Conformation of circular DNA in two dimensions

Adsorption characteristics of Janus tadpole polymers

The shape of Janus particles is directly connected to their adsorption behavior. Janus tadpole polymers offer a unique topological architecture that includes competition between entropic, enthalpic, and topological terms in the adsorption free energy; accordingly, non-trivial adsorption behavior patterns are expected. We study the surface adsorption of Janus tadpole polymers by means of Monte Carlo simulations, finding that, depending on which part of the tadpole polymers is preferentially adsorbing on the surface, very different types of behavior for both the adsorbed polymeric phase and of the brush arise. The adsorbed phase and the brush mutually influence each other, leading to a variety of phenomena such as nematic ordering of the adsorbed stiff tadpole tails and intriguing changes in the territoriality of adsorbed ring polymers on the surface. We analyze in detail our findings, revealing the mechanisms behind the organization and ordering, and opening up new possibilities to tune and control the structure of such systems.

Universal scaling of the osmotic pressure for dense, quasi-two-dimensionally confined polymer melts reveals transitions between fractal dimensions

A scaling law for the osmotic pressure of quasi-two-dimensional polymer melts as a function of concentration is obtained, which shows fractal characteristics. Structural properties such as the chains' contour length and their inner-monomer pair distribution function display fractal scaling properties as well. These predictions are confirmed with mesoscale numerical simulations. The chains are swollen and highly entangled, yet Flory's exponent is always ν = 1/2. The melt can be considered a fluid of "blobs" whose size becomes renormalized in terms of the contour's length while the fractal dimension df increases monotonically between 5/4 and 2, as the monomer concentration is increased. The semidilute scaling of the pressure is recovered when df = 1. Our results agree with recent experiments and with numerical reports on quasi-2d melts. This work provides a new paradigm to study and interpret thermodynamic and structural data in low-dimensional polymer melts, namely as fractal macromolecular objects.

Effects of Microfluidic Shear on the Plasmid DNA Structure: Implications for Polymeric Gene Delivery Vectors

Microfluidic manufacturing of advanced gene delivery vectors necessitates consideration of the effects of microfluidic shear forces on the structural integrity of plasmid DNA (pDNA). In this paper, we expose pDNA to variable shear forces in a two-phase, gas-liquid microfluidic reactor and apply gel electrophoresis to analyze the products of on-chip shear-induced degradation. The effects of shear rate, solvent environment, pDNA size, and copolymer complexation on shear-induced degradation are investigated. We find that small naked pDNA (pUC18, 2.7 kb) exhibits shear rate-dependent shear degradation in the microfluidic channels in a mixed organic solvent (dioxane/water/acetic acid; 90/10/<0.1 w/w/w), with the extents of both supercoil isoform relaxation and complete fragmentation increasing as the maximum shear rates increase from 4 × 105 to 2 × 106 s-1. However, over the same range of shear rates, the same pDNA sample shows no evidence of microfluidic shear-induced degradation in a pure aqueous environment. Quiescent control experiments in the same mixed organic solvent prove that a combination of solvent and shear forces is involved in the observed shear-induced degradation. Furthermore, we show that shear degradation effects in mixed organic solvents can be significantly attenuated by complexation of pDNA with the block copolymer polycaprolactone-block-poly(2-vinylpyridine) prior to exposure to microfluidic shear. Finally, we demonstrate that medium (pDSK519, 8.1 kb) and large (pRK290, 20 kb) naked pDNA are more sensitive to shear-induced microfluidic degradation in the mixed organic solvent environment than small pDNA, with both plasmids showing complete fragmentation even at the lowest shear rate, although we found no evidence of shear-induced damage in water for the largest investigated naked pDNA even at the highest flow rate. The resulting understanding of the interplay of the solvent and shear effects during microfluidic processing should inform microfluidic manufacturing routes to new gene therapy formulations.

