Mesoscopic modeling for nucleic acid chain dynamics

Models and simulations of structural DNA nanotechnology reveal fundamental principles of self-assembly

DNA is not only a centrally important molecule in biology: the specificity of bonding that allows it to be the primary information storage medium for life has also allowed it to become one of the most promising materials for designing intricate, self-assembling structures at the nanoscale. While the applications of these structures are both broad and highly promising, the self-assembly process itself has attracted interest not only for the practical applications of designing structures with more efficient assembly pathways, but also due to a desire to understand the principles underlying self-assembling systems more generally, of which DNA-based systems provide intriguing and unique examples. Here, we review the fundamental physical principles that underpin the self-assembly process in the field of DNA nanotechnology, with a specific focus on simulation and modelling and what we can learn from them. In particular, we compare and contrast DNA origami and bricks and briefly outline other approaches, with an overview of concepts such as cooperativity, nucleation and hysteresis; we also explain how nucleation barriers can be controlled and why they can be helpful in ensuring error-free assembly. While high-resolution models may be needed to obtain accurate system-specific properties, often very simple coarse-grained models are sufficient to extract the fundamentals of the underlying physics and can enable us to gain deep insight. By combining experimental and simulation approaches to understand the details of the self-assembly process, we can optimise its yields and fidelity, which may in turn facilitate its use in practical applications.

Structure, stability and specificity of the binding of ssDNA and ssRNA with proteins

Recognition of single-stranded DNA (ssDNA) or single-stranded RNA (ssRNA) is important for many fundamental cellular functions. A variety of single-stranded DNA-binding proteins (ssDBPs) and single-stranded RNA-binding proteins (ssRBPs) have evolved that bind ssDNA and ssRNA, respectively, with varying degree of affinities and specificities to form complexes. Structural studies of these complexes provide key insights into their recognition mechanism. However, computational modeling of the specific recognition process and to predict the structure of the complex is challenging, primarily due to the heterogeneity of their binding energy landscape and the greater flexibility of ssDNA or ssRNA compared with double-stranded nucleic acids. Consequently, considerably fewer computational studies have explored interactions between proteins and single-stranded nucleic acids compared with protein interactions with double-stranded nucleic acids. Here, we report a newly developed energy-based coarse-grained model to predict the structure of ssDNA–ssDBP and ssRNA–ssRBP complexes and to assess their sequence-specific interactions and stabilities. We tuned two factors that can modulate specific recognition: base–aromatic stacking strength and the flexibility of the single-stranded nucleic acid. The model was successfully applied to predict the binding conformations of 12 distinct ssDBP and ssRBP structures with their cognate ssDNA and ssRNA partners having various sequences. Estimated binding energies agreed well with the corresponding experimental binding affinities. Bound conformations from the simulation showed a funnel-shaped binding energy distribution where the native-like conformations corresponded to the energy minima. The various ssDNA–protein and ssRNA–protein complexes differed in the balance of electrostatic and aromatic energies. The lower affinity of the ssRNA–ssRBP complexes compared with the ssDNA–ssDBP complexes stems from lower flexibility of ssRNA compared to ssDNA, which results in higher rate constants for the dissociation of the complex (k_off) for complexes involving the former.

Quantifying bimolecular self-assembly is pivotal to understanding cellular function. In recent years, a large progress has been made in understanding the structure and biophysics of protein-protein interactions. Particularly, various computational tools are available for predicting these structures and to estimate their stability and the driving forces of their formation. The understating of the interactions between proteins and nucleic acids, however, is still limited, presumably due to the involvement of non-specific interactions as well as the high conformational plasticity that may demand an induced-fit mechanism. In particular, the interactions between proteins and single-stranded nucleic acids (i.e., single-stranded DNA and RNA) is very challenging due to their high flexibility. Furthermore, the interface between proteins and single-stranded nucleic acids is often chemically more heterogeneous than the interface between proteins and double-stranded DNA. In this study, we developed a coarse-grained computational model to predict the structure of complexes between proteins and single-stranded nucleic acids. The model was applied to estimate binding affinities and the estimated binding energies agreed well with the corresponding experimental binding affinities. The kinetics of association as well as the specificity of the complexes between proteins and ssDNA are different than those with ssRNA, mostly due to differences in their conformational flexibility.

