Nanobiology of RNA Polymerase - American Chemical Society

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Nanobiology of RNA Polymerase: Biological Consequence of Inhomogeneity in Reactant Nobuo Shimamoto* Faculty of Life Sciences, Kyoto Sangyo University, Kamigamo-Motoyama, Kita-Ku, Kyoto, 603-8555 Japan Abbreviations References

1. INTRODUCTION After the acquisition of basic knowledge on gene expression, the most spectacular development in biology is the disappearance of the high wall that previously separated biology from chemistry and physics. This has been realized with the emergence of new techniques that had never been imagined to be applied to biology 50 years ago: new optical techniques include various kinds of new microscopies, development of photodetection close to the physical limitation in terms of sensitivity, and laser-related techniques such as laser tweezers. Atomic force microscopy and its related techniques have long been struggling to squeeze into biology, although they have been essential in the semiconductor industry since their invention. However, they are now starting to exert their power after the increased need for visualization of the structures of biological molecules under physiological conditions. The new techniques also supplemented the values of X-ray crystallography and nuclear magnetic resonance (NMR) distance geometries. In addition, there are so many new versions of traditional biochemical methods, such as crosslinking and footprinting techniques. Among the enzymes, RNA polymerase, more exactly, DNAdependent RNA polymerase, is one of the earliest to which these techniques have been applied in a mechanistic study. This is because most researchers, irrespective of biologists, biochemists, or enzymologists, tend to think that the RNA polymerase molecule is more like a machine than an enzyme molecule merely reducing the free energy of a transition state. It is a tiny complex machine with multiple functions: searching for a promoter; melting DNA within a promoter−RNA polymerase complex simply by binding; selecting cognate substrates by reading DNA sequence; changing functions accompanied with its departure from the promoter according to translocation; and releasing and recruiting transcription factors during phosphodiester bond formation, pausing, and dissociating programmed on DNA or RNA. To understand these more machine-like processes, researchers cannot limit their techniques to the conventional and established ones. Although these developments are their greatest contribution to the understanding of nature, it must be a creation of new concepts that will form the bases for developing science, rather than expansion of observation.

CONTENTS 1. 2. 3. 4.

Introduction Stages in Transcription Homogeneity in a Reactant Kinetic System in the Analysis of Transcription Reaction 5. Nanosystem in the Analysis of Transcription Reaction 6. Elongation Rate in Single-Molecule Experiments 7. Inhomogeneity in Elongation Rate and RNA Polymerase Molecules 8. Microscopic Mechanism of Elongation 9. Two-Pawl Ratchet Model 10. Handling of the Brownian-Motion Process 11. Brownian and Kinetic Versions of the Two-Pawl Ratchet Model 12. Inhomogeneity in Initiation Complex: Abortive and Productive Initiation Complexes 13. Reversibility of Promoters and Hysteresis in Initiation 14. DNA Scrunching 15. Mechanism of Abortive Intiation Incorporating Backtracking 16. σ70 Release 17. Danger of Misinterpretation of FRET Results 18. Promoter Search and One-Dimensional Diffusion 19. Biological Significance of One-Dimensional Diffusion Appendix 1: Transition-State Theory Appendix 2: Reaction Driven by Brownian Motion Author Information Corresponding Author Notes Biography Acknowledgments © XXXX American Chemical Society

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Special Issue: 2013 Gene Expression Received: January 7, 2013

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dx.doi.org/10.1021/cr400006b | Chem. Rev. XXXX, XXX, XXX−XXX

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In arguing the mechanisms of action of RNA polymerase, we emphasized recent developments in concepts gained in the molecular motions in finding a promoter on DNA; the movements of peptide and DNA segments during a single addition of nucleotide to the 3′-end of the transcript; and the way to store energy required for large-scale changes of the protein−DNA complex, including the orientation, bending, and melting of DNA, as well as dissociation of a protein component. These behaviors of the complex molecule are understood as the movements of various parts of protein, DNA, and RNA, which facilitate transcription reactions and have been preserved in evolution, rather than as the detailed list of interactions between the components. The introduction of molecular motion in biology may broaden molecular biology. The notion of the behavior of a molecule can now be more referenced by the preformative “nano”, and thus, this field, with the full notion of molecular motion, is termed “nanobiology”. Its aim is to handle the problems of how the behaviors of one or a small number of specific molecules build macroscopic and physiological phenomena. Thus, I do not use nanobiology as biology studied with nanotechnology. This review focuses on the heterogeneity of elongation complex (sections 6−11), initiation complex (sections 12−17), and DNA-RNA polymerase complex (sections 18 and 19) on the basis of intra- and intermolecular movements. The molecular bases of handling a chemical reaction including transcription reactions are discussed in sections 2−5 as well as Appendices 1 and 2. I also describe the danger in the use of new techniques without understanding their limitations. I argue mostly on the basis of Escherichia coli RNA polymerase, but the argument would be valid to a large extent for other RNA polymerases and other polymerases. The general topics of single-molecule and structural studies of RNA polymerases have been reviewed in several papers.1−4

Figure 1. Comparison of current classification (blue) and original classification (numbered). The processes involved in current classification are in parentheses. The initiation factor σ70 and core enzyme are shown in orange and pink, respectively.

as structural changes of the transcription complexes rather than a group of chemical reactions specific to each classification. Transcription can be regulated both at initiation and elongation/termination. In E. coli, the regulation at initiation generally shows a larger dynamic range than that at elongation/ termination. For example, the dynamic range of the transcriptional regulation in initiation of the trp operon is 70-fold and 1 order of magnitude larger than the famous regulation in elongation/termination coupled with translation of the trp leader region.10 A pause and a resumption of elongation are more distinct in eukaryotes than in bacteria.11,12

3. HOMOGENEITY IN A REACTANT The stages of transcription introduced in the preceding section are composed of many chemical reactions including binding/ dissociation as well as conformation change of the protein− DNA complex. Clarifying the transcription stages in terms of these reactions has been the main target of the mechanistic study on transcription. Although the exactness in determining a rate constant or an equilibrium constant obtained may not be the most significant in biology, the determination of the minimal mechanism relies on the principles of chemical kinetics. The kinetic analysis is based on a hypothesis called massaction law, which was first proposed as an empirical formula explaining affinity with concentrations.13 The law essentially claims the following equation, the rate equation, d [product] = k[reactant] (1) dt where the rate constant k must be independent of time and concentrations. Although this equation is widely used, it is not a universal truth and theoretically requires an implicit condition.14 In short, the reactant molecules must be homogeneous in terms of reaction probability. In the real experiments, a kinetic model containing rate equations is first assumed, and the model is then examined mainly by the consistence of the observed time courses of the reaction with those predicted from the model. Unfortunately, such a consistence in a limited experimental condition is not necessarily enough to prove the homogeneity. Furthermore, an exact model tends to yield

2. STAGES IN TRANSCRIPTION Transcription was first proposed to be separated into four stages, (1) template binding, (2) chain initiation, (3) chain elongation, and (4) chain termination,5 or later into three stages by combining stages 1 and 2 under the name of initiation. The resultant complex formed at the end of stage 1 is the active promoter−RNA polymerase complex called the “open complex”. A part of double-stranded DNA is melted to become single-stranded so that incoming ribonucleoside triphosphate (NTP) is recognized at the substrate binding site.6,7 Later, a step called promoter clearance8 or promoter escape9 was inserted between stages 2 and 3 (Figure 1). These functional subdivisions do not necessarily correspond to chemical reactions, such as the formation of a single phosphodiester bond, and even the seemingly simple word “binding” involves complex reactions, as introduced in a later section. Furthermore, two or more associated reactions distribute into two subdivisions, as in the case of initiation and elongation. What distinguishes elongation from termination is the potential for forming a phosphodiester bond. However, this criterion is blurred by the presence of elongation pause, which also associates with termination. Termination is now thought to be stripping RNA away from the RNA−DNA heteroduplex formed in RNA polymerase, rather than the absence of forming a phosphodiester bond. Therefore, the division between elongation and termination is not clear. In addition, it should be noted that these classifications shown in Figure 1 are made B


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Figure 2. Typical biochemical assays of transcription: (A) single-round transcription assay, (B) forced abortive assay, (C) DNA walking assay, (D) reconstituted elongation assay, and (E) inversed pulse-chase assay. The σ subunit and core enzyme are depicted in the same way as shown in Figure 1.

4. KINETIC SYSTEM IN THE ANALYSIS OF TRANSCRIPTION REACTION DNA-dependent RNA polymerases exist in several different quaternary structures. The simplest is composed of a single polypeptide such as bacteriophage T7 RNA polymerase and mitochondrial RNA polymerase. Bacteriophage polymerases show structural similarities to some DNA polymerases such as E. coli DNA polymerase I, DNA polymerase II, and human Pol α, and thus, they are generically called single-subunit polymerases. Cellular RNA polymerases in Archaea and Eukaryotes have three times more subunits than bacterial RNA polymerase, which comprises five or six subunits. However, the critical development of the mechanistic study of RNA polymerase has been made in the belief that RNA polymerases of all creatures essentially share the same mechanism of catalysis. Nascent RNA is elongated by the same RNA polymerase molecule without dissociating from the template DNA molecules. Such property is called processivity. Various kinetic assays have been developed for the functional analysis of the activity and processivity of RNA polymerase, in addition to the most primitive but relevant in vivo one, multiround transcription assay, in which RNA polymerase is added to a solution containing DNA and substrate 4NTP, followed by the measurement of poly- or oligo-RNA. Single-round transcription assay is used for tracing the fate of the open complex which has been preformed in the preincubation period (Figure 2A). A competitor of DNA binding of RNA polymerase is added

complex equations, which are not easy to follow, and the model is hardly thought to be convincing. These difficulties have decreased the challenges to analyze a complex reaction system like transcription with chemical kinetics. However, this is not the worst for chemical kinetics. The distance between chemical kinetics and biology sometimes yields an ignorance of the basic hypothesis, the homogeneity, in the following two cases. In the first case, a rate constant is sometimes defined to be an average of the rate constants of the reactant under various conditions, and the result is mistakenly supposed to be the averaged behavior of the reactant. Such an approximation is not allowed, because rate equations are generally nonlinear. This incorrect logic of the averages introduces time dependence in a rate constant k, making eq 1 meaningless. The second case is more intellectual than the first. The transition-state theory, which explains the constant k, is mistakenly applied to the system that has intrinsically inhomogeneous reactant molecules. As explained in Appendix 1, the transition-state theory is constructed on several assumptions that guarantee the homogeneity in the reactant. It is now possible to trace the behaviors of single molecules, and a kinetic model can be directly examined in terms of the homogeneity. It should be noted that there is a system that cannot be analyzed by chemical kinetics because of the intrinsic inhomogeneity. Such examples of RNA polymerase reactions are described in Sections 7−12, 14−16, and 19 and generally explained in Appendix 2. It will be helpful to discuss such examples in the field of transcription. C


