A dynamic model for transcription elongation and sequence-dependent short pauses by RNA polymerase

TEMPLATE-DIRECTED BIOPOLYMERIZATION: TAPE-COPYING TURING MACHINES

DNA, RNA and proteins are among the most important macromolecules in a living cell. These molecules are polymerized by molecular machines. These natural nano-machines polymerize such macromolecules, adding one monomer at a time, using another linear polymer as the corresponding template. The machine utilizes input chemical energy to move along the template which also serves as a track for the movements of the machine. In the Alan Turing year 2012, it is worth pointing out that these machines are "tape-copying Turing machines". We review the operational mechanisms of the polymerizer machines and their collective behavior from the perspective of statistical physics, emphasizing their common features in spite of the crucial differences in their biological functions. We also draw the attention of the physics community to another class of modular machines that carry out a different type of template-directed polymerization. We hope this review will inspire new kinetic models for these modular machines.

A dynamic model for processive transcription elongation and backtracking long pauses by multisubunit RNA polymerases

RNA polymerases are enzymes that transcribe genes from DNA onto strands of RNA. The transcription elongation by multisubunit RNA polymerases is processive but nonuniform: one enzyme can translocate along the DNA template for thousands of nucleotide addition steps but, sometimes, it can enter backtracking long pauses. Here, we present a Brownian ratchet model for the processive transcription elongation and the backtracking long pauses, which is developed based on the available structural and biochemical studies. Using the model, we analytically study the dynamics of the transcription elongation, such as the effects of external force and NTP concentration on the transcription velocity free of pauses, and the dynamics of backtracking long pauses, such as the probabilities of entering and returning from the backtracking pauses, with the analytical results in good agreement with the available single molecule experimental data. Values of several parameters for both Escherichia coli and Saccharomyces cerevisiae RNA polymerases such as their affinities for the DNA/RNA substrate during transcription elongation are determined. Moreover, some testable predictions are presented.

Development of a "modular" scheme to describe the kinetics of transcript elongation by RNA polymerase

Transcript elongation by RNA polymerase involves the sequential appearance of several alternative and off-pathway states of the transcript elongation complex (TEC), and this complicates modeling of the kinetics of the transcription elongation process. Based on solutions of the chemical master equation for such transcription systems as a function of time, we here develop a modular scheme for simulating such kinetic transcription data. This scheme deals explicitly with the problem of TEC desynchronization as transcript synthesis proceeds, and develops kinetic modules to permit the various alternative states of the TECs (paused states, backtracked states, arrested states, and terminated states) to be introduced one-by-one as needed. In this way, we can set up a comprehensive kinetic model of appropriate complexity to fit the known transcriptional properties of any given DNA template and set of experimental conditions, including regulatory cofactors. In the companion article, this modular scheme is successfully used to model kinetic transcription elongation data obtained by bulk-gel electrophoresis quenching procedures and real-time surface plasmon resonance methods from a template of known sequence that contains defined pause, stall, and termination sites.

Modeling translocation dynamics of strand displacement DNA synthesis by DNA polymerase I

A model is presented for the translocation dynamics of the strand displacement DNA synthesis by DNA polymerases such as polymerase I family. (i) The model gives an explanation to the experimental results which showed that the rate of strand displacement DNA synthesis is nearly consistent with that of single stranded primer extension synthesis, although the two are expected to have substantial differences in their energetics. (ii) During strand displacement DNA synthesis, the pausing at the specific sequence is considered to be due to an affinity of the fingers subdomain for the specific sequence of dsDNA downstream of the single strand. The theoretical results on the sequence-dependent pausing dynamics such as the mean pausing lifetimes and the distribution of the pausing lifetime are consistent with the experimental data. Moreover, predicted results are presented for the binding affinity of the fingers subdomain for the specific sequence of dsDNA and the dependence of the mean sequence-dependent pausing lifetime on the external force acting on the polymerase.

The Influence of Look-Ahead on the Error Rate of Transcription

In this paper we study the error rate of RNA synthesis in the look-ahead model for the random walk of RNA polymerase along DNA during transcription. The model's central assumption is the existence of a window of activity in which ribonucleoside triphosphates (rNTPs) bind reversibly to the template DNA strand before being hydrolyzed and linked covalently to the nascent RNA chain. An unknown, but important, integer parameter of this model is the window size w. Here, we use mathematical analysis and computer simulation to study the rate at which transcriptional errors occur as a function of w. We find dramatic reduction in the error rate of transcription as w increases, especially for small values of w. The error reduction method provided by look-ahead occurs before hydrolysis and covalent linkage of rNTP to the nascent RNA chain, and is therefore distinct from error correction mechanisms that have previously been considered.

Molecular motors that digest their track to rectify Brownian motion: processive movement of exonuclease enzymes

A general model is presented for the processive movement of molecular motors such as λ-exonuclease, RecJ and exonuclease I that use digestion of a DNA track to rectify Brownian motion along this track. Using this model, the translocation dynamics of these molecular motors is studied. The sequence-dependent pausing of λ-exonuclease, which results from a site-specific high affinity DNA interaction, is also studied. The theoretical results are consistent with available experimental data. Moreover, the model is used to predict the lifetime distribution and force dependence of these paused states.

A possible mechanism of processive nucleotide and repeat additions by the telomerase

Telomerase is a specialized cellular ribonucleoprotein complex that can synthesize long stretches of a DNA primer by using an intrinsic RNA template sequence. This requires that the telomerase must be able to carry out both nucleotide and repeat additions. Here, based on available structures and experimental data, a model is presented to describe these two addition activities. In the model, the forward movement of the polymerase active site along the template during the processive nucleotide addition is rectified through the incorporation of a matched base, via the Brownian ratchet mechanism. The unpairing of the DNA:RNA hybrid and then repositioning of product 3'-end after each round of repeat synthesis, which are prerequisites for the processive repeat addition, are caused by a force acting on the primer. The force results from the conformational transition of the stem III pseudoknot, which is mechanically induced by the rotation of TERT fingers together with stem IV loop towards the polymerase active site upon a nucleotide binding. Based on the model, the dynamics of processive nucleotide and repeat additions by recombinant Tetrahymena telomerase is studied analytically, which gives good quantitative explanations to the previous experimental results. Moreover, some predicted results are presented. In particular, it is shown that the repeat addition processivity is mainly determined by the difference between the free-energy change required to disrupt the DNA:RNA hybrid and that required to unfold the stem III pseudoknot. A large difference in free energy corresponds to a low repeat addition processivity while a small difference in free energy corresponds to a high repeat addition processivity.