Multivariate exploratory tools for microarray data analysis

The ultimate success of microarray technology in basic and applied biological sciences depends critically on the development of statistical methods for gene expression data analysis. The most widely used tests for differential expression of genes are essentially univariate. Such tests disregard the multidimensional structure of microarray data. Multivariate methods are needed to utilize the information hidden in gene interactions and hence to provide more powerful and biologically meaningful methods for finding subsets of differentially expressed genes. The objective of this paper is to develop methods of multidimensional search for biologically significant genes, considering expression signals as mutually dependent random variables. To attain these ends, we consider the utility of a pertinent distance between random vectors and its empirical counterpart constructed from gene expression data. The distance furnishes exploratory procedures aimed at finding a target subset of differentially expressed genes. To determine the size of the target subset, we resort to successive elimination of smaller subsets resulting from each step of a random search algorithm based on maximization of the proposed distance. Different stopping rules associated with this procedure are evaluated. The usefulness of the proposed approach is illustrated with an application to the analysis of two sets of gene expression data.     

Persistent solutions for age-dependent pair-formation models

Conditions on the vital rates and the mating function are derived which imply existence or nonexistence of exponentially growing persistent age-distributions for age-dependent pair-formation models.     

Mathematical models and simulations of bacterial growth and chemotaxis in a diffusion gradient chamber

The diffusion gradient chamber (DGC) is a novel device developed to study the response of chemotactic bacteria to combinations of nutrients and attractants [7]. Its purpose is to characterize genetic variants that occur in many biological experiments. In this paper, a mathematical model which describes the spatial distribution of a bacterial population within the DGC is developed. Mathematical analysis of the model concerning positivity and boundedness of the solutions are given. An ADI (Alternating Direction Implicit) method is constructed for finding numerical solutions of the model and carrying out computer simulations. The numerical results of the model successfully reproduced the patterns that were observed in the experiments using the DGC. Received: 3 June 1997 / Revised version: 15 August 2000 / Published online: 20 December 2000     

Membrane Transport Generated by the Osmotic and Hydrostatic Pressure. Correlation Relation for Parameters L p, σ, and ω

Standard approach to membrane transport generated by osmotic andhydrostatic pressures, developed by Kedem and Katchalsky, is based onprinciples of thermodynamics of irreversible processes. In this paper wepropose an alternative technique. We derive transport equations from fewfairly natural assumptions and a mechanistic interpretation of the flows.In particular we postulate that a sieve-type membrane permeability isdetermined by the pore sizes and these are random within certain range.Assuming that an individual pore is either permeable or impermeable tosolute molecules, the membrane reflection coefficient depends on the ratioof permeable and impermeable pores. Considering flows through permeableand impermeable pores separately, we derive equations for the total volumeflux, solute flux and the solvent flux across the membrane. Comparing themechanistic equations to the Kedem-Katchalsky equations we find the formereasier to interpret physically. Based on the mechanistic equations we alsoderive a correlation relation for the membrane transport parameters L _p,, and . This relation eliminates the need for experimentaldetermination of all three phenomenological parameters, which in somecases met with considerable difficulties.     

Generalized linear mixture models for handling nonignorable dropouts in longitudinal studies

This paper presents a method for analysing longitudinal data when there are dropouts. In particular, we develop a simple method based on generalized linear mixture models for handling nonignorable dropouts for a variety of discrete and continuous outcomes. Statistical inference for the model parameters is based on a generalized estimating equations (GEE) approach (Liang and Zeger, 1986). The proposed method yields estimates of the model parameters that are valid when nonresponse is nonignorable under a variety of assumptions concerning the dropout process. Furthermore, the proposed method can be implemented using widely available statistical software. Finally, an example using data from a clinical trial of contracepting women is used to illustrate the methodology.     

Down regulation of ribosomal protein mRNAs during neuronal differentiation of human NTERA2 cells

We have analysed the expression of 32 ribosomal protein (RP) mRNAs during retinoic acid induced neuronal differentiation of human NTERA2 cells. Except for a new S27 variant (S27v), all were down regulated both in selectively replated differentiated neurons and the most differentiated continuous cultures, i.e., non-replated cultures. However, the expression profiles of the individual RP mRNAs were different, most (L3, L7, L8, L10, L13, L23a, L27a, L36a, L39, P0, S2, S3, S3a, S4X, S6, S9, S12, S13, S16, S19, S20, S23, and S27a) exhibited a constant down regulation, whereas a few were either initially constant (L11, L32, S8, and S11) or up regulated (L6, L15, L17, L31, and S27y) and then down regulated. The expression of S27v remained elevated in the most differentiated continuous cultures but was down regulated in replated differentiated neurons. The down regulation of RP mRNAs was variable: the expression levels in differentiated replated neurons were between 10% (S3) and 90% (S11) of the levels in undifferentiated cells. The ratio between rRNA and RP mRNA changed during the differentiation; in differentiated neurons there were, on average, about half the number of RP mRNAs per rRNA as compared to undifferentiated cells. The expression profiles of a few translation-related proteins were also determined. EF1alpha1, EF1beta1, and EF1delta were down regulated, whereas the expression of the neuron and muscle specific EF1alpha2 increased. The reduction in the expression of RP mRNAs was coordinated with a reduction in the expression level of the proliferation marker PCNA. The expression levels of most RP mRNAs were lower in purified differentiated post-mitotic neurons than in the most differentiated continuous cultures, despite similar levels of PCNA, suggesting that both the differentiation state and the proliferative status of the cells affect the expression of RP mRNAs.     

A linear mixed-effects model for multivariate censored data

We apply a linear mixed-effects model to multivariate failure time data. Computation of the regression parameters involves the Buckley-James method in an iterated Monte Carlo expectation-maximization algorithm, wherein the Monte Carlo E-step is implemented using the Metropolis-Hastings algorithm. From simulation studies, this approach compares favorably with the marginal independence approach, especially when there is a strong within-cluster correlation.     

Differential expression of four genes encoding 1-aminocyclopropane-1-carboxylate synthase in Lupinus albus during germination, and in response to indole-3-acetic acid and wounding

1-Aminocyclopropane-1-carboxylate (ACC) synthase (ACS; EC 4.4.1.14) is the key regulatory enzyme of the ethylene biosynthetic pathway and is encoded by a multigene family in Arabidopsis thaliana, tomato, mung bean and other plants. Southern blot analysis revealed the existence of at least five ACS genes in white lupin (Lupinus albus L.) genome. Four complete and one partial sequences representing different ACS genes were cloned from the lupin genomic library. The levels of expression of two of the genes, LA-ACS1 and LA-ACS3, were found to increase after hypocotyl wounding. Apparently, these two genes were up-regulated by exogenous IAA treatment of seedlings. The LA-ACS3 mRNA levels were also elevated in the apical part of hypocotyl, which is reported to contain a high endogenous auxin concentration. This gene may be involved in the auxin- and ethylene-controlled apical hook formation. The expression of the LA-ACS4 gene was found to be almost undetectable. This gene may represent a “silent” twin of LA-ACS5 as these two genes share a considerable level of homology in coding and non-coding regions. The LA-ACS5 mRNA is strongly up-regulated in the embryonic axis of germinating seeds at the time of radicle emergence, and was also found in roots and hypocotyls of lupin seedlings. Received: 19 July 1999 / Accepted: 3 March 2000