Twist-stretch Coupling Research Articles

An effective model of DNA like helicoidal structure: with length fluctuation nonlinearity

One of the natural helicoidal nanostructure, which thermomechanical features are studied carefully with the help of different mechanical models, is a DNA cell / molecule. Our study proves that the experimentally determined nonlinear fluctuations of the molecular length of DNA can be better understood by modeling the molecule as a helicoidal pretwisted nanostrip sensor with nonlinear function. The calculations presented here are in good agreement with the experimental data within 10%. Other used by many researchers mechanical models such as an elastic rod, wormlike chain (WLC), accordion bellows, or an elastic core wrapped with rigid wires do not show the possible variance nonlinearity of thermomechanical DNA molecular length fluctuations. We have found that the nonlinear variance of the length fluctuations is an intrinsic property of the micro-nano-sensors with helicoidal shape. This model allows us to estimate the persistence length and twist-stretch coupling of a DNA molecule as well. It also shows the molecule's overwinding possibility at initial stretching with correct numerical representation.

Identification of Phase Transition and Twist-Stretch Coupling During DNA Supercoiling

As a single DNA molecule is supercoiled under tension, the onset of a phase transition is most definitively revealed by a torque plateau. However, in the absence of direct torque detection, a change in the observed extension has often been used to identify the onset of a phase transition. Here by directly measuring torque using an angular optical trap, we show that an extension maximum, which has previously been assumed to be indicative of the onset of a phase transition from a B to sc-P-form DNA, in fact does not coincide with the onset of a torque plateau at a phase transition.

Twist–stretch coupling and phase transition during DNA supercoiling

As a single DNA molecule is positively supercoiled under constant tension, its extension initially increases due to a negative twist-stretch coupling. The subsequent attainment of an extension maximum has previously been assumed to be indicative of the onset of a phase transition from B- to scP-DNA. Here we show that an extension maximum in fact does not coincide with the onset of a phase transition. This transition is evidenced by a direct observation of a torque plateau using an angular optical trap. Instead we find that the shape of the extension curve can be well explained with a theory that incorporates both DNA twist-stretch coupling and bending fluctuations. This theory also provides a more accurate method of determining the value of the twist-stretch coupling modulus, which has possibly been underestimated in previous studies that did not take into consideration the bending fluctuations. Our study demonstrates the importance of torque detection in the correct identification of phase transitions as well as the contribution of the twist-stretch coupling and bending fluctuations to DNA extension.

Twist-stretch correlation of DNA

We present an elastic model for B-form DNA with variable radius to study the elastic twist-stretch coupling of stretched DNA. In this model, only two strain variables as well as the changes in the energy of the hydrogen and covalent bonds of DNA during the deformation are considered. It is found that, depending on the elastic constants, the correlation between twisting and stretching of a helical molecule can be positive or negative. It is shown that for the suitable elastic constants in the model, the twist-stretch coupling of DNA behaves nonmonotonically, and contrary to intuition, the DNA twisting and stretching are positively correlated for small distortions. This result is entirely consistent with recent experimental results.

Strain-dependent twist–stretch elasticity in chiral filaments

Coupling between axial and torsional degrees of freedom often modifies the conformation and expression of natural and synthetic filamentous aggregates. Recent studies on chiral single-walled carbon nanotubes and B-DNA reveal a reversal in the sign of the twist-stretch coupling at large strains. The similarity in the response in these two distinct supramolecular assemblies and at high strains suggests a fundamental, chirality-dependent nonlinear elastic behaviour. Here we seek the link between the microscopic origin of the nonlinearities and the effective twist-stretch coupling using energy-based theoretical frameworks and model simulations. Our analysis reveals a sensitive interplay between the deformation energetics and the sign of the coupling, highlighting robust design principles that determine both the sign and extent of these couplings. These design principles have already been exploited by nature to dynamically engineer such couplings, and have broad implications in mechanically coupled actuation, propulsion and transport in biology and technology.

