Thermal denaturation of fluctuating finite DNA chains: the role of bending rigidity in bubble nucleation

Stretching multistate flexible chains and loops

Polymer loop structure commonly appears in biological phenomena, such as DNA looping and DNA denaturation. When a chain forms a loop, its elastic behavior differs from that of an open chain due to the loss of entropy. In the case of reversible loop formation, interesting behavior emerges related to the multistate nature of the conformations. In this study, we model a multistate reversible loop as a looping Gaussian chain, which can bind (close) reversibly at one or several points to form a loop, or a zipping Gaussian loop, which can zip reversibly to form a double-stranded chain. For each model, we calculate the force-extension relations in the fixed-extension (Helmholtz) and the fixed-force (Gibbs) statistical ensembles. Unlike the single Gaussian chain or loop, the multilevel systems demonstrate qualitatively distinct tensile elasticity and ensemble inequivalence. In addition, we investigate a Gaussian necklace consisting of reversible alternating blocks of the zipped chain and loop and obtain the force-temperature phase diagram. The phase diagram implies a force-induced phase transition from a completely looped (denatured) state to a mixed (bound) state.

Statistical physics and mesoscopic modeling to interpret tethered particle motion experiments

Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques provide raw data such as the tracked particle amplitude of movement, from which relevant information about DNA conformations or states must be recovered. Solving this inverse problem appeals to specific theoretical tools that have been designed in the two last decades, together with the data pre-processing procedures that ought to be implemented to avoid biases inherent to these experimental techniques. These statistical tools and models are reviewed in this paper.

ation of the igh ensitiv Label-Free

A highly sensitive electrochemical biosensor with a signal amplification platform of electrodeposited gold nanoparticle (AuNP) has been developed and characterized. The sizes of the synthesized AuNP were found to be critical for the performance of biosensor in which the sizes were dependent on HAuCl₄ and acid concentrations; as well as on scan cycles and scan rates in the gold electro-reduction step. Systematic investigations of the adsorption of proteins with different sizes from aqueous electrolyte solution onto the electrodeposited AuNP surface were performed with a potentiometric method and calibrated by design of experiment (DOE). The resulting amperometric glucose biosensors was demonstrated to have a low detection limit (> 50M) and a wide linear range after optimization with AuNP electrodeposition.

Ionic effects on the temperature-force phase diagram of DNA

Double-stranded DNA (dsDNA) undergoes a structural transition to single-stranded DNA (ssDNA) in many biologically important processes such as replication and transcription. This strand separation arises in response either to thermal fluctuations or to external forces. The roles of ions are twofold, shortening the range of the interstrand potential and renormalizing the DNA elastic modulus. The dsDNA-to-ssDNA transition is studied on the basis that dsDNA is regarded as a bound state while ssDNA is regarded as an unbound state. The ground state energy of DNA is obtained by mapping the statistical mechanics problem to the imaginary time quantum mechanics problem. In the temperature-force phase diagram the critical force F _c (T) increases logarithmically with the Na⁺ concentration in the range from 32 to 110 mM. Discussing this logarithmic dependence of F _c (T) within the framework of polyelectrolyte theory, it inevitably suggests a constraint on the difference between the interstrand separation and the length per unit charge during the dsDNA-to-ssDNA transition.

Rigidity of melting DNA

The temperature dependence of DNA flexibility is studied in the presence of stretching and unzipping forces. Two classes of models are considered. In one case the origin of elasticity is entropic due to the polymeric correlations, and in the other the double-stranded DNA is taken to have an intrinsic rigidity for bending. In both cases single strands are completely flexible. The change in the elastic constant for the flexible case due to thermally generated bubbles is obtained exactly. For the case of intrinsic rigidity, the elastic constant is found to be proportional to the square root of the bubble number fluctuation.