Calculation of π and Classification of Self-avoiding Lattices via DNA Configuration

Numerical simulation (e.g. Monte Carlo simulation) is an efficient computational algorithm establishing an integral part in science to understand complex physical and biological phenomena related with stochastic problems. Aside from the typical numerical simulation applications, studies calculating numerical constants in mathematics, and estimation of growth behavior via a non-conventional self-assembly in connection with DNA nanotechnology, open a novel perspective to DNA related to computational physics. Here, a method to calculate the numerical value of π, and way to evaluate possible paths of self-avoiding walk with the aid of Monte Carlo simulation, are addressed. Additionally, experimentally obtained variation of the π as functions of DNA concentration and the total number of trials, and the behaviour of self-avoiding random DNA lattice growth evaluated through number of growth steps, are discussed. From observing experimental calculations of π (π_exp) obtained by double crossover DNA lattices and DNA rings, fluctuation of π_exp tends to decrease as either DNA concentration or the number of trials increases. Based upon experimental data of self-avoiding random lattices grown by the three-point star DNA motifs, various lattice configurations are examined and analyzed. This new kind of study inculcates a novel perspective for DNA nanostructures related to computational physics and provides clues to solve analytically intractable problems.

Structurally detailed coarse-grained model for Sec-facilitated co-translational protein translocation and membrane integration

We present a coarse-grained simulation model that is capable of simulating the minute-timescale dynamics of protein translocation and membrane integration via the Sec translocon, while retaining sufficient chemical and structural detail to capture many of the sequence-specific interactions that drive these processes. The model includes accurate geometric representations of the ribosome and Sec translocon, obtained directly from experimental structures, and interactions parameterized from nearly 200 μs of residue-based coarse-grained molecular dynamics simulations. A protocol for mapping amino-acid sequences to coarse-grained beads enables the direct simulation of trajectories for the co-translational insertion of arbitrary polypeptide sequences into the Sec translocon. The model reproduces experimentally observed features of membrane protein integration, including the efficiency with which polypeptide domains integrate into the membrane, the variation in integration efficiency upon single amino-acid mutations, and the orientation of transmembrane domains. The central advantage of the model is that it connects sequence-level protein features to biological observables and timescales, enabling direct simulation for the mechanistic analysis of co-translational integration and for the engineering of membrane proteins with enhanced membrane integration efficiency.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Coarse-graining DNA for simulations of DNA nanotechnology

To simulate long time and length scale processes involving DNA it is necessary to use a coarse-grained description. Here we provide an overview of different approaches to such coarse-graining, focussing on those at the nucleotide level that allow the self-assembly processes associated with DNA nanotechnology to be studied. OxDNA, our recently-developed coarse-grained DNA model, is particularly suited to this task, and has opened up this field to systematic study by simulations. We illustrate some of the range of DNA nanotechnology systems to which the model is being applied, as well as the insights it can provide into fundamental biophysical properties of DNA.

A coarse-grained model for DNA-functionalized spherical colloids, revisited: effective pair potential from parallel replica simulations

We discuss a coarse-grained model recently proposed by Starr and Sciortino [J. Phys.: Condens. Matter 18, L347 (2006)] for spherical particles functionalized with short single DNA strands. The model incorporates two key aspects of DNA hybridization, i.e., the specificity of binding between DNA bases and the strong directionality of hydrogen bonds. Here, we calculate the effective potential between two DNA-functionalized particles of equal size using a parallel replica protocol. We find that the transition from bonded to unbonded configurations takes place at considerably lower temperatures compared to those that were originally predicted using standard simulations in the canonical ensemble. We put particular focus on DNA-decorations of tetrahedral and octahedral symmetry, as they are promising candidates for the self-assembly into a single-component diamond structure. Increasing colloid size hinders hybridization of the DNA strands, in agreement with experimental findings.