From rigid base pairs to semiflexible polymers: Coarse-graining DNA

The elasticity of double-helical DNA on a nm length scale is captured in detail by the rigid base-pair model, whose conformation variables are the relative positions and orientations of adjacent base pairs. Corresponding sequence-dependent elastic potentials have been obtained from all-atom MD simulation and from high-resolution structural data. On the scale of 100 nm, DNA is successfully described by a continuous wormlike chain model with homogeneous elastic properties, characterized by a set of four elastic constants which have been measured in single-molecule experiments. We present here a theory that links these experiments on different scales, by systematically coarse-graining the rigid base-pair model to an effective wormlike chain description. The average helical geometry of the molecule is accounted for exactly, and repetitive as well as random sequences are considered. Structural disorder is shown to produce a small, additive and short-range correction to thermal conformation fluctuations as well as to entropic elasticity. We also discuss the limits of applicability of the homogeneous wormlike chain on short scales, quantifying the anisotropy of bending stiffness, the non-Gaussian bend angle distribution and the variability of stiffness, all of which are noticeable below a helical turn. The coarse-grained elastic parameters show remarkable overall agreement with experimental wormlike chain stiffness. For the best-matching potential, bending persistence lengths of dinucleotide repeats span a range of 37-53 nm, with a random DNA value of 43 nm. While twist stiffness is somewhat underestimated and stretch stiffness is overestimated, the counterintuitive negative sign and the magnitude of the twist-stretch coupling agree with recent experimental findings.

Sequence-Dependent Twist-Stretch Coupling in DNA

Recent single-molecule micromanipulation experiments on DNA subject to small distortion revealed positive coupling between DNA stretching and twisting—for instance, DNA elongates when overtwisted. Here we propose a method to calculate the twist-stretch coupling constant specific to a DNA fragment of a given sequence. The method employs a sequence-dependent dinucleotide force field and is based on constrained minimization of the fragment’s deformation energy. Using a force field inferred from atomistic molecular dynamics simulations, we obtain the twist-stretch coupling for random sequence to be 0.30 nm/turn, close to experimental values. An exhaustive calculation for all oligomers of nine basepairs yields values between 0.14 and 0.45 nm/turn, positively correlated with the contents of pyrimidine-purine steps in the sequence. Our method is simple to use and allows one to explore the hypothesis that some sequences may be optimized for twist-stretch coupling.

On structural transitions, thermodynamic equilibrium, and the phase diagram of DNA and RNA duplexes under torque and tension

A precise understanding of the flexibility of double stranded nucleic acids and the nature of their deformed conformations induced by external forces is important for a wide range of biological processes including transcriptional regulation, supercoil and catenane removal, and site-specific recombination. We present, at atomic resolution, a simulation of the dynamics involved in the transitions from B-DNA and A-RNA to Pauling (P) forms and to denatured states driven by application of external torque and tension. We then calculate the free energy profile along a B- to P-transition coordinate and from it, compute a reversible pathway, i.e., an isotherm of tension and torque pairs required to maintain P-DNA in equilibrium. The reversible isotherm maps correctly onto a phase diagram derived from single molecule experiments, and yields values of elongation, twist, and twist-stretch coupling in agreement with measured values. We also show that configurational entropy compensates significantly for the large electrostatic energy increase due to closer-packed P backbones. A similar set of simulations applied to RNA are used to predict a novel structure, P-RNA, with its associated free energy, equilibrium tension, torque and structural parameters, and to assign the location, on the phase-diagram, of a putative force-torque-dependent RNA "triple point."

DNA overwinds when stretched

DNA is often modelled as an isotropic rod, but its chiral structure suggests the possible importance of anisotropic mechanical properties, including coupling between twisting and stretching degrees of freedom. Simple physical intuition predicts that DNA should unwind under tension, as it is pulled towards a denatured structure. We used rotor bead tracking to directly measure twist-stretch coupling in single DNA molecules. Here we show that for small distortions, contrary to intuition, DNA overwinds under tension, reaching a maximum twist at a tension of approximately 30 pN. As tension is increased above this critical value, the DNA begins to unwind. The observed twist-stretch coupling predicts that DNA should also lengthen when overwound under constant tension, an effect that we quantitatively confirm. We present a simple model that explains these unusual mechanical properties, and also suggests a possible origin for the anomalously large torsional rigidity of DNA. Our results have implications for the action of DNA-binding proteins that must stretch and twist DNA to compensate for variability in the lengths of their binding sites. The requisite coupled DNA distortions are favoured by the intrinsic mechanical properties of the double helix reported here.

Statistical mechanics of triangulated ribbons.

