Persistence Length of PEGMA Bottle Brushes Determined by Pyrene Excimer Fluorescence

Seven pyrene-labeled poly(oligo(ethylene glycol) methyl ether methacrylate)s (PyEG5-PEGnMAs) were prepared with n = 0, 3, 4, 5, 7, 9, and 19 ethylene glycol units by copolymerizing a small amount of penta(ethylene glycol) 1-pyrenemethyl ether methacrylate with an EGnMA monomer. The conformation of the PyEG5-PEGnMA polymers evolved from a random coil for PyEG5-PEG0MA or poly(methyl methacrylate) to a polymeric bottle brush (PBB) architecture with increasing side chain length. The fluorescence decays of the PyEG5-PEGnMA samples were fitted according to the fluorescence blob model (FBM) whose parameters were used, in combination with the Kratky-Porod equation, to calculate the persistence length of these polymers. The persistence lengths obtained from the PEF experiments were found to increase with the square of the number (NS) of non-hydrogen atoms in the side chain as expected theoretically. The persistence lengths found with the PyEG5-PEGnMA samples in DMF also matched those found earlier for another series of PEGnMA samples labeled with 1-pyrenebutanol. The good agreement found between the persistence lengths obtained with the PEGnMA samples labeled with two different pyrene derivatives illustrates the robustness of the method and its applicability for measuring the unknown persistence length of polydisperse polymer samples.

Switch-like compaction of poly(ADP-ribose) upon cation binding

Poly(ADP-ribose) (PAR) is a homopolymer of adenosine diphosphate ribose that is added to proteins as a posttranslational modification to regulate numerous cellular processes. PAR also serves as a scaffold for protein binding in macromolecular complexes, including biomolecular condensates. It remains unclear how PAR achieves specific molecular recognition. Here, we use single-molecule fluorescence resonance energy transfer (smFRET) to evaluate PAR flexibility under different cation conditions. We demonstrate that, compared to RNA and DNA, PAR has a longer persistence length and undergoes a sharper transition from extended to compact states in physiologically relevant concentrations of various cations (Na+, Mg2+, Ca2+, and spermine4+). We show that the degree of PAR compaction depends on the concentration and valency of cations. Furthermore, the intrinsically disordered protein FUS also served as a macromolecular cation to compact PAR. Taken together, our study reveals the inherent stiffness of PAR molecules, which undergo switch-like compaction in response to cation binding. This study indicates that a cationic environment may drive recognition specificity of PAR.

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.

Durability of Aligned Microtubules Dependent on Persistence Length Determines Phase Transition and Pattern Formation in Collective Motion

Collective motion is a ubiquitous phenomenon in nature. The collective motion of cytoskeleton filaments results mainly from dynamic collisions and alignments; however, the detailed mechanism of pattern formation still needs to be clarified. In particular, the influence of persistence length, which is a measure of filament flexibility, on collective motion is still unclear and lacks experimental verifications although it is likely to directly affect the orientational flexibility of filaments. Here, we investigated the collective motion of microtubules with different persistence lengths using a microtubule-kinesin motility system. We showed that local interactions between microtubules significantly vary depending on their persistence length. We demonstrated that the bundling of microtubules is enhanced by more durable alignment, rather than by greater likelihood of alignment. An agent-based computational model confirmed that the rigidity-dependent durability of microtubule alignment dominates their collective behavior.

Environment-Dependent Stability and Mechanical Properties of DNA Origami Six-Helix Bundles with Different Crossover Spacings

The internal design of DNA nanostructures defines how they behave in different environmental conditions, such as endonuclease-rich or low-Mg²⁺ solutions. Notably, the inter-helical crossovers that form the core of such DNA objects have a major impact on their mechanical properties and stability. Importantly, crossover design can be used to optimize DNA nanostructures for target applications, especially when developing them for biomedical environments. To elucidate this, two otherwise identical DNA origami designs are presented that have a different number of staple crossovers between neighboring helices, spaced at 42- and 21- basepair (bp) intervals, respectively. The behavior of these structures is then compared in various buffer conditions, as well as when they are exposed to enzymatic digestion by DNase I. The results show that an increased number of crossovers significantly improves the nuclease resistance of the DNA origami by making it less accessible to digestion enzymes but simultaneously lowers its stability under Mg²⁺ -free conditions by reducing the malleability of the structures. Therefore, these results represent an important step toward rational, application-specific DNA nanostructure design.

Conformation of Ring Single-Stranded DNA Measured by DNA Origami Structures

Measuring the mechanical properties of single-stranded DNA (ssDNA) is a complex challenge that has been addressed lately by different methods. We measured the persistence length of ring ssDNA using a combination of special DNA origami structure, a self-avoiding ring-polymer simulation model and a non-parametric estimation statistics. The method overcomes the complexities set forth by previously used methods. We designed the DNA origami nano structures and measured the ring ssDNA polymer conformations using atomic force microscopy. We then calculated its radius of gyration, which was used as a fitting parameter for finding the persistence length. As there is no simple formulation for the radius of gyration distribution, we developed a simulation program consisting of a self-avoiding ring polymer to fit the persistence length to the experimental data. ssDNA naturally forms stem loops, which should be taken into account in fitting a model to the experimental measurement. To overcome that hurdle, we found the possible loops using minimal energy considerations and used it in our fitting procedure of the persistence length. Due to the statistical nature of the loops formation, we calculated the persistence length for different percentages of loops that are formed. In the range of 25-75% loop formation, we found the persistence length to be 1.9-4.4 nm and for 50% loop formation we get a persistence length of 2.83±0.63nm. This estimation narrows the previously known persistence length, and provides tools for finding the conformations of ssDNA.

