Computed modeling of humeral mid-shaft fracture treated by bundle nailing

Elastic bundle nailing is a method for simple humeral mid-shaft fracture osteosynthesis. The aim of our subsequent numerical simulations was to find out torsional and bending stiffness of an elastic bundle nailed humerus. Parametrical 3D numerical model was developed. The diameter of nails was the varying parameter of 1.8, 2.5, 3 and 4 mm. From our results can be seen that the bending stiffness in bundle nailing technique does not depend on nail diameter. On the contrary the torsional stiffness does highly depend on nail diameter. The dependency of the maximal stress on a nail diameter during bending and torsion of the humerus is non-linear. It can be seen that the higher diameter is used the higher stress occurs. Achieved results allow us for the recommendation of optimal nail diameter for this method, which lies between 2 and 3 mm.     

Force and flexibility of flailing myxobacteria

Myxococcus xanthus is a common Gram-negative bacterium that moves by a process called gliding motility. In myxobacteria, two distinct mechanisms for gliding have been discovered. S-type motility requires the extension, attachment, and retraction of type IV pili. The other mechanism, designated as A-type motility, may be driven by the secretion and swelling of slime; however, experiments to confirm or refute this model are still lacking and the force exerted by this mechanism has not been measured. A previously published experiment found that when an M. xanthus cell became stuck at one end, the cell underwent flailing motions. Based on this experiment, I propose an elastic model that can estimate the force produced by the A-motility engine and the bending modulus of a single myxobacterial cell. The model estimates a bending modulus of 3 x 10(-14) erg cm and a force between 50-150 pN. This force is comparable to that predicted by slime extrusion, and the bending modulus is 30-fold smaller than that measured in Bacillus subtilis. This model suggests experiments that can further quantify this process.     

How human IgGs against DNA recognize oligonucleotides and DNA

In the literature, there are no available data on how anti‐DNA antibodies recognize DNA. In the present work, to study the molecular mechanism of DNA recognition by antibodies, we have used anti‐DNA IgGs from blood sera of patients with multiple sclerosis. A stepwise increase in ligand complexity approach was used to estimate the relative contributions of virtually every nucleotide unit of different single‐ (ss) and double‐stranded (ds) oligonucleotides to their affinity for IgG fraction having high affinity to DNA‐cellulose. DNA‐binding site disposed on the heavy chain demonstrates higher affinity to different dNMPs (K_d = 0.63μM‐3.8μM) than the site located on the light chain (28μM‐170μM). The heavy and light chains interact independently forming relatively strong contacts with 2 to 4 nucleotides of short homo‐ and hetero‐d(pN)_2‐9. Then the increase in the affinity of different d(pN)_n became minimal, and at n ≥ 8 to 9, all dependencies reached plateaus: approximately 3.2nM to 20nM and approximately 200nM to 460nM for the heavy and light chains, respectively. A similar situation was observed for different ribooligonucleotides, in which their affinity is 6‐fold to 100‐fold lower than that for d(pN)_n. Transition from ss to ds d(pN)_n leads to a moderate increase in affinity of ligands to DNA‐binding site of heavy chains, while light chains demonstrate the same affinity for ss and ds d(pN)_n. Long supercoiled DNA interacts with both heavy and light chains with affinity of approximately 10‐fold higher than that for short oligonucleotides. The thermodynamic models were constructed to describe the interactions of IgGs light and heavy chains with DNA.     

Measurements of single DNA molecule packaging dynamics in bacteriophage lambda reveal high forces, high motor processivity, and capsid transformations

Molecular motors drive genome packaging into preformed procapsids in many double-stranded (ds)DNA viruses. Here, we present optical tweezers measurements of single DNA molecule packaging in bacteriophage lambda. DNA-gpA-gpNu1 complexes were assembled with recombinant gpA and gpNu1 proteins and tethered to microspheres, and procapsids were attached to separate microspheres. DNA binding and initiation of packaging were observed within a few seconds of bringing these microspheres into proximity in the presence of ATP. The motor was observed to generate greater than 50 picoNewtons (pN) of force, in the same range as observed with bacteriophage phi29, suggesting that high force generation is a common property of viral packaging motors. However, at low capsid filling the packaging rate averaged approximately 600 bp/s, which is 3.5-fold higher than phi29, and the motor processivity was also threefold higher, with less than one slip per genome length translocated. The packaging rate slowed significantly with increasing capsid filling, indicating a buildup of internal force reaching 14 pN at 86% packaging, in good agreement with the force driving DNA ejection measured in osmotic pressure experiments and calculated theoretically. Taken together, these experiments show that the internal force that builds during packaging is largely available to drive subsequent DNA ejection. In addition, we observed an 80 bp/s dip in the average packaging rate at 30% packaging, suggesting that procapsid expansion occurs at this point following the buildup of an average of 4 pN of internal force. In experiments with a DNA construct longer than the wild-type genome, a sudden acceleration in packaging rate was observed above 90% packaging, and much greater than 100% of the genome length was translocated, suggesting that internal force can rupture the immature procapsid, which lacks an accessory protein (gpD).     

