Random Trap Research Articles

Duality between random trap and barrier models

We discuss the physical consequences of a duality between two models with quenched disorder, in which particles propagate in one dimension among random traps or across random barriers. We derive an exact relation between their diffusion fronts at fixed disorder and deduce from this that their disorder-averaged diffusion fronts are exactly equal. We use effective dynamics schemes to isolate the different physical processes by which particles propagate in the models and discuss how the duality arises from a correspondence between the rates for these different processes.

Brownian particles in random and quasicrystalline potentials: How they approach the equilibrium

We study the Brownian motion of an ensemble of single colloidal particles in a random square and a quasicrystalline potential when they start from non-equlibrium. For both potentials, Brownian dynamics simulations reveal a widespread subdiffusive regime before the diffusive long-time limit is reached in thermal equilibrium. We develop a random trap model based on a distribution for the depths of trapping sites that reproduces the results of the simulations in detail. Especially, it gives analytic formulas for the long-time diffusion constant and the relaxation time into the diffusive regime. Aside from detailed differences, our work demonstrates that quasicrystalline potentials can be used to mimic aspects of random potentials.

Occupation times of random walks in confined geometries: From random trap model to diffusion-limited reactions

We consider a random walk in confined geometry, starting from a site and eventually reaching a target site. We calculate analytically the distribution of the occupation time on a third site, before reaching the target site. The obtained distribution is exact and completely explicit in the case or parallelepipedic confining domains. We discuss implications of these results in two different fields: The mean first passage time for the random trap model is computed in dimensions greater than 1 and is shown to display a nontrivial dependence with the source and target positions. The probability of reaction with a given imperfect center before being trapped by another one is also explicitly calculated, revealing a complex dependence both in geometrical and chemical parameters.

DNA Damage Photoinduced by Titanium Dioxide in the Presence of Anionic Vesicles under UV Illumination: Influence of Sodium Chloride Concentration

The DNA damage caused by TiO2 under in vitro conditions by UV-A exposure in the presence of anionic vesicles of Aerosol OT (AOT) was investigated. The supercoiled form (S) in DNA plasmids was converted to the linear form (L) via the relaxed form (R). The DNA damage was slower in the presence of AOT vesicles prepared in aqueous NaCl solution. Moreover, the presence of AOT vesicles in solution after 6 h of UV irradiation was confirmed with an optical microscope. Probably, a fraction of the DNA was protected by random trapping during sonication. However, the addition of NaCl needed for the vesicle formation can decrease the TiO2 activity. On the other hand, in the absence of vesicles the NaCl concentration led to a profound influence on the adsorption of DNA onto the TiO2 surface. During UV irradiation, the degradation rate of DNA increased with increasing the salt concentration. Solutions containing vesicles were prepared at various NaCl concentrations between 10 mM and 75 mM. Consequently, the salt concentration had no significant effect on the DNA damage. The presence of NaCl can play a deleterious role during the photoinduced process. However, the encapsulation of a fraction of DNA is not excluded. In such conditions, the DNA could be protected against the reactive oxygen species.

Diffusion‐Influenced Reversible Trapping Problem in the Presence of an External Field

We investigate the field effect on the diffusion-influenced reversible trapping problem in one dimension. The exact Green function for a particle undergoing diffusive motion between two static reversible traps with a constant external field is obtained. From the Green function, we derive the various survival probabilities. Two types of trap distribution for the many-body problem are considered, the periodic and random distributions. The mean survival probability is obtained for the crossing-forbidden case for the two types of trap distribution. For the periodic distribution it decays exponentially. For the random trap distribution, similar to the irreversible case, there exists a critical field strength at which the long time asymptotic behavior undergoes a kinetic transition from the power law to exponential behaviors. The difference between equilibrium concentrations for the two types of trap distribution due to the fluctuation effect of trap concentration vanishes as the field strength increases.

Herpetofaunal Diversity of Alligator River National Wildlife Refuge, North Carolina

