It has been speculated that bubble formation of several base-pairs due to thermal fluctuations is indicatory for biological active sites. Recent evidence, based on experiments and molecular dynamics (MD) simulations using the Peyrard-Bishop-Dauxois model, seems to point in this direction. However, sufficiently large bubbles appear only seldom which makes an accurate calculation difficult even for minimal models. In this letter, we introduce a new method that is orders of magnitude faster than MD. Using this method we show that the present evidence is unsubstantiated.
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 question of the value of the pitch angle of DNA is visited from the perspective of a geometrical analysis of transcription. It is suggested that for transcription to be possible, the pitch angle of B-DNA must be smaller than the angle of zero-twist. At the zero-twist angle the double helix is maximally rotated and its strain-twist coupling vanishes. A numerical estimate of the pitch angle for B-DNA based on differential geometry is compared with numbers obtained from existing empirical data. The crystallographic studies shows that the pitch angle is approximately 38 deg., less than the cor…
We report results showing that thermally-induced openings of double stranded DNA coincide with the location of functionally relevant sites for transcription. Investigating both viral and bacterial DNA gene promoter segments, we found that the most probable opening occurs at the transcription start site. Minor openings appear to be related to other regulatory sites. Our results suggest that coherent thermal fluctuations play an important role in the initiation of transcription. Essential elements of the dynamics, in addition to sequence specificity, are nonlinearity and entropy, provided by loc…
Zygotic genome activation (ZGA), the onset of transcription after initial quiescence, is a major developmental step in many species, which occurs after ten cell divisions in Zebrafish embryos. How transcription factor-chromatin interactions evolve during early development to support ZGA is largely unknown. We established single molecule tracking in live developing Zebrafish embryos using reflected light-sheet microscopy to visualize the general transcription factor TATA-binding protein (TBP), and developed a novel data acquisition and analysis scheme to extract kinetic information during fast …
DNA looping has been observed to enhance and suppress transcriptional noise but it is uncertain which of these two opposite effects is to be expected for given conditions. Here, we derive analytical expressions for the main quantifiers of transcriptional noise in terms of the molecular parameters and elucidate the role of DNA looping. Our results rationalize paradoxical experimental observations and provide the first quantitative explanation of landmark individual-cell measurements at the single molecule level on the classical lac operon genetic system [Choi et al., Science 322, 442-446 (2008)…
The formation of DNA loops by proteins and protein complexes that bind at distal DNA sites plays a central role in many cellular processes, such as transcription, recombination, and replication. Here we review the basic thermodynamic concepts underlying the assembly of macromolecular complexes on looped DNA and the effects that this process has in the properties of gene regulation. Beyond the traditional view of DNA looping as a mechanism to increase the affinity of regulatory molecules for their cognate sites, recent developments indicate that DNA looping can also lead to the suppression of c…
DNA looping participates in transcriptional regulation, for instance, by allowing distal binding sites to act synergistically. Here we study this process and compare different regulatory mechanisms based on repression with and without looping. Within a simple mathematical model for the lac operon, we show that regulation based on DNA looping, in addition to increasing the repression level, can reduce the fluctuations of transcription and, at the same time, decrease the sensitivity to changes in the number of regulatory proteins. Looping is thus able to circumvent some of the constraints inhere…
The Hill coefficient is often used as a direct measure of the cooperativity of binding processes. It is an essential tool for probing properties of reactions in many biochemical systems. Here we analyze existing experimental data and demonstrate that the Hill coefficient characterizing the binding of transcription factors to their cognate sites can in fact be larger than one -- the standard indication of cooperativity -- even in the absence of any standard cooperative binding mechanism. By studying the problem analytically, we demonstrate that this effect occurs due to the disordered binding e…
