Simulation of DNA catenanes

Structure and Thermodynamics of Linear, Ring, and Catenane Polymers in Solutions and at Liquid-Liquid Interfaces

In recent decades, advances in the syntheses of mechanically interlocked macromolecules, such as catenanes, have led to much greater interest in the applications of these complexes, from molecular motors and actuators to nanoscale computational memory and nanoswitches. Much remains to be understood, however, regarding how catenated ring compounds behave as a result of the effects of different solvents as well as the effects of solvent/solvent interfaces. In this work, we have investigated, using molecular dynamics simulations, the effects of solvation of poly(ethylene oxide) chains of different topologies─linear, ring, and [2]catenane─in two solvents both considered favorable toward PEO (water, toluene) and at the water/toluene interface. Compared to ring and [2]catenane molecules, the linear PEO chain showed the largest increase in size at the water/toluene interface compared to bulk water or bulk toluene. Perhaps surprisingly, observations indicate that the tendency of all three topologies to extend at the water/toluene interface may have more to do with screening the interaction between the two solvents than with optimizing specific solvent-polymer contacts.

Polycatenanes: synthesis, characterization, and physical understanding

Chemical composition and architecture are two key factors that control the physical and material properties of polymers. Some of the more unusual and intriguing polymer architectures are the polycatenanes, which are a class of polymers that contain mechanically interlocked rings. Since the development of high yielding synthetic routes to catenanes, there has been an interest in accessing their polymeric counterparts, primarily on account of the unique conformations and degrees of freedom offered by non-bonded interlocked rings. This has lead to the synthesis of a wide variety of polycatenane architectures and to studies aimed at developing structure-property relationships of these interesting materials. In this review, we provide an overview of the field of polycatenanes, exploring synthesis, architecture, properties, simulation, and modelling, with a specific focus on some of the more recent developments.

Pairing nanoarchitectonics of oligodeoxyribonucleotides with complex diversity: concatemers and self-limited complexes

The development of approaches to the design of two- and three-dimensional self-assembled DNA-based nanostructures with a controlled shape and size is an essential task for applied nanotechnology, therapy, biosensing, and bioimaging. We conducted a comprehensive study on the formation of various complexes from a pair of oligonucleotides with two transposed complementary blocks that can be linked through a nucleotide or non-nucleotide linker. A methodology is proposed to prove the formation of a self-limited complex and to determine its molecularity. It is based on the "opening" of a self-limited complex with an oligonucleotide that effectively binds to a duplex-forming block. The complexes assembled from a pair of oligonucleotides with different block length and different linker sizes and types were investigated by theoretical analysis, several experimental methods (a gel shift assay, atomic force microscopy, and ultraviolet melting analysis), and molecular dynamics simulations. The results showed a variety of complexes formed by only a pair of oligonucleotides. Self-limited associates, concatemer complexes, or mixtures thereof can arise if we change the length of a duplex and loop-forming blocks in oligonucleotides or via introduction of overhangs and chemical modifications. We postulated basic principles of rational design of native self-limited DNA complexes of desired structure, shape, and molecularity. Our foundation makes self-limited complexes useful tools for nanotechnology, biological studies, and therapeutics.

Sliding dynamics of multi-rings on a semiflexible polymer in poly[n]catenanes

The sliding dynamics of one- or multi-ring structures along a semiflexible cyclic polymer in radial poly[n]catenanes is investigated using molecular dynamics simulations. The fixed and fluctuating (non-fixed) semiflexible central cyclic polymers are considered, respectively. With increasing bending energy of the central cyclic polymer, for the fixed case, the diffusion coefficient increases monotonically due to the reduction of the tortuous sliding path, while for the fluctuating case, the diffusion coefficient decreases. This indicates that the contribution of the polymer fluctuation is suppressed by a further increase in the stiffness of the central cyclic chain. Compared with the one ring case, the mean-square displacement of the multiple rings exhibits a unique sub-diffusive behavior at intermediate time scales due to the repulsion between two neighboring rings. In addition, for the multi-ring system, the whole set of rings exhibit relatively slower diffusion, but faster local dynamics of threading rings and rotational diffusion of the central cyclic polymer arise. These results may help us to understand the diffusion motion of rings in radial poly[n]catenanes from a fundamental point of view and control the sliding dynamics in molecular designs.

Hydrodynamic interactions in topologically linked ring polymers

Despite decades of interdisciplinary research on topologically linked ring polymers, their dynamics remain largely unstudied. These systems represent a major scientific challenge as they are often subject to both topological and hydrodynamic interactions (HI), which render dynamical solutions either mathematically intractable or computationally prohibitive. Here we circumvent these limitations by preaveraging the HI of linked rings. We show that the symmetry of ring polymers leads to a hydrodynamic decoupling of ring dynamics. This decoupling is valid even for nonideal polymers and nonequilibrium conditions. Physically, our findings suggest that the effects of topology and HI are nearly independent and do not act cooperatively to influence polymer dynamics. We use this result to develop highly efficient Brownian dynamics algorithms that offer enormous performance improvements over conventional methods and apply these algorithms to simulate catenated ring polymers at equilibrium, confirming the independence of topological effects and HI. The methods developed here can be used to study and simulate large systems of linked rings with HI, including kinetoplast DNA, Olympic gels, and poly[n]catenanes.