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elongated,27 the difference between the reconstituted complex and the one prepared via initiation has not been compared. Figure 2E depicts the inversed pulse-chase assay, in which the order of the addition of a labeled NTP and a nonlabeled NTP for chase is inversed. This method is the most sensitive method to detect the inhomogeneity in the initiation complex by using the fact that the initiation of the full-length synthesis completes earlier than that of abortive transcription.28 During the initial stage of incubation with the unlabeled substrates, the complex that has initiated incorporates unlabeled NTPs into its transcript. At a time point of t, [γ-32P]-labeled initiator NTP is added together with the other unlabeled 3NTPs and heparin. Then the unlabeled and [γ-32P]-labeled transcripts are fully elongated for a sufficient period. The labeled transcript, whether it is the full-length or authentic abortive one, incorporated the initiator NTP at a time later than t. Since this assay is a single-round assay by the addition of heparin, the amount of labeled transcripts decreases according to t. If the full-length and authentic abortive transcripts are synthesized by a common initiation complex, they should show analogous decay curves. If not, there should be initiation complex preferential for the full-length or authentic abortive transcripts. All the promoters except the T7A1 promoter so far tested showed that the decay of the full-length transcript is more rapid than that of the abortive ones, which indicated the existence of the initiation complex specific to abortive initiation.15,28−30

together with NTPs to the preincubated mixture of a template DNA and RNA polymerase. Usually, heparin is selected as the inhibitor, but a DNA fragment containing a tight binding site or another promoter can be used when its product RNA is distinguished from the product from the original promoter. In this assay, it is essential to add an inhibitor in an excess amount over the original promoter DNA fragment.15 Since heparin is an inhomogeneous reagent and different lots have different affinities for RNA polymerase, this has been sometimes ignored in past studies. In such reports, the yield of the product or the elongation rate was unreliable. The forced abortive assay is a traditional system composed of an exclusion of few NTPs from the substrate to limit the RNA length16 (Figure 2B). This system can be subjected to the steady-state analysis to measure Km and kcat.17 Initiator NTP can be replaced by di- or trinucleotide including the initiating nucleotide,18 and one can design a template DNA yielding the transcript at any desired length.19 For analyzing the initiation mechanism, the forced abortive assay relies on the homogeneity of the initiation complex retaining a transcript of n bases, which is discussed in detail in sections 12−15 as the sequential mechanism of abortive initiation. This hypothesis has essentially no supporting evidence. Without the hypothesis, it is difficult to provide a clear conclusion with this assay. The DNA walking assay uses the same technique, the exclusion of unnecessary elongation substrates. In addition, the initiation or elongation complex is isolated from the NTP solution for preparing the complex. The transcript of the isolated complex then elongates a new set of substrate NTPs (Figure 2C). The isolation of the complex is performed by a spin column,20 a minute column,21 immmobilized RNA polymerase,22 or immmobilized template DNA.23 This method can be applied to observe every step of single-nucleotide addition, and thus is called “walking”. This method shares a common defect with the forced abortive assay, but if abortive transcripts are removed during the preparation, the active ternary complex regains homogeneity in terms of elongation. However, as shown in a pioneering study,24 inactive complex, such as the abortive complex and the backtracked complex, which is later described in detail, were not distinguished. Therefore, the analysis requires the measurement of the potential for the full-length and abortive syntheses. Sometimes the productive complex is stable enough to be stored at 4 °C for days18 and thus convenient for any elongation study. Since the results are obtained as the functions of the transcript length, one might misunderstand and conclude that the length is the cause of the analyzed phenomenon, even though the length is simply an experimental condition. This tautologic confusion sometimes occurred in interpreting a study of σ70 subunit release, as described in section 16. Furthermore, as explained in sections 8−10, the length of transcript and the position of RNA polymerase on DNA do not necessarily correspond with each other. Therefore, special caution is needed when one concludes that the length is the cause of a phenomenon. An active elongation complex with a transcript of a defined length can be reconstituted from its component and is subjected to an elongation assay25,26 (Figure 2D). This method opens up various types of termination assays. Before the invention of this method, a homogeneous elongation complex could not be prepared, and thus, this is also a good example proving the importance of homogeneity in the reaction with intermediates. However, except for the potential to be

5. NANOSYSTEM IN THE ANALYSIS OF TRANSCRIPTION REACTION The nanotechniques most frequently used in the studies of RNA polymerase are the single-molecule dynamics, in which the position of a molecule is traced in time to answer a mechanistic question. The position is usually determined under an optical microscope. The required positional accuracy may be smaller than the wavelength of visible light. In optical microscopy, there is a well-known principle called Abbe’s law, which claims the resolution is, at best, on the order of the wavelength. This smallest limit is defined to be the minimum separation between two bright spots to be distinguished from one another, and different from the positional accuracy. The accuracy means the error in determining the brightest point in a bright area, which is indifferent whether the bright area is composed of a single bright subregion or more. The accuracy is simply dependent on the light intensity, or number of photons, from the bright area and could be as small as subangstrom. The first application of the accuracy is video-enhanced microscopy, where the light intensity is processed as an electric signal31,32 In general, the light signal from a molecule is obtained as the scattering, diffraction, or fluorescence of a tagged label, such as a colloidal gold particle, bead, or a fluorophore, respectively. There are three optics to get such a light signal. The dark-field/ scattering optics generally gives the highest signal-to-noise ratio (S/N) (Figure 3A). A decreased background is obtained by the incident light at a total reflection angle (Figure 3B). The incident light generates evanescent nontransmitting light as thick as 150 nm above the surface and the light can excite a fluorescent tag. This illumination gives excellent S/N, because of much weaker background light than the conventional excitation. If the refractive index is large, then the position of a plastic bead can be determined by the conventional bright-field optics (Figure 3C). The positions of an RNA polymerase molecule on DNA molecules are traced on a fixed and usually extended DNA molecule, and its position is determined by the D


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graphite surface, although such an adsorption makes an environment different from those in an aqueous solution or in cytoplasm. AFM is also used for applying a force of 0.1− 1000 nN in nanofabrication. Video-enhanced microscopy, which was developed more than 30 years ago, is revived by being combined with a fluorescently photoactivatable green fluorescent protein (GFP).33 It is composed of simultaneous measurements of the positions of many bright spots sparsely scattered and named photoactivated localization microscopy or superresolution imaging, although the word “imaging” is somewhat misleading. This was used to detect localization and a local movement of RNA polymerase in cells.34,35

Figure 3. Three optical systems used in microscopy for determining the position of a particle. The incident light (yellow) and the emitted light (pale brown) from the labeling particle or sample (red) are shown. See the text for their merits and demerits.

6. ELONGATION RATE IN SINGLE-MOLECULE EXPERIMENTS The representative activity of RNA polymerase is chain elongation, which is composed of iterrative single-nucleotide adding reactions. In a single-molecule measurement, the position of RNA polymerase relative to DNA must be correlated to an absolute position determined by using one of the principles shown in Figure 3. Various ways of correlating elongation into the position have been tried by fixing a DNA, RNA, or RNA polymerase molecule. The rate of elongation or single-nucleotide addition was measured in an early pioneering experiment shown in Figure 6:

distance from the fixed end of DNA. If an end of DNA is fixed, both the position and the orientation are determined by fixing a bead at multiple neighboring positions. In this way, the relative rotational geometry of DNA and RNA polymerase molecules can be detected. An optical trap, namely laser tweezers, is suitable for trapping a DNA end immobilized on a plastic bead with free rotation (Figure 4). A magnetic trap fixes the rotational motion of a

Figure 4. The principle of the optical trap. When a laser beam is focused with an objective lens (yellow), a bead of a typical diameter of 0.5−2 μm with a large refractive index (black circle) tends to be trapped at the focus (X). Any part of the beam is inflected to the right as an example (orange with an arrow). The bead is dragged to the left (open arrow) by the reaction force of the force inflecting photons.

Figure 6. An enzyme molecule (pink) fixed on a matrix (green) and a particle (dark blue with white circle) attached at an end of a DNA molecule (brown). RNA (red) and the direction of DNA movement (arrow) are also shown. Brownian motion of the particle tethered by DNA makes it a large blurred image (graded blue background). At a light intensity, the diameter of the image (broken circle) is determined.

magnetic bead and is applied to detect DNA twist as a zcoordinate of the bead (Figure 5). The optical trap is used to apply a force of 0.1−50 pN, to extend DNA or stop elongation by applying an opposing force between the template DNA and an RNA polymerase molecule. A much more intuitive method is direct observation with an atomic force microscope (AFM) of both molecules which are loosely adsorbed on a flat mica or

Shafer et al.36 measured the size of the image of a gold particle blurred by Brownian motion and converted it to the length of the tether, which was the index of the RNA polymerase translocation. This method was refined by a specific way of fixing biotinylated RNA polymerase and by a selection of DNA sequence known for absence of regulatory signals causing a long pause.37 This method gave scattered values for the elongation rate of E. coli RNA polymerase of 7−20 base/s. Davenport et al. directly detected the one-dimensional movement of a similarly tethered bead fixed at the end of DNA extended by a mild bulk flow (Figure 7).38 They observed that elongation was sometimes interrupted and the enzyme paused, and the calculated rate was distributed with two peaks. If the temporal resolution is not enough, pauses are averaged as a continuous elongation, yielding an underestimated rate. The better the temporal or spatial resolution, the more pauses found. It turns out that there are plenty of pauses, from less than a second to the maximum observation period, and sometimes a long pause is accompanied with the backtracking of RNA polymerase so that the 3′-end of the transcript escapes from the active site to the outside of the transcription complex.39,40 Among various trials,41 the optical trap technique

Figure 5. Magnetic trap: An external magnetic field represented by the magnetic lines of force (curves with arrowheads) orients a magnetic bead and also pulls it upward. The DNA (brown) with an end fixed at the bead (orange) and the other at a matrix (green) is weakly stretched and supercoiled. A change of DNA supercoiling is detected as a change in the z coordinate of the bead. E


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P(n , t ) =

(kt ) exp( −kt ) n!

(2)

Therefore, the value of k is determined by the value of n/t averaged with this probability. Since a Poisson distribution gives (standard deviation of k)/(the average value of k) = {m/n(m − 1)}0.5, where m is the number of repeated independent measurements of k, for example, the number of molecules for which k is measured. In a sound experiment, the value of m is large enough to be m/(m − 1) ∼ 1, and thus, (standard deviation of k)/(the average value of k) is approximately equal to n−0.5. Figure 10 exemplifies the case of n = 50, which would give the standard deviation of 14% of the average value for k. However, the observed rates of elongation in the singlemolecule experiments gave much greater standard deviations than that predicted from the fixed rate, typically (standard deviation)/average = 0.3−0.5,2,37 and significantly deviated from the Poisson distribution. In most of the single-molecule experiments with high resolution, the elongation rate was predominantly maintained whether or not the elongation is interrupted by short and long elongation pauses. Therefore, the inhomogeneity in the elongation rates may be due to the inhomogeneity in the RNA polymerase molecules. At least for T7 RNA polymerase, the standard deviation within a molecule was small enough to be consistent with the Poisson distribution.45 Therefore, there must be multiple forms of the RNA polymerase or multiple local environments of the enzyme, or both. It was proposed that the multiple forms of RNA polymerase were caused by the errors in gene transcription and translation: one-third of E. coli RNA polymerase may include one or more missense mutations, if the error rates of transcription and translation are 10−5 and 10−4, respectively.46 If so, two-thirds of RNA polymerase must have the correct primary sequence, but such a partial homogeneity has never been observed in the distribution of the observed rate of elongation. Moreover, a substitution of amino acid residue does not necessarily result in a change in the activity of an enzyme, and the fraction with an altered elongation rate may not be large. Therefore, unknown post-translational modifications and inhomogeneity in the conformation of RNA polymerase must be considered. One interpretation is the contribution of a transient phenomenon called dynamic disorder in which domains in a protein molecule have a different relaxation time from its local equilibrium,47 but this concept is based on a single-molecule fluorescent measurement whose interpretation has been reconsidered48 (see section 18). The fixing of an RNA polymerase molecule places it in the vicinity of the artificial surface of a matrix or a bead. In the vicinity of the surface, the water molecules tend to form a structure depending on the surface, and a protein molecule tends to be affected by the altered hydrophobic interactions and electrostatic interactions, possibly leading to changes in the conformations.49−55 Although similar results were obtained by the fixing through linkers to a different subunit42 from the conventional β′ subunit, this evidence is too weak to deny the possibility. In a single molecule experiment, inactive molecules fixed on a surface are quite often found. This artifact can be diminished by treating the surface with a hydrophilic substance such as polyethylene glycol, but the complete removal of the artifact is difficult. More troublesome is that we do not have any suitable tools for determining the deviation from the true value as an artifact. Therefore, a possible source of the inhomogeneity

Figure 7. An enzyme molecule (pink) is immobilized to a bead (the right black circle) that is fixed at the apex of the pipet tip. Another bead (the left black circle) is attached at the downstream end of the DNA molecule (brown), which is extended by a constant horizontal bulk flow.