CENP-B-mediated DNA loops regulate activity and stability of human centromeres

Chromosome inheritance depends on centromeres, epigenetically specified regions of chromosomes. While conventional human centromeres are known to be built of long tandem DNA repeats, much of their architecture remains unknown. Using single-molecule techniques such as AFM, nanopores, and optical tweezers, we find that human centromeric DNA exhibits complex DNA folds such as local hairpins. Upon binding to a specific sequence within centromeric regions, the DNA-binding protein CENP-B compacts centromeres by forming pronounced DNA loops between the repeats, which favor inter-chromosomal centromere compaction and clustering. This DNA-loop-mediated organization of centromeric chromatin participates in maintaining centromere position and integrity upon microtubule pulling during mitosis. Our findings emphasize the importance of DNA topology in centromeric regulation and stability.

Intrinsic structure and dynamics of monolayer ring polymer melts

We present the general structural and dynamical characteristics of flexible ring polymers in narrowly confined two-dimensional (2D) melt systems using atomistic molecular dynamics simulations. The results are further analyzed via direct comparison with the 2D linear analogue as well as the three-dimensional (3D) ring and linear melt systems. It is observed that dimensional restriction in 2D confined systems results in an increase in the intrinsic chain stiffness of the ring polymer. Fundamentally, this arises from an entropic penalty on polymer chains along with a reduction in the available chain configuration states in phase space and spatial choices for individual segmental walks. This feature in combination with the intermolecular interactions between neighboring ring chains leads to an overall extended interpenetrated chain configuration for the 2D ring melt. In contrast to the generally large differences in structural and dynamical properties between ring and linear polymers in 3D melt systems, relatively similar local-to-global chain structures and dynamics are observed for the 2D ring and linear melts. This is attributed to the general structural similarity (i.e., extended double-stranded chain conformations), the less effective role of the chain ends, and the absence of complex topological constraints between chains (i.e., interchain entanglement and mutual ring threading) in the 2D confined systems compared with the corresponding 3D bulk systems.

Environmental Control of Amyloid Polymorphism by Modulation of Hydrodynamic Stress

The phenomenon of amyloid polymorphism is a key feature of protein aggregation. Unravelling this phenomenon is of great significance for understanding the underlying molecular mechanisms associated with neurodegenerative diseases and for the development of amyloid-based functional biomaterials. However, the understanding of the molecular origins and the physicochemical factors modulating amyloid polymorphs remains challenging. Herein, we demonstrate an association between amyloid polymorphism and environmental stress in solution, induced by an air/water interface in motion. Our results reveal that low-stress environments produce heterogeneous amyloid polymorphs, including twisted, helical, and rod-like fibrils, whereas high-stress conditions generate only homogeneous rod-like fibrils. Moreover, high environmental stress converts twisted fibrils into rod-like fibrils both in-pathway and after the completion of mature amyloid formation. These results enrich our understanding of the environmental origin of polymorphism of pathological amyloids and shed light on the potential of environmentally controlled fabrication of homogeneous amyloid biomaterials for biotechnological applications.

Nanoscale surface structures of DNA bound to Deinococcus radiodurans HU unveiled by atomic force microscopy

The Deinococcus radiodurans protein HU (DrHU) was shown to be critical for nucleoid activities, yet its functional and structural properties remain largely unexplored. We have applied atomic force microscopy (AFM) imaging to study DrHU binding to pUC19-DNA in vitro and analyzed the topographic structures formed at the nanoscale. At the single-molecule level, AFM imaging allows visualization of super-helical turns on naked DNA surfaces and characterization of free DrHU molecules observed as homodimers. When enhancing the molecular surface structures of AFM images by the Laplacian weight filter, the distribution of bound DrHUs was visibly varied as a function of the DrHU/DNA molar ratio. At a low molar ratio, DrHU binding was found to reduce the volume of condensed DNA configuration by about 50%. We also show that DrHU is capable of bridging distinct DNA segments. Moreover, at a low molar ratio, the binding orientation of individual DrHU dimers could be perceived on partially "open" DNA configuration. At a high molar ratio, DrHU stiffened the DNA molecule and enlarged the spread of the open DNA configuration. Furthermore, a lattice-like pattern could be seen on the surface of DrHU-DNA complex, indicating that DrHU multimerization had occurred leading to the formation of a higher order architecture. Together, our results show that the functional plasticity of DrHU in mediating DNA organization is subject to both the conformational dynamics of DNA molecules and protein abundance.

