BACKGROUND
many statistical algorithms combine microarray expression data and genome sequence data to find transcription factor binding motifs  in the low eukaryotic genomes.
an early work searches for the regulatory motifs that are associated with significant mean expression changes when they are in the promoter regions of genes; the motifs are then clustered according to their contributions across the arrays  <cit> .
several approaches fit expression data to motif occurrences by multivariate linear regression model; thereafter, the motifs are selected by classical covariate selection procedures  <cit> .
these works were validated in saccharomyces cerevisiae genome.
finding cis-regulatory elements in higher eukaryotes, however, remains a challenge.
in higher eukaryotes, the gene expression clusters often do not lead to successful identification of the transcription factor binding sites.
the difficulty arises from two aspects.
first, the complex regulatory mechanisms of higher eukaryotes impede the search of the genomes.
transcription factor binding sites, usually short , may appear in far upstream, e.g.,  <dig>  bases upstream from the transcription starting site, in the introns and even in the downstream regions.
furthermore, the transcription factors work in combinations  <cit> .
several approaches are proposed to overcome the difficulty.
for example, studies showed that cross-species genome alignment could guide the search for functional regulatory elements  <cit> .
only about 5% of the mammalian genome is under purifying selection  <cit> , and we can study a small subset of genome that is more likely to have important functions by focusing on common non-coding regions across the species.
second, the widely accepted distance measures for comparing expression profiles are inadequate for distinguishing genes from distinct regulatory mechanisms in higher eukaryotes.
the quality of the distance measure is fundamental for high-level analysis methods such as clustering algorithms to identify co-expressed gene groups.
from our experience in microarray data analysis, often genes with similar expression patterns share little common tfbms in their promoter regions.
we will propose a distance measure for expression profiles that correlates better with the regulatory distance than the widely used distance measures such as one minus correlation and one minus cosine correlation.
several studies have improved the quality of distance measures by accounting for the technical noise during the hybridization of mrna on gene chips  <cit> ; they, however, do not account for the regulatory information  <cit> .
RESULTS
data description
the performances of different distance measures were compared on seven experiments that consist overall  <dig> mouse oligonucleotide microarrays.
the regulatory pathways involved in the experiments shall vary across the data sets.
su et al.
<cit>  generated expression data,  <dig> arrays, from dissected mouse samples across  <dig> tissue types: the data represent a substantial description of the normal murine transcriptome because the samples mainly come from the normal physiological state.
storch et al.
<cit>  generated circadian gene expressions,  <dig> arrays, from mouse liver and heart: mice were synchronized to a 12-h light/dark cycle for  <dig> weeks and to the dim light for 42-h before the tissues were collected at 4-h intervals over two circadian cycles.
wang et al.
<cit>  generated gene expressions,  <dig> arrays, during the preimplantation development over  <dig> time points from germinal vesicle stage oocyte to expanded blastocyst.
zhao et al.
<cit>  generated muscle regeneration genes expressions,  <dig> arrays, across  <dig> time points up to  <dig> days after injecting a toxin into the mouse gastrocnemius muscle.
we have neocortex developmental gene expressions,  <dig> arrays, across the developmental time courses from embryonic  <dig>  days to  <dig> days postnatal.
in addition, we used  <dig> mouse expression profile data sets from the public expression profiling resource  <cit> : 1) forty samples from a balb/cj murine model of human asthma that used the ragweed pollen to sensitize and challenge the mice, 2) thirty brain hippocampus samples from neurofibromin- <dig> heterozygous and control mice,  <dig> samples each, collected from  <dig> to  <dig> days postnatal.
the mrna samples from su et al.