Effects of topological constraints on linked ring polymers in solvents of varying quality

We investigate the effects of topological constraints in catenanes composed of interlinked ring polymers on their size in a good solvent as well as on the location of their θ-point when the solvent quality is worsened. We mainly focus on poly[n]catenanes consisting of n ring polymers each of length m interlocked in a linear fashion. Using molecular dynamics simulations, we study the scaling of the poly[n]catenane's radius of gyration in a good solvent, assuming in general that Rg∼mμnν and we find that μ = 0.65 ± 0.02 and ν = 0.60 ± 0.01 for the range of n and m considered. These findings are further rationalized with the help of a mean-field Flory-like theory yielding the values of μ = 16/25 and ν = 3/5, consistent with the numerical results. We show that individual rings within catenanes feature a surplus swelling due to the presence of NL topological links. Furthermore, we consider poly[n]catenanes in solvents of varying quality and we demonstrate that the presence of topological links leads to an increase of its θ-temperature in comparison to isolated linear and ring chains with the following ordering: T > T > T. Finally, we show that the presence of links similarly raises the θ-temperature of a single linked ring in comparison to an unlinked one, bringing its θ-temperature close to the one of a poly[n]catenane.

Closing the DNA replication cycle: from simple circular molecules to supercoiled and knotted DNA catenanes

Due to helical structure of DNA, massive amounts of positive supercoils are constantly introduced ahead of each replication fork. Positive supercoiling inhibits progression of replication forks but various mechanisms evolved that permit very efficient relaxation of that positive supercoiling. Some of these mechanisms lead to interesting topological situations where DNA supercoiling, catenation and knotting coexist and influence each other in DNA molecules being replicated. Here, we first review fundamental aspects of DNA supercoiling, catenation and knotting when these qualitatively different topological states do not coexist in the same circular DNA but also when they are present at the same time in replicating DNA molecules. We also review differences between eukaryotic and prokaryotic cellular strategies that permit relaxation of positive supercoiling arising ahead of the replication forks. We end our review by discussing very recent studies giving a long-sought answer to the question of how slow DNA topoisomerases capable of relaxing just a few positive supercoils per second can counteract the introduction of hundreds of positive supercoils per second ahead of advancing replication forks.

Polymer models with optimal good-solvent behavior

We consider three different continuum polymer models, which all depend on a tunable parameter r that determines the strength of the excluded-volume interactions. In the first model, chains are obtained by concatenating hard spherocylinders of height b and diameter rb (we call them thick self-avoiding chains). The other two models are generalizations of the tangent hard-sphere and of the Kremer-Grest models. We show that for a specific value [Formula: see text], all models show optimal behavior: asymptotic long-chain behavior is observed for relatively short chains. For [Formula: see text], instead, the behavior can be parametrized by using the two-parameter model, which also describes the thermal crossover close to the θ point. The bonds of the thick self-avoiding chains cannot cross each other, and therefore the model is suited for the investigation of topological properties and for dynamical studies. Such a model also provides a coarse-grained description of double-stranded DNA, so that we can use our results to discuss under which conditions DNA can be considered as a model good-solvent polymer.

Effect of sequence-dependent rigidity on plectoneme localization in dsDNA

We use Monte-Carlo simulations to study the effect of variable rigidity on plectoneme formation and localization in supercoiled double-stranded DNA. We show that the presence of soft sequences increases the number of plectoneme branches and that the edges of the branches tend to be localized at these sequences. We propose an experimental approach to test our results in vitro, and discuss the possible role played by plectoneme localization in the search process of transcription factors for their targets (promoter regions) on the bacterial genome.

Disentangling DNA molecules

The widespread circular form of DNA molecules inside cells creates very serious topological problems during replication. Due to the helical structure of the double helix the parental strands of circular DNA form a link of very high order, and yet they have to be unlinked before the cell division. DNA topoisomerases, the enzymes that catalyze passing of one DNA segment through another, solve this problem in principle. However, it is very difficult to remove all entanglements between the replicated DNA molecules due to huge length of DNA comparing to the cell size. One strategy that nature uses to overcome this problem is to create the topoisomerases that can dramatically reduce the fraction of linked circular DNA molecules relative to the corresponding fraction at thermodynamic equilibrium. This striking property of the enzymes means that the enzymes that interact with DNA only locally can access their topology, a global property of circular DNA molecules. This review considers the experimental studies of the phenomenon and analyzes the theoretical models that have been suggested in attempts to explain it. We describe here how various models of enzyme action can be investigated computationally. There is no doubt at the moment that we understand basic principles governing enzyme action. Still, there are essential quantitative discrepancies between the experimental data and the theoretical predictions. We consider how these discrepancies can be overcome.

