A logistic regression mixture model for interval mapping of genetic trait loci affecting binary phenotypes

Often in genetic research, presence or absence of a disease is affected by not only the trait locus genotypes but also some covariates. The finite logistic regression mixture models and the methods under the models are developed for detection of a binary trait locus (BTL) through an interval-mapping procedure. The maximum-likelihood estimates (MLEs) of the logistic regression parameters are asymptotically unbiased. The null asymptotic distributions of the likelihood-ratio test (LRT) statistics for detection of a BTL are found to be given by the supremum of a chi2-process. The limiting null distributions are free of the null model parameters and are determined explicitly through only four (backcross case) or nine (intercross case) independent standard normal random variables. Therefore a threshold for detecting a BTL in a flanking marker interval can be approximated easily by using a Monte Carlo method. It is pointed out that use of a threshold incorrectly determined by reading off a chi2-probability table can result in an excessive false BTL detection rate much more severely than many researchers might anticipate. Simulation results show that the BTL detection procedures based on the thresholds determined by the limiting distributions perform quite well when the sample sizes are moderately large.     

Functional mapping of quantitative trait loci underlying growth trajectories using a transform-both-sides logistic model

The incorporation of developmental control mechanisms of growth has proven to be a powerful tool in mapping quantitative trait loci (QTL) underlying growth trajectories. A theoretical framework for implementing a QTL mapping strategy with growth laws has been established. This framework can be generalized to an arbitrary number of time points, where growth is measured, and becomes computationally more tractable, when the assumption of variance stationarity is made. In practice, however, this assumption is likely to be violated for age-specific growth traits due to a scale effect. In this article, we present a new statistical model for mapping growth QTL, which also addresses the problem of variance stationarity, by using a transform-both-sides (TBS) model advocated by Carroll and Ruppert (1984, Journal of the American Statistical Association 79, 321-328). The TBS-based model for mapping growth QTL cannot only maintain the original biological properties of a growth model, but also can increase the accuracy and precision of parameter estimation and the power to detect a QTL responsible for growth differentiation. Using the TBS-based model, we successfully map a QTL governing growth trajectories to a linkage group in an example of forest trees. The statistical and biological properties of the estimates of this growth QTL position and effect are investigated using Monte Carlo simulation studies. The implications of our model for understanding the genetic architecture of growth are discussed.     

A dynamical model of genetic networks for cell differentiation

A mathematical model is proposed which is able to describe the most important features of cell differentiation, without requiring specific detailed assumptions concerning the interactions which drive the phenomenon. On the contrary, cell differentiation is described here as an emergent property of a generic model of the underlying gene regulatory network, and it can therefore be applied to a variety of different organisms. The model points to a peculiar role of cellular noise in differentiation and leads to non trivial predictions which could be subject to experimental testing. Moreover, a single model proves able to describe several different phenomena observed in various differentiation processes.     

A logical model for growth and differentiation in multi-celled organisms

This paper is an attempt to provide a logical model for the process of growth and differentiation in a multi-cellular organism. More specifically it is intended to show how genetic information relating to macroscopic structure and coded in the form of a logical tree could be progressively embodied in the organism as it develops by repeated division from a single cell. The aim is to establish biological analogies rather than mathematical interest, and reproduction, adaption, and the coordinating action of hormones are discussed within the general logical framework.     

A logical model for growth and differentiation in multi-celled organisms

This paper is an attempt to provide a logical model for the process of growth and differentiation in a multi-cellular organism. More specifically it is intended to show how genetic information relating to macroscopic structure and coded in the form of a logical tree could be progressively embodied in the organism as it develops by repeated division from a single cell. The aim is to establish biological analogies rather than mathematical interest, and reproduction, adaption, and the coordinating action of hormones are discussed within the general logical framework.     