(Figure 4) with stretched DNA succeeded in getting a good resolution (Figure 8).42

Figure 8. An enzyme molecule (pink) is immobilized (black square) on the matrix (green) and the upstream end of a DNA molecule (brown) is attached at a bead (black circle), which is optically trapped. The trapping force extends the DNA, and the elongating RNA polymerase reels the DNA out. The bottom panel shows the design where the elongation moves the bead in the opposite direction, giving a force−velocity curve.43

Finally, the absolute resolution of 1 base was attained by the dumbbell method using a system composed of two laser traps (Figure 9)44 directly detecting backtracking of one to five bases. Elongation is resistant against the force as strong as about 10 pN38 and is completely inhibited by the force of about 20 pN.43

Figure 9. Dumbbell method. The enzyme (pink) and the DNA molecules (brown) are fixed on two beads (black circles) of different diameter, enabling a finer tuning of the force−distance relationship.

7. INHOMOGENEITY IN ELONGATION RATE AND RNA POLYMERASE MOLECULES The observation of the elongation rate showed a striking result: the obtained rate was inhomogeneous and could be dependent on RNA polymerase molecules. This means that eq 1 may not be applied in the case of the elongation by two or more molecules of RNA polymerase. At first, the mathematical background of a homogeneous and repetitive reaction is briefly introduced. Such a homogeneous reaction is described by a Poisson distribution. If an RNA polymerase molecule adds a nucleotide to the nascent RNA at a fixed rate of k, the probability of elongating RNA to n bases long during a reaction time t follows as eq 2. F


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Figure 10. (A) An example of the measurement of elongation, showing n = 50 bases in t = 2.3 s, giving an average rate of 22 base/s. (B) The Poisson distribution of k. If the elongation is composed of 50 independent steps with the same rate constant of k, the probability of getting a specific value of k is plotted against the true value of k (blue curves). If this measurement is repeated for m polymerase molecules, the standard deviation of k should be {nm/(m − 1)}0.5 and thus (standard deviation)/(average) ={m/n(m − 1)}0.5. Similar curves for n = 1−100 are also plotted (black curves). The probability is normalized to its maximum value, and the abscissa is normalized to the value of k giving the maximum probability, i.e., n/t.

the common structures of essential parts. Among the structures found in the vicinity of the active site, the most distinct was the bridge helix connecting two large subunits. It is bent in bacteria57 but rather straight in yeast. They supposed that the difference is not the difference in the species but in the timing during the catalysis and that the conformation change of the bridge helix pushes the 3′-end of RNA and the heteroduplex one by one, a mechanism similar to a mechanical clock, which yields the digital movement.59 This idea rapidly achieved consensus with the structure of another bacterial holoenzyme that showed an almost identical bending angle with that of RNA polymerase II. 60 This conformation change was connected with the vicinity involving the substrate-binding site called “trigger loop”,61,62 whose movement is critical to maintaining the transcriptional fidelity.63 The concerted movements of the bridge helix and the trigger loop are now modeled in a movie64 in consideration of genetic and biochemical evidence,44,65−75 although it involves many speculations. If the nucleotide addition is coupled with translocation of an elongation complex, namely, if the energy or power released in the addition reaction is utilized for the translocation, the elongation mechanism follows the power-stroke model, in which a chemical step and a mechanical movement are correlating one by one. The reactant state is then the NTP molecule plus the elongation complex molecule in pretranslocation conformation, while the product state is the pyrophosphate (PPi) molecule plus the complex at the posttranslocation state retaining the transcript with a nucleotide N added at the 3′-end (Figure 11). There is a transition state in a single-nucleotide addition from n to n + 1, and the activation energy is significantly high, namely, much higher than 0.5kBT, the average thermal fluctuation energy per degree of freedom, where kB is the Boltzmann constant and T is the absolute temperature. In this case, chemical kinetics is valid and a transition state can be defined as well as the reactant states. Since the single nucleotide addition is repeated until transcription is terminated, the potential profile is repeated and the potential energy is gradually decreased as n increases unless the single-nucleotide addition is equilibrated by the increase of PPi concentration (Figure 11). In vivo, PPi is hydrolyzed by an essential enzyme pyrophosphate to phosphate, and phosphate is excreted from the cell: normally the equilibrium is not

of the rate could be the artifact of the multiple conformation induced by the fixing of RNA polymerase on a matrix surface or a bead surface. Although researchers, especially the authors and close colleagues, do not hope for any phenomenon to be an artifact, we must refrain from optimistic interpretations and put more effort toward developing the suitable tools. Although this artifact due to fixing does not exist in cells, it does not necessarily mean RNA polymerase molecules should have a homogeneous rate constant in vivo. As a consequence of molecular crowding in cells, the elevated concentrations of macromolecules might enhance the formation of a stable complex of RNA polymerase and these macromolecules, which might introduce inhomogeneous activities of elongation. It is a speculation at present, but heterogeneous microenvironments have been observed to affect the movements of ribosome in living cells.35

8. MICROSCOPIC MECHANISM OF ELONGATION The structure of RNA polymerase had been one of the largest foci in structural biology since it copies the base sequence of DNA, as first shown by Hall and Spiegelman.56 For RNA elongation, a great mystery was the mechanism of translocation coupled with every single nucleotide addition. How is the digital movement by every base guaranteed and coupled with the reaction adding a nucleotide? The tertiary structure of RNA polymerase was expected to solve the mystery. The first high-resolution structure of the cellular enzyme was bacterial, the Thermus aquaticus core RNA polymerase, which lacks the initiation factor σA subunit,57 leading to the identification of the structure of some essential parts: (1) the channel for bent DNA, (2) the exit channel for RNA, (3) the secondary channel for backtracked RNA, and (4) a rudder structure peeling RNA off from DNA/RNA heteroduplex. The group of Kornberg then published the structure of yeast RNA polymerase II with the conviction that the greater concern is the eukaryotic enzyme, which is composed of distinctly different subunits by numbers and primary structure.58 However, the whole structures themselves, especially the essential parts, turned out to be very similar, indicating divergence from the same ancestor rather than convergence from different origins. Therefore, in their next report of the structure of elongation complex,59 they incorporated a productive hypothesis that all cellular RNA polymerases share G


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Figure 11. Power-stroke model of elongation. If the reactant state is a substrate NTP molecule plus the elongation complex molecule retaining the transcript of n bases long (red string), the product state is a pyrophosphate (PPi) molecule plus the elongation complex molecule retaining the transcript of n + 1 bases long (red string with N). The transition state (downward arrow) is energetically higher than the reactant state by energy much larger than 0.5kBT, the average energy of thermal motion per degree of freedom.

attained in a living cell. We provide a more exact description according to the transition-state theory in Appendix 1. It is merely an explanation of the theory, and thus, one who is familiar with the theory may skip it. However, we added the explanation for comparison with the alternative reaction theory for a reaction driven by Brownian motion, which is explained in Appendix 2.

9. TWO-PAWL RATCHET MODEL In a single nucleotide addition reaction by T7 RNA polymerase, the kinetic dissociation constant of substrate NTP, which is usually denoted as Km, was found to be larger than the true dissociation constant of NTP and to be dependent on the length of transcript.76 These results were interpreted such that the enzyme−NTP complex, ES complex, coexists and is rapidly equilibrated with other intermediates that do not bind NTP, making Km larger than the true dissociation constant. The number of these additional intermediates increases as the transcript is elongated, making the Km dependent on the length. In other words, the heteroduplex is not fixed at its cognate position where NTP binds to the substrate-binding site. The movement is rapid if compared with the whole single nucleotide. The NTP binding prefers the positioning at the cognate position and forward positions because of the space for the substrate, and in other words, the binding drives the forward translocation of the heteroduplex. This is in contrast to the power-stroke model, in which the formation of the phosphodiester bond drives the forward movement. The model proposed for T7 RNA polymerase was combined with the structure of RNA polymerase and mutants of the trigger loop, leading to a distinct proposal that the nucleotide addition and translocation are essentially composed of a pair of two-state systems or the two-pawl ratchet model: the oscillation or diffusive movement of the heteroduplex relative to the enzyme active site and the bend and stretch conformations of the bridge helix coupled with the trigger loops.77 The two oscillating systems make four states, and substrate binding adds one more state, which is boxed in Figure 12. The whole system can be either forward tracking or backtracking, while the insertion of the substrate NTP prevents backtracking. The seeming unidirectionality toward elongation is the consequence of the chemical reaction accompanied by the release of pyrophosphate. In addition to consistency with the obtained genetic and kinetic data, this model succeeded in explaining the elongation event, the backtracking event, the distributive positions during elongation, and the controlling function of

Figure 12. Two-pawl ratchet model. (A) The bridged helix, cooperatively with the trigger loop, oscillates between a stretching conformation and a bending conformation, forming a pawl. The heteroduplex of the transcript (red) and the template strand (brown) also oscillates relatively to the active site. These oscillations may be Brownian motion (double-headed arrow) or a reaction with activation energy (normal arrows). The base positions in the heteroduplex are numbered so that the RNA 3′-end is −1 and that for the next NTP binding is +1. The position of the heteroduplex relative to the active site is numbered by n (pretranslocation), n + 1 (post-translocation), n + 2 (forward tracked), and so on, with n being the transcript length. (B) Another pawl is the substrate NTP (blue). It collides with the stretching helix and prevents the counterclockwise movement of the heteroduplex, which otherwise randomly oscillates relative to the active site. The intermediates I−V within the blue box are rapidly equilibrated. In this panel, the rapid equilibrium is assumed to be attained by Brownian motions, but any reactions more rapid than the chemical process involving the PPi release are available, as shown in Figure 14. Phosphodiester is formed from V, and backtracking occurs from I. The intermediates III and IV at n + 1 may be reversibly converted into those at n + i (i > 1), but these conversions are not shown in this panel for simplicity. Pyrophosphate (PPi) is released, and the release makes the single-nucleotide addition irreversible, when PPi concentration is negligible.

the substrate loop, without hypothesizing any additional special devices, soon acquiring a consensus. This model was further supported by the experiment shown in Figure 8: either n or n + 1, but nothing in-between, was observed for the position of the heteroduplex under a tensile force opposed to elongation for E. coli enzyme.78 In the powerH


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stroke model, an in-between position would be expected because the position should be that of the transition state. Furthermore, in a two-pawl ratchet model, the force favors the conformations with no substrate rather than those with it. This situation is the same as the classic kinetic model of inhibition by a competitive inhibitor, expecting an increasing value of Km as an increasing force. In contrast, in the power-stroke model, the force should decrease the energy of the transition state and thus decrease kcat. For T7 RNA polymerase, a single-subunit RNA polymerase in the experiment shown in the bottom panel of Figure 8, the inhibition by a force increased the value of Km,69 kinetically consistent with this model. Although this two-pawl ratchet model was also named the “Brownian ratchet”,77 the description of the original article is misleading. The main text suggests that these oscillations are Brownian motion. However, the authors provided a kinetic rationalization in the supplement and suppose a rate constant and excitation energy for one of the oscillations, the bend− stretch transition of the bridge helix. There could be several definitions of Brownian motion, but the most general one is the time evolution of a particle under the fluctuating stochastic force generated by the thermal motion of solvent molecules. In this case, the reaction should not have any significant activation energy and occurs mainly by thermal fluctuation with the thermal energy, namely, as small as 0.5kBT. A kinetic version of the Brownian ratchet model thus involves an inconsistency, which is discussed in more detail later.

