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We discuss the temporal efficiency of template-directed polymer synthesis, such as DNA replication and transcription, under a given template string. To weigh the synthesis speed and accuracy on the same scale, we propose a template-directed synthesis (TDS) rate, which contains an expression analogous to that for the Shannon entropy. Increasing the synthesis speed accelerates the TDS rate, but the TDS rate is lowered if the produced sequences are diversified. We apply the TDS rate to some production system models and investigate how the balance between the speed and the accuracy is affected by changes in the system conditions.

In this work we propose a model for the DNA double helix within the tight-binding framework that incorporates the helicity of the molecules. We have studied the localization properties of three DNA sequences, the periodic poly(dG)-poly(dC) and poly(dA)-poly(dT) sequences and the random ATGC sequence (where A is adenine, T is thymine, G is guanine, and C is cytosine), all of which are coupled to the backbone with random site energies representing the environmental fluctuations. We observe that due to the helicity of DNA, electron transport is greatly enhanced and there exists an almost disorder-strength-independent critical value of the hopping integral, which accounts for the helicity of DNA, for which the electronic states become maximally extended. We have also investigated the effect of backbone energetics on the transmission and I-V characteristics of DNA.

One issue in genome maintenance is how DNA repair proteins find lesions at rates that seem to exceed diffusion-limited search rates. We propose a phenomenon where DNA damage induces nucleosomal rearrangements which move lesions to potential rendezvous points in the chromatin structure. These rendezvous points are the dyad and the linker DNA between histones, positions in the chromatin which are more likely to be accessible by repair proteins engaged in a random search. The feasibility of this mechanism is tested by considering the statistical mechanics of DNA containing a single lesion wrapped onto the nucleosome. We consider lesions which make the DNA either more flexible or more rigid by modeling the lesion as either a decrease or an increase in the bending energy. We include this energy in a partition function model of nucleosome breathing. Our results indicate that the steady state for a breathing nucleosome will most likely position the lesion at the dyad or in the linker, depending on the energy of the lesion. A role for DNA binding proteins and chromatin remodelers is suggested based on their ability to alter the mechanical properties of the DNA and DNA-histone binding, respectively. We speculate that these positions around the nucleosome potentially serve as rendezvous points where DNA lesions may be encountered by repair proteins which may be sterically hindered from searching the rest of the nucleosomal DNA. The strength of the repositioning is strongly dependent on the structural details of the DNA lesion and the wrapping and breathing of the nucleosome. A more sophisticated evaluation of this proposed mechanism will require detailed information about breathing dynamics, the structure of partially wrapped nucleosomes, and the structural properties of damaged DNA.

Long polymer chains are ubiquitous in biological systems and their mechanical properties have significant impact upon biological processes. Of particular interest is the situation in which polymer chains are wound around each other or around other objects. We have analyzed the parameters of a long Gaussian polymer chain wound around a cylinder as a function of the torque applied to the ends of the chain. We have shown that for sufficiently long polymer chains, an average winding angle and a characteristic radius of the chain can be determined from a modified Bessel function of purely imaginary order, in which the value of the order is equivalent to the applied torque, normalized to the product of the absolute temperature and the Boltzmann constant. The obtained results are consistent with a simplified interpretation in terms of "torsional blobs," and this could be extended to nonideal chains with excluded volumes. We have also extended our results to the case of a polymer chain rotating in viscous medium. Our results could be used to estimate the mechanical strains that appear in DNA and RNA during transcription, as these might initiate formation of unusual DNA structures, invasion of RNA into the DNA duplex (R-loop formation), and modulation of the interactions of DNA and RNA with proteins.

