Analytical description of extension, torque, and supercoiling radius of a stretched twisted DNA.
ABSTRACT: We study the mixture of extended and supercoiled DNA that occurs in a twisted DNA molecule under tension. Closed-form asymptotic solutions for the supercoiling radius, extension, and torque of the molecule are obtained in the high-force limit where electrostatic and elastic effects dominate. We demonstrate that experimental data obey the extension and torque scaling laws apparent in our formulas, in the regime where thermal fluctuation effects are quenched by applied force.
Project description:As a single DNA molecule is positively supercoiled under constant tension, its extension initially increases due to a negative twist-stretch coupling. The subsequent attainment of an extension maximum has previously been assumed to be indicative of the onset of a phase transition from B- to scP-DNA. Here we show that an extension maximum in fact does not coincide with the onset of a phase transition. This transition is evidenced by a direct observation of a torque plateau using an angular optical trap. Instead we find that the shape of the extension curve can be well explained with a theory that incorporates both DNA twist-stretch coupling and bending fluctuations. This theory also provides a more accurate method of determining the value of the twist-stretch coupling modulus, which has possibly been underestimated in previous studies that did not take into consideration the bending fluctuations. Our study demonstrates the importance of torque detection in the correct identification of phase transitions as well as the contribution of the twist-stretch coupling and bending fluctuations to DNA extension.
Project description:PURPOSE:We hypothesised that intercarpal K-wire fixation of adjacent carpal bones would reduce torque and lever force within a fractured scaphoid bone. METHODS:In eight cadaver wrists, a scaphoid osteotomy was stabilised using a locking nail, which also functioned as a sensor to measure isometric torque and lever forces between the fragments. The wrist was moved through 80% of full range of motion (ROM) to generate torque and force within the scaphoid. Testing was performed with and without loading of the wrist and K-wire stabilisation of the adjacent carpal bones. RESULTS:Average torque and lever force values were 49.6 ± 25.1 Nmm and 3.5 ± 0.9?N during extension and 41 ± 26.7?Nmm and 8.1 ± 2.8?N during flexion. Torque and lever force did not depend on scaphoid size, individual wrist ROM, or deviations of the sensor versus the anatomic axis. K-wire fixation did not produce significant changes in average torque and lever force values except with wrist radial abduction (P = 0.0485). Other than wrist extension, torque direction was not predictable. CONCLUSION:In unstable scaphoid fractures, we suggest securing rotational stability with selected implants for functional postoperative care. Wrist ROM within 20% extension and radial abduction to 50% flexion limit torque and lever force exacerbation between scaphoid fragments.
Project description:<h4>Background</h4>With aging, the ability to generate muscle force decreases, contributing to declines in physical functions such as walking. While most studies assess muscle force by peak torque, the rate of torque development (RTD) reflects a dynamic component of muscle performance that is important for physical function. Using data from the Baltimore Longitudinal Study of Aging, we assessed whether RTD adds significantly to peak torque in associations with lower extremity performance. If so, RTD may help identify weak older adults for screening and intervention.<h4>Methods</h4>We assessed associations of RTD and peak torque with physical performance independent of demographics, BMI, body composition, and each other in 1089 Baltimore Longitudinal Study of Aging participants (49.7% women; aged 26 to 96 years; women, 64.0 ± 13.8 years; men, 68.4 ± 14.4 years). Peak torque was assessed by isometric and 30 deg/s isokinetic knee extension tests. Peak RTD was operationalized as the maximum torque-time slope among successive 50 ms epochs over the first 3 s of a test of knee extension isometric strength, with the knee joint positioned at 120 deg of flexion. A battery of lower extremity performance tests included gait speed during a 6 m walk at usual and fast pace (6 m usual and fast), time to complete a 400 m walk at fast pace (400 m), distance covered in a 2.5 min walk at normal pace (2.5 min), time to complete 5 and 10 chair stands, and two summary tests of lower extremity performance. Sex-stratified generalized linear regression models were adjusted for age, race, BMI, appendicular lean mass, and whole body fat mass.<h4>Results</h4>In men, independent of either measure of peak torque and cofactors, RTD was a significant (P < 0.05) predictor of all lower extremity performance tests except the 400 m and 2.5 min walks. In women, independent of peak torque, RTD was only a significant independent correlate of the 6 m fast walk (P < 0.001).<h4>Conclusions</h4>RTD independently contributes to physical functions in men but less in women. The mechanisms underlying the sex difference are unclear and require further study.
