Extreme value statistics of mutation accumulation in renewing cell populations

The emergence of a predominant phenotype within a cell population is often triggered by the chance accumulation of a sequence of rare genomic DNA mutations within a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to bypass their natural defense mechanism. The risk of such an event is thus determined by the extremal accumulation of mutations across tissue cells. To address this risk, here we study the statistics of the maximum mutation numbers in a generic, but tested, model of a renewing cell population. By drawing an analogy between the genealogy of a cell population and the theory of branching random walks, we obtain analytical estimates for the probability of exceeding a threshold number of mutations to trigger a proliferative advantage of a cell over its neighbors, and determine how the statistical distribution of maximum mutation numbers scales with age and cell population size.EPSR

Mixed population of competing TASEPs with a shared reservoir of particles

We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths, entry and exit rates, competing for a finite reservoir of particles. We present relations for the partitioning of particles between the reservoir and the lattices: these relations allow us to show that competition for particles can have non-trivial effects on the phase behavior of individual lattices. For a system with non-identical lattices, we find that when a subset of lattices undergoes a phase transition from low to high density, the entire set of lattice currents becomes independent of total particle number. We generalize our approach to systems with a continuous distribution of lattice parameters, for which we demonstrate that measurements of the current carried by a single lattice type can be used to extract the entire distribution of lattice parameters. Our approach applies to populations of TASEPs with any distribution of lattice parameters, and could easily be extended beyond the mean-field case.Comment: 12 pages, 8 figure

Single-Bottleneck Approximation for Driven Lattice Gases with Disorder and Open Boundary Conditions

We investigate the effects of disorder on driven lattice gases with open boundaries using the totally asymmetric simple exclusion process as a paradigmatic example. Disorder is realized by randomly distributed defect sites with reduced hopping rate. In contrast to equilibrium, even macroscopic quantities in disordered non-equilibrium systems depend sensitively on the defect sample. We study the current as function of the entry and exit rates and the realization of disorder and find that it is, in leading order, determined by the longest stretch of consecutive defect sites (single-bottleneck approximation, SBA). Using results from extreme value statistics the SBA allows to study ensembles with fixed defect density which gives accurate results, e.g. for the expectation value of the current. Corrections to SBA come from effective interactions of bottlenecks close to the longest one. Defects close to the boundaries can be described by effective boundary rates and lead to shifts of the phase transitions. Finally it is shown that the SBA also works for more complex models. As an example we discuss a model with internal states that has been proposed to describe transport of the kinesin KIF1A.Comment: submitted to J. Stat. Mec

Particle interactions and lattice dynamics: Scenarios for efficient bidirectional stochastic transport?

Intracellular transport processes driven by molecular motors can be described by stochastic lattice models of self-driven particles. Here we focus on bidirectional transport models excluding the exchange of particles on the same track. We explore the possibility to have efficient transport in these systems. One possibility would be to have appropriate interactions between the various motors' species, so as to form lanes. However, we show that the lane formation mechanism based on modified attachment/detachment rates as it was proposed previously is not necessarily connected to an efficient transport state and is suppressed when the diffusivity of unbound particles is finite. We propose another interaction mechanism based on obstacle avoidance that allows to have lane formation for limited diffusion. Besides, we had shown in a separate paper that the dynamics of the lattice itself could be a key ingredient for the efficiency of bidirectional transport. Here we show that lattice dynamics and interactions can both contribute in a cooperative way to the efficiency of transport. In particular, lattice dynamics can decrease the interaction threshold beyond which lanes form. Lattice dynamics may also enhance the transport capacity of the system even when lane formation is suppressed.Comment: 25 pages, 17 figures, 2 table

Asymmetric Exclusion Processes with Disorder: Effect of Correlations

Multi-particle dynamics in one-dimensional asymmetric exclusion processes with disorder is investigated theoretically by computational and analytical methods. It is argued that the general phase diagram consists of three non-equilibrium phases that are determined by the dynamic behavior at the entrance, at the exit and at the slowest defect bond in the bulk of the system. Specifically, we consider dynamics of asymmetric exclusion process with two identical defect bonds as a function of distance between them. Two approximate theoretical methods, that treat the system as a sequence of segments with exact description of dynamics inside the segments and neglect correlations between them, are presented. In addition, a numerical iterative procedure for calculating dynamic properties of asymmetric exclusion systems is developed. Our theoretical predictions are compared with extensive Monte Carlo computer simulations. It is shown that correlations play an important role in the particle dynamics. When two defect bonds are far away from each other the strongest correlations are found at these bonds. However, bringing defect bonds closer leads to the shift of correlations to the region between them.Comment: 11 pages, 15 eps figures, RevtexI

