BACKGROUND
comparative genomic hybridization , developed by kallioniemi et al.
<cit> , has made a significant impact on molecular cytogenetics as a powerful tool for detection of chromosome copy number aberrations.
however, cgh to metaphase chromosomes provides limited resolution at the 5– <dig> mb level.
solinas-toldo et al.
<cit>  introduced a matrix-cgh technique in which target dna was immobilized onto glass slides and hybridized with tumor dna.
array cgh techniques utilizing printed microarrays or pre-fabricated high density oligonucleotide arrays were further refined to increase the sensitivity to detect single gene gains and losses  <cit> .
more recently several genome-wide approaches using high-density oligonucleotide microarrays or snp chips have been developed  <cit> .
experiments such as these have identified considerable copy number variation across the human genome  <cit> .
similar chromosomal imbalances are seen in evolving populations of bacteria, where deletions, duplications and amplifications of large regions of the chromosome, some including up to 2% of the genome, are observed  <cit> .
in this study, we used the genechip e. coli antisense genome array to study dna gene copy number variation in evolving populations of e. coli.
when e. coli are incubated in batch culture for long periods of time without the addition of nutrients, novel mutants expressing the growth advantage in stationary phase  phenotype appear  <cit> .
these mutants have the ability to outcompete other cells in the population, even though all cells initially had identical genotypes.
previously characterized mutations conferring the gasp phenotype included point mutations, small deletions and insertions, and transposition events  <cit> , .
in this study we characterize the larger scale changes associated with deletions and duplications that can include hundreds of kilobases of the genome.
we describe an unconventional approach for copy number detection using commercially available e. coli high-density expression arrays that includes raw data normalization, background correction, data transformation based on a physical model of the microarray hybridization process, and deletion/duplication detection using a hidden markov model approach.
RESULTS
affymetrix platform
although the genechip e. coli antisense genome array was designed primarily as a tool for expression analysis, it was also created to maximize the amount of e. coli k- <dig> genome sequence covered.
in addition to probes for all annotated genes in the e. coli genome, probes for small unannotated genes, untranslated rna, and uncharacterized intergenic regions were included in the design.
the array contains probe sets to detect the antisense strand of more than  <dig>  known open reading frames.
in addition, over  <dig>  intergenic sequences were interrogated in both directions, permitting accurate copy number detection of potential genome fragments.
e. coli antisense genome arrays are an intermediate between classical expression chips and newly developed tiling arrays, which are more suitable for acgh analysis due to their denser genomic coverage.
array experiments were performed according to a customized protocol; bacterial strains, culture media, and cell growth conditions are described in  <cit> .
the custom sample preparation protocol used in preparing the hybridization cocktail for the affymetrix experiment was adapted from  <cit> .
normalization
due to variations in dna yield between preparations of replicate samples, the dataset analyzed here presents an example of systematic errors attributable to variation in biological samples, where median chip intensities vary 100-fold across the dataset.
we introduce a new method for normalization, as well as for finding systematic biases associated with variations in experimental conditions; see figure  <dig>
the resulting normalized distributions are shown in figure  <dig>  visual exploration of the intensity distributions shows that the proposed method  performs well and does not introduce apparent artifacts as, for example, invariant set normalization  appears to do.
notice that despite similarity in post-normalized distributions, the signal distributions vary significantly in the tails, where duplications and amplifications are presumably located.
spatial normalization
our preliminary analysis revealed strong effects of spatial non-uniformity of chip intensity on copy number prediction.
it appears that for these experiments, correction for spatial artifacts is the critical step in the analysis.
due to the nature of the experiment, it can be assumed that the target concentration remains the same unless a region of amplification or deletion occurs in a given sample.
hence, for a given position, a deviation from the median log-intensity should be randomly distributed around zero.
the observed spatial artifacts were usually contiguous and stretched over significant areas covering multiple probes.
this systematic local deviation from the median profile could be detected and then removed.
we addressed this problem by constructing a median profile of the chips using normalized data for the entire dataset.
then we generated two-dimensional residual maps for each chip and applied spatial smoothing using cubic splines; see figures  <dig> and  <dig>
signal transformation
analysis of raw background-corrected signal intensities revealed a strong sequence-dependent probe effect characteristic of all expression microarray data.
raw signal intensities yield a wide distribution, heavily skewed towards low values.
