Transformation of expression intensities across generations of Affymetrix microarrays using sequence matching and regression modeling

The utility of previously generated microarray data is severely limited owing to small study size, leading to under-powered analysis, and failure of replication. Multiplicity of platforms and various sources of systematic noise limit the ability to compile existing data from similar studies. We present a model for transformation of data across different generations of Affymetrix arrays, developed using previously published datasets describing technical replicates performed with two generations of arrays. The transformation is based upon a probe set-specific regression model, generated from replicate measurements across platforms, performed using correlation coefficients. The model, when applied to the expression intensities of 5069 shared, sequence-matched probe sets in three different generations of Affymetrix Human oligonucleotide arrays, showed significant improvement in inter generation correlations between sample-wide means and individual probe set pairs. The approach was further validated by an observed reduction in Euclidean distance between signal intensities across generations for the predicted values. Finally, application of the model to independent, but related datasets resulted in improved clustering of samples based upon their biological, as opposed to technical, attributes. Our results suggest that this transformation method is a valuable tool for integrating microarray datasets from different generations of arrays.     

Analysis of matched mRNA measurements from two different microarray technologies

MOTVIATION: The existence of several technologies for measuring gene expression makes the question of cross-technology agreement of measurements an important issue. Cross-platform utilization of data from different technologies has the potential to reduce the need to duplicate experiments but requires corresponding measurements to be comparable. METHODS: A comparison of mRNA measurements of 2895 sequence-matched genes in 56 cell lines from the standard panel of 60 cancer cell lines from the National Cancer Institute (NCI 60) was carried out by calculating correlation between matched measurements and calculating concordance between cluster from two high-throughput DNA microarray technologies, Stanford type cDNA microarrays and Affymetrix oligonucleotide microarrays. RESULTS: In general, corresponding measurements from the two platforms showed poor correlation. Clusters of genes and cell lines were discordant between the two technologies, suggesting that relative intra-technology relationships were not preserved. GC-content, sequence length, average signal intensity, and an estimator of cross-hybridization were found to be associated with the degree of correlation. This suggests gene-specific, or more correctly probe-specific, factors influencing measurements differently in the two platforms, implying a poor prognosis for a broad utilization of gene expression measurements across platforms.     

The noise of membrane capacitance measurements in the whole-cell recording configuration

High-resolution measurement of membrane capacitance in the whole-cell-recording configuration can be used to detect small changes in membrane surface area that accompany exocytosis and endocytosis. We have investigated the noise of membrane capacitance measurements to determine the fundamental limits of resolution in actual cells in the whole-cell mode. Two previously overlooked sources of noise are particularly evident at low frequencies. The first noise source is accompanied by a correlation between capacitance estimates, whereas the second noise source is due to "1/f-like" current noise. An analytic expression that summarizes the noise from thermal and 1/f sources is derived, which agrees with experimental measurements from actual cells over a large frequency range. Our results demonstrate that the optimal frequencies for capacitance measurements are higher than previously believed. Finally, we demonstrate that the capacitance noise at high frequencies can be reduced by compensating for the voltage drop of the sine wave across the series resistance.     

Are data from different gene expression microarray platforms comparable?

Many commercial and custom-made microarray formats are routinely used for large-scale gene expression surveys. Here, we sought to determine the level of concordance between microarray platforms by analyzing breast cancer cell lines with in situ synthesized oligonucleotide arrays (Affymetrix HG-U95v2), commercial cDNA microarrays (Agilent Human 1 cDNA), and custom-made cDNA microarrays from a sequence-validated 13K cDNA library. Gene expression data from the commercial platforms showed good correlations across the experiments (r = 0.78-0.86), whereas the correlations between the custom-made and either of the two commercial platforms were lower (r = 0.62-0.76). Discrepant findings were due to clone errors on the custom-made microarrays, old annotations, or unknown causes. Even within platform, there can be several ways to analyze data that may influence the correlation between platforms. Our results indicate that combining data from different microarray platforms is not straightforward. Variability of the data represents a challenge for developing future diagnostic applications of microarrays.     

Comparison of gene expression microarray data with count-based RNA measurements informs microarray interpretation

Background

Although numerous investigations have compared gene expression microarray platforms, preprocessing methods and batch correction algorithms using constructed spike-in or dilution datasets, there remains a paucity of studies examining the properties of microarray data using diverse biological samples. Most microarray experiments seek to identify subtle differences between samples with variable background noise, a scenario poorly represented by constructed datasets. Thus, microarray users lack important information regarding the complexities introduced in real-world experimental settings. The recent development of a multiplexed, digital technology for nucleic acid measurement enables counting of individual RNA molecules without amplification and, for the first time, permits such a study.

