Modeling and Estimation for Real-Time Microarrays

Microarrays are used for collecting information about a large number of different genomic particles simultaneously. Conventional fluorescent-based microarrays acquire data after the hybridization phase. During this phase, the target analytes (e.g., DNA fragments) bind to the capturing probes on the array and, by the end of it, supposedly reach a steady state. Therefore, conventional microarrays attempt to detect and quantify the targets with a single data point taken in the steady state. On the other hand, a novel technique, the so-called real-time microarray, capable of recording the kinetics of hybridization in fluorescent-based microarrays has recently been proposed. The richness of the information obtained therein promises higher signal-to-noise ratio, smaller estimation error, and broader assay detection dynamic range compared to conventional microarrays. In this paper, we study the signal processing aspects of the real-time microarray system design. In particular, we develop a probabilistic model for real-time microarrays and describe a procedure for the estimation of target amounts therein. Moreover, leveraging on system identification ideas, we propose a novel technique for the elimination of cross hybridization. These are important steps toward developing optimal detection algorithms for real-time microarrays, and to understanding their fundamental limitations

Modeling the kinetics of hybridization in microarrays

Conventional fluorescent-based microarrays acquire data after the hybridization phase. In this phase the targets analytes (i.e., DNA fragments) bind to the capturing probes on the array and supposedly reach a steady state. Accordingly, microarray experiments essentially provide only a single, steady-state data point of the hybridization process. On the other hand, a novel technique (i.e., realtime microarrays) capable of recording the kinetics of hybridization in fluorescent-based microarrays has recently been proposed in [5]. The richness of the information obtained therein promises higher signal-to-noise ratio, smaller estimation error, and broader assay detection dynamic range compared to the conventional microarrays. In the current paper, we develop a probabilistic model of the kinetics of hybridization and describe a procedure for the estimation of its parameters which include the binding rate and target concentration. This probabilistic model is an important step towards developing optimal detection algorithms for the microarrays which measure the kinetics of hybridization, and to understanding their fundamental limitations

Compressive Sensing DNA Microarrays

Compressive sensing microarrays (CSMs) are DNA-based sensors that operate using group testing and compressive sensing (CS) principles. In contrast to conventional DNA microarrays, in which each genetic sensor is designed to respond to a single target, in a CSM, each sensor responds to a set of targets. We study the problem of designing CSMs that simultaneously account for both the constraints from CS theory and the biochemistry of probe-target DNA hybridization. An appropriate cross-hybridization model is proposed for CSMs, and several methods are developed for probe design and CS signal recovery based on the new model. Lab experiments suggest that in order to achieve accurate hybridization profiling, consensus probe sequences are required to have sequence homology of at least 80% with all targets to be detected. Furthermore, out-of-equilibrium datasets are usually as accurate as those obtained from equilibrium conditions. Consequently, one can use CSMs in applications in which only short hybridization times are allowed

Can Zipf's law be adapted to normalize microarrays?

BACKGROUND: Normalization is the process of removing non-biological sources of variation between array experiments. Recent investigations of data in gene expression databases for varying organisms and tissues have shown that the majority of expressed genes exhibit a power-law distribution with an exponent close to -1 (i.e. obey Zipf's law). Based on the observation that our single channel and two channel microarray data sets also followed a power-law distribution, we were motivated to develop a normalization method based on this law, and examine how it compares with existing published techniques. A computationally simple and intuitively appealing technique based on this observation is presented. RESULTS: Using pairwise comparisons using MA plots (log ratio vs. log intensity), we compared this novel method to previously published normalization techniques, namely global normalization to the mean, the quantile method, and a variation on the loess normalization method designed specifically for boutique microarrays. Results indicated that, for single channel microarrays, the quantile method was superior with regard to eliminating intensity-dependent effects (banana curves), but Zipf's law normalization does minimize this effect by rotating the data distribution such that the maximal number of data points lie on the zero of the log ratio axis. For two channel boutique microarrays, the Zipf's law normalizations performed as well as, or better than existing techniques. CONCLUSION: Zipf's law normalization is a useful tool where the Quantile method cannot be applied, as is the case with microarrays containing functionally specific gene sets (boutique arrays)