Re-entrant cholesteric phase in DNA liquid-crystalline dispersion particles

In this research, we observe and rationalize theoretically the transition from hexagonal to cholesteric packing of double-stranded (ds) DNA in dispersion particles. The samples were obtained by phase exclusion of linear ds DNA molecules from water-salt solutions of poly(ethylene glycol)—PEG—with concentrations ranging from 120 mg ml^?1 to 300 mg ml^?1. In the range of PEG concentrations from 120 mg ml^?1 to 220 mg ml^?1 at room temperature, we find ds DNA molecule packing, typical of classical cholesterics. The corresponding parameters for dispersion particles obtained at concentrations greater than 220 mg ml^?1 indicate hexagonal packing of the ds DNA molecules. However, slightly counter-intuitively, the cholesteric-like packing reappears upon the heating of dispersions with hexagonal packing of ds DNA molecules. This transition occurs when the PEG concentration is larger than 220 mg ml^?1. The obtained new cholesteric structure differs from the classical cholesterics observed in the PEG concentration range 120–220 mg ml^?1 (hence, the term ‘re-entrant’). Our conclusions are based on the measurements of circular dichroism spectra, X-ray scattering curves and textures of liquid-crystalline phases. We propose a qualitative (similar to the Lindemann criterion for melting of conventional crystals) explanation of this phenomenon in terms of partial melting of so-called quasinematic layers formed by the DNA molecules. The quasinematic layers change their spatial orientation as a result of the competition between the osmotic pressure of the solvent (favoring dense, unidirectional alignment of ds DNA molecules) and twist Frank orientation energy of adjacent layers (favoring cholesteric-like molecular packing).     

Freezing shortens the lifetime of DNA molecules under tension

DNA samples are commonly frozen for storage. However, freezing can compromise the integrity of DNA molecules. Considering the wide applications of DNA molecules in nanotechnology, changes to DNA integrity at the molecular level may cause undesirable outcomes. However, the effects of freezing on DNA integrity have not been fully explored. To investigate the impact of freezing on DNA integrity, samples of frozen and non-frozen bacteriophage lambda DNA were studied using optical tweezers. Tension (5–35 pN) was applied to DNA molecules to mimic mechanical interactions between DNA and other biomolecules. The integrity of the DNA molecules was evaluated by measuring the time taken for single DNA molecules to break under tension. Mean lifetimes were determined by maximum likelihood estimates and variances were obtained through bootstrapping simulations. Under 5 pN of force, the mean lifetime of frozen samples is 44.3 min with 95% confidence interval (CI) between 36.7 min and 53.6 min while the mean lifetime of non-frozen samples is 133.2 min (95% CI: 97.8–190.1 min). Under 15 pN of force, the mean lifetimes are 10.8 min (95% CI: 7.6–12.6 min) and 78.5 min (95% CI: 58.1–108.9 min). The lifetimes of frozen DNA molecules are significantly reduced, implying that freezing compromises DNA integrity. Moreover, we found that the reduced DNA structural integrity cannot be restored using regular ligation process. These results indicate that freezing can alter the structural integrity of the DNA molecules.     

Calculation of line tension in various models of lipid bilayer pore edge

The line tension of the edge of the lipid bilayer pore is calculated on the basis of the elastic theory of continuous liquid-crystal medium. Three types of deformations of the membrane were taken into account: bending, lateral stretching/compression, and tilt of the lipidic tails. Various models of structure of the pore edge are considered: models of the cylindrical shape with given radius and optimum radius, “extrapolational” model, “two-coordinate” model, and model with a hydrophobic cavity (“void”). Models can be conventionally divided into two classes. The first class includes models in which membrane monolayers are in contact with each other everywhere. Models of the second class admit appearance of a hydrophobic cavity between monolayers. Models of the first class yield value of the line tension γ, strongly differing from that known from the literature (～10 pN). For example, the value of the line tension γ obtained in the cylindrical model equals to 21 pN; in the two-coordinate model, 19 pN, and in the extrapolational model, 62 pN. At the same time, the model with cavity gives the value of γ eqal ～10 pN, provided that surface tension at the boundary of the lipid tails is close to zero. This value is in a good agreement with the literature data.     