Figure 13. Diffusion-controlled binding in kinetic description. (A) Two reactant molecules (red circle and blue circle) undergo the Brownian motion and collide with each other. Most collisions result in the formation of their complexes without any time-consuming conformation changes. The encounter radius (r) is the distance between their gravity centers when they react. (B) Equation 4 is the probability of the red molecule to reach the sphere of the radius r per unit time. This calculation assumes that the concentrations are constant throughout the space and independent of the positions of two molecules. The assumption is actually an approximation, and the time cost in establishing the homogeneous concentration is ignored. (C) Equation 3 is based on the assumption that the proximal red molecule 1 and the distal molecule 2 collide with the blue molecule with equal probability, namely, the collision probability is independent of the distance between molecules, which is an obvious paradox.

10. HANDLING OF THE BROWNIAN-MOTION PROCESS To make clear the difference between the Brownian and kinetic systems, we here consider the original Brownian motion, the diffusion of a macromolecule in aqueous solution. A protein binding to DNA is sometimes supposed to be diffusioncontrolled or diffusion-limiting, namely, most of the collisions of the protein molecules with DNA molecules lead to complex formation with no time-consuming conformation changes (Figure 13A). Such an association is conventionally expressed in eq 3. rate of association = kdif [protein][DNA]

much larger than the experimental values except in a rare case.79 Therefore, the description by a rate equation is merely an approximation and should not be used when molecular motion or mechanical description is argued. There are two changes in the description of chemical reaction (Table 1). The first change introduces the homogeneity in the reactant molecules to validate chemical kinetics.14 The second change introduces the following thermodynamic approximations (case III). All the movements of the reactant molecules except the one along the reaction coordinate are supposed to reach equilibrium much more rapidly than the reaction in consideration. The detail of this approximation is described in Appendix 1 as the transition-state theory, and the reaction can occur only when the total energy of a set of reactant molecules exceed the activation energy. If one takes a movie of the set of reactant molecules in the time domain of the movement along the reaction coordinate, all their other intramolecular and intermolecular movements are blurred and averaged in this case. In other words, while the reactant molecules wait for a large enough thermal activation, other movements have been equilibrated. However, a reaction is not necessarily slow enough for the transition-state theory to be applied. It could be as fast as some other intramolecular and intermolecular movements. In the case of the diffusion-controlled binding shown in Figure 13, the binding is as rapid as the thermal motion of molecules, which is Brownian motion (case I in Table 1). The energy of such movements can be high or low, and there is no threshold. Instead, the three-dimensional trajectories of the reactant molecules must satisfy a condition: both reactant molecules

(3)

The value of kdif is provided by the Debye−Smoluchowski equation: kdif =

4πr(Dprotein + DDNA )NA 1000

(4)

In eq 4, r is the encounter radius (Figure 13B), Dprotein and DDNA are the diffusion coefficients of the protein and DNA, NA is Avogadro’s number, and 1000 is required for the dimension of the concentration to be molar when length is expressed in centimeters. The electrostatic attraction or repulsion is ignored in this simple form. The diffusion coefficients are measured by sedimentation experiments, for example, and the value of r is given by the values of the Stokes radii. Notably, the kinetic formulation brings about a paradox shown in Figure 13C. In this case, the solution homogeneity is an assumption to introduce eq 3, and thus, the molecular motion or Brownian process is ignored. For the kinetic handling, the agreement between the experimental values of kdif, 107−109 M−1 s−1, and theoretical values has been considered as a support. However, the theoretical value calculated by eq 4 for most proteins is about 1010 M−1 s−1, I


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Table 1. Three Cases of Chemical Reaction case

reaction probability of a reactant molecule

behaviors are described by

I

depends on molecules

equations of motion, Langevin equation

II

homogeneous

rate equation, diffusion equation

III

homogeneous

rate equation, transition-state theory, thermodynamic functions

must approach within the distance of r. In this case, the transition-state cannot be defined and only equations of motion, or the Langevin equation for the system at constant temperature, can be applied. Details are described in Appendix 2. In case II, the rate equation is valid. This case is not discussed here in further detail, because it includes the quantum transfer of electrons and the complex chemical reactions, wherein the reaction coordinate is described in two or more dimensional space.

activation energy cannot be defined cannot be defined defined (≫kBT)

reaction coordinate case by case one or moredimensional one-dimensional

other freedoms may be coupled may be coupled equilibrated

If the intermediates I−V in the blue box have similar potential energy and if the exchange among them occurs more rapidly than the following phosphodiester formation and pyrophosphate release, both versions explain the results obtained by Bar-Nahum et al.77 In the presence of a force against translocation, the reaction should be halted at the intermediate II irrespective of the versions, giving the digital positioning observed by Abbondanzieri et al.78 Such a preference of intermediate II toward intermediate V increases Km but maintains kcat in both versions, yielding a competitive inhibition.69 Therefore, both versions are possible. If the Brownian version is correct, the description provided in the supplements77 is inappropriate. If the transition-state version is correct, further analysis of the two-pawl mechanism may be necessary.

11. BROWNIAN AND KINETIC VERSIONS OF THE TWO-PAWL RATCHET MODEL The proposed two-pawl ratchet model for elongation has two versions, Brownian processes or a transition-state process. These two ways of driving the two-pawl ratchet mechanism are shown in Figure 14. In every cycle of single-nucleotide addition, there should be a decrease of free energy due to the transfer of NMP moiety from PPi to the 3′-end of RNA accompanied by the release of PPi.

12. INHOMOGENEITY IN INITIATION COMPLEX: ABORTIVE AND PRODUCTIVE INITIATION COMPLEXES Abortive transcription is an iterative synthesis of transcripts released at the length much shorter than the full-length transcript in the presence of 4NTP. It thus coexists with the full-length transcription. It was first identified in the transcripts synthesized by E. coli RNA polymerase on one of the strongest promoters of λ phage DNA, λPR,80 and then found on many E. coli transcription units.9,18,81,82 The yield of abortive transcripts depends on the promoter sequence involving both the initially transcribed sequence and untranscribed upstream sequence. Their existence has been evidenced mainly by transcription systems composed of purified proteins, but some abortive transcripts were observed irrespective of the difficulty in distinguishing them from degraded RNA in vivo.83 So far, the reports that have claimed its absence are primarily due to the decreased sensitivity upon using [α-P32]-labeled NTP in place of [γ-P32]-labeled initiator NTP or secondarily due to the use of RNA polymerase contaminated by GreB,84 which inhibits abortive transcription.85 It may be a consensus that all RNA polymerases catalyze abortive transcription. Abortive transcription is a futile reaction, and thus, it is likely to have biological significance or inevitable spilth of initiation. In fact, abortive transcripts are shown to be inevitable byproducts of transcription regulation in E. coli. Several genes, such as the atp operon, whose transcriptions are enhanced in an aerobic and rich nutrient condition, are shown to be controlled by this mechanism through the Gre factors.30 Since this enhancement occurs in initiation, the Gre factors, which were first found as elongation factors86,87 are initiation factors, too. A transcript with misincorporation by slippage synthesis tends to be aborted during initiation, and thus, abortive transcription could contribute to fidelity.88 The activation by switching from abortive transcription to the fulllength transcription is not limited to the Gre factors. The cAMP receptor protein (CRP) makes the malT promoter

Figure 14. Brownian version (A) and kinetic (transition-state theory) version (B) of the two-pawl ratchet model. The blue boxes shown in Figure 12 are denoted as the blue boxes in a reduced size in these panels. The details of a blue box, the intermediates I−V, and the accompanying reactions are shown for Brownian and transition-state theory version in panels C and D, respectively. In panel C, a conversion between the intermediates (double-headed arrow) is a Brownian process, and thus, a rate constant cannot be defined. Similarly, ki cannot be defined, if the phosphodiester formation as well as PPi release is also a Brownian process. The backtracking reaction is also the same, and these putative rate constants are thus in parentheses. In the transition-state theory version (panels B and D), rate constants can be assigned for all the processes, and an arrow indicates a reaction with an activation energy. The transition state could be either within the blue box or the pyrophosphate (PPi) release, and the activation energy should be much larger than kBT. J


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Figure 15. Two alternative mechanisms of authentic abortive initiation, with the σ70 subunit (orange), the core enzyme (pink), template DNA (brown), and synthesized RNA (red). (A) The sequential mechanism. Abortive product n bases long is released from the common ternary complex retaining the transcript of n bases long. Homogeneity in the ternary complex retaining an n base long transcript is assumed, and abortive release is considered to be a stochastic failure of elongation. (B) Branched mechanism. Abortive transcript is released from an abortive form of the ternary complex which cannot synthesize the full-length product. Inhomogeneity in the ternary complex retaining an n base long transcript is assumed.

productive, and the productive conformation remains long after CRP is dissociated with heparin.89 Furthermore, transcription activator C of phage Mu activates the transcription of mom gene by switching from abortive to productive mode.90 These transcription activators are known to interact with the initiation complex with different mechanisms from the Gre factors, but the common consequence suggests the existence of a common feature in these seemingly different regulatory mechanisms. Recently, four to six base long abortive products synthesized by bacteriophage T7 RNA polymerase are proved to be functional. The transcripts prevent an intramolecular hairpin formation in gene 10 mRNA required in termination, enhancing the expression of downstream genes.91 Interestingly, some functional abortive transcripts are slippage products containing misincorporated nucleotides and have more specific activities than the abortive transcripts with no misincorporation. There is confusion about the term “abortive transcription”, which has seriously impeded the understanding of transcription for decades. Sometimes the same name has been used in the kinetic assay shown in Figure 2B,C, where the transcript is forced to be released by the exclusion of the next substrate. The initiation complex prepared in this way, at least its fraction, generally keeps the ability to be elongated into the runoff transcript. In contrast, the initiation complex that is going to abort the transcript does not produce the full-length transcript.28 This property is confirmed for the isolated initiation complex.92 Therefore, to avoid confusion with the forced abortive assay, I here use “authentic abortive transcription” when there is a danger of confusion. In chemical kinetics, a minimal mechanism should be kept until counterevidence is obtained. According to this principle, abortive initiation was once supposed to be a stochastic mistake by the same initiation intermediate complex retaining an oligo RNA, which is supposed to be unique in terms of the transcript length in the pioneering studies of several decades ago.9,17,82 In other words, the initiation complex retaining an n base transcript has two fates: one is the release of an n base abortive transcript and the other is the initiation complex retaining an n + 1 base transcript (Figure 15A).18

In contrast, the commitment to abortive transcription tells the existence of the ternary complex specialized for abortive transcription, which is named the moribund complex, and the other is called the productive (initiation) complex here. A moribund complex usually cannot be converted into a productive complex by itself. These two forms are due to different conformations because holoenzyme prepared from elongation complex and purified σ70 subunit produced the abortive and the full-length transcripts in the same ratio as the original holoenzyme preparation of RNA polymerase.28 This also means that the difference in conformation is canceled by dissociation from DNA. Figure 15B shows the evidenced mechanism of abortive initiation. Therefore, the initiation complex retaining an n base long transcript is inhomogeneous.

