Literature data on the properties of DNA open states are reviewed and analyzed. These states are formed as a result of strong DNA fluctuations and have a great impact on a number of biochemical processes; among them is charge transfer in DNA, for example. A comparative analysis of experimental data on the kinetics and thermodynamics of DNA open states for a wide temperature range was carried out. Discrepancies between the results of various experiments have been explained. Three types of DNA open states are recognized based on their differences in thermodynamic properties and other characteristics. Besides, an up-to-date definition of the term "open state" is given. A review is carried out for simple mathematical models of DNA in most of which the state of one pair is described by one or two variables. The main problems arising in theoretical investigations of heterogeneous DNA in the framework of models of this level are considered. The role of each group of models in interpretation of experimental data is discussed. Special consideration is given to the studies of the transfer and localization of the nucleotide pairs oscillations' energy by mechanical models. These processes are shown to play a key role in the dynamics of a heterogeneous duplex. Their theoretical interpretation is proven to be very important for the development of modern molecular biology and biophysics. The main features of the theoretical approaches are considered which enabled describing various experimental data. Prospects of the models' development are described, particular details of their optimization are suggested, and possible ways of modernization of some experimental techniques are discussed.
We characterize the equation of state for a simple three-dimensional DNA hairpin model using a Metropolis Monte Carlo algorithm. This algorithm was run at constant temperature and fixed separation between the terminal ends of the strand. From the equation of state, we compute the compressibility, thermal expansion coefficient, and specific heat along with adiabatic path.
The stability and dynamics of a double-stranded DNA (dsDNA) is affected by the preferential occupancy of small monovalent molecular ions. Small metal and molecular ions such as sodium and alkyl ammonium have crucial biological functions in human body, affect the thermodynamic stability of the duplex DNA and exhibit preferential binding. Here, using atomistic molecular dynamics simulations we investigate the preferential binding of metal ion such as Na+ and molecular ions such as tetramethyl ammonium (TMA+) and 2-hydroxy-N,N,N-trimethylethanaminium (CHO+) to double stranded DNA. The thermodynam…
Using theory and simulations, we carried out a first systematic characterization of DNA unzipping via nanopore translocation. Starting from partially unzipped states, we found three dynamical regimes depending on the applied force, f: (i) heterogeneous DNA retraction and rezipping (f < 17pN), (ii) normal (17pN < f < 60pN) and (iii) anomalous (f > 60pN) drift-diffusive behavior. We show that the normal drift-diffusion regime can be effectively modelled as a one-dimensional stochastic process in a tilted periodic potential. We use the theory of stochastic processes to recover the potential from …
The force induced unzipping transition of a double stranded DNA is considered from a purely thermodynamic point of view. This analysis provides us with a set of relations that can be used to test microscopic theories and experiments. The thermodynamic approach is based on the hypothesis of impenetrability of the force in the zipped state. The melting and the unzipping transitions are considered in the same framework and compared with the existing statistical model results. The analysis is then extended to a possible continuous unzipping transition.
Overstretching of B-DNA is currently understood as force-induced melting. Depending on the geometry of the stretching experiment, the force threshold for the overstretching transition is around 65 or 110 pN. Although the mechanisms behind force-induced melting have been correctly described by Rouzina and Bloomfield \cite{RouzinaBloomfield2001a}, neither force threshold has been exactly calculated by theory. In this work, a detailed analysis of the force-extension curve is presented, based on a description of single-stranded DNA in terms of the discrete Kratky-Porod model, consistent with (i) t…
The imaginary time path integral formalism is applied to a nonlinear Hamiltonian for a short fragment of heterogeneous DNA with a stabilizing solvent interaction term. Torsional effects are modeled by a twist angle between neighboring base pairs stacked along the molecule backbone. The base pair displacements are described by an ensemble of temperature dependent paths thus incorporating those fluctuational effects which shape the multisteps thermal denaturation. By summing over $\sim 10^7 - 10^8$ base pair paths, a large number of double helix configurations is taken into account consistently …
Test experiments of hybridization in DNA microarrays show systematic deviations from the equilibrium isotherms. We argue that these deviations are due to the presence of a partially hybridized long-lived state, which we include in a kinetic model. Experiments confirm the model predictions for the intensity vs. free energy behavior. The existence of slow relaxation phenomena has important consequences for the specificity of microarrays as devices for the detection of a target sequence from a complex mixture of nucleic acids.