To unveil the electronic states of divalent metal ion incorporated M-DNAs, where M is Mg, Mn, Ni, Co, or Fe, optical absorption spectra have been studied in aqueous solutions of single-stranded (SS) 30 mer DNA of poly(dA) (adenine), poly(dG) (guanine), poly(dT) (thymine), poly(dC) (cytosine), salmon-sperm DNA (B-DNA), and M-DNA. The absorption spectrum of the double-stranded (DS) B-DNA can be reproduced with the sum of the four absorption spectra of the SS oligo-DNAs in the ratio corresponding to the composition of B-DNA. This observation suggests that the interactions between complementary strands of DS DNA are negligibly weaker than the bandwidths of the optical spectra. In the metal-incorporated M-DNAs, except for Fe-DNA, the absorption spectra show no significant qualitative change from that of B-DNA. Quantitatively, however, the absorption intensity decreases by ≈ 15% uniquely in a DS poly(dA)-poly(dT) solution with adding MCl(2), while nothing happens quantitatively and qualitatively in any SS oligo-DNA and DS poly(dG)-poly(dC) solutions, suggesting some suppression of the electronic excitation only in the Adenine-M-Thymine complex. In contrast, remarkable differences have been observed in Fe-DNA, prepared with FeCl(2) and B-DNA. New absorption bands appear in the intragap energy of Fe-DNA, in addition to the suppression of the interband absorption peak of DNA at 4.8 eV. The intragap absorption is attributed to the appearance of Fe(3+) species with the same spectral feature as that of FeCl(3), that is, purely ionic Fe(3+) species. This observation suggests that FeCl(2) + B-DNA forms Fe-DNA with hydrated Fe(3+) ions with ionic bonds. Thus, it is concluded that the charge transfer from Fe(2+) to DNA has occurred in Fe-DNA and that the transferred charges are expected to be located in the nearby bases.

We show results of our high force (up to 1.8 nN) atomic force microscopy force spectroscopy measurements of a double stranded DNA. We have found that the force spectra of torsionally constrained molecules display a small plateau occurring at a force of approximately 1 nN. This transition is absent in molecules with rotational freedom. Based on all-atom molecular dynamics simulations, we suggest that this plateau is a result of reducing the diameter of a double helix through extreme stretching. The simulation suggests that the molecule is forced into a form resembling an underwound P-DNA, with bases protruding outside of the backbones. These results broaden our understanding of the fundamental aspects of DNA nanomechanics.

Thermal denaturation of DNA is often studied with coarse-grained models in which native sequential base pairing is mimicked by the existence of attractive interactions only between monomers at the same position along strands (Poland and Scheraga models). Within this framework, the existence of a three-stranded DNA bound state in conditions where a duplex DNA would be in the denaturated state was recently predicted from a study of three directed polymer models on simplified hierarchical lattices (d>2) and in 1+1 dimensions. Such a phenomenon which is similar to the Efimov effect in nuclear physics was named Efimov-DNA. In this paper we study the melting of the three-stranded DNA on a Sierpinski gasket of dimensions d<2 by assigning extra weight factors to fork openings and closings, to induce a two-strand DNA melting. In such a context we can find again the existence of the Efimov-DNA-like state but quite surprisingly we discover also the presence of a different phase, to be called a mixed state, where the strands are pair-wise bound but without three chain contacts. Whereas the Efimov DNA turns out to be a crossover near melting, the mixed phase is a thermodynamic phase.

We study the problem of the self-assembly of nanoparticles (NPs) into finite mesoscopic structures with a programmed local morphology and complex overall shape. Our proposed building blocks are NPs that are directionally functionalized with DNA. The combination of directionality and selectivity of interactions allows one to avoid unwanted metastable configurations, which have been shown to lead to slow self-assembly kinetics even in much simpler systems. With numerical simulations, we show that a variety of target mesoscopic objects can be designed and self-assembled in near perfect yield. They include cubes, pyramids, boxes, and even an Empire State Building model. We summarize our findings with a set of design strategies that leads to the successful self-assembly of a wide range of mesostructures.

In order to determine a proper value for the density of dry DNA films we have used a method based upon the measurement of interference effects in transmission spectra of thin DNA layers. Our results show that the methodology is effective and the density of DNA in this state, 1.407 g/cm(3), is much lower than the commonly used 1.7 g/cm(3). Obtaining accurate values for the DNA film density will allow the optical constants for DNA to be recalculated, which were previously obtained assuming a higher DNA density. Furthermore, since our recent investigations have shown a strong dependence of the sample composition on DNA film formation and thus on its density, such a method will be important in characterizing particle interactions with DNA film and their dose dependence.

