Dependence of DNA Persistence Length on Ionic Strength of Solutions with Monovalent and Divalent Salts: A Joint Theory–Experiment Study

Mechanical response of double-stranded DNA: Bend, twist, and overwind

We employed all-atom molecular dynamics simulations to explore the mechanical response of bending, twisting, and overwinding for double-stranded DNA (dsDNA). We analyzed the bending and twisting deformations, as well as their stiffnesses, using the tilt, roll, and twist modes under stretching force. Findings indicate that the roll and twist angles vary linearly with the stretching force but show opposite trends. The tilt, roll, and twist elastic moduli are considered constants, while the coupling between roll and twist modes slightly decreases under stretching force. The effect of the stretching force on the roll and twist modes, including both their deformations and elasticities, exhibits sequence-dependence, with symmetry around the base pair step. Furthermore, we examined the overwinding path and mechanism of dsDNA from the perspective of the stiffness matrix, based on the tilt, roll, and twist modes. The correlations among tilt, roll, and twist angles imply an alternative overwinding pathway via twist-roll coupling when dsDNA is stretched, wherein entropic contribution prevails.

Effect of ethanol on the elasticities of double-stranded RNA and DNA revealed by magnetic tweezers and simulations

The elasticities of double-stranded (ds) DNA and RNA, which are critical to their biological functions and applications in materials science, can be significantly modulated by solution conditions such as ions and temperature. However, there is still a lack of a comprehensive understanding of the role of solvents in the elasticities of dsRNA and dsDNA in a comparative way. In this work, we explored the effect of ethanol solvent on the elasticities of dsRNA and dsDNA by magnetic tweezers and all-atom molecular dynamics simulations. We found that the bending persistence lengths and contour lengths of dsRNA and dsDNA decrease monotonically with the increase in ethanol concentration. Furthermore, the addition of ethanol weakens the positive twist-stretch coupling of dsRNA, while promotes the negative twist-stretch coupling of dsDNA. Counter-intuitively, the lower dielectric environment of ethanol causes a significant re-distribution of counterions and enhanced ion neutralization, which overwhelms the enhanced repulsion along dsRNA/dsDNA, ultimately leading to the softening in bending for dsRNA and dsDNA. Moreover, for dsRNA, ethanol causes slight ion-clamping across the major groove, which weakens the major groove-mediated twist-stretch coupling, while for dsDNA, ethanol promotes the stretch-radius correlation due to enhanced ion binding and consequently enhances the helical radius-mediated twist-stretch coupling.

Effect of temperature on anisotropic bending elasticity of dsRNA: an all-atom molecular dynamics simulation

Employing all-atom molecular dynamics simulations, we examined the temperature-dependent behavior of bending elasticity in double-stranded RNA (dsRNA). Specifically, we focused on the bending persistence length and its constituent components, namely, the tilt and roll stiffness. Our results revealed a near-linear decrease in these stiffness components as a function of temperature, thereby highlighting the increased flexibility of dsRNA at elevated temperatures. Furthermore, our data revealed a significant anisotropy in dsRNA bending elasticity, which diminished with increasing temperature, attributable to marked disparities in tilt and roll stiffness components. We delineated the underlying biophysical mechanisms and corroborated our findings with extant literature. These observations offer salient implications for advancing our understanding of nucleic acid elasticity, and are pertinent to potential medical applications.

Systematic assessment of the flexibility of uracil damaged DNA

Uracil is a common DNA lesion which is recognized and removed by uracil DNA-glycosylase (UDG) as a part of the base excision repair pathway. Excision proceeds by base flipping, and UDG efficiency is thought to depend on the ease of deformability of the bases neighboring the lesion. We used molecular dynamics simulations to assess the flexibility of a large library of dsDNA strands, containing all tetranucleotide motifs with U:A, U:G, T:A or C:G base pairs. Our study demonstrates that uracil damaged DNA largely follows trends in flexibility of undamaged DNA. Measured bending persistence lengths, groove widths, step parameters and base flipping propensities demonstrate that uracil increases the flexibility of DNA, and that U:G base paired strands are more flexible than U:A strands. Certain sequence contexts are more deformable than others, with a key role for the 3' base next to uracil. Flexibilities are large when this base is an A or G, and repressed for a C or T. A 5' T adjacent to the uracil strongly promotes flexibility, but other 5' bases are less influential. DNA bending is correlated to step deformations and base flipping, and bending aids flipping. Our study implies that the link between substrate flexibility and UDG efficiency is widely valid, helps explain why UDG prefers to bind U:G base paired strands, and suggests that the DNA bending angle of the UDG-substrate complex is optimal for base flipping.Communicated by Ramaswamy H. Sarma.

Influence of temperature on bend, twist and twist-bend coupling of dsDNA

The temperature-dependent bend and twist elasticities of dsDNA, as well as their couplings, were explored through all-atom molecular dynamics simulations. Three rotational parameters, tilt, roll, and twist, were employed to assess the bend and twist elasticities through their stiffness matrix. Our analysis indicates that the bend and twist stiffnesses decrease as the temperature rises, primarily owing to entropic influences stemming from thermodynamic fluctuations. Furthermore, the couplings between these rotational parameters also exhibit a decline with increasing temperature, although the roll-twist coupling displays greater strength than the tilt-roll and tilt-twist couplings, attributed to its more robust correction component. We elucidated the influence of temperature on bend and twist elasticities based on the comparisons between various models and existing data.

