Optimizing the random search of a finite-lived target by a Lévy flight.

In many random search processes of interest in chemistry, biology, or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results on a minimal model system, a one-dimensional searcher performing a discrete time random walk, or Lévy flight. In contrast with the case of a permanent target, the capture probability and the conditional mean first passage time can be optimized. The optimal Lévy index takes a nontrivial value, even in the long lifetime limit, and exhibits an abrupt transition as the initial distance to the target is varied. Depending on the target lifetime, this transition is discontinuous or continuous, separated by a nonconventional tricritical point. These results pave the way to the optimization of search processes under time constraints.

Variantes citogenéticas en pacientes con síndrome de Turner diagnosticadas en un hospital de tercer nivel de atención en Ecuador / Cytogenetic variants in patients with Turner syndrome diagnosed in a third level care hospital in Ecuador

Resumen Introducción: El Síndrome de Turner (ST) es una alteración cromosómica sexual causada por la ausencia parcial o completa del cromosoma X, además de mosaicismos y otras alteraciones estructurales del cromosoma X o Y; está presente en 1 de 2500 nacidas vivas. Objetivo: Describir las variantes citogenéticas de pacientes con síndrome de Turner y evaluar su asociación con el fenotipo de presentación y la edad del diagnóstico. Método: Estudio retrospectivo de corte transversal de una serie de 82 casos de síndrome de Turner. Los cariotipos fueron realizados utilizando el medio RPMI-1640; las preparaciones de cromosomas se obtuvieron utilizando técnicas estándar y se analizaron mediante bandas GTG con una resolución de 400-450 bandas, donde se contó con 20-50 metafases para reducir la probabilidad de no detección de mosaicismo. Resultados: 45 (55.6%) fueron diagnosticadas, con monosomía clásica del cromosoma X, mientras 29 (35,8%) mostraron anomalías estructurales del cromosoma X y 7 (8,6%) se asociaron a mosaicos numéricos del cromosoma X. Solo 21 (26%) pacientes fueron diagnosticadas por debajo de los 12 años, mientras el resto 60 (74%) se detectaron entre la adolescencia y la adultez. La baja estatura fue una característica universal en todos los grupos de estudio. Conclusiones: Las fórmulas cromosómicas en el síndrome de Turner pueden ser muy variadas y tener diversas implicaciones en el fenotipo; se destaca la baja talla como un criterio clínico relevante en la sospecha clínica.

Abstract Introduction: Turner Syndrome (TS) is a sexual chromosomal alteration caused by the partial or complete absence of the X chromosome, in addition to mosaicisms and other structural alterations of the X or Y chromosome; It is present in 1 in 2,500 live births. Objective: To describe the cytogenetic variants of Turner syndrome patients and to evaluate their association with the phenotype at presentation and age at diagnosis. Methods: Retrospective cross-sectional study of a series of 82 cases of Turner syndrome. Karyotypes were performed using RPMI-1640 medium; Chromosome preparations were obtained using standard techniques and analyzed by GTG banding with a resolution of 400-450 bands where 20-50 metaphases were counted to reduce the probability of missing mosaicism. Results: 45 (55.6%) were diagnosed with classic monosomy of the X chromosome, while 29 (35.8%) showed structural abnormalities of the X chromosome and 7 (8.6%) were associated with numerical mosaics of the X chromosome. Only 21 (26%) patients were diagnosed under 12 years of age, while the rest 60 (74%) were detected between adolescence and adulthood. Short stature was a universal characteristic in all study groups. Conclusions: The chromosomal formulas in Turner syndrome can be variable and have different implications in the phenotype; short stature stands out as a relevant clinical criterion in clinical suspicion.

First hitting times between a run-and-tumble particle and a stochastically gated target.

We study the statistics of the first hitting time between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of the motion of the particle, which can be absorbed by the target only in its visible phase. We obtain the mean first hitting time when the motion takes place in a finite domain with reflecting boundaries. Considering the turning rate of the particle as a tuning parameter, we find that ballistic motion represents the best strategy to minimize the mean first hitting time. However, the relative fluctuations of the first hitting time are large and exhibit nonmonotonous behaviors with respect to the turning rate or the target transition rates. Paradoxically, these fluctuations can be the largest for targets that are visible most of the time, and not for those that are mostly invisible or rapidly transiting between the two states. On the infinite line, the classical asymptotic behavior ∝t^{-3/2} of the first hitting time distribution is typically preceded, due to target intermittency, by an intermediate scaling regime varying as t^{-1/2}. The extent of this transient regime becomes very long when the target is most of the time invisible, especially at low turning rates. In both finite and infinite geometries, we draw analogies with partial absorption problems.

First Hitting Times to Intermittent Targets.

In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we study the first hitting time statistics of a one-dimensional Brownian particle searching for a target site that switches stochastically between visible and hidden phases. At high crypticity, an unexpected rate limited power-law regime emerges for the first hitting time density, which markedly differs from the classic t^{-3/2} scaling for steady targets. Our problem admits an asymptotic mapping onto a mixed, or Robin, boundary condition. Similar results are obtained with non-Markov targets and particles diffusing anomalously.

Skeletal muscle biopsy analysis in reducing body myopathy and other FHL1-related disorders.

FHL1 mutations have been associated with various disorders that include reducing body myopathy (RBM), Emery-Dreifuss-like muscular dystrophy, isolated hypertrophic cardiomyopathy, and some overlapping conditions. We report a detailed histochemical, immunohistochemical, electron microscopic, and immunoelectron microscopic analyses of muscle biopsies from 18 patients carrying mutations in FHL1: 14 RBM patients (Group 1), 3 Emery-Dreifuss muscular dystrophy patients (Group 2), and 1 patient with hypertrophic cardiomyopathy and muscular hypertrophy (Group 2). Group 1 muscle biopsies consistently showed RBs associated with cytoplasmic bodies. The RBs showed prominent FHL1 immunoreactivity whereas desmin, αB-crystallin, and myotilin immunoreactivity surrounded RBs. By electron microscopy, RBs were composed of electron-dense tubulofilamentous material that seemed to spread progressively between the myofibrils and around myonuclei. By immunoelectron microscopy, FHL1 protein was found exclusively inside RBs. Group 2 biopsies showed mild dystrophic abnormalities without RBs; only minor nonspecific myofibrillar abnormalities were observed under electron microscopy. Molecular analysis revealed missense mutations in the second FHL1 LIM domain in Group 1 patients and ins/del or missense mutations within the fourth FHL1 LIM domain in Group 2 patients. Our findings expand the morphologic features of RBM, clearly demonstrate the localization of FHL1 in RBs, and further illustrate major morphologic differences among different FHL1-related myopathies.