Relationship between gene expression and observed intensities in DNA microarrays—a modeling study

A theoretical study of the physical properties which determine the variation in signal strength from probe to probe on a microarray is presented. A model which incorporates probe-target hybridization, as well as the subsequent dissociation which occurs during stringent washing of the microarray, is introduced and shown to reasonably describe publicly available spike-in experiments carried out at Affymetrix. In particular, this model suggests that probe-target dissociation during the stringent wash plays a critical role in determining the observed hybridization intensities. In addition, it is demonstrated that non-specific hybridization introduces uncertainties which significantly limit the ability of any model to accurately quantify absolute gene expression levels while, in contrast, target folding appears to have little effect on these results. Finally, for data from target spike-in experiments, our model is shown to compare favorably with an existing statistical model in determining target concentration levels.     

Understanding the physics of oligonucleotide microarrays: the Affymetrix spike-in data reanalysed

The Affymetrix U95 and U133 Latin-Square spike-in datasets are reanalysed, together with a dataset from a version of the U95 spike-in experiment without a complex non-specific background. The approach uses a physico-chemical model which includes the effects of the specific and non-specific hybridization and probe folding at the microarray surface, target folding and hybridization in the bulk RNA target solution and duplex dissociation during the post-hybridization washing phase. The model predicts a three-parameter hyperbolic response function that fits well with fluorescence intensity data from all the three datasets. The importance of the various hybridization and washing effects in determining each of the three parameters is examined, and some guidance is given as to how a practical algorithm for determining specific target concentrations might be developed.     

A model of technical variation of microarray signals.

We describe a mathematical model of signal from single-channel direct hybridization microarray platforms. The model establishes a linear relationship between microarray signals and their standard deviations from a minimum set of assumptions. We use the model to precisely define important microarray quality characteristics: resolved fold change and dynamic range. The definitions lead to closed form expressions relating these characteristics to physical parameters of the microarray experiment in the case when both specific and nonspecific binding of target to probe are governed by the Langmuir hybridization isotherm. The predictions of the model are in close agreement to data obtained from spike-in experiments. Given the generality of the model, the introduced definitions of dynamic range and resolved concentration fold-change can be used to conduct cross-platform comparisons and to guide improvement of the microarray platform.     

Beyond Affymetrix arrays: expanding the set of known hybridization isotherms and observing pre-wash signal intensities

Microarray hybridization studies have attributed the nonlinearity of hybridization isotherms to probe saturation and post-hybridization washing. Both processes are thought to distort ‘true’ target abundance because immobilized probes are saturated with excess target and stringent washing removes loosely bound targets. Yet the paucity of studies aimed at understanding hybridization and dissociation makes it difficult to align physicochemical theory to microarray results. To fill the void, we first examined hybridization isotherms generated on different microarray platforms using a ribosomal RNA target and then investigated hybridization signals at equilibrium and after stringent wash. Hybridization signal at equilibrium was achieved by treating the microarray with isopropanol, which prevents nucleic acids from dissolving into solution. Our results suggest that (i) the shape of hybridization isotherms varied by microarray platform with some being hyperbolic or linear, and others following a power-law; (ii) at equilibrium, fluorescent signal of different probes hybridized to the same target were not similar even with excess of target and (iii) the amount of target removed by stringent washing depended upon the hybridization time, the probe sequence and the presence/absence of nonspecific targets. Possible physicochemical interpretations of the results and future studies are discussed.     

Use of hybridization melting kinetics for detecting Phytophthora species using three-dimensional microarrays: demonstration of a novel concept for the differentiation of detection targets

Microarray-based detection is limited by variable and inconsistent hybridization intensities across the diversity of probes used in each array. In this paper, we introduce a novel concept for the differentiation of detection targets using duplex melting kinetics. A microarray assay was developed on a PamChip microarray enabling the differentiation of target Phytophthora species using the melting kinetics of probe-target duplexes. In the majority of cases the hybridization kinetics of target and non-target duplexes differed significantly. Analysis of the melting kinetics of duplexes formed by probes with target and non-target DNA was found to be an effective method for determining specific hybridization and was independent of fluctuations in hybridization signal intensity. This form of analysis was more robust than the traditional approach based on hybridization intensity, and enabled the detection of individual Phytophthora species and mixtures thereof.     

