The ability to sequence cost-effectively all of the coding regions of a given individual genome is rapidly approaching, with the potential for whole-genome resequencing not far behind. Initiatives are currently underway to phenotype hundreds of thousands of individuals for major human traits. Here, we determine the power for de novo discovery of genes related to human traits by resequencing all human exons in a clinical population. We analyze the potential of the gene discovery strategy that combines multiple rare variants from the same gene and treats genes, rather than individual alleles, as the units for the association test. By using computer simulations based on deep resequencing data for the European population, we show that genes meaningfully affecting a human trait can be identified in an unbiased fashion, although large sample sizes would be required to achieve substantial power.association studies | polymorphism | rare variants | sequencing W hole-genome association studies based on genotyping have recently demonstrated potential for identifying SNPs and haplotypes associated with a range of common clinical phenotypes (1-3). However, only a small fraction of observed phenotypic variation is currently attributable to identified allelic variants. Association studies are fundamentally limited by previously known genetic variation, featuring predominantly high-frequency SNPs. By contrast, deep resequencing has the potential to reveal a vast trove of low-frequency alleles. Low-cost-high-throughput sequencing technologies hold the potential to propel discovery of gene-phenotype associations incorporating low-frequency allelic variation on a large scale.Although knowledge of all variants segregating in the population would seem to increase the power of genetic analysis, this prospect faces daunting statistical challenges, because an expanding pool of variants requires more stringent multiple testing correction, whereas the power to detect association with lowfrequency variants is reduced. This problem may be surmounted by pooling allelic variants in a single candidate gene (4-6) or pathway (7-9). However, if most variation in a gene or pathway is neutral, this pooling strategy will not provide a sufficient signalto-noise ratio (10). To enrich variation in functionally significant alleles, the analysis should be limited to nonsynonymous coding variation as one obvious functional class. Site-directed mutagenesis and comparative genomics have shown that the large fraction of de novo missense mutations are of functional significance (11)(12)(13)(14). Consequently, many mildly deleterious coding variants are expected to be segregating in the human population at low allele frequencies, as was originally proposed by Tomoko Ohta in the "nearly neutral theory" of molecular evolution (15). Indeed, the statistically significant excess of combined rare missense variation in individuals at phenotypic extremes was detected in candidate gene studies for several phenotypes (4-6). ResultsSimulation of Resequencing Studies. Al...

The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, H and θ, and the cylinder's parabolic radius R. As H/R → 0, the proximity force approximation becomes exact. The opposite limit of R/H → 0 corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.PACS numbers: 42.25. Fx, 03.70.+k, Casimir's computation of the force between two parallel metallic plates [1] originally inspired much theoretical interest as a macroscopic manifestation of quantum fluctuations of the electromagnetic field in vacuum. Following its experimental confirmation in the past decade [2], however, it is now an important force to reckon with in the design of microelectromechanical systems [3]. Potential practical applications have motivated the development of numerical methods to compute Casimir forces for objects of any shape [4]. The simplest and most commonly used methods for dealing with complex shapes rely on pairwise summations, as in the proximity force approximation (PFA), which limits their applicability.Recently we have developed a formalism [5,6] that relates the Casimir interaction among several objects to the scattering of the electromagnetic field from the objects individually. (For additional perspectives on the scattering formalism, see references in [6].) This approach simplifies the problem, since scattering is a well-developed subject. In particular, the availability of scattering formulae for simple objects, such as spheres and cylinders, has enabled us to compute the Casimir force between two spheres [5], a sphere and a plate [7], multiple cylinders [8], etc. In this work we show that parabolic cylinders provide another example where the scattering amplitudes can be computed exactly. We then use the exact results for scattering from perfect mirrors to compute the Casimir force between a parabolic cylinder and a plate. In the limiting case when the radius of curvature at its tip vanishes, the parabolic cylinder becomes a semi-infinite plate (a knife's edge), and we can consider how the energy depends on the boundary condition it imposes and the angle it makes to the plane.The surface of a parabolic cylinder in Cartesian coordinates is described by y = (x 2 − R 2 )/2R for all z, as shown in Fig. 1, where R is the radius of curvature at the tip. In parabolic cylinder coordinates [9], defined through x = µλ, y = (λ 2 − µ 2 )/2, z = z, the surface is simply µ = µ 0 = √ R for −∞ < λ, z < ∞. One advantage of the latter coordinate system is that the Helmholtz equationwhich we consider for imaginary wavenumber k = iκ, admits separable solutions. Since sending λ → −λ and µ → −µ returns us to the same point, we restr...

Supplementary data are available at Bioinformatics online.