Monte Carlo simulations of a polymer chain conformation. The effectiveness of local moves algorithms and estimation of entropy

A linear chain on a simple cubic lattice was simulated by the Metropolis Monte Carlo method using a combination of local and non-local chain modifications. Kink-jump, crankshaft, reptation and end-segment moves were used for local changes of the chain conformation, while for non-local chain rearrangements the "cut-and-paste" algorithm was employed. The statistics of local micromodifications was examined. An approximate method for estimating the conformational entropy of a polymer chain, based on the efficiency of the kink-jump motion respecting chain continuity and excluded volume constraints, was proposed. The method was tested by calculating the conformational entropy of the undisturbed chain, the chain under tension and in different solvent conditions (athermal, theta and poor) and also of the chain confined in a slit. The results of these test calculations are qualitatively consistent with expectations. Moreover, the obtained values of the conformational entropy of self avoiding chain with ends fixed over different separations, agree very well with the available literature data.

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Moving beyond Watson-Crick models of coarse grained DNA dynamics

DNA produces a wide range of structures in addition to the canonical B-form of double-stranded DNA. Some of these structures are stabilized by Hoogsteen bonds. We developed an experimentally parameterized, coarse-grained model that incorporates such bonds. The model reproduces many of the microscopic features of double-stranded DNA and captures the experimental melting curves for a number of short DNA hairpins, even when the open state forms complicated secondary structures. We demonstrate the utility of the model by simulating the folding of a thrombin aptamer, which contains G-quartets, and strand invasion during triplex formation. Our results highlight the importance of including Hoogsteen bonding in coarse-grained models of DNA.

Lattice model of oligonucleotide hybridization in solution. I. Model and thermodynamics

A coarse-grained lattice model of DNA oligonucleotides is proposed to investigate the general mechanisms by which single-stranded oligonucleotides hybridize to their complementary strands in solution. The model, based on a high-coordination cubic lattice, is simple enough to allow the direct simulation of DNA solutions, yet capturing how the fundamental thermodynamic processes are microscopically encoded in the nucleobase sequences. Physically relevant interactions are considered explicitly, such as interchain excluded volume, anisotropic base-pairing and base-stacking, and single-stranded bending rigidity. The model is studied in detail by a specially adapted Monte Carlo simulation method, based on parallel tempering and biased trials, which is designed to overcome the entropic and enthalpic barriers associated with the sampling of hybridization events of multiple single-stranded chains in solution. This methodology addresses both the configurational complexity of bringing together two complementary strands in a favorable orientation (entropic barrier) and the energetic penalty of breaking apart multiple associated bases in a double-stranded state (enthalpic barrier). For strands with sequences restricted to nonstaggering association and homogeneous pairing and stacking energies, base-pairing is found to dominate the hybridization over the translational and conformational entropy. For strands with sequence-dependent pairing corresponding to that of DNA, the complex dependence of the model's thermal stability on concentration, sequence, and degree of complementarity is shown to be qualitatively and quantitatively consistent both with experiment and with the predictions of statistical mechanical models.

