy of a compact cylinder under the condition ϵμ=c−2\epsilon\mu = c^{-2}

The Casimir energy of an infinite compact cylinder placed in a uniform unbounded medium is investigated under the continuity condition for the light velocity when crossing the interface. As a characteristic parameter in the problem the ratio $\xi^2=(\epsilon_1-\epsilon_2)^2/ (\epsilon_1+\epsilon_2)^-2 = (\mu_1-\mu_2)^2/(\mu_1+ \mu_2)^2 \le 1$ is used, where $\epsilon_1$ and $\mu_1$ are, respectively, the permittivity and permeability of the material making up the cylinder and $\epsilon_2$ and $\mu_2$ are those for the surrounding medium. It is shown that the expansion of the Casimir energy in powers of this parameter begins with the term proportional to $\xi^4$. The explicit formulas permitting us to find numerically the Casimir energy for any fixed value of $\xi^2$ are obtained. Unlike a compact ball with the same properties of the materials, the Casimir forces in the problem under consideration are attractive. The implication of the calculated Casimir energy in the flux tube model of confinement is briefly discussed.Comment: REVTeX, 12 pages, 1 figure in a separate fig1.eps file, 1 table; minor corrections in English and misprints; version to be published in Phys. Rev. D1

Effects of common mutations in the SARS-CoV-2 Spike RBD and its ligand the human ACE2 receptor on binding affinity and kinetics

The interaction between the SARS-CoV-2 virus Spike protein receptor binding domain (RBD) and the ACE2 cell surface protein is required for viral infection of cells. Mutations in the RBD are present in SARS-CoV-2 variants of concern that have emerged independently worldwide. For example, the B.1.1.7 lineage has a mutation (N501Y) in its Spike RBD that enhances binding to ACE2. There are also ACE2 alleles in humans with mutations in the RBD binding site. Here we perform a detailed affinity and kinetics analysis of the effect of five common RBD mutations (K417N, K417T, N501Y, E484K, and S477N) and two common ACE2 mutations (S19P and K26R) on the RBD/ACE2 interaction. We analysed the effects of individual RBD mutations and combinations found in new SARS-CoV-2 Alpha (B.1.1.7), Beta (B.1.351), and Gamma (P1) variants. Most of these mutations increased the affinity of the RBD/ACE2 interaction. The exceptions were mutations K417N/T, which decreased the affinity. Taken together with other studies, our results suggest that the N501Y and S477N mutations enhance transmission primarily by enhancing binding, the K417N/T mutations facilitate immune escape, and the E484K mutation enhances binding and immune escape

Detection of an atmosphere around the super-Earth 55 Cancri e

We report the analysis of two new spectroscopic observations of the super-Earth 55 Cancri e, in the near infrared, obtained with the WFC3 camera onboard the HST. 55 Cancri e orbits so close to its parent star, that temperatures much higher than 2000 K are expected on its surface. Given the brightness of 55 Cancri, the observations were obtained in scanning mode, adopting a very long scanning length and a very high scanning speed. We use our specialized pipeline to take into account systematics introduced by these observational parameters when coupled with the geometrical distortions of the instrument. We measure the transit depth per wavelength channel with an average relative uncertainty of 22 ppm per visit and find modulations that depart from a straight line model with a 6$\sigma$ confidence level. These results suggest that 55 Cancri e is surrounded by an atmosphere, which is probably hydrogen-rich. Our fully Bayesian spectral retrieval code, T-REx, has identified HCN to be the most likely molecular candidate able to explain the features at 1.42 and 1.54 $\mu$m. While additional spectroscopic observations in a broader wavelength range in the infrared will be needed to confirm the HCN detection, we discuss here the implications of such result. Our chemical model, developed with combustion specialists, indicates that relatively high mixing ratios of HCN may be caused by a high C/O ratio. This result suggests this super-Earth is a carbon-rich environment even more exotic than previously thought.Comment: 10 pages, 10 figures, 4 tables, Accepted for publication in Ap