A mechanistic model for genetic machinery of ontogenetic growth

Two different genetic mechanisms can be proposed to explain variation in growth trajectories. The allelic sensitivity hypothesis states that growth trajectory is controlled by the time-dependent expression of alleles at the deterministic quantitative trait loci (dQTL) formed during embryogenesis. The gene regulation hypothesis states that the differentiation in growth process is due to the opportunistic quantitative trait loci (oQTL) through their mediation with new developmental signals. These two hypotheses of genetic control have been elucidated in the literature. Here, we propose a new statistical model for discerning these two mechanisms in the context of growth trajectories by integrating growth laws within a QTL-mapping framework. This model is developed within the maximum-likelihood context, implemented with a grid approach for estimating the genomic positions of the deterministic and opportunistic QTL and the simplex algorithm for estimating the growth curve parameters of the genotypes at these QTL and the parameters modeling the residual (co)variance matrix. Our model allows for extensive hypothesis tests for the genetic control of growth processes and developmental events by these two types of QTL. The application of this new model to an F(2) progeny in mice leads to the detection of deterministic and opportunistic QTL on chromosome 1 for mouse body mass growth. The estimates of QTL positions and effects from our model are broadly in agreement with those by traditional interval-mapping approaches. The implications of this model for biological and biomedical research are discussed.     

A Sizer model for cell differentiation in Arabidopsis thaliana root growth

Plant roots grow due to cell division in the meristem and subsequent cell elongation and differentiation, a tightly coordinated process that ensures growth and adaptation to the changing environment. How the newly formed cells decide to stop elongating becoming fully differentiated is not yet understood. To address this question, we established a novel approach that combines the quantitative phenotypic variability of wild‐type Arabidopsis roots with computational data from mathematical models. Our analyses reveal that primary root growth is consistent with a Sizer mechanism, in which cells sense their length and stop elongating when reaching a threshold value. The local expression of brassinosteroid receptors only in the meristem is sufficient to set this value. Analysis of roots insensitive to BR signaling and of roots with gibberellin biosynthesis inhibited suggests distinct roles of these hormones on cell expansion termination. Overall, our study underscores the value of using computational modeling together with quantitative data to understand root growth.     

A non-parametric mixture model for genome-enabled prediction of genetic value for a quantitative trait

A Bayesian nonparametric form of regression based on Dirichlet process priors is adapted to the analysis of quantitative traits possibly affected by cryptic forms of gene action, and to the context of SNP-assisted genomic selection, where the main objective is to predict a genomic signal on phenotype. The procedure clusters unknown genotypes into groups with distinct genetic values, but in a setting in which the number of clusters is unknown a priori, so that standard methods for finite mixture analysis do not work. The central assumption is that genetic effects follow an unknown distribution with some “baseline” family, which is a normal process in the cases considered here. A Bayesian analysis based on the Gibbs sampler produces estimates of the number of clusters, posterior means of genetic effects, a measure of credibility in the baseline distribution, as well as estimates of parameters of the latter. The procedure is illustrated with a simulation representing two populations. In the first one, there are 3 unknown QTL, with additive, dominance and epistatic effects; in the second, there are 10 QTL with additive, dominance and additive × additive epistatic effects. In the two populations, baseline parameters are inferred correctly. The Dirichlet process model infers the number of unique genetic values correctly in the first population, but it produces an understatement in the second one; here, the true number of clusters is over 900, and the model gives a posterior mean estimate of about 140, probably because more replication of genotypes is needed for correct inference. The impact on inferences of the prior distribution of a key parameter (M), and of the extent of replication, was examined via an analysis of mean body weight in 192 paternal half-sib families of broiler chickens, where each sire was genotyped for nearly 7,000 SNPs. In this small sample, it was found that inference about the number of clusters was affected by the prior distribution of M. For a set of combinations of parameters of a given prior distribution, the effects of the prior dissipated when the number of replicate samples per genotype was increased. Thus, the Dirichlet process model seems to be useful for gauging the number of QTLs affecting the trait: if the number of clusters inferred is small, probably just a few QTLs code for the trait. If the number of clusters inferred is large, this may imply that standard parametric models based on the baseline distribution may suffice. However, priors may be influential, especially if sample size is not large and if only a few genotypic configurations have replicate phenotypes in the sample.     