<cit>  were hybridized on affymetrix mg_u74a chips.
the samples from all other data sets were hybridized on either moe430a or mg_u74av <dig> chips.
we then mapped  <dig> known mouse tfbm matrices to the regions from  <dig> base upstream to  <dig> base downstream relative to transcription starting site of all genes in two mouse gene chips.
only top 10% regions most well aligned across the genomes of three species were used in the motif mapping.
the known binding motifs and the information on their corresponding binding proteins were obtained from the online database transfac  <cit> .
these known tfbms represent a small portion of all transcription factors in mouse.
linking co-expression and co-regulation, in mouse
for each of seven data sets, we first selected  <dig>  probe sets with the most variable expression patterns.
then for each pair of genes, we identified the common tfbms in the promoter regions of both genes.
the redundancy of some probe sets with a common target gene or of some genes with overlapping promoter regions was taken into account .
we defined the measure of the regulatory similarity between a gene pair as the number of the common tfbms in their promoter regions .
a significantly large number of tfbms in the promoter region of a gene may indicate the validity of their regulatory role on the gene  <cit> .
here, we extended the idea to define the regulatory similarity between two genes.
then, we defined the expression distance between a gene pair as  <dig> minus correlation between two profiles.
figure 1a shows the observed median expression distance of gene pairs as a function of the regulatory similarity between the two genes.
the figure demonstrates that genes that share large number of common tfbms are more likely to have highly correlated expression patterns: sometimes, the effect is present only when they share enough common tfbms.
for each data set, the correlation was computed between the median expression distance and regulatory similarity.
to calculate the significance of such correlation, we permuted the mapping between genes and their promoter regions  <dig> times.
note that some p-values are not statistically significant in the figure.
in the next section, we propose a simple distance measure between the expression profiles that correlates stronger with the regulatory similarity.
a new distance measure for comparing expression profiles
when the medians of two expression profiles over n samples ,  are m and m, we define the distance between two profiles as following:
∑i=1n{log⁡2)−log⁡2)}2
mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaadagcaaqaamaaqahabawaaiwaaeaacyggsbabcqggvbwbcqggnbwzdawgaawcbagaegomaidabeaakiabcicaomaalyaabagaemieag3aasbaasqaaiabdmgapbqabaaakeaacqwgtbqbcqggoaakcqwg4baecqggpaqkaagaeiykakiaeyoei0iagiibawmaei4ba8maei4zac2aasbaasqaaiabikdayaqabagccqggoaakdawcgaqaaiabdmha5naabaaaleaacqwgpbqaaeqaaagcbagaemyba0maeiikagiaemyeaknaeiykakcaaiabcmcapagaay5eaiaaw2haamaacaaaleqabagaegomaidaaaqaaiabdmgapjabg2da9iabigdaxaqaaiabd6gaubqdcqghris5aawcbeaaaaa@5541@
the distance measure is equivalent as the euclidian distance between two standardized profiles ,  where x˜i
mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaacuwg4baegaacamaabaaaleaacqwgpbqaaeqaaaaa@2fbb@ = log <dig> ), y˜i
mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaacuwg5bqegaacamaabaaaleaacqwgpbqaaeqaaaaa@2fbd@ = log <dig> ).
the distance is zero when two expression profiles have identical fold-changes between all samples.
when two profiles are close by this new distance measure, they also have high pearson's correlation: when two profiles have zero distance by the new measure, the pearson's correlation is one.
when two profiles have high correlation, however, they are not necessarily close by the new distance measure.
this property enables us to further select co-expressed genes among highly correlated genes.
figure  <dig> compares how two different expression distance measures correlate with the regulatory similarity in  <dig> data sets.
the p-values and correlations are computed the way previously described for each data set and for each distance measure.
table  <dig> summarizes the result with seven different distance measures.
all seven distance measures correlate with the regulatory distances.
in contrast, when we use the euclidian distance without any standardization, such correlations shown in figure  <dig> disappear and the plots become noisy .
this is because the probes in oligonucleotide arrays have different affinities; the signals from different probes are incomparable without a proper standardization.
the figure and the table show that, while all other six distance measures perform similar, the new distance measure correlates best with the regulatory similarity.
only the new distance measure correlates significantly with the regulatory similarity in all seven data sets.
such improvement is expected since it is likely that many genes in the close regulatory distance at the molecular level should not only share their linear patterns but also have similar fold-changes across the samples.
interestingly, such link is extremely strong regardless of the choice of distance measure in the neurofibromatosis data, the only tumor data in our analysis.
we attribute this to the inclusion of the transcription factors that are playing major role in this illness in the  <dig> available tfbms in the binding analysis.
two main transcription factor complexes, nf- <dig> and nf- <dig>  relating to the illness are included in the binding analysis.