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.     

Physicochemical perspectives on DNA microarray and biosensor technologies

Detection and sequence-identification of nucleic acid molecules is often performed by binding, or hybridization, of specimen "target" strands to immobilized, complementary "probe" strands. A familiar example is provided by DNA microarrays used to carry out thousands of solid-phase hybridization reactions simultaneously to determine gene expression patterns or to identify genotypes. The underlying molecular process, namely sequence-specific recognition between complementary probe and target molecules, is fairly well understood in bulk solution. However, this knowledge proves insufficient to adequately understand solid-phase hybridization. For example, equilibrium binding constants for solid-phase hybridization can differ by many orders of magnitude relative to solution values. Kinetics of probe-target binding are affected. Surface interactions, electrostatics and polymer phenomena manifest themselves in ways not experienced by hybridizing strands in bulk solution. The emerging fundamental understanding provides important insights into application of DNA microarray and biosensor technologies.     

Position of the fluorescent label is a crucial factor determining signal intensity in microarray hybridizations

A key issue in applications of short oligonucleotide-based microarrays is how to design specific probes with high sensitivity. Some details of the factors affecting microarray hybridization remain unclear, hampering a reliable quantification of target nucleic acids. We have evaluated the effect of the position of the fluorescent label [position of label (POL)] relative to the probe-target duplex on the signal output of oligonucleotide microarrays. End-labelled single-stranded DNA targets of different lengths were used for hybridization with perfect-match oligonucleotide probe sets targeting different positions of the same molecule. Hybridization results illustrated that probes targeting the labelled terminus of the target showed significantly higher signals than probes targeting other regions. This effect was independent of the target gene, the fluorophore and the slide surface chemistry. Comparison of microarray signal patterns of fluorescently end-labelled, fluorescently internally random-labelled and radioactively end-labelled target-DNAs with the same set of oligonucleotide probes identified POL as a critical factor affecting signal intensity rather than binding efficiency. Our observations define a novel determinant for large differences of signal intensities. Application of the POL effect may contribute to better probe design and data interpretation in microarray applications.     

Mismatch formation in solution and on DNA microarrays: how modified nucleosides can overcome shortcomings of imperfect hybridization caused by oligonucleotide composition and base pairing

The DNA microarray technology is a well-established and widely used technology although it has several drawbacks. The accurate molecular recognition of the canonical nucleobases of probe and target is the basis for reliable results obtained from microarray hybridization experiments. However, the great flexibility of base pairs within the DNA molecule allows the formation of various secondary structures incorporating Watson-Crick base pairs as well as non-canonical base pair motifs, thus becoming a source of inaccuracy and inconsistence. The first part of this report provides an overview of unusual base pair motifs formed during molecular DNA interaction in solution highlighting selected secondary structures employing non-Watson-Crick base pairs. The same mispairing phenomena obtained in solution are expected to occur for immobilized probe molecules as well as for target oligonucleotides employed in microarray hybridization experiments the effect of base pairing and oligonucleotide composition on hybridization is considered. The incorporation of nucleoside derivatives as close shape mimics of the four canonical nucleosides into the probe and target oligonucleotides is discussed as a chemical tool to resolve unwanted mispairing. The second part focuses non-Watson-Crick base pairing during hybridization performed on microarrays. This is exemplified for the unusual stable dG.dA base pair.     

Development of thermodynamic models for simulating probe dissociation profiles in fluorescence in situ hybridization

Stringency in ribosomal RNA (rRNA)-targeted fluorescence in situ hybridization (FISH) is typically adjusted with formamide, and the optimum formamide concentration at which the probe can hybridize with the target rRNA, but not with rRNAs with mismatches, is to be found experimentally. This is a difficult task when target or closest non-target organisms are not available in pure culture, or when there are numerous non-targets of concern. The objective of this work was to formulate mechanistic models capable of simulating the effect of formamide on probe dissociation. Using a previously described equilibrium model of FISH [Yilmaz and Noguera (2004) Applied and Environmental Microbiology 70(12):7126-7139] as the basis, the effect of formamide on free energy changes of probe-target duplex formation (DeltaG(1)(0)) and folding of target region (DeltaG(3)(0)) was simulated to be linear, and models differing in the definitions of the slopes of these relationships (m(1) and m(3)) were calibrated using experimental dissociation profiles for 27 probes targeting the 16S rRNA of Escherichia coli (E. coli). A good level of predictive power was obtained when m(1) was linearly related to probe length and when m(3) was made proportional to DeltaG(3)(0). The effect of single mismatches on probe dissociation with formamide was also studied, although at a preliminary level. The expected changes in DeltaG(1)(0) with the introduction of mismatches were not sufficient to capture the overall trends of mismatched dissociation profiles. In conclusion, this study offers the first theoretical method to calculate dissociation profiles for perfectly matched probes, and suggests a direction to systematically evaluate the effect of formamide on mismatched probes.     

