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Anatomy of Escherichia coli σ70 promoters

Information theory was used to build a promoter model that accounts for the −10, the −35 and the uncertainty of the gap between them on a common scale. Helical face assignment indicated that base −7, rather than −11, of the −10 may be flipping to initiate transcription. We found that the sequence conservation of σ70 binding sites is 6.5 ± 0.1 bits. Some promoters lack a −35 region, but have a 6.7 ± 0.2 bit extended −10, almost the same information as the bipartite promoter. These results and similarities between the contacts in the extended −10 binding and the −35 suggest that the flexible bipartite σ factor evolved from a simpler polymerase. Binding predicted by the bipartite model is enriched around 35 bases upstream of the translational start. This distance is the smallest 5′ mRNA leader necessary for ribosome binding, suggesting that selective pressure minimizes transcript length. The promoter model was combined with models of the transcription factors Fur and Lrp to locate new promoters, to quantify promoter strengths, and to predict activation and repression. Finally, the DNA-bending proteins Fis, H-NS and IHF frequently have sites within one DNA persistence length from the −35, so bending allows distal activators to reach the polymerase.


INTRODUCTION
Transcriptional regulation is essential to the viability of the cell (1)(2)(3). In prokaryotes, many molecules can contribute to or detract from the stability of the initiation complex (4). The minimum requirement for RNA polymerase binding is recognition of the promoter by the s factor (5)(6)(7)(8). In general, prokaryotic RNA polymerases can interchange a number of s factors which bind and initiate different groups of genes (9). s 70 is the most commonly used s factor in Escherichia coli and it is responsible for the initiation of most genes (9). This paper will only focus on promoters bound by s 70 .
To successfully model initiation, it is necessary to construct a model that unifies multiple components. The conventional model for promoter recognition by s 70 is the binding of two regions upstream of the transcription start point, named the À10 and À35 because of their spacing relative to the first transcribed base (10,11). The initiation complex is also further stabilized by the C-terminal domain of the two a subunits of the core enzyme (aCTD), which can either interact directly with upstream DNA or with regulatory proteins (12). To add to the complexity of the system, recognition of the À10 alone can be sufficient for initiation to occur (13)(14)(15). The initiating polymerase can be thought of as moving ship that needs to be anchored down (16). The varying affinities of the binding components for the promoter would correlate to varying weights holding the polymerase in place. The sum of these components must have enough energy to stabilize the polymerase against thermal noise. Therefore, in order to model promoter binding, we need to consider the relative affinity of each molecule affecting the stability of the initiation complex.
In addition, the s factor is flexible. That is, the distance between the À10 and À35 binding sites is not fixed. This flexibility affects the affinity of the polymerase for the sequence (10). If we treat s factor bound to core as a simple harmonic oscillator, then expansion or contraction of the polymerase when binding to promoters with varying spacings would strain the molecule and reduce the amount of energy available for stabilization. Since the initiation rate is affected by spacing (10,(17)(18)(19)(20)(21), our model needs to take into account this internal strain.
Traditionally three possible spacings have been proposed at which the À10 and the À35 bind relative to each other, 17 ± 1 bases, but initiation over a larger range, 15-20 bases, has been shown (10,19,22). These spacings correspond to the number of bases between the 3 0 end of the À35 hexamer and the 5 0 end of the À10 hexamer. The observed optimal spacing of 17 bases (10) places the centers of the two hexamers on the same face of the DNA 23 bases apart, $2 helical twists of B-form DNA (23), suggesting that the polymerase has a DNA-structure-dependent contact.
There is also a correlation between the extent of negative supercoiling and the amount of transcription from a promoter (21,22), which demonstrates that the s factor is sensitive to genomic structure (24,25).
Although neural networks and hidden Markov models (HMMs) have been used to model promoter binding (26)(27)(28), constructing these models usually requires the untenable assumption that large stretches of sequence do not contain sites, and the resulting parameters have not been easy to interpret. Other attempts have been made to model promoters using methods not based on HMMs (29)(30)(31)(32)(33), but these methods do not uniformly measure the contribution of all components in the initiation complex (À10, À35 and gap). Hertz and Stormo (31) presented a model in which they subtracted the gap penalty for the optimal spacing from each gap value, so that there was no penalty for having the optimal spacing. Their formula to evaluate gap penalties implies that a set of sites that have several equiprobable gap lengths would have no penalties, even though flexibility decreases information (34) (http://www. ccrnp.ncifcrf.gov/$toms/paper/flexrbs/). The method used in this paper, which was previously used to investigate ribosome binding sites (34), does account for gap variability with equiprobable gap lengths. In addition, promoter strengths are not determined purely by the binding of the s factor. Transcriptional activators and repressors contribute to and detract from the accessibility of DNA by the RNA polymerase. In order to uniformly model the flexible binding of the s 70 in conjunction with transcriptional regulators, we used information theory.
Prokaryotic ribosomes, like the s factor, have two binding elements separated by a variable distance. In previous work, we used information theory to model 95% of the E. coli ribosome binding sites (34). This flexible model took into account the conservation of both the initiation codon and Shine-Dalgarno regions, and the statistics of the variable spacing between them. Here we applied the same theory to the s 70 promoter components (À35, À10 and their spacing) to create a cohesive model of promoter binding.
An important difference between the ribosome model and the promoter model is that the ribosome model is only composed of two binding elements. The promoter model can be made up of a large number of binding elements with parameters governing how each element behaves, and how the elements interact with each other. This paper shows how an internally consistent multi-part model can be constructed directly from experimentally proven sites, and discusses how this model can be used to predict and identify control systems. We are also interested in understanding the fundamental workings of the RNA polymerase. To this end, we examined the variation in the promoter as a function of spacing, global trends in accessory molecule binding relative to the promoters, and the relationship between ribosome binding sites and promoters. We also propose that the flexible bipartite binding site evolved from a rigid extended À10 binding mode.

Constructing the promoter model
We built our s 70 binding model by aligning and refining the sequences upstream of 599 experimentally determined transcription starts reported in the RegulonDb database (42) and 85 starts from the PromEC database (43) that were not included in RegulonDb. To align binding sites we used the malign program to maximize the information of either the À10 or À35 by shuffling the sequences (44) (http://www.ccrnp. ncifcrf.gov/$toms/paper/malign). To refine the model, we iteratively removed all sequences with an information content <0 bits of information (45,46) (http://www.ccrnp.ncifcrf.gov/ $toms/paper/edmm/; http://www.ccrnp.ncifcrf.gov/$toms/ paper/ri/) until we converged on a consistent set of sequences. Since there is both a variable spacing between the À10 and the transcription start point, and between the À35 and the À10, this process was not trivial, and we describe below how we converged on our final model.
