Fisher's geometrical model of evolutionary adaptation - beyond spherical geometry

Fisher's geometrical model of evolutionary adaptation has recently been used in a variety of contexts of interest to evolutionary biologists. The renewed interest in this model strongly motivates generalizations that make it a more realistic description of evolutionary adaptation. Previously, the distribution of mutant effects has, for analytical tractability, rather than biological realism, been taken as spherically symmetric. Here we substantially extend Fisher's model, by allowing a wider class of mutational distributions that incorporate mutational bias and more general deviations from spherical symmetry such as correlations between mutant effects. We also incorporate work on generalized fitness landscapes, thereby reducing the number of artificial assumptions underlying the model. The generalized model exhibits a substantially increased flexibility and a far richer underlying geometry. We find that the distribution characterizing selection coefficients of new mutations is expressed in terms of a number of geometrical invariants associated with mutation, selection and the parental phenotype

Fisher's microscope and Haldane's ellipse

Fisher’s geometrical model was introduced to study the phenotypic size of mutations contributing to adaptation. However, as pointed out by Haldane, the model involves a simplified picture of the action of natural selection, and this calls into question its generality. In particular, Fisher’s model assumes that each trait contributes independently to fitness. Here, we show that Haldane’s concerns may be incorporated into Fisher’s model solely by allowing the intensity of selection to vary between traits. We further show that this generalization may be achieved by introducing a single, intuitively defined quantity that describes the phenotype prior to adaptation. Comparing the process of adaptation under the original and generalized models, we show that the generalization may bias results toward either larger or smaller mutations. The applicability of Fisher’s model is then discussed

Mutation and selection in a large population

In this paper we study a large, but finite population, in which mutation and selection occur at a single genetic locus in a diploid organism. We provide theoretical results for the equilibrium allele frequencies, their variances and covariances and their equilibrium distribution, when the population size is larger than the reciprocal of the mean mutation rate. [[We are also able to infer that the equilibrium distribution of allele frequencies takes the form of a constrained multivariate Gaussian distribution.]] Our results provide a rapid way of obtaining useful information in the case of complex mutation and selection schemes when the population size is large. We present numerical simulations to test the applicability of our theoretical formulations. The results of these simulations are in very reasonable agreement with the theoretical predictions

An engineering study of hybrid adaptation of wind tunnel walls for three-dimensional testing

Solid wall tunnels having only upper and lower walls flexing are described. An algorithm for selecting the wall contours for both 2 and 3 dimensional wall flexure is presented and numerical experiments are used to validate its applicability to the general test case of 3 dimensional lifting aircraft models in rectangular cross section wind tunnels. The method requires an initial approximate representation of the model flow field at a given lift with wallls absent. The numerical methods utilized are derived by use of Green's source solutions obtained using the method of images; first order linearized flow theory is employed with Prandtl-Glauert compressibility transformations. Equations are derived for the flexed shape of a simple constant thickness plate wall under the influence of a finite number of jacks in an axial row along the plate centerline. The Green's source methods are developed to provide estimations of residual flow distortion (interferences) with measured wall pressures and wall flow inclinations as inputs

PC3 prostate tumor-initiating cells with molecular profile FAM65Bhigh/MFI2low/LEF1low increase tumor angiogenesis

<p>Abstract</p> <p>Background</p> <p>Cancer stem-like cells are proposed to sustain solid tumors by virtue of their capacity for self-renewal and differentiation to cells that comprise the bulk of the tumor, and have been identified for a variety of cancers based on characteristic clonal morphologies and patterns of marker gene expression.</p> <p>Methods</p> <p>Single cell cloning and spheroid culture studies were used to identify a population of cancer stem-like cells in the androgen-independent human prostate cancer cell line PC3.</p> <p>Results</p> <p>We demonstrate that, under standard culture conditions, ~10% of PC3 cells form holoclones with cancer stem cell characteristics. These holoclones display high self-renewal capability in spheroid formation assays under low attachment and serum-free culture conditions, retain their holoclone morphology when passaged at high cell density, exhibit moderate drug resistance, and show high tumorigenicity in scid immunodeficient mice. PC3 holoclones readily form spheres, and PC3-derived spheres yield a high percentage of holoclones, further supporting their cancer stem cell-like nature. We identified one gene, <it>FAM65B</it>, whose expression is consistently up regulated in PC3 holoclones compared to paraclones, the major cell morphology in the parental PC3 cell population, and two genes, <it>MFI2 </it>and <it>LEF1</it>, that are consistently down regulated. This molecular profile, FAM65B^high/MFI2^low/LEF1^low, also characterizes spheres generated from parental PC3 cells. The PC3 holoclones did not show significant enriched expression of the putative prostate cancer stem cell markers CD44 and integrin α2β1. PC3 tumors seeded with holoclones showed dramatic down regulation of <it>FAM65B </it>and dramatic up regulation of <it>MFI2 </it>and <it>LEF1</it>, and unexpectedly, a marked increase in tumor vascularity compared to parental PC3 tumors, suggesting a role of cancer stem cells in tumor angiogenesis.</p> <p>Conclusions</p> <p>These findings support the proposal that PC3 tumors are sustained by a small number of tumor-initiating cells with stem-like characteristics, including strong self-renewal and pro-angiogenic capability and marked by the expression pattern <it>FAM65B^high/MFI2^low/LEF1^low</it>. These markers may serve as targets for therapies designed to eliminate cancer stem cell populations associated with aggressive, androgen-independent prostate tumors such as PC3.</p

Impact of methoxyacetic acid on mouse Leydig cell gene expression

<p>Abstract</p> <p>Background</p> <p>Methoxyacetic acid (MAA) is the active metabolite of the widely used industrial chemical ethylene glycol monomethyl ether, which is associated with various developmental and reproductive toxicities, including neural toxicity, blood and immune disorders, limb degeneration and testicular toxicity. Testicular toxicity is caused by degeneration of germ cells in association with changes in gene expression in both germ cells and Sertoli cells of the testis. This study investigates the impact of MAA on gene expression in testicular Leydig cells, which play a critical role in germ cell survival and male reproductive function.</p> <p>Methods</p> <p>Cultured mouse TM3 Leydig cells were treated with MAA for 3, 8, and 24 h and changes in gene expression were monitored by genome-wide transcriptional profiling.</p> <p>Results</p> <p>A total of 3,912 MAA-responsive genes were identified. Ingenuity Pathway analysis identified reproductive system disease, inflammatory disease and connective tissue disorder as the top biological functions affected by MAA. The MAA-responsive genes were classified into 1,366 early responders, 1,387 mid-responders, and 1,138 late responders, based on the time required for MAA to elicit a response. Analysis of enriched functional clusters for each subgroup identified 106 MAA early response genes involved in transcription regulation, including 32 genes associated with developmental processes. 60 DNA-binding proteins responded to MAA rapidly but transiently, and may contribute to the downstream effects of MAA seen for many mid and late response genes. Genes within the phosphatidylinositol/phospholipase C/calcium signaling pathway, whose activity is required for potentiation of nuclear receptor signaling by MAA, were also enriched in the set of early MAA response genes. In contrast, many of the genes responding to MAA at later time points encode membrane proteins that contribute to cell adhesion and membrane signaling.</p> <p>Conclusions</p> <p>These findings on the progressive changes in gene expression induced by MAA in a cultured Leydig cell model may help elucidate signaling pathways that lead to the testicular pathophysiological responses induced by MAA exposure and may identify useful biomarkers of MAA toxicity.</p