DNA shape readout is an important mechanism of target site recognition by transcription factors, in addition to the sequence readout. Several models of transcription factor-DNA binding which consider DNA shape have been developed in recent years. We present a new biophysical model of protein-DNA interaction by considering the DNA shape features, which is based on a neighbour dinucleotide dependency model BayesPI2. The parameters of the new model are restricted to a subspace spanned by the 2-mer DNA shape features, which allowing a biophysical interpretation of the new parameters as position-de…
Much of the complexity observed in gene regulation originates from cooperative protein-DNA binding. While studies of the target search of proteins for their specific binding sites on the DNA have revealed design principles for the quantitative characteristics of protein-DNA interactions, no such principles are known for the cooperative interactions between DNA-binding proteins. We consider a simple theoretical model for two interacting transcription factor (TF) species, searching for and binding to two adjacent target sites hidden in the genomic background. We study the kinetic competition of …
Gene regulation involves a hierarchy of events that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. The effects of DNA sequence on these processes have typically been studied based either on its quantitative connection with single-domain binding free energies or on empirical rules that combine different DNA motifs to predict gene expression trends on a genomic scale. The middle-point approach that quantitatively bridges these two extremes, however, remains largely unexplored. Here, we provide an integrated approach to accurately predict g…
We develop revised theoretical ideas on the mechanism by which the transcription factor proteins locate their specific binding sites on DNA faster than the three-dimensional (3D) diffusion controlled rate limit. We demonstrate that the 3D-diffusion controlled rate limit can be enhanced when the protein molecule reads several possible binding stretches of the template DNA via one-dimensional (1D) diffusion upon each 3D-diffusion mediated collision or nonspecific binding event. The overall enhancement of site-specific association rate is directly proportional to the maximum possible sliding leng…
We study theoretical ``design principles'' for transcription factor-DNA interaction in bacteria, focusing particularly on the statistical interaction of the transcription factors (TF's) with the genomic background (i.e., the genome without the target sites). We introduce and motivate the concept of `programmability', i.e. the ability to set the threshold concentration for TF binding over a wide range merely by mutating the binding sequence of a target site. This functional demand, together with physical constraints arising from the thermodynamics and kinetics of TF-DNA interaction, leads us to…
We investigate the distribution of bubble lifetimes and bubble lengths in DNA at physiological temperature, by performing extensive molecular dynamics simulations with the Peyrard-Bishop-Dauxois (PBD) model, as well as an extended version (ePBD) having a sequence-dependent stacking interaction, emphasizing the effect of the sequences' guanine-cytosine (GC)/adenine-thymine (AT) content on these distributions. For both models we find that base pair-dependent (GC vs AT) thresholds for considering complementary nucleotides to be separated are able to reproduce the observed dependence of the meltin…
The binding of a transcription factor (TF) to a DNA operator site can initiate or repress the expression of a gene. Computational prediction of sites recognized by a TF has traditionally relied upon knowledge of several cognate sites, rather than an ab initio approach. Here, we examine the possibility of using structure-based energy calculations that require no knowledge of bound sites but rather start with the structure of a protein-DNA complex. We study the PurR E. coli TF, and explore to which extent atomistic models of protein-DNA complexes can be used to distinguish between cognate and no…
Recent experiments show that transcription factors (TFs) indeed use the facilitated diffusion mechanism to locate their target sequences on DNA in living bacteria cells: TFs alternate between sliding motion along DNA and relocation events through the cytoplasm. From simulations and theoretical analysis we study the TF-sliding motion for a large section of the DNA-sequence of a common E. coli strain, based on the two-state TF-model with a fast-sliding search state and a recognition state enabling target detection. For the probability to detect the target before dissociating from DNA the TF-sear…
The damping effect to the DNA bubble is investigated within the Peyrard-Bishop model. In the continuum limit, the dynamics of the bubble of DNA is described by the damped nonlinear Schrodinger equation and studied by means of variational method. It is shown that the propagation of solitary wave pattern is not vanishing in a non-viscous system. Inversely, the solitary wave vanishes soon as the viscous force is introduced.