discussion
we established that a simple expression distance measure that considers both the linear trends and expression fold-changes across the samples performs better than widely accepted distance measures do.
before clustering the gene expression profiles generated from oligonucleotide arrays, a proper standardization is essential because of the different affinities of the probes.
we proposed a simple standardization that leads to the clustering of co-regulated genes more successfully than other widely used methods do.
in addition, we demonstrated the correlation between the expression distance and the regulatory distance, in mouse.
in yeast genome, the hypothesis that genes with similar expression patterns are likely to be regulated via the same mechanisms has been quantitatively tested with large-scale data  <cit> .
our study of such relationship between co-expression and co-regulation in a mammalian genome provide a groundwork for current efforts to develop the combined analysis methods for expression and cis-regulatory data.
we note that, however, the statistically significant correlations are between regulatory similarity and median expression distance.
the direct correlation between regulatory similarity and expression distance is not significant.
this is expected because of our simplistic definition of regulatory similarity and the limited number  of known tfbms from the murine genome.
here, we used the strength of such link to compare different expression distance measures but not to emphasize the correlation between the expression distance measure and the regulatory similarity.
following the work on yeast  <cit> , we attempted to introduce the 2nd order of regulatory distances by accounting indirect regulatory relationship between genes but the results were similar.
conceptual comparison of the new distance measure with others
one minus correlation is widely accepted as the distance measure between expression profiles; it captures the linear relationship between expression patterns.
it fails, however, to account the fold-changes in expression between samples.
when one minus correlation is the distance measure to cluster co-expressed gene groups, each cluster consist genes with similar linear expression patterns but with varying fold-changes between samples.
as an illustration, figure  <dig> shows a typical gene cluster in a heatmap diagram.
it is the tightest gene cluster on the mice cortex developmental data generated by a sophisticated clustering algorithm  <cit> .
the genes in the diagram have tight linear expression pattern but their fold-changes between samples are highly variable.
such variability is a general phenomenon when one minus correlation is the distance measure.
this was the motivation to define a better distance measure; we hypothesized that many genes in the close regulatory distance at molecular level not only share their linear patterns but also have similar fold-changes in expression across the samples.
in our experience, clustering analysis with correlation as the distance measure often results in large gene groups.
in practice, it is desirable to reduce the gene numbers and increase the regulatory relevance since the genes are often the starting points for costly biological experiments.
with the new distance measure, we identified gene clusters in mice cortex data with both similar linear pattern and similar fold-changes across the samples with smaller cluster sizes.
another popular standardization approach is the pearson's correlation on the log-transformed data.
one minus pearson's correlation is square root of euclidian distance after centering and re-scaling the data.
hence, the regulatory information in the scale of log fold-changes is lost.
in addition, no longer the genes with similar linear trends will cluster together.
in contrast, the new distance measure, after log transformation, involves centering but not re-scaling.
table  <dig> suggests that the scale of log fold-changes contains significant co-regulation information.
the preservation of the inherent regulatory information in expression profiles depend on both the hybridization process and the expression index calculation methods.
here, all samples were hybridized according to the affymetrix protocol and the expression indices were computed by the multi-array model based approach  <cit> .
meta data analysis
we proposed the log transformation with base  <dig>  when expression data from multiple experiments are combined, however, often variation from certain experiments dominates the analysis.
we suggest using different bases for log-transformation in each experiment, e.g., 280th percentile of the interquantile ranges of all genes.
CONCLUSIONS
the study reveals that the proposed distance measure for comparing expression profiles reflects the inherent regulatory information better than widely accepted distance measures such as the pearson's correlation or cosine correlation, with or without log transformation.
the distance measure enables us to identify genes with large number of common regulatory elements.