Direct Profiling of Environmental Microbial Populations by Thermal Dissociation Analysis of Native rRNAs Hybridized to Oligonucleotide Microarrays

Oligonucleotide microarrays were used to profile directly extracted rRNA from environmental microbial populations without PCR amplification. In our initial inspection of two distinct estuarine study sites, the hybridization patterns were reproducible and varied between estuarine sediments of differing salinities. The determination of a thermal dissociation curve (i.e., melting profile) for each probe-target duplex provided information on hybridization specificity, which is essential for confirming adequate discrimination between target and nontarget sequences.     

Direct profiling of environmental microbial populations by thermal dissociation analysis of native rRNAs hybridized to oligonucleotide microarrays

Oligonucleotide microarrays were used to profile directly extracted rRNA from environmental microbial populations without PCR amplification. In our initial inspection of two distinct estuarine study sites, the hybridization patterns were reproducible and varied between estuarine sediments of differing salinities. The determination of a thermal dissociation curve (i.e., melting profile) for each probe-target duplex provided information on hybridization specificity, which is essential for confirming adequate discrimination between target and nontarget sequences.     

Conditions to ensure competitive hybridization in two-color microarray: a theoretical and experimental analysis

We derived a theoretical model that explains certain biases observed in the two-color microarray hybridization experiments reported in the literature. We show that true competition is achieved only when the hybridization kinetics of the two differentially labeled probes are the same. If the hybridization kinetics of the two differentially labeled probes is different, which can occur when the labeling and hybridization conditions for the two probes are dissimilar, then differential expression observed becomes a function of the amount of the target (i.e., DNA spotted on the slide). We use this model to validate the microarray methodology by determining the differential expression of four select Arabidopsis genes and two human genes (beta-actin and GAPDH) as a function of the amount of target arrayed. We show through both modeling and experiments that the rate constants for Cy5- and Cy3-labeled probes are the same under our exrimental conditions. Therefore, the target concentrations need not greatly exceed the probe concentration. It is obvious from the data presented that a simple treatment of an individual hybridization rate calculation does notfully describe what is occuring in today's complex, multispecies experiments. The method of validation is easily implemented to ensure data reliability by two-color microarray.     

Specificity of randomly generated genomic DNA fragment probes on a DNA array

The use of randomly generated DNA fragment sequences as probes on DNA arrays offers a unique potential for exploring unsequenced microorganisms. In this study, the detection specificity was evaluated with respect to probe-target sequence similarity using genomic DNAs of four Pseudomonas strains. Genome fragments averaging 2000?bp were found to be specific enough to discriminate 85-90% similarity under highly stringent hybridization conditions. Such stringent conditions compromised signal intensities; however, specific signals remained detectable at the highest stringency (at 75?°C hybridization) with negligible false negatives. These results suggest that, without any probe design or selection, genomic fragments can provide a reasonable specificity for microbial diagnostics or species delineation by DNA-DNA similarities.     

DNA hybrids stabilized by heterologies.

The double D-loop DNA hybrid contains four DNA strands following hybridization of two RecA protein coated complementary single-stranded DNA probes with a homologous region of a double-stranded DNA target. A remarkable feature of the double D-loop DNA hybrids is their kinetic stabilities at internal sites within linear DNA targets after removal of RecA protein from hybrids. We report here that heterologous DNA inserts in one or both probe strands affect the kinetic stability of protein-free double D-loop hybrids. DNA heterologies normally distort DNA-DNA hybrids and consequently accelerate hybrid dissociation. In contrast, heterologous DNA inserts impede dissociation of double D-loops, especially when the insert sequences interact with each other by DNA base pairing. We propose a mechanism for this kinetic stabilization by heterologous DNA inserts based on the hypothesis that the main pathway of dissociation of double D-loop DNA hybrids is a DNA branch migration process involving the rotation of both probe-target duplexes in the hybrids. Heterologous DNA inserts constrain rotation of probe-target duplexes and consequently impede hybrid dissociation. Potential applications of the stabilized double D-loops for gene targeting are discussed.     

