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Proc Natl Acad Sci U S A. 2007 August 28; 104(35): 13948–13953. Published online 2007 August 20. doi: 10.1073/pnas.0700672104. | PMCID: PMC1955771 |
Copyright © 2007 by The National Academy of Sciences of the USA Biophysics How gene order is influenced by the biophysics of transcription regulation Grigory Kolesov,* Zeba Wunderlich,† Olga N. Laikova,‡ Mikhail S. Gelfand,§ and Leonid A. Mirny*¶ *Harvard–MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA 02139; †Biophysics Program, Harvard University, Cambridge, MA 02138; ‡State Scientific Center GosNIIGenetika, Moscow 117545, Russia; and §Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow 127994, Russia Received January 24, 2007. What are the forces that shape the structure of prokaryotic genomes: the order of genes, their proximity, and their orientation? Coregulation and coordinated horizontal gene transfer are believed to promote the proximity of functionally related genes and the formation of operons. However, forces that influence the structure of the genome beyond the level of a single operon remain unknown. Here, we show that the biophysical mechanism by which regulatory proteins search for their sites on DNA can impose constraints on genome structure. Using simulations, we demonstrate that rapid and reliable gene regulation requires that the transcription factor (TF) gene be close to the site on DNA the TF has to bind, thus promoting the colocalization of TF genes and their targets on the genome. We use parameters that have been measured in recent experiments to estimate the relevant length and times scales of this process and demonstrate that the search for a cognate site may be prohibitively slow if a TF has a low copy number and is not colocalized. We also analyze TFs and their sites in a number of bacterial genomes, confirm that they are colocalized significantly more often than expected, and show that this observation cannot be attributed to the pressure for coregulation or formation of selfish gene clusters, thus supporting the role of the biophysical constraint in shaping the structure of prokaryotic genomes. Our results demonstrate how spatial organization can influence timing and noise in gene expression. Keywords: diffusion, genetics, genomics, protein–DNA interactions, spatial effects The colocalization of prokaryotic transcription factor (TF) genes and their binding sites is known from the pioneering work of Jacob and Monod ( 1) on the lactose operon and has been shown to be widespread ( 2– 4) and essential for the formation of regulatory motifs ( 5). Some have hypothesized that TF-binding site colocalization is advantageous, in part, because it could expedite a TF's search for its site ( 2, 5– 7) (the rapid search hypothesis). In prokaryotes, this speed-up by colocalization is possible because transcription and translation are coupled spatially and temporally. Therefore, TFs are synthesized near their genes and can rapidly bind colocalized sites ( A). The arrival time of a TF to its site ultimately controls the timing of gene regulation, whereas fluctuations in the arrival time can lead to bursts of gene activity and noise in gene regulation. The rapid search hypothesis suggests that colocalization is favorable because expediting TF arrival makes regulation faster and more reliable. Both experimentally (see ref. 8 for an overview) and theoretically ( 9– 13), many have studied the broader question: how can a TF find its cognate site on DNA among ≈10 7 decoy sites in a fraction of a minute while moving in the crowded environment of the cell and hampered by other DNA-bound proteins? The general model of the process includes 3D spatial diffusion of the TF through the cell volume and 1D sliding of a TF along DNA. According to this model, the search process consists of multiple rounds of search, alternating between 1D sliding and 3D spatial diffusion, leading to the expression for the mean search time, ts, obtained (in different forms) by several groups ( 9– 13):