A lattice kinetic Monte-Carlo method for simulating chromosomal dynamics and other (non-)equilibrium bio-assemblies

Biological assemblies in living cells such as chromosomes constitute large many-body systems that operate in a fluctuating, out-of-equilibrium environment. Since a brute-force simulation of that many degrees of freedom is currently computationally unfeasible, it is necessary to perform coarse-grained stochastic simulations. Here, we develop all tools necessary to write a lattice kinetic Monte-Carlo (LKMC) algorithm capable of performing such simulations. We discuss the validity and limits of this approach by testing the results of the simulation method in simple settings. Importantly, we illustrate how at large external forces Metropolis-Hastings kinetics violate the fluctuation-dissipation and steady-state fluctuation theorems and discuss better alternatives. Although this simulation framework is rather general, we demonstrate our approach using a DNA polymer with interacting SMC condensin loop-extruding enzymes. Specifically, we show that the scaling behavior of the loop-size distributions that we obtain in our LKMC simulations of this SMC-DNA system is consistent with that reported in other studies using Brownian dynamics simulations and analytic approaches. Moreover, we find that the irreversible dynamics of these enzymes under certain conditions result in frozen, sterically jammed polymer configurations, highlighting a potential pitfall of this approach.

Statistical Properties of Lasso-Shape Polymers and Their Implications for Complex Lasso Proteins Function

The shape and properties of closed loops depend on various topological factors. One of them is loop-threading, which is present in complex lasso proteins. In this work, we analyze the probability of loop-threading by the tail and its influence on the shape of the loop measured by the radius of gyration, distention, asphericity, and prolateness. In particular, we show that the probability of a trivial lasso for phantom polymer is non-zero even for an infinite structure, as well as that the threading flattens the loop by restricting its motion in one dimension. These results are further used to show that there are fewer non-trivial protein lassos than expected and select potentially functional complex lasso proteins.

Self-avoiding walks and connective constants in clustered scale-free networks

Various types of walks on complex networks have been used in recent years to model search and navigation in several kinds of systems, with particular emphasis on random walks. This gives valuable information on network properties, but self-avoiding walks (SAWs) may be more suitable than unrestricted random walks to study long-distance characteristics of complex systems. Here we study SAWs in clustered scale-free networks, characterized by a degree distribution of the form P(k)∼k^{-γ} for large k. Clustering is introduced in these networks by inserting three-node loops (triangles). The long-distance behavior of SAWs gives us information on asymptotic characteristics of such networks. The number of self-avoiding walks, a_{n}, has been obtained by direct enumeration, allowing us to determine the connective constant μ of these networks as the large-n limit of the ratio a_{n}/a_{n-1}. An analytical approach is presented to account for the results derived from walk enumeration, and both methods give results agreeing with each other. In general, the average number of SAWs a_{n} is larger for clustered networks than for unclustered ones with the same degree distribution. The asymptotic limit of the connective constant for large system size N depends on the exponent γ of the degree distribution: For γ>3, μ converges to a finite value as N→∞; for γ=3, the size-dependent μ_{N} diverges as lnN, and for γ<3 we have μ_{N}∼N^{(3-γ)/2}.

Structural Behavior of a Semiflexible Polymer Chain in an Array of Nanoposts

The structural properties of a flexible and semiflexible circular chain confined in an array of parallel nanoposts with a square lattice cross-sectional projection were studied using coarse-grained molecular dynamics simulations. To address the effect of the circular topology, a comparison with linear analogs was also carried out. In the interpretation of the chain structural properties, the geometry of the post array is considered as a combination of a channel approximating the interstitial volume with the diameter dc and a slit approximating the passage aperture with the width wp. The number of interstitial volumes occupied by a chain monotonically increases with the decreasing ratio dc/wp regardless of the way the geometry of the post array is varied. However, depending on how the array geometry is modified, the chain span along the posts displays a monotonic (constant post separation) or a non-monotonic behavior (constant passage width) when plotted as a function of the post diameter. In the case of monotonic trend, the width of interstitial spaces increases with the increasing chain occupation number, while, in the case of non-monotonic trend, the width of interstitial spaces decreases with the increasing chain occupation number. In comparison with linear topology, for circular topology, the stiffness affects more significantly the relative chain extension along the posts and less significantly the occupation number. The geometrical parameters of the post arrays are stored in the single-chain structure factors. The characteristic humps are recognized in the structure factor which ensue from the local increase in the density of segments in the circular chains presented in an interstitial volume or from the correlation of parallel chain fragments separated by a row of posts. Although the orientation correlations provide qualitative information about the chain topology and the character of confinement within a single interstitial volume, information about the array periodicity is missing.