Visualization of DNA Damage and Protection by Atomic Force Microscopy in Liquid

DNA damage is closely related to cancer and many aging-related diseases. Peroxynitrite is a strong oxidant, thus a typical DNA damage agent, and is a major mediator of the inflammation-associated pathogenesis. For the first time, we directly visualized the process of DNA damage by peroxynitrite and DNA protection by ectoine via atomic force microscopy in liquid. We found that the persistence length of DNA decreases significantly by adding a small amount of peroxynitrite, but the observed DNA chains are still intact. Specifically, the persistence length of linear DNA in a low concentration of peroxynitrite (0 µM to 200 µM) solution decreases from about 47 nm to 4 nm. For circular plasmid DNA, we observed the enhanced superhelices of plasmid DNA due to the chain soften. When the concentration of peroxynitrite was above 300 µM, we observed the fragments of DNA. Interestingly, we also identified single-stranded DNAs during the damage process, which is also confirmed by ultraviolet spectroscopy. However, if we added 500 mM ectoine to the high concentration PN solution, almost no DNA fragments due to double strand breaks were observed because of the protection of ectoine. This protection is consistent with the similar effect for DNA damage caused by ionizing radiation and oxygenation. We ascribe DNA protection to the preferential hydration of ectoine.

Bottom-Up Coarse-Grained Modeling of DNA

Recent advances in methodology enable effective coarse-grained modeling of deoxyribonucleic acid (DNA) based on underlying atomistic force field simulations. The so-called bottom-up coarse-graining practice separates fast and slow dynamic processes in molecular systems by averaging out fast degrees of freedom represented by the underlying fine-grained model. The resulting effective potential of interaction includes the contribution from fast degrees of freedom effectively in the form of potential of mean force. The pair-wise additive potential is usually adopted to construct the coarse-grained Hamiltonian for its efficiency in a computer simulation. In this review, we present a few well-developed bottom-up coarse-graining methods, discussing their application in modeling DNA properties such as DNA flexibility (persistence length), conformation, "melting," and DNA condensation.

Coarse-Grained Simulation of Mechanical Properties of Single Microtubules With Micrometer Length

Microtubules are one of the most important components in the cytoskeleton and play a vital role in maintaining the shape and function of cells. Because single microtubules are some micrometers long, it is difficult to simulate such a large system using an all-atom model. In this work, we use the newly developed convolutional and K-means coarse-graining (CK-CG) method to establish an ultra-coarse-grained (UCG) model of a single microtubule, on the basis of the low electron microscopy density data of microtubules. We discuss the rationale of the micro-coarse-grained microtubule models of different resolutions and explore microtubule models up to 12-micron length. We use the devised microtubule model to quantify mechanical properties of microtubules of different lengths. Our model allows mesoscopic simulations of micrometer-level biomaterials and can be further used to study important biological processes related to microtubule function.

Cryoelectron Tomography Reveals Nanoscale Organization of the Cytoskeleton and Its Relation to Microtubule Curvature Inside Cells

Microtubules (MTs) are the most rigid elements of the cytoskeleton with in vitro persistence lengths (L_p) in the range of 1-6 mm. In cellular environments, however, MTs often appear strongly curved. This has been attributed to the forces acting upon them in situ where they are embedded in composite networks of different cytoskeletal elements. Hitherto, the nanoscale organization of these networks has remained largely uncharacterized. Cryo-electron tomography (cryo-ET) allowed to visualize and analyze the in situ structure of cytoskeletal networks in pristinely preserved cellular environments and at high resolution. Here, we studied the molecular organization of MTs and their interactions with the composite cytoskeleton in frozen-hydrated HeLa and P19 cells at different cell-cycle stages. We describe modulation of MT curvature correlated with the surrounding molecular architecture, and show that nanoscale defects occur in curved MTs. The data presented here contribute to constructing realistic models of cytoskeletal biomechanics.

DNA Nunchucks: Nanoinstrumentation for Single-Molecule Measurement of Stiffness and Bending

Bending of double-stranded DNA (dsDNA) has important applications in biology and engineering, but measurement of DNA bend angles is notoriously difficult and rarely dynamic. Here we introduce a nanoscale instrument that makes dynamic measurement of the bend in short dsDNAs easy enough to be routine. The instrument works by embedding the ends of a dsDNA in stiff, fluorescently labeled DNA nanotubes, thereby mechanically magnifying their orientations. The DNA nanotubes are readily confined to a plane and imaged while freely diffusing. Single-molecule bend angles are rapidly and reliably extracted from the images by a neural network. We find that angular variance across a population increases with dsDNA length, as predicted by the worm-like chain model, although individual distributions can differ significantly from one another. For dsDNAs with phased A₆-tracts, we measure an intrinsic bend of 17 ± 1° per A₆-tract, consistent with other methods, and a length-dependent angular variance that indicates A₆-tracts are (80 ± 30)% stiffer than generic dsDNA.

Tailoring the Mechanical Stiffness of DNA Nanostructures Using Engineered Defects

As scaffolded DNA origami enables the construction of diverse DNA nanostructures with predefined shapes, precise modulation of their mechanical stiffness remains challenging. We demonstrate a modular design method to widely and precisely control the mechanical flexibility of scaffolded DNA origami nanostructures while maintaining their overall structural integrity and geometric characteristics. Individually engineered defects that are short single-stranded DNA (ssDNA) gaps could reduce up to 70% of the bending stiffness of DNA origami constructs with different cross-sectional shapes. We further developed a computational analysis platform predicting the bending stiffness of a defect-engineered DNA nanostructure quickly during the design process, to offer an efficient way of designing various DNA constructs with required mechanical stiffness in a desired shape for a targeted function.

Imaging DNA Equilibrated onto Mica in Liquid Using Biochemically Relevant Deposition Conditions

For over 25 years, imaging of DNA by atomic force microscopy has been intensely pursued. Ideally, such images are then used to probe the physical properties of DNA and characterize protein-DNA interactions. The atomic flatness of mica makes it the preferred substrate for high signal-to-noise ratio (SNR) imaging, but the negative charge of mica and DNA hinders deposition. Traditional methods for imaging DNA and protein-DNA complexes in liquid have drawbacks: DNA conformations with an anomalous persistence length ( p), low SNR, and/or ionic deposition conditions detrimental to preserving protein-DNA interactions. Here, we developed a process to bind DNA to mica in a buffer containing both MgCl₂ and KCl that resulted in high SNR images of equilibrated DNA in liquid. Achieving an equilibrated 2D configuration ( i. e., p = 50 nm) not only implied a minimally perturbative binding process but also improved data quality and quantity because the DNA's configuration was more extended. In comparison to a purely NiCl₂-based protocol, we showed that an 8-fold larger fraction (90%) of 680-nm-long DNA molecules could be quantified. High-resolution images of select equilibrated molecules revealed the right-handed structure of DNA with a helical pitch of 3.5 nm. Deposition and imaging of DNA was achieved over a wide range of monovalent and divalent ionic conditions, including a buffer containing 50 mM KCl and 3 mM MgCl₂. Finally, we imaged two protein-DNA complexes using this protocol: a restriction enzyme bound to DNA and a small three-nucleosome array. We expect such deposition of protein-DNA complexes at biochemically relevant ionic conditions will facilitate biophysical insights derived from imaging diverse protein-DNA complexes.

