Torque-induced deformations of charged elastic DNA rods: thin helices,loops, and precursors of DNA supercoiling

We study the deformations of charged elastic rods under applied end forces and torques. For neutral filaments, we analyze the energetics of initial helical deformations and loop formation. We supplement this elastic approach with electrostatic energies of bent filaments and find critical conditions for buckling depending on the ionic strength of the solution. We also study force-induced loop opening, for parameters relevant for DNA. Finally, some applications of this nano-mechanical DNA model to salt-dependent onset of the DNA supercoiling are discussed.     

Optical measurement of mechanical forces inside short DNA loops

Knowledge of the mechanical properties of double-stranded DNA (dsDNA) is essential to understand the role of dsDNA looping in gene regulation and the mechanochemistry of molecular machines that operate on dsDNA. Here, we use a newly developed tool, force sensors with optical readout, to measure the forces inside short, strained loops composed of both dsDNA and single-stranded DNA. By varying the length of the loops and their proportion of dsDNA, it was possible to vary their internal forces from 1 pN to >20 pN. Surprisingly, internal loop forces changed erratically as the amount of dsDNA was increased for a given loop length, with the effect most notable in the smallest loop (57 nucleotides). Monte Carlo simulations based on the helical wormlike chain model accurately predict internal forces when more than half of the loop is dsDNA but fail otherwise. Mismatches engineered into the double-stranded regions increased flexibility, suggesting that Watson-Crick basepaired dsDNA can withstand high compressive forces without recourse to multibase melts. Fluorescence correlation spectroscopy further excluded transient melting (microsecond to millisecond duration) as a mechanism for relief of compressive forces in the tested dsDNAs. DNA loops with integrated force sensors may allow the comprehensive mapping of the elasticity of short dsDNAs as a function of both sequence and salt.     

Lac Repressor Mediated DNA Looping: Monte Carlo Simulation of Constrained DNA Molecules Complemented with Current Experimental Results

Tethered particle motion (TPM) experiments can be used to detect time-resolved loop formation in a single DNA molecule by measuring changes in the length of a DNA tether. Interpretation of such experiments is greatly aided by computer simulations of DNA looping which allow one to analyze the structure of the looped DNA and estimate DNA-protein binding constants specific for the loop formation process. We here present a new Monte Carlo scheme for accurate simulation of DNA configurations subject to geometric constraints and apply this method to Lac repressor mediated DNA looping, comparing the simulation results with new experimental data obtained by the TPM technique. Our simulations, taking into account the details of attachment of DNA ends and fluctuations of the looped subsegment of the DNA, reveal the origin of the double-peaked distribution of RMS values observed by TPM experiments by showing that the average RMS value for anti-parallel loop types is smaller than that of parallel loop types. The simulations also reveal that the looping probabilities for the anti-parallel loop types are significantly higher than those of the parallel loop types, even for loops of length 600 and 900 base pairs, and that the correct proportion between the heights of the peaks in the distribution can only be attained when loops with flexible Lac repressor conformation are taken into account. Comparison of the in silico and in vitro results yields estimates for the dissociation constants characterizing the binding affinity between O1 and Oid DNA operators and the dimeric arms of the Lac repressor.     

Coarse-grained modeling reveals the impact of supercoiling and loop length in DNA looping kinetics

Measurements of protein-mediated DNA looping reveal that in vivo conditions favor the formation of loops shorter than those that occur in vitro, yet the precise physical mechanisms underlying this shift remain unclear. To understand the extent to which in vivo supercoiling may explain these shifts, we develop a theoretical model based on coarse-grained molecular simulation and analytical transition state theory, enabling us to map out looping energetics and kinetics as a function of two key biophysical parameters: superhelical density and loop length. We show that loops on the scale of a persistence length respond to supercoiling over a much wider range of superhelical densities and to a larger extent than longer loops. This effect arises from a tendency for loops to be centered on the plectonemic end region, which bends progressively more tightly with superhelical density. This trend reveals a mechanism by which supercoiling favors shorter loop lengths. In addition, our model predicts a complex kinetic response to supercoiling for a given loop length, governed by a competition between an enhanced rate of looping due to torsional buckling and a reduction in looping rate due to chain straightening as the plectoneme tightens at higher superhelical densities. Together, these effects lead to a flattening of the kinetic response to supercoiling within the physiological range for all but the shortest loops. Using experimental estimates for in vivo superhelical densities, we discuss our model’s ability to explain available looping data, highlighting both the importance of supercoiling as a regulatory force in genetics and the additional complexities of looping phenomena in vivo.     