In the past century, habitat alteration and fragmentation have increased dramatically, which increases the need for improving our understanding of how species and biological communities react to these modifications. A national strategy on biological diversity has focused attention on how these habitat modifications affect species, especially herpetofauna (i.e., changes in species richness, community evenness and similarity, and dominant/rare species). As part of this strategy, we surveyed Alligator River National Wildlife Refuge, a coastal, mixed second-growth forested swamp (MFS) and pocosin wetland (PW), in North Carolina for amphibians and reptiles from September 2000 to August 2001. We randomly selected three sites (3 x 3 km) in two major habitat types (MFS, PW) and completed random surveys and trapping using transects, quadrats, nighttime aural road surveys, drift fences, canal transects, coverboards, incidental captures, and evening road surveys. We also col- lected herpetofauna opportunistically throughout the refuge to establish an updated species list. For analysis, we used Shannon-Weiner species diversity (H'), evenness (J'), species richness and species detectability (COMDYN4), and community percent similarity index to determine herpetofaunal community differences. We estimated 39 species in MFS and 32 species in PW (P < 0.10). Species detectability was similar between habitats (0.84 to 0.86). More reptilian species (+ 31%) inhabited MFS than PW, but estimated amphibian species richness was identical (17 spp.). H' was higher (P < 0.0001) for PW (2.6680) than for MFS (2.1535) because of lower J' in the latter (0.6214 vs. 0.8010). Dominance of three Rana species caused lower J' and H' in MFS. Similarity between the communities was 56.6%; we estimated 22-24 species in common for each habitat (95% CI = 18 to 31 spp.). We verified 49 of the 52 herpetofaunal species on the refuge that were known to exist in the area. Restoration of natural water flows may affect herpetofaunal diversity, which may be monitored during a restoration project. Currently, the refuge retains historical levels of herpetofaunal diversity for the region.

Two ways to trap a gene in mice

Two ways to trap a gene in mice

Gene targeting using a promoterless gene trap vector (“targeted trapping”) is an efficient method to mutate a large fraction of genes

A powerful tool for postgenomic analysis of mammalian gene function is gene targeting in mouse ES cells. We report that homologous recombination using a promoterless gene trap vector ("targeting trapping") yields targeting frequencies averaging above 50%, a significant increase compared with current approaches. These high frequencies appear to be due to the stringency of selection with promoterless constructs, because most random insertions are silent and eliminated by drug selection. The promoterless design requires that the targeted gene be expressed in ES cells at levels exceeding a certain threshold (which we estimate to be approximately 1% of the transferrin receptor gene expression level, for the secretory trap vector used here). Analysis of 127 genes that had been trapped by random (nontargeted) gene trapping with the same vector shows that virtually all are expressed in ES cells above this threshold, suggesting that targeted and random trapping share similar requirements for expression levels. In a random sampling of 130 genes encoding secretory proteins, about half were expressed above threshold, suggesting that about half of all secretory genes are accessible by either targeted or random gene trapping. The simplicity and high efficiency of the method facilitate systematic targeting of a large fraction of the genome by individual investigators and large-scale consortia alike.

Gene Trap Mutagenesis-based Forward Genetic Approach Reveals That the Tumor Suppressor OVCA1 Is a Component of the Biosynthetic Pathway of Diphthamide on Elongation Factor 2

OVCA1 is a tumor suppressor identified by positional cloning from chromosome 17p13.3, a hot spot for chromosomal aberration in breast and ovarian cancers. It has been shown that expression of OVCA1 is reduced in some tumors and that it regulates cell proliferation, embryonic development, and tumorigenesis. However, the biochemical function of OVCA1 has remained unknown. Recently, we isolated a novel mutant resistant to diphtheria toxin and Pseudomonas exotoxin A from the gene trap insertional mutants library of Chinese hamster ovary cells. In this mutant, the Ovca1 gene was disrupted by gene trap mutagenesis, and this disruption well correlated with the toxin-resistant phenotype. We demonstrated direct evidence that the tumor suppressor OVCA1 is a component of the biosynthetic pathway of diphthamide on elongation factor 2, the target of bacterial ADP-ribosylating toxins. A functional genetic approach utilizing the random gene trap mutants library of mammalian cells should become a useful strategy to identify the genes responsible for specific phenotypes.

Suppression of nonsense-mediated mRNA decay permits unbiased gene trapping in mouse embryonic stem cells

An international collaborative project has been proposed to inactivate all mouse genes in embryonic stem (ES) cells using a combination of random and targeted insertional mutagenesis techniques. Random gene trapping will be the first choice in the initial phase, and gene-targeting experiments will then be carried out to individually knockout the remaining ‘difficult-to-trap’ genes. One of the most favored techniques of random insertional mutagenesis is promoter trapping, which only disrupts actively transcribed genes. Polyadenylation (poly-A) trapping, on the other hand, can capture a broader spectrum of genes including those not expressed in the target cells, but we noticed that it inevitably selects for the vector integration into the last introns of the trapped genes. Here, we present evidence that this remarkable skewing is caused by the degradation of a selectable-marker mRNA used for poly-A trapping via an mRNA-surveillance mechanism, nonsense-mediated mRNA decay (NMD). We also report the development of a novel poly-A-trap strategy, UPATrap, which suppresses NMD of the selectable-marker mRNA and permits the trapping of transcriptionally silent genes without a bias in the vector-integration site. We believe the UPATrap technology enables a simple and straightforward approach to the unbiased inactivation of all mouse genes in ES cells.