where M is the total length of DNA in the cell, s is the sliding length, i.e., the mean number of base pairs scanned in a single round of sliding, and τ 1D and τ 3D are the mean durations of a single round of 1D sliding and 3D diffusion, respectively. However, it is not intuitively clear why colocalization would cause a speed-up, because in Eq. 1, as in traditional reaction rate theory, the search (reaction) time is distance-independent. The distance (and time) independence of the reaction rate is characteristic of 3D systems, whereas reactions in 2D and 1D systems are distance-dependent ( 14). Here, we systematically investigate the rapid search hypothesis and assess it against the alternative but complementary views that colocalization is due to coregulation or self-regulation or to enable horizontal transfer of functionally coupled genes (the selfish gene cluster hypothesis) ( 15, 16). We approach the problem by taking the following three steps: we ( i) estimate the TF search time in bacteria and determine the degree of acceleration provided by TF-binding site colocalization, ( ii) estimate the extent of colocalization in bacterial genomes, and ( iii) consider and rule out alternative explanations of colocalization. We demonstrate that the requirement for rapid search imposes a significant constraint on the evolution of gene order, an interesting case where a biophysical mechanism influences genome organization. How Much Acceleration Can Be Achieved by Colocalization? To connect the search time calculations to DNA conformation, we note that Eq. 1 implicitly assumes that each round of sliding is independent: the rounds of 3D diffusion between the slide completely randomize the position of the TF. To relax this assumption, we considered two types of 3D motion: small hops and large-scale jumps ( B). Hops are rapid reassociations of a TF to the same region of DNA. Elegant biochemical experiments have demonstrated hopping of DNA-binding proteins on DNA ( 17). We found that hops results from the geometry of the problem: Once a TF dissociates from DNA, it is much more likely to associate again to the same region of DNA than to other remote strands. We also demonstrated that hops are short and can be accounted for by replacing the sliding length s by an effective sliding length  , where nhops is the mean number of hops a TF makes before a jump ( C). Using simulations of spatial diffusion through a realistic geometry and density of nonspecific DNA, we estimated nhops ≈5–6 ( 46). Using simulations, we calculated search time as a function of the initial distance between a TF and its site ( L). Here, we observe two types of searches. When released from the ribosome, a TF can bind DNA near the 3′ end of its gene and start sliding and hopping along DNA. If the cognate site is reached this way, the average search time is fast (≈0.3 sec; C). Alternatively, if a TF dissociates from DNA and jumps before binding its site, then it must sample the whole genome to find its site, and the search is slow (≈150 min; C). The choice between these scenarios is controlled by a single length scale, the effective sliding length  ≈ 660 bp, with a range between 70 and 2,000 bp, for a typical TF. Sites at distance L < se are likely to be found quickly, whereas more distant site require a slow global search. A shows the average search time ( ts) for 10 TFs, B shows the probability of a fast search ( pfast) as a function of L, and C shows the distribution of times of fast and slow runs ( 46). Connecting back to the theory, our slow searches are described by Eq. 1. But why are they so slow? Although the form of Eq. 1 is intuitive, it does not show how the value of ts depends on the physical properties of the system. The sliding length s determines the number of rounds of search needed to find the slide. The search time also depends on the ratio of the time spent on the DNA to the time spent in the cytoplasm: τ 1D/τ 3D. This ratio is controlled by the affinity of a TF for nonspecific DNA, KdNS, and the total concentration of nonspecific DNA in the cell, [DNA]. Although sliding can increase the rate of search by reducing the number of rounds of search, it requires a TF to have an affinity for nonspecific DNA, which in turn can slow down search. The balance between these factors controls the global efficiency of search. To show these dependencies, Eq. 1 can be written in the following form [see supporting information (SI) Text]:
where the first term is the search time in the absence of sliding and nonspecific binding, whereas the second term provides the balance between the speed-up due to sliding ( 1/ s) and the slow-down due to the nonspecific binding (the ratio of KdNS and [DNA]). Note that 3D and 1D diffusion coefficients are agglomerated into kon, the on rate of a TF to bind DNA by a spatial diffusion [the Smoluchowski rate ( 18)], and s, respectively. As we showed earlier ( 10), search time is minimized when equal time is spent on DNA and in the solvent (i.e., τ 1D = τ 3D). However, in vivo, the strong affinity for nonspecific DNA [ KdNS ≈ 10 −3 to 10 −6 M ( 19)] and the high concentration of DNA inside the cell [[DNA] = 10 −2 M ( 20)] cause TFs to spend a significant amount of their time on nonspecific DNA (τ 1D/τ 3D = [DNA]/ KdNS ≈ 10 1 to 10 4). This nonoptimal time partitioning leads to search times from 15 to 500 min