13. REVERSIBILITY OF PROMOTERS AND HYSTERESIS IN INITIATION The promoters for σ70 holoenzyme form their open complexes by incubating with the enzyme without any supply of exogenous energy. Such open complexes are resistant to heparin, which is a competitive inhibitor of RNA polymerase binding to DNA, for several to several tens of minutes. This resistance was once used as a definition of open complex. However, a strong promoter for E. coli RNA polymerase,93 the A1 promoter of bacteriophage T7, shows an exceptional property. Its open complex can be dissociated within a minute by adding heparin.15,94 It is thus called “reversible”, and the heparin-resistant promoters are called “irreversible”. This reversibility is closely related to abortive transcription. The single-round transcription (Figure 2A) on the T7A1 promoter produces the stoichiometric amount of the full-length transcript to open complex, unlike the other ordinal promoters, such as the λPR and the lacUV5 promoters, which produce significantly less than the stoichiometry.88 The rifampicinchallenging assay,95 which measures the amount of active RNA polymerase by using rifampicin in place of heparin as shown in Figure 2D, is based on this stoichiometric synthesis on the T7A1 promoter. Moreover, little accumulation of moribund complex on the T7A1 promoter has been evidenced by the K


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photobreaching (FRAP) study in cells,34 showing that half of RNA polymerase molecules in cells are diffusive by a micrometer distance within 5 s and that the other half is undiffused for longer than 30 s. The actively transcribing molecules explain 40% of the undiffused fraction. The rest, 60%, was too large to be explained by the paused backtracking molecules, but the moribund complex and the recently found σ70-dependent pausing complex104 may explain the 60%.

inversed pulse-chase assay (Figure 2E). There are syntheses of abortive transcripts on this promoter, but the abortive and the full-length syntheses are synchronously completed.29 However, these exceptional properties of the T7A1promoter are not due to a different initiation mechanism but due to a different dependence on salt concentration. At a low salt concentration of several of ten millimolar, these distinct characteristics of the promoter disappear, and the promoter behaves like the λPR promoter,29 showing the generality of the branched mechanism (Figure 15B). This generality extends at least for cyanobacterial RNA polymerases.96 There are two ways to make the λPR promoter more reversible like the T7A1, and they both result in the decreased ratio of the amount of abortive transcripts to that of the full-length transcript. One15 is the σ70 mutants P504L and S506F97 in region 3, which is one of the four conserved regions among bacterial σ’s.98−100 The other is the addition of the Gre factors.85 According to the electron microscopic observation of chromosomal rrn operons,101 transcription complex molecules make a long train with the constant intermolecular distance of about 60 bp, which corresponds to a frequent and regular initiation at every 2−3 s. When the operons were competed with the rrnB multicopy plasmid to reduce the cytosolic RNA polymerase, the intermolecular distance within a train was still maintained. Therefore, the rrn promoters, if once initiated, tend to be kept initiated to make a train with an intermolecular distance of 60 bp irrespective of the decreased intracellular concentration of RNA polymerase. Similarly, the promoters, once turned off, tend to remain inactive. This persistence of the active and inactive states is a kind of hysteresis with a memory effect of previous states. Such persistence longer than 100 s102,103 cannot be explained by the rapid association and dissociation of DNA protein complexes of RNA polymerase and transcription factors. In living single E. coli cells, mRNA molecules, which are fluorescently labeled with MS2-GFP fusion molecules, are directly counted.102 There is no Poisson behavior of activation, which is predicted from the induction by simple binding/ dissociation of RNA polymerase and the repressor. The observed time courses show hysteresis: the synthesis of mRNA requires preactivation of the gene. This requirement is universal for 20 E. coli promoters in the single-molecule/ single-cell FISH experiment, and only the probability for switching off the preactivated state is dependent on the expression level of each mRNA.103 This suggests the existence of a universal regulatory mechanism independent of genes. A hysteresis requires a memory, and the binding and the dissociation of RNA polymerase as well as various repressors cannot explain the memory and the existence of the universal mechanism. The inhibition of transcription by abortive transcription is unique. The RNA polymerase itself behaves as a repressor in the form of a moribund complex by blocking the promoter, which can introduce hysteresis. The persistent preactivation state can be assigned to the unoccupied state of a promoter, which can produce a train of transcription complex molecules, and the regular intermolecular distance is explained by the rate-limiting promoter clearance at a saturated concentration of RNA polymerase. Blocking a promoter by a moribund complex may be the off state, and then the probability of turning off should depend on a promoter sequence as well as the concentration of initiation factors, both of which determine the expression level. This interpretation is consistent with the results of fluorescence recovery after the

14. DNA SCRUNCHING The initiation or elongation complexes retaining a definite length of transcript are footprinted on DNA by using the DNA walking assay (Figure 2C)9,20,21,82 or by forced abortive assay (Figure 2B).17,24 The former is known to protect a larger DNA segment than the latter. In these studies, the longest transcript retained in the initiation complex is 12−16 bases, depending on the promoter, similar to authentic abortive transcripts. The transition from initiation to elongation complex is a large-scale conformation change including σ70 subunit release and alteration of the orientation of DNA (see refs 105, 106). In these footprinting studies, the upstream boundary of the DNA protected by the initiation complex made by the forced abortive assay is unchanged during synthesis. In contrast, the downstream boundary moves with elongation.21 Therefore, three possibilities were proposed: RNA polymerase or DNA or both must be distorted to keep the unchanged upstream boundary and changed downstream boundary. Among these, distortion of DNA, namely, DNA scrunching (Figure 16), is consistent with the results of two nanobiological experiments. In the first experiment, the magnetic bead system (Figure 5) detecting the change in total DNA length was used, and the observed shortening of the DNA length within the transcription complex was as large as the length predicted by DNA scrunching.107 In another experiment by fluorescence resonance energy transfer (FRET), the results were interpreted such that the distance from σ70 region 2 to the upstream DNA base at −20 is constant, but the distance to the downstream base +20 decreases, which is consistent with DNA scrunching.106 These studies also claimed DNA scrunching in abortive synthesis; however, their assay was the forced abortive transcription with an exclusion of the next substrate NTP shown in part B or C of Figure 2. Therefore, these experiments examined the mixture of productive and authentic abortive complexes. Furthermore, the necessary condition for DNA scrunching, the constant upstream boundary of the protected DNA segment, has never been observed in the footprinting experiments for authentic abortive transcription. Instead, different footprinting patterns were observed, as shown in the next section. A moribund complex on the λPR promoter maintains the σ70 subunit that is not released unless it is converted into the productive initiation complex by a Gre factor.85 Thus, the abortive synthesis is unlikely to involve the same transition as the full-length synthesis. If DNA scrunching provides energy for the transition from initiation into elongation, as has been previously proposed9 and more recently discussed,108 there is no need to store energy in abortive transcription in the form of DNA scrunching. Therefore, DNA scrunching is likely to occur in productive initiation, but there is no evidence for authentic abortive transcription. L


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Figure 17. A new model of abortive transcription incorporating backtracking. The second channel (broken lines) is shown, and the others are presented in the same way as in Figure 16. (A) The productive open complex which is firmly fixed to σ70 subunit (the same as in Figure 16A). (B) The abortive version of the open complex with the promoter DNA loosely fixed to the σ70 subunit, and the DNA bubble becomes smaller. (C) The moribund complex with more exposed region 3 is symbolically illustrated by the DNA above region 3. The initiating NTP (red) is shown. (D) The backtracked moribund complex releasing an abortive transcript (red) from the second channel. The template strand segment formed a heteroduplex before the backtracking.

Figure 16. Schematic illustration of DNA scrunching and transition to the elongation complex. The transcription initiation site on the template strand (brown box) is denoted. (A) In the open complex, the −35 box interacts with region 4 of σ70 (orange) and the −10 box of the nontemplate strand with region 2. (B) Along with RNA synthesis, both strands are scrunching and distort regions 2 and 3 as well as the core enzyme. (C) The distortion energy is released by the large-scale conformation change involving σ70 release and the duplex formation of the scrunching DNA, leading to a change in the bend angle of DNA.

that σ70 subunit has reduced interactions with a promoter DNA, if compared with the subunit in the open or the productive complex. Because of the weaker bindings, region 3 is more exposed, and DNA is less distorted, resulting in the enhanced protein footprinting of region 3 and a smaller DNA bubble in the moribund complex than that found in the open complex. The weaker binding allows the backtracking and oscillating movements of heteroduplex, as is supposed in an elongation complex, and yields the distributed upstream borders of the protected region on the nontemplate strand at backtracked positions. The template strand is unprotected against Exo III due to these movements as well as the weaker binding to region 3. Since the observed backtracking was close to 20 bases, it exceeds the maximum length of abortive transcripts, 12−16 bases for E. coli RNA polymerase. Therefore, backtracking squeezes abortive transcripts out of the heteroduplex, and releases them through the second channel from which the 3′end of a long backtracked transcript protrudes. This backtracking model explains the slow elongation of the abortive transcript, because the catalytic center is far from the 3′-OH of the transcript most of the time. The conversion of a moribund complex without any transcription factors requires dissociation from DNA,28 suggesting that there are productive and abortive versions of the binary complex of RNA polymerase and DNA, namely, an abortive version of open complex (Figure 17). The summed band intensity of footprinting of the nontemplate strand near the promoter increases from the binary complex to the moribund complex with the reaction time up to 20 min.92 The abortive open complex may be barely or diffusively footprinted and, thus, not be footprinted very visibly. Its conversion into a moribund complex may give the increasing and distinct footprints on the strand.

15. MECHANISM OF ABORTIVE INTIATION INCORPORATING BACKTRACKING The footprint study during authentic abortive transcription92 had been done before the three-dimensional model of RNA polymerase57 and the two-pawl ratchet model77 were proposed. It is now possible to construct a model for structural and catalytic mechanism for abortive transcription. There are six observations to be explained by the proposed model: (1) the rapid distributive backtracking up to 20 bases after the addition of NTPs, (2) the absence of protection against Exo III digestion of the template strand, (3) a smaller size of the DNA bubble during abortive synthesis, (4) a more enhanced hydroxide radical footprinting of the entire region 3 of σ70 subunit, (5) the C-terminal half of region 4.2 of σ70 subunit in the moribund complex being more like a holoenzyme than an open complex,92,109 and (6) the moribund complex being converted into the productive complex by transcription factors of different types in a way dependent on the promoter.85,89,90 The backtracking, the absence of protection against Exo III, and enhanced protein footprinting all suggest a looser fixing between DNA and holoenzyme than that in productive initiation. In an open complex, the fixing is mainly composed of the following interactions with σ70 subunit and a promoter DNA: the bindings between region 2 and the −10 box of the nontemplate strand110−122 (also see ref 1), between region 4 and the −35 box in the duplex DNA,123−125 and between region 3 and the bases at −4 to −3 of the template strand.126 The core of the new model for abortive initiation (Figure 17) is M


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As mentioned before, mutations of region 3 of σ70 tend to convert a moribund complex into a productive complex. Two mutations of the former half of the region (region 3.1) make RNA polymerase less abortive, as mentioned in a preceding section15 (Figure 18). A promoter with an extended −10

cooperativity was observed for enhanced elongation by two or more polymerase molecules in the same transcription unit,128 and the predominant consequence is the inhibition of backtracking of the complex.129 In contrast, the backtracking causes an opposite effect in the initiation complex from productive to moribund according to the backtracking model, raising the possibility of a negative effect on transcription. In fact, when two RNA polymerase molecules start transcription from the same promoter, the trailing polymerase molecule commits slippage synthesis and aborts the transcript, including misincorporation,88 being consistent with the backtracking model.