Accumulation and Stretching of DNA Molecules in Temperature-Induced Concentration Gradients

Temperature fields provide a noninvasive approach for manipulating individual macromolecules in solution. Utilizing thermophoresis and other secondary effects resulting from the inhomogeneous distribution of crowding agents, one may gain valuable insights into the interactions of molecular mixtures. In this report, we examine the steady-state concentration distribution and dynamics of DNA molecules in a poly(ethylene glycol) (PEG)/water solution when exposed to localized temperature gradients generated by optical heating of a thin chrome layer at a liquid-solid boundary. This allowed us to experimentally investigate the interplay between DNA thermophoresis and PEG-induced entropic depletion effects. Our quantitative analysis demonstrates that the depletion effects dominate over DNA thermophoresis, causing the DNA polymers to migrate toward the heat source. Additionally, we explore the transient stretching of individual DNA molecules in thermally induced PEG gradients and estimate the contributing forces.

Genome organization in double-stranded DNA viruses observed by cryoET

Double-stranded DNA (dsDNA) viruses package their genetic material into protein cages with diameters usually a few hundred times smaller than the length of their genome. Compressing the relatively stiff and highly negatively charged dsDNA into a small volume is energetically costly and mechanistically enigmatic. Multiple models of dsDNA packaging have been proposed based on various experimental evidence and simulation methods, but direct observation of any viral genome organization is lacking. Here, using cryoET and an improved data processing scheme that utilizes information from the encaging protein shell, we present 3D views of dsDNA genome inside individual viral particles at resolution that densities of neighboring DNA duplexes are readily separable. These cryoET observations reveal a "rod-and-coil" fold of the dsDNA that is conserved among herpes simplex virus type 1 (HSV-1) with a spherical capsid, bacteriophage T4 with a prolate capsid, and bacteriophage T7 with a proteinaceous core inside the capsid. Finally, inspired by the genome arrangement in partially packaged T4 particles, we propose a mechanism for the genome packaging process in dsDNA viruses.

Partition complex structure can arise from sliding and bridging of ParB dimers

In many bacteria, chromosome segregation requires the association of ParB to the parS-containing centromeric region to form the partition complex. However, the structure and formation of this complex have been unclear. Recently, studies have revealed that CTP binding enables ParB dimers to slide along DNA and condense the centromeric region through the formation of DNA bridges. Using semi-flexible polymer simulations, we demonstrate that these properties can explain partition complex formation. Transient ParB bridges organize DNA into globular states or hairpins and helical structures, depending on bridge lifetime, while separate simulations show that ParB sliding reproduces the multi-peaked binding profile observed in Caulobacter crescentus. Combining sliding and bridging into a unified model, we find that short-lived ParB bridges do not impede sliding and can reproduce both the binding profile and condensation of the nucleoprotein complex. Overall, our model elucidates the mechanism of partition complex formation and predicts its fine structure.

Full Site-Specific Addressability in DNA Origami-Templated Silica Nanostructures

DNA nanotechnology allows for the fabrication of nanometer-sized objects with high precision and selective addressability as a result of the programmable hybridization of complementary DNA strands. Such structures can template the formation of other materials, including metals and complex silica nanostructures, where the silica shell simultaneously acts to protect the DNA from external detrimental factors. However, the formation of silica nanostructures with site-specific addressability has thus far not been explored. Here, it is shown that silica nanostructures templated by DNA origami remain addressable for post silicification modification with guest molecules even if the silica shell measures several nm in thickness. The conjugation of fluorescently labeled oligonucleotides is used to different silicified DNA origami structures carrying a complementary ssDNA handle as well as DNA-PAINT super-resolution imaging to show that ssDNA handles remain unsilicified and thus ensure retained addressability. It is also demonstrated that not only handles, but also ssDNA scaffold segments within a DNA origami nanostructure remain accessible, allowing for the formation of dynamic silica nanostructures. Finally, the power of this approach is demonstrated by forming 3D DNA origami crystals from silicified monomers. These results thus present a fully site-specifically addressable silica nanostructure with complete control over size and shape.

Temperature dependence of DNA elasticity: An all-atom molecular dynamics simulation study

We used all-atom molecular dynamics simulation to investigate the elastic properties of double-stranded DNA (dsDNA). We focused on the influences of temperature on the stretch, bend, and twist elasticities, as well as the twist-stretch coupling, of the dsDNA over a wide range of temperature. The results showed that the bending and twist persistence lengths, together with the stretch and twist moduli, decrease linearly with temperature. However, the twist-stretch coupling behaves in a positive correction and enhances as the temperature increases. The potential mechanisms of how temperature affects dsDNA elasticity and coupling were investigated by using the trajectories from atomistic simulation, in which thermal fluctuations in structural parameters were analyzed in detail. We analyzed the simulation results by comparing them with previous simulation and experimental data, which are in good agreement. The prediction about the temperature dependence of dsDNA elastic properties provides a deeper understanding of DNA elasticities in biological environments and potentially helps in the further development of DNA nanotechnology.

Theoretical and computational analysis of the electrophoretic polymer mobility inversion induced by charge correlations

Electrophoretic (EP) mobility reversal is commonly observed for strongly charged macromolecules in multivalent salt solutions. This curious effect takes place, e.g., when a charged polymer, such as DNA, adsorbs excess counterions so that the counterion-dressed surface charge reverses its sign, leading to the inversion of the polymer drift driven by an external electric field. In order to characterize this seemingly counterintuitive phenomenon that cannot be captured by electrostatic mean-field theories, we adapt here a previously developed strong-coupling-dressed Poisson-Boltzmann approach to the cylindrical geometry of the polyelectrolyte-salt system. Within the framework of this formalism, we derive an analytical polymer mobility formula dressed by charge correlations. In qualitative agreement with polymer transport experiments, this mobility formula predicts that the increment of the monovalent salt, the decrease of the multivalent counterion valency, and the increase of the dielectric permittivity of the background solvent suppress charge correlations and increase the multivalent bulk counterion concentration required for EP mobility reversal. These results are corroborated by coarse-grained molecular dynamics simulations showing how multivalent counterions induce mobility inversion at dilute concentrations and suppress the inversion effect at large concentrations. This re-entrant behavior, previously observed in the aggregation of like-charged polymer solutions, calls for verification by polymer transport experiments.