 many statistical algorithms combine microarray expression data and genome sequence data to find transcription factor binding motifs in the low eukaryotic genomes. an early work searches for the regulatory motifs that are associated with significant mean expression changes when they are in the promoter regions of genes; the motifs are then clustered according to their contributions across the arrays. several approaches fit expression data to motif occurrences by multivariate linear regression model; thereafter, the motifs are selected by classical covariate selection procedures. these works were validated in saccharomyces cerevisiae genome. finding cis-regulatory elements in higher eukaryotes, however, remains a challenge. in higher eukaryotes, the gene expression clusters often do not lead to successful identification of the transcription factor binding sites. the difficulty arises from two aspects. first, the complex regulatory mechanisms of higher eukaryotes impede the search of the genomes. transcription factor binding sites, usually short, may appear in far upstream, e.g., bases upstream from the transcription starting site, in the introns and even in the downstream regions. furthermore, the transcription factors work in combinations. several approaches are proposed to overcome the difficulty. for example, studies showed that cross-species genome alignment could guide the search for functional regulatory elements. only about 5% of the mammalian genome is under purifying selection, and we can study a small subset of genome that is more likely to have important functions by focusing on common non-coding regions across the species. second, the widely accepted distance measures for comparing expression profiles are inadequate for distinguishing genes from distinct regulatory mechanisms in higher eukaryotes. the quality of the distance measure is fundamental for high-level analysis methods such as clustering algorithms to identify co-expressed gene groups. from our experience in microarray data analysis, often genes with similar expression patterns share little common tfbms in their promoter regions. we will propose a distance measure for expression profiles that correlates better with the regulatory distance than the widely used distance measures such as one minus correlation and one minus cosine correlation. several studies have improved the quality of distance measures by accounting for the technical noise during the hybridization of mrna on gene chips; they, however, do not account for the regulatory information.  data description the performances of different distance measures were compared on seven experiments that consist overall mouse oligonucleotide microarrays. the regulatory pathways involved in the experiments shall vary across the data sets. su et al. generated expression data, arrays, from dissected mouse samples across tissue types: the data represent a substantial description of the normal murine transcriptome because the samples mainly come from the normal physiological state. storch et al. generated circadian gene expressions, arrays, from mouse liver and heart: mice were synchronized to a 12-h light/dark cycle for weeks and to the dim light for 42-h before the tissues were collected at 4-h intervals over two circadian cycles. wang et al. generated gene expressions, arrays, during the preimplantation development over time points from germinal vesicle stage oocyte to expanded blastocyst. zhao et al. generated muscle regeneration genes expressions, arrays, across time points up to days after injecting a toxin into the mouse gastrocnemius muscle. we have neocortex developmental gene expressions, arrays, across the developmental time courses from embryonic days to days postnatal. in addition, we used mouse expression profile data sets from the public expression profiling resource: 1) forty samples from a balb/cj murine model of human asthma that used the ragweed pollen to sensitize and challenge the mice, 2) thirty brain hippocampus samples from neurofibromin- heterozygous and control mice, samples each, collected from to days postnatal. the mrna samples from su et al. were hybridized on affymetrix mg_u74a chips. the samples from all other data sets were hybridized on either moe430a or mg_u74av chips. we then mapped known mouse tfbm matrices to the regions from base upstream to base downstream relative to transcription starting site of all genes in two mouse gene chips. only top 10% regions most well aligned across the genomes of three species were used in the motif mapping. the known binding motifs and the information on their corresponding binding proteins were obtained from the online database transfac. these known tfbms represent a small portion of all transcription factors in mouse. linking co-expression and co-regulation, in mouse for each of seven data sets, we first selected probe sets with the most variable expression patterns. then for each pair of genes, we identified the common tfbms in the promoter regions of both genes. the redundancy of some probe sets with a common target gene or of some genes with overlapping promoter regions was taken into account. we defined the measure of the regulatory similarity between a gene pair as the number of the common tfbms in their promoter regions. a significantly large number of tfbms in the promoter region of a gene may indicate the validity of their regulatory role on the gene. here, we extended the idea to define the regulatory similarity between two genes. then, we defined the expression distance between a gene pair as minus correlation between two profiles. figure 1a shows the observed median expression distance of gene pairs as a function of the regulatory similarity between the two genes. the figure demonstrates