A molecular dynamics simulation method is used to study the translocation of a single strand DNA through nanopores opened on graphene membranes. Simulation results uncover that the translocation time for four DNA strands (20G, 20A, 20T, and 20C) is proportional to the size of the four DNA bases. However, the change of the ionic current is caused not only by the physical blockade of the DNA, but also induced by the change of the ion distribution once the negatively charged DNA enters the nanopore. An electric double layer will be formed and causes higher cation and lower anion concentration near the DNA strand surface, which makes the ionic current blockade not sensitive to the base size for a single-layer graphene nanopore. Increasing the graphene membrane thickness can enhance the DNA physical blockage effect on ionic current and improve the nanopore sensitivity to the four DNA bases.

The closure of long equilibrated denaturation bubbles in DNA is studied using Brownian dynamics simulations. A minimal mesoscopic model is used where the double helix is made of two interacting bead-spring freely rotating strands, with a nonzero torsional modulus in the duplex state, κ(φ)=200 to 300k(B)T. For DNAs of lengths N=40 to 100 base pairs (bps) with a large initial bubble in their middle, long closure times of 0.1 to 100μs are found. The bubble starts winding from both ends until it reaches a ≈10 bp metastable state due to the large elastic energy stored in the bubble. The final closure is limited by three competing mechanisms depending on κ(φ) and N: arms diffusion until their alignment, bubble diffusion along the DNA until one end is reached, or local Kramers process (crossing over a torsional energy barrier). For clamped ends or long DNAs, the closure occurs via this last temperature-activated mechanism, yielding a good quantitative agreement with the experiments.

We study the influence of a terahertz field on thermal properties of DNA molecules. A Peyrard-Bishop-Dauxois model with the inclusion of a solvent interaction term is considered. The terahertz field is included as a sinusoidal driven force in the equation of motion. We show how under certain field and system parameters, the melting transition and bubble formation are modified.

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.

Replication and transcription are two important processes in living systems. To execute such processes, various proteins work far away from equilibrium in a staggered way. Motivated by this, aspects of hysteresis during unzipping of DNA under a periodic drive are studied. A steady-state phase diagram of a driven DNA is proposed which is experimentally verifiable. As a two-state system, we also compare the results of DNA with that of an Ising magnet under an asymmetrical variation of the magnetic field.

When subject to constant tension, a DNA or RNA hairpin will typically make abrupt transitions between the open and closed state. Although the transition kinetics are an intrinsic property of the molecule, the transition rates measured in single-molecule experiments can be influenced by the configuration of the measurement system. We investigate the transition kinetics for a DNA hairpin held under constant force by an optical trap as a function of microsphere size and double-stranded DNA handle length. We find the apparent transition lifetime cannot be expressed as a function of the drag coefficient of the microsphere alone or as a function of time scales relevant to the optical trap. The apparent transition lifetime is found to be a linear function of the factor β(eff)·α(handle), where β(eff) is the effective drag coefficient of the microsphere near the surface and α(handle) is the stiffness of the DNA tether. The results provide insight into the perturbation to the hairpin transition kinetics due to experimental configuration and guidance for designing single-molecule experiments which determine the intrinsic molecular kinetics.

We present a study of the bend angle distribution of semiflexible polymers of short and intermediate lengths within the wormlike chain model. This enables us to calculate the elastic response of a stiff molecule to a bending moment. Our results go beyond the Hookean regime and explore the nonlinear elastic behavior of a single molecule. We present analytical formulas for the bend angle distribution and for the moment-angle relation. Our analytical study is compared against numerical Monte Carlo simulations. The functional forms derived here can be applied to fluorescence microscopic studies on actin and DNA. Our results are relevant to recent studies of "kinks" and cyclization in short and intermediate length DNA strands.

By considering the detailed structure of DNA in the base pair level, two possible definitions of the persistence length are compared. One definition is related to the orientation of the terminal base pairs, and the other is based on the vectors which connect two adjacent base pairs at each end of the molecule. It is shown that although these definitions approach each other for long DNA molecules, they are dramatically different on short length scales. We show analytically that the difference mostly comes from the shear flexibility of the molecule and can be used to measure the shear modulus of DNA.

We discuss generalizations of a previously published coarse-grained description [Mergell et al., Phys. Rev. E 68, 021911 (2003)] of double stranded DNA (dsDNA). The model is defined at the base-pair level and includes the electrostatic repulsion between neighbor helices. We show that the model reproduces mechanical and elastic properties of several DNA nanostructures (DNA origamis). We also show that electrostatic interactions are necessary to reproduce atomic force microscopy measurements on planar DNA origamis.