Heat conductivity of DNA double helix

Thermal conductivity of isolated single molecule DNA fragments is of importance for nanotechnology, but has not yet been measured experimentally. Theoretical estimates based on simplified (1D) models predict anomalously high thermal conductivity. To investigate thermal properties of single molecule DNA we have developed a 3D coarse-grained (CG) model that retains the realism of the full all-atom description, but is significantly more efficient. Within the proposed model each nucleotide is represented by 6 particles or grains; the grains interact via effective potentials inferred from classical molecular dynamics (MD) trajectories based on a well-established all-atom potential function. Comparisons of 10 ns long MD trajectories between the CG and the corresponding all-atom model show similar root-mean-square deviations from the canonical B-form DNA, and similar structural fluctuations. At the same time, the CG model is 10 to 100 times faster depending on the length of the DNA fragment in the simulation. Analysis of dispersion curves derived from the CG model yields longitudinal sound velocity and torsional stiffness in close agreement with existing experiments. The computational efficiency of the CG model makes it possible to calculate thermal conductivity of a single DNA molecule not yet available experimentally. For a uniform (polyG-polyC) DNA, the estimated conductivity coefficient is 0.3 W/mK which is half the value of thermal conductivity for water. This result is in stark contrast with estimates of thermal conductivity for simplified, effectively 1D chains ("beads on a spring") that predict anomalous (infinite) thermal conductivity. Thus, full 3D character of DNA double-helix retained in the proposed model appears to be essential for describing its thermal properties at a single molecule level.

Structural, mechanical, and thermodynamic properties of a coarse-grained DNA model

We explore in detail the structural, mechanical, and thermodynamic properties of a coarse-grained model of DNA similar to that recently introduced in a study of DNA nanotweezers [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, Phys. Rev. Lett. 134, 178101 (2010)]. Effective interactions are used to represent chain connectivity, excluded volume, base stacking, and hydrogen bonding, naturally reproducing a range of DNA behavior. The model incorporates the specificity of Watson-Crick base pairing, but otherwise neglects sequence dependence of interaction strengths, resulting in an "average base" description of DNA. 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 single strands and duplexes, and the elastic torsional and stretching moduli of double helices. We also explore the model's representation of more complex motifs involving dangling ends, bulged bases and internal loops, and the effect of stacking and fraying on the thermodynamics of the duplex formation transition.

Analysis of a DNA simulation model through hairpin melting experiments

We compare the predictions of a two-bead Brownian dynamics simulation model to melting experiments of DNA hairpins with complementary AT or GC stems and noninteracting loops in buffer A. This system emphasizes the role of stacking and hydrogen bonding energies, which are characteristics of DNA, rather than backbone bending, stiffness, and excluded volume interactions, which are generic characteristics of semiflexible polymers. By comparing high throughput data on the open-close transition of various DNA hairpins to the corresponding simulation data, we (1) establish a suitable metric to compare the simulations to experiments, (2) find a conversion between the simulation and experimental temperatures, and (3) point out several limitations of the model, including the lack of G-quartets and cross stacking effects. Our approach and experimental data can be used to validate similar coarse-grained simulation models.

DNA melting in slit pores: a reaction density functional theory

A reaction density functional theory (R-DFT) is developed for chemical reactions in confined space by integrating reaction thermodynamics and DFT for chain fluids. The theory is applied to investigate DNA melting in slit pores, with nucleotides represented by coarse-grained charged Lennard-Jones particles. Three types of slit pores are considered for DNA melting: repulsive pore, attractive pore, and under electric field. In repulsive pores, the melting temperature increases slightly with reducing pore width, and the increase magnitude is nearly the same for DNA of different chain lengths. The double-strand DNA (dsDNA) and single-strand DNA (ssDNA) are located in the slit center, particularly for long DNA due to the effect of configuration entropy. In attractive pores, the melting temperature increases with increasing wall-fluid interaction. The DNA chains are preferentially adsorbed near the slit walls with a strong wall-fluid interaction. Under electric field, the melting temperature increases slightly and is more distinct for shorter DNA.

