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）
In the DNA-RNA polymerase complex, RNA polymerase (RNAP) selectively incorporates ribonucleoside triphosphates according to the base information encoded in DNA, elongates the RNA strand, and progresses along the template. The state of the template DNA therefore conditions RNAP binding and chemical transitions. Conversely, from the viewpoint of DNA, the binding state and coordinate position of RNAP condition the local structural response of DNA. As RNAP advances, upstream DNA reanneals, downstream DNA opens, the RNA-DNA hybrid constrains the local geometry, and local bending and twisting of the DNA are updated. We introduce an interface dissipation, Σint, that provides an exchange-symmetric measure of path irreversibility at the DNA-RNAP interface, independent of whether DNA or RNAP is assigned the role of observer or observed. Irreversibility is quantified by the path-space Kullback-Leibler (KL) divergence between the forward path measure and its time-reversed counterpart, from which the dissipation of the joint system and those of the marginal systems are defined. The non-negativity of the interface dissipation derived in this work does not rely on RNAP-specific kinetic assumptions; rather, it holds for general path processes for which the relevant KL divergences and conditional path measures are well defined. RNAP transcription is treated as a biophysical application of this general theorem to the DNA-RNAP interface.
We show that non-steric molecular interactions between RNA polymerase (RNAP) motors that move simultaneously on the same DNA track determine strongly the kinetics of transcription elongation. With a focus on the role of collisions and cooperation, we introduce a stochastic model that allows for the exact analytical computation of the stationary properties of transcription elongation as a function of RNAP density, their interaction strength, nucleoside triphosphate concentration, and rate of pyrophosphate release. Cooperative pushing, i.e., an enhancement of the average RNAP velocity and elonga…
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…
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…
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…
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…
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 kineti…
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.
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…
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 …
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…
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…
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…
The homochirality of the molecules of life has been a vexing problem with no generally accepted solution to date. Since a racemic mixture of chiral nucleotides frustrates the extension and replication of RNA and DNA, understanding the origin of homochirality has important implications to the investigation of the origin of life. Here we suggest a novel solution to the homochirality problem based on a recently proposed thermodynamic dissipation theory for the origin of life. Homochirality is suggested to have been incorporated gradually into the emerging life as a result of asymmetric right- ove…
The presence of low dimensional chaos in the protein secondary structures, using the binary coded $α$-helices and $β$-sheet motifs, has been investigated. In order to analyse symbolic DNA/RNA sequences the assignment, based on the purine/pyrimidine and strong/wea k H - bond classification sheme, of binary numbers to the nucleotides was made. We have found that this assignment leads to different averaged fractal dimensions for $α$-helices and $β$-sheets. When embedded in the two dimensional phase space the binary string structures show the attractor type behavior which depends on the value of t…
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…
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Although RNAs play many cellular functions little is known about the dynamics and thermodynamics of these molecules. In principle, all-atom molecular dynamics simulations can investigate these issues, but with current computer facilities, these simulations have been limited to small RNAs and to short times. HiRe-RNA, a recently proposed high-resolution coarse-grained for RNA that captures many geometric details such as base pairing and stacking, is able to fold RNA molecules to near-native structures in a short computational time. So far it had been applied to simple hairpins, and here we pres…
DNA and RNA are generally regarded as central molecules in molecular biology. Recent advancements in the field of DNA/RNA nanotechnology successfully used DNA/RNA as programmable molecules to construct molecular machines and nanostructures with predefined shapes and functions. The key mechanism for dynamic control of the conformations of these DNA/RNA nanodevices is a reaction called strand displacement, in which one strand in a formed duplex is replaced by a third invading strand. While DNA/RNA strand displacement has mainly been used to de-novo design molecular devices, we argue in this revi…