Results

Using a set of human leukocyte subset RNA samples, we compared previously acquired microarray expression values with RNA molecule counts determined by the nCounter Analysis System (NanoString Technologies) in selected genes. We found that gene measurements across samples correlated well between the two platforms, particularly for high-variance genes, while genes deemed unexpressed by the nCounter generally had both low expression and low variance on the microarray. Confirming previous findings from spike-in and dilution datasets, this “gold-standard” comparison demonstrated signal compression that varied dramatically by expression level and, to a lesser extent, by dataset. Most importantly, examination of three different cell types revealed that noise levels differed across tissues.

Conclusions

Microarray measurements generally correlate with relative RNA molecule counts within optimal ranges but suffer from expression-dependent accuracy bias and precision that varies across datasets. We urge microarray users to consider expression-level effects in signal interpretation and to evaluate noise properties in each dataset independently.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-649) contains supplementary material, which is available to authorized users.     

Evaluation of gene expression measurements from commercial microarray platforms

Multiple commercial microarrays for measuring genome-wide gene expression levels are currently available, including oligonucleotide and cDNA, single- and two-channel formats. This study reports on the results of gene expression measurements generated from identical RNA preparations that were obtained using three commercially available microarray platforms. RNA was collected from PANC-1 cells grown in serum-rich medium and at 24 h following the removal of serum. Three biological replicates were prepared for each condition, and three experimental replicates were produced for the first biological replicate. RNA was labeled and hybridized to microarrays from three major suppliers according to manufacturers’ protocols, and gene expression measurements were obtained using each platform’s standard software. For each platform, gene targets from a subset of 2009 common genes were compared. Correlations in gene expression levels and comparisons for significant gene expression changes in this subset were calculated, and showed considerable divergence across the different platforms, suggesting the need for establishing industrial manufacturing standards, and further independent and thorough validation of the technology.     

Multimarker analysis and imputation of multiple platform pooling-based genome-wide association studies

For many genome-wide association (GWA) studies individually genotyping one million or more SNPs provides a marginal increase in coverage at a substantial cost. Much of the information gained is redundant due to the correlation structure inherent in the human genome. Pooling-based GWA studies could benefit significantly by utilizing this redundancy to reduce noise, improve the accuracy of the observations and increase genomic coverage. We introduce a measure of correlation between individual genotyping and pooling, under the same framework that r(2) provides a measure of linkage disequilibrium (LD) between pairs of SNPs. We then report a new non-haplotype multimarker multi-loci method that leverages the correlation structure between SNPs in the human genome to increase the efficacy of pooling-based GWA studies. We first give a theoretical framework and derivation of our multimarker method. Next, we evaluate simulations using this multimarker approach in comparison to single marker analysis. Finally, we experimentally evaluate our method using different pools of HapMap individuals on the Illumina 450S Duo, Illumina 550K and Affymetrix 5.0 platforms for a combined total of 1 333 631 SNPs. Our results show that use of multimarker analysis reduces noise specific to pooling-based studies, allows for efficient integration of multiple microarray platforms and provides more accurate measures of significance than single marker analysis. Additionally, this approach can be extended to allow for imputing the association significance for SNPs not directly observed using neighboring SNPs in LD. This multimarker method can now be used to cost-effectively complete pooling-based GWA studies with multiple platforms across over one million SNPs and to impute neighboring SNPs weighted for the loss of information due to pooling.     

Evaluation of Microarray Preprocessing Algorithms Based on Concordance with RT-PCR in Clinical Samples

Background

Several preprocessing algorithms for Affymetrix gene expression microarrays have been developed, and their performance on spike-in data sets has been evaluated previously. However, a comprehensive comparison of preprocessing algorithms on samples taken under research conditions has not been performed.

Methodology/Principal Findings

We used TaqMan RT-PCR arrays as a reference to evaluate the accuracy of expression values from Affymetrix microarrays in two experimental data sets: one comprising 84 genes in 36 colon biopsies, and the other comprising 75 genes in 29 cancer cell lines. We evaluated consistency using the Pearson correlation between measurements obtained on the two platforms. Also, we introduce the log-ratio discrepancy as a more relevant measure of discordance between gene expression platforms. Of nine preprocessing algorithms tested, PLIER+16 produced expression values that were most consistent with RT-PCR measurements, although the difference in performance between most of the algorithms was not statistically significant.