Recovering Sparse Signals Using Sparse Measurement Matrices in Compressed DNA Microarrays

Microarrays (DNA, protein, etc.) are massively parallel affinity-based biosensors capable of detecting and quantifying a large number of different genomic particles simultaneously. Among them, DNA microarrays comprising tens of thousands of probe spots are currently being employed to test multitude of targets in a single experiment. In conventional microarrays, each spot contains a large number of copies of a single probe designed to capture a single target, and, hence, collects only a single data point. This is a wasteful use of the sensing resources in comparative DNA microarray experiments, where a test sample is measured relative to a reference sample. Typically, only a fraction of the total number of genes represented by the two samples is differentially expressed, and, thus, a vast number of probe spots may not provide any useful information. To this end, we propose an alternative design, the so-called compressed microarrays, wherein each spot contains copies of several different probes and the total number of spots is potentially much smaller than the number of targets being tested. Fewer spots directly translates to significantly lower costs due to cheaper array manufacturing, simpler image acquisition and processing, and smaller amount of genomic material needed for experiments. To recover signals from compressed microarray measurements, we leverage ideas from compressive sampling. For sparse measurement matrices, we propose an algorithm that has significantly lower computational complexity than the widely used linear-programming-based methods, and can also recover signals with less sparsity

Physico-chemical foundations underpinning microarray and next-generation sequencing experiments

Hybridization of nucleic acids on solid surfaces is a key process involved in high-throughput technologies such as microarrays and, in some cases, next-generation sequencing (NGS). A physical understanding of the hybridization process helps to determine the accuracy of these technologies. The goal of a widespread research program is to develop reliable transformations between the raw signals reported by the technologies and individual molecular concentrations from an ensemble of nucleic acids. This research has inputs from many areas, from bioinformatics and biostatistics, to theoretical and experimental biochemistry and biophysics, to computer simulations. A group of leading researchers met in Ploen Germany in 2011 to discuss present knowledge and limitations of our physico-chemical understanding of high-throughput nucleic acid technologies. This meeting inspired us to write this summary, which provides an overview of the state-of-the-art approaches based on physico-chemical foundation to modeling of the nucleic acids hybridization process on solid surfaces. In addition, practical application of current knowledge is emphasized

A comparison of the Benjamini-Hochberg procedure with some Bayesian rules for multiple testing

In the spirit of modeling inference for microarrays as multiple testing for sparse mixtures, we present a similar approach to a simplified version of quantitative trait loci (QTL) mapping. Unlike in case of microarrays, where the number of tests usually reaches tens of thousands, the number of tests performed in scans for QTL usually does not exceed several hundreds. However, in typical cases, the sparsity $p$ of significant alternatives for QTL mapping is in the same range as for microarrays. For methodological interest, as well as some related applications, we also consider non-sparse mixtures. Using simulations as well as theoretical observations we study false discovery rate (FDR), power and misclassification probability for the Benjamini-Hochberg (BH) procedure and its modifications, as well as for various parametric and nonparametric Bayes and Parametric Empirical Bayes procedures. Our results confirm the observation of Genovese and Wasserman (2002) that for small p the misclassification error of BH is close to optimal in the sense of attaining the Bayes oracle. This property is shared by some of the considered Bayes testing rules, which in general perform better than BH for large or moderate $p$'s.Comment: Published in at http://dx.doi.org/10.1214/193940307000000158 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Towards MRI microarrays

Superparamagnetic iron oxide nanometre scale particles have been utilised as contrast agents to image staked target binding oligonucleotide arrays using MRI to correlate the signal intensity and relaxation times in different NMR fluids