Oligonucleotide microchips as genosensors for determinative and environmental studies in microbiology.

The utility of parallel hybridization of environmental nucleic acids to many oligonucleotides immobilized in a matrix of polyacrylamide gel pads on a glass slide (oligonucleotide microchip) was evaluated. Oligonucleotides complementary to small-subunit rRNA sequences of selected microbial groups, encompassing key genera of nitrifying bacteria, were shown to selectively retain labeled target nucleic acid derived from either DNA or RNA forms of the target sequences. The utility of varying the probe concentration to normalize hybridization signals and the use of multicolor detection for simultaneous quantitation of multiple probe-target populations were demonstrated.     

Standardization of protocols in cDNA microarray analysis

Systematic variations can occur at various steps of a cDNA microarray experiment and affect the measurement of gene expression levels. Accepted standards integrated into every cDNA microarray analysis can assess these variabilities and aid the interpretation of cDNA microarray experiments from different sources. A universally applicable approach to evaluate parameters such as input and output ratios, signal linearity, hybridization specificity and consistency across an array, as well as normalization strategies, is the utilization of exogenous control genes as spike-in and negative controls. We suggest that the use of such control sets, together with a sufficient number of experimental repeats, in-depth statistical analysis and thorough data validation should be made mandatory for the publication of cDNA microarray data.     

Mechanistic approach to the problem of hybridization efficiency in fluorescent in situ hybridization

In fluorescent in situ hybridization (FISH), the efficiency of hybridization between the DNA probe and the rRNA has been related to the accessibility of the rRNA when ribosome content and cell permeability are not limiting. Published rRNA accessibility maps show that probe brightness is sensitive to the organism being hybridized and the exact location of the target site and, hence, it is highly unpredictable based on accessibility only. In this study, a model of FISH based on the thermodynamics of nucleic acid hybridization was developed. The model provides a mechanistic approach to calculate the affinity of the probe to the target site, which is defined as the overall Gibbs free energy change (DeltaG degrees overall) for a reaction scheme involving the DNA-rRNA and intramolecular DNA and rRNA interactions that take place during FISH. Probe data sets for the published accessibility maps and experiments targeting localized regions in the 16S rRNA of Escherichia coli were used to demonstrate that DeltaG degrees overall is a strong predictor of hybridization efficiency and superior to conventional estimates based on the dissociation temperature of the DNA/rRNA duplex. The use of the proposed model also allowed the development of mechanistic approaches to increase probe brightness, even in seemingly inaccessible regions of the 16S rRNA. Finally, a threshold DeltaG degrees overall of -13.0 kcal/mol was proposed as a goal in the design of FISH probes to maximize hybridization efficiency without compromising specificity.     

Stability, specificity and fluorescence brightness of multiply-labeled fluorescent DNA probes.

In this work, we studied the fluorescence and hybridization of multiply-labeled DNA probes which have the hydrophilic fluorophore 1-(straightepsilon-carboxypentynyl)-1'-ethyl- 3,3,3', 3'-tetramethylindocarbocyanine-5,5'-disulfonate (Cy3) attached via either a short or long linker at the C-5 position of deoxyuridine. We describe the effects of labeling density, fluorophore charge and linker length upon five properties of the probe: fluorescence intensity, the change in fluorescence upon duplex formation, the quantum yield of fluorescence (Phif), probe-target stability and specificity. For the hydrophilic dye Cy3, we have demonstrated that the fluorescence intensity andPhifare maximized when labeling every 6th base using the long linker. With a less hydrophilic dye, a labeling density this high could not be achieved without serious quenching of the fluorescence. The target specificity of multiply-labeled DNA probes was just as high as compared to the unmodified control probe, however, a less stable probe-target duplex is formed that exhibits a lower melting temperature. A mechanism that accounts for this destabilization is proposed which is consistent with our data. It involves dye-dye and dye-nucleotide interactions which appear to stabilize a single-stranded conformation of the probe.