16. σ70 RELEASE The σ70 subunit of E. coli RNA polymerase is dissociated during the transition from the initiation to the elongation mode, which was directly shown first by turning over130 and then by fluorescence anisotropy,131 ultracentrifugation,132 and immmobilization.85,133 In biology, this release is required for the regulatory mechanism called sigma switch, where the σ70 subunit is replaced by another σ subunit to change the recognition of a group of promoters.134 This regulatory switch is likely to be the most ancestral transcriptional regulation by protein factors, because some bacteria have only a few other transcription factors but retain several alternative σ factors (Nobuyuki Fujita, personal communication). As a result of σ70 release during transcription, the turning over of σ70 is more rapid than that of core RNA polymerase. Since the major transcription in growing E. coli cells is performed by σ70 holoenzyme, the amount of σ70 required is less than the stoichiometric amount of core RNA polymerase. In fact, the amount of σ70 is one third of that of core enzyme in the growing phase.130,135−137 However, in the stationary phase, the transcription level is much reduced, but the amounts of core enzyme and σ70 are not much reduced.138 Thus, σ70 does not need to independently turn over, although there are mechanisms for inactivating σ70 in the stationary phase by Rsd139 and 6S RNA.140 Interestingly, the holoenzyme prepared from a stationary phase, but not the one from the growing phase, keeps binding σ70 during elongation,133 suggesting the persistent retention to be a phase-dependent regulation of σ70 cycle. The mechanism of σ70 release was first analyzed in poly(UA) synthesis on the assumption called the length model: the ternary complex with a transcript with n bases stably retains the subunit while that with n + 1 bases cannot.141 Comparing the amount of the released σ70 with the distribution of the transcript length, 9 ± 2 bases were assigned to the critical length, n. On this assumption, the time at which σ70 is released after the addition of NTPs must be strongly dependent on the NTP concentrations. However, no such concentration dependence was observed for the time course of the release in the transcription from the T7A1 promoter, where the release and the elongation were both stopped by EDTA and the released σ70 was separated from the transcription complex with ultracentrifugation.132 The release of σ70 occurs about 5 s after the addition of 4NTP, and the average transcript length is six bases or less at a low NTP concentration and 50 bases or longer at a saturating concentration. Therefore, the release itself is rate-limiting and is preceded with a rapid triggering step, which could depend on the transcript length. This likely model is called the stochastic model and was also supported in vivo by

Figure 18. Two region 3 mutants and the template DNA. The mutated residues (yellow) are located near the end of region 3.1 of σ70 (brown). The beginning of region 3.2 makes the protruding σ finger contacting −4 and −3 bases of the template strand (cyan).126 The mutated residues (yellow) are expected to change the interaction of the finger and the template strand. The nontemplate strand (blue), dinucleotide transcript (red), and the β′ subunit (gray) are also shown. The β subunit, which covers this region, is removed in this figure. The coordinates are obtaind from 4G7O in the Protein Data Bank.

sequence can be initiated by T. aquaticus holoenzyme with the mutant σA lacking the latter half of the region (region 3.2) and its downstream, which removes the polypeptide, narrowing the entrance of the RNA exit channel. The mutant enzyme becomes less abortive than the wild-type.116 The effect of the mutant enzyme was interpreted as the reduced collision between a nascent transcript and the entrance127 on the assumption of the sequential mechanism of abortive transcription (Figure 15A). However, the putative collision requires a transcript of five bases or longer and cannot explain the fact that the abortive transcripts shorter than five bases are generally more abundant than the longer ones. In contrast, their abundance can be explained by more frequent backtracking of two to four bases than a larger one in the backtracking model (Figure 17). The model provides a new insight into the difference between initiation and elongation. There is a dilemma in transcription: RNA polymerase must be accurately fixed at a specific DNA site to initiate transcription as programmed, but the same enzyme must not be fixed at a DNA site during elongation. The dilemma is solved by the conformation change of transcription complex from initiation form into an elongation one. For cellar RNA polymerases, the initiation factors such as bacterial σ factors fix the enzyme at a promoter on DNA in the initiation form but lose the fixing activity in the elongation form of the complex. In other words, productive initiation is attained by eliminating the oscillating movement of the DNA, which is inevitable in the two-pawl ratchet mechanism of elongation. In the backtracking model, abortive initiation is a kind of elongation version of initiation, and abortive initiation may be an inevitable sacrifice associated with the solution of the dilemma. The collision of two transcribing RNA polymerase molecules will inhibit the backtracking of the leading transcription complex and enhance that of the trailing molecule. A positive N


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the Chip assay, and σ38 and σ32 were also shown to be released stochastically.134 The crystal structure of the promoter complex provided a possible mechanism of the release.127 As mentioned in the previous section, the transcript of length longer than five bases collides with the linker domain of σ70, and thus, a longer transcript should push regions 3 and 4 away from the core enzyme. This is consistent with the stochastic model with the triggering step occurring at five or six bases. This pushing could trigger the large-scale conformation changes during the promoter clearance,116 and the transcript can be kept elongated by several tens of bases during this process. The authentic holoenzyme and the one reconstituted from the core enzyme and purified σ70 showed different activities, not only initiation but also elongation, where σ70 was released from core enzyme.142 This result suggests the existence of persistent multiple conformations in the initiation complex and in the elongation complex, which is called structural imprinting, although it has not been fully explained. The β′ subunit was fused to the σ70 subunit to examine the effect of the increased local concentration of the σ70 subunit. The strain with the gene of the fused σ70-β′ is viable and shows a sigma switch phenomena similar to the wild-type, indicating that minor σ factors can replace such σ70 in vivo.143 This indicates that either the affinity of the σ70 subunit for elongation complex is weak enough to maintain σ70 binding or the fusing does not increase the local concentration of σ70.

18. PROMOTER SEARCH AND ONE-DIMENSIONAL DIFFUSION As a Brownian process, RNA polymerase performs onedimensional diffusion along DNA in searching for a promoter 149 (Figure 19). One-dimensional diffusion is

17. DANGER OF MISINTERPRETATION OF FRET RESULTS Irrespective of the bulky accumulation of evidence in vitro and in vivo as well as its convincing significance, the concept of σ70 release suffered the possibility of nonexistence. By singlemolecule fluorescence resonance energy transfer (FRET), only a slow release was reported instead of a rapid complete release accompanied with elongation.144,145 However, these reports may not be able to disprove the existence of σ70 release. First, the way of interpreting FRET data has recently been exposed to serious criticism. The interpretation in the reports is based on an assumption that the donor and the acceptor fluorophores are randomly oriented, namely, the square of a parameter called “orientation factor” would be 2/3. This assumption is now questioned, and improved methods have been proposed146 with a correction of overinterpretation of a classic theory.147 Furthermore, an inevitable averaging by the limited time resolution of a photodetection system also causes an artifact.148 A second difficulty also exists in the interpretation of data. Originally, a single-molecule FRET had been developed to avoid the artifact due to the contamination of the fluorescently unlabeled fraction of a sample at the cost of fluorescent intensity. In the analysis of data, the thresholds of fluorescent intensity separating the complex state and the dissociated state have been arbitrarily determined from the time courses of the limited fluorescent intensity superimposed by significant levels of noise. However, different values of the threshold are shown to lead to opposite conclusions, and thus, the selection of an objective threshold is essential.48 Third, a difficulty in the experiments is that the promoter mainly examined was the lac UV5 promoter from which only 6% of the promoter complex produces the full-length product.88 Therefore, there is a possibility that the observed slow release is due to the retention of the subunit in a moribund complex rather than the absence of a distinct release.

Figure 19. Promoter search by one-dimensional diffusion. The holo RNA polymerase is drawn as in Figure 15 and moves along the template DNA (brown) until a tight complex is formed with a promoter (yellow). Since the probability to be the promoter complex at position A is less than the probability to be at position B, this sequential reaction, driven by the diffusion process, cannot be described by chemical kinetics but should be treated by the Langevin equation or the diffusion equation.

classified into three modes:150 (1) sliding, in which a protein molecule keeps contact with one DNA segment; (2) intersegment transfer, in which a protein molecule transiently contacts with two DNA segments; and (3) hopping, in which a protein molecule transiently contacts with no DNA segments but is kept in the atmosphere of DNA (Figure 20). Since hopping is sometimes confused with three-dimensional diffusion, in which a protein molecule is in the completely dissociated state between two binding events, it is thus rephrased later as “intradomain association and dissociation”.151 It involves the translational movement along the DNA helical axis on one side of the cylindrical surface of DNA. At least for RNA polymerase, the groove tracking is confirmed as a coupling of translational and rotational motions,152 sliding along DNA. The biological significance of groove tracking is a continuous reading of the DNA sequence without the need of selecting a reading frame. In contrast, the other modes, as well as three-dimensional diffusion, require occasional agreement of the reading frame, thus increasing the trial numbers while searching for a promoter. O


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and it tends to be connected to the hypothesis that the acceleration of association would be proportional to the compression. However, for E. coli LacI, the diffusion coefficient of the one-dimensional diffusion along DNA is on the order of magnitude of 10−9 cm2 s−1 and 100−1000-fold smaller than the coefficient of the three-dimensional diffusion, 10−7−10−6 cm2 s−1.154,155 This difference is successfully explained by the hydrodynamic friction with water against the rotational motion inherent in sliding.156 A difference of 1000-fold is also found for RNA polymerase,157,158 suggesting its sliding. In spite of the difference, the existence of one-dimensional diffusion of LacI in vivo159 indicates the ability of the compression of volume to accelerate association. The index, sliding distance, is defined as the length of DNA averagely covered with the random sliding motion during a single protein−DNA binding event and is measured to be 300−1000 bp for E. coli RNA polymerase at moderate salt concentrations.160,161 In the detection of sliding by single-molecule dynamics, the visualization method is critical. The RNA polymerase labeled with a quantum dot was observed not to slide.161 The diffusion coefficient of the polymerase with the bulky quantum dot was reported to be 10−15−10−14 cm2 s−1, the same as that of the quantum dot itself, and the coefficient is 10−6−10−5-fold smaller than that of the unlabeled RNA polymerase. Since the sliding distance is proportional to the square root of the diffusion coefficient multiplied by the lifetime of the nonspecific complex, it should be about one base or less. Therefore, the labeled polymerase molecules should dissociate from a nonspecific site without any significant sliding. The result is a good negative control in proving the sliding of RNA polymerase rather than its absence.161 Little sliding of σ54 holoenzyme in its promoter search was detected in an experiment by the total internal reflection fluorescent microscopy (TIRFM).162 Since the σ is the major subunit contacting with DNA, this does not contradict the existence of sliding of σ70 holoenzyme. TIRFM may also underestimate the effect of sliding similarly to the quantum-dot labeling, because evanescent light is used to detect only molecules existing as close to the surface as ∼100 nm or less. In the vicinity of a surface, the ordered water molecules increase viscosity. This large viscosity and a possible steric hindrance by the wall slow sliding down near a surface. The same surface effects have been warned and delicately taken care of in the history of surface plasmon resonance,163 which also uses evanescent light with a surface. A bulk flow should be introduced to compensate the decreased diffusion near the surface, and conditions for measuring the rate constants and the equilibrium constant should be different.164 In experiments using evanescent light, therefore, quantitative interpretations must be cautious, but qualitative conclusions are more reliable. In fact, atomic force microscopy has successfully detected sliding of σ70 holoenzyme and other one-dimensional movements along DNA, which are slowed down on a surface.165,166 Irrespective of the existence of acceleration of association by sliding, the assessment of the biological significance of the acceleration may be reserved, because protein bindings to DNA are not the slowest step for the function of most DNA binding proteins. For E. coli RNA polymerase, elongation of the average size of a transcription unit, 1−2 kbp, requires at least 30 s even without any significant pauses, while the promoter binding completes within 2−3 s34,157 at the longest, which is even faster than the 5 s of σ70 release.132,134 Therefore, the acceleration of association by sliding causes few physiological effects. By

Figure 20. Three modes of one-dimensional diffusion. The holo RNA polymerase is drawn as in Figure 15. (A) Sliding. (B) Intersegment transfer. (C) Hopping or intradomain association and dissociation.