Influence of ionic conditions on knotting in a coarse-grained model for DNA

We investigate knotting probabilities of long double-stranded DNA strands in a coarse-grained Kratky-Porod model for DNA with Monte Carlo simulations. Various ionic conditions are implemented by adjusting the effective diameter of monomers. We find that the occurrence of knots in DNA can be reinforced considerably by high salt conditions and confinement between plates. Likewise, knots can almost be dissolved completely in a low salt scenario. Comparisons with recent experiments confirm that the coarse-grained model is able to capture and quantitatively predict topological features of DNA and can be used for guiding future experiments on DNA knots.

Mechanical Constraint Effect on DNA Persistence Length

Persistence length is a significant criterion to characterize the semi-flexibility of DNA molecules. The mechanical constraints applied on DNA chains in new single-molecule experiments play a complex role in measuring DNA persistence length; however, there is a difficulty in quantitatively characterizing the mechanical constraint effects due to their complex interactions with electrostatic repulsions and thermal fluctuations. In this work, the classical buckling theory of Euler beam and Manning's statistical theories of electrostatic force and thermal fluctuation force are combined for an isolated DNA fragment to formulate a quantitative model, which interprets the relationship between DNA persistence length and critical buckling length. Moreover, this relationship is further applied to identify the mechanical constraints in different DNA experiments by fitting the effective length factors of buckled fragments. Then, the mechanical constraint effects on DNA persistence lengths are explored. A good agreement among the results by theoretical models, previous experiments, and present molecular dynamics simulations demonstrates that the new superposition relationship including three constraint-dependent terms can effectively characterize changes in DNA persistence lengths with environmental conditions, and the strong constraint-environment coupling term dominates the significant changes of persistence lengths; via fitting effective length factors, the weakest mechanical constraints on DNAs in bulk experiments and stronger constraints on DNAs in single-molecule experiments are identified, respectively. Moreover, the consideration of DNA buckling provides a new perspective to examine the bendability of short-length DNA.

Single-Molecule Methods for Investigating the Double-Stranded DNA Bendability

The various DNA-protein interactions associated with the expression of genetic information involve double-stranded DNA (dsDNA) bending. Due to the importance of the formation of the dsDNA bending structure, dsDNA bending properties have long been investigated in the biophysics field. Conventionally, DNA bendability is characterized by innate averaging data from bulk experiments. The advent of single-molecule methods, such as atomic force microscopy, optical and magnetic tweezers, tethered particle motion, and single-molecule fluorescence resonance energy transfer measurement, has provided valuable tools to investigate not only the static structures but also the dynamic properties of bent dsDNA. Here, we reviewed the single-molecule methods that have been used for investigating dsDNA bendability and new findings related to dsDNA bending. Single-molecule approaches are promising tools for revealing the unknown properties of dsDNA related to its bending, particularly in cells.

Effect of mono- and multi-valent ionic environments on the in-lattice nanoparticle-grafted single-stranded DNA

Polyelectrolyte (PE) chains respond in a complex manner to multivalent salt environments, and this behavior depends on pH, temperature, and the presence of specific counter ions. Although much work has been done to understand the behaviour of free PE chains, it is important to reveal their behaviour on a nanoparticle's surface, where surface constraints, particle geometry, and multi-chain environment can affect their behaviour and contribute to particles' assembly states. Our work investigates, using in situ small-angle X-ray scattering (SAXS), the morphology of PE (single-stranded DNA) chains grafted onto the surface of spherical gold nanoparticles assembled in a lattice in the presence of monovalent, divalent and trivalent salts. For divalent salts, the DNA brush length was found to decrease at a faster rate with salt concentration than in the monovalent salt environment, while trivalent salts led to chain collapse. Using a power law analysis and the modified Daoud-Cotton model, we have obtained insight into the mechanism of a nanoparticle-grafted chain's response to ionic environments. Our analysis suggests that the decrease in brush length is due to the conventional electrostatic screening for monovalent systems, whereas for divalent systems both electrostatic screening and divalent ion bridging must be considered.

Dielectric Manipulation of Polymer Translocation Dynamics in Engineered Membrane Nanopores

The alteration of the dielectric membrane properties by membrane engineering techniques such as carbon nanotube (CNT) coating opens the way to novel molecular transport strategies for biosensing purposes. In this article, we predict a macromolecular transport mechanism enabling the dielectric manipulation of the polymer translocation dynamics in dielectric membrane pores confining mixed electrolytes. In the giant permittivity regime of these engineered membranes governed by attractive polarization forces, multivalent ions adsorbed by the membrane nanopore trigger a monovalent ion separation and set an electroosmotic counterion flow. The drag force exerted by this flow is sufficiently strong to suppress and invert the electrophoretic velocity of anionic polymers and also to generate the mobility of neutral polymers whose speed and direction can be solely adjusted by the charge and concentration of the added multivalent ions. These features identify the dielectrically generated transport mechanism as an efficient means to drive overall neutral or weakly charged analytes that cannot be controlled by an external voltage. We also reveal that, in anionic polymer translocation, multivalent cation addition into the monovalent salt solution amplifies the electric current signal by several factors. The signal amplification is caused by the electrostatic many-body interactions replacing the monovalent polymer counterions by the multivalent cations of higher electric mobility. The strength of this electrokinetic charge discrimination points out the potential of multivalent ions as current amplifiers capable of providing boosted resolution in nanopore-based biosensing techniques.