The Persistence Length of Semiflexible Polymers in Lattice Monte Carlo Simulations

While applying computer simulations to study semiflexible polymers, it is a primary task to determine the persistence length that characterizes the chain stiffness. One frequently asked question concerns the relationship between persistence length and the bending constant of applied bending potential. In this paper, theoretical persistence lengths of polymers with two different bending potentials were analyzed and examined by using lattice Monte Carlo simulations. We found that the persistence length was consistent with theoretical predictions only in bond fluctuation model with cosine squared angle potential. The reason for this is that the theoretical persistence length is calculated according to a continuous bond angle, which is discrete in lattice simulations. In lattice simulations, the theoretical persistence length is larger than that in continuous simulations.

Nanochannel-Confined TAMRA-Polypyrrole Stained DNA Stretching by Varying the Ionic Strength from Micromolar to Millimolar Concentrations

Large DNA molecules have been utilized as a model system to investigate polymer physics. However, DNA visualization via intercalating dyes has generated equivocal results due to dye-induced structural deformation, particularly unwanted unwinding of the double helix. Thus, the contour length increases and the persistence length changes so unpredictably that there has been a controversy. In this paper, we used TAMRA-polypyrrole to stain single DNA molecules. Since this staining did not change the contour length of B-form DNA, we utilized TAMRA-polypyrrole stained DNA as a tool to measure the persistence length by changing the ionic strength. Then, we investigated DNA stretching in nanochannels by varying the ionic strength from 0.06 mM to 47 mM to evaluate several polymer physics theories proposed by Odijk, de Gennes and recent papers to deal with these regimes.

Measuring the Conformation and Persistence Length of Single-Stranded DNA Using a DNA Origami Structure

Measuring the mechanical properties of single-stranded DNA (ssDNA) is a challenge that has been addressed by different methods lately. The short persistence length, fragile structure, and the appearance of stem loops complicate the measurement, and this leads to a large variability in the measured values. Here we describe an innovative method based on DNA origami for studying the biophysical properties of ssDNA. By synthesizing a DNA origami structure that consists of two rigid rods with an ssDNA segment between them, we developed a method to characterize the effective persistence length of a random-sequence ssDNA while allowing the formation of stem loops. We imaged the structure with an atomic force microscope (AFM); the rigid rods provide a means for the exact identification of the ssDNA ends. This leads to an accurate determination of the end-to-end distance of each ssDNA segment, and by fitting the measured distribution to the ideal chain polymer model we measured an effective persistence length of 1.98 ± 0.72 nm. This method enables one to measure short or long strands of ssDNA, and it can cope with the formation of stem loops that are often formed along ssDNA. We envision that this method can be used for measuring stem loops for determining the effect of repetitive nucleotide sequences and environmental conditions on the mechanical properties of ssDNA and the effect of interacting proteins with ssDNA. We further noted that the method can be extended to nanoprobes for measuring the interactions of specific DNA sequences, because the DNA origami rods (or similar structures) can hold multiple fluorescent probes that can be easily detected.

Effects of Design Choices on the Stiffness of Wireframe DNA Origami Structures

DNA origami is a powerful method for the creation of 3D nanoscale objects, and in the past few years, interest in wireframe origami designs has increased due to their potential for biomedical applications. In DNA wireframe designs, the construction material is double-stranded DNA, which has a persistence length of around 50 nm. In this work, we study the effect of various design choices on the stiffness versus final size of nanoscale wireframe rods, given the constraints on origami designs set by the DNA origami scaffold size. An initial theoretical analysis predicts two competing mechanisms limiting rod stiffness, whose balancing results in an optimal edge length. For small edge lengths, the bending of the rod's overall frame geometry is the dominant factor, while the flexibility of individual DNA edges has a greater contribution at larger edge lengths. We evaluate our design choices through simulations and experiments and find that the stiffness of the structures increases with the number of sides in the cross-section polygon and that there are indications of an optimal member edge length. We also ascertain the effect of nicked DNA edges on the stiffness of the wireframe rods and demonstrate that ligation of the staple breakpoint nicks reduces the observed flexibility. Our simulations also indicate that the persistence length of wireframe DNA structures significantly decreases with increasing monovalent salt concentration.

Nanoscale inhibition of polymorphic and ambidextrous IAPP amyloid aggregation with small molecules

Understanding how small molecules interface amyloid fibrils on the nanoscale is of importance for developing therapeutic treatment against amyloid-based diseases. Here we show, for the first time, that human islet amyloid polypeptide (IAPP) in the fibrillar form is polymorphic and ambidextrous possessing multiple periodicities. Upon interfacing with small molecule epigallocatechin gallate (EGCG), IAPP aggregation was rendered off pathway assuming the form of soft and disordered clusters, while mature IAPP fibrils displayed kinks and branching but conserved the twisted fibril morphology. These nanoscale phenomena resulted from competitive interactions between EGCG and the IAPP amyloidogenic region, as well as end capping of the fibrils by the small molecule. This information is crucial to delineating IAPP toxicity implicated in type 2 diabetes and developing new inhibitors against amyloidogenesis.