A framework for detecting and characterizing genetic background-dependent imprinting effects

Genomic imprinting, where the effects of alleles depend on their parent-of-origin, can be an important component of the genetic architecture of complex traits. Although there has been a rapidly increasing number of studies of genetic architecture that have examined imprinting effects, none have examined whether imprinting effects depend on genetic background. Such effects are critical for the evolution of genomic imprinting because they allow the imprinting state of a locus to evolve as a function of genetic background. Here we develop a two-locus model of epistasis that includes epistatic interactions involving imprinting effects and apply this model to scan the mouse genome for loci that modulate the imprinting effects of quantitative trait loci (QTL). The inclusion of imprinting leads to nine orthogonal forms of epistasis, five of which do not appear in the usual two-locus decomposition of epistasis. Each form represents a change in the imprinting status of one locus across different classes of genotypes at the other locus. Our genome scan identified two different locus pairs that show complex patterns of epistasis, where the imprinting effect at one locus changes across genetic backgrounds at the other locus. Thus, our model provides a framework for the detection of genetic background-dependent imprinting effects that should provide insights into the background dependence and evolution of genomic imprinting. Our application of the model to a genome scan supports this assertion by identifying pairs of loci that show reciprocal changes in their imprinting status as the background provided by the other locus changes.     

A generalized two-sex logistic model

We provide a generalization of the logistic two-sex model with ephemeral pair-bonds and with stable couples without assuming any specific mathematical form for fertility, mortality and the mating function. In particular, we establish a necessary and sufficient condition on the fertility/mortality density-dependent ratio that ensures the existence of the logistic behaviour. Several differences and similarities between the two models are also provided.     

A model for differentiation

A model is proposed, in which differentiation is attributed to colinearity between polymerase states and promotors. The promotors are considered the equal of ordinal numbers, and the state of a polymerase molecule is changed by the activity of the products of the gene it has transcribed. Introns are assumed to be involved in this possibility. Repeated sequences function as labels of chromosomes and chromosome regions, and interact with the diffusing RNA polymerase molecules aimed at a given class of promotors, increasing the speed of specific interactions. The possibility that a quantitative code, with a form of scansion, exists to order promotors as well as repeated sequences, is discussed. A correlation between the base sequence of repeats and promotors is predicted.     

A 3-D constrained mixture model for mechanically mediated vascular growth and remodeling

In contrast to the widely applied approach to model soft tissue remodeling employing the concept of volumetric growth, microstructurally motivated models are capable of capturing many of the underlying mechanisms of growth and remodeling; i.e., the production, removal, and remodeling of individual constituents at different rates and to different extents. A 3-dimensional constrained mixture computational framework has been developed for vascular growth and remodeling, considering new, microstructurally motivated kinematics and constitutive equations and new stress and muscle activation mediated evolution equations. Our computational results for alterations in flow and pressure, using reasonable physiological values for rates of constituent growth and turnover, concur with findings in the literature. For example, for flow-induced remodeling, our simulations predict that, although the wall shear stress is restored completely, the circumferential stress is not restored employing realistic physiological rate parameters. Also, our simulations predict different levels of thickening on inner versus outer wall locations, as shown in numerous reports of pressure-induced remodeling. Whereas the simulations are meant to be illustrative, they serve to highlight the experimental data currently lacking to fully quantify mechanically mediated adaptations in the vasculature.     

A new statistic for detecting genetic differentiation

A new statistic for detecting genetic differentiation of subpopulations is described. The statistic can be calculated when genetic data are collected on individuals sampled from two or more localities. It is assumed that haplotypic data are obtained, either in the form of DNA sequences or data on many tightly linked markers. Using a symmetric island model, and assuming an infinite-sites model of mutation, it is found that the new statistic is as powerful or more powerful than previously proposed statistics for a wide range of parameter values.     