Flexible, charged biopolymers in monovalent and mixed-valence salt: Regimes of anomalous electrostatic stiffening and of salt insensitivity

The conformations of biological polyelectrolytes (PEs), such as polysaccharides, proteins, and nucleic acids, affect how they behave and interact with other biomolecules. Relative to neutral polymers, PEs in solution are more locally rigid due to intrachain electrostatic repulsion, the magnitude of which depends on the concentration of added salt. This is typically quantified using the Odijk-Skolnick-Fixman (OSF) electrostatic-stiffening model, in which salt-dependent Debye-Hückel (DH) screening modulates intrachain repulsion. However, the applicability of this approach to flexible PEs has long been questioned. To investigate this, we use high-precision single-molecule elasticity measurements to infer the scaling with salt of the local stiffness of three flexible biopolymers (hyaluronic acid, single-stranded RNA, and single-stranded DNA) in both monovalent and mixed-valence salt solutions. In monovalent salt, we collapse the data across all three polymers by accounting for charge spacing, and find a common power-law scaling of the electrostatic persistence length with ionic strength with an exponent of 0.66±0.02. This result rules out simple OSF pictures of electrostatic stiffening. It is roughly compatible with a modified OSF picture developed by Netz and Orland; alternatively, we posit the exponent can be explained if the relevant electrostatic screening length is the interion spacing rather than the DH length. In mixed salt solutions, we find a regime where adding monovalent salt, in the presence of multivalent salt, does not affect PE stiffness. Using coarse-grained simulations, and a three-state model of condensed, chain-proximate, and bulk ions, we attribute this regime to a "jacket" of ions surrounding the PE that regulates the chain's effective charge density as ionic strength varies. The size of this jacket in simulations is again consistent with a screening length controlled by interion spacing rather than the DH length. Taken together, our results describe a unified picture of the electrostatic stiffness of polyelectrolytes in the mixed-valence salt conditions of direct relevance to cellular and intercellular biological systems.

Devices for Nanoscale Guiding of DNA through a 2D Nanopore

We fabricate on-chip solid-state nanofluidic-2D nanopore systems that can limit the range of motion for DNA in the sensing region of a nanopore. We do so by creating devices containing one or more silicon nitride pores and silicon nitride pillars supporting a 2D pore that orient DNA within a nanopore device to a restricted geometry, yet allow the free motion of ions to maintain a high signal-to-noise ratio. We discuss two concepts with two and three independent electrical connections and corresponding nanopore chip device architectures to achieve this goal in practice. Here, we describe device fabrication and transmission electron microscope (TEM) images, and provide simulated translocations based on the finite element analysis in 3D to demonstrate its merit. In both methods, there is a main 2D nanopore which we refer to as a "sensing" nanopore (monolayer MoS₂ in this paper). A secondary layer is either an array of guiding pores sharing the same electrode pair as the sensing pore (Method 1) or a single, independently contacted, guiding pore (Method 2). These pores are constructed parallel to the "sensing" pore and serve as "guiding" elements to stretch and feed DNA into the atomically thin sensing pore. We discuss the practical implementation of these concepts with nanofluidic and Si-based technology, including detailed fabrication steps and challenges involved for DNA applications in solution.

Ion-dependent DNA configuration in bacteriophage capsids

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.

A molecular view of DNA flexibility

DNA dynamics can only be understood by taking into account its complex mechanical behavior at different length scales. At the micrometer level, the mechanical properties of single DNA molecules have been well-characterized by polymer models and are commonly quantified by a persistence length of 50 nm (~150 bp). However, at the base pair level (~3.4 Å), the dynamics of DNA involves complex molecular mechanisms that are still being deciphered. Here, we review recent single-molecule experiments and molecular dynamics simulations that are providing novel insights into DNA mechanics from such a molecular perspective. We first discuss recent findings on sequence-dependent DNA mechanical properties, including sequences that resist mechanical stress and sequences that can accommodate strong deformations. We then comment on the intricate effects of cytosine methylation and DNA mismatches on DNA mechanics. Finally, we review recently reported differences in the mechanical properties of DNA and double-stranded RNA, the other double-helical carrier of genetic information. A thorough examination of the recent single-molecule literature permits establishing a set of general 'rules' that reasonably explain the mechanics of nucleic acids at the base pair level. These simple rules offer an improved description of certain biological systems and might serve as valuable guidelines for future design of DNA and RNA nanostructures.

Mechanical properties of DNA and DNA nanostructures: comparison of atomistic, Martini and oxDNA models

The flexibility and stiffness of small DNA molecules play a fundamental role ranging from several biophysical processes to nano-technological applications. Here, we estimate the mechanical properties of short double-stranded DNA (dsDNA) with lengths ranging from 12 base-pairs (bp) to 56 bp, paranemic crossover (PX) DNA and hexagonal DNA nanotubes (DNTs) using two widely used coarse-grained models - Martini and oxDNA. To calculate the persistence length (Lp) and the stretch modulus (γ) of the dsDNA, we incorporate the worm-like chain and elastic rod model, while for the DNTs, we implement our previously developed theoretical framework. We compare and contrast all of the results with previously reported all-atom molecular dynamics (MD) simulations and experimental results. The mechanical properties of dsDNA (Lp ∼ 50 nm, γ ∼ 800-1500 pN), PX DNA (γ ∼ 1600-2000 pN) and DNTs (Lp ∼ 1-10 μm, γ ∼ 6000-8000 pN) estimated using the Martini soft elastic network and oxDNA are in very good agreement with the all-atom MD and experimental values, while the stiff elastic network Martini reproduces values of Lp and γ which are an order of magnitude higher. The high flexibility of small dsDNA is also depicted in our calculations. However, Martini models proved inadequate to capture the salt concentration effects on the mechanical properties with increasing salt molarity. oxDNA captures the salt concentration effect on the small dsDNA mechanics. But it is found to be ineffective for reproducing the salt-dependent mechanical properties of DNTs. Also, unlike Martini, the time evolved PX DNA and DNT structures from the oxDNA models are comparable to the all-atom MD simulated structures. Our findings provide a route to study the mechanical properties of DNA and DNA based nanostructures with increased time and length scales and has a remarkable implication in the context of DNA nanotechnology.