The study on one-dimensional diffusion has suffered by stretching the interpretation of experimental results obtained for a particular protein, as if two or more modes were mutually exclusive. Another stretching is a denial of one mode by the finding of the other. These modes are not mutually exclusive, and it is obvious that absence of the evidence is not the evidence for absence. A third stretching occurs by the experimental design based on the misunderstanding of sliding, which is discussed in the next section.

19. BIOLOGICAL SIGNIFICANCE OF ONE-DIMENSIONAL DIFFUSION Most DNA binding proteins must bind to specific sites to exert their functions, but the specific sites are buried in nonspecific sites existing in excess (Figure 21). The physical significance of one-dimensional diffusion is the compression of the volume in which a protein molecule must diffuse into a specific site,150,153

Figure 21. The distribution of specific (s, thick line) and nonspecific (ns, thin lines) sites. Their size is supposed to be 19 bp in this figure. A nonspecific site exists at every base pair irrespective of the size, except near an end of DNA. Therefore, the number of nonspecific sites on a long DNA is almost equal to its DNA length in base pairs. P


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direct149,152 and indirect157,160,167,168 detections, the sliding of E. coli RNA polymerase has been shown to exist. Does the acceleration of association have no biological significance, and would the sliding exist with the status quo? There is one possibility in which the acceleration of association that is not rate limiting exerts a significant effect on the whole process: the accelerated association could enhance the rapid pre-equilibrium binding before the ratelimiting step. However, if each state of the nonspecific complex at a site on DNA is a thermodynamic state, then the detailed balance must be established between all the nonspecific and specific complex states, leading to the thermodynamic consequence that the affinity of RNA polymerase for a promoter is independent of the pathways of binding. In this case, the binding affinity through one-dimensional diffusion should be the same as that through direct association and dissociation by three-dimensional diffusion.169 In other words, if an acceleration of association is observed, its effect should be compensated with the acceleration of dissociation of the same amplitude in every pathway without changing the affinity. In consequence, if nonspecific and specific complex states are thermodynamic states, one-dimensional diffusion or the length of DNA may accelerate the association to a specific site but should not change the affinity. In fact, EcoRI endonuclease,170 λCro repressor,171 and E. coli IHF172 showed no change in the affinities for different lengths of DNA (Table 2).

possibility that the nonspecific complex is not a thermodynamic state and thus irrelevant to the detailed balance in binding equilibrium for some proteins. For E. coli RNA polymerase, Riccetti et al. reported a small length effect when a DNA fragment that harbors four T7A1 promoters in tandem orientations were subjected to transcription.160 The effect is not biologically significant, but it first showed a polar length effect. E. coli RNA polymerase is preincubated with the DNA and then 4NTPs, as well as heparin, were added to allow a single-round transcription (Figure 2A). Since each promoter initiates the syntheses of different lengths of transcripts, one can determine which promoter has formed what quantity of open complex (Figure 22). On the DNA construct which was for comparison of the

Figure 22. Length effects with polarity for RNA polymerase. The DNA fragment (brown) harbors four identical T7A1 promoters (yellow) in tandem. RNA polymerase was preincubated with these reversible promoters in excess, and the single-round transcription was performed. The amount of the runoff transcript from a promoter (angled arrows) turned out to be independent of its upstream length but dependent on its downstream length. The longer downstream segments, up to 300 bp, further enhanced its transcription.160

Table 2. Length Effects on Protein Affinity for a Specific Site proteins EcoRI methyltransferase E. coli LacI

length effect (fold effect)

DNA length (bp)

20

14−775

12−10000

21−50000 55−3300

E. coli RNA polymerase EcoRI endonuclease Cro repressor E. coli IHF

2 (downstream)

66−69

1 (upstream) 1

79−440 −

1 1

− −

ref Surby and Reich, 1996173 Winter et al., 1981174 Khoury et al., 1990175 Riccetti et al., 1988160

upstream length, the four promoters synthesized the same amount of transcript irrespective of the upstream lengths from 79 to 440 bp. However, in the construct for comparison of downstream lengths from 66 to 301 bp, the amount was increased up to 2 fold depending on the length. The authors putatively supposed that the open complex was irreversibly formed on this promoter and interpreted the results as an acceleration of association by one-dimensional diffusion along the downstream DNA segment. However, the same group denied the supposition of irreversible formation of the open complex at the T7A1 promoter and showed that heparin deprives RNA polymerase from the open complex formed on this promoter in 1 min,94 which is much shorter than the preincubation period of 10 min. As described in a preceding section, the T7A1 promoter forms reversible open complex. Therefore, this is the polar length effect on the RNA polymerase binding affinity for the T7A1 promoter, which may claim a deviation from detailed balance at equilibrium in case I in Table 1. These results tempted us to re-examine our results obtained in our single-molecule experiment which showed one-dimensional diffusion of E. coli RNA polymerase in promoter search.149 The depth of the potential well along a groove (in the case of sliding or along the contour coordinate in the case of hopping) for an RNA polymerase molecule can be estimated from the data in the way shown in Figure 23. The observed velocity of RNA polymerase during one-dimensional diffusion along DNA, vslide, was compared with the velocity of the parallel component of bulk flow, vpara. The value of vslide was a little lower than vpara on DNA, roughly 0.3−0.7-fold from the obtained data.149 If DNA provides repetitive potential peaks

Jack et al., 1982170 Kim et al., 1987171 Yang and Nash, 1995172

However, there are several reports on other proteins suggesting the effect of one-dimensional diffusion on binding affinity (Table 1). Surby and Reich report 20-fold enhanced affinity of a monomeric enzyme, EcoRI methyltransferase, when the DNA fragment harboring a single specific site is extended from 14 to 775 bp DNA, and they proposed a model involving sliding and breaking the detailed balance between association and dissociation at the end of the DNA.173 In the first series of the one-dimensional diffusion study by von Hippel and associates,174 12−10 000-fold enhancement of affinity was reported for LacI. Lu’s group also reported a change in the affinity of LacI by more than 10-fold for 55−3300 bp operator DNA.175 Since LacI is tetrameric and has two DNA binding sites, this enhancement might not be due to the diffusion but to the second binding to the additional operators lacO2 and lacO3, which were found after their reports. However, an enhancement of about 20-fold was still observed for 21, 26, and 80 bp DNA, which should have only lacO1,174 denying the effect of the second binding. These DNA length effects suggest a Q


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The DNA length effect, if larger than several fold, will be one of biological significance for Brownian systems. Its understanding requires the dynamics of molecules, which will be a new central target of nanobiology.

APPENDIX 1: TRANSITION-STATE THEORY Let us say the reactant molecules are composed of NA atoms, and NA is a huge number, because the reactant contains a molecule of transcription complex composed of RNA polymerase, DNA, and possibly RNA, as well as a NTP molecule. Since hydration of protein is essential for its structure, NA must involve a number of hydrating water molecules. All the positions of the NA atoms can be determined by a point in a 3NA-dimensional space, the representing point hereafter. The point and the space are respectively presented as a black dot and a gray plane in Figure 24A. The z-axis is the total energy of the reactant molecules, and the potential energy forms a curved surface in the 3NA−energy space. The potential surface within the reactant state or the product state forms a well with the transition state in between (Figure 24B). The fate of the reactants corresponds to the movement of the representing point in the 3NA−energy space that always exists above the potential energy surface because kinetic energy is positive (Figure 24A). The representing point moves according to mechanical equations. Without a detailed knowledge of the molecules constituting the thermal bath maintaining the temperature, the point is inevitably considered to experience random thermal fluctuation. In other words, the point moves according to the mechanical equation with a stochastic force, namely, the Langevin equation. Among the three example trajectories shown in Figure 24C, two did not fall into the product well, corresponding to no reaction. In contrast, one reached a point above the product well and fell into the well to become the product; i.e., the reaction occurred. The falling process is nothing more than the dissipation of the high energy by the repeated collisions with solvent molecules. The lower the energy, the more frequent a thermal fluctuation. Thus, the points at low energy in the reactant well will have exchanged their positions with each other before a fluctuation with high enough energy for the reaction occurs, as shown in Figure 24D. Therefore, the trajectory fills up the reactant well in addition to the higher energy state above the pass. In other words, the reactants experience a sufficient number of low-energy thermal fluctuations to be considered to be random. The number of molecules with activated energy above the pass is then proportional to the number of molecules with the energy lower than the pass independent of the trajectories they experienced with the proportional coefficient of exp(−energy/kBT). This is the core of the transition-state theory,176 and the reaction probability becomes independent of the history of each molecule and only dependent on its energy. An equal energy plane above the pass also covers the product states. A dropping down in the product well by the energy dissipation is the very reaction. This rephrasing of “filling up” by “random” process is an assumption called an ergodic condition. Once this condition is accepted for an isothermal system, the possibility for each position of the representative point is proportional to exp(−energy/kBT). Since the fluctuation of energy occurs much more frequently than the reaction, the reactant molecules become homogeneous in terms of reaction, enabling them to be described by eq 1. Although the rephrasing is mathematically denied for the generic Hamiltonian system,177 we would like to leave this long-living

Figure 23. Microscopic explanation of friction between a sliding protein molecule and DNA during sliding. A sliding protein molecule makes random thermal motions along a DNA groove. The total energy of the trace of the protein molecule (thin blue lines) and the potential wells (thick corve) are plotted against the coordinate along a contour. There is a bulk flow from left to right with a velocity, which is 10−6 of the average thermal velocity of the motion.149 While the rightward transition by thermal motion occurred 100 000 times, the bulk flow decreases one leftward transition on average, namely, 99 999 times leftward transitions. Therefore, the effect of bulk flow is negligible, and the distribution of the traces is essentially the same as that at thermal equilibrium. The protein molecule above the red line can be freely dragged across the potential walls between the wells (able to transfer), while that in the well stays in the same well (unable to transfer). The fraction of the traces above the red line should be proportional to the ratio of vslide to vpara and was observed to be 0.3−0.7.149

and wells for a protein molecule during sliding (Figure 23), vslide is approximated by eq 5. ⎛ 2h ⎞ vslide = vpara exp⎜ − ⎟ ⎝ kBT ⎠

or

⎛ 2h ⎞ exp⎜ − ⎟ = 0.3−0.7 ⎝ kBT ⎠ (5)

where h is the potential depth of the well, which yielded the value of h to be 0.2−0.6kBT, close to the average thermal energy per degree of freedom. The observed one-dimensional diffusion of RNA polymerase involves sliding because a coupling between translational and rotational motions has been observed.152 Although there is a difference in the Brownian motion in solution and in sliding as mentioned above, namely, the sliding protein molecule must experience both translational and rotational collisions with water molecules along the sliding pathway, this does not affect the macroscopic equation of eq 5, because it only slows down the fluctuation speed, which is not explicitly involved in the equation. Because the value of h is close to 0.5kBT, there is no significant activation energy. The transfer from a nonspecific site occurs by a Brownian process and thus cannot be described by chemical kinetics or thermodynamically approximated, as discussed in section 10. Therefore, each nonspecific complex cannot form a thermodynamic state. In other words, the molecule coming from the left flanking nonspecific site tends to transfer to the right nonspecific site, and vice versa. The transfer reaction between nonspecific sites depends on the history of a molecule and thus is described by the Langevin equation but not by chemical kinetics. The detailed balance between the flanking nonspecific sites is no longer guaranteed because they are not thermodynamic sites. In this case, as evidenced for several proteins including E. coli RNA polymerase, one-dimensional diffusion can have the length effect on the affinity for a specific site. Brownian motion of protein drives both three-dimensional and one-dimensional diffusions, where the detailed balance becomes irrelevant. Although only the 2-fold effect was found for RNA polymerase, more than 10-fold effects have been found for other proteins. R


