We modeled transcriptional activity of the chromosome as a one-dimensional spatial series of transcript abundances. Transcript abundances were measured in cells grown in batch cultures to OD₆₀₀ = 0.5 in LB or M9 medium supplemented with 0.2% glucose (cultures reached stationary phase at OD₆₀₀ = 3.5 in LB medium and at 2.5 in M9 medium). Samples of total RNA extracted using hot-phenol method 18 were labeled with Cy-fluorophors and hybridized against genomic DNA as a reference. We carried out two types of hybridization: one using genomic DNA from the same cells from which we extracted the RNA and the other using genomic DNA from cultures with arrested initiation of DNA replication that completed ongoing rounds of replication. Two different types of genomic reference produced indistinguishable results in spectral analysis, and for the sake of simplicity we present here the analysis of results obtained in hybridizations against genomic DNA isolated from non-replicating cultures. The mRNA abundances have been recorded for almost every gene in the chromosome by two-color hybridization on whole-genome DNA microarrays. The data are publicly available at the Gene Expression Omnibus 19, accession numbers GSE1730 and GSE1735. To determine the degree of similarity in transcriptional activity of individual genes as a function of their position on the chromosome we calculated the autocorrelation function (ACF) as a function of the distance between genes, where the distance is measured as the number of intervening genes (Figure 1).

Independent of the growth conditions, the ACF could be characterized as a decaying function whose largest statistically significant portion assumes positive values and corresponds to relatively short gene-to-gene distances (fewer than 100 genes; Figure 1a, data not shown). By definition 20, the portion of the ACF that constitutes significant correlations may reflect the existing stable structure in the series. Thus, it is likely that the transcription of any two genes, separated on the chromosome by a distance less than or equal to the length of the structured portion of the series, is similarly affected on average across the entire chromosome. Scrambling the linear order of genes leads to the loss of structure in the series (Figure 1b), indicating that the relative positioning of genes determines the autocorrelation properties.

If the autocorrelation reflects dominant patterns of co-transcription, then by determining the properties of the ACF we should be able to describe these patterns. Any one-dimensional pattern could be characterized by the stability (the distance between two genes at which transcriptional similarity drops to 50% of the average correlation between immediate neighbors) and by the range of stable correlations (maximal length of an average stable co-transcribed chromosomal region). Following the two-parameter exponential fitting of at least eight independently measured ACFs, we determined that the transcriptional correlations decay by half in the rich medium over 7.5 kilobases (kb) (Table 1, 0 minute entry).

The range of local transcriptional patterns was measured as the maximal length of a continuous, significantly correlated region of the chromosome that is not affected by experimental error. We determined that in rich medium up to 16 genes in a row could demonstrate apparently coherent transcriptional activity (Figure 1c). The short-range correlations of the transcriptional series obtained in minimal medium had comparable characteristics (data not shown). While it is expected that genes organized in operons would show significant autocorrelation, the stability as well as the significant range of autocorrelations observed here extend far beyond those expected if gene expression was only coordinated within operons, which have an average size of three genes 21.

In addition to continuous transcriptional correlations over short distances, we also observed individual, statistically significant spikes in correlations of transcriptional activities of genes located about 100 and 700 kilobases (kb) apart. To investigate such long-range transcriptional patterns in more detail we decomposed the original signal of transcript abundances into a series of harmonics. The frequency spectrum of transcript abundances is shown in Figure 2. Four frequencies appear to be significant (at 95% confidence level) in the spatial series obtained from the cultures grown in LB medium: 690^-1 kb^-1; 129^-1 kb^-1, 115^-1 kb^-1 and 103^-1 kb^-1. The sequential signal recorded in the mid-exponential cells grown in M9 salts supplemented with glucose contained similar significant frequencies (Figure 2b): 690^-1 kb^-1, a clump of frequencies around 115^-1 kb^-1 and a free-standing frequency of 414^-1 kb^-1.