The equilibrium statistical properties of DNA denaturation bubbles are examined in detail within the framework of the Peyrard-Bishop-Dauxois model. Bubble formation in homogeneous DNA is found to depend crucially on the presence of nonlinear base-stacking interactions. Small bubbles extending over less than 10 base pairs are associated with much larger free energies of formation per site than larger bubbles. As the critical temperature is approached, the free energy associated with further bubble growth becomes vanishingly small. An analysis of average displacement profiles of bubbles of varyi…
Transcription factor proteins bind specific DNA sequences to control the expression of genes. They contain DNA binding domains which belong to several super-families, each with a specific mechanism of DNA binding. The total number of transcription factors encoded in a genome increases with the number of genes in the genome. Here, we examined the number of transcription factors from each super-family in diverse organisms. We find that the number of transcription factors from most super-families appears to be bounded. For example, the number of winged helix factors does not generally exceed 300,…
In the demanding biosensing environment, improving selection efficiency strategies has become an issue of great significance. DNA minicircles containing between 200 and 400 base-pairs, also named microDNA, are representative of the supercoiled DNA loops found in nature. Their short size makes them extremely susceptible to writhe and twist, which is known to play a central role in DNA denaturation. We investigate minicircle lengths and superhelical densities that induce DNA denaturation bubbles of nanometer size and control well-defined long-life. Mesoscopic modeling and accelerated dynamics si…
We present a general framework to study the thermodynamic denaturation of double-stranded DNA under superhelical stress. We report calculations of position- and size-dependent opening probabilities for bubbles along the sequence. Our results are obtained from transfer-matrix solutions of the Zimm-Bragg model for unconstrained DNA and of a self-consistent linearization of the Benham model for superhelical DNA. The numerical efficiency of our method allows for the analysis of entire genomes and of random sequences of corresponding length ($10^6-10^9$ base pairs). We show that, at physiological c…
Transcription factor binding to the surface of DNA regulatory regions is one of the primary causes of regulating gene expression levels. A probabilistic approach to model protein-DNA interactions at the sequence level is through Position Weight Matrices (PWMs) that estimate the joint probability of a DNA binding site sequence by assuming positional independence within the DNA sequence. Here we construct conditional PWMs that depend on the motif signatures in the flanking DNA sequence, by conditioning known binding site loci on the presence or absence of additional binding sites in the flanking…
We analyse transcriptional bursting within a stochastic non-equilibrium model which accounts for the coupling between the dynamics of DNA supercoiling and gene transcription. We find a clear signature of bursty transcription when there is a separation between the timescales of transcription initiation and supercoiling dissipation - the latter may either be diffusive or mediated by topological enzymes, such as type I or type II topoisomerases. In multigenic DNA domains we observe either bursty transcription, or transcription waves; the type of behaviour can be selected for by controlling gene a…
Understanding the inherent timescales of large bubbles in DNA is critical to a thorough comprehension of its physicochemical characteristics, as well as their potential role on helix opening and biological function. In this work we employ the coarse-grained Peyrard-Bishop-Dauxois model of DNA to study relaxation dynamics of large bubbles in homopolymer DNA, using simulations up to the microsecond time scale. By studying energy autocorrelation functions of relatively large bubbles inserted into thermalised DNA molecules, we extract characteristic relaxation times from the equilibration process …
It appears that thermally activated DNA bubbles of different sizes play central roles in important genetic processes. Here we show that the probability for the formation of such bubbles is regulated by the number of soft AT pairs in specific regions with lengths which at physiological temperatures are of the order of (but not equal to) the size of the bubble. The analysis is based on the Peyrard- Bishop-Dauxois model, whose equilibrium statistical properties have been accurately calculated here with a transfer integral approach.
We study the thermodynamic and dynamic behaviors of twist-induced denaturation bubbles in a long, stretched random sequence of DNA. The small bubbles associated with weak twist are delocalized. Above a threshold torque, the bubbles of several tens of bases or larger become preferentially localized to \AT-rich segments. In the localized regime, the bubbles exhibit ``aging'' and move around sub-diffusively with continuously varying dynamic exponents. These properties are derived using results of large-deviation theory together with scaling arguments, and are verified by Monte-Carlo simulations.
We develop a theoretical framework on the mechanism of combinatorial binding of transcription factors (TFs) with their specific binding sites on DNA. We consider three possible mechanisms viz. monomer, hetero-oligomer and coordinated recruitment pathways. In the monomer pathway, combinatorial TFs search for their targets in an independent manner and the protein-protein interactions among them will be insignificant. The protein-protein interactions are very strong so that the hetero-oligomer complex of TFs as a whole searches for the cognate sites in case of hetero-oligomer pathway. The TF whic…