Molecular thermodynamic model for DNA melting in ionic and crowded solutions

A molecular thermodynamic model is developed to predict DNA melting in ionic and crowded solutions. Each pair of nucleotides in the double-stranded DNA and each nucleotide in the single-stranded DNA are respectively represented by two types of charged Lennard-Jones spheres. The predicted melting curves and melting temperatures T(m) of the model capture the general feature of DNA melting and match fairly well with the available simulation and experimental results. It is found that the melting curve is steeper and T(m) is higher for DNA with a longer chain. With increasing the fraction of the complementary cytosine-guanine (CG) base pairs, T(m) increases almost linearly as a consequence of the stronger hydrogen bonding of the CG base pair than that of adenine-thymine (AT) base pair. At a greater ionic concentration, T(m) is higher due to the shielding effect of counterions on DNA strands. It is observed that T(m) increases in the presence of crowder because the crowder molecules occupy a substantial amount of system volume and suppress the entropy increase for DNA melting. At a given concentration, a larger crowder exhibits a greater suppression for DNA melting and hence a higher T(m). At the same packing fraction, however, a smaller crowder leads to a higher T(m).

Prediction of RNA multiloop and pseudoknot conformations from a lattice-based, coarse-grain tertiary structure model

We present a semiquantitative lattice model of RNA folding, which is able to reproduce complex folded structures such as multiloops and pseudoknots without relying on the frequently employed ad hoc generalization of the Jacobson-Stockmayer loop entropy. We derive the model parameters from the Turner description of simple secondary structural elements and pay particular attention to the unification of mismatch and coaxial stacking parameters as well as of border and nonlocal loop parameters, resulting in a reduced, unified parameter set for simple loops of arbitrary type and size. For elementary structures, the predictive power of the model is comparable to the standard secondary structure approaches, from which its parameters are derived. For complex structures, our approach offers a systematic treatment of generic effects of chain connectivity as well as of excluded volume or attractive interactions between and within all elements of the secondary structure. We reproduce the native structures of tRNA multiloops and of viral frameshift signal pseudoknots.

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.

DNA nanotweezers studied with a coarse-grained model of DNA

We introduce a coarse-grained rigid nucleotide model of DNA that reproduces the basic thermodynamics of short strands, duplex hybridization, single-stranded stacking, and hairpin formation, and also captures the essential structural properties of DNA: the helical pitch, persistence length, and torsional stiffness of double-stranded molecules, as well as the comparative flexibility of unstacked single strands. We apply the model to calculate the detailed free-energy landscape of one full cycle of DNA "tweezers," a simple machine driven by hybridization and strand displacement.

Coarse-Grained Brownian Dynamics Simulations of the 10-23 DNAzyme

Deoxyribozymes (DNAzymes) are single-stranded DNA that catalyze nucleic acid biochemistry. Although a number of DNAzymes have been discovered by in vitro selection, the relationship between their tertiary structure and function remains unknown. We focus here on the well-studied 10-23 DNAzyme, which cleaves mRNA with a catalytic efficiency approaching that of RNase A. Using coarse-grained Brownian dynamics simulations, we find that the DNAzyme bends its substrate away from the cleavage point, exposing the reactive site and buckling the DNAzyme catalytic core. This hypothesized transition state provides microscopic insights into experimental observations concerning the size of the DNAzyme/substrate complex, the impact of the recognition arm length, and the sensitivity of the enzymatic activity to point mutations of the catalytic core. Upon cleaving the pertinent backbone bond in the substrate, we find that the catalytic core of the DNAzyme unwinds and the overall complex rapidly extends, in agreement with experiments on the related 8-17 DNAzyme. The results presented here provide a starting point for interpreting experimental data on DNAzyme kinetics, as well as developing more detailed simulation models. The results also demonstrate the limitations of using a simple physical model to understand the role of point mutations.

