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

Abstract

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.

Figure 1.

Schematic illustration of the hook plot that presents the log-intensity difference of probe pairs interrogating the same transcript (such as PM and MM probes) taken from one array hybridization as a function of their mean log-intensity (panel a). The probes in the increasing part, the maximum and the decaying part are dominated by non-specific (N), specific (S) hybridization and by asymptotic saturation (as), respectively. The horizontal position of the hook plot, its width and height vary in a characteristic fashion owing to different experimental effects (panel b, see arrows): optical scaling of the intensity owing to changes of the scanner settings or the labeling, shift the whole hook curve in horizontal direction; alterations of the non-specific background level owing to changes of the amount of RNA and/or of its composition, alter the width of the curve and shift only the increasing part in horizontal direction; modifications of the MM design and/or of the hybridization conditions (i.e. the ionic strength), change the vertical dimensions of the hook and, finally, alterations of the post-hybridization washing efficiency mainly affect the height and width of the hook curve. The plots in the right part of panel b compare pairs of hook curves taken from an experimental series referring to the effects schematically illustrated in the left part. The thick curves are experimental data and the thin curves are theoretical hook curves calculated according to the competitive Langmuir binding model. Panel c shows the so-called degradation ‘hooks’: The thick data-curves are calculated using probe intensity data of two different arrays hybridized with RNA of different quality as plots of the smoothed log-3′/5′-intensity ratio-versus-mean where the 3′ and 5′ values are mean log-intensity values using the three probes from each probe set nearest the 3′ and 5′ ends of the respective transcript, respectively. Good-quality RNA (orange curve, RIN is the RNA Integrity Number) shows a lower maximum than bad-quality RNA (blue curve), indicating a decreased 3′/5′-intensity gradient of probes along the transcript. The log-intensity difference vanishes for predominantly non-specifically hybridized probes that are insensitive for RNA quality. Also for saturated probes, the obtained signal difference decreases [see (31) for details].

Figure 2.

Typical behavior of the coverage function θ(x) for a PM/MM pair of probes plotted on linear (upper) and log (lower) scales before (left) and after (middle) post-hybridization washing is accounted for. The coverage fraction θ is the fraction of probe molecules on a feature that have formed probe–target duplexes; x is the concentration of target RNA in the hybridization solution specific to the PM probe sequence. The right-hand plots are measured fluorescence intensities in arbitrary units for one of the probes of the Affymetrix U95 Latin Square spike-in experiment, together with fits of these data to the response function Eq. (1). The PM responses are shown in black and the MM in red.

Figure 3.

Collapsing master curves for all salt concentrations. The probes are grafted by self-assembling of thiols. Enthalpy ΔH⁰ and entropy ΔS⁰ are extracted from linear fits [adopted from (46)].

Figure 4.

Bulging loop on a probe.

Figure 5.

Signal intensity as a function of loop length and position, hybridization temperature 317 K.

Figure 6.

Averaged signal intensity over loop length (top) and loop position (bottom).

Figure 7.

Comparison between the experimental data and the model.

Figure 8.

Comparison of experimental data (filled symbols) and expected isotherm (dashed line). In this plot, I is the measured fluorescence intensities from the microarray spots, while ΔΔG is the hybridization free energy as obtained from the nearest-neighbor model measured with respect to the PM free energy, for which ΔΔG = 0. The experiments are obtained from an Agilent custom array [for more details see (57)].

Figure 9.

Surface-attached 50-mer probe response to designed anticomplementary 50-mer targets, bearing a continuous complementary stretch of varying length (6, 9, 12, 15, 18, or 21 nucleotides). The placement of the complementary stretch is central (diamonds) or terminal (squares). Dotted line indicates the average background intensity across the experiment; solid line indicates the signal intensity due to hybridization of a perfectly matched 50-mer target. (A) target alone and (B) in presence of an equal concentration of unlabeled PM.

Figure 10.

A map of surface hybridization regimes as a function of probe coverage S₀ and salt concentration C_B, and as reported in (65). See text for details.

Figure 11.

Theoretical and experimental melting curves on glass. Experiment: PM (circles) and single MM (triangles) 19-mer oligonucleotides synthesized on glass surface. Theory: fluctuating surface coverage (solid lines) and homogeneous (dashed lines) density of probes.

Figure 12.

ToF-SIMS images of the P ion in single printed DNA spots show large variability of DNA concentration in and across the microarray spots. Spots are printed from 20 and 40 μM DNA concentration drops (from left to right) with 100% of the DNA tagged with Cy3. Image size (400 × 400 μm). The Cy3 fluorescence images of the same spots are shown for comparison.

Figure 13.

Calibration curve for a probe (panel A); grey lines represent individual probe replicates, black line—averages. Histogram of concentrations determined from signal intensities and calibrated probes (panel B); open circles represent true concentrations.

Figure 14.

M(A) plot of the average expression differences M between chromosome 5 trisomic Arabidopsis thaliana plants and disomics (y-axis) as a function of average expression A (x-axis).