Nanomechanics of self-assembled DNA building blocks

DNA has become a powerful platform to design functional nanodevices. DNA nanodevices are often composed of self-assembled DNA building blocks that differ significantly from the structure of native DNA. In this study, we present Flow Force Microscopy as a massively parallel approach to study the nanomechanics of DNA self-assemblies on the single-molecular level. The high-throughput experiments performed in a simple microfluidic channel enable statistically meaningful studies with nanometer scale precision in a time frame of several minutes. A surprisingly high flexibility was observed for a typical construct used in DNA origami, reflected in a persistence length of 10.2 nm, a factor of five smaller than for native DNA. The enhanced flexibility is attributed to the discontinuous backbone of DNA self-assemblies that facilitate base pair opening by thermal fluctuations at the end of hybridized oligomers. We believe that the results will contribute to the fundamental understanding of DNA nanomechanics and help to improve the design of DNA nanodevices with applications in biological analysis and clinical research.

Nucleosome plasticity is a critical element of chromatin liquid-liquid phase separation and multivalent nucleosome interactions

Liquid-liquid phase separation (LLPS) is an important mechanism that helps explain the membraneless compartmentalization of the nucleus. Because chromatin compaction and LLPS are collective phenomena, linking their modulation to the physicochemical features of nucleosomes is challenging. Here, we develop an advanced multiscale chromatin model-integrating atomistic representations, a chemically-specific coarse-grained model, and a minimal model-to resolve individual nucleosomes within sub-Mb chromatin domains and phase-separated systems. To overcome the difficulty of sampling chromatin at high resolution, we devise a transferable enhanced-sampling Debye-length replica-exchange molecular dynamics approach. We find that nucleosome thermal fluctuations become significant at physiological salt concentrations and destabilize the 30-nm fiber. Our simulations show that nucleosome breathing favors stochastic folding of chromatin and promotes LLPS by simultaneously boosting the transient nature and heterogeneity of nucleosome-nucleosome contacts, and the effective nucleosome valency. Our work puts forward the intrinsic plasticity of nucleosomes as a key element in the liquid-like behavior of nucleosomes within chromatin, and the regulation of chromatin LLPS.

DNA mechanics and its biological impact

Almost all nucleoprotein interactions and DNA manipulation events involve mechanical deformations of DNA. Extraordinary progresses in single-molecule, structural, and computational methods have characterized the average mechanical properties of DNA, such as bendability and torsional rigidity, in high resolution. Further, the advent of sequencing technology has permitted measuring, in high-throughput, how such mechanical properties vary with sequence and epigenetic modifications along genomes. We review these recent technological advancements, and discuss how they have contributed to the emerging idea that variations in the mechanical properties of DNA play a fundamental role in regulating, genome-wide, diverse processes involved in chromatin organization.

Physical constraints in polymer modeling of chromatin associations with the nuclear periphery at kilobase scale

Interactions of chromatin with the nuclear lamina imposes a radial genome distribution important for nuclear functions. How physical properties of chromatin affect these interactions is unclear. We used polymer simulations to model how physical parameters of chromatin affect its interaction with the lamina. Impact of polymer stiffness is greater than stretching on its configurations at the lamina; these are manifested as trains describing extended interactions, and loops describing desorbed regions . Conferring an attraction potential leads to persistent interaction and adsorption-desorption regimes manifested by fluctuations between trains and loops. These are modulated by polymer stiffness and stretching, with a dominant impact of stiffness on resulting structural configurations. We infer that flexible euchromatin is more prone to stochastic interactions with lamins than rigid heterochromatin characterizing constitutive LADs. Our models provide insights on the physical properties of chromatin as a polymer which affect the dynamics and patterns of interactions with the nuclear lamina.

Determinants of cyclization-decyclization kinetics of short DNA with sticky ends

Cyclization of DNA with sticky ends is commonly used to measure DNA bendability as a function of length and sequence, but how its kinetics depend on the rotational positioning of the sticky ends around the helical axis is less clear. Here, we measured cyclization (looping) and decyclization (unlooping) rates (k_loop and k_unloop) of DNA with sticky ends over three helical periods (100-130 bp) using single-molecule fluorescence resonance energy transfer (FRET). k_loop showed a nontrivial undulation as a function of DNA length whereas k_unloop showed a clear oscillation with a period close to the helical turn of DNA (∼10.5 bp). The oscillation of k_unloop was almost completely suppressed in the presence of gaps around the sticky ends. We explain these findings by modeling double-helical DNA as a twisted wormlike chain with a finite width, intrinsic curvature, and stacking interaction between the end base pairs. We also discuss technical issues for converting the FRET-based cyclization/decyclization rates to an equilibrium quantity known as the J factor that is widely used to characterize DNA bending mechanics.