Project description:Torsional stress in linear biopolymers such as DNA and chromatin has important consequences for nanoscale biological processes. We have developed a new method to directly measure torque on single molecules. Using a cylindrical magnet, we manipulate a novel probe consisting of a nanorod with a 0.1 microm ferromagnetic segment coupled to a magnetic bead. We achieve controlled introduction of turns into the molecule and precise measurement of torque and molecule extension as a function of the number of turns at low pulling force. We show torque measurement of single DNA molecules and demonstrate for the first time measurements of single chromatin fibers.
Project description:DNA responds to small changes in force and torque by over- or undertwisting, forming plectonemes, and/or melting bubbles. Although transitions between either twisted and plectonemic conformations or twisted and melted conformations have been described as first-order phase transitions, we report here a broadening of these transitions when the size of a topological domain spans several kilobasepairs. Magnetic tweezers measurements indicate the coexistence of three conformations at subpicoNewton force and linking number densities ?-0.06. We present a statistical physics model for DNA domains of several kilobasepairs by calculating the full partition function that describes this three-state coexistence. Real-time analysis of short DNA tethers at constant force and torque shows discrete levels of extension, representing discontinuous changes in the size of the melting bubble, which should reflect the underlying DNA sequence. Our results provide a comprehensive picture of the structure of underwound DNA at low force and torque and could have important consequences for various biological processes, in particular those that depend on local DNA melting, such as the initiation of replication and transcription.
Project description:Cellular DNA is regularly subject to torsional stress during genomic processes, such as transcription and replication, resulting in a range of supercoiled DNA structures. For this reason, methods to prepare and study supercoiled DNA at the single-molecule level are widely used, including magnetic, angular-optical, micropipette, and magneto-optical tweezers. However, it is currently challenging to combine DNA supercoiling control with spatial manipulation and fluorescence microscopy. This limits the ability to study complex and dynamic interactions of supercoiled DNA. Here we present a single-molecule assay that can rapidly and controllably generate negatively supercoiled DNA using a standard dual-trap optical tweezers instrument. This method, termed Optical DNA Supercoiling (ODS), uniquely combines the ability to study supercoiled DNA using force spectroscopy, fluorescence imaging of the whole DNA, and rapid buffer exchange. The technique can be used to generate a wide range of supercoiled states, with between <5 and 70% lower helical twist than nonsupercoiled DNA. Highlighting the versatility of ODS, we reveal previously unobserved effects of ionic strength and sequence on the structural state of underwound DNA. Next, we demonstrate that ODS can be used to directly visualize and quantify protein dynamics on supercoiled DNA. We show that the diffusion of the mitochondrial transcription factor TFAM can be significantly hindered by local regions of underwound DNA. This finding suggests a mechanism by which supercoiling could regulate mitochondrial transcription in vivo. Taken together, we propose that ODS represents a powerful method to study both the biophysical properties and biological interactions of negatively supercoiled DNA.
Project description:The bacterial flagellar hook is a short, highly curved tubular structure connecting the basal body as a rotary motor and the filament as a helical propeller to function as a universal joint to transmit motor torque to the filament regardless of its orientation. This highly curved form is known to be part of a supercoil as observed in the polyhook structure. The subunit packing interactions in the Salmonella hook structure solved in the straight form gave clear insights into the mechanisms of its bending flexibility and twisting rigidity. Salmonella FlgE consists of four domains, D0, Dc, D1 and D2, arranged from inside to outside of the tube, and an atomic model of the supercoiled hook built to simulate the hook shape observed in the native flagellum suggested that the supercoiled form is stabilized by near-axial interactions of the D2 domains on the inner surface of the supercoil. Here we show that the deletion of domain D2 from FlgE makes the hook straight, providing evidence to support the proposed hook supercoiling mechanism that it is the near-axial interactions between the D2 domains that stabilize the highly curved hook structure.