We introduce a probabilistic model for protein sliding motion along DNA during the search of a target sequence. The model accounts for possible effects due to sequence-dependent interaction between the nonspecific DNA and the protein. As an example, we focus on T7 RNA-polymerase and exploit the available information about its interaction at the promoter site in order to investigate the influence of bacteriophage T7 DNA sequence on the dynamics of the sliding process. Hydrogen bonds in the major groove are used as the main sequence-dependent interaction between RNA-polymerase and DNA. The resul…
Recent experiments showed that multiple copies of the molecular machine RNA polymerase (RNAP) can efficiently synthesize mRNA collectively in the active state of the promoter. However, environmentally-induced promoter repression results in long-distance antagonistic interactions that drastically reduce the speed of RNAPs and cause a quick arrest of mRNA synthesis. The mechanism underlying this transition between cooperative and antagonistic dynamics remains poorly understood. In this Letter, we introduce a continuum deterministic model for the translocation of RNAPs, where the speed of an RNAP…
The structural flexibility of nucleic acids plays a key role in many fundamental life processes, such as gene replication and expression, DNA-protein recognition, and gene regulation. To obtain a thorough understanding of nucleic acid flexibility, extensive studies have been performed using various experimental methods and theoretical models. In this review, we will introduce the progress that has been made in understanding the flexibility of nucleic acids including DNAs and RNAs, and will emphasize the experimental findings and the effects of salt, temperature, and sequence. Finally, we will …
The volume occupied by unconstrained bacterial DNA in physiological solutions exceeds 1000 times the volume of the cell. Still, it is confined to a well defined region of the cell called the nucleoid, which occupies only a fraction of the cell volume. There is still no general agreement on the mechanism leading to the compaction of the DNA and the formation of the nucleoid. However, advances in in vivo sub-wavelength resolution microscopy techniques have recently allowed the observation of the nucleoid at an unprecedented level of detail. In particular, these observations show that the compact…
We study unzipping of a complementary RNA-DNA helix applied to an external force, focusing on the force-force correlations. While at the microscopic level these are given by the sequence, the experiment measures effective, macroscopic correlations. The latter are sequence-independent, i.e. universal, and constitute the central object of the underlying field theory of disordered systems. Comparing field-theory predictions and the exact solution of a 1-d toy model with the experiment, we find an excellent agreement, confirming fundamental theoretical concepts via a biologically inspired experime…
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…
Ion-mediated interaction is critical to the structure and stability of nucleic acids. Recent experiments suggest that the multivalent ion-induced aggregation of double-stranded (ds) RNAs and DNAs may strongly depend on the topological nature of helices, while there is still lack of an understanding on the relevant ion-mediated interactions at atomistic level. In this work, we have directly calculated the potentials of mean force (PMF) between two dsRNAs and between two dsDNAs in Cobalt Hexammine ion (Co-Hex) solutions by the atomistic molecular dynamics simulations. Our calculations show that …
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…
On the basis of first-principles GW calculations, we study the quasiparticle properties of the guanine, adenine, cytosine, thymine, and uracil DNA and RNA nucleobases. Beyond standard G0W0 calculations, starting from Kohn-Sham eigenstates obtained with (semi)local functionals, a simple self-consistency on the eigenvalues allows to obtain vertical ionization energies and electron affinities within an average 0.11 eV and 0.18 eV error respectively as compared to state-of-the-art coupled-cluster and multi-configurational perturbative quantum chemistry approaches. Further, GW calculations predict …
In this study, we compare the charge transport properties of multiple (double stranded) dsRNA sequences with corresponding dsDNA sequences. Recent studies have presented a contradictory picture of relative charge transport efficiencies in A-form DNA:RNA hybrids and dsDNA. Using a multiscale modelling framework, we compute conductance of dsDNA and dsRNA using Landauer formalism in coherent limit and Marcus-Hush theory in the incoherent limit. We find that dsDNA conducts better than dsRNA in both the charge transport regimes. Our analysis shows that the structural differences in the twist angle …