Conclusions/Significance

Our results support the choice of PLIER+16 for the preprocessing of clinical Affymetrix microarray data. However, other algorithms performed similarly and are probably also good choices.     

Biological assessment of robust noise models in microarray data analysis

MOTIVATION: Although several recently proposed analysis packages for microarray data can cope with heavy-tailed noise, many applications rely on Gaussian assumptions. Gaussian noise models foster computational efficiency. This comes, however, at the expense of increased sensitivity to outlying observations. Assessing potential insufficiencies of Gaussian noise in microarray data analysis is thus important and of general interest. RESULTS: We propose to this end assessing different noise models on a large number of microarray experiments. The goodness of fit of noise models is quantified by a hierarchical Bayesian analysis of variance model, which predicts normalized expression values as a mixture of a Gaussian density and t-distributions with adjustable degrees of freedom. Inference of differentially expressed genes is taken into consideration at a second mixing level. For attaining far reaching validity, our investigations cover a wide range of analysis platforms and experimental settings. As the most striking result, we find irrespective of the chosen preprocessing and normalization method in all experiments that a heavy-tailed noise model is a better fit than a simple Gaussian. Further investigations revealed that an appropriate choice of noise model has a considerable influence on biological interpretations drawn at the level of inferred genes and gene ontology terms. We conclude from our investigation that neglecting the over dispersed noise in microarray data can mislead scientific discovery and suggest that the convenience of Gaussian-based modelling should be replaced by non-parametric approaches or other methods that account for heavy-tailed noise.     

Optimal Feedback Strength for Noise Suppression in Autoregulatory Gene Networks

Autoregulatory feedback loops, where the protein expressed from a gene inhibits or activates its own expression are common gene network motifs within cells. In these networks, stochastic fluctuations in protein levels are attributed to two factors: intrinsic noise (i.e., the randomness associated with mRNA/protein expression and degradation) and extrinsic noise (i.e., the noise caused by fluctuations in cellular components such as enzyme levels and gene-copy numbers). We present results that predict the level of both intrinsic and extrinsic noise in protein numbers as a function of quantities that can be experimentally determined and/or manipulated, such as the response time of the protein and the level of feedback strength. In particular, we show that for a fixed average number of protein molecules, decreasing response times leads to attenuation of both protein intrinsic and extrinsic noise, with the extrinsic noise being more sensitive to changes in the response time. We further show that for autoregulatory networks with negative feedback, the protein noise levels can be minimal at an optimal level of feedback strength. For such cases, we provide an analytical expression for the highest level of noise suppression and the amount of feedback that achieves this minimal noise. These theoretical results are shown to be consistent and explain recent experimental observations. Finally, we illustrate how measuring changes in the protein noise levels as the feedback strength is manipulated can be used to determine the level of extrinsic noise in these gene networks.     

Statistical analysis of fluorescence correlation spectroscopy: the standard deviation and bias

We present a detailed statistical analysis of fluorescence correlation spectroscopy for a wide range of timescales. The derivation is completely analytical and can provide an excellent tool for planning and analysis of FCS experiments. The dependence of the signal-to-noise ratio on different measurement conditions is extensively studied. We find that in addition to the shot noise and the noise associated with correlated molecular dynamics there is another source of noise that appears at very large lag times. We call this the "particle noise," as its behavior is governed by the number of particles that have entered and left the laser beam sample volume during large dwell times. The standard deviations of all the points on the correlation function are calculated analytically and shown to be in good agreement with experiments. We have also investigated the bias associated with experimental correlation function measurements. A "phase diagram" for FCS experiments is constructed that demonstrates the significance of the bias for any given experiment. We demonstrate that the value of the bias can be calculated and added back as a first-order correction to the experimental correlation function.     

