28 pages, 16 figures (19 PostScript files). This is a small-size version with a significantly reduced quality of the figures. The original version has been submitted to Physical Review E
A versatile approach to modeling the conformations and energetics of DNA loops is presented. The model is based on the classical theory of elasticity, modified to describe the intrinsic twist and curvature of DNA, the DNA bending anisotropy, and electrostatic properties. All the model parameters are considered to be functions of the loop arclength, so that the DNA sequence-specific properties can be modeled. The model is applied to the test case study of a DNA loop clamped by the lac repressor protein. Several topologically different conformations are predicted for various lengths of the loop. The dependence of the predicted conformations on the parameters of the problem is systematically investigated. Extensions of the presented model and the scope of the model's applicability, including multi-scale simulations of protein-DNA complexes and building all-atom structures on the basis of the model, are discussed.
Many proteins interact with and deform double-stranded DNA in cells. Single-molecule experiments have studied the elasticity of DNA with helix-deforming proteins, including proteins that bend DNA. These experiments increase the need for theories of DNA elasticity which include helix-deforming proteins. Previous theoretical work on bent DNA has examined a long DNA molecule with many nonspecifically binding proteins. However, recent experiments used relatively short DNA molecules with a single, well-defined bend site. Here we develop a simple theoretical description of the effect of a single ben…
A unified model is constructed to study the recently observed DNA entropic elasticity, cooperative extensibility, and supercoiling property. With the introduction of a new structural parameter (the folding angle $ϕ$), bending deformations of sugar-phosphate backbones, steric effects of nucleotide basepairs, and short-range basestacking interactions are considered. The comprehensive agreement of theoretical results with experimental observations on both torsionally relaxed and negatively supercoiled DNAs strongly indicates that, basestacking interactions, although short-ranged in nature, domina…
The binding of proteins onto DNA contributes to the shaping and packaging of genome as well as to the expression of specific genetic messages. With a view to understanding the interplay between the presence of proteins and the deformation of DNA involved in such processes, we developed a new method to minimize the elastic energy of DNA fragments at the mesoscale level. Our method makes it possible to obtain the optimal pathways of protein-decorated DNA molecules for which the terminal base pairs are spatially constrained. We focus in this work on the deformations induced by selected architectu…
Allosteric interactions in DNA are crucial for various biological processes. These interactions are quantified by measuring the change in free energy as a function of the distance between the binding sites for two ligands. Here we show that trends in the interaction energy of ligands binding to DNA can be explained within an elastic birod model. The birod model accounts for the deformation of each strand as well as the change in stacking energy due to perturbations in position and orientation of the bases caused by the binding of ligands. The strain fields produced by the ligands decay with di…
Polymer architecture plays critical roles in both bulk rheological properties and microscale macromolecular dynamics in entangled polymer solutions and composites. Ring polymers, in particular, have been the topic of much debate due to the inability of the celebrated reptation model to capture their observed dynamics. Macrorheology and differential dynamic microscopy (DDM) are powerful methods to determine entangled polymer dynamics across scales, yet they typically require different samples under different conditions, preventing direct coupling of bulk rheological properties to the underlying…
DNA nanotubes are tubular structures composed of DNA crossover molecules. We present a bottom up approach for construction and characterization of these structures. Various possible topologies of nanotubes are constructed such as 6-helix, 8-helix and tri-tubes with different sequences and lengths. We have used fully atomistic molecular dynamics simulations to study the structure, stability and elasticity of these structures. Several nanosecond long MD simulations give the microscopic details about DNA nanotubes. Based on the structural analysis of simulation data, we show that 6-helix nanotube…
We use optical tweezers to perform stretching experiments on DNA molecules when interacting with the drugs daunomycin and ethidium bromide, which intercalate the DNA molecule. These experiments are performed in the low-force regime from zero up to 2 pN. Our results show that the persistence length of the DNA-drug complexes increases strongly as the drug concentration increases up to some critical value. Above this critical value, the persistence length decreases abruptly and remains practically constant for larger drug concentrations. The contour length of the molecules increases monotonically…
Several recent experiments suggest that sharply bent DNA has a surprisingly high bending flexibility, but the cause of this flexibility is poorly understood. Although excitation of flexible defects can explain these results, whether such excitation can occur with the level of DNA bending in these experiments remains unclear. Intriguingly, the DNA contained preexisting nicks in most of these experiments but whether nicks might play a role in flexibility has never been considered in the interpretation of experimental results. Here, using full-atom molecular dynamics simulations, we show that nic…
