Diffusion on random site percolation clusters. Theory and NMR microscopy experiments with model objects

Quasi two-dimensional random site percolation model objects were fabricate based on computer generated templates. Samples consisting of two compartments, a reservoir of H$_2$O gel attached to a percolation model object which was initially filled with D$_2$O, were examined with NMR (nuclear magnetic resonance) microscopy for rendering proton spin density maps. The propagating proton/deuteron inter-diffusion profiles were recorded and evaluated with respect to anomalous diffusion parameters. The deviation of the concentration profiles from those expected for unobstructed diffusion directly reflects the anomaly of the propagator for diffusion on a percolation cluster. The fractal dimension of the random walk, $d_w$, evaluated from the diffusion measurements on the one hand and the fractal dimension, $d_f$, deduced from the spin density map of the percolation object on the other permits one to experimentally compare dynamical and static exponents. Approximate calculations of the propagator are given on the basis of the fractional diffusion equation. Furthermore, the ordinary diffusion equation was solved numerically for the corresponding initial and boundary conditions for comparison. The anomalous diffusion constant was evaluated and is compared to the Brownian case. Some ad hoc correction of the propagator is shown to pay tribute to the finiteness of the system. In this way, anomalous solutions of the fractional diffusion equation could experimentally be verified for the first time.Comment: REVTeX, 12 figures in GIF forma

Towards deterministic equations for Levy walks: the fractional material derivative

Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We derive a generalized dynamical formulation for Levy walks in which the fractional equivalent of the material derivative occurs. Our approach will be useful for the dynamical formulation of Levy walks in an external force field or in phase space for which the description in terms of the continuous time random walk or its corresponding generalized master equation are less well suited

Chord distribution functions of three-dimensional random media: Approximate first-passage times of Gaussian processes

The main result of this paper is a semi-analytic approximation for the chord distribution functions of three-dimensional models of microstructure derived from Gaussian random fields. In the simplest case the chord functions are equivalent to a standard first-passage time problem, i.e., the probability density governing the time taken by a Gaussian random process to first exceed a threshold. We obtain an approximation based on the assumption that successive chords are independent. The result is a generalization of the independent interval approximation recently used to determine the exponent of persistence time decay in coarsening. The approximation is easily extended to more general models based on the intersection and union sets of models generated from the iso-surfaces of random fields. The chord distribution functions play an important role in the characterization of random composite and porous materials. Our results are compared with experimental data obtained from a three-dimensional image of a porous Fontainebleau sandstone and a two-dimensional image of a tungsten-silver composite alloy.Comment: 12 pages, 11 figures. Submitted to Phys. Rev.

Synthesis of Various Classes of Cyanine Fluorophores and Their Application In In Vivo Tissue Imaging

A novel series of near-infrared fluorescent contrast agents was developed and characterized. Their physicochemical and optical properties were measured. By altering functional groups of cyanine fluorophores, the selective targeting of endocrine glands, exocrine glands, cartilage and bone using NIR fluorescence to visualize the targeted tissue has been reported. These agents have high specificity for tissue targeting inherent to the chemical structure of the fluorophore. After a single low-dose intravenous injection these agents have high specificity for tissue targeting inherent to the chemical structure of the fluorophore. The results lay the foundation for future improvements in optical imaging in endocrine surgery, tissue engineering, joint surgery, and cartilage-specific drug development

Unsymmetrical Trimethine Cyanine Dyes: Synthesis, Optical Properties, and Evaluations as Inhibitors of Protein Arginine Methyl Transferases

Carbocyanine dyes are a class of organic compounds that possess two nitrogen containing heterocycles that act as electron donors and acceptors connected by a conjugated methine bridge. This thesis will present the synthetic methodology of symmetrical and unsymmetrical trimethine cyanine dyes in three chapters. The first chapter is a review on the synthesis and application of unsymmetric cyanine dyes. The second will describe the synthesis of unsymmetrical trimethine cyanine dyes and how their optical properties differ from symmetrical dyes. The third chapter will not only discuss the synthetic procedure for synthesis of symmetrical trimethine cyanine dyes, but also will show how varying the N-alkyl substituents and hydrophobicity of the heterocycles affects the dyes interaction with and ability to be used as inhibitors for protein arginine methyltransferases (PRMTs). Several synthesized compounds have displayed lower IC50 values for the inhibition of PRMT1 and PRMT5 comparable to that of current inhibitors

Mean first-passage time of surface-mediated diffusion in spherical domains

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.Comment: to appear in J. Stat. Phy

Kinetics of active surface-mediated diffusion in spherically symmetric domains

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. We generalize the results of [J. Stat. Phys. {\bf 142}, 657 (2011)] and consider a biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.Comment: Published online in J. Stat. Phy

Transfer RNA-derived small RNAs in the cancer transcriptome

The cellular lifetime includes stages such as differentiation, proliferation, division, senescence and apoptosis.These stages are driven by a strictly ordered process of transcription dynamics. Molecular disruption to RNA polymerase assembly, chromatin remodelling and transcription factor binding through to RNA editing, splicing, post-transcriptional regulation and ribosome scanning can result in significant costs arising from genome instability. Cancer development is one example of when such disruption takes place. RNA silencing is a term used to describe the effects of post-transcriptional gene silencing mediated by a diverse set of small RNA molecules. Small RNAs are crucial for regulating gene expression and microguarding genome integrity.RNA silencing studies predominantly focus on small RNAs such as microRNAs, short-interfering RNAs and piwi-interacting RNAs. We describe an emerging renewal of inter-est in a‘larger’small RNA, the transfer RNA (tRNA).Precisely generated tRNA-derived small RNAs, named tRNA halves (tiRNAs) and tRNA fragments (tRFs), have been reported to be abundant with dysregulation associated with cancer. Transfection of tiRNAs inhibits protein translation by displacing eukaryotic initiation factors from messenger RNA (mRNA) and inaugurating stress granule formation.Knockdown of an overexpressed tRF inhibits cancer cell proliferation. Recovery of lacking tRFs prevents cancer metastasis. The dual oncogenic and tumour-suppressive role is typical of functional small RNAs. We review recent reports on tiRNA and tRF discovery and biogenesis, identification and analysis from next-generation sequencing data and a mechanistic animal study to demonstrate their physiological role in cancer biology. We propose tRNA-derived small RNA-mediated RNA silencing is an innate defence mechanism to prevent oncogenic translation. We expect that cancer cells are percipient to their ablated control of transcription and attempt to prevent loss of genome control through RNA silencing