DNA-protein interactions explored by atomic force microscopy

DNA-protein interactions play an important role in all living organisms on Earth. The advent of atomic force microscopy permitted for the first time to follow and to characterize interaction forces between these two molecular species. After a short description of the AFM and its imaging modes we review, in a chronological order some of the studies that we think importantly contributed to the field.

Spatial confinement induces hairpins in nicked circular DNA

In living cells, DNA is highly confined in space with the help of condensing agents, DNA binding proteins and high levels of supercoiling. Due to challenges associated with experimentally studying DNA under confinement, little is known about the impact of spatial confinement on the local structure of the DNA. Here, we have used well characterized slits of different sizes to collect high resolution atomic force microscopy images of confined circular DNA with the aim of assessing the impact of the spatial confinement on global and local conformational properties of DNA. Our findings, supported by numerical simulations, indicate that confinement imposes a large mechanical stress on the DNA as evidenced by a pronounced anisotropy and tangent-tangent correlation function with respect to non-constrained DNA. For the strongest confinement we observed nanometer sized hairpins and interwound structures associated with the nicked sites in the DNA sequence. Based on these findings, we propose that spatial DNA confinement in vivo can promote the formation of localized defects at mechanically weak sites that could be co-opted for biological regulatory functions.

Hyperplectonemes: A Higher Order Compact and Dynamic DNA Self-Organization

Bacterial chromosome has a compact structure that dynamically changes its shape in response to bacterial growth rate and growth phase. Determining how chromatin remains accessible to DNA binding proteins, and transcription machinery is crucial to understand the link between genetic regulation, DNA structure, and topology. Here, we study very large supercoiled dsDNA using high-resolution characterization, theoretical modeling, and molecular dynamics calculations. We unveil a new type of highly ordered DNA organization forming in the presence of attractive DNA-DNA interactions, which we call hyperplectonemes. We demonstrate that their formation depends on DNA size, supercoiling, and bacterial physiology. We compare structural, nanomechanic, and dynamic properties of hyperplectonemes bound by three highly abundant nucleoid-associated proteins (FIS, H-NS, and HU). In all these cases, the negative supercoiling of DNA determines molecular dynamics, modulating their 3D shape. Overall, our findings provide a mechanistic insight into the critical role of DNA topology in genetic regulation.

Comparison of a stripe and slab confinement for ring and linear macromolecules in nanochannel

The combined effects of the channel asymmetry and the closed chain topology on the chain extension, structure factor, and the orientation correlations were studied using coarse-grained molecular dynamics simulations for moderate chain lengths. These effects are related to applications in linearization experiments with a DNA molecule in nanofluidic devices. According to the aspect ratio, the channels are classified as a stripe or slabs. The chain segments do not have any freedom to move in the direction of the narrowest stripe size, being approximately the same size as the segment size. The chains of both ring and linear topologies are extended more in a stripe than in a slab; this effect is strengthened for a ring. For a ring in a stripe, the extension-confinement strength dependence leads to effective Flory exponents even larger than 3/4, which is characteristic for a self-avoiding two-dimensional chain. While the chain extension-confinement strength dependence for both topologies conforms to the de Gennes regime in a stripe, a linear chain undergoes gradual transition to the pseudoideal regime as the slab height increases in the slab-like confinement. For a confined circle, the onset of the pseudoideal regime is shifted to larger slab heights. The structure factor confirms the absence of the pseudoideal and extended de Gennes regime in a stripe and the transition from the extended to the pseudoideal regime of a circular and linear chain upon increasing the slab heights.