Gene trap mutagenesis-based forward genetic approach reveals that the tumor suppressor OVCA1 is a component of the biosynthetic pathway of diphthamide on elongation factor-2

OVCA1 is a tumor suppressor identified by positional cloning from chromosome 17p13.3, a hot spot for chromosomal aberration in breast and ovarian cancers. It has been shown that expression of OVCA1 is reduced in some tumors and that it regulates cell proliferation, embryonic development, and tumorigenesis. However, the biochemical function of OVCA1 has remained unknown. Recently, we isolated a novel mutant resistant to diphtheria toxin and Pseudomonas exotoxin A from the gene trap insertional mutants library of Chinese hamster ovary cells. In this mutant, the Ovca1 gene was disrupted by gene trap mutagenesis, and this disruption well correlated with the toxin-resistant phenotype. We demonstrated direct evidence that the tumor suppressor OVCA1 is a component of the biosynthetic pathway of diphthamide on elongation factor 2, the target of bacterial ADP-ribosylating toxins. A functional genetic approach utilizing the random gene trap mutants library of mammalian cells should become a useful strategy to identify the genes responsible for specific phenotypes.

Random walk and trapping processes on scale-free networks

In this work I investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. I perform extensive simulations for the calculation of the mean squared displacement, the network coverage, and the survival probability on a network with a concentration c of static traps. It is shown that the random walkers remain close to their origin, but cover a large part of the network at the same time. This behavior is markedly different than usual random walk processes in the literature. For the trapping problem I numerically compute Phi(n,c) , the survival probability of mobile species at time n , as a function of the concentration of trap nodes, c . Comparison of these results to the Rosenstock approximation indicate that this is an adequate description for networks with 2<gamma<3 and yield an exponential decay. For gamma>3 the behavior is more complicated and one needs to employ a truncated cumulant expansion.

Expression profiling with arrays of randomly disrupted genes in mouse embryonic stem cells leads to in vivo functional analysis.

DNA arrays are capable of profiling the expression patterns of many genes in a single experiment. After finding a gene of interest in a DNA array, however, labor-intensive gene-targeting experiments sometimes must be performed for the in vivo analysis of the gene function. With random gene trapping, on the other hand, it is relatively easy to disrupt and retrieve hundreds of genes/gene candidates in mouse embryonic stem (ES) cells, but one could overlook potentially important gene-disruption events if only the nucleotide sequences and not the expression patterns of the trapped DNA segments are analyzed. To combine the benefits of the above two experimental systems, we first created approximately 900 genetrapped mouse ES cell clones and then constructed arrays of cDNAs derived from the disrupted genes. By using these arrays, we identified a novel gene predominantly expressed in the mouse brain, and the corresponding ES cell clone was used to produced mice homozygous for the disrupted allele of the gene. Detailed analysis of the knockout mice revealed that the gene trap vector completely abolished gene expression downstream of its integration site. Therefore, identification of a gene or novel gene candidate with an interesting expression pattern by using this type of DNA array immediately allows the production of knockout mice from an ES cell clone with a disrupted allele of the sequence of interest.

Spatial gliding, temporal trapping, and anomalous transport

We introduce and study a model of stochastic dynamics, governed by Markovian laws of motion in a phase space filled with random traps. The resulting (non-Markovian) stochastic trapped motion alternates intermittently between periods of spatial gliding, where the motion ‘glides’ the underlying Markovian dynamics, and periods of temporal trapping, where the motion is halted in random traps. We investigate the asymptotics and scaling limits of this model. We prove that when the random trappings are heavy-tailed then Mittag–Leffler functions and probability laws emerge and govern the functional structure and statistics of the system, and that the time flow has a random fractal structure whose fractal exponent (dimension) is determined by the ‘heaviness’ of the trappings. We study the effect of random trapping on general Lévy dynamics. We prove that subjecting Lévy dynamics to heavy-tailed trapping will always result in: (i) sub-diffusive behavior—when the underlying Lévy dynamics are of finite variance; and (ii) space–time fractal behavior—when the underlying Lévy dynamics are scale-invariant. Furthermore, we explore the issue of first exit times. To that end, a general Feynman–Kac framework for trapped processes is developed, and a method of transforming ‘trapped’ Feynman–Kac equations to ‘standard’ ones is established. The study of first exit times enables us to quantitatively connect macroscopic observations to microscopic behavior in general Markovian dynamics subjected to random trapping. In the case of Lévy dynamics, first exit times from balls are computed, and the relationships between their statistics and the statistics of the trapped motion are derived.