In recent years, significant progress in understanding the properties of supercoiled DNA has been obtained due to nanotechniques that made stretching and twisting of single molecules possible. Quantitative interpretation of such experiments requires accurate knowledge of torques inside manipulated DNA. This paper argues that it is not possible to transfer the entire magnitudes of external torques to the twisting stress of the double helix, and that a reducing torque transfer coefficient (TTC < 1) should always be assumed. This assertion agrees with simple physical intuition and is supported by the results of all-atom molecular dynamics (MD) simulations. According to MD, the TTCs around 0.8 are observed in nearly optimal conditions. Reaching higher values requires special efforts and it should be difficult in practice. The TTC can be partially responsible for the persistent discrepancies between the twisting rigidity of DNA measured by different methods.

Nonspecific binding of regulatory proteins to DNA can be an important mechanism for target search and storage. This seems to be the case for the lambda repressor protein (CI), which maintains lysogeny after infection of E. coli. CI binds specifically at two distant regions along the viral genome and induces the formation of a repressive DNA loop. However, single-molecule imaging as well as thermodynamic and kinetic measurements of CI-mediated looping show that CI also binds to DNA nonspecifically and that this mode of binding may play an important role in maintaining lysogeny. This paper presents a robust phenomenological approach using a recently developed method based on the partition function, which allows calculation of the number of proteins bound nonspecific to DNA from measurements of the DNA extension as a function of applied force. This approach was used to analyze several cycles of extension and relaxation of λ DNA performed at several CI concentrations to measure the dissociation constant for nonspecific binding of CI (~100 nM), and to obtain a measurement of the induced DNA compaction (~10%) by CI.

Synthetic biomolecular spiders with "legs" made of single-stranded segments of DNA can move on a surface covered by single-stranded segments of DNA called substrates when the substrate DNA is complementary to the leg DNA. If the motion of a spider does not affect the substrates, the spider behaves asymptotically as a random walk. We study the diffusion coefficient and the number of visited sites for spiders moving on the square lattice with a substrate in each lattice site. The spider's legs hop to nearest-neighbor sites with the constraint that the distance between any two legs cannot exceed a maximal span. We establish analytic results for bipedal spiders, and investigate multileg spiders numerically. In experimental realizations legs usually convert substrates into products (visited sites). The binding of legs to products is weaker, so the hopping rate from the substrates is smaller. This makes the problem non-Markovian and we investigate it numerically. We demonstrate the emergence of a counterintuitive behavior-the more spiders are slowed down on unvisited sites, the more motile they become.

We study the internal nonlinear dynamics of an inhomogeneous short lattice DNA model by solving numerically the governing discrete perturbed sine-Gordon equations under the limits of a uniform and a nonuniform angular rotation of bases. The internal dynamics is expressed in terms of open-state configurations represented by kink and antikink solitons with fluctuations. The inhomogeneity in the strands and hydrogen bonds as well as nonuniformity in the rotation of bases introduce fluctuations in the profile of the solitons without affecting their robust nature and the propagation. These fluctuations spread into the tail regions of the soliton in the case of periodic inhomogeneity. However, the localized form of inhomogeneity generates amplified fluctuations in the profile of the soliton. The fluctuations are expected to enhance the denaturation process in the DNA molecule.

Recent experiments have shown the double-stranded (ds) DNAs readily bend and loop over the scale much shorter than their persistence length (50 nm). In an effort to unveil this seemingly surprising phenomenon, we study the emergence of bubbles in short ds DNA loops by simulating the breathing DNA model. We analyze the bubble size distributions and the melting curves for varying contour lengths, which are critically compared with those of linear DNA of the same lengths. We analytically evaluate the free energies associated with double-strand bending and single-strand bubble formation to explain the simulation data. It is found that in shorter looped DNA the bubbles are more easily initiated and formed to release the large bending energy, giving rise to melting at a lower temperature and a lower contour length., (© 2012 American Physical Society)

In living cells, proteins combine three-dimensional bulk diffusion and one-dimensional 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 robust mechanism to speed up intracellular diffusion-limited reactions. The parameter range we focus on is relevant for in vitro systems and for facilitated diffusion on yeast chromatin., (© 2012 American Physical Society)