The influence of salt on the structure and energetics of supercoiled DNA.

We present a detailed computational study of the influence of salt on the configurations, energies, and dynamics of supercoiled DNA. A potential function that includes both elastic and electrostatic energy components is employed. Specifically, the electrostatic term, with salt-dependent coefficients, is modeled after Stigter's pioneering work on the effective diameter of DNA as a function of salt concentration. Because an effective charge per unit length is used, the electrostatic formulation does not require explicit modeling of phosphates and can be used to study long DNAs at any desired resolution of charge. With explicit consideration of the electrostatic energy, an elastic bending constant corresponding to the nonelectrostatic part of the bending contribution to the persistence length is used. We show, for a series of salt concentrations ranging from 0.005 to 1.0 M sodium, how configurations and energies of supercoiled DNA (1000 and 3000 base pairs) change dramatically with the simulated salt environment. At high salt, the DNA adopts highly compact and bent interwound states, with the bending energy dominating over the other components, and the electrostatic energy playing a minor role in comparison to the bending and twisting terms. At low salt, the DNA supercoils are much more open and loosely interwound, and the electrostatic components are dominant. Over the range of three decades of salt examined, the electrostatic energy changes by a factor of 10. The buckling transition between the circle and figure-8 is highly sensitive to salt concentration: this transition is delayed as salt concentration decreases, with a particularly sharp increase below 0.1 M. For example, for a bending-to-twisting force constant ratio of A/C = 1.5, the linking number difference (delta LK) corresponding to equal energies for the circle and figure-8 increases from 2.1 to 3.25 as salt decreases from 1.0 to 0.005 M. We also present in detail a family of three-lobed supercoiled DNA configurations that are predicted by elasticity theory to be stable at low delta Lk. To our knowledge, such three-dimensional structures have not been previously presented in connection with DNA supercoiling. These branched forms have a higher bending energy than the corresponding interwound configurations at the same delta Lk but, especially at low salt, this bending energy difference is relatively small in comparison with the total energy, which is dominated by the electrostatic contributions. Significantly, the electrostatic energies of the three-lobed and (straight) interwound forms are comparable at each salt environment.(ABSTRACT TRUNCATED AT 400 WORDS)     

Roles of DNA looping in enhancer-blocking activity

Enhancer-promoter interactions in eukaryotic genomes are often controlled by sequence elements that block the actions of enhancers. Although the experimental evidence suggests that those sequence elements contribute to forming loops of chromatin, the molecular mechanism of how such looping affects the enhancer-blocking activity is still largely unknown. In this article, the roles of DNA looping in enhancer blocking are investigated by numerically simulating the DNA conformation of a prototypical model system of gene regulation. The simulated results show that the enhancer function is indeed blocked when the enhancer is looped out so that it is separated from the promoter, which explains experimental observations of gene expression in the model system. The local structural distortion of DNA caused by looping is important for blocking, so the ability of looping to block enhancers can be lost when the loop length is much larger than the persistence length of the chain.     

Electrostatic effects in short superhelical DNA

We present Monte Carlo simulations of the equilibrium configurations of short closed circular DNA that obeys a combined elastic, hard-sphere, and electrostatic energy potential. We employ a B-spline representation to model chain configuration and simulate the effects of salt on chain folding by varying the Debye screening parameter. We obtain global equilibrium configurations of closed circular DNA, with several imposed linking number differences, at two salt concentrations (specifically at the extremes of no added salt and the high salt regime), and for different chain lengths. Minimization of the composite elastic/long-range potential energy under the constraints of ring closure and fixed chain length is found to produce structures that are consistent with the configurations of short supercoiled DNA observed experimentally. The structures generated under the constraints of an electrostatic potential are less compact than those subjected only to an elastic term and a hard-sphere constraint. For a fixed linking number difference greater than a critical value, the interwound structures obtained under the condition of high salt are more compact than those obtained under the condition of no added salt. In the case of no added salt, the electrostatic energy plays a dominant role over the elastic energy in dictating the shape of the closed circular DNA. The DNA supercoil opens up with increasing chain length at low salt concentration. A branched three-leaf rose structure with a fixed linking number difference is higher in energy than the interwound form at both salt concentrations employed here.     