To align the À10, we embedded the DNA sequences À15 to À3 bases upstream of the transcription start site in random DNA, so that our alignment would not be biased by the À35 or by the preference of adenine at the transcription start point. We realigned the À10 region to maximize the information by using the malign program (44) over the range of À12 to À7 bases upstream of the transcription start, allowing for the sequences to shift up to 3 bases in either direction. Since nearby transcription start points could potentially use the same À10, we identified and removed transcription starts from our dataset that were within 15 bases of another site with a lower genomic coordinate (arbitrarily chosen) and had the same orientation. This prevented the same À10 from appearing multiple times in our model, and decreased the size of our dataset from 684 to 620 starts. We then did a cyclic refinement on these sites to remove sequences from our dataset that were not identified as sites by our model. To do this, all sites that had an information content (46) <0 bits were removed, and the model was rebuilt. The zero-bit cutoff was used because it represents a version of the second law of thermodynamics: sites with positive information correspond to negative DG of binding (45,46). This approach was successfully used for constructing ribosome (34) and splice site models (47). Removing and rebuilding was continued until no negative sites remained in the set. This reduced our number of sites from 620 to 559. The refined multiple alignment gave us a well conserved À10 region (Figure 1). At each position, the base conservation of the À10 corresponds to the number of mutants found at that position by genetic studies (11).
We do not adhere to the conventional numbering system used in describing the distance between the À10 and the À35. The conventional numbering of the spacer is the number of bases between the two hexamers (10). That is, ttgacaNNNtataat would have a spacing of three. Since the convention for position numbering in asymmetric sequence logos is to choose a strongly conserved base, we will refer to the second base in each hexamer as zero, and all spacings will be reported as the difference between those coordinates. Therefore, all values for our spacing are 6 bases greater than the numbering used previously. For example, tTga-cannntAtaat would have a spacing of nine (the difference between the capital T in the À35 hexamer and the capital A in the À10 hexamer), rather than three. Therefore, the classical spacing of 17 bases is 23 in our notation. The only way we would be able to adhere to the conventional numbering system would be to assign a base outside one of the hexamers as the zero coordinate. This would be confusing in sequence analysis using sequence walkers (48), (http://www.ccrnp. ncifcrf.gov/$toms/paper/walker/). Furthermore, each sequence walker always has the integer zero in its coordinate system so that one can easily and unambiguously locate a binding site and then specifically identify bases within the binding site.
Aligning the À35 was more difficult than aligning the À10. The traditional model of RNA polymerase binding only allows for three different spacings between the À35 and the À10 (11). Mutational data have shown that this range could be expanded to six positions (10), but that at these expanded spacings the amount of transcription is reduced substantially. The optimal spacing of 23 bp (McClure's spacing of 17 bp) (11) places both hexamers on the same face of the DNA within their respective major grooves (23), indicating that the spacing may be dependent upon DNA structure. Therefore, a new alignment method is needed that takes into account the structure of the DNA.
The algorithm for aligning the À35 is different from our previous approach of aligning upstream sequences in flexible models [i.e. modeling the Shine-Dalgarno relative to the initiation codon in ribosome binding sites (34)]. As with ribosomes, our approach was to create a model de novo from experimental data, so as to avoid biases in previous models. Using a sequence logo (49) (http://www.ccrnp.ncifcrf.gov/ $toms/paper/logopaper/), we observed a weak conservation upstream of the aligned À10s in the region expected for the À35, 23 bp upstream. We determined that the conservation of this region was low because a number of sites with a different spacing were overlapping, reducing the total sequence conservation. We performed a cyclic refinement of the region which corresponds to the À35 hexamer at the optimal spacing from the À10 in order to pull out a preliminary À35 model. This cyclic refinement gave a reasonably well conserved À35 sequence logo, which matched the conventional hexamer consensus (11,50) (http://www.ccrnp.ncifcrf.gov/$toms/ papers/zen), and this alignment was used for an initial model. After refinement, we used malign to allow for the sites to be moved 1 base in either direction, so as to maximize the information in this refined À35.
Using the program multiscan, the initial À35 model was scanned over the region upstream of the À10 of every promoter in order to find the À35 which most closely matched this model for each site. Of the 559 promoters scanned, 421 had a À35 site >0 bits in the range of 21-26 bases upstream of the À10 [this corresponds to McClure's spacing of 15-20 bases (10)]. The alignment having the strongest site was used, and the total site strength was calculated using the flexible information equation described previously (34): where w is 10.6 bases (one turn of B-form DNA), center is 23 bases (the optimal spacing between the À35 and the À10), and d is the distance of the À35 from the À10, in bases. This equation describes the major groove accessibility (41,51) in which direct contacts are more accessible and contacts on the opposite face of the DNA are not accessible. The surprisal was then calculated for each position using the gap surprisal equation published previously: GSðdÞ ¼ Àlog 2 nðdÞ n þ eðnÞ ðbits/spacingÞ: 3 n(d) is the accessibility at spacing d, and n is the sum of all accessibility values over the allowed values of d. e(n) is a small sample correction value (34,37). By using these equations to model the structure of DNA, we gave preference to À35 sequences which were in physically reasonable positions.
Once we had identified the À35, the À10 and the spacing for each promoter, we dispensed with the 'scaffolding' equations described above and built a flexible model directly from the sequence data. We did a further cyclic refinement on this set by removing promoters with a flexible information <0 bits, reducing the number of promoters from 421 to 401. Our final model, therefore, contains 59% of the sites that are in our original database. Transcriptional regulators can provide informational contacts through the aCTD and this could account for some of the information used by polymerases (52). As a result, many promoters may have poorly conserved, or highly variable, s binding sites. The refinement process made the model self-consistent (containing similar sites) and it can therefore be regarded as a basal promoter model. The excluded sites are not consistent with this basal model, and presumably they initiate by some method other than the sole recognition of the À10 and À35 (such as an extended À10 or activation by another protein).
Promoter binding and transcriptional regulation is more complex than our previous flexible modeling system was able to handle because of the contribution of activation proteins (52). Therefore, we created an algorithm that not only considers the strength of the two-part s 70 site, but also can include the information contributed by activating proteins. In order to do this we used the multiscan algorithm.

Multiscan algorithm
Multiscan is an extension of the biscan program that is used to model the flexible prokaryotic ribosome (34). Translational initiation in prokaryotes requires contact at both the P site (or initiation region, IR) and the Shine-Dalgarno (SD). Because of the flexibility of the ribosome, these contacts can occur at different spacings, anywhere between 4 and 18 bases. In order to assess the information present in ribosome binding sites, the contributions of the Shine-Dalgarno, the initiation region and the spacing between them all have to be considered. The equation for calculating the information for a two-part model with variable spacing was given in Equation (1).
The RNA polymerase is similar to the ribosome in that it makes two contacts (the À10 and theÀ35) with some variable distance between them. Therefore, the flexible information analysis used with ribosomes can also be used to describe the binding of the s factor to the promoter. The difference between translational and transcriptional initiation is that auxiliary proteins can also bind to either activate or repress transcription. So in order to model the promoter correctly, we need to calculate the information of all the molecules that contribute or interfere.
For activators, as an initial simple model, we assume that their information contributes additively to the total information of the promoter (53), so the new equation is as follows: ðr Act R i ðActÞÀ GSðd À35/Act ÞÞ ðbits/siteÞ‚ 4 where R i (Act) is the individual information of some activator protein site, and GS(d À35/Act ) is the gap surprisal value at spacing d between the activating protein site and the À35.