Energy localization and shape transformations in semiflexible polymer rings

Shape transformations in driven and damped molecular chains are considered. Closed chains of weakly coupled molecular subunits under the action of spatially homogeneous time-periodic external field are studied. The coupling between the internal excitations and the bending degrees of freedom of the chain modifies the local bending rigidity of the chain. In the absence of driving the array takes a circular shape. When the energy pumped into the system exceeds some critical value the chain undergoes a nonequilibrium phase transition: The circular shape of the aggregate becomes unstable and the chain takes the shape of an ellipse or, in general, of a polygon. The excitation energy distribution becomes spatially nonuniform: It localizes in such places where the chain is more flat. The weak interaction of the chain with a flat surface restricts the dynamics to a flat manifold.

Size distribution of ring polymers

We present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For non-interacting and local-interaction models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively, and are shown to be identical in dimension d ≥ 2, albeit with pronounced finite size effects at the critical dimension, d = 2. A symmetry of the problem reveals that dimension d and 4 - d are equivalent, thus the celebrated Airy distribution describing the areal distribution of the d = 1 Brownian excursion describes also a polymer in three dimensions. For a self-avoiding polymer in dimension d we find numerically that the fluctuations of the scaled averaged distance are nearly identical in dimension d = 2, 3 and are well described to a first approximation by the non-interacting excursion model in dimension 5.

Marked difference in conformational fluctuation between giant DNA molecules in circular and linear forms

We performed monomolecular observations on linear and circular giant DNAs (208 kbp) in an aqueous solution by the use of fluorescence microscopy. The results showed that the degree of conformational fluctuation in circular DNA was ca. 40% less than that in linear DNA, although the long-axis length of circular DNA was only 10% smaller than that of linear DNA. Additionally, the relaxation time of a circular chain was shorter than that of a linear chain by at least one order of magnitude. The essential features of this marked difference between linear and circular DNAs were reproduced by numerical simulations on a ribbon-like macromolecule as a coarse-grained model of a long semiflexible, double-helical DNA molecule. In addition, we calculated the radius of gyration of an interacting chain in a circular form on the basis of the mean field model, which provides a better understanding of the present experimental trend than a traditional theoretical equation.

Coupled binding-bending-folding: The complex conformational dynamics of protein-DNA binding studied by atomistic molecular dynamics simulations

BACKGROUND

Protein-DNA binding often involves dramatic conformational changes such as protein folding and DNA bending. While thermodynamic aspects of this behavior are understood, and its biological function is often known, the mechanism by which the conformational changes occur is generally unclear. By providing detailed structural and energetic data, molecular dynamics simulations have been helpful in elucidating and rationalizing protein-DNA binding.

SCOPE OF REVIEW

This review will summarize recent atomistic molecular dynamics simulations of the conformational dynamics of DNA and protein-DNA binding. A brief overview of recent developments in DNA force fields is given as well.

MAJOR CONCLUSIONS

Simulations have been crucial in rationalizing the intrinsic flexibility of DNA, and have been instrumental in identifying the sequence of binding events, the triggers for the conformational motion, and the mechanism of binding for a number of important DNA-binding proteins.

GENERAL SIGNIFICANCE

Molecular dynamics simulations are an important tool for understanding the complex binding behavior of DNA-binding proteins. With recent advances in force fields and rapid increases in simulation time scales, simulations will become even more important for future studies. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Gaussian semiflexible rings under angular and dihedral restrictions

Semiflexible polymer rings whose bonds obey both angular and dihedral restrictions [M. Dolgushev and A. Blumen, J. Chem. Phys. 138, 204902 (2013)], are treated under exact closure constraints. This allows us to obtain semianalytic results for their dynamics, based on sets of Langevin equations. The dihedral restrictions clearly manifest themselves in the behavior of the mean-square monomer displacement. The determination of the equilibrium ring conformations shows that the dihedral constraints influence the ring curvature, leading to compact folded structures. The method for imposing such constraints in Gaussian systems is very general and it allows to account for heterogeneous (site-dependent) restrictions. We show it by considering rings in which one site differs from the others.