Gal repressosome contains an antiparallel DNA loop

Gal repressosome assembly and repression of the gal operon in Escherichia coli occurs when two dimeric GalR proteins and the histone-like HU protein bind to cognate sites causing DNA looping. Structure-based genetic analysis defined the GalR surfaces interacting to form a stacked, V-shaped, tetrameric structure. Stereochemical models of the four possible DNA loops compatible with the GalR tetramer configuration were constructed using the sequence-dependent structural parameters of the interoperator DNA and conformation changes caused by GalR and asymmetric HU binding. Evaluation of their DNA elastic energies gave unambiguous preference to a loop structure in which the two gal operators adopt an antiparallel orientation causing undertwisting of DNA.     

Wrapping of flanking non-operator DNA in lac repressor-operator complexes: implications for DNA looping

In our studies of lac repressor tetramer (T)-lac operator (O) interactions, we observed that the presence of extended regions of non-operator DNA flanking a single lac operator sequence embedded in plasmid DNA produced large and unusual cooperative and anticooperative effects on binding constants (Kobs) and their salt concentration dependences for the formation of 1:1 (TO) and especially 1:2 (TO2) complexes. To explore the origin of this striking behavior we report and analyze binding data on 1:1 (TO) and 1:2 (TO2) complexes between repressor and a single O(sym) operator embedded in 40 bp, 101 bp, and 2514 bp DNA, over very wide ranges of [salt]. We find large interrelated effects of flanking DNA length and [salt] on binding constants (K(TO)obs, K(TO2)obs) and on their [salt]-derivatives, and quantify these effects in terms of the free energy contributions of two wrapping modes, designated local and global. Both local and global wrapping of flanking DNA occur to an increasing extent as [salt] decreases. Global wrapping of plasmid-length DNA is extraordinarily dependent on [salt]. We propose that global wrapping is driven at low salt concentration by the polyelectrolyte effect, and involves a very large number (>/similar 20) of coulombic interactions between DNA phosphates and positively charged groups on lac repressor. Coulombic interactions in the global wrap must involve both the core and the second DNA-binding domain of lac repressor, and result in a complex which is looped by DNA wrapping. The non-coulombic contribution to the free energy of global wrapping is highly unfavorable ( approximately +30-50 kcal mol(-1)), which presumably results from a significant extent of DNA distortion and/or entropic constraints. We propose a structural model for global wrapping, and consider its implications for looping of intervening non-operator DNA in forming a complex between a tetrameric repressor (LacI) and one multi-operator DNA molecule in vivo and in vitro. The existence of DNA wrapping in LacI-DNA interactions motivates the proposal that most if not all DNA binding proteins may have evolved the capability to wrap and thereby organize flanking regions of DNA.     

Gene repression by minimal lac loops in vivo

The inflexibility of double-stranded DNA with respect to bending and twisting is well established in vitro. Understanding apparent DNA physical properties in vivo is a greater challenge. Here, we exploit repression looping with components of the Escherichia coli lac operon to monitor DNA flexibility in living cells. We create a minimal system for testing the shortest possible DNA repression loops that contain an E. coli promoter, and compare the results to prior experiments. Our data reveal that loop-independent repression occurs for certain tight operator/promoter spacings. When only loop-dependent repression is considered, fits to a thermodynamic model show that DNA twisting limits looping in vivo, although the apparent DNA twist flexibility is 2- to 4-fold higher than in vitro. In contrast, length-dependent resistance to DNA bending is not observed in these experiments, even for the shortest loops constraining <0.4 persistence lengths of DNA. As observed previously for other looping configurations, loss of the nucleoid protein heat unstable (HU) markedly disables DNA looping in vivo. Length-independent DNA bending energy may reflect the activities of architectural proteins and the structure of the DNA topological domain. We suggest that the shortest loops are formed in apical loops rather than along the DNA plectonemic superhelix.     