A Random Sampling of Salt Marsh Harvest Mice in a Muted Tidal Marsh

Successful conservation of an endangered species, such as the salt marsh harvest mouse (SMHM; Reithrodontomys raviventris), requires detailed knowledge of the species' habitat and microhabitat associations. Identifying critical habitat features, however; can be problematic. We designed and implemented a randomized sampling regime with a large sample size of sites (n = 40) to identify potential microhabitat requirements or habitat constraints affecting the localized distribution of the southern subspecies of SMHM (R. r. raviventris) We used the random trapping technique to determine SMHM distribution across a muted-tidal, predominantly pickleweed (Salicornia virginica) marsh at the Dot Edwards San Francisco Bay National Wildlife Refuge, California, USA. We tested the null hypothesis that this species' distribution is not associated with pickleweed salinity, sympatric rodent species, or the site location (peripheral vs. interior). We found SMHM throughout the marsh and detected no association with interior versus peripheral sites. We detected no associations between SMHM and sympatric rodent species. Pickleweed salinities ranged between 200 and 899 mmol/kg Cl - . In the prebreeding phase. SMHM were randomly dispersed. However, in the breeding and postbreeding phases, the population was clumped and associated with sites having mid-range (500-699 mmol/kg Cl - ) salinities in pickleweed. Managers and biologists attempting to conserve SMHM in managed marshes need to be concerned with maintaining this mid-range salinity level in pickleweed. We found that SMHM were absent from areas of low salinity (200-499 mmol/kg Cl - ) and were rare in hypersaline areas (699 mmol/kg Cl - ). Mid-range pickleweed salinities can be created and maintained in managed SMHM habitat only via fresh infusions of sea water on a natural tidal basis.

Discrete tunneling current fluctuations in metal–water–metal tunnel junctions

We have studied electron tunneling through water between two metal electrodes supported on a solid substrate and observed random fluctuations in the tunneling current between two discrete levels. The two-level fluctuations persist when changing the concentration and the valency of the ions, and pH of the water solutions. A given two-level fluctuation is, in general, not affected by the applied bias voltage, but it is usually disrupted by changing the width of the tunnel gap. We attribute the discrete conductance fluctuations to random trapping or escaping of a single electron in or from a localized state in the tunnel gap.

Hopping diffusion of two coupled particles in the random trap model.

We show that the hopping dynamics of two strongly connected particles can be mapped exactly to single particle dynamics. In this way we are able to calculate the exact asymptotic diffusion coefficient of two connected particles on a linear chain in the random trap model. In particular we calculate the diffusion coefficient for exponentially distributed site energies and show that there exists a critical temperature below which a subdiffusive behavior appears. It turns out that this critical temperature is twice higher than the critical temperature in the single particle case [S. Havlin, B. L. Trus, and G. H. Weiss, J. Phys. A: Math. Gen. 19, L817 (1986)].

Deviations from perfect memory in spin glass temperature cycling experiments

We study the deviations from perfect memory in negative temperature cycle spin glass experiments. It is known that the a.c. susceptibility after the temperature is raised back to its initial value is superimposed to the reference isothermal curve for large enough temperature jumps ΔT (perfect memory). For smaller ΔT, the deviation from this perfect memory has a striking non monotonous behavior: the `memory anomaly' is negative for small ΔT's, becomes positive for intermediate ΔT's, before vanishing for still larger ΔT's. We show that this interesting behavior can be reproduced by simple Random Energy trap models. We discuss an alternative interpretation in terms of droplets and temperature chaos.

Electrophoresis of Composite Molecular Objects. 2. Competition between Sieving and Frictional Effects in Polymer Solutions

We previously showed that labeling one end of single-stranded DNA molecules with a neutral label like streptavidin increases the interband separation of these hybrid DNA molecules when they are electrophoresed in denaturing cross-linked polyacrylamide gels. This separation process is called trapping electrophoresis because the dynamical properties of the analytes are strongly affected by random steric trapping in the gel. End-labeled ssDNA molecules can also be electrophoretically separated in free solution. This process is called end-labeled free solution electrophoresis, and the separation is then due to the extra hydrodynamic friction provided by the streptavidin label. In this article, we present a study of the capillary electrophoresis of DNA molecules end-labeled with streptavidin in the presence of non-cross-linked polymer solutions ranging from semidilute to ultradilute conditions. In the semidilute limit, sieving interactions dominate, and small DNA molecules move faster than larger ones. In the ultradilute limit, however, we recover free-solution-like separations where small molecules are more retarded than larger ones. We also observe a fascinating transition between these two regimes, for intermediate polymer concentrations and DNA sizes, where the competition between trapping, sieving, and frictional effects leads to nonmonotonic mobility−size relationships. Our theoretical analysis suggests a universal relationship between the mobility of labeled and unlabeled DNA molecules in all electrophoretic conditions.

The Random Trap Model and the D&lt;sub&gt;0&lt;/sub&gt;-Q Correlation in Disordered Structures

The Random Trap Model and the D&lt;sub&gt;0&lt;/sub&gt;-Q Correlation in Disordered Structures