Magnetic tweezers were employed to investigate the interactions between DNA and cisplatin (transplatin). Cisplatin shortened DNA and reduced its persistence length more significantly than transplatin due to the formation of many more diadducts than those formed by transplatin. Interestingly, the presence of transplatin could enhance the ability of cisplatin in shortening DNA. An optimal concentration ratio of transplatin to cisplatin existed at which cisplatin showed the highest ability in shortening DNA. Moreover, abrupt length changes were also observed when DNA was treated with a mixture of cisplatin and transplatin at high concentrations. A model was proposed to qualitatively explain well these results., (© 2012 American Physical Society)

We study the nonlinear dynamics of a homogeneous DNA chain that is based on site-dependent finite stacking and pairing enthalpies. We introduce an extended nonlinear Schrödinger equation describing the dynamics of modulated wave in DNA model. We obtain envelope bright solitary waves with compact support as a solution. Analytical criteria of existence of this solution are derived. The stability of bright compactons is confirmed by numerical simulations of the exact equations of the lattice. The impact of the finite stacking energy is investigated, and we show that some of these compact bright solitary waves are robust, while others decompose very quickly depending on the finite stacking parameters., (© 2012 American Physical Society)

We study the mean turnaround time of a Brownian needle in a narrow planar strip. When the needle is only slightly shorter than the width of the strip, the computation becomes a nonstandard narrow escape problem. We develop a boundary layer method, based on a conformal mapping of cusplike narrow straits, to obtain an explicit asymptotic approximation to the mean turnaround time. Our result suggests that two-dimensional domains lying between parallel walls may play a significant role in DNA repair., (© 2012 American Physical Society)

Recent single-molecule experiments have observed that formation of a plectonemically supercoiled region in a stretched, twisted DNA proceeds via abrupt formation of a small plectonemic "bubble." A detailed mesoscopic model is presented for the formation of plectonemic domains, including their positional entropy, and the influence of small chiral loops or "curls" along the extended DNA. Curls begin to appear just before plectoneme formation, and are more numerous at low salt concentrations (<20 mM univalent ions) and at low forces (<0.5 pN). However, plectonemic domains quickly become far more stable slightly beyond the transition to supercoiling at moderate forces and physiological salt conditions. At the supercoiling transition, for shorter DNAs (2 kb) only one supercoiled domain appears, but for longer DNAs at lower forces (<0.5 pN) positional entropy favors formation of more than one plectonemic domain; a similar effect occurs for low salt. Although they are not the prevalent mode of supercoiling, curls are a natural transition state for binding of DNA-loop-trapping enzymes; we show how addition of loop-trapping enzymes can modify the supercoiling transition. The behavior of DNA torque is also discussed, including the effect of the measurement apparatus torque stiffness, which can play a role in determining how large the torque "overshoot" is at the buckling transition., (© 2012 American Physical Society)

We performed experiments and simulations to investigate the influence of hydrodynamic interaction on the diffusion dynamics of circular and linear λ-DNA confined in nanoslits. Contrary to the common assumption that intrachain hydrodynamic interaction (HI) is completely screened when polymers are confined in channels with height h smaller than the radius of gyration R(g), it is found that the HI is partially screened and approaches complete screening only for R(g)≪h. For λ-DNA, the HI becomes nearly completely screened only when the channel height is smaller than the Kuhn length. In addition, the dynamics of linear and circular λ-DNA in very strong confinement is shown to be independent of the chain topology.

Base pair opening in an inhomogeneous, DNA double helical molecular chain with flexible strands is investigated by studying its internal dynamics. For the study, a generalized model which takes into account the energies involved in stacking and hydrogen bonds along with inhomogeneity, helicity, and phonons coupled to the stacking and hydrogen bonds is proposed. The internal dynamics of the proposed DNA model is governed by a perturbed nonlinear Schrödinger equation. The unperturbed, completely integrable nonlinear Schrödinger equation which admits soliton solutions and forming a bubble corresponds to DNA dynamics with homogeneous and rigid strands. The results of the soliton perturbation analysis show that the inhomogeneity in stacking and hydrogen bonds in localized and periodic forms and the helicity do not alter the amplitude under perturbation. However, the flexibility of the strands diminishes the perturbed amplitude. On the other hand, the velocity of the soliton and bubble are unaltered due to all the above effects. However, the position and phase of the soliton and the bubble vary linearly in time. While the position of the soliton depends on the initial velocity, the phase depends on both the initial velocity and the initial amplitude of the soliton. The above effects introduce small fluctuation in the tail of the soliton, without affecting the robust nature of the soliton and the bubble during propagation. The soliton and the bubble obtained as solutions of the internal dynamics of the DNA molecule represent an opening of the base pairs which is essential for the transcription process.