a common approach to modeling the probe effect is to fit a log-additive model with normal error to the background-adjusted and normalized probe intensities.
we used a similar model in fitting our probe intensity data; see methods section.
the result of this procedure is shown in figure  <dig>  which demonstrates a dramatic reduction in signal variability across all regions.
removing probe-specific variation enhances sensitivity and allows for superior detection of genomic alterations.
it was noticed that deleted regions appear to be noisier, due to a less efficient prediction of non-specific hybridization that is a function of many factors such as random cross-hybridizations that are difficult to predict.
hmm-based dna copy number inference
the goals in our experiment include accurate detection of chromosomal changes  and precise inference of the boundaries of copy number alterations  in each gasp mutant.
although the major aberrations in a genome are frequently evident by inspection, several approaches have been developed to improve detection in the face of measurement noise.
the simplest apply thresholds.
if the ratio profile has only a few well-spaced ratio levels, then thresholds can be chosen by examination of the distribution of all measured ratios  <cit> .
use of smoothing by averaging the ratios on neighboring array elements improves the behavior of thresholding but blurs the locations of boundaries and reduces the amplitude of aberrations involving fewer elements than the smoothing window.
more sophisticated analytical approaches rely on the fact that copy-number changes involve chromosome segments, and so copy numbers at contiguous loci should be identical, except for an occasional abrupt step to a new plateau.
these methods assess statistically the status of each array element in the context of its neighbors  <cit> .
despite a general similarity, this study is different to classical arraycgh studies in cancer research, where impurities in the sample and intrinsic heterogeneity of copy number among cells present a greater challenge to algorithms for inferring copy numbers and breakpoints.
even if the underlying biological process is discrete , the signal in a classical arraycgh analysis is viewed as being continuous, since possible values for chromosomal copy number in the test sample may vary considerably.
this is especially true in the case of clinical tumor samples that contain mixtures of different cell types.
in contrast, each dna sample in this study was harvested from a single homogeneous e. coli colony, yielding changes in signal reflecting discrete changes in dna copy number.
we chose to use a hidden markov model   <cit>  to distinguish genuine copy number changes from random microarray noise and to localize the start and end points of each copy number alteration.
a key feature is the ability of the hmm to make correct inferences in regions where the data show high variance and might otherwise lead to mistaken conclusions  <cit> .
a limitation of the hmm-based methods in the usual arraycgh setting is that they assume invariance of the true hybridization signal intensity along chromosomal regions with the same copy number; however, the experimental design of our study makes this assumption reasonable.
another argument for choosing an hmm is its relative ease of interpretation.
a model was fitted to a pre-assigned state space, i.e.
deletion/no change/amplification, while for methods that do not control the number of possible states a significant post-processing effort is required.
comparisons of several methods for segmenting conventional acgh data are given in  <cit> .
we visualize genomic alteration data according to their relative chromosome positions, so that the relationship between copy-number changes and their physical locations can be investigated in greater detail; see figure  <dig>
CONCLUSIONS
we have developed a method for inferring dna copy number from experiments performed on affymetrix high density expression chips.
our methodology includes a novel normalization method, specifically optimized for this type of data, that dramatically improved the quality of copy number extraction.
with some modification our approach could be applied to gene expression profiling experiments and should significantly reduce noise.
the suggested data transformation allows for efficient separation of the probe effect from different copy number signals, and the hmm-based method leads to accurate copy number detection.
the molecular mechanisms that generate large-scale deletions, duplications, and amplifications in evolving bacterial populations are not well understood.
for example, at present we cannot determine whether homologous or non-homologous recombination events are responsible for creating deletion mutations.
since oligonucleotide-based arrays allow more precise mapping of the endpoints of these events, as more and more endpoints are mapped we may be able to determine the mechanisms leading to deletion events.
similar approaches may yield clues to the mechanisms of duplication and amplification as well.