Physical origin of DNA unzipping

In DNA transcription, the base pairs are unzipped in response to the enzymatic forces, separating apart two intertwined nucleotide strands. Consequently, the double-stranded DNA (dsDNA), in which two nucleotide strands wind about each other, transits structurally to the single-stranded DNA (ssDNA) in which two nucleotide strands are completely unwound and separated. The large interstrand separation is intimately related to the softening nucleotide strands. This conceptual framework is reinforced with the flow of the bending modulus toward zero under recursion relations derived from the momentum shell renormalization group. Interestingly, the stretch modulus remains the same under recursion relations. The renormalization of the bending modulus to zero has a profound implication that ssDNA has the shorter bending persistence length than does dsDNA in accordance with experiments.

Mechanistic Influence of Nanometer Length-Scale Surface Chemistry on DNA Hybridization

Hybridization of surface-immobilized oligonucleotides to their complementary counterparts is central to the rational design of novel nanodevices and DNA sensors. In this study, we have adopted a unified approach of combining sensing experiments with molecular dynamics simulations to characterize the hybridization of a 23 nucleotide long single-strand probe DNA tethered to a gold surface. Experiments indicate significant conformational changes of DNA in close vicinity (∼1 nm) of the gold surface upon hybridization and also conformational heterogeneity within hybridized DNA, consistent with simulation results. Simulations show that the conformational heterogeneity on a gold surface arises due to stabilization of surface-adsorbed partial and full duplexes, resulting in impeded hybridization in comparison to what observed on a repulsive surface. Furthermore, these simulations indicate that hybridization could be improved by tuning the nonspecific adsorption on a nanopatterned surface with an optimal patterning length. Simulations were performed on the probe tethered to gold nanodots of varying (2-8 nm) diameter. An improved hybridization of the present probe sequence was only observed for the 6 nm gold dots patterned on a repulsive surface. Results reveal that the 2D nanoconfinement provided by the 6 nm gold dot is optimal for reducing conformational heterogeneity for the specific sequence used in this study. Thus, improved DNA hybridization can be achieved on a gold nanodot patterned repulsive surface, where the optimal dot diameter will depend on the probe length and sequence. In summary, this study provides mechanistic insights onto hybridization on gold and offers a unique method toward improved hybridization on a nanopatterned surface with an optimized patterning length.

Elasticity of cross-linked semiflexible biopolymers under tension

Aiming at the mechanical properties of cross-linked biopolymers, we set up and analyze a model of two weakly bending wormlike chains subjected to a tensile force, with regularly spaced inter-chain bonds (cross-links) represented by harmonic springs. Within this model, we compute the force-extension curve and the differential stiffness exactly and discuss several limiting cases. Cross-links effectively stiffen the chain pair by reducing thermal fluctuations transverse to the force and alignment direction. The extra alignment due to cross-links increases both with growing number and with growing strength of the cross-links, and is most prominent for small force f. For large f, the additional, cross-link-induced extension is subdominant except for the case of linking the chains rigidly and continuously along their contour. In this combined limit, we recover asymptotically the elasticity of a weakly bending wormlike chain without constraints, stiffened by a factor of 4. The increase in differential stiffness can be as large as 100% for small f or large numbers of cross-links.

Stretching and bending fluctuations of short DNA molecules

Recent measurements of the distribution of end-to-end distance in short DNA molecules infer cooperative stretching fluctuations. The assumptions underlying the analysis can be questioned if transient, thermally induced defects producing a localized decrease in bending stiffness are present in thermal equilibrium, such as regions in which DNA melts locally (bubbles), sustains large-angle bends (kinks), or can locally transform into an alternative (S-DNA) state. We study a generalized discrete worm-like chain model for DNA, capable of describing these experiments, showing that the model yields accurate fits to available experimental data. Our results indicate that DNA bending arising from such localized defects, rather than solely stretching, can be an equal contributor to end-to-end distance fluctuations for 35-bp DNA and contributes nontrivially to such fluctuations at all scales below the persistence length. The analysis suggests that such fluctuations should exhibit a scale-dependent cooperativity, specifically relevant in determining the behavior of short chains, but which saturates rapidly to a length-independent value for longer DNA, to ensure a consistent physical description of DNA across multiple scales. Our approach provides a minimal, yet accurate, coarse-grained description of DNA at the subpersistence length scales of current experimental interest.