We use a simple nonlinear scaler displacement model to calculate the distribution of effects created by a shear stress on a double-stranded DNA (dsDNA) molecule and the value of shear force F(c) that is required to separate the two strands of a molecule at a given temperature. It is shown that for molecules of base pairs fewer than than 21, the entire single strand moves in the direction of applied force, whereas for molecules having base pairs more than 21, part of the strand moves in the opposite direction under the influence of force acting on the other strand. This result as well as the calculated values of F(c) as a function of length of dsDNA molecules are in very good agreement with the experimental values of Hatch et al. [Phys. Rev. E 78, 011920 (2008)].

We show that the simple analytical model proposed by Zhang and Marko [Phys. Rev. E 77, 031916 (2008)] to illustrate Maxwell relations for single-DNA experiments can be improved by including the zero-force entropy of a Gaussian chain. The resulting model is in excellent agreement with the discrete persistent-chain model and is in a form convenient for analyzing experimental data.

Using the Langevin dynamics simulation, we have studied the effects of shear force on the rupture of short double-stranded DNA at different temperatures. We show that the rupture force increases linearly with chain length and approaches the asymptotic value in accordance with the experiment. The qualitative nature of these curves remains almost the same for different temperatures but with a shift in the force. We observe three different regimes in the extension of covalent bonds (backbone) under shear force.

The theory of DNA dynamics is exceedingly complex and not easily explained. In the past two decades, by adapting methods of statistical physics, the dynamics of DNA in contact with a thermal bath is widely studied. In this paper, the thermal denaturation of DNA in the framework of the Peyrard-Bishop-Dauxois (PBD) model through the Rényi dimension is investigated. As a result, the Rényi dimension spectrum of the melting transition process reveals the multifractal nature of the dynamics of the Peyrard-Bishop-Dauxois model. Also, it can be concluded that the Rényi dimension (D(q)) at negative values of q is the characteristic signature of pre-melting and thermal denaturation of DNA. Furthermore, this approach is in excellent agreement with previous experimental studies.

It is known that for a particle held in an optical trap the interaction of thermal fluctuations with a nonconservative scattering force can cause a persistent nonequilibrium probability flux in the particle position. We investigate position fluctuations associated with this nonequilibrium flux analytically and through simulation. We introduce a model which reproduces the nonequilibrium effects, and in which the magnitude of additional position fluctuations can be calculated in closed form. The ratio of additional nonconservative fluctuations to direct thermal fluctuations scales inversely with the square root of trap power, and is small for typical experimental parameters. In a simulated biophysical experiment the nonconservative scattering force does not significantly increase the observed fluctuations in the length of a double-stranded DNA tether.

We quantified the Manning free (uncondensed) counterions fraction θ for dilute aqueous solutions of rodlike polyions: 150 bp DNA fragments, in the presence of a very low concentration of monovalent salt c(salt)<0.05 mM. Conductivity measurements of these solutions for DNA base pair concentration range 0.015≤c≤8 mM were complemented by fluorescence correlation spectroscopy (FCS) measurements of the DNA polyion diffusion coefficient D(p)(c). We observed a crossover in the normalized conductivity σ(c)/c that nearly halved across the c=0.05-1 mM range, while D(p)(c) remained rather constant, as we established by FCS. Analyzing these data we extracted θ(c)=0.30-0.45, and taking the Manning asymmetry field effect on polyelectrolyte conductivity into account we got θ(c)=0.40-0.60. We relate the θ(c) variation to gradual DNA denaturation occurring, in the very low salt environment, with the decrease in DNA concentration itself. The extremes of the experimental θ(c) range occur toward the highest, above 1 mM, and the lowest, below 0.05 mM, DNA concentrations and correspond to the theoretical θ values for dsDNA and ssDNA, respectively. Therefore, we confirmed Manning condensation and conductivity models to be valuable in description of dilute solutions of rodlike polyions., (©2011 American Physical Society)