Orientation of DNA Minicircles Balances Density and Topological Complexity in Kinetoplast DNA

Kinetoplast DNA (kDNA), a unique mitochondrial structure common to trypanosomatid parasites, contains thousands of DNA minicircles that are densely packed and can be topologically linked into a chain mail-like network. Experimental data indicate that every minicircle in the network is, on average, singly linked to three other minicircles (i.e., has mean valence 3) before replication and to six minicircles in the late stages of replication. The biophysical factors that determine the topology of the network and its changes during the cell cycle remain unknown. Using a mathematical modeling approach, we previously showed that volume confinement alone can drive the formation of the network and that it induces a linear relationship between mean valence and minicircle density. Our modeling also predicted a minicircle valence two orders of magnitude greater than that observed in kDNA. To determine the factors that contribute to this discrepancy we systematically analyzed the relationship between the topological properties of the network (i.e., minicircle density and mean valence) and its biophysical properties such as DNA bending, electrostatic repulsion, and minicircle relative position and orientation. Significantly, our results showed that most of the discrepancy between the theoretical and experimental observations can be accounted for by the orientation of the minicircles with volume exclusion due to electrostatic interactions and DNA bending playing smaller roles. Our results are in agreement with the three dimensional kDNA organization model, initially proposed by Delain and Riou, in which minicircles are oriented almost perpendicular to the horizontal plane of the kDNA disk. We suggest that while minicircle confinement drives the formation of kDNA networks, it is minicircle orientation that regulates the topological complexity of the network.

Efficient deformation algorithm for plasmid DNA simulations

BACKGROUND

Plasmid DNA molecules are closed circular molecules that are widely used in life sciences, particularly in gene therapy research. Monte Carlo methods have been used for several years to simulate the conformational behavior of DNA molecules. In each iteration these simulation methods randomly generate a new trial conformation, which is either accepted or rejected according to a criterion based on energy calculations and stochastic rules. These simulation trials are generated using a method based on crankshaft motion that, apart from some slight improvements, has remained the same for many years.

RESULTS

In this paper, we present a new algorithm for the deformation of plasmid DNA molecules for Monte Carlo simulations. The move underlying our algorithm preserves the size and connectivity of straight-line segments of the plasmid DNA skeleton. We also present the results of three experiments comparing our deformation move with the standard and biased crankshaft moves in terms of acceptance ratio of the trials, energy and temperature evolution, and average displacement of the molecule. Our algorithm can also be used as a generic geometric algorithm for the deformation of regular polygons or polylines that preserves the connections and lengths of their segments.

CONCLUSION

Compared with both crankshaft moves, our move generates simulation trials with higher acceptance ratios and smoother deformations, making it suitable for real-time visualization of plasmid DNA coiling. For that purpose, we have adopted a DNA assembly algorithm that uses nucleotides as building blocks.

Local nucleosome dynamics facilitate chromatin accessibility in living mammalian cells

Genome information, which is three-dimensionally organized within cells as chromatin, is searched and read by various proteins for diverse cell functions. Although how the protein factors find their targets remains unclear, the dynamic and flexible nature of chromatin is likely crucial. Using a combined approach of fluorescence correlation spectroscopy, single-nucleosome imaging, and Monte Carlo computer simulations, we demonstrate local chromatin dynamics in living mammalian cells. We show that similar to interphase chromatin, dense mitotic chromosomes also have considerable chromatin accessibility. For both interphase and mitotic chromatin, we observed local fluctuation of individual nucleosomes (~50 nm movement/30 ms), which is caused by confined Brownian motion. Inhibition of these local dynamics by crosslinking impaired accessibility in the dense chromatin regions. Our findings show that local nucleosome dynamics drive chromatin accessibility. We propose that this local nucleosome fluctuation is the basis for scanning genome information.

Unlinking of supercoiled DNA catenanes by type IIA topoisomerases

It was found recently that DNA catenanes, formed during replication of circular plasmids, become positively (+) supercoiled, and the unlinking of such catenanes by type IIA topoisomerases proceeds much more efficiently than the unlinking of negatively (-) supercoiled catenanes. In an attempt to explain this striking finding we studied, by computer simulation, conformational properties of supercoiled DNA catenanes. Although the simulation showed that conformational properties of (+) and (-) supercoiled replication catenanes are very different, these properties per se do not give any advantage to (+) supercoiled over (-) supercoiled DNA catenanes for unlinking. An advantage became evident, however, when we took into account the established features of the enzymatic reaction catalyzed by the topoisomerases. The enzymes create a sharp DNA bend in the first bound DNA segment and allow for the transport of the second segment only from inside the bend to its outside. We showed that in (-) supercoiled DNA catenanes this protein-bound bent segment becomes nearly inaccessible for segments of the other linked DNA molecule, inhibiting the unlinking.