Microarray standard data set and figures of merit for comparing data processing methods and experiment designs

MOTIVATION: There is a very large and growing level of effort toward improving the platforms, experiment designs, and data analysis methods for microarray expression profiling. Along with a growing richness in the approaches there is a growing confusion among most scientists as to how to make objective comparisons and choices between them for different applications. There is a need for a standard framework for the microarray community to compare and improve analytical and statistical methods. RESULTS: We report on a microarray data set comprising 204 in-situ synthesized oligonucleotide arrays, each hybridized with two-color cDNA samples derived from 20 different human tissues and cell lines. Design of the approximately 24 000 60mer oligonucleotides that report approximately 2500 known genes on the arrays, and design of the hybridization experiments, were carried out in a way that supports the performance assessment of alternative data processing approaches and of alternative experiment and array designs. We also propose standard figures of merit for success in detecting individual differential expression changes or expression levels, and for detecting similarities and differences in expression patterns across genes and experiments. We expect this data set and the proposed figures of merit will provide a standard framework for much of the microarray community to compare and improve many analytical and statistical methods relevant to microarray data analysis, including image processing, normalization, error modeling, combining of multiple reporters per gene, use of replicate experiments, and sample referencing schemes in measurements based on expression change. AVAILABILITY/SUPPLEMENTARY INFORMATION: Expression data and supplementary information are available at http://www.rii.com/publications/2003/HE_SDS.htm     

An explicit expression for determining cometabolism kinetics using progress curve analysis

We present an explicit expression for describing the kinetics of cometabolic biotransformation of environmental pollutants. This expression is based on the Lambert W function and explicitly relates the substrate concentration, S, to time, t, the two experimentally measured variables. This explicit relationship simplifies kinetic parameter estimation as differential equation solution and iterative estimation of the substrate concentration are eliminated. The applicability of this new expression for nonlinear kinetic parameter estimation was first demonstrated using noise containing synthetic data where final estimates of the kinetic parameters were very close to their actual values. Subsequently 1.1.1-trichloroethane degradation data at initial concentrations of 750 and 375 μM were described using the explicit expression resulting in r and K(s) estimates of 0.26 μM/mg d and 28.08 μM and 0.30 μM/mg d and 28.70 μM, respectively, very similar to 0.276 μM/mg d and 31.2 μM, respectively, that were reported in the original study. The new explicit expression presented in this study simplifies estimation of cometabolic kinetic parameters and can be easily used across all computational platforms thereby providing an attractive alternative for progress curve analysis.     

Comparison of gene expression measurements from cDNA and 60-mer oligonucleotide microarrays

As the data generated by microarray technology continue to amass, it is necessary to compare and combine gene expression data from different platforms. To evaluate the performance of cDNA and long oligonucleotide (60-mer) arrays, we generated gene expression profiles for two cancer cell lines and compared the data between the two platforms. All 6182 unique genes represented on both platforms were included in the analysis. A limited correlation (r = 0.4708) was obtained and the difference in measurement of low-expression genes was considered to contribute to the limited correlation. Further restriction of the data set to differentially expressed genes detected in cDNA microarrays (1205 genes) and oligonucleotide arrays (1325 genes) showed modest correlations of 0.7076 and 0.6441 between the two platforms. Quantitative real-time PCR measurements of a set of 10 genes showed better correlation with oligonucleotide arrays. Our results demonstrate that there is substantial variation in the data generated from cDNA and 60-mer oligonucleotide arrays. Although general agreement was observed in measurements of differentially expressed genes, we suggest that data from different platforms could not be directly amassed.     

An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence

Interbody fusion device subsidence has been reported clinically. An enhanced understanding of the mechanical behaviour of the surrounding bone would allow for accurate predictions of vertebral subsidence. The multiaxial inelastic behaviour of trabecular bone is investigated at a microscale and macroscale level. The post-yield behaviour of trabecular bone under hydrostatic and confined compression is investigated using microcomputed tomography-derived microstructural models, elucidating a mechanism of pressure-dependent yielding at the macroscopic level. Specifically, microstructural trabecular simulations predict a distinctive yield point in the apparent stress–strain curve under uniaxial, confined and hydrostatic compression. Such distinctive apparent stress–strain behaviour results from localised stress concentrations and material yielding in the trabecular microstructure. This phenomenon is shown to be independent of the plasticity formulation employed at a trabecular level. The distinctive response can be accurately captured by a continuum model using a crushable foam plasticity formulation in which pressure-dependent yielding occurs. Vertebral device subsidence experiments are also performed, providing measurements of the trabecular plastic zone. It is demonstrated that a pressure-dependent plasticity formulation must be used for continuum level macroscale models of trabecular bone in order to replicate the experimental observations, further supporting the microscale investigations. Using a crushable foam plasticity formulation in the simulation of vertebral subsidence, it is shown that the predicted subsidence force and plastic zone size correspond closely with the experimental measurements. In contrast, the use of von Mises, Drucker–Prager and Hill plasticity formulations for continuum trabecular bone models lead to over prediction of the subsidence force and plastic zone.