Negatively charged DNA can be compacted by positively charged dendrimers and the degree of compaction is a delicate balance between the strength of the electrostatic interaction and the elasticity of DNA. We report various elastic properties of short double stranded DNA (dsDNA) and the effect of dendrimer binding using fully atomistic molecular dynamics and numerical simulations. In equilibrium at room temperature, the contour length distribution P(L) and end-to-end distance distribution P(R) are nearly Gaussian, the former gives an estimate of the stretch modulus γ_1 of dsDNA in quantitative …
For an understanding of DNA elasticity at high mechanical loads (F > 30 pN), its helical nature needs to be taken into account, in the form of coupling between the twist and stretch degrees of freedom. The prevailing model for DNA elasticity, the worm-like chain, was previously extended to include this twist-stretch coupling, giving rise to the twistable worm-like chain. Motivated by DNA's charged nature, and the known effects of ionic charges on the molecule's persistence length and stretch modulus, we explored the impact of buffer ionic conditions on twist-stretch coupling. After developing …
Single-molecule experiments in which force is applied to DNA or RNA molecules have enabled important discoveries of nucleic acid properties and nucleic acid-enzyme interactions. These experiments rely on a model of the polymer force-extension behavior to calibrate the experiments; typically the experiments use the worm-like chain (WLC) theory for double-stranded DNA and RNA. This theory agrees well with experiments for long molecules. Recent single-molecule experiments have used shorter molecules, with contour lengths in the range of 1-10 persistence lengths. Most WLC theory calculations to da…
We present an atomistic model of pillared DNA nanotubes (DNTs) and their elastic properties which will facilitate further studies of these nanotubes in several important nanotechnological and biological applications. In particular, we introduce a computational design to create an atomistic model of a 6-helix DNT (6HB) along with its two variants, 6HB flanked symmetrically by two double helical DNA pillars (6HB+2) and 6HB flanked symmetrically by three double helical DNA pillars (6HB+3). Analysis of 200 ns all-atom simulation trajectories in the presence of explicit water and ions shows that th…
Storage and retrieval of the genetic information in cells is a dynamic process that requires the DNA to undergo dramatic structural rearrangements. DNA looping is a prominent example of such a structural rearrangement that is essential for transcriptional regulation in both prokaryotes and eukaryotes, and the speed of such regulations affects the fitness of individuals. Here, we examine the in vitro looping dynamics of the classic Lac repressor gene-regulatory motif. We show that both loop association and loop dissociation at the DNA-repressor junctions depend on the elastic deformation of the…
Complex DNA topological structures, including polymer loops, are frequently observed in biological processes when protein molecules simultaneously bind to several distant sites on DNA. However, the molecular mechanisms of formation of these systems remain not well understood. Existing theoretical studies focus only on specific interactions between protein and DNA molecules at target sequences. However, the electrostatic origin of primary protein-DNA interactions suggests that interactions of proteins with all DNA segments should be considered. Here we theoretically investigate the role of non-…
The elastic properties of the double-stranded DNA handles used in optical tweezers experiments on biomolecules are customarily modeled by an extensible worm-like chain model. Fitting such model to experimental data however is no trivial task, as the function depends on four parameters in a highly non-linear fashion. We hereby propose a method to bypass the fitting procedure and obtain an empirical force vs. extension curve that accurately reproduce the elasticity of the handles.
Base pair mismatch can relieve mechanical stress in highly strained DNA molecules, but how it affects their kinetic stability is not known. Using single-molecule Fluorescence Resonance Energy Transfer (FRET), we measured the lifetimes of tightly bent DNA loops with and without base pair mismatch. Surprisingly, for loops captured by stackable sticky ends, the mismatch decreased the loop lifetime despite reducing the overall bending stress, and the decrease was largest when the mismatch was placed at the DNA midpoint. These findings show that base pair mismatch transfers bending stress to the op…
It is well known that the structural deformations (stressed states) of DNA molecule play a crucial role in its biological functions including gene expression. For instance, looping in DNA (often mediated by protein binding) is a crucial step in many gene regulatory mechanisms. We use the mechanical rod model of DNA molecules to simulate its structural interactions with proteins (enzymes) during gene expression. Our rod model can simulate the nonlinear dynamics of loop and supercoil formation in DNA on long length scales. The formulation accounts for the structural stiffness of the DNA strand, …
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.