for a single TF. Clearly, having multiple copies of a TF significantly speeds up the search (linear with the number of copies). However, available in vivo measurements suggest there are only ≈10 copies of lactose repressor per cell ( 21), whereas there are >200 copies of ArcA per cell ( 22), a global regulator with >50 targets in the cell. Therefore, the acceleration of binding provided by colocalization can have a significant effect on gene regulation for low-copy-number TFs. If the TF is a repressor, rapid binding leaves little time for a polymerase to bind a promoter and start transcription, so bursts of gene activity are short and rare, consistent with recent single-molecule experiments ( 23, 24). However, if it takes ≈15 min for a pool of ≈10 repressors to bind a site ( A), the bursts of gene activity are long, making repression leaky and inefficient. Slow searches make the time required for transcription regulation comparable with the duplication time of bacteria, thus putting slowly regulating bacteria at significant disadvantage. To summarize, simulations show that TF binding is slow if TFs are not colocalized and have low copy number. Rapid search can be achieved by either colocalization or by increasing the copy number of each TF, arguably a more costly solution. Therefore, colocalization provides a significant advantage for low-copy-number TFs. How Widespread Is Colocalization That Cannot Be Attributed to Co/Self-Regulation in Bacteria? To unravel the extent of colocalization, we examined the distances between LacI/GalS family TFs and their binding sites. We grouped TFs into two categories: global TFs ( 25, 26), which are pleiotropic and regulate more than four operons (FruR, PurR, and CcpA), and local TFs, which regulate fewer than four operons. To focus on colocalization because of rapid search, we excluded from consideration all sites that can have a role in coregulation of the TF and its regulated transcription units (TUs) or self-regulation of the TF ( A). presents the distribution of the distance between TFs and their TUs for local and global TFs. Each distribution is compared with expected distribution of distances between random locations on chromosomes. The distribution for local TFs ( B) is strikingly different from those of global TFs ( C) and the expected random distribution; there is a significant excess of local TF-site pairs at distances below se ≈ 1,000 bp. This result clearly demonstrates that widespread colocalization of TFs and their sites cannot be explained solely by requirements for co- or self-regulation ( 2, 5, 27). Global regulators exhibit no significant colocalization, suggesting that they must achieve a speed-up in recognition by being present in high copy numbers, a claim supported by experimental evidences. For example, under normal growth conditions, the estimated transcript number of the global regulator crp is two orders of magnitude greater than that of lacI ( 28). (See SI Fig. 6 for systematic analysis of expression levels for local and global TFs.) Thus far, we have demonstrated that the rapid search hypothesis is biophysically feasible and that colocalization is widespread, even when coregulation effects are excluded, but we have not shown that the selfish gene cluster hypothesis does not explain colocalization. To test this, we considered the relative orientation of a TF gene and the TU it regulates. We compared two TF–TU orientations: downstream unidirectional and convergent (). Other orientations are not considered because they can be due to co/self-regulation (A). Although both orientations provide the same recombination distance (i.e., both orientations are equal under the selfish gene cluster hypothesis), rapid search favors the unidirectional orientation because it provides a smaller travel distance (B). In case of the convergent orientation, the travel distance is larger because the site is separated from the TF by a whole TU (≈1–5 kbp). presents the frequency of TF–TU pairs in these orientations. Remarkably, colocalized TF–TU pairs in the unidirectional orientation are eight times more common than convergent pairs. For a control, we compared TF–TU pairs located at larger distances and observed no difference in frequencies of the two orientations. The strong prevalence of unidirectional arrangements for colocalized TF–TU pairs suggests that the major driving force behind TF-site colocalization cannot be the pressure to form selfish gene clusters, but may be due to the rapid search mechanism. Although it is possible that unidirectional arrangements may be caused by a functional requirement for read-through, we observed the effect at lengths too long for this to be the cause. To test a