Since the initiation complex is stabilized by the contacts between the aCTD and the regulatory protein (12), the information contribution of an activator is in those contacts, and not in the contacts between the activator and the DNA. Data on these protein-protein contacts are not available through DNA sequences. However, the higher the affinity of the activator for the DNA, the greater the probability of it being bound simultaneously with the polymerase. Therefore, to a first approximation, we can model the indirect contribution of information by the activator as a modulation of the activator information by the protein-protein interaction. We represent this modulation by r Act , with 0 < r Act < 1.
Since the informatics of interactions with the aCTD are unknown, we will use a r Act ¼ 1. This algorithm only includes the activator site and corresponding gap surprisal if they contribute positive information, since that corresponds to favorable binding (46). In addition, the number of potential activators is limited only by the length of the sequence. That is, if multiple activators bind in a range relative to the RNA polymerase that has been observed to be advantageous to transcription initiation, then they are all included into the total information for the site. At present, the algorithm does not account for the possibility of repression of one activator by another (54).
Although it seems reasonable to assume that activator protein information can be scaled by r Act and added to the total information of the promoter, it is not clear that repressor information should be subtracted. Since repressors block the binding of the polymerase to the DNA, or, in cases such as GalR, cause DNA loops that block binding (55), they do not decrease the strength of the contact but, if present, totally prevent contact from occurring. Therefore, it does not matter what the strength of the repressor is, because a repressor bound to a 1 bit site will prevent initiation as well as a repressor bound to a 10 bit site. The difference between the two is that the 10 bit site will be bound more frequently, so the relative site strengths between the polymerase and the repressor (as well as the concentration of both molecules) can be used to predict the frequency of transcription, but not the ability of the polymerase to bind.

Promoter analysis using the s 70 model
Sequence logos for promoter components were made using the programs delila, alist, encode, rseq, dalvec and makelogo as described previously (49,51). We used the programs diffinst, genhis and genpic to generate the spacing distribution between the binding components.
During our refinement process, we identified 138 experimentally verified promoters that did not have an upstream À35. We used this subset to build the extended À10 model ( Figure 3). These sites contained a weakly conserved TG two bases upstream of the À10 hexamer. We cyclicly refined (34) these sites over the range À4 to À3 and automatically isolated a subset of 84 sites that turned out to resemble the extended À10 9mer reported previously (13).
To determine spacings between the À10 and the translational initiation codon ( Figure 4), we scanned our promoter model over the 250 bases upstream of all genes in E. coli (56). The site range we used for both the À10 and the À35 was À1 to +4, the range of the hexamer ( Figure 1). We plotted the number of occurrences at each distance between the zero position of the À10 and the translational start point of the strongest upstream promoter. To eliminate interference between the À10 model and the initiation codon, we only included sites in our plot that were at least 4 bases upstream of the gene start. We also plotted the number of occurrences at each distance between the À10s of the experimentally determined sites in our model and their respective downstream translational start.
In order to analyze individual sequences using our s 70 model and a transcriptional regulator, we used sequence walker technology (46,48,57). Flexible sites were located using multiscan and displayed as sequence walkers using lister. For Figures 5 and 6, we merely scanned our models over these regions to see how our analysis compared to biochemical data known about these systems. Our Fur model was built from 24 biochemically characterized binding sites (manuscript in preparation) and our Lrp model comes from (34). Once we were confident of the predictive capabilities of our models, we searched for uncharacterized Fur controlled genes in E. coli, two of which are presented in this paper ( Figure 7).
To identify these novel control elements, we scanned the entire genome for Fur sites that overlapped the s 70 binding sites within 200 bases of translational start points. These two were chosen because of the strength of both the Fur and s 70 sites, and their proximity to each other. Gel shifts confirmed that these sites are bound by Fur (data not shown).
Finally, the relative binding plots ( Figure 8) were generated by scanning Fis, H-NS and IHF models over the range À1000 to +1000 bases relative to the transcription start, the À10 and the À35 of all promoters in our model. The frequency of sites was determined at each position relative to a promoter component by dividing the number of predicted sites by the number of promoters. The frequency of sites in the genome was determined by scanning the entire genome with all three regulators, and then dividing by the genome size. We only presented data over the range À400 to +200 because the distributions were flat outside of those ranges and matched the frequency of sites in the entire genome. The Fis and IHF models come from previously published works (39,41,58), while our H-NS model has not been published but resembles another published model (59).
To compute the intergenic density distributions ( Figure 8, red curves), we determined the distance from each promoter part (start, À10 and À35) to the closest upstream and downstream coding region for all sites in our model. We used the EcoGene12 genome annotation to determine coding regions (56). We only used promoters whose zero coordinates are not within coding regions. Out of 401 promoters, 359 transcriptional starts, 356 À10s and 349 À35s were not within a coding region. We then counted the number of sequences that had a non-coding base at each spacing upstream and downstream of the promoter. This curve was then normalized and fit to the relative binding plots in Figure 8, scaled so that the curves are just above the other data points in the graphs, and the zero occurrences level was set equal to the genomic frequency.

The s 70 model
Our dataset for s 70 promoters consisted of both the RegulonDb and the PromEC databases (42,43). Unlike eukaryotic start points, which contain $3 bits of information (60), there did not appear to be much information at this prokaryotic transcription start point, only 0.39 ± 0.06 bits ( Figure 1). There does appear to be a slight preference for an adenine as the first base, but it is weak. Interestingly, this preference is more conserved in early promoters of bacteriophage T4 (61) where, presumably, it contributes to the phage taking over the cell. Realignment of the start region by allowing shifts of 1 base in either direction (44) gives a pattern of 1.33 bits (data not shown). Since a choice of 1 in 3 requires log 2 3 ¼ 1.58 bits, this pattern is not significant.
We were quite easily able to align the À10 relative to the transcription start points ( Figure 1). The distance between the À10 and the transcription start point varied between À14 and À8 bases, with the most common spacing of À11 (this is the distance between the transcription start point and the zero position of the À10 logo). The À10 sites contained 4.78 ± 0.11 bits of information over the range of À1 to +4, the range of the hexamer.
The most striking feature of the À10 logo is the strongly conserved T (position +4) where the protein is likely to face the minor groove of the DNA. In other logos for DNA-binding proteins, conservation of bases rarely exceeds 1 bit in the minor groove (62), because in B-form DNA the exposed groups in the minor groove can only be used to distinguish A or T from C or G, but not all four bases individually (63). High conservation in the minor groove suggests that this base is being contacted atypically. Several possibilities are that the helix is distorted when bound, it is interacting with s 70 in the open complex (64), or that it is being flipped out of the helix to initiate open complex formation, as may occur in DNA replication (41).