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…
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…
Many fundamental biological processes are regulated by protein-DNA complexes called {\it synaptosomes}, which possess multiple interaction sites. Despite the critical importance of synaptosomes, the mechanisms of their formation remain not well understood. Because of the multi-site nature of participating proteins, it is widely believed that their search for specific sites on DNA involves the formation and breaking of DNA loops and sliding in the looped configurations. In reality, DNA in live cells is densely covered by other biological molecules that might interfere with the formation of syna…
In living cells, proteins combine 3D bulk diffusion and 1D sliding along the DNA to reach a target faster. This process is known as facilitated diffusion, and we investigate its dynamics in the physiologically relevant case of confined DNA. The confining geometry and DNA elasticity are key parameters: we find that facilitated diffusion is most efficient inside an isotropic volume, and on a flexible polymer. By considering the typical copy numbers of proteins in vivo, we show that the speedup due to sliding becomes insensitive to fine tuning of parameters, rendering facilitated diffusion a robu…
The bacterial genome is organized in a structure called the nucleoid by a variety of associated proteins. These proteins can form complexes on DNA that play a central role in various biological processes, including chromosome segregation. A prominent example is the large ParB-DNA complex, which forms an essential component of the segregation machinery in many bacteria. ChIP-Seq experiments show that ParB proteins localize around centromere-like parS sites on the DNA to which ParB binds specifically, and spreads from there over large sections of the chromosome. Recent theoretical and experiment…
DNA in sperm cells must undergo an extreme compaction to almost crystalline packing levels. To produce this dense packing, DNA is condensed by protamine, a positively charged protein that loops the DNA into a toroid. Our goal is to determine the pathway and mechanism for toroid formation. We first imaged short-length (L=217-1023 nm) DNA molecules in 0-5.0 $μ$M protamine using an atomic force microscope (AFM). At low protamine concentrations (0.2-0.6 $μ$M), molecules dramatically condensed, folding into a flower structure. Dynamic folding measurements of the DNA using a tethered particle motion…
The in vivo free energy of looping double-stranded DNA by the lac repressor has a remarkable behavior whose origins are not fully understood. In addition to the intrinsic periodicity of the DNA double helix, the in vivo free energy has an oscillatory component of about half the helical period and oscillates asymmetrically with an amplitude significantly smaller than predicted by current theories. Here, we show that the in vivo behavior is accurately accounted for by the simultaneous presence of two distinct conformations of looped DNA. Our analysis reveals that these two conformations have dif…
A simple model of DNA based on two interacting polymers has been used to study the unzipping of a double stranded DNA subjected to a periodic force. We propose a dynamical transition, where without changing the physiological condition, it is possible to bring DNA from the zipped/unzipped state to a new dynamic (hysteretic) state by varying the frequency of the applied force. Our studies reveal that the area of the hystersis loop grows with the same exponents as of the isotropic spin systems. These exponents are amenable to verification in the force spectroscopic experiments.
DNA loop formation is one of several mechanisms used by organisms to regulate genes. The free energy of forming a loop is an important factor in determining whether the associated gene is switched on or off. In this paper we use an elastic rod model of DNA to determine the free energy of forming short (50--100 basepair), protein mediated DNA loops. Superhelical stress in the DNA of living cells is a critical factor determining the energetics of loop formation, and we explicitly account for it in our calculations. The repressor protein itself is regarded as a rigid coupler; its geometry enters …
Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. This paper presents calculations of a lattice-gas model of charge inversion for the adsorption of charged dimers on DNA. Each adsorption site is assumed to have either a vacancy or a positively-charged dimer attached with the dimer oriented either parallel or perpendicular to the double helix DNA chain. The entropy and charge distributions of these three species are calculated including the lowest order fluctuation corrections to mean-field theory. We find that the in…
The free energy of looping DNA by proteins and protein complexes determines to what extent distal DNA sites can affect each other. We inferred its in vivo value through a combined computational-experimental approach for different lengths of the loop and found that, in addition to the intrinsic periodicity of the DNA double helix, the free energy has an oscillatory component with about half the helical period. Moreover, the oscillations have such an amplitude that the effects of regulatory molecules become strongly dependent on their precise DNA positioning and yet easily tunable by their coope…
Loop formation in long molecules occurs many places in nature, from solutions of carbon nanotubes to polymers inside a cell. In this article, we review theoretical studies of the static and dynamic properties of polymer loops. For example, long polymers must search many configurations to find a "target" binding site, while short polymers are stiff and resist bending. In between, there is an optimal loop size, which balances the entropy of long loops against the energetic cost of short loops. We show that such simple pictures of loop formation can explain several long-standing observations in D…