Single-Molecule Sensing of DNA Intercalating Drugs in Water

The occurrence of pharmaceutical residues in surface water is raising environmental concern. To accompany the evolution of measures for natural resources protection, sensing methods enabling sensitive and rapid water quality monitoring are needed. We recently managed the parallelization of the Tethered Particle Motion (TPM), a single molecule technique, sensitive to the conformational changes of DNA. Here, we investigate the capacity of high throughput TPM (htTPM) to detect drugs that intercalate into DNA. As a proof-of-concept we analyze the htTPM signal for two DNA intercalating dyes, namely, YOYO-1 and SYTOX orange. The efficient detection of intercalating drugs is then demonstrated with doxorubicin. We further evaluate the possibility to detect carbamazepine, an antiepileptic massively prescribed and persistent in water, which had been described to interact with DNA through intercalation. Our results corroborated by other techniques show that, in fact, carbamazepine is not a DNA intercalator. The comparison of the results obtained with different aqueous buffers and solutions allows us to identify optimal conditions for the monitoring of intercalation compounds by htTPM.

Electrophoretic Mobility of DNA in Solutions of High Ionic Strength

The free-solution mobilities of small single-stranded DNA (ssDNA) and double-stranded DNA (dsDNA) have been measured by capillary electrophoresis in solutions containing 0.01-1.0 M sodium acetate. The mobility of dsDNA is greater than that of ssDNA at all ionic strengths because of the greater charge density of dsDNA. The mobilities of both ssDNA and dsDNA decrease with increasing ionic strength until approaching plateau values at ionic strengths greater than ∼0.6 M. Hence, ssDNA and dsDNA appear to interact in a similar manner with the ions in the background electrolyte. For dsDNA, the mobilities predicted by the Manning electrophoresis equation are reasonably close to the observed mobilities, using no adjustable parameters, if the average distance between phosphate residues (the b parameter) is taken to be 1.7 Å. For ssDNA, the predicted mobilities are close to the observed mobilities at ionic strengths ≤0.01 M if the b-value is taken to be 4.1 Å. The predicted and observed mobilities diverge strongly at higher ionic strengths unless the b-value is reduced significantly. The results suggest that ssDNA strands exist as an ensemble of relatively compact conformations at high ionic strengths, with b-values corresponding to the relatively short phosphate-phosphate distances through space.

Coating and Stabilization of Liposomes by Clathrin-Inspired DNA Self-Assembly

The self-assembly of the protein clathrin on biological membranes facilitates essential processes of endocytosis and has provided a source of inspiration for materials design by the highly ordered structural appearance. By mimicking the architecture of the protein building blocks and clathrin self-assemblies to coat liposomes with biomaterials, advanced hybrid carriers can be derived. Here, we present a method for fabricating DNA-coated liposomes by hydrophobically anchoring and subsequently connecting DNA-based triskelion structures on the liposome surface inspired by the assembly of the protein clathrin. Dynamic light scattering, ζ-potential, confocal microscopy, and cryo-electron microscopy measurements independently demonstrate successful DNA coating. Nanomechanical measurements conducted with atomic force microscopy show that the DNA coating enhances the mechanical stability of the liposomes relative to uncoated ones. Furthermore, we provide the possibility to reverse the coating process by triggering the disassembly of the DNA coats through a toehold-mediated displacement reaction. Our results describe a straightforward, versatile, and reversible approach for coating and stabilizing lipid vesicles through the assembly of rationally designed DNA structures. This method has potential for further development toward the ordered arrangement of tailored functionalities on the surface of liposomes and for applications as hybrid nanocarriers.

Opposite Effects of High-Valent Cations on the Elasticities of DNA and RNA Duplexes Revealed by Magnetic Tweezers

We report that trivalent cobalt hexammine cations decrease the persistence length, stretching modulus, helical density, and size of plectonemes formed under torque of DNA but increase those of RNA. Divalent magnesium cations, however, decrease the persistence lengths, contour lengths, and sizes of plectonemes while increasing the helical densities of both DNA and RNA. The experimental results are explained by different binding modes of the cations on DNA and RNA in our all-atom molecular dynamics simulations. The significant variations of the helical densities and structures of DNA and RNA duplexes induced by high-valent cations may affect interactions of the duplexes with proteins.

Molecular flexibility of DNA as a key determinant of RAD51 recruitment

The timely activation of homologous recombination is essential for the maintenance of genome stability, in which the RAD51 recombinase plays a central role. Biochemically, human RAD51 polymerises faster on single‐stranded DNA (ssDNA) compared to double‐stranded DNA (dsDNA), raising a key conceptual question: how does it discriminate between them? In this study, we tackled this problem by systematically assessing RAD51 binding kinetics on ssDNA and dsDNA differing in length and flexibility using surface plasmon resonance. By directly fitting a mechanistic model to our experimental data, we demonstrate that the RAD51 polymerisation rate positively correlates with the flexibility of DNA. Once the RAD51‐DNA complex is formed, however, RAD51 remains stably bound independent of DNA flexibility, but rapidly dissociates from flexible DNA when RAD51 self‐association is perturbed. This model presents a new general framework suggesting that the flexibility of DNA, which may increase locally as a result of DNA damage, plays an important role in rapidly recruiting repair factors that multimerise at sites of DNA damage.