DNA kinks and bubbles: temperature dependence of the elastic energy of sharply bent 10-nm-size DNA molecules

A 10-nm-long DNA molecule can bend through large angles reversibly. Past the linear regime, its equilibrium nonlinear bending elasticity is governed by a critical bending torque τ(c)≈30pN×nm at which the molecule develops a kink. This nonlinearity has long been attributed to the nucleation of a bubble or melted region in the molecule. Here we measure the temperature dependence of the critical bending torque for nicked DNA, and determine that the entropy associated with the kink in the nonlinear regime is negligible. Thus in the case of nicked DNA the kink is not a bubble, but a compact region deformed beyond a yield strain. We further argue that, with our boundary conditions, the same is likely true for intact DNA. The present measurements confirm that the critical bending torque τ(c) is a materials parameter of DNA mechanics analogous to the bending modulus B≈200pN×nm.

Mesoscopic models for DNA stretching under force: New results and comparison with experiments

Single-molecule experiments on double-stranded B-DNA stretching have revealed one or two structural transitions, when increasing the external force. They are characterized by a sudden increase of DNA contour length and a decrease of the bending rigidity. The nature and the critical forces of these transitions depend on DNA base sequence, loading rate, salt conditions and temperature. It has been proposed that the first transition, at forces of 60-80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA, while the second one, at stronger forces, is a strand peeling resulting in single-stranded DNAs (ssDNA), similar to thermal denaturation. But due to experimental conditions these two transitions can overlap, for instance for poly(dA-dT). In an attempt to propose a coherent picture compatible with this variety of experimental observations, we derive an analytical formula using a coupled discrete worm-like chain-Ising model. Our model takes into account bending rigidity, discreteness of the chain, linear and non-linear (for ssDNA) bond stretching. In the limit of zero force, this model simplifies into a coupled model already developed by us for studying thermal DNA melting, establishing a connection with previous fitting parameter values for denaturation profiles. Our results are summarized as follows: i) ssDNA is fitted, using an analytical formula, over a nano-Newton range with only three free parameters, the contour length, the bending modulus and the monomer size; ii) a surprisingly good fit on this force range is possible only by choosing a monomer size of 0.2 nm, almost 4 times smaller than the ssDNA nucleobase length; iii) mesoscopic models are not able to fit B to ssDNA (or S to ss) transitions; iv) an analytical formula for fitting B to S transitions is derived in the strong force approximation and for long DNAs, which is in excellent agreement with exact transfer matrix calculations; v) this formula fits perfectly well poly(dG-dC) and λ-DNA force-extension curves with consistent parameter values; vi) a coherent picture, where S to ssDNA transitions are much more sensitive to base-pair sequence than the B to S one, emerges. This relatively simple model might allow one to further study quantitatively the influence of salt concentration and base-pairing interactions on DNA force-induced transitions.

High-energy deformation of filaments with internal structure and localized torque-induced melting of DNA

We develop a continuum elastic approach to examining the bending mechanics of semiflexible filaments with a local internal degree of freedom that couples to the bending modulus. We apply this model to study the nonlinear mechanics of a double-stranded DNA oligomer (shorter than its thermal persistence length) whose free ends are linked by a single-stranded DNA chain. This construct, studied by H. Qu and G. Zocchi [Europhys. Lett. 94, 18003 (2011)], displays nonlinear strain softening associated with the local melting of the double-stranded DNA under applied torque and serves as a model system with which to study the nonlinear elasticity of DNA under large energy deformations. We show that one can account quantitatively for the observed bending mechanics using an augmented wormlike chain model, the helix-coil wormlike chain. We also predict that the highly bent and partially molten dsDNA should exhibit particularly large end-to-end fluctuations associated with the fluctuation of the length of the molten region, and propose appropriate experimental tests. We suggest that the augmented wormlike chain model discussed here is a useful analytic approach to the nonlinear mechanics of DNA or other biopolymer systems.