The short supercoiled circular DNA molecules are shown to be glassy systems and canonical Metropolis Monte Carlo simulations of the systems tend to get stuck in local metastable energy basins. A novel Monte Carlo algorithm is developed to alleviate the problem of ``ergodicity breaking'' of the glassy systems, in which the Markov process is driven by an explicitly analytic weight factor with enhanced probability in both low- and high-energy regions. To characterize the degree of puckering of the supercoiled DNA loops, a new quantity of aplanarity is introduced as the shortest principal axis of …
We introduce a three-state model for a single DNA chain under tension that distinguishes between B-DNA, S-DNA and M (molten or denatured) segments and at the same time correctly accounts for the entropy of molten loops, characterized by the exponent c in the asymptotic expression S ~ - c ln n for the entropy of a loop of length n. Force extension curves are derived exactly employing a generalized Poland-Scheraga approach and compared to experimental data. Simultaneous fitting to force-extension data at room temperature and to the denaturation phase transition at zero force is possible and allo…
All known life forms are based upon a hierarchy of interwoven feedback loops, operating over a cascade of space, time and energy scales. Among the most basic loops are those connecting DNA and proteins. For example, in genetic networks, DNA genes are expressed as proteins, which may bind near the same genes and thereby control their own expression. In this molecular type of self-reference, information is mapped from the DNA sequence to the protein and back to DNA. There is a variety of dynamic DNA-protein self-reference loops, and the purpose of this remark is to discuss certain geometrical an…
Using Monte Carlo simulations, we study the hysteresis in unzipping of a double stranded DNA whose ends are subjected to a time dependent periodic force with frequency ($ω$) and amplitude ($G$). For the static force, i.e., $ω\to 0$, the DNA is in equilibrium with no hysteresis. On increasing $ω$, the area of the hysteresis loop initially increases and becomes maximum at frequency $ω^{*}(G)$, which depends on the force amplitude $G$. If the frequency is further increased, we find that for lower amplitudes the loop area decreases monotonically to zero, but for higher amplitudes it has an oscilla…
Molecular transport of biomolecules plays a pivotal role in the machinery of life. Yet, this role is poorly understood due the lack of quantitative information. Here, the role and properties of the C-terminal region of Escherichia coli Hfq is reported, involved in controlling the flow of a DNA solution. A combination of experimental methodologies has been used to probe the interaction of Hfq with DNA and to measure the rheological properties of the complex. A physical gel with a temperature reversible elasticity modulus is formed due to formation of non-covalent crosslinks. The mechanical resp…
In this work we present a computational study of the Kinetoplast genome, modelled as a large number of semiflexible unknotted loops, which are allowed to link with each other. As the DNA density increases, the systems shows a percolation transition between a gas of unlinked rings and a network of linked loops which spans the whole system. Close to the percolation transition, we find that the mean valency of the network, i.e. the average number of loops which are linked to any one loop, is around 3 as found experimentally for the Kinetoplast DNA. Even more importantly, by simulating the digesti…
Dynamics of a single stranded DNA, which can form a hairpin have been studied in the constant force ensemble. Using Langevin dynamics simulations, we obtained the force-temperature diagram, which differs from the theoretical prediction based on the lattice model. Probability analysis of the extreme bases of the stem revealed that at high temperature, the hairpin to coil transition is entropy dominated and the loop contributes significantly in its opening. However, at low temperature, the transition is force driven and the hairpin opens from the stem side. It is shown that the elastic energy pl…
Many structures inside the cell such as nucleosomes and protein-mediated DNA loops contain sharply bent double-stranded (ds) DNA. Therefore, the energetics of strong dsDNA bending constitutes an essential part of cellular thermodynamics. Although the thermomechanical behavior of long dsDNA is well described by the worm-like chain (WLC) model, the length limit of such elastic behavior remains controversial. To investigate the energetics of strong dsDNA bending, we measured the opening rate of small dsDNA loops with contour lengths of 40-200 bp using Fluorescence Resonance Energy Transfer (FRET)…
The thermodynamical stability of DNA minicircles is investigated by means of path integral techniques. Hydrogen bonds between base pairs on complementary strands can be broken by thermal fluctuations and temporary fluctuational openings along the double helix are essential to biological functions such as transcription and replication of the genetic information. Helix unwinding and bubble formation patterns are computed in circular sequences with variable radius in order to analyze the interplay between molecule size and appearance of helical disruptions. The latter are found in minicircles wit…
The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double stranded helix, released by a loop denaturation, is absorbed by \emph{supercoils}. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent $c$. However the first order transition displayed by the PS model for $c>2$ in linear DNA is replaced by a continuous transition with arbitrarily high order as $c$ approaches 2…