 comparative genomic hybridization, developed by kallioniemi et al., has made a significant impact on molecular cytogenetics as a powerful tool for detection of chromosome copy number aberrations. however, cgh to metaphase chromosomes provides limited resolution at the 5– mb level. solinas-toldo et al. introduced a matrix-cgh technique in which target dna was immobilized onto glass slides and hybridized with tumor dna. array cgh techniques utilizing printed microarrays or pre-fabricated high density oligonucleotide arrays were further refined to increase the sensitivity to detect single gene gains and losses. more recently several genome-wide approaches using high-density oligonucleotide microarrays or snp chips have been developed. experiments such as these have identified considerable copy number variation across the human genome. similar chromosomal imbalances are seen in evolving populations of bacteria, where deletions, duplications and amplifications of large regions of the chromosome, some including up to 2% of the genome, are observed. in this study, we used the genechip e. coli antisense genome array to study dna gene copy number variation in evolving populations of e. coli. when e. coli are incubated in batch culture for long periods of time without the addition of nutrients, novel mutants expressing the growth advantage in stationary phase phenotype appear. these mutants have the ability to outcompete other cells in the population, even though all cells initially had identical genotypes. previously characterized mutations conferring the gasp phenotype included point mutations, small deletions and insertions, and transposition events,. in this study we characterize the larger scale changes associated with deletions and duplications that can include hundreds of kilobases of the genome. we describe an unconventional approach for copy number detection using commercially available e. coli high-density expression arrays that includes raw data normalization, background correction, data transformation based on a physical model of the microarray hybridization process, and deletion/duplication detection using a hidden markov model approach.  affymetrix platform although the genechip e. coli antisense genome array was designed primarily as a tool for expression analysis, it was also created to maximize the amount of e. coli k- genome sequence covered. in addition to probes for all annotated genes in the e. coli genome, probes for small unannotated genes, untranslated rna, and uncharacterized intergenic regions were included in the design. the array contains probe sets to detect the antisense strand of more than known open reading frames. in addition, over intergenic sequences were interrogated in both directions, permitting accurate copy number detection of potential genome fragments. e. coli antisense genome arrays are an intermediate between classical expression chips and newly developed tiling arrays, which are more suitable for acgh analysis due to their denser genomic coverage. array experiments were performed according to a customized protocol; bacterial strains, culture media, and cell growth conditions are described in. the custom sample preparation protocol used in preparing the hybridization cocktail for the affymetrix experiment was adapted from. normalization due to variations in dna yield between preparations of replicate samples, the dataset analyzed here presents an example of systematic errors attributable to variation in biological samples, where median chip intensities vary 100-fold across the dataset. we introduce a new method for normalization, as well as for finding systematic biases associated with variations in experimental conditions; see figure the resulting normalized distributions are shown in figure visual exploration of the intensity distributions shows that the proposed method performs well and does not introduce apparent artifacts as, for example, invariant set normalization appears to do. notice that despite similarity in post-normalized distributions, the signal distributions vary significantly in the tails, where duplications and amplifications are presumably located. spatial normalization our preliminary analysis revealed strong effects of spatial non-uniformity of chip intensity on copy number prediction. it appears that for these experiments, correction for spatial artifacts is the critical step in the analysis. due to the nature of the experiment, it can be assumed that the target concentration remains the same unless a region of amplification or deletion occurs in a given sample. hence, for a given position, a deviation from the median log-intensity should be randomly distributed around zero. the observed spatial artifacts were usually contiguous and stretched over significant areas covering multiple probes. this systematic local deviation from the median profile could be detected and then removed. we addressed this problem by constructing a median profile of the chips using normalized data for the entire dataset. then we generated two-dimensional residual maps for each chip and applied spatial smoothing using cubic splines; see figures and signal transformation analysis of raw background-corrected signal intensities revealed a strong sequence-dependent probe effect characteristic of all expression microarray data. raw signal intensities yield a wide distribution, heavily skewed towards low values. a common approach to modeling the probe effect is to fit a log-additive model with normal error to the background-adjusted and normalized probe intensities. we used a similar model in fitting our probe intensity data; see methods section. the result of this procedure is shown in figure which demonstrates a dramatic reduction in signal variability across all regions. removing probe-specific variation enhances sensitivity and allows for superior detection of genomic alterations. it was noticed that deleted regions appear to be noisier, due to a less efficient prediction of non-specific hybridization that is a function of many factors such as random cross-hybridizations that are difficult to predict. hmm-based dna copy number inference the goals in our experiment include accurate detection of chromosomal changes and precise inference of the boundaries of copy number alterations in each