Total positive curvature of circular DNA

The properties of double-stranded DNA and other chiral molecules depend on the local geometry, i.e., on curvature and torsion, yet the paths of closed chain molecules are globally restricted by topology. When both of these characteristics are to be incorporated in the description of circular chain molecules, e.g., plasmids, it is shown to have implications for the total positive curvature integral. For small circular micro-DNAs it follows as a consequence of Fenchel's inequality that there must exist a minimum length for the circular plasmids to be double stranded. It also follows that all circular micro-DNAs longer than the minimum length must be concave, a result that is consistent with typical atomic force microscopy images of plasmids. Predictions for the total positive curvature of circular micro-DNAs are given as a function of length, and comparisons with circular DNAs from the literature are presented.

Chain relaxation dynamics of DNA adsorbing at a solid-liquid interface

We have used scanning force microscopy (SFM) to elucidate the dynamic behavior of open (torsionally unconstrained) circular and long linear DNA molecules during the relaxation process following adsorption onto mica. We find that bending stress and excluded volume effects drive the conformational equilibration via segmental out-of-plane dynamics.

Density functional theory for inhomogeneous ring polymeric fluids

The modeling of ring polymers remains a challenge in classical density functional theory (DFT) due to the difficulty in solving the direct bond connectivity of the ring architecture without free ends. By considering the feature that all of the segments in a ring are equivalent, we give an algorithm to solve the integral of direct bond connectivity for ideal ring polymers, and therefore propose a DFT for inhomogeneous ring polymers, where the excess free energy functional is extended from an equation of state (EOS). This EOS exhibits better agreement than other EOSs for the compressibility factors, compared to Monte Carlo data. Importantly, the DFT satisfactorily reproduces the data of the configurational-bias Monte Carlo (CBMC) simulations for ring polymers. The local density profiles from the DFT show that the bead density of inhomogeneous ring fluids is independent of ring size, which is also confirmed by the CBMC simulations. Interestingly, the behavior of solvation force for ring polymers is quite similar to that of the polymers with infinite chain length.

Probing the elasticity of DNA on short length scales by modeling supercoiling under tension

The wormlike-chain (WLC) model is widely used to describe the energetics of DNA bending. Motivated by recent experiments, alternative, so-called subelastic chain models were proposed that predict a lower elastic energy of highly bent DNA conformations. Until now, no unambiguous verification of these models has been obtained because probing the elasticity of DNA on short length scales remains challenging. Here we investigate the limits of the WLC model using coarse-grained Monte Carlo simulations to model the supercoiling of linear DNA molecules under tension. At a critical supercoiling density, the DNA extension decreases abruptly due to the sudden formation of a plectonemic structure. This buckling transition is caused by the large energy required to form the tightly bent end-loop of the plectoneme and should therefore provide a sensitive benchmark for model evaluation. Although simulations based on the WLC energetics could quantitatively reproduce the buckling measured in magnetic tweezers experiments, the buckling almost disappears for the tested linear subelastic chain model. Thus, our data support the validity of a harmonic bending potential even for small bending radii down to 3.5 nm.

DNA Bending through Large Angles Is Aided by Ionic Screening

We used adaptive umbrella sampling on a modified version of the roll angle to simulate the bending of DNA dodecamers. Simulations were carried out with the AMBER and CHARMM force fields for 10 sequences in which the central base pair step was varied. On long length scales, the DNA behavior was found to be consistent with the worm-like chain model. Persistence lengths calculated directly from the simulated structures and indirectly through the use of sequence-independent coarse-grained models based on simulation data were similar to literature values. On short length scales, the free energy cost of bending DNA was found to be consistent with the worm-like chain model for small and intermediate bending angles. At large angles, the bending free energy as a function of the roll angle became linear, suggesting a relative increase in flexibility at larger roll angles. Counterions congregated on the concave side of the highly bent DNA and screened the repulsion of the phosphate groups, facilitating the bending.