Quantitative Modeling of Nucleosome Unwrapping from Both Ends

In eukaryotic cells, DNA is packaged into chromatin where nucleosomes are the basic packaging unit. Important cellular processes including gene expression, DNA replication, and DNA repair require nucleosomal DNA to be unwrapped so that functional proteins can access their target sites, which otherwise are sterically occluded. A key question in this process is what the unwrapped conformations individual nucleosomes adopt within chromatin are. Here, we develop a concurrent nucleosome unwrapping model to address this question. We hypothesize that for a given end-to-end distance of the nucleosomal DNA, the nucleosomal DNA stochastically unwraps from the histone core from both ends independently and that this combination of unwrapping from both sides results in a significant increase in the average distance between the DNA extending from both sides of the nucleosomes. We test our model on recently published experiments using a DNA origami nanocaliper that quantifies nucleosome unwrapping and achieve good agreement between experiment and model prediction. We then investigate the DNA origami caliper distribution when attached to a hexasome (a nucleosome lacking an H2A/H2B dimer). A significant shift in the caliper angle distribution caused by the asymmetric structural features of the hexasome seen experimentally is consistent with the model. Our modeling approach may be more broadly useful to the interpretation of other studies of nucleosome dynamics, chromatin dynamics, and regulatory processes involving nucleosome unwrapping, as well as more generally to optimization of future DNA origami designs to probe mechanical properties of biomolecules.

Harnessing Avidity: Quantifying the Entropic and Energetic Effects of Linker Length and Rigidity for Multivalent Binding of Antibodies to HIV-1

IgG antibodies increase their apparent affinities by using both of their Fabs to simultaneously attach to antigens. HIV-1 foils this strategy by having few, and highly separated, Envelope (Env) spike targets for antibodies, forcing most IgGs to bind monovalently. Here, we develop a statistical mechanics model of synthetic diFabs joined by DNA linkers of different lengths and flexibilities. This framework enables us to translate the energetic and entropic effects of the linker into the neutralization potency of a diFab. We demonstrate that the strongest neutralization potencies are predicted to require a rigid linker that optimally spans the distance between two Fab binding sites on an Env trimer and that avidity can be further boosted by incorporating more Fabs into these constructs. These results inform the design of multivalent anti-HIV-1 therapeutics that utilize avidity effects to remain potent against HIV-1 in the face of the rapid mutation of Env spikes.

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Synthetic antibodies that bivalently bind to HIV-1 can markedly enhance avidity

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Linkers that enable bivalent binding are fully characterized by the linker entropy

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Properly sized rigid linkers outperform long, flexible linkers

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Avidity can be further enhanced by increasing antibody valency

Statistical physics and mesoscopic modeling to interpret tethered particle motion experiments

Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques provide raw data such as the tracked particle amplitude of movement, from which relevant information about DNA conformations or states must be recovered. Solving this inverse problem appeals to specific theoretical tools that have been designed in the two last decades, together with the data pre-processing procedures that ought to be implemented to avoid biases inherent to these experimental techniques. These statistical tools and models are reviewed in this paper.

Parallelized DNA tethered bead measurements to scrutinize DNA mechanical structure

Tethering beads to DNA offers a panel of single molecule techniques for the refined analysis of the conformational dynamics of DNA and the elucidation of the mechanisms of enzyme activity. Recent developments include the massive parallelization of these techniques achieved by the fabrication of dedicated nanoarrays by soft nanolithography. We focus here on two of these techniques: the Tethered Particle motion and Magnetic Tweezers allowing analysis of the behavior of individual DNA molecules in the absence of force and under the application of a force and/or a torque, respectively. We introduce the experimental protocols for the parallelization and discuss the benefits already gained, and to come, for these single molecule investigations.

New Aspects of Magnesium Function: A Key Regulator in Nucleosome Self-Assembly, Chromatin Folding and Phase Separation

Metal cations are associated with many biological processes. The effects of these cations on nucleic acids and chromatin were extensively studied in the early stages of nucleic acid and chromatin research. The results revealed that some monovalent and divalent metal cations, including Mg²⁺, profoundly affect the conformations and stabilities of nucleic acids, the folding of chromatin fibers, and the extent of chromosome condensation. Apart from these effects, there have only been a few reports on the functions of these cations. In 2007 and 2013, however, Mg²⁺-implicated novel phenomena were found: Mg²⁺ facilitates or enables both self-assembly of identical double-stranded (ds) DNA molecules and self-assembly of identical nucleosomes in vitro. These phenomena may be deeply implicated in the heterochromatin domain formation and chromatin-based phase separation. Furthermore, a recent study showed that elevation of the intranuclear Mg²⁺ concentration causes unusual differentiation of mouse ES (embryonic stem) cells. All of these phenomena seem to be closely related to one another. Mg²⁺ seems to be a key regulator of chromatin dynamics and chromatin-based biological processes.

How does temperature impact the conformation of single DNA molecules below melting temperature?

The double stranded DNA molecule undergoes drastic structural changes during biological processes such as transcription during which it opens locally under the action of RNA polymerases. Local spontaneous denaturation could contribute to this mechanism by promoting it. Supporting this idea, different biophysical studies have found an unexpected increase in the flexibility of DNA molecules with various sequences as a function of the temperature, which would be consistent with the formation of a growing number of locally denatured sequences. Here, we take advantage of our capacity to detect subtle changes occurring on DNA by using high throughput tethered particle motion to question the existence of bubbles in double stranded DNA under physiological salt conditions through their conformational impact on DNA molecules ranging from several hundreds to thousands of base pairs. Our results strikingly differ from previously published ones, as we do not detect any unexpected change in DNA flexibility below melting temperature. Instead, we measure a bending modulus that remains stable with temperature as expected for intact double stranded DNA.