Determination of the elastic properties of short ssDNA molecules by mechanically folding and unfolding DNA hairpins

The characterization of elastic properties of biopolymers is crucial to understand many molecular reactions determined by conformational bending fluctuations of the polymer. Direct measurement of such elastic properties using single‐molecule methods is usually hindered by the intrinsic tendency of such biopolymers to form high‐order molecular structures. For example, single‐stranded deoxyribonucleic acids (ssDNA) tend to form secondary structures such as local double helices that prevent the direct measurement of the ideal elastic response of the ssDNA. In this work, we show how to extract the ideal elastic response in the entropic regime of short ssDNA molecules by mechanically pulling two‐state DNA hairpins of different contour lengths. This is achieved by measuring the force dependence of the molecular extension and stiffness on mechanically folding and unfolding the DNA hairpin. Both quantities are fit to the worm‐like chain elastic model giving values for the persistence length and the interphosphate distance. This method can be used to unravel the elastic properties of short ssDNA and RNA sequences and, more generally, any biopolymer that can exhibit a cooperative two‐state transition between mechanically folded and unfolded states (such as proteins). © 2014 Wiley Periodicals, Inc. Biopolymers 101: 1193–1199, 2014.     

Counterintuitive DNA Sequence Dependence in Supercoiling-Induced DNA Melting

The metabolism of DNA in cells relies on the balance between hybridized double-stranded DNA (dsDNA) and local de-hybridized regions of ssDNA that provide access to binding proteins. Traditional melting experiments, in which short pieces of dsDNA are heated up until the point of melting into ssDNA, have determined that AT-rich sequences have a lower binding energy than GC-rich sequences. In cells, however, the double-stranded backbone of DNA is destabilized by negative supercoiling, and not by temperature. To investigate what the effect of GC content is on DNA melting induced by negative supercoiling, we studied DNA molecules with a GC content ranging from 38% to 77%, using single-molecule magnetic tweezer measurements in which the length of a single DNA molecule is measured as a function of applied stretching force and supercoiling density. At low force (<0.5pN), supercoiling results into twisting of the dsDNA backbone and loop formation (plectonemes), without inducing any DNA melting. This process was not influenced by the DNA sequence. When negative supercoiling is introduced at increasing force, local melting of DNA is introduced. We measured for the different DNA molecules a characteristic force F _char, at which negative supercoiling induces local melting of the dsDNA. Surprisingly, GC-rich sequences melt at lower forces than AT-rich sequences: F _char = 0.56pN for 77% GC but 0.73pN for 38% GC. An explanation for this counterintuitive effect is provided by the realization that supercoiling densities of a few percent only induce melting of a few percent of the base pairs. As a consequence, denaturation bubbles occur in local AT-rich regions and the sequence-dependent effect arises from an increased DNA bending/torsional energy associated with the plectonemes. This new insight indicates that an increased GC-content adjacent to AT-rich DNA regions will enhance local opening of the double-stranded DNA helix.     

Structural Basis for Elastic Mechanical Properties of the DNA Double Helix

In this article, we investigate the principal structural features of the DNA double helix and their effects on its elastic mechanical properties. We develop, in the pursuit of this purpose, a helical continuum model consisting of a soft helical core and two stiff ribbons wrapping around it. The proposed model can reproduce the negative twist-stretch coupling of the helix successfully as well as its global stretching, bending, and torsional rigidities measured experimentally. Our parametric study of the model using the finite element method further reveals that the stiffness of phosphate backbones is a crucial factor for the counterintuitive overwinding behavior of the duplex and its extraordinarily high torsional rigidity, the major-minor grooves augment the twist-stretch coupling, and the change of the helicity might be responsible for the transition from a negative to a positive twist-stretching coupling when a tensile force is applied to the duplex.     