Brownian dynamics simulations of single-stranded DNA hairpins

We present a Brownian dynamics model which we use to study the kinetics and thermodynamics of single-stranded DNA hairpins, gaining insights into the role of stem mismatches and the kinetics rates underlying the melting transition. The model is a base-backbone type in which the DNA bases and sugar-phosphate backbone are represented as single units (beads) in the context of the Brownian dynamics simulations. We employ a minimal number of bead-bead interactions, leading to a simple computational scheme. To demonstrate the veracity of our model for DNA hairpins, we show that the model correctly captures the effects of base stacking, hydrogen bonding, and temperature on both the thermodynamics and the kinetics of hairpin formation and melting. When cast in dimensionless form, the thermodynamic results obtained from the present model compare favorably with default predictions of the m-fold server, although the present model is not sufficiently robust to provide dimensional results. The kinetic data at low temperatures indicate frequent but short-lived opening events, consistent with the measured chain end-to-end probability distribution. The model is also used to study the effect of base mismatches in the stem of the hairpin. With the parameters used here, the model overpredicts the relative shift in the melting temperature due to mismatches. The melting transition can be primarily attributed to a rapid increase in the hairpin opening rate rather than an equivalent decrease in the closing rate, in agreement with single-molecule experimental data.

The self-assembly of DNA Holliday junctions studied with a minimal model

In this paper, we explore the feasibility of using coarse-grained models to simulate the self-assembly of DNA nanostructures. We introduce a simple model of DNA where each nucleotide is represented by two interaction sites corresponding to the sugar-phosphate backbone and the base. Using this model, we are able to simulate the self-assembly of both DNA duplexes and Holliday junctions from single-stranded DNA. We find that assembly is most successful in the temperature window below the melting temperatures of the target structure and above the melting temperature of misbonded aggregates. Furthermore, in the case of the Holliday junction, we show how a hierarchical assembly mechanism reduces the possibility of becoming trapped in misbonded configurations. The model is also able to reproduce the relative melting temperatures of different structures accurately and allows strand displacement to occur.

DNA closed nanostructures: a structural and Monte Carlo simulation study

DNA nanoconstructs are obtained in solution by using six unique 42-mer DNA oligonucleotides, whose sequences have been designed to form a pseudohexagonal structure. The required flexibility is provided by the insertion of two non-base-paired thymines in the middle of each sequence that work as flexible hinges and constitute the corners of the nanostructure when formed. We show that hexagonally shaped nanostructures of about 7 nm diameter and their corresponding linear open constructs are formed by self-assembly of the specifically designed linear oligonucleotides. The structural and dynamical characterization of the nanostructure is obtained in situ for the first time by using dynamic light scattering (DLS), a noninvasive method that provides a fast dynamic and structural analysis and allows the characterization of the different synthetic DNA nanoconstructs in solution. A validation of the LS results is obtained through Monte Carlo (MC) simulations and atomic force microscopy (AFM). In particular, a mesoscale molecular model for DNA, developed by Knotts et al., is exploited to perform MC simulations and to obtain information about the conformations as well as the conformational flexibilities of these nanostructures, while AFM provides a very detailed particle analysis that yields an estimation of the particle size and size distribution. The structural features obtained by MC and AFM are in good agreement with DLS, showing that DLS is a fast and reliable tool for characterization of DNA nanostructures in solution.

A mesoscale model of DNA and its renaturation

A mesoscale model of DNA is presented (3SPN.1), extending the scheme previously developed by our group. Each nucleotide is mapped onto three interaction sites. Solvent is accounted for implicitly through a medium-effective dielectric constant and electrostatic interactions are treated at the level of Debye-Hückel theory. The force field includes a weak, solvent-induced attraction, which helps mediate the renaturation of DNA. Model parameterization is accomplished through replica exchange molecular dynamics simulations of short oligonucleotide sequences over a range of composition and chain length. The model describes the melting temperature of DNA as a function of composition as well as ionic strength, and is consistent with heat capacity profiles from experiments. The dependence of persistence length on ionic strength is also captured by the force field. The proposed model is used to examine the renaturation of DNA. It is found that a typical renaturation event occurs through a nucleation step, whereby an interplay between repulsive electrostatic interactions and colloidal-like attractions allows the system to undergo a series of rearrangements before complete molecular reassociation occurs.

