A scale invariant clustering of genes on human chromosome 7

BACKGROUND: Vertebrate genes often appear to cluster within the background of nontranscribed genomic DNA. Here an analysis of the physical distribution of gene structures on human chromosome 7 was performed to confirm the presence of clustering, and to elucidate possible underlying statistical and biological mechanisms. RESULTS: Clustering of genes was confirmed by virtue of a variance of the number of genes per unit physical length that exceeded the respective mean. Further evidence for clustering came from a power function relationship between the variance and mean that possessed an exponent of 1.51. This power function implied that the spatial distribution of genes on chromosome 7 was scale invariant, and that the underlying statistical distribution had a Poisson-gamma (PG) form. A PG distribution for the spatial scattering of genes was validated by stringent comparisons of both the predicted variance to mean power function and its cumulative distribution function to data derived from chromosome 7. CONCLUSION: The PG distribution was consistent with at least two different biological models: In the microrearrangement model, the number of genes per unit length of chromosome represented the contribution of a random number of smaller chromosomal segments that had originated by random breakage and reconstruction of more primitive chromosomes. Each of these smaller segments would have necessarily contained (on average) a gamma distributed number of genes. In the gene cluster model, genes would be scattered randomly to begin with. Over evolutionary timescales, tandem duplication, mutation, insertion, deletion and rearrangement could act at these gene sites through a stochastic birth death and immigration process to yield a PG distribution. On the basis of the gene position data alone it was not possible to identify the biological model which best explained the observed clustering. However, the underlying PG statistical model implicated neutral evolutionary mechanisms as the basis for this clustering

Large-scale genomic correlations in Arabidopsis thaliana relate to chromosomal structure

BACKGROUND: The chromosomes of the plant Arabidopsis thaliana contain various genomic elements, distributed with appreciable spatial heterogeneity. Clustering of and/or correlations between these elements presumably should reflect underlying functional or structural factors. We studied the positional density fluctuations and correlations between genes, indels, single nucleotide polymorphisms (SNPs), retrotransposons, 180 bp tandem repeats, and conserved centromeric sequences (CCSs) in Arabidopsis in order to elucidate any patterns and possible responsible factors for their genomic distributions. RESULTS: The spatial distributions of all these elements obeyed a common pattern: the density profiles of each element within chromosomes exhibited low-frequency fluctuations indicative of regional clustering, and the individual density profiles tended to correlate with each other at large measurement scales. This pattern could be attributed to the influence of major chromosomal structures, such as centromeres. At smaller scales the correlations tended to weaken – evidence that localized cis-interactions between the different elements had a comparatively minor, if any, influence on their placement. CONCLUSION: The conventional notion that retrotransposon insertion sites are strongly influenced by cis-interactions was not supported by these observations. Moreover, we would propose that large-scale chromosomal structure has a dominant influence on the intrachromosomal distributions of genomic elements, and provides for an additional shared hierarchy of genomic organization within Arabidopsis

Chance mechanisms affecting the burden of metastases

BACKGROUND: The burden of cancer metastases within an individual is commonly used to clinically characterize a tumor's biological behavior. Assessments like these implicitly assume that spurious effects can be discounted. Here the influence of chance on the burden of metastasis is studied to determine whether or not this assumption is valid. METHODS: Monte Carlo simulations were performed to estimate tumor burdens sustained by individuals with cancer, based upon empirically derived and validated models for the number and size distributions of metastases. Factors related to the intrinsic metastatic potential of tumors and their host microenvironments were kept constant, to more clearly demonstrate the contribution from chance. RESULTS: Under otherwise identical conditions, both the simulated numbers and the sizes of metastases were highly variable. Comparable individuals could sustain anywhere from no metastases to scores of metastases, and the sizes of the metastases ranged from microscopic to macroscopic. Despite the marked variability in the number and sizes of the metastases, their respective growth times were rather more narrowly distributed. In such situations multiple occult metastases could develop into fully overt lesions within a comparatively short time period. CONCLUSION: Chance can have a major effect on the burden of metastases. Random variability can be so great as to make individual assessments of tumor biology unreliable, yet constrained enough to lead to the apparently simultaneous appearance of multiple overt metastases

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

A Scale Invariant Distribution of the Prime Numbers

The irregular distribution of prime numbers amongst the integers has found multiple uses, from engineering applications of cryptography to quantum theory. The degree to which this distribution can be predicted thus has become a subject of current interest. Here, we present a computational analysis of the deviations between the actual positions of the prime numbers and their predicted positions from Riemann’s counting formula, focused on the variance function of these deviations from sequential enumerative bins. We show empirically that these deviations can be described by a class of probabilistic models known as the Tweedie exponential dispersion models that are characterized by a power law relationship between the variance and the mean, known by biologists as Taylor’s power law and by engineers as fluctuation scaling. This power law behavior of the prime number deviations is remarkable in that the same behavior has been found within the distribution of genes and single nucleotide polymorphisms (SNPs) within the human genome, the distribution of animals and plants within their habitats, as well as within many other biological and physical processes. We explain the common features of this behavior through a statistical convergence effect related to the central limit theorem that also generates 1/f noise