The high fidelity of DNA polymerase is critical for the faithful replication of genomic DNA. Several approaches were proposed to quantify the fidelity of DNA polymerase. Direct measurements of the error frequency of the replication products definitely give the true fidelity but turn out very hard to implement. Two biochemical kinetic approaches, the steady-state assay and the transient-state assay, were then suggested and widely adopted. In these assays, the error frequency is indirectly estimated by using the steady-state or the transient-state kinetic theory combined with the measured kinetic rates. However, whether these indirectly estimated fidelities are equivalent to the true fidelity has never been clarified theoretically, and in particular there are different strategies to quantify the proofreading efficiency of DNAP but often lead to inconsistent results. The reason for all these confusions is that it's mathematically challenging to formulate a rigorous and general theory of the true fidelity. Recently we have succeeded to establish such a theoretical framework. In this paper, we develop this theory to make a comprehensive examination on the theoretical foundation of the kinetic assays and the relation between fidelities obtained by different methods. We conclude that while the steady-state assay and the transient-state assay can always measure the true fidelity of exonuclease-deficient DNA polymerases, they only do so for exonuclease-efficient DNA polymerases conditionally (the proper way to use these assays to quantify the proofreading efficiency is also suggested). We thus propose a new kinetic approach, the single-molecule assay, which indirectly but precisely characterizes the true fidelity of either exonuclease-deficient or exonuclease-efficient DNA polymerases.
Kinetic theory and thermodynamics are applied to DNA polymerases with exonuclease activity, taking into account the dependence of the rates on the previously incorportated nucleotide. The replication fidelity is shown to increase significantly thanks to this dependence at the basis of the mechanism of exonuclease proofreading. In particular, this dependence can provide up to a hundred-fold lowering of the error probability under physiological conditions. Theory is compared with numerical simulations for the DNA polymerases of T7 viruses and human mitochondria.
A kinetic theory is developed for exonuclease-deficient DNA polymerases, based on the experimental observation that the rates depend not only on the newly incorporated nucleotide, but also on the previous one, leading to the growth of Markovian DNA sequences from a Bernoullian template. The dependences on nucleotide concentrations and template sequence are explicitly taken into account. In this framework, the kinetic and thermodynamic properties of DNA replication, in particular, the mean growth velocity, the error probability, and the entropy production in terms of the rate constants and the …
A DNA polymerase (DNAP) replicates a template DNA strand. It also exploits the template as the track for its own motor-like mechanical movement. In the polymerase mode it elongates the nascent DNA by one nucleotide in each step. But, whenever it commits an error by misincorporating an incorrect nucleotide, it can switch to an exonuclease mode. In the latter mode it excises the wrong nucleotide before switching back to its polymerase mode. We develop a stochastic kinetic model of DNA replication that mimics an {\it in-vitro} experiment where a single-stranded DNA, subjected to a mechanical tens…
Exchange-Symmetric Dissipation at the DNA-RNA Polymerase Interface
Graduate School of Science, Tohoku University（东北大学大学院理学研究科）；Department of Drug Discovery Medicine, Graduate School of Medicine, Kyoto University（京都大学大学院医学研究科药物发现医学系）
We present a method for controlled connection of gold electrodes with dsDNA molecules (locally on a chip) by utilizing polymerase to elongate single-stranded DNA primers attached to the electrodes. Thiol-modified oligonucleotides are directed and immobilized to nanoscale electrodes by means of dielectrophoretic trapping, and extended in a procedure mimicking PCR, finally forming a complete dsDNA molecule bridging the gap between the electrodes. The technique opens up opportunities for building from the bottom-up, for detection and sensing applications, and also for molecular electronics.