We explore in detail the structural, mechanical and thermodynamic properties of a coarse-grained model of DNA similar to that introduced in Thomas E. Ouldridge, Ard A. Louis, Jonathan P.K. Doye, Phys. Rev. Lett. 104 178101 (2010). Effective interactions are used to represent chain connectivity, excluded volume, base stacking and hydrogen bonding, naturally reproducing a range of DNA behaviour. We quantify the relation to experiment of the thermodynamics of single-stranded stacking, duplex hybridization and hairpin formation, as well as structural properties such as the persistence length of si…
We introduce a sequence-dependent parametrization for a coarse-grained DNA model [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, J. Chem. Phys. 134, 085101 (2011)] originally designed to reproduce the properties of DNA molecules with average sequences. The new parametrization introduces sequence-dependent stacking and base-pairing interaction strengths chosen to reproduce the melting temperatures of short duplexes. By developing a histogram reweighting technique, we are able to fit our parameters to the melting temperatures of thousands of sequences. To demonstrate the flexibility of the mod…
DNA bending is biologically important for genome regulation and is relevant to a range of nanotechnological systems. Recent results suggest that sharp bending is much easier than implied by the widely-used worm-like chain model; many of these studies, however, remain controversial. We use a coarse-grained model, previously fitted to DNA's basic thermodynamic and mechanical properties, to explore strongly bent systems. We find that as the end-to-end distance is decreased sufficiently short duplexes undergo a transition to a state in which the bending strain is localized at a flexible kink that …
I present a Hamiltonian model and a computational method suitable to evaluate structural and thermodynamic properties of helical molecules embedded in crowded environments which may confine the space available to the base pair fluctuations. It is shown that, for the specific case of a short DNA fragment in a nanochannel, the molecule is markedly over-twisted and stretched by narrowing the width of the channel.
The objective of the present study was to develop an understanding of short single-stranded DNA (ssDNA) to assist the development of new DNA-based biosensors. A ssDNA model containing twelve bases was constructed from the 130-145 codon sequence of the p53 gene. Various thermodynamic macroscopic observables such as temperature, energy distributions, as well as root mean square deviation (RMSD) of the nucleic acid backbone of the ssDNA were studied using molecular dynamics (MD) simulations. The AMBER program was used for building the structural model of the ssDNA, and atomistic MD simulations in…
DNA nanotechnology promises to provide controllable self-assembly on the nanoscale, allowing for the design of static structures, dynamic machines and computational architectures. In this article I review the state-of-the art of DNA nanotechnology, highlighting the need for a more detailed understanding of the key processes, both in terms of theoretical modelling and experimental characterisation. I then consider coarse-grained models of DNA, mesoscale descriptions that have the potential to provide great insight into the operation of DNA nanotechnology if they are well designed. In particular…
We introduce an extended version of oxDNA, a coarse-grained model of DNA designed to capture the thermodynamic, structural and mechanical properties of single- and double-stranded DNA. By including explicit major and minor grooves, and by slightly modifying the coaxial stacking and backbone-backbone interactions, we improve the ability of the model to treat large (kilobase-pair) structures such as DNA origami which are sensitive to these geometric features. Further, we extend the model, which was previously parameterised to just one salt concentration ([Na$^+$]=0.5M), so that it can be used fo…
Under supercoiling constraints, naked DNA, such as a large part of bacterial DNA, folds into braided structures called plectonemes. The double-helix can also undergo local structural transitions, leading to the formation of denaturation bubbles and other alternative structures. Various polymer models have been developed to capture these properties, with Monte-Carlo (MC) approaches dedicated to the inference of thermodynamic properties. In this chapter, we explain how to perform such Monte-Carlo simulations, following two objectives. On one hand, we present the self-avoiding supercoiled Worm-Li…
The capture and translocation of biomolecules through nanometer-scale pores are processes with a potential large number of applications, and hence they have been intensively studied in the recent years. The aim of this paper is to review existing models of the capture process by a nanopore, together with some recent experimental data of short single- and double-stranded DNA captured by Cytolysin A (ClyA) nanopore. ClyA is a transmembrane protein of bacterial origin which has been recently engineered through site-specific mutations, to allow the translocation of double- and single-stranded DNA.…
The thermodynamic properties of DNA circular molecules are investigated by a new path integral computational method which treats in the real space the fundamental forces stabilizing the molecule. The base pair and stacking contributions to the classical action are evaluated separately by simulating a broad ensemble of twisted conformations. We obtain, for two short sequences, a free energy landscape with multiple wells corresponding to the most convenient values of helical repeat. Our results point to a intrinsic flexibility of the circular structures in which the base pair fluctuations move t…
DNA supercoiling, the under or overwinding of DNA, is a key physical mechanism both participating to compaction of bacterial genomes and making genomic sequences adopt various structural forms. DNA supercoiling may lead to the formation of braided superstructures (plectonemes), or it may locally destabilize canonical B-DNA to generate denaturation bubbles, left-handed Z-DNA and other functional alternative forms. Prediction of the relative fraction of these structures has been limited because of a lack of predictive polymer models that can capture the multiscale properties of long DNA molecule…
Organization and maintenance of the chromosomal DNA in living cells strongly depends on the DNA interactions with a plethora of DNA-binding proteins. Single-molecule studies show that formation of nucleoprotein complexes on DNA by such proteins is frequently subject to force and torque constraints applied to the DNA. Although the existing experimental techniques allow to exert these type of mechanical constraints on individual DNA biopolymers, their exact effects in regulation of DNA-protein interactions are still not completely understood due to the lack of systematic theoretical methods able…