Dynamics of supercoiled and relaxed pTZ18U plasmids probed with a long-lifetime metal-ligand complex

[Ru(bpy)2(dppz)](2+) (bpy = 2,2'-bipyridine, dppz = dipyrido- [3,2-a:2',3'-c]phenazine) (RuBD), a long-lifetime metalligand complex, displays favorable photophysical properties. These include long lifetime, polarized emission, but no significant fluorescence from the complex that is not bound to DNA. To show the usefulness of this luminophore (RuBD) for probing the bending and torsional dynamics of nucleic acids, its intensity and anisotropy decays when intercalated into supercoiled and relaxed pTZ18U plasmids were examined using frequency-domain fluorometry with a blue light-emitting diode (LED) as the modulated light source. The mean lifetimes for the supercoiled plasmids (< tau > = 148 ns) were somewhat shorter than those for the relaxed plasmids (< tau > = 160 ns). This suggests that the relaxed plasmids were shielded more efficiently from water. The anisotropy decay data also showed somewhat shorter slow rotational correlation times for supercoiled plasmids (288 ns) than for the relaxed plasmids (355 ns). The presence of two rotational correlation times suggests that RuBD reveals both the bending and torsional motions of the plasmids. These results indicate that RuBD can be useful for studying both the bending and torsional dynamics of nucleic acids.     

Calculated compression,bending, shearing,torsion, and base-tilting force constants of B- and A-form poly(dG)·poly(dC)

Force constants associated with large-scale motions of the DNA double-helical homopolymer poly(dG)·poly(dC) are projected out of a long-range atom–atom Coulomb force field. Force constants for both B- and A-conformations have been calculated. Using the Coulomb interaction as previously incorporated into our DNA normal mode calculations, we obtain the forces determined by this long-range interaction. These include compression, bending, shearing, torsion, and base tilting. We show, quantitatively, how the shearing and torsional transverse interactions fall off with intercell distance more rapidly than the compressional (longitudinal) interactions. Reasonable values for the elastic moduli of B- and A-DNA are calculated. An important prediction of the present interaction theory is that although the single adjustable strength parameter in the Coulomb force field was chosen so as to reproduce an experimental value for the longitudinal sound velocity, the transverse torsional potential resulting from this fitted force field is in excellent agreement with results reported from supercoiling data and fluorescence measurements.     

DNA-duplex linker for AFM-SELEX of DNA aptamer against human serum albumin

DNA-duplex interactions in thymines and adenins are used as a linker for the novel methodology of Atomic Force Microscope-Systematic Evolution of Ligands by EXpotential enrichment (AFM-SELEX). This study used the hydrogen bonds in 10 mer of both thymines (T10) and adenines (A10). Initially, the interactive force in T10-A10 was measured by AFM, which returned an average interactive force of approximately 350 pN. Based on this result, DNA aptamers against human serum albumin could be selected in the 4th round, and 15 different clones could be sequenced. The lowest dissociation constant of the selected aptamer was identified via surface plasmon resonance, and it proved to be identical to that of the commercial aptamer. Therefore, specific hydrogen bonds in DNA can be useful linkers for AFM-SELEX.     

Evaluation of elastic properties of atomistic DNA models

A number of intriguing aspects in dynamics of double-helical DNA is related to the coupling between its macroscopic and microscopic states. A link between the elastic properties of long DNA chains and their atom-level dynamics can be established by comparing the worm-like chain model of polymer DNA with the conformational ensembles produced by molecular dynamics simulations. This problem is complicated by the complexity of the DNA structure, the small size of DNA fragments, and relatively short trajectory durations accessible in computer simulations of microscopic DNA dynamics. A careful study of all these aspects has been performed by using longer DNA fragments and increased durations of MD trajectories as compared to earlier such investigations. Special attention is paid to the necessary conditions and criteria of time convergence, and the possibility to increase the sampling by using constrained DNA models and simplified simulation conditions. It is found that dynamics of 25-mer duplexes with regular sequences agrees well with the worm-like chain theory and that accurate evaluation of DNA elastic parameters requires at least two turns of the double helix and approximately 20-ns duration of trajectories. Bond length and bond-angle constraints affect the estimates within numerical errors. In contrast, simplified treatment of solvation can strongly change the observed elastic parameters of DNA. The elastic parameters evaluated for AT- and GC-alternating duplexes reasonably agree with experimental data and suggest that, in different basepair sequences, the torsional and stretching elasticities vary stronger than the bending stiffness.     