Shape of adsorbed supercoiled plasmids: an equilibrium description

Inspired by recent atomic force microscope (AFM) images of plasmids deposited on oppositely charged supported lipid bilayers from salt free solution, we propose a model for strongly adsorbed supercoiled cyclic stiff polyelectrolytes. We discuss how the excess linking number Lk of the deposited cycle is shared between writhe Wr and twist Tw at equilibrium and obtain the typical number of self-crossings in the deposited cycle as a function of surface charge density. The number of crossings at equilibrium is simply determined by the crossing penalty which is a local quantity and by the excess linking number. The number of crossings is well defined despite versatile plasmid shapes. For moderate numbers of crossings the loops are rather small and localized along the primary cycle, as expected from entropic loops. In the regime of many crossings, the cycle takes the shape of a regular flat ply ruled by local stiffness. The model allows for a semiquantitative comparison with the AFM images of deposited plasmids which are strongly charged.

Sub-persistence-length complex scaling behavior in lysozyme amyloid fibrils

We combine atomic force microscopy single-molecule analysis with polymer physics concepts to study molecular conformations of lysozyme amyloid fibrils. We resolve a wavy structure of the fibrils in which the scaling behavior varies at multiple length scales. Bond and pair correlation functions, end-to-end distribution, and wormlike chain model identify three characteristic length scales. At short length scales (≈150 nm), there is a first bending transition of the fibrils corresponding to a bending length L(b). At larger length scales (>2L(b)), fibrils become pseudoperiodic and start to undulate. Finally, at length scales larger than the persistence length (~ μm), the fibrils become flexible and follow a 2D self-avoiding random walk. We interpret these results in terms of the twisting of the fibrils and the impact this has on the area moment of inertia and the propensity of the fibril to bend.

DNA origami-based nanoribbons: assembly, length distribution, and twist

A variety of polymerization methods for the assembly of elongated nanoribbons from rectangular DNA origami structures are investigated. The most efficient method utilizes single-stranded DNA oligonucleotides to bridge an intermolecular scaffold seam between origami monomers. This approach allows the fabrication of origami ribbons with lengths of several micrometers, which can be used for long-range ordered arrangement of proteins. It is quantitatively shown that the length distribution of origami ribbons obtained with this technique follows the theoretical prediction for a simple linear polymerization reaction. The design of flat single layer origami structures with constant crossover spacing inevitably results in local underwinding of the DNA helix, which leads to a global twist of the origami structures that also translates to the nanoribbons.

Conformation of ring polymers in 2D constrained environments

The combination of ring closure and spatial constraints has a fundamental effect on the statistics of semiflexible polymers such as DNA. However, studies of the interplay between circularity and constraints are scarce and single-molecule experimental data concerning polymer conformations are missing. By means of atomic force microscopy we probe the conformation of circular DNA molecules in two dimensions and in the concentrated regime (above the overlap concentration c*). Molecules in this regime experience a collapse, and their statistical properties agree very well with those of simulated vesicles under pressure. Some circular molecules also create confining regions in which other molecules are trapped. Thus we show further that spatially confined molecules fold into specific conformations close to those found for linear chains, and strongly dependent on the size of the confining box.

Effect of spontaneous twist on DNA minicircles

Monte Carlo simulations are used to study the effect of spontaneous (intrinsic) twist on the conformation of topologically equilibrated minicircles of dsDNA. The twist, writhe, and radius of gyration distributions and their moments are calculated for different spontaneous twist angles and DNA lengths. The average writhe and twist deviate in an oscillatory fashion (with the period of the double helix) from their spontaneous values, as one spans the range between two neighboring integer values of intrinsic twist. Such deviations vanish in the limit of long DNA plasmids.

Looping probabilities of elastic chains: a path integral approach

We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end points. Our approximation formula for the looping pdf is of quite general applicability as, in contrast to most prior approaches, no assumption is made of either uniformity of the elastic chain, nor of a straight intrinsic shape. If the chain is uniform the Jacobi system evaluated at certain minimum energy configurations has constant coefficients. In such cases our approximate pdf can be evaluated in an entirely explicit, closed form. We illustrate our analysis with a planar example of this type and compute an approximate probability of cyclization, i.e., of forming a closed loop, from a uniform elastic chain whose intrinsic shape is an open circular arc.