Rouse model with transient intramolecular contacts on a timescale of seconds recapitulates folding and fluctuation of yeast chromosomes

DNA folding and dynamics along with major nuclear functions are determined by chromosome structural properties, which remain, thus far, elusive in vivo. Here, we combine polymer modeling and single particle tracking experiments to determine the physico-chemical parameters of chromatin in vitro and in living yeast. We find that the motion of reconstituted chromatin fibers can be recapitulated by the Rouse model using mechanical parameters of nucleosome arrays deduced from structural simulations. Conversely, we report that the Rouse model shows some inconsistencies to analyze the motion and structural properties inferred from yeast chromosomes determined with chromosome conformation capture techniques (specifically, Hi-C). We hence introduce the Rouse model with Transient Internal Contacts (RouseTIC), in which random association and dissociation occurs along the chromosome contour. The parametrization of this model by fitting motion and Hi-C data allows us to measure the kinetic parameters of the contact formation reaction. Chromosome contacts appear to be transient; associated to a lifetime of seconds and characterized by an attractive energy of -0.3 to -0.5 kBT. We suggest attributing this energy to the occurrence of histone tail-DNA contacts and notice that its amplitude sets chromosomes in 'theta' conditions, in which they are poised for compartmentalization and phase separation.

Extremely sensitive and wide-range silver ion detection via assessing the integrated surface potential of a DNA-capped gold nanoparticle

With the rapid development of nanotechnology and its associated waste stream, public concern is growing over the potential toxicity exposure to heavy metal ions poses to the human body and the environment. Herein, we report an extremely sensitive Kelvin probe force microscopy (KPFM)-based platform for detecting nanotoxic materials (e.g. Ag⁺) accomplished by probing the integrated surface potential differences of a single gold nanoparticle on which an interaction between probe DNA and target DNA occurs. This interaction can amplify the surface potential of the nanoparticle owing to the coordination bond mediated by Ag⁺ (cytosine-Ag⁺-cytosine base pairs). Interestingly, compared with conventional methods, this platform is capable of extremely sensitive Ag⁺ detection (∼1 fM) in a remarkably wide-range (1 fM to 1 μM). Furthermore, this platform enables Ag⁺ detection in a practical sample (general drinking water), and this KPFM-based technique may have the potential to detect other toxic heavy metal ions and single nucleotide polymorphisms by designing specific DNA sequences.

Dependence of DNA Persistence Length on Ionic Strength and Ion Type

Even though the persistence length L_{P} of double-stranded DNA plays a pivotal role in cell biology and nanotechnologies, its dependence on ionic strength I lacks a consensual description. Using a high-throughput single-molecule technique and statistical physics modeling, we measure L_{P} in the presence of monovalent (Li^{+}, Na^{+}, K^{+}) and divalent (Mg^{2+}, Ca^{2+}) metallic and alkyl ammonium ions, over a large range 0.5  mM≤I≤5  M. We show that linear Debye-Hückel-type theories do not describe even part of these data. By contrast, the Netz-Orland and Trizac-Shen formulas, two approximate theories including nonlinear electrostatic effects and the finite DNA radius, fit our data with divalent and monovalent ions, respectively, over the whole I range. Furthermore, the metallic ion type does not influence L_{P}(I), in contrast to alkyl ammonium monovalent ions at high I.

Energy required to pinch a DNA plectoneme

DNA supercoiling plays an important role from a biological point of view. One of its consequences at the supramolecular level is the formation of DNA superhelices named plectonemes. Normally separated by a distance on the order of 10 nm, the two opposite double strands of a DNA plectoneme must be brought closer if a protein or protein complex implicated in genetic regulation is to be bound simultaneously to both strands, as if the plectoneme was locally pinched. We propose an analytic calculation of the energetic barrier, of elastic nature, required to bring closer the two loci situated on the opposed double strands. We examine how this energy barrier scales with the DNA supercoiling. For physically relevant values of elastic parameters and of supercoiling density, we show that the energy barrier is in the k_{B}T range under physiological conditions, thus demonstrating that the limiting step to loci encounter is more likely the preceding plectoneme slithering bringing the two loci side by side.

Sequence-Dependent Three Interaction Site Model for Single- and Double-Stranded DNA

We develop a robust coarse-grained model for single- and double-stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduce the experimentally measured salt and sequence-dependence of the size of single-stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force, the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin and could be described by a standard polymer model. We also show that the persistence length of double-stranded DNA, formed from two complementary ssDNAs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific trends. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.

Radial distribution function of semiflexible oligomers with stretching flexibility

The radial distribution of the end-to-end distance R_ee is crucial for quantifying the global size and flexibility of a linear polymer. For semiflexible polymers, several analytical formulas have been derived for the radial distribution of R_ee ignoring the stretching flexibility. However, for semiflexible oligomers, such as DNA or RNA, the stretching flexibility can be rather pronounced and can significantly affect the radial distribution of R_ee. In this study, we obtained an extended formula that includes the stretch modulus to describe the distribution of R_ee for semiflexible oligomers on the basis of previous formulas for semiflexible polymers without stretching flexibility. The extended formula was validated by extensive Monte Carlo simulations over wide ranges of the stretch modulus and persistence length, as well as all-atom molecular dynamics simulations of short DNAs and RNAs. Additionally, our analyses showed that the effect of stretching flexibility on the distribution of R_ee becomes negligible for DNAs longer than ∼130 base pairs and RNAs longer than ∼240 base pairs.

A bead-spring chain as a one-dimensional polyelectrolyte gel

The physical principles underlying expansion of a single-chain polyelectrolyte coil caused by Coulomb repulsions among its ionized groups, and the expansion of a cross-linked polyelectrolyte gel, are probably the same. In this paper, we analyze a "one-dimensional" version of a gel, namely, a linear chain of charged beads connected by Hooke's law springs. In the Debye-Hückel range of relatively weak Coulomb strength, where counterion condensation does not occur, the springs are realistically stretched on a nanolength scale by the repulsive interactions among the beads, if we use a spring constant normalized by the inverse square of the solvent Bjerrum length. The persistence length and radius of gyration counter-intuitively decrease when Coulomb strength is increased, if analyzed in the framework of an OSF-type theory; however, a buckling theory generates the increase that is consistent with bead-spring simulations.