Effects of nucleoid proteins on DNA repression loop formation in Escherichia coli

The intrinsic stiffness of DNA limits its ability to be bent and twisted over short lengths, but such deformations are required for gene regulation. One classic paradigm is DNA looping in the regulation of the Escherichia coli lac operon. Lac repressor protein binds simultaneously to two operator sequences flanking the lac promoter. Analysis of the length dependence of looping-dependent repression of the lac operon provides insight into DNA deformation energetics within cells. The apparent flexibility of DNA is greater in vivo than in vitro, possibly because of host proteins that bind DNA and induce sites of flexure. Here we test DNA looping in bacterial strains lacking the nucleoid proteins HU, IHF or H-NS. We confirm that deletion of HU inhibits looping and that quantitative modeling suggests residual looping in the induced operon. Deletion of IHF has little effect. Remarkably, DNA looping is strongly enhanced in the absence of H-NS, and an explanatory model is proposed. Chloroquine titration, psoralen crosslinking and supercoiling-sensitive reporter assays show that the effects of nucleoid proteins on looping are not correlated with their effects on either total or unrestrained supercoiling. These results suggest that host nucleoid proteins can directly facilitate or inhibit DNA looping in bacteria.     

Geometry of mediating protein affects the probability of loop formation in DNA

Recent single molecule experiments have determined the probability of loop formation in DNA as a function of the DNA contour length for different types of looping proteins. The optimal contour length for loop formation as well as the probability density functions have been found to be strongly dependent on the type of looping protein used. We show, using Monte Carlo simulations and analytical calculations, that these observations can be replicated using the wormlike-chain model for double-stranded DNA if we account for the nonzero size of the looping protein. The simulations have been performed in two dimensions so that bending is the only mode of deformation available to the DNA while the geometry of the looping protein enters through a single variable which is representative of its size. We observe two important effects that seem to directly depend on the size of the enzyme: 1), the overall propensity of loop formation at any given value of the DNA contour length increases with the size of the enzyme; and 2), the contour length corresponding to the first peak as well as the first well in the probability density functions increases with the size of the enzyme. Additionally, the eigenmodes of the fluctuating shape of the looped DNA calculated from simulations and theory are in excellent agreement, and reveal that most of the fluctuations in the DNA occur in regions of low curvature.     

Real-time observation of DNA looping dynamics of Type IIE restriction enzymes NaeI and NarI

Many restriction enzymes require binding of two copies of a recognition sequence for DNA cleavage, thereby introducing a loop in the DNA. We investigated looping dynamics of Type IIE restriction enzymes NaeI and NarI by tracking the Brownian motion of single tethered DNA molecules. DNA containing two endonuclease recognition sites spaced a few 100 bp apart connect small polystyrene beads to a glass surface. The position of a bead is tracked through video microscopy. Protein-mediated looping and unlooping is then observed as a sudden specific change in Brownian motion of the bead. With this method we are able to directly follow DNA looping kinetics of single protein–DNA complexes to obtain loop stability and loop formation times. We show that, in the absence of divalent cations, NaeI induces DNA loops of specific size. In contrast, under these conditions NarI mainly creates non-specific loops, resulting in effective DNA compaction for higher enzyme concentrations. Addition of Ca²⁺ increases the NaeI-DNA loop lifetime by two orders of magnitude and stimulates specific binding by NarI. Finally, for both enzymes we observe exponentially distributed loop formation times, indicating that looping is dominated by (re)binding the second recognition site.     

Do Femtonewton Forces Affect Genetic Function? A Review

Protein-Mediated DNA looping is intricately related to gene expression. Therefore any mechanical constraint that disrupts loop formation can play a significant role in gene regulation. Polymer physics models predict that less than a piconewton of force may be sufficient to prevent the formation of DNA loops. Thus, it appears that tension can act as a molecular switch that controls the much larger forces associated with the processive motion of RNA polymerase. Since RNAP can exert forces over 20 pN before it stalls, a ‘substrate tension switch’ could offer a force advantage of two orders of magnitude. Evidence for such a mechanism is seen in recent in vitro micromanipulation experiments. In this article we provide new perspective on existing theory and experimental data on DNA looping in vitro and in vivo. We elaborate on the connection between tension and a variety of other intracellular mechanical constraints including sequence specific curvature and supercoiling. In the process, we emphasize that the richness and versatility of DNA mechanics opens up a whole new paradigm of gene regulation to explore.