Twisting DNA under a constant applied force reveals a thermally activated transition into a state with a supercoiled structure known as a plectoneme. Using transition-state theory, we predict the rate of this plectoneme nucleation to be of order 10(4) Hz. We reconcile this with experiments that have measured hopping rates of order 10 Hz by noting that the viscous drag on the bead used to manipulate the DNA limits the measured rate. We find that the intrinsic bending caused by disorder in the base-pair sequence is important for understanding the free-energy barrier that governs the transition. Both analytic and numerical methods are used in the calculations. We provide extensive details on the numerical methods for simulating the elastic rod model with and without disorder., (©2011 American Physical Society)

We describe and solve a discrete persistent-chain model of protein binding on DNA, involving an extra σ(i) at a site i of the DNA. This variable takes the value 1 or 0, depending on whether or not the site is occupied by a protein. In addition, if the site is occupied by a protein, there is an extra energy cost ɛ. For a small force, we obtain analytic expressions for the force-extension curve and the fraction of bound protein on the DNA. For higher forces, the model can be solved numerically to obtain force-extension curves and the average fraction of bound proteins as a function of applied force. Our model can be used to analyze experimental force-extension curves of protein binding on DNA, and hence deduce the number of bound proteins in the case of nonspecific binding., (©2011 American Physical Society)

Collective response of DNA to terahertz electric fields is studied in a simple pair bond model. We confirm, with some caveats, a previous observation of destabilizing DNA breather modes and explore the parameter dependence of these modes. It is shown that breather modes are eliminated under reasonable physical conditions and that thermal effects are significant., (©2011 American Physical Society)

We find a parametric resonance in the gigahertz range of DNA dynamics, generated by pumping hypersound. The resonance may be accompanied by the formation of localized phonon modes due to the random structure of elastic modulii of DNA.

Using Monte Carlo simulations, we deconvolved the sliding and hopping kinetics of GFP-LacI proteins on elongated DNA from their experimentally observed seconds-long diffusion trajectories. Our simulations suggest the following results: (i) in each diffusion trajectory, a protein makes on average hundreds of alternating slides and hops with a mean sliding time of several tens of milliseconds; (ii) sliding dominates the root-mean-square displacement of fast diffusion trajectories, whereas hopping dominates slow ones; (iii) flow and variations in salt concentration have limited effects on hopping kinetics, while in vivo DNA configuration is not expected to influence sliding kinetics; and (iv) the rate of occurrence for hops longer than 200 nm agrees with experimental data for EcoRV proteins.

Recent experiments [J. van Mameren, Proc. Natl. Acad. Sci. U.S.A. 106, 18231 (2009)] provide a detailed spatial picture of overstretched DNA, showing that under certain conditions the two strands of the double helix separate at about 65 pN. It was proposed that this observation rules out the existence of an elongated, hybridized form of DNA (S-DNA). Here, we argue that the S-DNA picture is consistent with the observation of unpeeling during overstretching. We demonstrate that assuming the existence of S-DNA does not imply DNA overstretching to consist of the complete or near-complete conversion of the molecule from B to S form. Instead, this assumption implies in general a more complex dynamic coexistence of hybridized and unhybridized forms of DNA. We argue that such coexistence can rationalize several recent experimental observations.

DNA-coated colloids are a popular model system for self-assembly through tunable interactions. The DNA-encoded linkages between particles theoretically allow for very high specificity, but generally no directionality or long-range interactions. We introduce a two-dimensional lattice model for particles of many different types with short-range isotropic interactions that are pairwise specific. For this class of models, of which the DNA-coated colloids are one example, we address the fundamental question whether it is possible to reliably design the interactions so that the ground state is unique and corresponds to a given crystal structure. First, we determine lower limits for the interaction range between particles, depending on the complexity of the desired pattern and the underlying lattice. Then, we introduce a proof-of-principle "recipe" for determining the pairwise interactions that exactly satisfies this minimum criterion, and we show that it is sufficient to uniquely determine the ground state for a large class of crystal structures. Finally, we verify these results using Monte Carlo simulations.