RNA polymerase (RNAP) is a mobile molecular workshop that polymerizes a RNA molecule by adding monomeric subunits one by one, while moving step by step on the DNA template itself. Here we develop a theoretical model by incorporating the steric interactions of the RNAPs and their mechanochemical cycles which explicitly captures the cyclical shape changes of each motor. Using this model, we explain not only the dependence of the average velocity of a RNAP on the externally applied load force, but also predict a {\it nonmotonic} variation of the average velocity on external torque. We also show t…
We give unambiguous theoretical analyses and show that the exclusive biochemical reaction involved in a single nucleotide insertion into the DNA primer can be efficiently tracked using the renormalized van der Waals (vdW) interaction of a stronger type, the Hermansson blue-shifting hydrogen bond effect, and the Arunan composite hydrogen-vdW bond. We find that there are two biochemical steps involved to complete the insertion of a single base (cytosine) into the 3$'$ end of a DNA primer. First, the O3$'$ (from a DNA primer) initiates the nucleophilic attack on P$_α$ (from an incoming dCTP), in …
Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally-inactive backtracked state is determined by a kinetic competition between 1D diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-pass…
RNA polymerase (RNAP) is an enzyme that synthesizes a messenger RNA (mRNA) strand which is complementary to a single-stranded DNA template. From the perspective of physicists, an RNAP is a molecular motor that utilizes chemical energy input to move along the track formed by a ssDNA. In some circumstances, which are described in this paper, a large number of RNAPs move simultaneously along the same track. We refer to such collective movements of the RNAPs as RNAP traffic because of the similarities between the collective dynamics of the RNAPs on ssDNA track and that of vehicles in highway traff…
RNA polymerase (RNAP) is an enzyme that synthesizes a messenger RNA (mRNA) strand which is complementary to a single-stranded DNA template. From the perspective of physicists, an RNAP is a molecular motor that utilizes chemical energy input to move along the track formed by a DNA. In many circumstances, which are described in this paper, a large number of RNAPs move simultaneously along the same track; we refer to such collective movements of the RNAPs as RNAP traffic. Here we develop a theoretical model for RNAP traffic by incorporating the steric interactions between RNAPs as well as the mec…
To mitigate errors induced by the cell's heterogeneous noisy environment, its main information channels and production networks utilize the kinetic proofreading (KPR) mechanism. Here, we examine two extensively-studied KPR circuits, DNA replication by the T7 DNA polymerase and translation by the E. coli ribosome. Using experimental data, we analyze the performance of these two vital systems in light of the fundamental bounds set by the recently-discovered thermodynamic uncertainty relation (TUR), which places an inherent trade-off between the precision of a desirable output and the amount of e…
DNA polymerase (DNAP) is a dual-purpose enzyme that plays two opposite roles in two different situations during DNA replication. It plays its normal role as a {\it polymerase} catalyzing the elongation of a new DNA molecule by adding a monomer. However, it can switch to the role of an {\it exonuclease} and shorten the same DNA by cleavage of the last incorporated monomer from the nascent DNA. Just as misincorporated nucleotides can escape exonuclease causing replication error, correct nucleotide may get sacrificed unnecessarily by erroneous cleavage. The interplay of polymerase and exonuclease…
We introduce a two-species exclusion model to describe the key features of the conflict between the RNA polymerase (RNAP) motor traffic, engaged in the transcription of a segment of DNA, concomitant with the progress of two DNA replication forks on the same DNA segment. One of the species of particles ($P$) represents RNAP motors while the other ($R$) represents replication forks. Motivated by the biological phenomena that this model is intended to capture, a maximum of only two $R$ particles are allowed to enter the lattice from two opposite ends whereas the unrestricted number of $P$ particl…
Polymerization of RNA from a template DNA is carried out by a molecular machine called RNA polymerase (RNAP). It also uses the template as a track on which it moves as a motor utilizing chemical energy input. The time it spends at each successive monomer of DNA is random; we derive the exact distribution of these "dwell times" in our model. The inverse of the mean dwell time satisfies a Michaelis-Menten-like equation and is also consistent with a general formula derived earlier by Fisher and Kolomeisky for molecular motors with unbranched mechano-chemical cycles. Often many RNAP motors move si…