Self consistent field theory of virus assembly

The ground state dominance approximation (GSDA) has been extensively used to study the assembly of viral shells. In this work we employ the self-consistent field theory (SCFT) to investigate the adsorption of RNA onto positively charged spherical viral shells and examine the conditions when GSDA does not apply and SCFT has to be used to obtain a reliable solution. We find that there are two regimes in which GSDA does work. First, when the genomic RNA length is long enough compared to the capsid radius, and second, when the interaction between the genome and capsid is so strong that the genome is basically localized next to the wall. We find that for the case in which RNA is more or less distributed uniformly in the shell, regardless of the length of RNA, GSDA is not a good approximation. We observe that as the polymer-shell interaction becomes stronger, the energy gap between the ground state and first excited state increases and thus GSDA becomes a better approximation. We also present our results corresponding to the genome persistence length obtained through the tangent-tangent correlation length and show that it is zero in case of GSDA but is equal to the inverse of the energy gap when using SCFT.

Fiber Network Formation in Semi-Flexible Polymer Solutions: An Exploratory Computational Study

The formation of gels through the bundling of semi-flexible polymer chains into fiber networks is ubiquitous in diverse manufactured and natural materials, and, accordingly, we perform exploratory molecular dynamics simulations of a coarse-grained model of semi-flexible polymers in a solution with attractive lateral interchain interactions to understand essential features of this type of gel formation. After showing that our model gives rise to fibrous gels resembling real gels of this kind, we investigate how the extent of fiber bundling influences the "melting" temperature, T m , and the emergent rigidification of model bundled fibers having a fixed number of chains, N, within them. Based on our preliminary observations, we suggest the fiber size is kinetically selected by a reduced thermodynamic driving force and a slowing of the dynamics within the fibers associated with their progressive rigidification with the inclusion of an increasing number of chains in the bundle.

Guidance and Self-Sorting of Active Swimmers: 3D Periodic Arrays Increase Persistence Length of Human Sperm Selecting for the Fittest

Male infertility is a reproductive disease, and existing clinical solutions for this condition often involve long and cumbersome sperm sorting methods, including preprocessing and centrifugation-based steps. These methods also fall short when sorting for sperm free of reactive oxygen species, DNA damage, and epigenetic aberrations. Although several microfluidic platforms exist, they suffer from structural complexities, i.e., pumps or chemoattractants, setting insurmountable barriers to clinical adoption. Inspired by the natural filter-like capabilities of the female reproductive tract for sperm selection, a model-driven design, featuring pillar arrays that efficiently and noninvasively isolate highly motile and morphologically normal sperm, with lower epigenetic global methylation, from raw semen, is presented. The Simple Periodic ARray for Trapping And isolatioN (SPARTAN) created here modulates the directional persistence of sperm, increasing the spatial separation between progressive and nonprogressive motile sperm populations within an unprecedentedly short 10 min assay time. With over 99% motility of sorted sperm, a 5-fold improvement in morphology, 3-fold increase in nuclear maturity, and 2-4-fold enhancement in DNA integrity, SPARTAN offers to standardize sperm selection while eliminating operator-to-operator variations, centrifugation, and flow. SPARTAN can also be applied in other areas, including conservation ecology, breeding of farm animals, and design of flagellar microrobots for diagnostics.

Hierarchical Assembly of DNA Filaments with Designer Elastic Properties

The elastic features of protein filaments are encoded in their component units and in the way they are connected, thus defining a biunivocal relationship between the monomer and the result of its self-assembly. Using DNA origami approaches, we constructed a reconfigurable module, composed of two quasi-independent domains and four possible interfaces, capable of facial and lateral growing through specific recognition patterns. Whereas the flexibility of the intra-domains region can be regulated by switchable DNA motifs, the inter-domain interfaces feature mutually and self-complementary shapes, whose pairwise association leads to filaments of programmable periodicity and variable persistence length. Thus, we show here that the assembly pathway leading to oligomeric chains can be finely tuned and fully controlled, enabling the emulation of protein-like filaments using a single construction principle. Our approach results in artificial materials with a large variety of ultrastructures and bending strengths comparable, or even superior, to their natural counterparts.

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

Mechanical properties of complex, polymer-based soft matter, such as cells or biopolymer networks, can be understood in neither the classical frame of flexible polymers nor of rigid rods. Underlying filaments remain outstretched due to their non-vanishing backbone stiffness, which is quantified via the persistence length (lp), but they are also subject to strong thermal fluctuations. Their finite bending stiffness leads to unique, non-trivial collective mechanics of bulk networks, enabling the formation of stable scaffolds at low volume fractions while providing large mesh sizes. This underlying principle is prevalent in nature (e.g., in cells or tissues), minimizing the high molecular content and thereby facilitating diffusive or active transport. Due to their biological implications and potential technological applications in biocompatible hydrogels, semiflexible polymers have been subject to considerable study. However, comprehensible investigations remained challenging since they relied on natural polymers, such as actin filaments, which are not freely tunable. Despite these limitations and due to the lack of synthetic, mechanically tunable, and semiflexible polymers, actin filaments were established as the common model system. A major limitation is that the central quantity lp cannot be freely tuned to study its impact on macroscopic bulk structures. This limitation was resolved by employing structurally programmable DNA nanotubes, enabling controlled alteration of the filament stiffness. They are formed through tile-based designs, where a discrete set of partially complementary strands hybridize in a ring structure with a discrete circumference. These rings feature sticky ends, enabling the effective polymerization into filaments several microns in length, and display similar polymerization kinetics as natural biopolymers. Due to their programmable mechanics, these tubes are versatile, novel tools to study the impact of lp on the single-molecule as well as the bulk scale. In contrast to actin filaments, they remain stable over weeks, without notable degeneration, and their handling is comparably straightforward.

Wrinkles in Polytetrafluoroethylene on Polystyrene: Persistence Lengths and the Effect of Nanoinclusions

We characterize wrinkling on the surfaces of prestrained polystyrene sheets coated with thin polytetrafluoroethylene skins using a combination of mechanical strain measurements and 3D finite element simulations. The simulations show that wrinkle wavelength increases with skin thickness, in agreement with a well-known continuum model and recent experiments. The wrinkle amplitudes also increase with strain. Nanoinclusions, such as holes and patterned lines, influence wrinkle patterns over limited distances, and these distances are shown to scale with the wrinkle wavelengths. Good agreement between experimental and simulated influence distances is observed. The inclusions provide strain relief, and they behave as if they are attracting adjacent material when the sheets are under strain. The wrinkles have stiffnesses in much the same way as do polymers (but at different length scales), a property that is quantified for polymers using persistence lengths. We show that the concept of persistence length can be useful in characterizing the wrinkle properties that we have observed. However, the calculated persistence lengths do not vary systematically with thickness and strain, as interactions between neighboring wrinkles produce confinement that is analogous to the kinetic confinement of polymers.