We use computer simulations and scaling arguments to investigate statistical and structural properties of a semiflexible ribbon composed of isosceles triangles. We study two different models, one where the bending energy is calculated from the angles between the normal vectors of adjacent triangles, the second where the edges are viewed as semiflexible polymers so that the bending energy is related to the angles between the tangent vectors of next-nearest-neighbor triangles. The first model can be solved exactly whereas the second is more involved. It was recently introduced by Liverpool and Golestanian, Phys. Rev. Lett. 80, 405 (1998); Phys. Rev. E 62, 5488 (2000) as a model for double-stranded biopolymers such as DNA. Comparing observables such as the autocorrelation functions of the tangent vectors and the bond-director field, the probability distribution functions of the end-to-end distance, and the mean-squared twist we confirm the existence of local twist correlation, but find no indications for other predicted features such as twist-stretch coupling, kinks, or oscillations in the autocorrelation function of the bond-director field.

Adaptive elastic properties of chromatin fiber

Chromatin is a complex of DNA and specific proteins forming an intermediary level of organization of eukaryotic genomes, between double-stranded DNA and chromosome. Within a generic modeling of chromatin assembly, we investigate the interplay between the mechanical properties of the chromatin fiber and its biological functions. A quantitative step is to relate the mechanics at the DNA level and the mechanics described at the chromatin fiber level. It allows to calculate the complete set of chromatin elastic constants (twist and bend persistence lengths, stretch modulus and twist–stretch coupling constant), in terms of DNA elastic properties and geometric features of the fiber. These elastic constants are strongly sensitive to the local architecture of the fiber and we argue that this tunable elasticity might be a key feature in chromatin functions, for instance in the initiation and regulation of transcription. Moreover, this analysis provides a framework to interpret micromanipulation studies of chromatin fiber and suggests further experiments involving intercalators to scan the tunable elasticity of the fiber.

Chromatin: a tunable spring at work inside chromosomes.

This paper focuses on mechanical aspects of chromatin biological functioning. Within a basic geometric modeling of the chromatin assembly, we give a complete set of elastic constants (twist and bend persistence lengths, stretch modulus and twist-stretch coupling constant) of the so-called 30-nm chromatin fiber, in terms of DNA elastic properties and geometric properties of the fiber assembly. The computation naturally embeds the fiber within a current analytical model known as the "extensible wormlike rope," allowing a straightforward prediction of the force-extension curves. We show that these elastic constants are strongly sensitive to the linker length, up to 1 bp, or equivalently to its twist, and might locally reach very low values, yielding a highly flexible and extensible domain in the fiber. In particular, the twist-stretch coupling constant, reflecting the chirality of the chromatin fiber, exhibits steep variations, and sign changes when the linker length is varied. We argue that this tunable elasticity might be a key feature for chromatin function, for instance, in the initiation and regulation of transcription.

Entropic Elasticity of Twist-Storing Polymers

We investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modeled as a fluctuating rod with bend stiffness A kT and twist stiffness C kT. In such a model, thermal bend fluctuations couple geometrically to an applied torque through the relation Lk = Tw + Wr. We explore this coupling and find agreement between the predictions of our model and recent experimental results on single lambda-DNA molecules. This analysis affords an experimental determination of the microscopic twist stiffness (averaged over a helix repeat). Quantitative agreement between theory and experiment is obtained using C=109 nm. The theory further predicts a thermal reduction of the effective twist rigidity induced by bend fluctuations. Finally, we find a small reflection of molecular chirality in the experimental data and interpret it in terms of a twist-stretch coupling of the DNA duplex.

Torsional directed walks, entropic elasticity, and DNA twist stiffness.

DNA and other biopolymers differ from classical polymers because of their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the "torsional directed walk." Motivated by a recent experiment on single lambda-DNA molecules [Strick, T. R., Allemand, J.-F., Bensimon, D., Bensimon, A. & Croquette, V. (1996) Science 271, 1835-1837], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C = 120 nm and D = 50 nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.

Microscopic Elasticity of DNA from Torsionally-Constrained Stretching

AbstractWe investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modelled as an inextensible chain with bend rigidity A, twist rigidity C, and twist-stretch coupling D. In such a model, thermal bend fluctuations couple geometrically to an applied torque through the relation Lk = Tw + Wr. We explore this coupling and find excellent agreement between the predictions of our model and the single λ-DNA molecule stretching experiments of Strick et al. [Science 271 (1996) 1835]. This analysis affords an experimental determination of the microscopic twist rigidity C. Quantitative agreement between theory and experiment is obtained using C = 120 nm and D = 50 nm. The theory further predicts a thermal reduction of the effective twist rigidity induced by bend fluctuations.