We develope a theoretical framework, based on exclusion process, that is motivated by a biological phenomenon called transcript slippage (TS). In this model a discrete lattice represents a DNA strand while each of the particles that hop on it unidirectionally, from site to site, represents a RNA polymerase (RNAP). While walking like a molecular motor along a DNA track in a step-by-step manner, a RNAP simultaneously synthesizes a RNA chain; in each forward step it elongates the nascent RNA molecule by one unit, using the DNA track also as the template. At some special "slippery" position on the…
DNA dependent RNA polymerase core subunits abb' conserved residues at frequencies most closely matched with codons at stage 10.4-11.1 in code evolution. An excess of acidic residues (stage 2 additions) lowered this estimate, but not by more than 2.3 stages. With 1 tryptophan (stage 14 addition) in 529 conserved residues, abb' significantly under-represented this amino acid, consistent with a cut-off in its residue profile before completion of the genetic code. Residue profiles in FEN-1 homologs and DNA topoisomerase I-5' placed their origin at stage 11-13. Prokaryote septation protein, FtsZ, a…
Monitoring the kinetics and conformational dynamics of single enzymes is crucial in order to better understand their biological functions as these motions and structural dynamics are usually unsynchronized among the molecules. Detecting the enzyme-reactant interactions and associated conformational changes of the enzyme on a single molecule basis, however, remain as a challenge with established optical techniques due to the commonly required labeling of the reactants or the enzyme itself. The labeling process is usually non-trivial and the labels themselves might skew the physical properties o…
Information has an entropic character which can be analyzed within the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is performed sufficiently slowly. Structural and recent single-molecule assays have provided dynamic details of polymerase machinery with insight into information processing. We introduce a rigorous characterization of Shannon Information in biomolecular systems and apply it to DNA replication in the limit of no dissipation. Specifically, we devise an equilibri…
The hybridization and dehybridization of DNA subject to tension is relevant to fundamental genetic processes and to the design of DNA-based mechanobiology assays. While strong tension accelerates DNA melting and decelerates DNA annealing, the effects of tension weaker than 5 pN are less clear. In this study, we developed a DNA bow assay, which uses the bending rigidity of double-stranded DNA (dsDNA) to exert weak tension on a single-stranded DNA (ssDNA) target in the range of 2 pN to 6 pN. Combining this assay with single-molecule FRET, we measured the hybridization and dehybridization kinetic…
Analyzing the physical and chemical properties of single DNA based molecular machines such as polymerases and helicases often necessitates to track stepping motion on the length scale of base pairs. Although high resolution instruments have been developed that are capable of reaching that limit, individual steps are oftentimes hidden by experimental noise which complicates data processing. Here, we present an effective two-step algorithm which detects steps in a high bandwidth signal by minimizing an energy based model (Energy based step-finder, EBS). First, an efficient convex denoising schem…
Transcription is the first step of gene expression, in which a particular segment of DNA is copied to RNA by the enzyme RNA polymerase (RNAP). Despite many details of the complex interactions between DNA and RNA synthesis disclosed experimentally, much of physical behavior of transcription remains largely unknown. Understanding torsional mechanics of DNA and RNAP together with its nascent RNA and RNA-bound proteins in transcription maybe the first step towards deciphering the mechanism of gene expression. In this study, based on the balance between viscous drag on RNA synthesis and torque resu…
DNA strand displacement, where a single-stranded nucleic acid invades a DNA duplex, is pervasive in genomic processes and DNA engineering applications. The kinetics of strand displacement have been studied in bulk; however, the kinetics of the underlying strand exchange were obfuscated by a slow bimolecular association step. Here, we use a novel single-molecule Fluorescence Resonance Energy Transfer (smFRET) approach termed the "fission" assay to obtain the full distribution of first passage times of unimolecular strand displacement. At a frame time of 4.4 ms, the first passage time distributi…
DNA condensation by multivalent cations plays a crucial role in genome packaging in viruses and sperm heads, and has been extensively studied using single-molecule experimental methods. In those experiments, the values of the critical condensation forces have been used to estimate the amplitude of the attractive DNA-DNA interactions. Here, to describe these experiments, we developed an analytical model and a rigid body Langevin dynamics assay to investigate the behavior of a polymer with self-interactions, in the presence of a traction force applied at its extremities. We model self-interactio…