We had greater difficulty aligning the À35 perhaps because the À35 is often replaced by activators (1,52). Traditionally, the placement of the À35 relative to the À10 is ±1 base relative to the most frequent position of 23 bases [McClure's 17 (11), see Materials and Methods]. Experimental data have shown initiation at a range of À2 to +3 relative to the most frequent position (10,19,22). When we allowed for our model to include sites in this expanded spacing, we identified 107 promoters (>0 bits) that had no possible À35 in the traditional range, suggesting that binding does occur at these peripheral spacings. The amount of conservation in the À35, as in the À10, was low compared with other DNAbinding proteins (37) (4.02 ± 0.09 bits). The conserved region of the À35 appears to fill only one-half of the major groove, as there is an abrupt termination of conservation on the 5 0 edge (Figure 1), which is consistent with the abrupt termination of contacts in the s A /À35 co-crystal and the 5 0 most edge of the polymerase (65). [s A is the primary sigma factor in Thermus aquaticus, corresponding to s 70 in E. coli (8)]. This suggests that there is space for other binding components to come in and to help stabilize the complex. This is supported by the observation that positive control mutants are immediately adjacent to the portion of s which binds into the À35 groove (65). As shown by the sine waves in Figure 1, when we place the G at +1 of the À35 close to the center of the major groove [as observed in the co-crystal (65)], at the optimal spacing of 23 bases, the T at +4 of the À10 is exactly positioned in the minor groove. This agrees with the proposal that position +4 (À7 in conventional numbering) is contacted atypically, for example by base flipping to initiate transcription (41).
We allowed for the spacing range between the two hexamers to be between 21 and 26 bases. The optimal spacing between the zero coordinates of the À35 and À10 was 23 bases. The spacing distribution appeared to be approximately Gaussian with an uncertainty of 2.32 ± 0.04 bits.
The total sequence conservation (R sequence ) for the s 70 model (À35, gap, À10) is 6.48 ± 0.14 bits (Figure 1). It contains 401 of the 684 sites in our combined RegulonDb-PromEC database. As discussed in Materials and Methods, the number of sites in our dataset was reduced through a series of refinements in order to identify a consistent subset of promoters that presumably can initiate without accessory molecules.
To see how the s 70 promoter varies with spacing, logos were made for each of the spacing classes ( Figure 2).
The logos for the three most frequently used spacings (22,23,24) look fairly similar. In these three cases, the bulk of the À35 logo falls in the major groove on the same DNA face as the À10, two helical turns away. The further spacings do look a little different, but this could be from smaller sample sizes. The logo for spacing 25 is the most unique, having what appears to be a distorted À10 (prominent T at position +1 and poorly conserved Ts at À1 and at +4). Also, at spacing 21 the logo is a little different with perhaps a slightly more conserved T (22 cases) instead of G (18 cases) in the third position of the À35 hexamer (position À20).
The conservation of the À35 at each spacing in Figure 2 appears to follow the sine wave. That is, the conserved bases do not go above the wave, except at position À26 of spacing 25. This suggests that the polymerase preferentially contacts the two components when they are on the same face of the DNA (23), but that the s 4.2 region (which contacts the À35) can rotate relative to the s 2.4 region (which contacts the À10) or that the DNA twist can change. It has been suggested that models be made for each spacing class (32); this may be useful for sequences outside of the central three spacings. Differences in logos outside of the three similar central spacings (22)(23)(24) could be caused by awkward contacts with the polymerase at the extremes of rotation of the À35 relative to the À10.
We looked at the À10 as a function of spacing relative to the transcription start point (data not shown). There was a slight increase in the conservation of the 5 0 T of the À10 hexamer at greater spacings. Besides that, there was little variability in the logos of the different spacing classes. The amount of information at the transcription start point was small ($0.4 bits) for all spacings, and the slight variability between them could be accounted for by noise.
To avoid duplicate sites, we had excluded 64 promoters from our dataset which were within 15 bases of another transcript start (see Materials and Methods). Having built the model, we went back and scanned it over these regions to see if we could predict promoters upstream of more complex overlapping transcripts (data not shown). In 25 cases, for every experimentally determined transcriptional start point there were one or more distinct predicted promoters. In 17 of the 64 cases there was only one predicted promoter and both transcripts fell within the known distance distribution of 8-14 bases downstream from the À10 (Figure 1). In 10 cases there was only one predicted promoter and only one of the transcripts fell within 8-14 bases downstream. Twelve of the starts had no predicted promoter upstream, suggesting that these transcripts are regulated. These results confirm that the basal model functions reasonably well on sequences from which it was not constructed. From left to right: sequence logo of À35 binding sites, spacing distribution between À35 and À10 binding sites, sequence logo of À10 binding sites, spacing distribution between À10 binding sites and the transcription start point, sequence logo of transcription start points. In a logo, the height of each letter is proportional to the frequency of that base at each position, and the height of the letter stack is the conservation in bits (49). Error bars are shown at the top of the stacks. The total information in the À35 and À10, less the gap uncertainty between them, is (4.02 ± 0.09) + (4.78 ± 0.11) À (2.32 ± 0.04) ¼ 6.48 ± 0.14 bits. The sine wave on each logo represents the 10. To further verify our promoter model, we scanned it over the starts of 36 small RNAs presented by Hershberg et al. (66) (data not shown). The model identified promoters upstream of 23 of the 36 starts. That is, $64% of the sites had a promoter with a total information >0 bits from 8 to 14 bases (Figure 1) upstream of the small RNA transcription start. This percentage is similar to that of empirically determined promoters that formed a coherent 'basal' set in our refinement process (59%), suggesting that initiation by the basal machinery may only occur $60% of the time both in general and at small RNAs. None of these sites has been used to build our model. Therefore, this result again shows that our model can identify the promoters of transcriptional starts that were not included in the model.
The conservation of bases that we observed in our model resembled previous non-information theory based alignments (11), mutation data (10,11,20), an in vivo selection assay (67), and the À10 sequence logo published previously for a smaller dataset (41). The mutation data of Moyle et al. Creating a model for the À35 was difficult, presumably because many promoters are activated and the activator could take over the sequence conservation from the À35, as proposed by Raibaud and Schwartz (52). To test this hypothesis we scanned the 14 sequences in the E. coli genome reported to be positively activated by Raibaud and Schwartz and determined which À35 was strongest in the 10 bp window they allowed. In contrast to the 4.0 ± 0.1 bits in our À35 model, these À35 sequences in activated promoters were no more than 1 ± 4 bits. The weak conservation of positively activated sites probably does explain why creating a À35 model is difficult. To our knowledge this is the only published dataset of confirmed positively activated E. coli promoters.

The extended minus 10
Initiation has been shown to occur in the absence of a À35 in conjunction with an extension to the À10 region (13,14). During our refinement process, a subset of 138 promoters did not have a predicted À35 binding site, and these were subsequently removed from the flexible basal model. A sequence logo revealed that the removed subset of promoters contained a weakly conserved TG upstream of the À10 hexamer, in the region identified as the extended À10. We therefore did a cyclic refinement of the two bases containing the weakly conserved TG, and a well-conserved extended À10 emerged (Figure 3). There was no conservation of bases observed outside of the range À4 to +4. Interestingly, the new bases in the À10 appear to follow the sine wave (41), and this region is protected, suggesting that it is bound in the major groove. The R sequence for the extended À10 over the range of À4 to +4 bases is 6.74 ± 0.25 bits, almost the same value as the total R sequence for the flexible s 70 model, which includes the À35 and the gap surprisal. There was also a slight increase in the strength of the À10 hexamer (À1 to +4) from 4.78 ± 0.11 bits in the flexible model to 5.05 ± 0.23 bits in the extended À10 model.

