Diffusive scaling of the Kob-Andersen model in Zd\mathbb{Z}^d

We consider the Kob-Andersen model, a cooperative lattice gas with kinetic constraints which has been widely analyzed in the physics literature in connection with the study of the liquid/glass transition. We consider the model in a finite box of linear size $L$ with sources at the boundary. Our result, which holds in any dimension and significantly improves upon previous ones, establishes for any positive vacancy density $q$ a purely diffusive scaling of the relaxation time $T_{\rm rel}$ of the system. Furthermore, as $q\downarrow 0$ we prove upper and lower bounds on $L^{-2} T_{\rm rel} (q,L)$ which agree with the physicists belief that the dominant equilibration mechanism is a cooperative motion of rare large droplets of vacancies. The main tools combine a recent set of ideas and techniques developed to establish universality results for kinetically constrained spin models, with methods from bootstrap percolation, oriented percolation and canonical flows for Markov chains

Self-Diffusion Coefficient in the Kob-Andersen Model

The Kob-Andersen model is a fundamental example of a kinetically constrained lattice gas, that is, an interacting particle system with Kawasaki type dynamics and kinetic constraints. In this model, a particle is allowed to jump when sufficiently many neighboring sites are empty. We study the motion of a single tagged particle and in particular its convergence to a Brownian motion. Previous results showed that the path of this particle indeed converges in diffusive time-scale, and the purpose of this paper is to study the rate of decay of the self-diffusion coefficient for large densities. We find upper and lower bounds matching to leading behavior

Hausdorff Dimension of the Record Set of a Fractional Brownian Motion

We prove that the Hausdorff dimension of the record set of a fractional Brownian motion with Hurst parameter $H$ equals $H$

Removal of Hepatitis C Virus-Infected Cells by a Zymogenized Bacterial Toxin

Hepatitis C virus (HCV) infection is a major cause of chronic liver disease and has become a global health threat. No HCV vaccine is currently available and treatment with antiviral therapy is associated with adverse side effects. Moreover, there is no preventive therapy for recurrent hepatitis C post liver transplantation. The NS3 serine protease is necessary for HCV replication and represents a prime target for developing anti HCV therapies. Recently we described a therapeutic approach for eradication of HCV infected cells that is based on protein delivery of two NS3 protease-activatable recombinant toxins we named “zymoxins”. These toxins were inactivated by fusion to rationally designed inhibitory peptides via NS3-cleavable linkers. Once delivered to cells where NS3 protease is present, the inhibitory peptide is removed resulting in re-activation of cytotoxic activity. The zymoxins we described suffered from two limitations: they required high levels of protease for activation and had basal activities in the un-activated form that resulted in a narrow potential therapeutic window. Here, we present a solution that overcame the major limitations of the “first generation zymoxins” by converting MazF ribonuclease, the toxic component of the E. coli chromosomal MazEF toxin-antitoxin system, into an NS3-activated zymoxin that is introduced to cells by means of gene delivery. We constructed an expression cassette that encodes for a single polypeptide that incorporates both the toxin and a fragment of its potent natural antidote, MazE, linked via an NS3-cleavable linker. While covalently paired to its inhibitor, the ribonuclease is well tolerated when expressed in naïve, healthy cells. In contrast, activating proteolysis that is induced by even low levels of NS3, results in an eradication of NS3 expressing model cells and HCV infected cells. Zymoxins may thus become a valuable tool in eradicating cells infected by intracellular pathogens that express intracellular proteases