Thermal and mechanical denaturation properties of a DNA model with three sites per nucleotide

In this paper, we show that the coarse grain model for DNA, which has been proposed recently by Knotts et al. [J. Chem. Phys. 126, 084901 (2007)], can be adapted to describe the thermal and mechanical denaturation of long DNA sequences by adjusting slightly the base pairing contribution. The adjusted model leads to (i) critical temperatures for long homogeneous sequences that are in good agreement with both experimental ones and those obtained from statistical models, (ii) a realistic step-like denaturation behaviour for long inhomogeneous sequences, and (iii) critical forces at ambient temperature of the order of 10 pN, close to measured values. The adjusted model furthermore supports the conclusion that the thermal denaturation of long homogeneous sequences corresponds to a first-order phase transition and yields a critical exponent for the critical force equal to σ = 0.70. This model is both geometrically and energetically realistic, in the sense that the helical structure and the grooves, where most proteins bind, are satisfactorily reproduced, while the energy and the force required to break a base pair lie in the expected range. It therefore represents a promising tool for studying the dynamics of DNA-protein specific interactions at an unprecedented detail level.

Stacking interactions in denaturation of DNA fragments

A mesoscopic model for heterogeneous DNA denaturation is developed in the framework of the path integral formalism. The base pair stretchings are treated as one-dimensional, time-dependent paths contributing to the partition function. The size of the paths ensemble, which measures the degree of cooperativity of the system, is computed versus temperature consistently with the model potential physical requirements. It is shown that the ensemble size strongly varies with the molecule backbone stiffness providing a quantitative relation between stacking and features of the melting transition. The latter is an overall smooth crossover which begins from the adenine-thymine-rich portions of the fragment. The harmonic stacking coupling shifts, along the T -axis, the occurrence of the multistep denaturation but it does not change the character of the crossover. The methods to compute the fractions of open base pairs versus temperature are discussed: by averaging the base pair displacements over the path ensemble, we find that such fractions signal the multisteps of the transition in good agreement with the indications provided by the specific heat plots.

Denaturation patterns in heterogeneous DNA

The thermodynamical properties of heterogeneous DNA sequences are computed by path-integral techniques applied to a nonlinear model Hamiltonian. The base pairs relative displacements are interpreted as time-dependent paths whose amplitudes are consistent with the model potential for the hydrogen bonds between complementary strands. The portion of configuration space contributing to the partition function is determined, at any temperature, by selecting the ensemble of paths which fulfill the second law of thermodynamics. For a short DNA fragment, the denaturation is signaled by a succession of peaks in the specific-heat plots while the entropy grows continuously versus T. Thus, the opening of the double strand with bubble formation appears as a smooth crossover due to base pair fluctuation effects which are accounted for by the path-integral method. The multistep transition is driven by the adenine-thymine- (AT) rich regions of the DNA fragment. The base pairs path ensemble shows an enhanced degree of cooperativity at about the same temperatures for which the specific-heat peaks occur. These findings establish a link between microscopic and macroscopic signatures of the transition. The fractions of mean base pair stretchings are computed by varying the AT base pairs content and taking some threshold values for the occurrence of the molecule denaturation.

Microscopic mechanism for experimentally observed anomalous elasticity of DNA in two dimensions

By exploring a recent model in which DNA bending elasticity, described by the wormlike chain model, is coupled to basepair denaturation, we demonstrate that small denaturation bubbles lead to anomalies in the flexibility of DNA at the nanometric scale, when confined in two dimensions (2D), as reported in atomic-force microscopy experiments. Our model yields very good fits to experimental data and quantitative predictions that can be tested experimentally. Although such anomalies exist when DNA fluctuates freely in three dimensions (3D), they are too weak to be detected. Interactions between bases in the helical double-stranded DNA are modified by electrostatic adsorption on a 2D substrate, which facilitates local denaturation. This work reconciles the apparent discrepancy between observed 2D and 3D DNA elastic properties and points out that conclusions about the 3D properties of DNA (and its companion proteins and enzymes) do not directly follow from 2D experiments by atomic-force microscopy.