gasp mutant. although the major aberrations in a genome are frequently evident by inspection, several approaches have been developed to improve detection in the face of measurement noise. the simplest apply thresholds. if the ratio profile has only a few well-spaced ratio levels, then thresholds can be chosen by examination of the distribution of all measured ratios. use of smoothing by averaging the ratios on neighboring array elements improves the behavior of thresholding but blurs the locations of boundaries and reduces the amplitude of aberrations involving fewer elements than the smoothing window. more sophisticated analytical approaches rely on the fact that copy-number changes involve chromosome segments, and so copy numbers at contiguous loci should be identical, except for an occasional abrupt step to a new plateau. these methods assess statistically the status of each array element in the context of its neighbors. despite a general similarity, this study is different to classical arraycgh studies in cancer research, where impurities in the sample and intrinsic heterogeneity of copy number among cells present a greater challenge to algorithms for inferring copy numbers and breakpoints. even if the underlying biological process is discrete, the signal in a classical arraycgh analysis is viewed as being continuous, since possible values for chromosomal copy number in the test sample may vary considerably. this is especially true in the case of clinical tumor samples that contain mixtures of different cell types. in contrast, each dna sample in this study was harvested from a single homogeneous e. coli colony, yielding changes in signal reflecting discrete changes in dna copy number. we chose to use a hidden markov model to distinguish genuine copy number changes from random microarray noise and to localize the start and end points of each copy number alteration. a key feature is the ability of the hmm to make correct inferences in regions where the data show high variance and might otherwise lead to mistaken conclusions. a limitation of the hmm-based methods in the usual arraycgh setting is that they assume invariance of the true hybridization signal intensity along chromosomal regions with the same copy number; however, the experimental design of our study makes this assumption reasonable. another argument for choosing an hmm is its relative ease of interpretation. a model was fitted to a pre-assigned state space, i.e. deletion/no change/amplification, while for methods that do not control the number of possible states a significant post-processing effort is required. comparisons of several methods for segmenting conventional acgh data are given in. we visualize genomic alteration data according to their relative chromosome positions, so that the relationship between copy-number changes and their physical locations can be investigated in greater detail; see figure  we have developed a method for inferring dna copy number from experiments performed on affymetrix high density expression chips. our methodology includes a novel normalization method, specifically optimized for this type of data, that dramatically improved the quality of copy number extraction. with some modification our approach could be applied to gene expression profiling experiments and should significantly reduce noise. the suggested data transformation allows for efficient separation of the probe effect from different copy number signals, and the hmm-based method leads to accurate copy number detection. the molecular mechanisms that generate large-scale deletions, duplications, and amplifications in evolving bacterial populations are not well understood. for example, at present we cannot determine whether homologous or non-homologous recombination events are responsible for creating deletion mutations. since oligonucleotide-based arrays allow more precise mapping of the endpoints of these events, as more and more endpoints are mapped we may be able to determine the mechanisms leading to deletion events. similar approaches may yield clues to the mechanisms of duplication and amplification as well. 
microarray-based comparative genomic hybridization has enabled the high-resolution detection of dna copy number aberrations. we have developed a robust and flexible methodology for high-resolution analysis of dna copy number of whole genomes, using affymetrix high-density expression oligonucleotide microarrays. copy number is obtained from fluorescence signals after processing with novel normalization, spatial artifact correction, data transformation and deletion/duplication detection. the sequencing of many genomes and tiling arrays consisting of millions of dna segments spanning entire genomes have made high-resolution copy number analysis possible. while many of the methods and algorithms developed for the analysis microarrays have focused on expression analysis, the same technology can be used to detect genetic alterations, using for example standard commercial affymetrix arrays.
 the sequencing of many genomes and tiling arrays consisting of millions of dna segments spanning entire genomes have made high-resolution copy number analysis possible. microarray-based comparative genomic hybridization has enabled the high-resolution detection of dna copy number aberrations. while many of the methods and algorithms developed for the analysis microarrays have focused on expression analysis, the same technology can be used to detect genetic alterations, using for example standard commercial affymetrix arrays. due to the nature of the resultant data, standard techniques for processing genechip expression experiments are inapplicable.  we have developed a robust and flexible methodology for high-resolution analysis of dna copy number of whole genomes, using affymetrix high-density expression oligonucleotide microarrays. copy number is obtained from fluorescence signals after processing with novel normalization, spatial artifact correction, data transformation and deletion/duplication detection. we applied our approach to identify deleted and amplified regions in e. coli mutants obtained after prolonged starvation.  the availability of affymetrix expression chips for a wide variety of organisms makes the proposed array cgh methodology useful more generally. 