We present numerical results on the temperature dependence of the distribution of bubble lengths in DNA segments of various guanine-cytosine (GC) concentrations. Base-pair openings are described by the Peyrard-Bishop-Dauxois model and the corresponding thermal equilibrium distributions of bubbles are obtained through Monte Carlo calculations for bubble sizes up to the order of a hundred base pairs. The dependence of the parameters of bubble length distribution on temperature and the GC content is investigated. We provide simple expressions which approximately describe these relations. The vari…
The local opening of DNA is an intriguing phenomenon from a statistical physics point of view, but is also essential for its biological function. For instance, the transcription and replication of our genetic code can not take place without the unwinding of the DNA double helix. Although these biological processes are driven by proteins, there might well be a relation between these biological openings and the spontaneous bubble formation due to thermal fluctuations. Mesoscopic models, like the Peyrard-Bishop-Dauxois model, have fairly accurately reproduced some experimental denaturation curves…
We propose a nonlinear model derived from first principles, to describe bubble dynamics of DNA. Our model equations include a term derived from the dissipative effect of intermolecular vibrational modes. Such modes are excited by the propagating bubble, and we term it "curvature dissipation". The equations we derive allow for stable pinned localized kinks which form the bubble. We perform the stability analysis and specify the energy requirements for the motion of the localized solutions. Our findings are consistent with properties of DNA dynamics, and can be used in models for denaturation bu…
Transcriptional activity has been shown to relate to the organization of chromosomes in the eukaryotic nucleus and in the bacterial nucleoid. In particular, highly transcribed genes, RNA polymerases and transcription factors gather into discrete spatial foci called transcription factories. However, the mechanisms underlying the formation of these foci and the resulting topological order of the chromosome remain to be elucidated. Here we consider a thermodynamic framework based on a worm-like chain model of chromosomes where sparse designated sites along the DNA are able to interact whenever th…
Biological information is not only stored in the digital chemical sequence of double helical DNA, but is also encoded in the mechanical properties of the DNA strands, which can influence biochemical processes involving its readout. For example, loop formation in the Lac operon can regulate the expression of key genes, and DNA supercoiling is closely correlated to rhythmic circardian gene expression in cyanobacteria. Supercoiling is also important for large scale organisation of the genome in both eukaryotic and prokaryotic cells. DNA can respond to torsional stress by writhing to form looped s…
We examine the binding of transcription factors to DNA in terms of an information transfer problem. The input of the noisy channel is the biophysical signal of a factor bound to a DNA site, and the output is a distribution of probable DNA sequences at this site. This task involves an inherent tradeoff between the information gain and the energetics of the binding interaction - high binding energies provide higher information gain but hinder the dynamics of the system as factors are bound too tightly. We show that adaptation of the binding interaction towards increasing information transfer und…
The base pair fluctuations and helix untwisting are examined for a circular molecule. A realistic mesoscopic model including twisting degrees of freedom and bending of the molecular axis is proposed. The computational method, based on path integral techniques, simulates a distribution of topoisomers with various twist numbers and finds the energetically most favorable molecular conformation as a function of temperature. The method can predict helical repeat, openings loci and bubble sizes for specific sequences in a broad temperature range. Some results are presented for a short DNA circle rec…
The paper uses mesoscopic, non-linear lattice dynamics based (Peyrard-Bishop-Dauxois, PBD) modeling to describe thermal properties of DNA below and near the denaturation temperature. Computationally efficient notation is introduced for the relevant statistical mechanics. Computed melting profiles of long and short heterogeneous sequences are presented, using a recently introduced reparametrization of the PBD model, and critically discussed. The statistics of extended open bubbles and bound clusters is formulated and results are presented for selected examples.
We propose a stochastic model for gene transcription coupled to DNA supercoiling, where we incorporate the experimental observation that polymerases create supercoiling as they unwind the DNA helix, and that these enzymes bind more favourably to regions where the genome is unwound. Within this model, we show that when the transcriptionally induced flux of supercoiling increases, there is a sharp crossover from a regime where torsional stresses relax quickly and gene transcription is random, to one where gene expression is highly correlated and tightly regulated by supercoiling. In the latter r…
The issue of the nucleation and slow closure mechanisms of non superhelical stress-induced denaturation bubbles in DNA is tackled using coarse-grained MetaDynamics and Brownian simulations. A minimal mesoscopic model is used where the double helix is made of two interacting bead-spring rotating strands with a prescribed torsional modulus in the duplex state. We demonstrate that timescales for the nucleation (resp. closure) of an approximately 10 base-pair bubble, in agreement with experiments, are associated with the crossing of a free-energy barrier of $22~k_{\rm B}T$ (resp. $13~k_{\rm B}T$) …
The distribution of bubble lengths in double-stranded DNA is presented for segments of varying guanine-cytosine (GC) content, obtained with Monte Carlo simulations using the Peyrard-Bishop-Dauxois model at 310 K. An analytical description of the obtained distribution in the whole regime investigated, i.e., up to bubble widths of the order of tens of nanometers, is available. We find that the decay lengths and characteristic exponents of this distribution show two distinct regimes as a function of GC content. The observed distribution is attributed to the anharmonic interactions within base pai…