Optical detection of nanometric thermal fluctuations to measure the stiffness of rigid superparamagnetic microrods

The rigidity of numerous biological filaments and crafted microrods has been conveniently deduced from the analysis of their thermal fluctuations. However, the difficulty of measuring nanometric displacements with an optical microscope has so far limited such studies to sufficiently flexible rods, of which the persistence length ([Formula: see text]) rarely exceeds 1 m at room temperature. Here, we demonstrate the possibility to probe 10-fold stiffer rods by a combination of superresolutive optical methods and a statistical analysis of the data based on a recent theoretical model that predicts the amplitude of the fluctuations at any location of the rod [Benetatos P, Frey E (2003) Phys Rev E Stat Nonlin Soft Matter Phys 67(5):051108]. Using this approach, we report measures of [Formula: see text] up to 0.5 km. We obtained these measurements on recently designed superparamagnetic [Formula: see text]40-[Formula: see text]m-long microrods containing iron-oxide nanoparticles connected by a polymer mesh. Using their magnetic properties, we provide an alternative proof of validity of these thermal measurements: For each individual studied rod, we performed a second measure of its rigidity by deflecting it with a uniform magnetic field. The agreement between the thermal and the magnetoelastic measures was realized with more than a decade of values of [Formula: see text] from 5.1 m to 129 m, corresponding to a bending modulus ranging from 2.2 to 54 (×[Formula: see text] Jm). Despite the apparent homogeneity of the analyzed microrods, their Young modulus follows a broad distribution from 1.9 MPa to 59 MPa and up to 200 MPa, depending on the size of the nanoparticles.

Nanoscale Structure and Elasticity of Pillared DNA Nanotubes

We present an atomistic model of pillared DNA nanotubes (DNTs) and their elastic properties which will facilitate further studies of these nanotubes in several important nanotechnological and biological applications. In particular, we introduce a computational design to create an atomistic model of a 6-helix DNT (6HB) along with its two variants, 6HB flanked symmetrically with two double helical DNA pillars (6HB+2) and 6HB flanked symmetrically by three double helical DNA pillars (6HB+3). Analysis of 200 ns all-atom simulation trajectories in the presence of explicit water and ions shows that these structures are stable and well behaved in all three geometries. Hydrogen bonding is well maintained for all variants of 6HB DNTs. From the equilibrium bending angle distribution, we calculate the persistence lengths of these tubes. The measured persistence lengths of these nanotubes are ∼10 μm, which is 2 orders of magnitude larger than that of dsDNA. We also find a gradual increase of persistence length with an increasing number of pillars, in quantitative agreement with previous experimental findings. To have a quantitative understanding of the stretch modulus of these tubes, we carried out nonequilibrium steered molecular dynamics (SMD). The linear part of the force-extension plot gives a stretch modulus in the range 6500 pN for 6HB without pillars, which increases to 11 000 pN for tubes with three pillars. The values of the stretch modulus calculated using contour length distribution obtained from equilibrium MD simulations are similar to those obtained from nonequilibrium SMD simulations. The addition of pillars makes these DNTs very rigid.

Modeling bond correlations in denatured proteins and polypeptides

Bond-orientational correlations for finite-length homopolypeptides and a selected group of denatured proteins are obtained by numerical simulations using a polypeptide model with a potential of mean force. These correlations characterize the stiffness of the polypeptide backbone and are generally described by either an exponential or a power-law decay in the asymptotic limit. However, for finite length polypeptides and unfolded proteins the correlations significantly deviate from either single exponential or power-law behavior. A heuristic model is developed to analyze the correlations of homopolypeptides, which depends on the chain length and the side-chain properties. The model contains power-law and multi-exponential terms, the latter which could be interpreted as local persistence lengths. In the asymptotic limit, the model reduces to the expected power-law behavior. Simulations of denatured proteins show that the power-law behavior of the correlations is significantly suppressed and only the multi-exponential term is needed to model the correlations. In addition, average persistence lengths (ranging from 2.0 to 2.5 nm) are obtained from the correlations by fitting single exponentials and shown to be in general agreement with experiments, which also assume single exponential decay. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 312-323, 2016.

The Contributions of the Amino and Carboxy Terminal Domains of Flightin to the Biomechanical Properties of Drosophila Flight Muscle Thick Filaments

Flightin is a myosin binding protein present in Pancrustacea. In Drosophila, flightin is expressed in the indirect flight muscles (IFM), where it is required for the flexural rigidity, structural integrity, and length determination of thick filaments. Comparison of flightin sequences from multiple Drosophila species revealed a tripartite organization indicative of three functional domains subject to different evolutionary constraints. We use atomic force microscopy to investigate the functional roles of the N-terminal domain and the C-terminal domain that show different patterns of sequence conservation. Thick filaments containing a C-terminal domain truncated flightin (fln^ΔC44) are significantly shorter (2.68 ± 0.06 μm; p < 0.005) than thick filaments containing a full length flightin (fln⁺; 3.21 ± 0.05 μm) and thick filaments containing an N-terminal domain truncated flightin (fln^ΔN62; 3.21 ± 0.06 μm). Persistence length was significantly reduced in fln^ΔN62 (418 ± 72 μm; p < 0.005) compared to fln⁺ (1386 ± 196μm) and fln^ΔC44(1128 ± 193 μm). Statistical polymer chain analysis revealed that the C-terminal domain fulfills a secondary role in thick filament bending propensity. Our results indicate that the flightin amino and carboxy terminal domains make distinct contributions to thick filament biomechanics. We propose these distinct roles arise from the interplay between natural selection and sexual selection given IFM’s dual role in flight and courtship behaviors.

Strong Resistance to Bending Observed for Nanoparticle Membranes

We demonstrate how gold nanoparticle monolayers can be curled up into hollow scrolls that make it possible to extract both bending and stretching moduli from indentation by atomic force microscopy. We find a bending modulus that is 2 orders of magnitude larger than predicted by standard continuum elasticity, an enhancement we associate with nonlocal microstructural constraints. This finding opens up new opportunities for independent control of resistance to bending and stretching at the nanoscale.