Anisotropy in sickle hemoglobin fibers from variations in bending and twist

We have studied the variations of twist and bend in sickle hemoglobin fibers. We find that these variations are consistent with an origin in equilibrium thermal fluctuations, which allows us to estimate the bending and torsional rigidities and effective corresponding material moduli. We measure bending by electron microscopy of frozen hydrated fibers and find that the bending persistence length, a measure of the length of fiber required before it starts to be significantly bent due to thermal fluctuations, is 130microm, somewhat shorter than that previously reported using light microscopy. The torsional persistence length, obtained by re-analysis of previously published experiments, is found to be only 2.5microm. Strikingly this means that the corresponding torsional rigidity of the fibers is only 6x10(-27)Jm, much less than their bending rigidity of 5x10(-25)Jm. For (normal) isotropic materials, one would instead expect these to be similar. Thus, we present the first quantitative evidence of a very significant material anisotropy in sickle hemoglobin fibers, as might arise from the difference between axial and lateral contacts within the fiber. We suggest that the relative softness of the fiber with respect to twist deformation contributes to the metastability of HbS fibers: HbS double strands are twisted in the fiber but not in the equilibrium crystalline state. Our measurements inform a theoretical model of the thermodynamic stability of fibers that takes account of both bending and extension/compression of hemoglobin (double) strands within the fiber.     

Membrane-based actuation for high-speed single molecule force spectroscopy studies using AFM

Atomic force microscopy (AFM)-based dynamic force spectroscopy of single molecular interactions involves characterizing unbinding/unfolding force distributions over a range of pulling speeds. Owing to their size and stiffness, AFM cantilevers are adversely affected by hydrodynamic forces, especially at pulling speeds >10 μm/s, when the viscous drag becomes comparable to the unbinding/unfolding forces. To circumvent these adverse effects, we have fabricated polymer-based membranes capable of actuating commercial AFM cantilevers at speeds ≥100 μm/s with minimal viscous drag effects. We have used FLUENT^®, a computational fluid dynamics (CFD) software, to simulate high-speed pulling and fast actuation of AFM cantilevers and membranes in different experimental configurations. The simulation results support the experimental findings on a variety of commercial AFM cantilevers and predict significant reduction in drag forces when membrane actuators are used. Unbinding force experiments involving human antibodies using these membranes demonstrate that it is possible to achieve bond loading rates ≥10⁶ pN/s, an order of magnitude greater than that reported with commercial AFM cantilevers and systems.     

Free body analysis,beam mechanics,and finite element modeling of the mandible of Alligator mississippiensis

The mechanical behavior of mammalian mandibles is well‐studied, but a comprehensive biomechanical analysis (incorporating detailed muscle architecture, accurate material properties, and three‐dimensional mechanical behavior) of an extant archosaur mandible has never been carried out. This makes it unclear how closely models of extant and extinct archosaur mandibles reflect reality and prevents comparisons of structure–function relationships in mammalian and archosaur mandibles. We tested hypotheses regarding the mechanical behavior of the mandible of Alligator mississippiensis by analyzing reaction forces and bending, shear, and torsional stress regimes in six models of varying complexity. Models included free body analysis using basic lever arm mechanics, 2D and 3D beam models, and three high‐resolution finite element models of the Alligator mandible, incorporating, respectively, isotropic bone without sutures, anisotropic bone with sutures, and anisotropic bone with sutures and contact between the mandible and the pterygoid flange. Compared with the beam models, the Alligator finite element models exhibited less spatial variability in dorsoventral bending and sagittal shear stress, as well as lower peak values for these stresses, suggesting that Alligator mandibular morphology is in part designed to reduce these stresses during biting. However, the Alligator models exhibited greater variability in the distribution of mediolateral and torsional stresses than the beam models. Incorporating anisotropic bone material properties and sutures into the model reduced dorsoventral and torsional stresses within the mandible, but led to elevated mediolateral stresses. These mediolateral stresses were mitigated by the addition of a pterygoid‐mandibular contact, suggesting important contributions from, and trade‐offs between, material properties and external constraints in Alligator mandible design. Our results suggest that beam modeling does not accurately represent the mechanical behavior of the Alligator mandible, including important performance metrics such as magnitude and orientation of reaction forces, and mediolateral bending and torsional stress distributions. J.Morphol. 2011. © 2011 Wiley‐Liss, Inc.     

Kinking the double helix by bending deformation

DNA bending and torsional deformations that often occur during its functioning inside the cell can cause local disruptions of the regular helical structure. The disruptions created by negative torsional stress have been studied in detail, but those caused by bending stress have only been analyzed theoretically. By probing the structure of very small DNA circles, we determined that bending stress disrupts the regular helical structure when the radius of DNA curvature is smaller than 3.5 nm. First, we developed an efficient method to obtain covalently closed DNA minicircles. To detect structural disruptions in the minicircles we treated them by single-strand-specific endonucleases. The data showed that the regular DNA structure is disrupted by bending deformation in the 64–65-bp minicircles, but not in the 85–86-bp minicircles. Our results suggest that strong DNA bending initiates kink formation while preserving base pairing.