SpatialSmooth :: Array surface spatial effect smoothing module

The spatial effect across array surface is the predominant within-slide experimental artifact that needs to be eliminated before any other normalization procedure carried out. Many approaches have been proposed to solve the spatial artifact problems on dual-channel cDNA arrays and oligos arrays, which are attributed to print-tip bias during spotting of the slides and usually have periodic patterns. e.g, the Print-tip Lowess normalization, which is a nonlieanr regression algorithm, based on the MA plot.

However, the methods to deal with dual-channel cDNA array is not suitable for High-desnity in situ synthesized microarray, becaus this spatial artifact ubiquitously observed on in situ synthesized microarrays has a different origin, which is supposed to be mainly from uneven sample washing, and the uneven signal distribution usually has a gradiant trend.

Sptial effect is different on different slides

As the four randomly selected examples of array surface 3D plots shows below, asymmetrical signal distribution on is one of the avoidable systemic errors resulted from uneven washing or scanning that has to be considered.

Distance-weighted factor calculation algorithm,

To remove this single-array variation, Nimble::SpatialSmooth module provides the function by a global distance-weighted smoothing algorithm as Affymetrix used in MAS 5.0 to correct both of the background and foreground intensity on the array surface.

Weighted background and foreground intensity adjustment

Comparing the array spatial signal distribution before and after the SpatialSmooth module done, we conclude that the algorithm really works and make the signals distribute balanced. To support this module, we also developed a program to draw the array surface, called SpatialDraw, which generate SVG images. Please refer to instruction category for detailed usage.

Background subtraction as a way of spatial correction is good or not?

The background subtraction processing in Affymetrix MAS 5.0 is the first step for correcting the probe intensities. As its algorithm described, the array is split up to 16 zones, and the lowest 2% of probe intensities in each zone is regarded as a default background value. The smoothed background intensity is the sum of all the weights to all the zone centers, and will be further subtracted from the probe intensity as a correction to foreground (Affymetrix 2002).

We also follow the Affymetrix MAS 5.0 background subtraction procedure as a correction to foreground intensity, using lowest 5% of probe intensity within each zone as the default background value. After the distance weighted spatial effect smoothing procedure on the background intensity (formula 1 shows), we substract the corrected background intensity from foreground intensity, but as the below left figure shows, background subtraction takes no effect on spatial bias. We also used the negative oligos (Intronic probes) as background to be smoothed and further subtracted from foreground intensity, the spatial effect still remians.

Based on the two analysis above, we conclude that the background substraction as a way of spatial effect correction is not a good idea, since this kind of spatial artifact impact both on the foreground, and background intensities, and because the foreground intensity is exponentially distributed, background subtraction will not take effect on foreground intensities. So, in our NMPP module, we suggest to do the spatial effect smoothing directly on foreground intensities.