Session A21: Focus Session: Dynamics of Transcription

A double-ratchet mechanism of transcription elongation and its control

Transcription, the process by which the genetic information encoded in DNA is transferred into RNA, is the first step in gene expression and it is the step at which most regulation occurs. A detailed understanding of the structural and mechanistic aspects of each step of transcription (initiation, elongation, termination and regulation) is one of the holy grails of biology. Here we characterize the motion of RNA polymerase (RNAP), the multi-subunit molecular motor that carries out the transcription process, during the elongation stage. We argue that during elongation RNAP moves by a complex Brownian ratchet mechanism in which the translocation along DNA and the binding of nucleotides into RNAP's catalytic center are coupled to a fluctuating internal degree of freedom associated with a protein sub-unit (the F-bridge) of RNAP. More precisely, the model is defined by a set of kinetic equations$^{ }$describing the competition for the catalytic site between an incoming nucleotide, the 3'-end of RNA, and the F-bridge which in its bent conformation blocks the active center. An important aspect of the model is the incorporation of the three ``active'' processes describing (i) the ejection of bound nucleotides from the active center through steric clashes with either the F-bridge in its bent conformation or with the 3'-end of RNA; and (ii) the forward translocation induced by bending of the F-bridge pushing against the 3'-end of RNA. The ``active'' processes do not imply a ``power stroke'' mechanism since the energy driving them is purely thermal. Indeed the model displays a route by which the system uses thermal fluctuations to control the rate, processivity and fidelity of transcription already before the irreversible chemical incorporation step. Moreover, the model qualitatively explains many aspects of both bio-chemical\footnote{Bar-Nahum, G., Epshtein, V., Ruckenstein, A.E., Rafikov, R., Mustaev, A., and Nudler, E. A ratchet mechanism of transcription elongation and its control. To appear in Cell, 2005.} and kinetic\footnote{Holmes, S.F., and Erie D.A. Downstream DNA sequence effects on transcription elongation. Allosteric binding of nucleoside triphosphates facilitates translocation via a ratchet motion. J Biol Chem. $278$, 35597-35608.} experiments on transcription elongation in \textit{E-coli} and makes a number of falsifiable predictions.   

Direct imaging of LacI repressor protein sliding along DNA

LacI repressor protein was observed in 1970 to bind to its operator site 100 times faster than allowed by diffusion [1]. A facilitated diffusion model incorporating1-D sliding and 3-D diffusion of the nonspecifically bound protein has been suggested to explain this phenomenon [2]. We have imaged the nonspecific binding of GFP-LacI monomers to elongated DNA molecules using single molecule imaging techniques. Upon binding to DNA, LacI proteins were observed to either be stationary, or slide along DNA. The characteristics of the sliding motion fit that of 1-D Brownian motion (with and without drift). The 1-D diffusion constant of the sliding proteins is 104 nm2/s, and it is 104 times lower than a typical protein's 3- D diffusion constant, 108 nm2/s. The characteristic dissociation time for both the stationary and the sliding proteins is 6s, and it is 100 times longer than the known dissociation time of 0.08s. The sliding length (DNA length scanned by the protein, not counting repeatedly scanned bases) ranges from 300 bp to 3000 bp, and it is significantly higher than the calculated optimal sliding length of 100 bp. We will discuss how these abnormal parameters alter the LacI specific binding speed. [1] A. D Riggs, S. Bougeois and M Cohn, J. Mol. Biol. 53, 401- 417 (1970). [2] O. G. Berg and C. Blomberg, Biophys. Chem., 4, 367-381 (1976).   

Thermodynamic DNA Looping by a Two-Site Restriction Endonuclease Studied using Optical Tweezers

Many enzyme-DNA interactions involve multimeric protein complexes that bind at two distant sites such that the DNA is looped. An example is the type IIe restriction enzyme Sau3AI$, $which requires two recognition sites to cleave the DNA. Here we study this process at the single DNA level using force measuring optical tweezers. We characterize cleavage rates of single DNA molecules in the presence of Sau3AI as a function of enzyme concentration, incubation time, and the fractional extension of the DNA molecule. Activity is completely inhibited by tensions of a few picoNewtons. By replacing Mg$^{2+}$ with Ca$^{2+}$, the Sau3AI dimers form but do not cleave the DNA, thus trapping DNA loops. We are able to pull apart these loops, measuring the force needed and the length of DNA released for each. We also characterize the number and length distributions of these loops as a function of incubation time and DNA fractional extension. The results of these studies are discussed in the context of a Brownian dynamics model of DNA looping.   

Bubbles in DNA

DNA melting proceeds through the formation of ?bubbles?. We have developed a new ensemble method by which we can directly measure the average length of the denaturation bubble and the statistical weights of the bubble states within the transition. For a bubble flanked by double-stranded regions, we find a nucleation size of $\sim $20 bases. In contrast, for bubbles opening at the ends of the molecule there is no nucleation threshold. An analysis of the statistical weight of intermediate states versus the length of the molecule L shows that the transition becomes strictly two-state only for L$\sim $1. We further find that a single mismatch in the oligomer sequence transforms a transition with many intermediate states into a nearly two-state transition. This observation can form the basis for an improved SNP (single nucleotide polymorphism) detection assay.   