Rapid range expansion increases genetic differentiation while causing limited reduction in genetic diversity in a damselfly

Many ectothermic species are currently expanding their geographic range due to global warming. This can modify the population genetic diversity and structure of these species because of genetic drift during the colonization of new areas. Although the genetic signatures of historical range expansions have been investigated in an array of species, the genetic consequences of natural, contemporary range expansions have received little attention, with the only studies available focusing on range expansions along a narrow front. We investigate the genetic consequences of a natural range expansion in the Mediterranean damselfly Coenagrion scitulum, which is currently rapidly expanding along a broad front in different directions. We assessed genetic diversity and genetic structure using 12 microsatellite markers in five centrally located populations and five recently established populations at the edge of the geographic distribution. Our results suggest that, although a marginal significant decrease in the allelic richness was found in the edge populations, genetic diversity has been preserved during the range expansion of this species. Nevertheless, edge populations were genetically more differentiated compared with core populations, suggesting genetic drift during the range expansion. The smaller effective population sizes of the edge populations compared with central populations also suggest a contribution of genetic drift after colonization. We argue and document that range expansion along multiple axes of a broad expansion front generates little reduction in genetic diversity, yet stronger differentiation of the edge populations.     

A cartilage growth mixture model with collagen remodeling: validation protocols

A cartilage growth mixture (CGM) model is proposed to address limitations of a model used in a previous study. New stress constitutive equations for the solid matrix are derived and collagen (COL) remodeling is incorporated into the CGM model by allowing the intrinsic COL material constants to evolve during growth. An analytical validation protocol based on experimental data from a recent in vitro growth study is developed. Available data included measurements of tissue volume, biochemical composition, and tensile modulus for bovine calf articular cartilage (AC) explants harvested at three depths and incubated for 13 days in 20% fetal borine serum (FBS) and 20% FBS+beta-aminopropionitrile. The proposed CGM model can match tissue biochemical content and volume exactly while predicting theoretical values of tensile moduli that do not significantly differ from experimental values. Also, theoretical values of a scalar COL remodeling factor are positively correlated with COL cross-link content, and mass growth functions are positively correlated with cell density. The results suggest that the CGM model may help us to guide in vitro growth protocols for AC tissue via the a priori prediction of geometric and biomechanical properties.     

A cartilage growth mixture model for infinitesimal strains: solutions of boundary-value problems related to in vitro growth experiments

A cartilage growth mixture (CGM) model is linearized for infinitesimal elastic and growth strains. Parametric studies for equilibrium and nonequilibrium boundary-value problems representing the in vitro growth of cylindrical cartilage constructs are solved. The results show that the CGM model is capable of describing the main biomechanical features of cartilage growth. The solutions to the equilibrium problems reveal that tissue composition, constituent pre-stresses, and geometry depend on collagen remodeling activity, growth symmetry, and differential growth. Also, nonhomogeneous growth leads to nonhomogeneous tissue composition and constituent pre-stresses. The solution to the nonequilibrium problem reveals that the tissue is nearly in equilibrium at all time points. The results suggest that the CGM model may be used in the design of tissue engineered cartilage constructs for the repair of cartilage defects; for example, to predict how dynamic mechanical loading affects the development of nonuniform properties during in vitro growth. Furthermore, the results lay the foundation for future analyses with nonlinear models that are needed to develop realistic models of cartilage growth.     

A genetic approach to characterizing complex promoters in E. coli

The chromosomal distributions of five families of mouse r-protein genes (S16, L18, L19, L30 and L32/33) were studied by Southern blot analysis of DNA from a panel of mouse-hamster hybrid cells containing various complements of mouse chromosomes. Our results indicated that members of a particular family are often located on more than one chromosome, that extensive clustering of many r-protein gene families on a few chromosomes is unlikely, and that there is no obligatory linkage of r-protein and rRNA genes.