that genes that share large number of common tfbms are more likely to have highly correlated expression patterns: sometimes, the effect is present only when they share enough common tfbms. for each data set, the correlation was computed between the median expression distance and regulatory similarity. to calculate the significance of such correlation, we permuted the mapping between genes and their promoter regions times. note that some p-values are not statistically significant in the figure. in the next section, we propose a simple distance measure between the expression profiles that correlates stronger with the regulatory similarity. a new distance measure for comparing expression profiles when the medians of two expression profiles over n samples, are m and m, we define the distance between two profiles as following: ∑i=1n{log⁡2)−log⁡2)}2 mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaadagcaaqaamaaqahabawaaiwaaeaacyggsbabcqggvbwbcqggnbwzdawgaawcbagaegomaidabeaakiabcicaomaalyaabagaemieag3aasbaasqaaiabdmgapbqabaaakeaacqwgtbqbcqggoaakcqwg4baecqggpaqkaagaeiykakiaeyoei0iagiibawmaei4ba8maei4zac2aasbaasqaaiabikdayaqabagccqggoaakdawcgaqaaiabdmha5naabaaaleaacqwgpbqaaeqaaagcbagaemyba0maeiikagiaemyeaknaeiykakcaaiabcmcapagaay5eaiaaw2haamaacaaaleqabagaegomaidaaaqaaiabdmgapjabg2da9iabigdaxaqaaiabd6gaubqdcqghris5aawcbeaaaaa@5541@ the distance measure is equivalent as the euclidian distance between two standardized profiles, where x˜i mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaacuwg4baegaacamaabaaaleaacqwgpbqaaeqaaaaa@2fbb@ = log ), y˜i mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaacuwg5bqegaacamaabaaaleaacqwgpbqaaeqaaaaa@2fbd@ = log ). the distance is zero when two expression profiles have identical fold-changes between all samples. when two profiles are close by this new distance measure, they also have high pearson's correlation: when two profiles have zero distance by the new measure, the pearson's correlation is one. when two profiles have high correlation, however, they are not necessarily close by the new distance measure. this property enables us to further select co-expressed genes among highly correlated genes. figure compares how two different expression distance measures correlate with the regulatory similarity in data sets. the p-values and correlations are computed the way previously described for each data set and for each distance measure. table summarizes the result with seven different distance measures. all seven distance measures correlate with the regulatory distances. in contrast, when we use the euclidian distance without any standardization, such correlations shown in figure disappear and the plots become noisy. this is because the probes in oligonucleotide arrays have different affinities; the signals from different probes are incomparable without a proper standardization. the figure and the table show that, while all other six distance measures perform similar, the new distance measure correlates best with the regulatory similarity. only the new distance measure correlates significantly with the regulatory similarity in all seven data sets. such improvement is expected since it is likely that many genes in the close regulatory distance at the molecular level should not only share their linear patterns but also have similar fold-changes across the samples. interestingly, such link is extremely strong regardless of the choice of distance measure in the neurofibromatosis data, the only tumor data in our analysis. we attribute this to the inclusion of the transcription factors that are playing major role in this illness in the available tfbms in the binding analysis. two main transcription factor complexes, nf- and nf- relating to the illness are included in the binding analysis. discussion we established that a simple expression distance measure that considers both the linear trends and expression fold-changes across the samples performs better than widely accepted distance measures do. before clustering the gene expression profiles generated from oligonucleotide arrays, a proper standardization is essential because of the different affinities of the probes. we proposed a simple standardization that leads to the clustering of co-regulated genes more successfully than other widely used methods do. in addition, we demonstrated the correlation between the expression distance and the regulatory distance, in mouse. in yeast genome, the hypothesis that genes with similar expression patterns are likely to be regulated via the same mechanisms has been quantitatively tested with large-scale data. our study of such relationship between co-expression and co-regulation in a mammalian genome provide a groundwork for current efforts to develop the combined analysis methods for expression and cis-regulatory data. we note that, however, the statistically significant correlations are between regulatory similarity and median expression distance. the direct correlation between regulatory similarity and expression distance is not significant. this is expected because of our simplistic definition of regulatory similarity and the limited number of known tfbms from the murine genome. here, we used the strength of such link to compare different expression distance measures but not to emphasize the correlation between the expression distance measure and the regulatory similarity. following the work on yeast, we attempted to introduce the 2nd order of regulatory distances by accounting indirect regulatory relationship between genes but the results were similar. conceptual comparison of the new distance measure with others one minus correlation is widely accepted as the distance measure between expression profiles; it captures the linear relationship between expression