The relationship between the promoter and the ribosome binding site
In order to determine if there are any spacing preferences between the zero coordinate of the À10 and the translational initiation codon, we scanned our s 70 model upstream of all 4122 annotated genes in E. coli (56). We saw one substantial peak in the spacing histogram of predicted promoters, $30-40 bases upstream of the ATG (Figure 4). We also plotted the distance between the À10s of the experimentally verified transcription starts and their corresponding translational start codons, which gave a similar peak around 35 bases ( Figure 4). In both plots, promoters were predicted as far as 200 bases upstream of the translational start. Similar results were obtained by Huerta and Collado-Vides (70). For all 401 promoters in our model, we did not see any correlation between promoter strength and the strength of its downstream ribosome binding site as measured by the individual information contents of each flexible model (data not shown). We did find that the lowest combined individual information of a promoter and an RBS was 3.49 bits.

Transcriptional regulation
We used the s 70 model in conjunction with transcriptional regulator models to study promoter structures in non-basal conditions. As an example, we show the experimentally verified Fur-controlled gene tonB (71) and the degree to which Fur represses it ( The results are conveniently displayed using sequence walkers, which show the individual contribution of each base to a binding site as the height of a letter, with the scale being in bits (46,48,57). Multiscan found a strong 11.7 bit RNA polymerase site, which was in our model, 8 bases upstream of the experimentally proven transcription start point (72). This is displayed as two sequence walkers, one for the À35 and one for the À10. To show that they are part of the same promoter, a dashed line is shown connecting the zero coordinates of each walker. Over this site there were two Fur binding sites (8.7 and 11.5 bits), one of which shows clear sequence competition with the À35 sequence walker (red box). That is, both sequence walkers show positive contributions of bases in the same major groove, so binding by s 70 and the dimeric Fur protein cannot occur simultaneously. This is a good example of how these models can show not only the affinity of the promoter and its competing repressor, but also the mechanism of transcriptional regulation. The translational start is 43 bases downstream of the À10, close to the optimal spacing indicated by our data (Figure 4).
As a second example, we used the transcriptional regulator Lrp (40), which can both activate and repress transcription in E. coli ( Figure 6). As with Fur at tonB (Figure 5), the sequence walkers readily show that Lrp repression of the dad operon (73-75) is probably caused by an occlusion of the promoter by the repressor in the À10 region (Figure 6a).
Since there are at least seven identified transcription start points for the dad operon (74,75), we used our model to see if we could identify the corresponding promoters. The three   . The optimal spacing of the À10 to the translational initiation codon is $35 bases. We plotted the distance between the zero coordinate of the À10 and the translational start point on the abscissa, and the number of promoters at that distance on the ordinate. The upper curve (black) represents data from a scan using our promoter model over the upstream regions of all 4122 genes in E. coli (56). The lower curve (red) represents the location of the À10 relative to translational initiation codons for experimentally verified transcription start points. The arrow pointing to the black curve indicates a peak at À35 bases.
most downstream starts marked in Figure 6a (transcripts 4, 5 and 7) presumably use the same promoter (total information 6.3 bits). These starts are 8, 11 and 13 bases from the À10, respectively, which are all reasonable distances between the À10 and transcription start (Figure 1). The next upstream start (transcript 3) is clearly the result of the binding of a 6.2 bit promoter 10 bases upstream. Transcript 6 may be initiated by a 3.0 bit promoter only 6 bases upstream, and transcript 2 is probably initiated by a 5.6 bit promoter 8 bases upstream (data not shown). Our model did not identify a potential promoter upstream of the start at transcript 1, suggesting that initiation at this point is stabilized by other accessory molecules; likely candidates are CRP (there is a 15.3 bit site 44 bases upstream of transcript 1) and Lrp (75). Interestingly, the computed strength of the dad promoters increases as they get closer to the gene start point but this effect is not observed in arcA (data not shown), which also has seven verified transcript starts (70). Two bound Lrp molecules (11.1 and 11.7 bits) could block the binding and initiation of the two downstream dad promoters and four subsequent downstream transcripts (3, 4, 5, 7), and possibly prevent the opening of transcript 6. The most downstream promoter (transcript 7) is 38 bases away from the translational start point, which produces a transcript only a few bases longer than needed to contain the conserved Shine-Dalgarno region (34), showing an optimization of cellular resources by minimizing the length of mRNAs. We predicted Lrp binding in the region protected by the upstream footprint, but the site was relatively weak at 1.5 bits (data not shown).
Lrp activation of the gltBDF (76) operon can also be predicted using sequence walkers (Figure 6b). In this instance, a strong Lrp-binding site (11.2 bits) is just upstream of a strong promoter (5.3 + 7.6 À 3.3 ¼ 9.6 bits). Since bits are additive, we suggest that the upstream Lrp site increases the overall affinity of the initiation complex for the promoter, giving a total information that could be as high as 20.8 bits. As mentioned in Materials and Methods, this value is an upper bound on the contribution to promoter binding by Lrp through the aCTD.
Based on the two examples in Figure 6, we propose that Lrp is stabilizing the aCTD (12) and promoting initiation when bound upstream of the s 70 binding site, but repressing initiation by occlusion when overlapping the s 70 binding site.  (48). Colored rectangles ('petals') behind the walkers identify the kind of site (by hue) and the strength of the site (by saturation) (112), (http://www.ccrnp.ncifcrf.gov/$toms/papers/t7island/). The connecting bar between parts of a flexible site transitions linearly between the corresponding colors. The s 70 binding site and the ribosome binding site were both located using flexible binding models (34), in that there are variable distances between binding components. The horizontal dashed line underneath the À10 walker (p10) and the À35 walker (p35) that is labeled 'Gap', gives the gap surprisal for whatever distance separates the two components, as well as the coordinate of the downstream component. The dashed line that is labeled 'total' gives the total information for the flexible site. Similar lines are underneath the ribosome binding site components (SD, IR). A Fur dimethyl sulfate protection footprint is marked (71,111), and two sequence walkers for Fur fall below it. The downstream side of the Fur protected sequence is somewhere in the region marked by asterisks. The sequence that the polymerase and Fur would both bind is marked with a red box. The transcription start point for tonB is marked with a black arrow, and the translational initiation start point is marked at position 1309113 with a bracket and an arrow. The sequences and coordinates on the map are from GenBank accession number U00096 (113).
Besides being able to dissect well-understood genetic control systems, we would like to be able to predict new ones for testing. Using a Fur model and the flexible sigma model, we identified a number of potential Fur repressed genes in the E. coli genome. We report two of these cases here (Figure 7). For yoeA (Figure 7a), two strong Fur binding sites (27.4 and 9.0 bits) overlap an average promoter (6.4 bits). The À10 is located 48 bases upstream of the translational start point. A similar result is seen with the fhuA gene (Figure 7b), where two strong Fur sites (10.7 and 19.5 bits, confirmed by gel shift experiments, data not shown) overlap an above-average promoter (7.3 bits) (77,78). The À10 is located 29 bases upstream of the fhuA coding region.