Controlling Cooperativity in β-Cyclodextrin-DNA Binding Reactions

We have investigated the interaction between the native neutral β-cyclodextrin (CD) and the DNA molecule by performing single-molecule stretching experiments with optical tweezers. In particular, we have monitored the changes of the mechanical properties of the CD-DNA complexes as a function of the CD concentration in the sample. By using a quenched disorder statistical model, we were also capable to extract important physicochemical information (equilibrium binding constants, cooperativity degree) of such interaction from the mechanical data. In addition, we have found that the interaction occurs by two different mechanisms, first with the formation of relatively large CD clusters along the double helix, which thereafter can locally denature the DNA molecule by forming hydrogen bonds with the base pairs that eventually flip out. A prediction of our quenched disorder model was that cooperativity could be controlled by adjusting the surface charge of β-CD molecules. This prediction is confirmed in the present work.

In Silico Measurements of Twist and Bend Moduli for β-Solenoid Protein Self-Assembly Units

We compute potentials of mean force for bend and twist deformations via force pulling and umbrella sampling experiments for four β-solenoid proteins (BSPs) that show promise in nanotechnology applications. In all cases, we find quasi-Hooke's law behavior until the point of rupture. Bending moduli show modest anisotropy for two-sided and three-sided BSPs, and little anisotropy for a four-sided BSP. There is a slight clockwise/counterclockwise asymmetry in the twist potential of mean force, showing greater stiffness when the applied twist follows the intrinsic twist. When we extrapolate to beam theory appropriate for amyloid fibrils of the BSPs, we find bend/twist moduli which are somewhat smaller than those in the literature for other amyloid fibrils. Twist persistence lengths are on the order of a micron, and bend persistence lengths are several microns. Provided the intrinsic twist can be reversed, these results support the usage of BSPs in biomaterials applications.

Actin Mechanics and Fragmentation

Cell physiological processes require the regulation and coordination of both mechanical and dynamical properties of the actin cytoskeleton. Here we review recent advances in understanding the mechanical properties and stability of actin filaments and how these properties are manifested at larger (network) length scales. We discuss how forces can influence local biochemical interactions, resulting in the formation of mechanically sensitive dynamic steady states. Understanding the regulation of such force-activated chemistries and dynamic steady states reflects an important challenge for future work that will provide valuable insights as to how the actin cytoskeleton engenders mechanoresponsiveness of living cells.

Site-specific cation release drives actin filament severing by vertebrate cofilin

Actin polymerization powers the directed motility of eukaryotic cells. Sustained motility requires rapid filament turnover and subunit recycling. The essential regulatory protein cofilin accelerates network remodeling by severing actin filaments and increasing the concentration of ends available for elongation and subunit exchange. Although cofilin effects on actin filament assembly dynamics have been extensively studied, the molecular mechanism of cofilin-induced filament severing is not understood. Here we demonstrate that actin filament severing by vertebrate cofilin is driven by the linked dissociation of a single cation that controls filament structure and mechanical properties. Vertebrate cofilin only weakly severs Saccharomyces cerevisiae actin filaments lacking this "stiffness cation" unless a stiffness cation-binding site is engineered into the actin molecule. Moreover, vertebrate cofilin rescues the viability of a S. cerevisiae cofilin deletion mutant only when the stiffness cation site is simultaneously introduced into actin, demonstrating that filament severing is the essential function of cofilin in cells. This work reveals that site-specific interactions with cations serve a key regulatory function in actin filament fragmentation and dynamics.

Resolving Internal Motional Correlations to Complete the Conformational Entropy Meter

Conformational entropy (SΩ) has long been used to theoretically characterize the dynamics of proteins, DNA, and other polymers. Though recent advances enabled its calculation also from simulations and nuclear magnetic resonance (NMR) relaxation experiments, correlated molecular motion has hitherto greatly hindered both numerical and experimental determination, requiring demanding empirical and computational calibrations. Herein, we show that these motional correlations can be estimated directly from the temperature-dependent SΩ series that reveal effective persistence lengths of the polymers, which we demonstrate by measuring SΩ of amphiphilic molecules in model lipid systems by spin-labeling electron paramagnetic resonance (EPR) spectroscopy. We validate our correlation-corrected SΩ meter against the basic biophysical interactions underlying biomembrane formation and stability, against the changes in enthalpy and diffusion coefficients upon phase transitions, and against the energetics of fatty acid dissociation. As the method can be directly applied to conformational analysis of proteins and other polymers, as well as adapted to NMR or polarized fluorescence techniques, we believe that the approach can greatly enrich the scope of experimentally available statistical thermodynamics, offering new physical insights into the behavior of biomolecules.

Active conformation control of unfolded proteins by hyperthermal collision with a metal surface

The physical and chemical properties of macromolecules like proteins are strongly dependent on their conformation. The degrees of freedom of their chemical bonds generate a huge conformational space, of which, however, only a small fraction is accessible in thermal equilibrium. Here we show that soft-landing electrospray ion beam deposition (ES-IBD) of unfolded proteins allows to control their conformation. The dynamics and result of the deposition process can be actively steered by selecting the molecular ion beam's charge state or tuning the incident energy. Using these parameters, protein conformations ranging from fully extended to completely compact can be prepared selectively on a surface, as evidenced on the subnanometer/amino acid resolution level by scanning tunneling microscopy (STM). Supported by molecular dynamics (MD) simulations, our results demonstrate that the final conformation on the surface is reached through a mechanical deformation during the hyperthermal ion surface collision. Our experimental results independently confirm the findings of ion mobility spectrometry (IMS) studies of protein gas phase conformations. Moreover, we establish a new route for the processing of macromolecular materials, with the potential to reach conformations that would be inaccessible otherwise.