The Fourier transform provides signal average characteristics and does not determine the frequencies at a particular spatial locality. To localize significant frequencies determined by Fourier transform and to find potentially significant local spikes of transcriptional activity, we subjected the spatial series of transcript abundances to a wavelet transform. The wavelet analysis revealed significant spectral components at the scales very similar to significant periods in the Fourier spectrum: approximately 125 kb and 600-700 kb (Figure 3a). In addition, in the range of scales from 100 to 1,000 kb, the wavelet transform identified pronounced local patterns at frequencies corresponding to 235^-1 kb^-1, 300^-1 kb^-1, 365^-1 kb^-1 and 555^-1 kb^-1. The wavelet spectrum also shows that patterns of transcriptional activity are not symmetrical with respect to the chromosome. The dominant patterns are localized largely in the left replichore (the half chromosome divided by the replication axis counter-clockwise from the oriC) and appear to be bounded by the origin of replication. The most dominant pattern wave in transcriptional series, represented by a period of about 600 kb, spreads for 2.3 megabases (Mb), from the origin of replication to the terC site. The second most pronounced pattern (around 125 kb) consistent with the Fourier spectrum results from the transcriptional activity between the origin of replication and terG, about 1.3 Mb away. While significant components of the wavelet spectrum consistent with the Fourier spectrum were largely distributed on the left replichore, the scales unique to the wavelet spectrum were narrowly distributed along the scattered parts of the right replichore.

Inhibition of transcription initiation by rifampicin completely eliminates significant frequencies from the spectra after 30 min of treatment (data not shown). We rationalized that if transcription is not only inhibited, but modulated, globally, we might be able to track changes in the transcriptional spectra. We used a topoisomerase inhibitor, norfloxacin, to try to modulate transcription in the cell by inhibiting topoisomerase activities. As supercoiling and transcription in the cell are expected to be tightly coupled 22, we anticipated that inhibition of DNA topoisomerization would affect spatial transcriptional patterns. Norfloxacin was used at a concentration that ensured 50% and 90% killing of a bacterial population after 10 minutes and 30 minutes treatment, respectively. We examined the local correlations in transcription following norfloxacin treatment and found that by 30 minutes the range of significant autocorrelations has been reduced by about 50% from 16.5 to 7.7 kb and the stability of local patterns was reduced from 7.5 to 4.3 kb (Table 1). We have observed changes in the amplitude (the magnitude of squared amplitudes integrated over space - the power - is plotted along the vertical axis in Figure 3) as well as in spatial ranges of significant wavelet components (Figure 3b,c). The most obvious changes in the wavelet spectrum can be described as a recession of the largest-scale wavelets from the terminus of replication in the left replichore. At a higher resolution, as seen in the local wavelet power spectrum in Figure 4, the spatial range of the characteristic 100-125 kb wavelet narrowed by 25 to 90%. Similarly, the Fourier analysis revealed that the main periods in untreated cells, including 115 kb and 690 kb, were significantly (p < 0.05) diminished by (in some case) 30 minutes with the drug (Figure 5).

In addition to modulation of the transcriptional spectra by non-equilibrium perturbations, we were interested in steady-state alterations in the process of transcription that would not be associated with irreversible changes in bacterial physiology. Such alterations may result from a compensation to a partial reduction in gyrase activity. A transient increase in transcription of the gyrase genes has been observed following inhibition of gyrase activity 23. We rationalized that a partial loss of function of the gyrase enzyme would be accompanied by a compensatory steady-state increase in transcription of the gyrase genes. We predicted these compensatory changes in transcription would be genome-wide rather than confined to the gyrase genes.