possibility that the observed prevalence of unidirectional TF–TU pairs is due to a bias toward unidirectional orientation of nearby operons ( 29), we compared the frequency of unidirectional and convergent orientations for pairs of nearby operons (TU–TU pairs) in EcoCyc ( C and SI Fig. 7). This control clearly demonstrates that observed 8-fold excess of unidirectional TF–TU pairs cannot be explained by a very mild trend for coalignment of nearby operons. Some examples of colocalized TF–TU pairs are shown in . Although our analysis above considers only a subset of TFs, the rapid search hypothesis is quite general. For example, although we excluded from our analysis TFs that are parts of operons or share promoters with their regulated TUs, such gene order is consistent with the rapid search mechanism, because functional organization and biophysical constraints are met simultaneously. Moreover, according to rapid search mechanism, self-regulating operons can benefit from having the TF gene on the first place in the operon (and thus closest to the target promoter). Indeed, we found >3-fold enrichment of TF genes among the first genes in multigene operons ( SI Fig. 8). We also showed that the global (pleiotropic) TFs do not colocalize with their target sites. Clearly, positioning of several regulated operons close to their TF gene is nearly impossible. Pleiotropic TFs are likely to achieve rapid search by being present in high copy number. We also note that, although TF genes and their sites may not be close along DNA, they may be proximal in space because of the organization of DNA in the cell ( 4, 30) or looping of DNA ( 31, 32), thus opening a possibility of gene regulation by DNA conformation ( 33, 34). DNA conformation may also play an important role in the search process ( 11) because, upon a jump, a TF may associate to DNA in a place that is likely to be proximal along the DNA sequence and still reach the site quickly, effectively increasing the distance that provides faster search up to ≈10 3 to 10 4 bp. This picture is consistent with observed periodicity in the distances between a TF gene and the target sites for pleiotropic TFs ( 4). The time it takes a transcription factor to find its binding site is a biologically relevant quantity for both activators and repressors. Prokaryotic activators are often activated by small molecules that diffuse very rapidly through the cell; therefore, the activation of activators is not the rate-limiting step. (Using a very conservative estimate, we find that a small molecule can bind its target protein in <1 sec.) In contrast to many eukaryotic activators, prokaryotic activators also do not reside on the promoters while inactive, waiting for activation. Instead, inactive activators diffuse in the cytoplasm and only upon activation find their cognate sites on DNA (e.g., catabolite activator protein) ( 20). Therefore, the binding of the activator to its binding site and the subsequent recruitment of RNA polymerase are the rate-limiting steps for the alteration of gene expression. The search time of repressors for their binding sites is also biologically relevant. In many cases, repressors regulate the production of proteins that are toxic to the cell when produced at inappropriate times. For example, the production of tetracycline resistance operon ( 35) or lactose permease when it is not needed confers a measurable fitness disadvantage ( 36). Slow search times lead to leaky repression, which increases the steady-state level of otherwise repressed toxic proteins in the cell. One surprising result of our study is that the global search by a low-copy-number TF for its site is slow. This result goes against previous estimates for the search time ( 10, 13, 37, 38) that predominantly used either unrealistically high diffusion coefficients and/or assumed that the fraction of time spent on DNA (or the sliding length) is optimized for fastest search. Our estimate, in contrast, relies on the measured affinity for nonspecific DNA, yielding a much lower rate of binding. As we and others ( 10, 11) have shown, strong affinity for nonspecific DNA can make search slow, even slower than search by 3D diffusion alone. Why do TFs have an affinity for nonspecific DNA that makes the search so slow? One possibility is that the affinity for nonspecific DNA is optimized for an equilibrium binding rather than for kinetics. This affinity controls the balance between binding the nonspecific DNA and cognate sites and enables a TF leave its site when the specific affinity to the cognate site drops because of binding of a ligand ( 20, 38). Our result does not contradict experiments that demonstrate very rapid (faster than 3D