Where DNA bending proteins bind relative to promoter components We searched for the relative placement of transcriptional regulators near the starts of all of the promoters in our model (Figure 8). We present data for models of Fis (39), H-NS (59) and IHF (41,58). All three proteins are transcriptional activators that are involved in chromosomal compaction (79).
We plotted the number of sites predicted at each position relative to the transcription start point, the À10 and the À35 in order to determine which component the regulators were primarily interacting with. We observed in these graphs that there tends to be a peak in the range of À300 to +100, maximizing at the À35 and the À10 alignments, but not at the transcription start. In all cases, fewer sites were predicted downstream than upstream of the promoter. Although these curves are not necessarily linear, to quantify this we did a linear regression for the regions À400 to 0 and from 0 to +200. The slope of the À400 to 0 line is always smaller than that for 0 to +200. The intersection of these two lines is consistently to the left of the alignment point for alignment by the start base, but close for the À10 and the À35. This is reasonably consistent with the idea that the transcriptional factors tend to cluster around the À35, as might be expected from the aCTD contact (53). Other proteins (Fnr, Fur, LexA, ArgR, CRP, TrpR and LacI) were also analyzed, but because they have higher information the models predicted fewer binding sites, so their graphs were too noisy to interpret.
We determined the range of non-coding sequences surrounding each promoter component in our dataset of dad (a)   T1  T2  T6  T3  T4   T5   T7  * *1236730 * *1236740 * *1236750 * *1236760 * * 1236770  5' a t t t t c a a c t g a g t t a t c a a g a t g t g a t t a g a t t a t t a t t c t t t t a c t g t a t 3 {-} p35-( 26) -p10 1236751 Gap 3.7 bits  |-| p35-p10 1236751 c t a c c g t t a t c g g a g t g g c t a t g c g a g t t g t c a t a c t g g 3' [  c c a g c a t t t t a t a c t g c c t t a a t t g g t a a t g a c g t t t c a t g c t a c t g t t t t t g c c t a a a a t 3' [    (76). As in Figure 5, the s 70 and ribosome binding sites are each internally connected by lines that report the gap surprisal and total information. Experimentally verified transcription start points are identified with black arrows and named according to Zhi et al. (75), and the dadA gene start is marked with a bracket and arrow at position 1236794. In (b), since Lrp helps to stabilize the initiation complex, its information is added into the total strength of the promoter. Since data on the distance between Lrp sites and the À35 are not available, we did not subtract a gap surprisal and therefore the gap surprisal is marked as NA (not applicable). The sequence and coordinates on the map are from GenBank accession number U00096 (113). 401 promoters (Figure 1). We counted the number of intergenic regions at various distances from each promoter component. These curves were then normalized to the graphs in Figure 8 so that they fit just above the data, and so that zero occurrences of intergenic regions was matched to the genomic baseline frequency for each protein (Figure 8, red curves). The curves matched fairly well, in that the curves downstream of the components are consistently steeper than the curves upstream of the promoter components.

DISCUSSION
Genetic control systems often consist of multiple binding components with variable distances between them. These variable distances can affect the stability of the binding complex. Our approach is to use experimentally demonstrated binding sites to construct models. Unlike neural networks, this approach avoids the assumption that untested stretches of nucleotide sequence do not contain binding sites, and it sets the model upon a firm foundation. Our model construction uses information theory, which not only allows measurements of the patterns at the binding sites, but can also account for distance preferences on the same quantitative and universal scale of bits (37). We previously used a flexible modeling method for ribosome binding sites (34). That successful application suggested that information theory can be applied to any multi-part binding system where binding is affected by the spacing between components. In this paper we show that the same approach works well to quantify prokaryotic promoters, which have two binding components at approximately À10 and À35 bases from the start of transcription (11).

A s 70 model based on information theory
The amount of sequence conservation in the À10 and in the À35 is fairly low, $5 and 4 bits, respectively. As is found for most DNA-binding proteins (41,62), both sequence logos appear to follow a sine wave, which represents the 10.6 base helical twist of B-form DNA (Figure 1). There are unique characteristics to each logo though.
We used the T. aquaticus s A /À35 co-crystal (65) to determine the location of where the s protein faces the major groove with respect to theÀ35. Using the average gap distance, this assignment places the major groove of the T-A base pair at position +4 of the À10 on exactly the opposite face of the DNA as the À35 (Figure 1). With this assignment, the well-conserved T at position +4 in the À10 logo exceeds the sine wave. In instances where conservation exceeds 1 bit in the minor groove, DNA distortion or base flipping was proposed (41). DNA breathes, opening base pairs on a millisecond time scale (80). By stabilizing this specific flipped-out base, the polymerase could initiate promoter opening. An enzymatic mechanism to initiate this process was proposed by Dubendorff et al. (81).
In addition, with the exception of +4, the pattern of sequence conservation of the extended À10 follows the sine wave ( Figure 3). This effect has been observed in numerous other sequence logos (51,62), and it can be used to precisely assign the location of protein contacts (41,82) (http://www. ccrnp.ncifcrf.gov/$toms/paper/repan3/), so the extended À10 pattern further suggests that the T at +4 faces the polymerase through the minor groove. Because position À1 has . Intergenic binding of DNA bending proteins relative to promoter components. These curves allow one to directly compare the density of non-coding regions to the number of DNA-binding protein sites at each position relative to experimentally determined promoter components. For all graphs, the abscissa is the position of the regulator binding site (either Fis, H-NS or IHF) relative to either the transcription start, the À10, or the À35 in our promoter model. A vertical line marks the zero coordinate of the promoter component. The ordinate is the frequency of sites at that spacing (sites per base). A solid horizontal line marks the frequency of sites per base predicted for the entire genome. Linear regression lines for À400 to 0 and 0 to 200 are shown. A distribution corresponding to the density of intergenic regions surrounding the experimentally verified promoters was fit to the data in each graph, and is shown as a solid red curve (see Materials and Methods). predominantly T instead of equiprobable A and T (Figure 1), it is unlikely to be bound by a minor groove contact in B-form DNA (62). This is consistent with our assignment that the major groove side of base À1 faces the polymerase.