A breathing wormlike chain model on DNA denaturation and bubble: effects of stacking interactions

DNA stably exists as a double-stranded structure due to hydrogen-bonding and stacking interactions between bases. The stacking interactions are strengthened when DNA is paired, which results in great enhancement of bending rigidity. We study the effects of this stacking-induced stiffness difference on DNA denaturation and bubble formations. To this end, we model double-stranded DNA as a duplex of two semiflexible chains whose persistence length varies depending on the base-pair distance. Using this model, we perform the Langevin dynamics simulation to examine the characteristics of the denaturation transition and the statistics of the bubbles. We find that the inclusion of the stacking interactions causes the denaturation transition to be much sharper than otherwise. At physiological temperature, the stacking interactions prohibit the initiation of bubble formation but promote bubbles, once grown, to retain the large size.

Borononucleotides: synthesis, and formation of a new reversible boronate internucleosidic linkage

The synthesis of a borononucleotide analogue of thymidine and its association towards the formation of new borono-linked dimers is described.

A coarse grain model for DNA

Understanding the behavior of DNA at the molecular level is of considerable fundamental and engineering importance. While adequate representations of DNA exist at the atomic and continuum level, there is a relative lack of models capable of describing the behavior of DNA at mesoscopic length scales. We present a mesoscale model of DNA that reduces the complexity of a nucleotide to three interactions sites, one each for the phosphate, sugar, and base, thereby rendering the investigation of DNA up to a few microns in length computationally tractable. The charges on these sites are considered explicitly. The model is parametrized using thermal denaturation experimental data at a fixed salt concentration. The validity of the model is established by its ability to predict several aspects of DNA behavior, including salt-dependent melting, bubble formation and rehybridization, and the mechanical properties of the molecule as a function of salt concentration.

Unified description of poly- and oligonucleotide DNA melting: nearest-neighbor, Poland-Sheraga, and lattice models

We show that a simple lattice model can provide a unified description of the thermal denaturation of DNA oligomers and polymers. The model quantitatively reproduces experimental melting curves and reduces in limiting cases to the nearest-neighbor model and a suitable modified Poland-Sheraga model. Our results support the interpretation of the cooperativity parameter sigma for bubble opening in terms of an interfacial (forking) free energy which also affects chain opening from the ends. The lattice model treats long-ranged excluded volume interactions between all parts of the molecule explicitly, provides access to an ensemble of three dimensional structures (and hence the response to external mechanical forces), and includes fluctuations in situations without pre-determined secondary structure.

Computer Simulation of the Ionic Atmosphere around Z-DNA

We describe a coarse-grained model for Z-DNA that mimics the DNA shape with a relatively small number of repulsive interaction sites. In addition, negative charges are placed at the phosphate positions. The ionic atmosphere around this grooved Z-DNA model is then investigated with Monte Carlo simulation. Cylindrically averaged concentration profiles as well as the spatial distribution of ions have been calculated. The results are compared to those for other DNA models differing in the repulsive core. This allows the examination of the effect of the DNA shape in the ionic distribution. It is seen that the penetrability of the ions to the DNA groove plays an important role in the ionic distribution. The results are also compared with those reported for B-DNA. In both conformers the ions are structured in alternating layers of positive and negative charge. In Z-DNA the layers are more or less concentric to the molecular axis. Besides, no coions enter into the single groove of this conformer. On the contrary, the alternating layers of B-DNA are also structured along the axial coordinate with some coions penetrating into the major groove. In both cases we have found five preferred locations of the counterions and two for the coions. The concentration of counterions reaches its absolute maximum at the narrow Z-DNA groove and at the minor groove of B-DNA, the value of the maximum being higher in the Z conformer.

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SMEs) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SMEs it is possible to manipulate molecules one at a time and measure distributions describing molecular properties, characterize the kinetics of biomolecular reactions and detect molecular intermediates. SMEs provide additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SMEs it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level, emphasizing the importance of SMEs to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SMEs from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOTs), magnetic tweezers (MTs), biomembrane force probes (BFPs) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation) and proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SMEs to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.