patterns. it fails, however, to account the fold-changes in expression between samples. when one minus correlation is the distance measure to cluster co-expressed gene groups, each cluster consist genes with similar linear expression patterns but with varying fold-changes between samples. as an illustration, figure shows a typical gene cluster in a heatmap diagram. it is the tightest gene cluster on the mice cortex developmental data generated by a sophisticated clustering algorithm. the genes in the diagram have tight linear expression pattern but their fold-changes between samples are highly variable. such variability is a general phenomenon when one minus correlation is the distance measure. this was the motivation to define a better distance measure; we hypothesized that many genes in the close regulatory distance at molecular level not only share their linear patterns but also have similar fold-changes in expression across the samples. in our experience, clustering analysis with correlation as the distance measure often results in large gene groups. in practice, it is desirable to reduce the gene numbers and increase the regulatory relevance since the genes are often the starting points for costly biological experiments. with the new distance measure, we identified gene clusters in mice cortex data with both similar linear pattern and similar fold-changes across the samples with smaller cluster sizes. another popular standardization approach is the pearson's correlation on the log-transformed data. one minus pearson's correlation is square root of euclidian distance after centering and re-scaling the data. hence, the regulatory information in the scale of log fold-changes is lost. in addition, no longer the genes with similar linear trends will cluster together. in contrast, the new distance measure, after log transformation, involves centering but not re-scaling. table suggests that the scale of log fold-changes contains significant co-regulation information. the preservation of the inherent regulatory information in expression profiles depend on both the hybridization process and the expression index calculation methods. here, all samples were hybridized according to the affymetrix protocol and the expression indices were computed by the multi-array model based approach. meta data analysis we proposed the log transformation with base when expression data from multiple experiments are combined, however, often variation from certain experiments dominates the analysis. we suggest using different bases for log-transformation in each experiment, e.g., 280th percentile of the interquantile ranges of all genes.  the study reveals that the proposed distance measure for comparing expression profiles reflects the inherent regulatory information better than widely accepted distance measures such as the pearson's correlation or cosine correlation, with or without log transformation. the distance measure enables us to identify genes with large number of common regulatory elements. 
the widely accepted measures are inadequate for distinguishing genes transcribed from distinct regulatory mechanisms in the complicated genomes of higher eukaryotes. the study reveals that the proposed distance measure for comparing expression profiles enables us to identify genes with large number of common regulatory elements because it reflects the inherent regulatory information better than widely accepted distance measures such as the pearson's correlation or cosine correlation with or without log transformation. finding cis-regulatory elements in higher eukaryote genomes, however, remains a challenge, as searching in the promoter regions of genes with similar expression patterns often fails. many statistical algorithms combine microarray expression data and genome sequence data to identify transcription factor binding motifs in the low eukaryotic genomes. by defining the regulatory similarity between a gene pair as the number of common known transcription factor binding motifs in the promoter regions, we compared the performance of several expression distance measures on seven mouse expression data sets. we propose a new distance measure that accounts for both the linear trends and fold-changes of expression across the samples. the difficulty is partially attributable to the poor performance of the similarity measures for comparing expression profiles.
 many statistical algorithms combine microarray expression data and genome sequence data to identify transcription factor binding motifs in the low eukaryotic genomes. finding cis-regulatory elements in higher eukaryote genomes, however, remains a challenge, as searching in the promoter regions of genes with similar expression patterns often fails. the difficulty is partially attributable to the poor performance of the similarity measures for comparing expression profiles. the widely accepted measures are inadequate for distinguishing genes transcribed from distinct regulatory mechanisms in the complicated genomes of higher eukaryotes.  by defining the regulatory similarity between a gene pair as the number of common known transcription factor binding motifs in the promoter regions, we compared the performance of several expression distance measures on seven mouse expression data sets. we propose a new distance measure that accounts for both the linear trends and fold-changes of expression across the samples.  the study reveals that the proposed distance measure for comparing expression profiles enables us to identify genes with large number of common regulatory elements because it reflects the inherent regulatory information better than widely accepted distance measures such as the pearson's correlation or cosine correlation with or without log transformation. 