Path integral method for DNA denaturation

The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillment of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature Tc*, whereas the fraction of unbound base pairs grows continuously around and above Tc*. The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus T. The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuously versus T while the specific heat displays a remarkable peak at Tc*. The location of the peak versus T varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second-order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.

Genome wide application of DNA melting analysis

Correspondences between functional and thermodynamic melting properties in a genome are being increasingly employed for ab initio gene finding and for the interpretation of the evolution of genomes. Here we present the first systematic genome wide comparison between biologically coding domains and thermodynamically stable regions. In particular, we develop statistical methods to estimate the reliability of the resulting predictions. Not surprisingly, we find that the success of the approach depends on the difference in GC content between the coding and the non-coding parts of the genome and on the percentage of coding base-pairs in the sequence. These prerequisites vary strongly between species, where we observe no systematic differences between eukaryotes and prokaryotes. We find a number of organisms in which the strong correlation of coding domains and thermodynamically stable regions allows us to identify putative exons or genes to complement existing approaches. In contrast to previous investigations along these lines we have not employed the Poland-Scheraga (PS) model of DNA melting but use the earlier Zimm-Bragg (ZB) model. The Ising-like form of the ZB model can be viewed as an approximation to the PS model, with averaged loop entropies included into the cooperative factor [Formula: see text]. This results in a speed-up by a factor of 20-100 compared to the Fixman-Freire algorithm for the solution of the PS model. We show that for genomic sequences the resulting systematic errors are negligible compared to the parameterization uncertainty of the models. We argue that for limited computing resources, available CPU power is better invested in broadening the statistical base for genomic investigations than in marginal improvements of the description of the physical melting behavior.

Coupling between denaturation and chain conformations in DNA: stretching, bending, torsion and finite size effects

We develop further a statistical model coupling denaturation and chain conformations in DNA (Palmeri et al 2007 Phys. Rev. Lett. 99 088103). Our discrete helical wormlike chain model takes explicitly into account the three elastic degrees of freedom, namely stretching, bending and torsion of the polymer. By integrating out these external variables, the conformational entropy contributes to bubble nucleation (opening of base-pairs), which sheds light on the DNA melting mechanism. Because the values of monomer length, bending and torsional moduli differ significantly in dsDNA and ssDNA, these effects are important. Moreover, we explore in this context the role of an additional loop entropy and analyze finite size effects in an experimental context, where polydA-polydT is clamped by two G-C strands, as well as for free polymers.

What do diffusion measurements tell us about membrane compartmentalisation? Emergence of the role of interprotein interactions

The techniques of diffusion analysis based on optical microscopy approaches have revealed a great diversity of the dynamic organisation of cell membranes. For a long period, two frameworks have dominated the way of representing the membrane structure: the membrane skeleton fences and the lipid raft models. Progresses in the methods of data analysis have shed light on the features and consequently the possible origin of membrane domains: Inter-protein interactions play a role in confinement. Innovative developments pushing forward the spatiotemporal resolution limits are currently emerging, which are likely to provide in the future a detailed understanding of the intimate functional dynamic organisation of the cell membrane.

Melting of persistent double-stranded polymers

Motivated by recent DNA-pulling experiments, we revisit the Poland-Scheraga model of melting a double-stranded polymer. We include distinct bending rigidities for both the double-stranded segments and the single-stranded segments forming a bubble. There is also bending stiffness at the branch points between the two segment types. The transfer matrix technique for single persistent chains is generalized to describe the branching bubbles. Properties of spherical harmonics are then exploited in truncating and numerically solving the resulting transfer matrix. This allows efficient computation of phase diagrams and force-extension curves (isotherms). While the main focus is on exposition of the transfer matrix technique, we provide general arguments for a reentrant melting transition in stiff double strands. Our theoretical approach can also be extended to study polymers with bubbles of any number of strands, with potential applications to molecules such as collagen.