We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer models; alternative calculations performed using the freely rotating chain and the discrete Kratky-Porod models are reported. Stem formation is modeled according to the Peyrard-Bishop-Dauxois Hamiltonian. The kinetics of opening and closing is described in terms of a diffusion-controlled motion in an effective free energy landscape. Melting profiles, dependence …
The strong bending of polymers is poorly understood. We propose a general quantitative framework of polymer bending that includes both the weak and strong bending regimes on the same footing, based on a single general physical principle. As the bending deformation increases beyond a certain (polymer-specific) point, the change in the convexity properties of the effective bending energy of the polymer makes the harmonic deformation energetically unfavorable: in this strong bending regime the energy of the polymer varies linearly with the average bending angle as the system follows the convex hu…
We study the dynamics of DNA hairpin formation using oxDNA, a nucleotide-level coarse-grained model of DNA. In particular, we explore the effects of the loop stacking interactions and non-native base pairing on the hairpin closing times. We find a non-monotonic variation of the hairpin closing time with temperature, in agreement with the experimental work of Wallace et al. [Proc. Nat. Acad. Sci. USA 2001, 98, 5584-5589]. The hairpin closing process involves the formation of an initial nucleus of one or two bonds between the stems followed by a rapid zippering of the stem. At high temperatures,…
Loop extrusion convincingly describes how certain Structural Maintenance of Chromosome (SMC) proteins mediate the formation of large DNA loops. Yet, most of the existing computational models cannot reconcile recent in vitro observations showing that condensins can traverse each other, bypass large roadblocks and perform steps longer than its own size. To fill this gap, we propose a three-dimensional (3D) "trans-grabbing" model for loop extrusion which not only reproduces the experimental features of loop extrusion by one SMC complex, but also predicts the formation of so-called "Z-loops" via t…
Advances in DNA nanotechnology have stimulated the search for simple motifs that can be used to control the properties of DNA nanostructures. One such motif, which has been used extensively in structures such as polyhedral cages, two-dimensional arrays, and ribbons, is a bulged duplex, that is two helical segments that connect at a bulge loop. We use a coarse-grained model of DNA to characterize such bulged duplexes. We find that this motif can adopt structures belonging to two main classes: one where the stacking of the helices at the center of the system is preserved, the geometry is roughly…
From a nanoscience perspective, cellular processes and their reduced in vitro imitations provide extraordinary examples for highly robust few or single molecule reaction pathways. A prime example are biochemical reactions involving DNA molecules, and the coupling of these reactions to the physical conformations of DNA. In this review, we summarise recent results on the following phenomena: We investigate the biophysical properties of DNA-looping and the equilibrium configurations of DNA-knots, whose relevance to biological processes are increasingly appreciated. We discuss how random DNA-loopi…
The success of DNA nanotechnology has been driven by the discovery of novel structural motifs with a wide range of shapes and uses. We present a comprehensive study of the T-motif, a 3-armed, planar, right-angled junction that has been used in the self-assembly of DNA polyhedra and periodic structures. The motif is formed through the interaction of a bulge loop in one duplex and a sticky end of another. The polarity of the sticky end has significant consequences for the thermodynamic and geometrical properties of the T-motif: different polarities create junctions spanning different grooves of …
We present Brownian dynamics simulations of the facilitated diffusion of a protein, modelled as a sphere with a binding site on its surface, along DNA, modelled as a semi-flexible polymer. We consider both the effect of DNA organisation in 3D, and of sequence heterogeneity. We find that in a network of DNA loops, as are thought to be present in bacterial DNA, the search process is very sensitive to the spatial location of the target within such loops. Therefore, specific genes might be repressed or promoted by changing the local topology of the genome. On the other hand, sequence heterogeneity…
A model of self-avoiding walk with suitable constraints on self-attraction is developed to describe the conformational behavior of a short RNA or a single stranded DNA molecule that forms hairpin structure and calculate the properties associated with coil-hairpin transition by enumerating all possible conformations of a chain of N monomers in two and three dimensions. The first and last five monomers of the chain have been allowed to pair and form the stem of the hairpin structure while the remaining monomers can form a loop. The coil-hairpin transition is found to be first order with large en…
The bacterial transcription factor LacI loops DNA by binding to two separate locations on the DNA simultaneously. Despite being one of the best-studied model systems for transcriptional regulation, the number and conformations of loop structures accessible to LacI remain unclear, though the importance of multiple co-existing loops has been implicated in interactions between LacI and other cellular regulators of gene expression. To probe this issue, we have developed a new analysis method for tethered particle motion, a versatile and commonly-used in vitro single-molecule technique. Our method,…
Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low temperature / low force compact (folded) structure and a high temperature / high force molten (unfolded) structure. The influence of c on phas…
