A stochastic model for the stepwise motion in actomyosin dynamics

A jump-diffusion process is proposed to describe the displacements performed by single myosin heads along actin filaments during the rising phases. The process consists of the superposition of a Wiener and a jump process, with jumps originated by sequences of Poisson-distributed energy-supplying pulses. In a previous paper, the amplitude of the jumps was described by a mixture of two Gaussian distributions. To embody the effects of ATP hydrolysis, we now refine such a model by assuming that the jumps' amplitude is described by a mixture of three Gaussian distributions. This model has been inspired by the experimental data of T. Yanagida and his co-workers concerning observations at single molecule processes level.Comment: 9 pages, 4 figure

Shock models governed by an inverse gamma mixed Poisson process

We study three classes of shock models governed by an inverse gamma mixed Poisson process (IGMP), namely a mixed Poisson process with an inverse gamma mixing distribution. In particular, we analyze (1) the extreme shock model, (2) the delta-shock model, and the (3) cumulative shock model. For the latter, we assume a constant and an exponentially distributed random threshold and consider different choices for the distribution of the amount of damage caused by a single shock. For all the treated cases, we obtain the survival function, together with the expected value and the variance of the failure time. Some properties of the inverse gamma mixed Poisson process are also disclosed

Piecewise deterministic processes following two alternating patterns

We propose a wide generalization of known results related to the telegraph process. Functionals of the simple telegraph process on a straight line and their generalizations on an arbitrary state space are studied. © Applied Probability Trust 2019

Younger age at onset and sex predict celiac disease in children and adolescents with type 1 diabetes: an Italian multicenter study

OBJECTIVE— To estimate the prevalence of biopsy-confirmed celiac disease in Italian children and adolescents with type 1 diabetes and to assess whether age at onset of type 1 diabetes is independently associated with diagnosis of celiac disease. RESEARCH DESIGNANDMETHODS— The study group was a clinic-based cohort of children and adolescents with type 1 diabetes cared for in 25 Italian centers for childhood diabetes. Yearly screening for celiac disease was performed using IgA/IgG anti-gliadin and IgA anti-endomysium antibodies. RESULTS— Of the 4,322 children and adolescents (age 11.8 4.2 years) identified with type 1 diabetes, biopsy-confirmed celiac disease was diagnosed in 292 (prevalence 6.8%, 95% confidence interval [CI] 6.0 –7.6), with a higher risk seen in girls than in boys (odds ratio [OR] 1.93, 1.51–2.47). In 89% of these, diabetes was diagnosed before celiac disease. In logistic regression analyses, being younger at onset of diabetes, being female, and having a diagnosis of a thyroid disorder were independently associated with the risk of having diabetes and celiac disease. In comparison with subjects who were older than 9 years at onset of diabetes, subjects who were younger than 4 years at onset had an OR of 3.27 (2.20–4.85). CONCLUSIONS— We have provided evidence that 1) the prevalence of biopsy-confirmed celiac disease in children and adolescents with type 1 diabetes is high (6.8%); 2) the risk of having both diseases is threefold higher in children diagnosed with type 1 diabetes at age 4 years than in those age 9 years; and 3) girls have a higher risk of having both diseases than boys

Certain functionals of squared telegraph processes

We investigate the stochastic process defined as the square of the (integrated) symmetric telegraph process. Specifically, we obtain its probability law and a closed form expression of the moment generating function. Some results on the first-passage time through a fixed positive level are also provided. Moreover, we analyze some functionals Φ(⋅,⋅) of two independent squared telegraph processes, both in the case Φ(u,v)=u+v and Φ(u,v)=u*v. Starting from this study, we provide some results on the probability density functions of the two-dimensional radial telegraph process and of the product of two independent symmetric telegraph processes. Some of the expressions obtained are given in terms of new results about derivatives of hypergeometric functions with respect to parameters

Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. This kind of processes are useful in the study of chain molecular diffusions. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subordinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in [Journal of Statistical Physics 154 (2014), 1352–1364]

Some results on brownian motion perturbed by alternating jumps in biological modeling

We consider the model of random evolution on the real line consisting in a Brownian motion perturbed by alternating jumps. We give the probability density of the process and pinpoint a connection with the limit density of a telegraph process subject to alternating jumps. We study the first-crossing-time probability in two special cases, in the presence of a constant upper boundary. © 2013 Springer-Verlag Berlin Heidelberg

On modeling the rising phase of myosin head displacements in single molecules processes

We consider a jump-diffusion process that appears to be suitable to describe the dis-placement performed during the rising phase by a single myosin head along an actin filament as reported in numerous current publications by T. Yanagida and his co-workers. We obtain the transition density of the considered process under the Markovian assumption that the instants of occurrence of the jumps are distributed according to a Poisson process. Two different distributions for the random amplitude of the jumps are considered in detail: the Gaussian distribution and a mixture of two Gaussian distributions. By means of the present phenomenological model, certain significant analogies and qualitative agreements with the biological data are pointed out