Distribution of first-reaction times with target regions on boundaries of shell-like domains

We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted "onion-shell" geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.

A real-time assay for cell-penetrating peptide-mediated delivery of molecular cargos

Cell-penetrating peptides (CPPs) are capable of transporting molecules to which they are tethered across cellular membranes. Unsurprisingly, CPPs have attracted attention for their potential drug delivery applications, but several technical hurdles remain to be overcome. Chief among them is the so-called ‘endosomal escape problem,’ i.e. the propensity of CPP-cargo molecules to be endocytosed but remain entrapped in endosomes rather than reaching the cytosol. Previously, a CPP fused to calmodulin that bound calmodulin binding site-containing cargos was shown to efficiently deliver cargos to the cytoplasm, effectively overcoming the endosomal escape problem. The CPP-adaptor, “TAT-CaM,” evinces delivery at nM concentrations and more rapidly than we had previously been able to measure. To better understand the kinetics and mechanism of CPP-adaptor-mediated cargo delivery, a real-time cell penetrating assay was developed in which a flow chamber containing cultured cells was installed on the stage of a confocal microscope to allow for observation ab initio. Also examined in this study was an improved CPP-adaptor that utilizes naked mole rat (Heterocephalus glaber) calmodulin in place of human and results in superior internalization, likely due to its lesser net negative charge. Adaptor-cargo complexes were delivered into the flow chamber and fluorescence intensity in the midpoint of baby hamster kidney cells was measured as a function of time. Delivery of 400 nM cargo was observed within seven minutes and fluorescence continued to increase linearly as a function of time. Cargo-only control experiments showed that the minimal uptake which occurred independently of the CPP-adaptor resulted in punctate localization consistent with endosomal entrapment. A distance analysis was performed for cell-penetration experiments in which CPP-adaptor-delivered cargo showing wider dispersions throughout cells as compared to an analogous covalently-bound CPP-cargo. Small molecule endocytosis inhibitors did not have significant effects upon delivery. The real-time assay is an improvement upon static endpoint assays and should be informative in a broad array of applications.

A real-time assay for cell-penetrating peptide-mediated delivery of molecular cargos

Cell-penetrating peptides (CPPs) are capable of transporting molecules to which they are tethered across cellular membranes. Unsurprisingly, CPPs have attracted attention for their potential drug delivery applications, but several technical hurdles remain to be overcome. Chief among them is the so-called ‘endosomal escape problem,’ i.e. the propensity of CPP-cargo molecules to be endocytosed but remain entrapped in endosomes rather than reaching the cytosol. Previously, a CPP fused to calmodulin that bound calmodulin binding site-containing cargos was shown to efficiently deliver cargos to the cytoplasm, effectively overcoming the endosomal escape problem. The CPP-adaptor, “TAT-CaM,” evinces delivery at nM concentrations and more rapidly than we had previously been able to measure. To better understand the kinetics and mechanism of CPP-adaptor-mediated cargo delivery, a real-time cell penetrating assay was developed in which a flow chamber containing cultured cells was installed on the stage of a confocal microscope to allow for observation ab initio . Also examined in this study was an improved CPP-adaptor that utilizes naked mole rat ( Heterocephalus glaber ) calmodulin in place of human and results in superior internalization, likely due to its lesser net negative charge. Adaptor-cargo complexes were delivered into the flow chamber and fluorescence intensity in the midpoint of baby hamster kidney cells was measured as a function of time. Delivery of 400 nM cargo was observed within seven minutes and fluorescence continued to increase linearly as a function of time. Cargo-only control experiments showed that the minimal uptake which occurred independently of the CPP-adaptor resulted in punctate localization consistent with endosomal entrapment. A distance analysis was performed for cell-penetration experiments in which CPP-adaptor-delivered cargo showing wider dispersions throughout cells as compared to an analogous covalently-bound CPP-cargo. Small molecule endocytosis inhibitors did not have significant effects upon delivery. The real-time assay is an improvement upon static endpoint assays and should be informative in a broad array of applications.

Monte Carlo tracking drift-diffusion trajectories algorithm for solving narrow escape problems

This study deals with a narrow escape problem, a well-know difficult problem of evaluating the probability for a diffusing particle to reach a small part of a boundary far away from the starting position of the particle. A direct simulation of the diffusion trajectories would take an enormous computer simulation time. Instead, we use a different approach which drastically improves the efficiency of the diffusion trajectory tracking algorithm by introducing an artificial drift velocity directed to the target position. The method can be efficiently applied to solve narrow escape problems for domains of long extension in one direction which is the case in many practical problems in biology and chemistry. The algorithm is meshless both in space and time, and is well applied to solve high-dimensional problems in complicated domains. We present in this paper a detailed numerical analysis of the method for the case of a rectangular parallelepiped. Both stationary and transient diffusion problems are handled.

The Kramers problem for SDEs driven by small, accelerated Lévy noise with exponentially light jumps

We establish Freidlin–Wentzell results for a nonlinear ordinary differential equation starting close to the stable state [Formula: see text], say, subject to a perturbation by a stochastic integral which is driven by an [Formula: see text]-small and [Formula: see text]-accelerated Lévy process with exponentially light jumps. For this purpose, we derive a large deviations principle for the stochastically perturbed system using the weak convergence approach developed by Budhiraja, Dupuis, Maroulas and collaborators in recent years. In the sequel, we solve the associated asymptotic first escape problem from the bounded neighborhood of [Formula: see text] in the limit as [Formula: see text] which is also known as the Kramers problem in the literature.