diffusion) association of TFs to their sites in vitro, because these experiments used concentrations of DNA much lower than that observed in the cell. Although we have only considered prokaryotes, TFs in eukaryotes also need to rapidly recognize their binding sites. In this case, colocalization will not help because transcription and translation are uncoupled, so they may compensate by ( i) having a high copy number for global regulators and ( ii) keeping local TFs constitutively bound to their sites and activating them when necessary [e.g., Gal4 ( 39)]. Slow spatial diffusion and compartmentalization ( 40) may favor colocalization in other cellular processes such as signal transduction (see ref. 41 for review) or interactions between receptors on the membrane ( 42). In summary, we used simulations to show that the colocalization of a TF gene and its sites is required for rapid, reliable regulation of gene expression by low-copy-number TFs. We demonstrated that widespread colocalization of local TFs and their targets in bacterial genomes exists and cannot be fully attributed to co/self-regulation or the selfish gene cluster hypothesis. We conclude that rapid and reliable gene regulation imposes a biophysical constraint on the organization of bacterial genomes, encouraging TF genes and their binding sites to be close. Simulating a Transcription Factor's Search for Its Binding Site. To explore the kinetic effects of TF–TU gene colocalization, we simulated a transcription factor's search for its binding site and varied the starting position of the TF. We modeled a typical prokaryotic genome as a string 10 7 bp and randomly selected a binding site. We placed the TF at a given distance along the chromosome from the binding site and then simulated alternating rounds of 3D diffusion and 1D sliding until the transcription factor found its binding site. Sliding along the chromosome was modeled as an explicit 1D random walk. We simulated 3D diffusion as a mixture of hops, short correlated motions through the cell volume, and jumps, long, uncorrelated movements. The details of the simulation are described in the SI Text and SI Table 1. Data Acquisition and Preparation. LacI family members were identified by using several databases and algorithms ( SI Text). The SignalX program ( 43) was used to identify the binding motifs for TFs and construct the recognition profiles. Candidate sites were identified by scanning the genomes with the constructed profiles. Only orthologous binding sites, that is, binding sites occurring upstream of orthologous operons were retained for further analysis. This resulted in identification of 159 TFs and 647 binding sites from 36 genomes. These data are deposited in the RegTransBase database ( http://regtransbase.lbl.gov). A summary of the data are presented in SI Table 2. Because of the reliability of the data, here, we present our analysis of the LacI data set. However, we carried out a similar analysis using the EcoCyc data set ( 44), which provides more complete, if slightly less reliable, TF–TU data, and the results are presented in SI Figs. 9 and 10. We defined several classes of transcription factors and binding sites. The global set includes the pleiotropic TFs (FruR, PurR, and CcpA), which each bind more than four sites on the genome, and their binding sites ( 25, 26), and the local set includes all of the nonpleiotropic TFs and their binding sites. To avoid the strong but unrelated signal generated by self-regulating TFs, we excluded binding sites residing within the 5′ operator region of the corresponding TF gene ( A). Measuring Distances Between Genetic Objects. The distance between two genetic objects was measured in base pairs and was defined as the distance between the two nearest nucleotides of the objects, regardless of the direction. In this article, we use TF–TU distance, the distance between a TF and the nearest regulated TU gene. We thank Mehran Kardar, Johnathan Widom, Shamil Sunyaev, Hanah Margalit, Nir Fridman, Ido Golding, and Alexander Grosberg for useful discussions. L.A.M. and G.K. are supported by the National Center for Biomedical Computing, i2b2. O.N.L. and M.S.G. are partially supported by International Association for the Promotion of Cooperation with Scientists from the New Independent States of the Former Soviet Union (INTAS) Grant 05-1000008-8028 and the Russian Academy of Sciences (program “Molecular and Cellular Biology”). M.S.G. is a Howard Hughes Medical Institute International Research Scholar. Z.W. is a Howard Hughes Medical Institute Predoctoral Fellow. | | BS | binding site | | | TF | transcription factor | | | TU | transcription unit. |
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