Using resistance to low concentrations of norfloxacin as a screening method, we selected mutants with increased levels of gyrA and/or gyrB transcripts. We characterized one spontaneous mutant of gyrase, resistant to 0.8 μg/ml of norfloxacin, which carries the D82G mutation in the gyrA allele and causes elevated levels of gyrA and gyrB mRNA in vivo and lowers supercoiling activity of DNA gyrase in vitro (K.S.J, Hiroshi Hiasa and A.B.K, unpublished work). This mutant had a normal rate of growth and cell density in stationary phase (less than 5% different from the isogenic wild-type strain in LB). As predicted, the compensatory transcriptional mechanism was not limited to transcriptional regulation of gyrase expression but had a global effect. Using microarrays we estimated that steady-state transcriptional activity of as many as 847 genes had changed in the mutant relative to the isogenic wild-type strain. The microarray results were in part confirmed by reverse transcription-PCR (RT-PCR) for 10 out of 10 randomly chosen differentially expressed genes with an observed change in transcript abundance of 50% or greater. The distribution of differentially expressed genes along the chromosome is shown in a histogram in Figure 6. Interestingly, transcription in the area of the chromosome spanning about 1.5 Mb from the vicinity of the terE site through the terG site appeared to be most affected in the mutant.

If transcriptional activity of the chromosome is differentially perturbed, that is, some regions are being more affected than others, then patterns that existed in unperturbed chromosome may no longer spread across regions with such an 'out of sync' activity, resulting in a partial spatial confinement of originally wider patterns. Moreover, if transcriptional activity is inhibited in a spatial locality, it may cause reduction, or even complete elimination, of local patterns. The wavelet power spectrum in Figure 3d unambiguously confirmed such truncation of wider patterns and the disappearance of significant local patterns in the area of the chromosome where transcription was spatially differentially affected. No changes in transcription have been observed in the gyrase mutant carrying an S83L mutation, a naturally occurring mutation that is not accompanied by a compensatory increase in gyrase transcription (data not shown).

While global and local patterns of transcription are likely to be due to multiple causes, our data suggest DNA gyrase as an important factor in pattern formation. It has been suggested that DNA gyrase is not randomly distributed along the chromosome of E. coli 24. We examined the distribution of DNA gyrase along the chromosome in a chromatin immunoprecipitation (ChIP) chip assay with GyrA-specific antibodies. The averaged and de-noised spatial signal recorded in eight ChIP-chip microarray experiments were analyzed through a wavelet transform. The contours of significant scales calculated from the gyrase-binding signal and the transcriptional signal obtained under identical growth condition are overlaid in Figure 7a. Similarities between the two spectra were quantified as the dot product of power vectors at corresponding scales (Figure 7b). We observed high positive correlation between the wavelet power spectra of gyrase distribution and transcriptional signal across multiple scales. We found no correlations between wavelet spectra of transcriptional signal and chromosomal distributions of several sequence-specific or nonspecific proteins, including Lrp, Topo IV, FtsK and LexA (data not shown; the results of these ChIP-chip experiments will be summarized in a separate paper).

All experiments in this study were carried out in E. coli K12 strain MG1655 obtained from the ATCC. Mutant gyrA^R alleles used in this study carried D82G (this study) and S83L 34 mutations. Wild-type and mutant gyrA^R alleles were linked to a Tn10 marker and P1 transduced into E. coli K12 MG1655 as described previously 35. MG1655 dnaC2 36 was used to obtain the DNA reference sample for transcript abundance measurements. Bacterial cultures were grown at 37°C in LB or M9 supplemented with 0.2% glucose.

Whole-genome DNA microarrays of E. coli were designed, printed and probed as described previously 1318. To ensure the success of PCR amplification and to minimize cross-hybridization we redesigned more than 700 primer pairs from the original set of primers supplied by Sigma-Genosys 37. The relative transcript abundances were determined as described 38. The RNA samples were extracted from the cultures grown to an OD₆₀₀ of 0.5-0.6 using the hot-phenol method 18. The experimental error of the measurements of RNA abundances was assessed from at least three independent replicates, where one replicate corresponds to the RNA sample from a bacterial culture grown from a separate colony. Differentially expressed genes were identified using two-class comparisons of the adjusted relative expression values by SAM 39 at 1% false-discovery rate at the 90th percentile. RT-PCR was carried out on ABI Prism 7900 according to the Applied Biosystems protocol with SYBR Green dye as a fluorescent probe.