Problems of search and recognition appear over different scales in biological systems. In this review we focus on the challenges posed by interactions between proteins, in particular transcription factors, and DNA and possible mechanisms which allow for a fast and selective target location. Initially we argue that DNA-binding proteins can be classified, broadly, into three distinct classes which we illustrate using experimental data. Each class calls for a different search process and we discuss the possible application of different search mechanisms proposed over the years to each class. The …
Cells receive a wide variety of cellular and environmental signals, which must be processed combinatorially to generate specific and timely genetic responses. We present here a theoretical study on the combinatorial control and integration of transcription signals, with the finding that cis-regulatory systems with specific protein-DNA interaction and glue-like protein-protein interactions, supplemented by distal activation or repression mechanisms, have the capability to execute a wide range of control functions encoded in the regulatory DNA sequences. Using a quantitative model based on the w…
Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibriums measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription fa…
A double-stranded DNA unravels thermally through intermediate denatured bubble segments. Intrinsically, fluctuations ensue at the bubble boundaries from non-equilibrium (NE) energy exchanges with the environment. However, such details gets obscured by large population kinetics at the macroscale, associating equilibrium pathway to the unravelling landscape. In this work, we capture evidence of fluctuation energetics with picoliter samples in a microfluidic cantilever. We exploit nanomechanical resonance to measure the NE energy exchanges through dissipation, revealing a crucial pre-melting tran…
DNA denaturation has long been a subject of intense study due to its relationship to DNA transcription and its fundamental importance as a nonlinear, structural transition. Many aspects of this phenomenon, however, remain poorly understood. Existing models fit quite well with experimental results on the fraction of unbound base pairs versus temperature. Yet, these same models give incorrect results for other essential quantities. For example, the predicted base pair fluctuation timescales - relevant to transcription - are orders of magnitude different from those observed experimentally. Here, …
Response time and transcription level are vital parameters of gene regulation. They depend on how fast transcription factors (TFs) find and how efficient they occupy their specific target sites. It is well known that target site search is accelerated by TF binding to and sliding along unspecific DNA and that unspecific associations alter the occupation frequency of a gene. However, whether target site search time and occupation frequency can be optimized simultaneously is mostly unclear. We developed a transparent and intuitively accessible state-based formalism to calculate search times to ta…
The identification of transcription factor binding sites (TFBSs) on genomic DNA is of crucial importance for understanding and predicting regulatory elements in gene networks. TFBS motifs are commonly described by Position Weight Matrices (PWMs), in which each DNA base pair independently contributes to the transcription factor (TF) binding, despite mounting evidence of interdependence between base pairs positions. The recent availability of genome-wide data on TF-bound DNA regions offers the possibility to revisit this question in detail for TF binding {\em in vivo}. Here, we use available fly…
Transcription factors are able to associate to their binding sites on DNA faster than the physical limit posed by diffusion. Such high association rates can be achieved by alternating between three-dimensional diffusion and one-dimensional sliding along the DNA chain, a mechanism dubbed Facilitated Diffusion. By studying a collection of transcription factor binding sites of Escherichia coli from the RegulonDB database and of Bacillus subtilis from DBTBS, we reveal a funnel in the binding energy landscape around the target sequences. We show that such a funnel is linked to the presence of gradi…
The formation of DNA loops by proteins and protein complexes is ubiquitous to many fundamental cellular processes, including transcription, recombination, and replication. Here we review recent advances in understanding the properties of DNA looping in its natural context and how they propagate to the cellular behavior through gene regulation. The results of connecting the molecular properties with cellular physiology indicate that looping of DNA in vivo is much more complex and easier than predicted from current models and reveals a wealth of previously unappreciated details.
Replication and transcription are two important processes in living systems. To execute such processes, various proteins work far away from equilibrium in a staggered way. Motivated by this, aspects of hysteresis during unzipping of DNA under a periodic drive in non-equilibrium conditions are studied. A steady state phase diagram of a driven DNA is proposed which is experimentally verifiable. As a two state system, we also compare the results of DNA with that of an Ising magnet under an asymmetrical variation of magnetic field.
In this paper, we propose a thermodynamic mechanism for the formation of transcriptional foci via the joint agglomeration of DNA-looping proteins and protein-binding domains on DNA: The competition between the gain in protein-DNA binding free energy and the entropy loss due to DNA looping is argued to result in an effective attraction between loops. A mean-field approximation can be described analytically via a mapping to a restricted random-graph ensemble having local degree constraints and global constraints on the number of connected components. It shows the emergence of protein clusters co…