We study the structural transition from B form of DNA to A form of DNA using group theoretic methods. The transition is not of the order-disorder type and hence to construct a Landau kind of theory for the transition we define a higher symmetry and relevant order parameters. We also discuss the issue of all the conformations, observed experimentally during the course of transition, being fundamentally different or not.

To rationalize the disentangling action of type II topoisomerases, an improved wormlike DNA model was used to delineate the degree of unknotting and decatenating achievable by selective segment passage at specific juxtaposition geometries and to determine how these activities were affected by DNA circle size and solution ionic strength. We found that segment passage at hooked geometries can reduce knot populations as dramatically as seen in experiments. Selective segment passage also provided theoretical underpinning for an intriguing empirical scaling relation between unknotting and decatenating potentials.

The protein-DNA interaction dynamics is studied by modeling the DNA bases as classical spins in a coupled spin system, which are bosonized and coupled to thermal phonons and longitudinal motion of the protein molecule in the nonviscous limit. The nonlinear dynamics of this protein-DNA complex molecular system is governed by the completely integrable nonlinear Schrödinger (NLS) equation which admits N -soliton solutions. The soliton excitations of the DNA bases in the two strands make localized base-pair opening and travel along the DNA chain in the form of a bubble. This may characterize the bubble generated during the transcription process, when an RNA polymerase binds to a promoter site in the DNA double helical chain. When the protein-DNA molecular system interacts with the surrounding viscous solvating water medium, the dynamics is governed by a perturbed NLS equation. This equation is solved using a multiple scale perturbation analysis, by treating the viscous effect as a weak perturbation, and the results show that the viscosity of the solvent medium damps out the soliton as time progresses.

We present experimental measurements of the equilibrium elastic energy of protein-DNA chimeras, for two different sets of attachment points of the DNA "molecular spring" on the surface of the protein. Combining these with measurements of the enzyme's activity under stress and a mechanical model of the system, we determine how the elastic energy is partitioned between the DNA and the protein. The analysis shows that the protein is mechanically stiffer than the DNA spring.

Molecular-dynamics simulations of a normal DNA duplex show that breathing events typically occur on the microsecond time scale. This paper analyzes a 12 base pairs DNA duplex containing the "rogue" base difluorotoluene (F) in place of a thymine base (T), for which the breathing events occur on the nanosecond time scale. Starting from a nonlinear Klein-Gordon lattice model and adding noise and damping, we obtain a mesoscopic model of the DNA duplex close to that observed in experiments and all-atom molecular dynamics simulations. The mesoscopic model is calibrated to data from the all-atom molecular dynamics package AMBER for a variety of twist angles of the DNA duplex. Defects are considered in the interchain interactions as well as in the along-chain interactions. This paper also discusses the role of the fluctuation-dissipation relations in the derivation of reduced (mesoscopic) models, the differences between the potential of mean force and the potential energies used in Klein-Gordon lattices, and how breathing can be viewed as competition between the along-chain elastic energy and the interchain binding energy.

We study the effects of intrinsic sequence-dependent curvature for a two-dimensional semiflexible biopolymer with short-range correlation in intrinsic curvatures. We show exactly that when not subjected to any external force, such a system is equivalent to a system with a well-defined intrinsic curvature and a proper renormalized persistence length. We find the exact expression for the distribution function of the equivalent system. However, we show that such an equivalent system does not always exist for the polymer subjected to an external force. We find that under an external force, the effect of sequence disorder depends upon the averaging order, the degree of disorder, and the experimental conditions, such as the boundary conditions. Furthermore, a short to moderate length biopolymer may be much softer or has a smaller apparent persistent length than what would be expected from the "equivalent system." Moreover, under a strong stretching force and for a long biopolymer, the sequence disorder is immaterial for elasticity. Finally, the effect of sequence disorder may depend upon the quantity considered.

We discuss a class of generalized wormlike chain models of polymers with spontaneous curvature and show that the density of states and consequently the entropy of such natively bent polymers are higher than that of straight ones. This effect changes the classical Langmuir binding isotherm by giving rise to enhanced binding of DNA-bending proteins.