Charge Diffusion in Semiconducting Polymers: Analytical Relation between Polymer Rigidity and Time Scales for Intrachain and Interchain Hopping

We study the charge diffusion of semiconducting polymer bulk using simplified coarse grained models to investigate the relation between charge diffusion coefficient and the characteristics time of intrachain and interchain hopping, τ1 and τ2. We consider the process of charge diffusion in several standard models of polymer chains (rigid chain, Gaussian chain, worm-like chain), and we achieve an analytical expression for the diffusion coefficient in terms of the characteristic times and the geometric parameters defining the chain models. The diffusion depends only on the intrachain hopping for the rigid chain and on the geometric average of intrachain and interchain hopping times for the Gaussian chain (the least rigid model), with an analytical interpolation available between two limits. The model highlights the importance of large persistence lengths for improved transport properties. In all cases, it is incorrect to consider the slower interchain hopping as the rate-determining step for the charge transport.

BIOPHYSICAL PROPERTIES OF NUCLEIC ACIDS AT SURFACES RELEVANT TO MICROARRAY PERFORMANCE

Both clinical and analytical metrics produced by microarray-based assay technology have recognized problems in reproducibility, reliability and analytical sensitivity. These issues are often attributed to poor understanding and control of nucleic acid behaviors and properties at solid-liquid interfaces. Nucleic acid hybridization, central to DNA and RNA microarray formats, depends on the properties and behaviors of single strand (ss) nucleic acids (e.g., probe oligomeric DNA) bound to surfaces. ssDNA's persistence length, radius of gyration, electrostatics, conformations on different surfaces and under various assay conditions, its chain flexibility and curvature, charging effects in ionic solutions, and fluorescent labeling all influence its physical chemistry and hybridization under assay conditions. Nucleic acid (e.g., both RNA and DNA) target interactions with immobilized ssDNA strands are highly impacted by these biophysical states. Furthermore, the kinetics, thermodynamics, and enthalpic and entropic contributions to DNA hybridization reflect global probe/target structures and interaction dynamics. Here we review several biophysical issues relevant to oligomeric nucleic acid molecular behaviors at surfaces and their influences on duplex formation that influence microarray assay performance. Correlation of biophysical aspects of single and double-stranded nucleic acids with their complexes in bulk solution is common. Such analysis at surfaces is not commonly reported, despite its importance to microarray assays. We seek to provide further insight into nucleic acid-surface challenges facing microarray diagnostic formats that have hindered their clinical adoption and compromise their research quality and value as genomics tools.

Heat-transfer-based detection of SNPs in the PAH gene of PKU patients

Conventional neonatal diagnosis of phenylketonuria is based on the presence of abnormal levels of phenylalanine in the blood. However, for carrier detection and prenatal diagnosis, direct detection of disease-correlated mutations is needed. To speed up and simplify mutation screening in genes, new technologies are developed. In this study, a heat-transfer method is evaluated as a mutation-detection technology in entire exons of the phenylalanine hydroxylase (PAH) gene. This method is based on the change in heat-transfer resistance (R_th) upon thermal denaturation of dsDNA (double-stranded DNA) on nanocrystalline diamond. First, ssDNA (single-stranded DNA) fragments that span the size range of the PAH exons were successfully immobilized on nanocrystalline diamond. Next, it was studied whether an R_th change could be observed during the thermal denaturation of these DNA fragments after hybridization to their complementary counterpart. A clear R_th shift during the denaturation of exon 5, exon 9, and exon 12 dsDNA was observed, corresponding to lengths of up to 123 bp. Finally, R_th was shown to detect prevalent single-nucleotide polymorphisms, c.473G>A (R158Q), c.932T>C (p.L311P), and c.1222C>T (R408W), correlated with phenylketonuria, displaying an effect related to the different melting temperatures of homoduplexes and heteroduplexes.

Investigation of the Polymeric Properties of α-Synuclein and Comparison with NMR Experiments: A Replica Exchange Molecular Dynamics Study

Intrinsically disordered proteins (IDPs) have been shown to be involved in a number of cellular functions, in addition to their predominance in diseased states. α-synuclein may be described as one such IDP implicated in the pathology of Parkinson's disease. Understanding the conformational characteristics of the monomeric state of α-synuclein is necessary for understanding the role of the monomer conformation in aggregation. Polymer theories have been applied to investigate the statistical properties of homopolymeric IDPs. Here we use Replica Exchange Molecular Dynamics (REMD) simulations using temperature as a proxy for solvent quality to examine how well these theories developed for homopolymeric chains describe heteropolymeric α-synuclein. Our results indicate that α-synuclein behaves like a homopolymer at the extremes of solvent quality, while in the intermediate solvent regime, the uneven distribution of charged residues along the sequence strongly influences the conformations adopted by the chain. We refine the ensemble extracted from the REMD simulations of α-synuclein, which shows the best qualitative agreement with experiment, by fitting to the experimental NMR Residual Dipolar Couplings (RDCs) and Paramagnetic Relaxation Enhancements (PREs). Our results demonstrate that the detailed shape of the RDC patterns are sensitive to the angular correlations that are local in sequence while longer range anti-correlations which arise from packing constraints affect the RDC magnitudes.

Tropomyosin flexural rigidity and single ca(2+) regulatory unit dynamics: implications for cooperative regulation of cardiac muscle contraction and cardiomyocyte hypertrophy

Striated muscle contraction is regulated by dynamic and cooperative interactions among Ca²⁺, troponin, and tropomyosin on the thin filament. While Ca²⁺ regulation has been extensively studied, little is known about the dynamics of individual regulatory units and structural changes of individual tropomyosin molecules in relation to their mechanical properties, and how these factors are altered by cardiomyopathy mutations in the Ca²⁺ regulatory proteins. In this hypothesis paper, we explore how various experimental and analytical approaches could broaden our understanding of the cooperative regulation of cardiac contraction in health and disease.