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…
{\it Transcription} is the process whereby RNA molecules are polymerized by molecular machines, called RNA polymerase (RNAP), using the corresponding DNA as the template. Recent {\it in-vivo} experiments with single cells have established that transcription takes place in "bursts" or "pulses". In this letter we present a model that captures not only the mechano-chemistry of individual RNAPs and their steric interactions but also the switching of the gene between the ON and OFF states. This model accounts for the statistical properties of the transcriptional bursts. It also shows how the quanti…
By resorting to the thick-chain model we discuss how the stretching response of a polymer is influenced by the self-avoidance entailed by its finite thickness. The characterization of the force versus extension curve for a thick chain is carried out through extensive stochastic simulations. The computational results are captured by an analytic expression that is used to fit experimental stretching measurements carried out on DNA and single-stranded RNA (poly-U) in various solutions. This strategy allows us to infer the apparent diameter of two biologically-relevant polyelectrolytes, namely DNA…
The emerging field of hybrid DNA - protein nanotechnology brings with it the potential for many novel materials which combine the addressability of DNA nanotechnology with versatility of protein interactions. However, the design and computational study of these hybrid structures is difficult due to the system sizes involved. To aid in the design and in silico analysis process, we introduce here a coarse-grained DNA/RNA-protein model that extends the oxDNA/oxRNA models of DNA/RNA with a coarse-grained model of proteins based on an anisotropic network model representation. Fully equipped with an…
The ongoing effort to detect and characterize physical entanglement in biopolymers has so far established that knots are present in many globular proteins and also abound in viral DNA packaged inside bacteriophages. RNA molecules, on the other hand, have not yet been systematically screened for the occurrence of physical knots. We have accordingly undertaken the systematic profiling of the ~6,000 RNA structures present in the protein data bank. The search identified no more than three deeply-knotted RNA molecules. These are ribosomal RNAs solved by cryo-em and consist of about 3,000 nucleotide…
RNA polymerase (RNAP) is molecular machine that polymerizes a RNA molecule, a linear heteropolymer, using a single stranded DNA (ssDNA) as the corresponding template; the sequence of monomers of the RNA is dictated by that of monomers on the ssDNA template. While polymerizing a RNA, the RNAP walks step-by-step on the ssDNA template in a specific direction. Thus, a RNAP can be regarded also as a molecular motor and the sites of start and stop of its walk on the DNA mark the two ends of the genetic message that it transcribes into RNA. Interference of transcription of two overlapping genes is be…
Several important biological processes are initiated by the binding of a protein to a specific site on the DNA. The strategy adopted by a protein, called transcription factor (TF), for searching its specific binding site on the DNA has been investigated over several decades. In recent times the effects obstacles, like DNA-binding proteins, on the search by TF has begun to receive attention. RNA polymerase (RNAP) motors collectively move along a segment of the DNA during a genomic process called transcription. This RNAP traffic is bound to affect the diffusive scanning of the same segment of th…
Transcription of the genetic message encoded chemically in the sequence of the DNA template is carried out by a molecular machine called RNA polymerase (RNAP). Backward or forward slippage of the nascent RNA with respect to the DNA template strand give rise to a transcript that is, respectively, longer or shorter than the corresponding template. We model a RNAP as a "Tape-copying Turing machine" (TCTM) where the DNA template is the input tape while the nascent RNA strand is the output tape. Although the TCTM always steps forward the process is assumed to be stochastic that has a probability of…
High-density oligonucleotide arrays are among the most rapidly expanding technologies in biology today. In the {\sl GeneChip} system, the reconstruction of the target concentration depends upon the differential signal generated from hybridizing the target RNA to two nearly identical templates: a perfect match (PM) and a single mismatch (MM) probe. It has been observed that a large fraction of MM probes repeatably bind targets better than the PMs, against the usual expectation from sequence-specific hybridization; this is difficult to interpret in terms of the underlying physics. We examine thi…