Single-molecule analysis of the full transcription cycle

By monitoring the extension of a mechanically stretched, supercoiled DNA molecule containing a single bacterial promoter, we have been able to directly observe in real time the change in DNA extension associated with topological unwinding of $\sim$1 helical turn of promoter DNA by RNAP during transcription initiation. We find that this stage of transcription initiation is extremely sensitive to the torque acting on the supercoiled DNA. Upon addition of limited sets of nucleotides, changes in the polymerase/promoter interaction which are related to the process of abortive initiation can be studied in detail. Upon addition of the full set of nucleotides, the subsequent stages of transcription -- promoter escape, productive elongation and transcription termination -- can also be observed in real-time. The changes in DNA topology which occur at each of these stages have been determined, and these results provide for the first global view of the entire transcription cycle at the resolution of single molecules. \newline \newline Co-authors: Richard H. Ebright, Chen-Yu Liu and Andrey Revyakin, HHMI \& Waksman Institute, Rutgers University.   

The effect of sequence correlation on bubble conformation in double-stranded DNA

Although DNA exists in its duplex structure stably at physiological temperature, it has been experimentally observed that DNA duplex locally denatures, allowing bubble conformation along the strand due to thermal fluctuation. Here we present a new stochastic formulation, using the Fokker-Planck and the equivalent Langevin equation for base pair distance of DNA, which are transformed from the Edwards equation that describes the base pair distance distribution with base pair index regarded as time. By simulating the Langevin equation, with a DNA sequence modelled by dichotomic random noise whose correlation decays exponentially, we study the effect of sequence correlation on the bubble size distribution for various sequence correlation lengths. For average bubble size, we obtain an exact analytical expression via the Fokker-Planck equation and discuss it in comparison with the simulation results.   

Observing dynamics of chromatin fibers in Xenopus egg extracts by single DNA manipulation using a transverse magnetic tweezer setup

We have studied assembly of chromatin on single DNAs using Xenopus egg extracts and a specially designed magnetic tweezer setup which generates controlled force in the focal plane of the objective, allowing us to visualize and measure DNA extension under a wide range of constant tensions. We found, in the absence of ATP, interphase extracts assembled nucleosomes against DNA tensions of up to 3.5 piconewtons (pN). We observed force-induced disassembly and opening-closing fluctuations indicating our experiments were in mechano-chemical equilibrium. We found that the ATP-depleted reaction can do mechanical work of 27 kcal/mol per nucleosome, providing a measurement of the free energy difference between core histone octamers on and off DNA. Addition of ATP leads to highly dynamic behavior: time courses show processive runs of assembly and disassembly of not observed in the -ATP case, with forces of 2 pN leading to nearly complete fiber disassembly. Our study shows that ATP hydrolysis plays a major role in nucleosome rearrangement and removal, and suggests that chromatin in vivo may be subject to continual assembly and disassembly.   

Electrostatics in Biomolecular Interactions: a Surface Charge Method

Biomolecular interactions determine how transcription factors recognize their DNA binding sites, how proteins interact with each other, and consequently how a biological system functions. Since both proteins and DNAs are significantly charged, electrostatic interactions are among the most important when studying biomolecular interactions. Although the fundamental equations for electrostatics are known, the solution in low symmetry situations with a high dielectric constant solvent (e.g. water) can be difficult to obtain in an appropriate form and with an acceptable degree of accuracy and amount of computation. In order to compute the electrostatic force, each atom is usually modeled as a dielectric sphere with a point charge at its center. Even the case of two spheres is non-trivial. The energetic calculations of such a system are still very crude and lack systematic control of accuracy. To establish a scheme where accuracy of the computation can be controlled systematically, we have established a new formulation where the surface charge distribution is used as a new variable. The surface charge has the advantage of reducing the number of degrees of freedom (from 3D to 2D), can accommodate the presence of ions, and is applicable to arbitrary geometrical shapes. The Poisson-Boltzmann equation is currently the most popular approach in dealing with ionic effects. This approach, unfortunately, suffers from several drawbacks. In this talk, I will describe these drawbacks in slightly more detail, and describe possible methods to circumvent these problems. The solution for general geometrical shapes can be obtained numerically by choosing a tiling of the surface and solving a corresponding set of linear algebraic equations (the finite-element method). These equations can be efficiently solved numerically for use in molecular dynamics simulations.   

On geometric measures of regulatory complexity

Transcriptional regulation of a gene in a network can be characterized by a vector that counts the numbers of binding sites in the gene's promoter region where a protein product of every other gene can bind. We analyze the distribution of such vectors in the full S. cerevisiae genome and notice that they form an interesting low dimensional structure. This is significant for analyses that attempt to integrate expression and sequence information for the reconstruction of transcriptional networks since, in this case, one should be able to use similarity of promoter regions and expression profiles as effective aids.