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Figure 24. Power-stroke model of elongation by the transition-state theory. The 3NA-dimensional coordinate space of all the atoms in the reactant molecules is symbolically expressed in a two-dimensional plane (gray plane). The reaction coordinate of elongation (horizontal line) is included in this plane. The microscopic potential is defined at every point in this plane, forming a curved surface in the symbolic three-dimensional space of energy and the gray plane. The potential surface makes an intersection (thick curve) with the vertical energy−reaction coordinate plane. The isoenergetic planes are colored in pink in panels A−C, while they are shown as dotted lines in panel D. (A) In the example, all the positions of the reactant atoms are indicated by a single point (black dot) in the gray plane, and the mechanical state of the reactant molecules is represented by the representing point (red dot). The relationship among the representing point, its potential energy, and its kinetic energy are shown. (B) The potential surface has two wells corresponding to the reactant and product states. The transition state (green) is the plane that stands at a pass between these wells, and the plane is perpendicular to the reaction coordinate. (C) The representing point moves in parallel to isoenergetic planes (pink) without a collision, and collision of a water molecule induces a jump to an altered total energy plane. Some trajectories (blue and gray) indicate no reaction, while another trajectory (red) corresponds to the reaction. (D) When a reaction rarely occurs, the trajectory fills all the 3NA-energy space. The lower the energy, the more often the trajectory visits, which is the thermodynamic assumption described in the text. The visiting probability of the reactant trajectory is displayed as the red gradation and is supposed to be in parallel to exp(−energy/kBT), a microcanonical distribution.

arrive at limited reactant initial states. Therefore, the distinct property of Brownian motion is that the arrival at the product position (the reaction) takes place before the trajectories have filled up to make reactant molecules homogeneous. In contrast to the case shown in Figure 24D, where the homogeneity has been established, the kinetic approximation, namely, eq 1, is invalid.14 This is the cause of the paradox shown in Figure 14C: the assumption of homogeneous concentration removes the dependence on the molecular histories, while the collisioncontrolled reaction depends on the individual histories. This is the reason why the trajectory must be determined by solving a Langevin equation by supposing a stochastic force. The same reason explains why the transition-state theory, as well as the thermodynamic assumption, is irrelevant to the reaction driven by Brownian motion. In both cases shown in Figures 24 and 25, the driving force of chemical reactions is nothing more than the molecular motion or thermal fluctuation, and the catalysis by the enzyme occurs much less frequently than the typical and frequent thermal fluctuation with an energy ∼0.5kBT. There are two ways to get such an infrequent thermal fluctuation. In one way,

problematic approximation untouched according to most textbooks of stochastic mechanics. In conclusion, the transition-state theory of reaction assumes homogeneity in the molecules in the reactant state.

APPENDIX 2: REACTION DRIVEN BY BROWNIAN MOTION In the total energy−3NA dimensional space which was also used in Figure 24, the potential energy profile of a reaction driven by Brownian motion is like the ruins of Petra, the famous historical city in Jordan which was mentioned in the Book of Exodus; however, it was first introduced to European people so late in the 19th century due to the difficult access in going through a narrow passage. The product state is connected to the reactant state with a narrow passage, but there are no high-energy states along the passage (Figure 25). The representing point infrequently goes through the passage because of its narrowness but not because of high energy. This is the biggest difference from the transition-state theory. Only with the limited combinations of the positions and velocities (and thus the reactant molecule energy) represented by the red dot can it S


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occasionally arrives at the specific site, and sometimes falls into the deep well at the site. During these Brownian processes, the protein molecule does not experience a high-energy state but is kept driven by a collision of water molecules irrespective of its energy. A nonspecific complex can neither form a homogeneous state nor a thermodynamic state because of the following reasons. There is only a low potential barrier of about 0.5kBT from the nonspecific site to the specific site, a barrier similar to those between nonspecific sites, at least for RNA polymerase (Figure 23). Furthermore, the formation of a specific complex occurs before the trajectory of the molecule fills up the 3NA− energy space. In consequence, at binding equilibrium, the detailed balance between such nonthermodynamic states is not guaranteed. The limited entrance in the narrow path in Figure 25 is sometimes mistakenly described as smaller entropy. Entropy, as well as the detailed balance, is a concept only validated after the thermodynamic states have been established. The time cost in the establishment is sometimes believed to be extremely short if compared with chemical reactions. However, this is not always short. The thermal fluctuations of large biopolymers such as DNA and proteins have slow components and can be slower than a chemical reaction. In this case, the establishment of a thermodynamic state is time-consuming and can be slower than a reaction. The rapid establishment of a thermodynamic state is not a universal truth and should not be confused with the timeindependence of phenomena described in the assumption of thermodynamics.

Figure 25. Reaction driven by Brownian motion. The 3NAdimensional space (gray), z-axis perpendicular to it, the reaction coordinate (elongation), and the isoenergetic surfaces (pale orange) are the same as in Figure 24. The section of the potential energy is drawn (thick black line). The potential energy going through the pass is almost as high as the well bottom of the reactants (about kBT or smaller), and the passage from the reactant state to the product state is narrow. It is so narrow that most trajectories (blue and gray trajectories) cannot arrive at the product state; thus, only a small number of trajectories (red) arrive at the product state. This arrival occurs before the nonreactive trajectory fills up the reactant state, namely, before the nonreactive trajectories experience all the possible configurations. Therefore, the reaction probability depends on the initial conditions of the reactant molecules, or on each trajectory. Another example is the diffusion-controlled association shown in Figure 14.

AUTHOR INFORMATION

the fluctuations are limited by the energy above a threshold, namely, the activation energy ≫kBT (Figure 24). Alternatively, the fluctuations are limited by the initial condition of each molecule irrelevant to the energy (Figure 25). In this case, the reaction takes place via a rarely occurring conformation of the reactants state with a low potential energy close to 0.5kBT. In other words, the reaction only happens in a limited case with a combination of sequentially ordered and simultaneously occurring molecular events. For example, if we suppose the Brownian version of a two-pawl ratchet model, the limited case is described as follows. The trigger loop forms a loose conformation for a substrate NTP molecule to approach the substrate-binding site, which is a space between the 3′-end of RNA and the stretched bridge helix of the RNA polymerase. To attain this local structure, the RNA−DNA hybrid, the trigger loop, the substrate NTP, and the bridge helix must locate at the specific positions with the specific shapes as well as the specific orientations in a definite sequence of events. Therefore, the reaction depends on the history of the individual set of the reactant molecules rather than just their total energy. In such mechanisms, kinetic assumption is inappropriate, and an equation of motion, such as the Langevin equation, is the appropriate tool. In the case of sliding along DNA, a protein molecule in a solution occasionally collides with a DNA molecule accompanied by the formation of a nonspecific complex and then diffuses along the groove, at least for RNA polymerase.152 During one-dimensional diffusion, the protein molecule is kept bound on DNA by an electrostatic force between the negatively charged DNA molecule and the positively charged DNAbinding site on the protein molecule;169 probably, to some extent, hydrophobic interactions may help the binding, too. The protein molecule travels along DNA across the low-energy barrier between the nonspecific sites as described with eq 5,

Corresponding Author

*Tel/Fax: +81-75-705-3078.E-mail: [email protected]. Notes

The authors declare no competing financial interest. Biography

Nobuo Shimamoto is now Professor of Nanobiology Research Laboratory at Kyoto Sangyo University in Kyoto, Japan. He has been interested in the mechanism of temporal changes in biological systems for 40 years. He started his study of enzyme kinetics, and subsequently obtained his Ph.D. in physics from Kyoto University in 1977. He then conducted postdoctoral research in biophysics of RNA polymerase at Albert Einstein College of Medicine of Yeshiva University in New York. He returned to a position of Assistant Professor at Hiroshima University and initiated research in several areas as a principal investigator for about 10 years, and at the National Institute of Genetics, Mishima, Japan, as Professor for about 20 years. His major topics of study during these periods have been the T


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mechanism of cooperative binding, the proof of RNA polymerase sliding along DNA, and the mechanism of abortive transcription. For years, he has been involved in organizing the Asian and Oceanian Conference of Transcription to combine good science with good authentic foods. He is one of the pioneering members of modern ballooning in Japan and organized the Japan Balloon Federation as its first president. He moved to the present university in 2010 and then started research on the mechanism of bacterial survival.

ACKNOWLEDGMENTS Dr. Jyun-ichi Tamizawa, Dr. Masa Imashimizu, and Dr. Hideki Nakayama are gratefully acknowledged for discussions, and Ms. Harriet Sallach graciously helped my writing. The Ministry of Education, Culture, Sports, Science and Technology of Japan, Kyoto Sangyo University, and Olympus Co. Ltd. supported this study. ABBREVIATIONS 3′-OH the hydroxyl residue at the 3′-end of RNA 4NTP ATP, UTP, CTP, and GTP AFM atomic force microscope DDNA diffusion coefficient of a DNA Dprotein diffusion coefficient of a protein FISH fluorescence in situ hybridization FRAP fluorescence recovery after photobreaching FRET fluorescence resonance energy transfer or Förster resonance energy transfer GFP green fluorescent protein h depth of the potential well at a nonspecific binding site k rate constant for single-nucleotide addition kB the Boltzmann constant kdif second-order rate constant of a diffusion-controlled reaction NMR nuclear magnetic resonance NTP ribonucleoside triphosphate P(n, t) probability of elongating RNA to n bases long during a reaction time t PPi pyrophosphate r distance between the gravity centers of two reactant molecules σ70 the major sigma subunit of E. coli RNA polymerase encoded by rpoD S/N signal-to-noise ratio T absolute temperature vpara component of the velocity of bulk flow parallel to the extended DNA vslide sliding velocity of RNA polymerase along DNA REFERENCES (1) Haugen, S. P.; Ross, W.; Gourse, R. L. Nat. Rev. Microbiol. 2008, 6, 507. (2) Larson, M. H.; Landick, R.; Block, S. M. Mol. Cell 2011, 41, 249. (3) Wang, F.; Greene, E. C. J. Mol. Biol. 2011, 412, 814. (4) Nudler, E. Cell 2012, 149, 1438. (5) Anthony, D. D.; Zeszotek, E. E.; Goldthwait, D. A. D. Proc. Natl. Acad. Sci. U. S. A. 1966, 56, 1026. (6) Chamberlin, M. J. In The Enzymes. Protein Synthesis DNA Synthesis and Repair RNA Synthesis Energy-Linked ATPases Synthetases; Boyer, P. D., Ed.; Elsevier: Amsterdam, 1974; Vol. 10, Chapter 10, p 333. (7) Nakanishi, S.; Adhya, S.; Gottesman, M.; Pastan, I. J. Biol. Chem. 1974, 249, 4050. (8) McClure, W. R. Proc. Natl. Acad. Sci. U. S. A. 1980, 77, 5634. (9) Carpousis, A. J.; Gralla, J. D. Biochemistry 1980, 19, 3245. U


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