Design and characterization of 1D nanotubes and 2D periodic arrays self-assembled from DNA multi-helix bundles

Among the key goals of structural DNA nanotechnology are to build highly ordered structures self-assembled from individual DNA motifs in 1D, 2D, and finally 3D. All three of these goals have been achieved with a variety of motifs. Here, we report the design and characterization of 1D nanotubes and 2D arrays assembled from three novel DNA motifs, the 6-helix bundle (6HB), the 6-helix bundle flanked by two helices in the same plane (6HB+2), and the 6-helix bundle flanked by three helices in a trigonal arrangement (6HB+3). Long DNA nanotubes have been assembled from all three motifs. Such nanotubes are likely to have applications in structural DNA nanotechnology, so it is important to characterize their physical properties. Prominent among these are their rigidities, described by their persistence lengths, which we report here. We find large persistence lengths in all species, around 1-5 μm. The magnitudes of the persistence lengths are clearly related to the designs of the linkages between the unit motifs. Both the 6HB+2 and the 6HB+3 motifs have been successfully used to produce well-ordered 2D periodic arrays via sticky-ended cohesion.

Effects of basic calponin on the flexural mechanics and stability of F-actin

The cellular actin cytoskeleton plays a central role in the ability of cells to properly sense, propagate, and respond to external stresses and other mechanical stimuli. Calponin, an actin-binding protein found both in muscle and non-muscle cells, has been implicated in actin cytoskeletal organization and regulation. In this work, we studied the mechanical and structural interaction of actin with basic calponin, a differentiation marker in smooth muscle cells, on a single filament level. We imaged fluorescently labeled thermally fluctuating actin filaments and found that at moderate calponin binding densities, actin filaments were more flexible, evident as a reduction in persistence length from 8.0 to 5.8 μm. When calponin-decorated actin filaments were subjected to shear, we observed a marked reduction of filament lengths after decoration with calponin, which we argue was due to shear-induced filament rupture rather than depolymerization. This increased shear susceptibility was exacerbated with calponin concentration. Cryo-electron microscopy results confirmed previously published negative stain electron microscopy results and suggested alterations in actin involving actin subdomain 2. A weakening of F-actin intermolecular association is discussed as the underlying cause of the observed mechanical perturbations.

Effects of the nucleoid protein HU on the structure, flexibility, and ring-closure properties of DNA deduced from Monte Carlo simulations

The histone-like HU (heat unstable) protein plays a key role in the organization and regulation of the Escherichia coli genome. The nonspecific nature of HU binding to DNA complicates analysis of the mechanism by which the protein contributes to the looping of DNA. Conventional models of the looping of HU-bound duplexes attribute the changes in biophysical properties of DNA brought about by the random binding of protein to changes in the effective parameters of an ideal helical wormlike chain. Here, we introduce a novel Monte Carlo approach to study the effects of nonspecific HU binding on the configurational properties of DNA directly. We randomly decorated segments of an ideal double-helical DNA with HU molecules that induce the bends and other structural distortions of the double helix find in currently available X-ray structures. We find that the presence of HU at levels approximating those found in the cell reduces the persistence length by roughly threefold compared with that of naked DNA. The binding of protein has particularly striking effects on the cyclization properties of short duplexes, altering the dependence of ring closure on chain length in a way that cannot be mimicked by a simple wormlike model and accumulating at higher-than-expected levels on successfully closed chains. Moreover, the uptake of protein on small minicircles depends on chain length, taking advantage of the HU-induced deformations of DNA structure to facilitate ligation. Circular duplexes with bound HU show much greater propensity than protein-free DNA to exist as negatively supercoiled topoisomers, suggesting a potential role of HU in organizing the bacterial nucleoid. The local bending and undertwisting of DNA by HU, in combination with the number of bound proteins, provide a structural rationale for the condensation of DNA and the observed expression levels of reporter genes in vivo.

Effect of flexibility and cis residues in single-molecule FRET studies of polyproline

Polyproline has recently been used as a spacer between donor and acceptor chromophores to help establish the accuracy of distances determined from single-molecule Förster resonance energy transfer (FRET) measurements. This work showed that the FRET efficiency in water is higher than expected for a rigid spacer and was attributed to the flexibility of the polypeptide. Here, we investigate this issue further, using a combination of single-molecule fluorescence intensity and lifetime measurements, NMR, theory, and molecular dynamics simulations of polyproline-20 that include the dyes and their linkers to the polypeptide. NMR shows that in water approximately 30% of the molecules contain internal cis prolines, whereas none are detectable in trifluoroethanol. Simulations suggest that the all-trans form of polyproline is relatively stiff, with persistence lengths of 9-13 nm using different established force fields, and that the kinks arising from internal cis prolines are primarily responsible for the higher mean FRET efficiency in water. We show that the observed efficiency histograms and distributions of donor fluorescence lifetimes are explained by the presence of multiple species with efficiencies consistent with the simulations and populations determined by NMR. In calculating FRET efficiencies from the simulation, we find that the fluctuations of the chromophores, attached to long flexible linkers, also play an important role. A similar simulation approach suggests that the flexibility of the chromophore linkers is largely responsible for the previously unexplained high value of R(0) required to fit the data in the classic study of Stryer and Haugland.

Allostery of actin filaments: molecular dynamics simulations and coarse-grained analysis

The structural and mechanical properties of monomeric actin (G-actin), the trimer nucleus, and actin filaments (F-actins) are determined as a function of the conformation of the DNase I-binding loop (DB loop) by using all-atom molecular dynamics simulations and coarse-grained (CG) analysis. Recent x-ray structures of ADP-bound G-actin (G-ADP) by Otterbein et al. [Otterbein, L. R., Graceffa, P. & Dominguez, R. (2001) Science 293, 708-711] and ATP-bound G-actin (G-ATP) by Graceffa and Dominguez [Graceffa, P. & Dominguez, R. (2003) J. Biol. Chem. 278, 34172-34180] indicate that the DB loop of actin does not have a well defined secondary structure in the ATP state but folds into an alpha-helix in the ADP state. MD simulations and CG analysis indicate that such a helical DB loop significantly weakens the intermonomer interactions of actin assemblies and thus leads to a wider, shorter, and more disordered filament. The computed persistence lengths of F-actin composed of G-ATP (16 microm) and of G-ADP (8.5 microm) agree well with the experimental values for the two states. Therefore, the loop-to-helix transition of the DB loop may be one of the factors that lead to the changes in structural and mechanical properties of F-actin after ATP hydrolysis. This result may provide a direct connection between the conformational changes of an actin monomer and the structural and mechanical properties of the cytoskeleton. The information provided by MD simulations also helps to understand the possible origin of the special features of actin dynamics.