Sclavi et al. used hydroxy radical footprinting to look at intermediates in open complex formation (83). They observed that protection at position 0 (À11 in conventional numbering) occurs after protection in the region of +3 to +5 (À8 to À6 in conventional numbering). This is consistent with the T at +4 (À7 in conventional numbering) initiating DNA melting through a base flipping mechanism (41), which would explain why this position appears anomalous in the sequence logo. In contrast, it has been proposed that flipping of the A at position À11 in the minus ten (our number 0) initiates DNA melting to form the open complex (84)(85)(86)(87)(88)(89)(90). If this is the case, why is our groove assignment 5 bases (180 ) different? One possibility is that the DNA helix could be distorted between the À35 and the À10, which our model does not account for. However, Young et al. showed that a small part of the s factor and the first 314 amino acids of the b subunit are sufficient to initiate promoter melting, which probably excludes DNA bending or twisting (91). Furthermore, a co-crystal structure of a fork-junction DNA bound to a holoenzyme (7) shows smoothly bent B-form DNA from the À35 to just before the À10. In this structure the extended À10 is contacted in the major groove, consistent with Figure 3. We conclude that DNA distortions are not sufficient to explain the discrepancy. If base À11 is flipping first, then it may be that À7 is bound specifically after promoter opening, but this mechanism is apparently inconsistent with the hydroxyl radical footprinting data (83). We have not found a satisfactory explanation for why our clear groove assignment implies that the flipped base is À7 while previous reports suggest À11.
The amount of conservation in the À35 is fairly weak. The clear absence of sequence conservation in the major groove immediately upstream of the À35 could leave room for activating proteins to bind and to stabilize the polymerase [this is supported by the s A /À35 co-crystal structure (65)]. By interacting with the polymerase near the À35 contact, accessory molecules could make s 70 a much more discriminate binder.
Penotti found that the distance between the human TATA sites and the transcriptional start is variable, with an uncertainty of $3 bits (60). He also observed that there are $3 bits of information at the start point itself. In other words, the information of the start (R sequence ) is just sufficient for it to be located with respect to the TATA (R frequency ), which is the smallest known example of this evolutionary principle (37,92) (http://www.ccrnp.ncifcrf.gov/$toms/ paper/ev/). Unlike eukaryotic transcription starts, there is a low conservation of bases at the transcription start point of E. coli (0.39 ± 0.06 bits). Because the average gap surprisal between the À10 and the transcriptional start (2.56 ± 0.04 bits) exceeds the information at the start point, we propose that the determination of which base to begin polymerization is influenced more by the detailed path of the RNA through the open complex (7), than by the actual base at the start.
The conventional spacing allowed between the À10 and the À35 only varies by 3 bases (11), but to account for experimental data (10,17,18), we allowed six bases. Most promoters do fall into the traditional three spacing classes, but binding at further spacings seems experimentally and statistically ( Figure 2) reasonable since 24% of the promoters have their strongest À35 outside of the three central spacings. The sequence logos for the most common spacings of 22, 23 and 24 are fairly similar, while those for the outside spacings are a little different. This suggests that at extreme spacings the polymerase may be contacting the promoter differently. At a spacing of 25, the least frequently bound spacing class, the most peculiar À10 logo is seen. The À10 at spacing 25 is unique, with a prominent T at position +1 and poorly conserved Ts at positions +4 and À1. Although this anomaly may simply be an artifact of the small sample (n ¼ 25), this spacing could be conformationally awkward for the polymerase, and this may in itself account for the rarity of promoters with a spacing of 25 bases. It has been shown that at higher superhelical densities, the rate of transcription significantly increased for promoters with this spacing (22), suggesting that activity from this spacing may require helical distortions.
The overall low information content of the entire s 70 binding site suggests that the RNA polymerase binds frequently along the genome (70,93). With a total information of 6.48 ± 0.14 bits, s 70 would bind approximately once in every 90 bases in random equiprobable DNA. This would lead to 10 times more transcripts than genes in E. coli. The promiscuous nature of the polymerase may be necessary to allow transcription of many different genes in the genome. The polymerase must bind independently of gene function, so it must be indiscriminate enough to bind to a variety of control regions. This suggests that transcription is frequently influenced not only by the strength of the sigma binding site, but also by regulatory molecules. It is also possible that many small RNAs are generated, as has been discovered recently [66,93,94].
In fragments from E. coli with lengths of 163 ± 24 bp, Kawano et al. found 0.76 promoters in one orientation (93). From this we compute R frequency ¼ Àlog 2 (2 · 0.76/163 ± 24) ¼ 6.7 ± 0.2 bits per site. This is remarkably close to the value for our model, R sequence ¼ 6.48 ± 0.14 bits per site, and it shows that, as with other genetic systems, the information in the binding sites is sufficient to locate the sites in the genome (37,92). This quantitatively demonstrates that information theory provides a reasonable basal model of polymerase binding.

Evolutionary implications of the extended minus 10
Surprisingly, we were easily able to isolate 84 promoters that lack a À35 and exhibit an extended À10 (13,14). The information content of extended À10 promoters is almost identical to the information content of the entire s 70 model (6.7 and 6.5 bits, respectively). That is, the information contribution of the À35 hexamer in the flexible promoter ( Figure 1) is approximately compensated by a short extension of the À10 (Figure 3). The additional information of the larger conserved region in the À35 is restricted by the information penalty of the gap surprisal. [The gap surprisal accounts for how the variable spacing between the À10 and À35 affects transcription (10,17,18)].
There is a correlation between the amount of conservation within binding sites (the average information content or R sequence ) and the amount of information needed to locate binding sites in the genome (37,92). Also, it appears that the information of a site (or group of sites) relates to the energetics of the system (45). Therefore, since these two promoter classes have a similar information content, we assume that they are equally able to be identified in the genome and to stabilize the polymerase. A single binding element, such as the extended À10, is a much simpler machine to evolve than a two-part flexible binder. The bacteriophage T7 RNA polymerase (95) has only one binding element (96), so having two widely separated parts is not essential for transcription. Therefore, we suggest that in prokaryotes the extended À10 may be an evolutionary predecessor to the modern bipartite promoter. Another possibility is that the bipartite promoter is the evolutionary predecessor of the extended À10, but this does not explain the origin of bipartite promoters.
Although they have a similar amount of information, the single-element promoter ( Figure 3) and the more complicated bipartite promoter (Figure 1) have differences in their sequence conservation. Not only is the conservation of the two upstream bases of the extended À10 lost in the bipartite promoter, but there is also a slight decrease in strength of the part of the extended À10 which corresponds to the bipartite À10 (5.05 bits to 4.78 bits, respectively, over the range À1 to +4). The information in the extended À10 that was lost from the bipartite promoter is important for the polymerase to function correctly. That information was apparently reallocated to the À35, so as to produce a promoter that was functionally equivalent to its predecessor. The energy lost by the internal strain of the flexing polymerase is compensated by the additional information of theÀ35. This is reminiscent of the apparent evolutionary information flow from the exon to the intron sides of both donor and acceptor splice junctions (97), (http://www.ccrnp.ncifcrf.gov/$toms/ paper/splice/).
An advantage of having two widely separated binding components may be to increase promoter strength disparities through interactions with transcriptional regulators. By having a larger binding region, there are more spatial opportunities for accessory proteins to affect the initiation complex. As shown in Figures 5 and 6, both the À10 and À35 are targeted by transcriptional repressors, so having two binding elements provides a larger target region within which to evolve repression.