Following the removal of the array-, pin- and dye-specific effects 4041, the estimated relative abundance values were ordered according to the position of a corresponding gene on the chromosome and subjected to spectral analysis. The spatial domain is defined as a function of the position of the center of mass of the open reading frame (ORF) or operon. In the search for significant frequencies, 2,071 positive frequencies were examined in a signal consisting of 4,143 samples corresponding to individual genes. The autocorrelation function of transcriptional spatial series was calculated as in 20:

with j = 0,1,2,...,J, where y_x is the series value at the index corresponding to a given ORF location, is the mean over all N observations and J is the number of genes in the genome minus 1. The standard error of autocorrelation estimates is determined as (N)^-1/2, where N is the number of samples in the series.

Information about the process of transcription could be extracted by identifying a pattern in the observed variations in gene activities followed by a search for the cause or explanation of the pattern. For instance, the pattern may consist of a defined dependence of transcriptional activity as a function of a chromosomal position, or it may consist of the dependence of transcriptional activity as a function of time following a treatment or during the cell cycle. This functional dependence may express itself as a linear variation or harmonic oscillation partially hidden behind the noise. We considered a physical variable Y that corresponds to the relative abundance of mRNA. This variable could be measured as a function of the position, x, on the E. coli chromosome. Values of Y are discretely recorded following two-color hybridization on the whole-genome DNA microarrays. Thus there is a finite series of values of x, {x_i}, i = 1, 2, 3,...., N (N corresponds to the total number of genes) and corresponding values of Y, {Y_i}, i = 1, 2, 3,...., N. We call {Y_i} a spatial series or sequential series. For the sake of convenience we approximated positions of the centers of mass of individual genes, {x_i}, as evenly spaced. A process is a rule or procedure that generates a sequential series, that is, a prescription for determining the values Y for a given set of values of x. We defined a spatial series recorded in one whole-genome hybridization as one realization of the process.

The nature of the data that we register using microarrays as well as the nature of the process itself is likely to be such that the rule(s) generating a sequential series specify the probability distribution of {Y_i} and not specific values that are the same at every realization. However, defining such a distribution did not seem feasible. Instead, we determined significant autocorrelation components in the spatial series by assessing the effect of experimental error on the significance of correlations. Following the recording of spatial series in at least three independent biological replicates, we simulated realizations of the process of transcription by resampling relative abundances in a gene-specific manner (see 42 for details of the bootstrap). For each of the realizations we calculated the ACF at all acceptable lags. We counted the number of times the ACF value appeared to be significant (α = 0.05) across all simulated realizations at each of the lags.

The Fourier spectrum was determined using the Lomb algorithm 43. To ensure comparability between the wavelet scale and the Fourier period we used the Morlet wavelet as a basis 44 in Matlab 6.5.1 45 or AutoSignal 1.6 46. The significance of the Fourier and wavelet peaks was estimated from peak-type critical limits. The critical limits were generated from Monte Carlo trials with uniformly spaced spatial domain coordinates. The null hypothesis was simulated using white noise as a background distribution.

Chromatin immunoprecipitation of DNA sequences bound by DNA gyrase and their detection using whole-genome DNA microarrays were adapted from 47. Briefly, cells were grown to an OD₆₀₀ of 0.5-0.6 in LB or M9 medium and DNA was cross-linked to proteins with formaldehyde at 1% (v/v) final concentration. Following incubation with monoclonal antibodies against the GyrA subunit of DNA gyrase (TopoGEN), the protein-DNA complexes were precipitated using Protein A-agarose beads (Sigma). Ligation-mediated PCR (LM-PCR; adaptor sequences: 5'-GCGGTGACCCGGGAGATCTGAATTC-3' and 5'-GAATTCAGATC-3') was used to amplify DNA following the reversal of cross-links. Sonicated genomic DNA served as a reference in two-color hybridizations, in which both the sample and the reference were labeled in the Klenow reaction following random amplification by LM-PCR.