Suitability versus fidelity for rating single-photon guns

The creation of specified quantum states is important for most, if not all, applications in quantum computation and communication. The quality of the state preparation is therefore an essential ingredient in any assessment of a quantum-state gun. We show that the fidelity, under the standard definitions is not sufficient to assess quantum sources, and we propose a new measure of suitability that necessarily depends on the application for the source. We consider the performance of single-photon guns in the context of quantum key distribution (QKD) and linear optical quantum computation. Single-photon sources for QKD need radically different properties than sources for quantum computing. Furthermore, the suitability for single-photon guns is discussed explicitly in terms of experimentally accessible criteria.Comment: 4 pages, 2 figures Revised per referee suggestion

Validation of DNA probes for molecular cytogenetics by mapping onto immobilized circular DNA

<p>Abstract</p> <p>Background</p> <p>Fluorescence <it>in situ </it>hybridization (FISH) is a sensitive and rapid procedure to detect gene rearrangements in tumor cells using non-isotopically labeled DNA probes. Large insert recombinant DNA clones such as bacterial artificial chromosome (BAC) or P1/PAC clones have established themselves in recent years as preferred starting material for probe preparations due to their low rates of chimerism and ease of use. However, when developing probes for the quantitative analysis of rearrangements involving genomic intervals of less than 100 kb, careful probe selection and characterization are of paramount importance.</p> <p>Results</p> <p>We describe a sensitive approach to quality control probe clones suspected of carrying deletions or for measuring clone overlap with near kilobase resolution. The method takes advantage of the fact that P1/PAC/BAC's can be isolated as circular DNA molecules, stretched out on glass slides and fine-mapped by multicolor hybridization with smaller probe molecules. Two examples demonstrate the application of this technique: mapping of a gene-specific ~6 kb plasmid onto an unusually small, ~55 kb circular P1 molecule and the determination of the extent of overlap between P1 molecules homologous to the human NF-κB2 locus.</p> <p>Conclusion</p> <p>The relatively simple method presented here does not require specialized equipment and may thus find widespread applications in DNA probe preparation and characterization, the assembly of physical maps for model organisms or in studies on gene rearrangements.</p

Extra c-myc oncogene copies in high risk cutaneous malignant melanoma and melanoma metastases

Amplification and overexpression of the c-myc gene have been associated with neoplastic transformation in a plethora of malignant tumours. We applied interphase fluorescence in situ hybridization (FISH) with a locus-specific probe for the c-myc gene (8q24) in combination with a corresponding chromosome 8 α-satellite probe to evaluate genetic alterations in 8 primary melanomas and 33 advanced melanomas and compared it to 12 melanocytic nevi, 7 safety margins and 2 cases of normal skin. Additionally, in metaphase spreads of 7 melanoma cell lines a whole chromosome 8 paint probe was used. We investigated the functionality of the c-myc gene by detecting c-myc RNA expression with RT-PCR and c-myc protein by immunohistochemistry. 4/8 primary melanomas and 11/33 melanoma metastases showed additional c-myc signals relative to the centromere of chromosome 8 copy number. None of the nevi, safety margins or normal skin samples demonstrated this gain. In 2/7 melanoma cell lines (C32 and WM 266–4) isochromosome 8q formation with a relative gain of c-myc copies and a loss of 8p was observed. The highest c-myc gene expression compared to GAPDH was found in melanoma metastases (17.5%). Nevi (6.6%) and primary melanomas (5.0%) expressed the c-myc gene on a lower level. 72.7% of the patients with c-myc extra copies had visceral melanoma metastases (UICC IV), patients without c-myc gain in 35.0% only. The collective with additional c-myc copies also expressed the gene on a significantly higher level. These results indicate that a c-myc gain in relation to the centromere 8 copy number might be associated with advanced cutaneous melanoma. © 2001 Cancer Research Campaign http://www.bjcancer.co

Toll-like receptor 4 signaling activates ERG function in prostate cancer and provides a therapeutic target

The TMPRSS2-ERG gene fusion and subsequent overexpression of the ERG transcription factor occurs in ∼50% of prostate tumors, making it the most common abnormality of the prostate cancer genome. While ERG has been shown to drive tumor progression and cancer-related phenotypes, as a transcription factor it is difficult to target therapeutically. Using a genetic screen, we identified the toll-like receptor 4 (TLR4) signaling pathway as important for ERG function in prostate cells. Our data confirm previous reports that ERG can transcriptionally activate TLR4 gene expression; however, using a constitutively active ERG mutant, we demonstrate that the critical function of TLR4 signaling is upstream, promoting ERG phosphorylation at serine 96 and ERG transcriptional activation. The TLR4 inhibitor, TAK-242, attenuated ERG-mediated migration, clonogenic survival, target gene activation and tumor growth. Together these data indicate a mechanistic basis for inhibition of TLR4 signaling as a treatment for ERG-positive prostate cancer

Mean field treatment of exclusion processes with random-force disorder

The asymmetric simple exclusion process with random-force disorder is studied within the mean field approximation. The stationary current through a domain with reversed bias is analyzed and the results are found to be in accordance with earlier intuitive assumptions. On the grounds of these results, a phenomenological random barrier model is applied in order to describe quantitatively the coarsening phenomena. Predictions of the theory are compared with numerical results obtained by integrating the mean field evolution equations.Comment: 21 pages, 14 figure