Why would the cell evolve a flexible bipartite binding mechanism? A possible explanation could be that this mechanism allows a polymerase bound to the promoter to sense genomic structure. Indeed, transcriptional initiation has been observed to vary with the superhelicity of the DNA (22,25,98,99). These differences in the rate of transcription could be from differences in the meltability of the promoter or the stability of the closed complex (11,22). Also, the spacing between the À10 and À35 is large, two helical turns of DNA, which increases polymerase sensitivity to the overall structure, since twist or bending effects are amplified over larger distances. Twist and bending strain could affect polymerase contacts at both the À10 and À35, as shown in Figure 2. Therefore, a large flexible bipartite polymerase may have the advantage of higher sensitivity for superhelical regulation, whereas a rigid single-groove binder could be much less sensitive.
The two extra bases of the extended À10 are similar to positions 0 and +1 of the À35 (Figures 1 and 3). In both cases there is a T > G next to a G > T. Both T-A and G-C base pairs have an exposed hydrogen acceptor and donor in the major groove (O4-N6 contact for T-A, O6-N4 contact for G-C) (51), suggesting that the polymerase could contact either base pair at these moieties. Preferences for T > G or vice versa should depend on the exact positioning of amino acid contacts between the polymerase and the base, since these contacts are in slightly different positions on the base. Indeed, according to models constructed by Barne et al. (14), glutamic acids E458 and E585 contact the extended À10 G at À3 and the À35 G at +1, respectively, suggesting a correspondence between these two regions. Furthermore, there is a gap in sequence conservation at position À2 between the À10 hexamer and the additionally conserved bases of the extended À10 ( Figure 3). Correspondingly, the amino acids that contact the two bases at À1 and À3, T440 and E458, are separated by 17 amino acids (14). These observations suggest that there are two separable binding elements contacting the À10 region. The similarities between the À35 and the extension of the À10 region suggest that the protein element recognizing the À10 extension was duplicated and then the duplicate merely drifted away from the À10 to form theÀ35. This is consistent with the structure of the s factor, which has two parts separated by an extended polypeptide (23).
In comparison to the E. coli s 70 and s 32 , both of which appear to contain two helix-turn-helix DNA-binding domains, the s 55 factor produced by bacteriophage T4 for late transcription, contains only one helix-turn-helix motif (1). Correspondingly, the T4 s 55 only recognizes a À10 region which contains about 16.2 bits of information (61). This is close to the 17.6 bits required to locate the 50 known late promoters in the E. coli genome (37). A pareddown RNA polymerase is able to recognize and open an extended À10 (91). These observations are consistent with the hypothesis that À10 recognition evolved first, followed by appearance of the À35.
The relationship between the promoter and the ribosome binding site The information content of the flexible ribosome binding site (34) is greater than the s 70 model, 9.28 ± 0.06 versus 6.48 ± 0.14 bits, respectively. This most simply suggests that there is often more than one promoter per coding region in the cell as, for example, shown in Figure 6 and suggested by Huerta and Collado-Vides (70). In addition, the information in the promoters is lower than that in ribosome binding sites because many promoters rely on activation. A quantitative estimation of these contributions would require detailed knowledge of the number of transcripts and activator binding sites throughout the genome.
When we scanned our promoter model upstream of all annotated genes in E. coli (56), our model frequently identified sites at a spacing of $35 bases between the zero coordinate of the À10 and the first base of the start codon ( Figure 4). The peak represents transcripts starting 11 bases downstream from the À10 (Figure 1) to produce an $24 bp mRNA leader. Accounting for the 12-14 bases of mRNA inside the polymerase (23,100) this leader leaves $10-12 bases exposed. This is just sufficient space to encode for a Shine-Dalgarno (3 bases on the 5 0 side), a typical spacer (most commonly 9 bases) and an initiation codon (2 bases on the 3 0 side, for a total of 14 bases) (34), and for the ribosome to dock as soon as 0-2 more bases have been synthesized (101). The 35 base spacing allows the earliest possible loading of ribosomes onto the mRNA. There is a gradual decrease in the number of sites upstream of the peak around À35, which suggests a preference for the polymerase to bind close to the translational start.

Transcriptional regulation
Our original dataset of experimentally verified transcription start points was larger than the number of sites in our final model (684 versus 401). The cyclic refinement that removed sites focused the original group down by selecting a subset that is coherent. The excluded sites were weak (information content is <0 bits) compared to the retained subset and are therefore presumably activated or use a different sigma factor. Also, as previously noted, the average information of unregulated promoters is fairly low (6.48 ± 0.14), implying that the polymerase binds frequently throughout the genome. These observations are consistent with the role of regulatory proteins to help stabilize weak promoters.
Intergenic regions have a composition that is different from coding regions, and protein-binding domains have evolved to bind the intergenic regions (59). As shown in Figure 4, the polymerase has a tendency to bind close to the translational start. Regulatory proteins have the same tendency ( Figure 8, circles), but this appears to be because the density of non-coding regions varies relative to the promoter (Figure 8, red curves). Interestingly, the steepness of the density curve is greater downstream of the promoter than upstream. This suggests that in each intergenic region, RNA polymerase binding sites tend to be located where they will maximize the amount of upstream regulatory DNA, while minimizing the length of transcribed mRNA. These effects would preserve cellular resources.
The À35 is the most upstream component of the promoter, and it is closest to the aCTD, to which activator proteins bind (12,53). This explains why the alignments shown in Figure 8 are best matched by the À35 and À10 in contrast to the start point of the flexible promoter.
Without DNA bending, activators more than 20 bases upstream would have difficulty binding to the aCTD (53), because at distances shorter than the persistence length (150-200 bp) DNA is like a rigid rod (102). Furthermore, pairs of DNA sites come together most easily when they are $300 bp apart (103,104). These physical limits mean that activators would be restricted to be either immediately upstream of the polymerase, as noted previously (105), or at least 300 bases away. DNA bending proteins and curved DNA, which is in the intergenic regions (79,106), loosen these restrictions and allow activators bound within 300 bases upstream of the promoter to function. This explains why Fis, H-NS and IHF are often found within 300 bases of the promoter (Figure 8), as noted previously by Ussery et al. (79). Given that DNA bending proteins exist, intergenic regions could evolve to be <300 bases and still allow activation by proteins further than a few bases upstream of the promoter. This leads to another cellular evolutionary conservation principle in which the cell maximizes potential activator access while minimizing total genome length. Thus the intergenic region distribution follows from the distributions of the DNA bending proteins, and the DNA bending protein locations are in turn a consequence of the persistence length of DNA.
The number of Fis dimers in the cell has been shown to drastically increase in response to nutritional upshifts (107). If a major role of Fis in the cell is to facilitate activation through DNA-bending within the persistence length, then these results show how Fis can act as a powerful global regulator, linking transcription to cellular nutrition (39,79,108).
Our individual information analysis (Figures 5-7) confirms that the mechanism of transcriptional control can be predicted by the spatial position of transcription factors (105). Sequence walkers reveal that proteins whose positions share information with the promoter will probably bind antagonistically, while those which do not interfere with the À35 or À10 may be activators. Quantification of promoter strengths, however, is a difficult task because of the number of components that can be involved in the stabilization, or occlusion, of the initiation complex. Our approach is simple, clear, powerful, and useful in the design and analysis of experiments aimed at understanding genetic control mechanisms.