Project description:Transcription by RNA polymerase can induce the formation of hypernegatively supercoiled DNA in vitro and in vivo. This phenomenon has been nicely explained by a "twin-supercoiled-domain" model of transcription where a positively supercoiled domain is generated ahead of the RNA polymerase and a negatively supercoiled domain behind it. In Escherichia coli topA strains, DNA gyrase selectively converts the positively supercoiled domain into negative supercoils to produce hypernegatively supercoiled DNA. In this article, in order to examine whether promoter strength affects transcription-coupled DNA supercoiling (TCDS), we developed a two-plasmid system in which a linear, non-supercoiled plasmid was used to express lac repressor constitutively while a circular plasmid was used to gage TCDS in E. coli cells. Using this two-plasmid system, we found that TCDS in topA strains is dependent on promoter strength. We also demonstrated that transcription-coupled hypernegative supercoiling of plasmid DNA did not need the expression of a membrane-insertion protein for strong promoters; however, it might require co-transcriptional synthesis of a polypeptide. Furthermore, we found that for weak promoters the expression of a membrane-insertion tet gene was not sufficient for the production of hypernegatively supercoiled DNA. Our results can be explained by the "twin-supercoiled-domain" model of transcription where the friction force applied to E. coli RNA polymerase plays a critical role in the generation of hypernegatively supercoiled DNA.
Project description:Although stroke survivors often display abnormal joint torque patterns, studies of torque-coupling in the lower limb are lacking, despite their potential impact on gait abnormalities.Twenty-two chronic ambulating stroke subjects and 11 age-matched control subjects produced isometric hip torques in the frontal and sagittal planes with the hemiparetic leg (or randomly selected leg for the control group) in postures that resemble stages of gait. The involuntary knee torques were also recorded although no feedback or instructions were given.In the toe-off and midswing postures, the stroke group had a significant torque bias toward extension and adduction, whereas the control group had a symmetric torque space. The stroke group also produced significantly smaller torques than the control group in the flexion and abduction/flexion directions. Finally, the stroke group displayed abnormal coupling of knee extension with hip adduction, unique to the toe-off position.Whereas gait abnormalities after stroke have been attributed to a number of factors, including sagittal plane strength impairments at the hip, knee, and ankle, our findings indicate that neuromechanical changes after stroke may play a significant role in determining the nature of the movement abnormality. Specifically, abnormal hip adduction and knee extension torque coupling was observed, in addition to direction-specific hip torque weakness. Future studies are needed to delineate the differential contributions of each potential factor to gait abnormalities. Understanding the underlying neuromechanical changes after stroke may aid the development of rehabilitation strategies.
Project description:The pathway of voluntary joint torque production includes motor neuron recruitment and rate-coding, sarcolemmal depolarization and calcium release by the sarcoplasmic reticulum, force generation by motor proteins within skeletal muscle, and force transmission by tendon across the joint. The direct source of energetic support for this process is ATP hydrolysis. It is possible to examine portions of this physiologic pathway using various in vivo and in vitro techniques, but an integrated view of the multiple processes that ultimately impact joint torque remains elusive. To address this gap, we present a comprehensive computational model of the combined neuromuscular and musculoskeletal systems that includes novel components related to intracellular bioenergetics function. Components representing excitatory drive, muscle activation, force generation, metabolic perturbations, and torque production during voluntary human ankle dorsiflexion were constructed, using a combination of experimentally-derived data and literature values. Simulation results were validated by comparison with torque and metabolic data obtained in vivo. The model successfully predicted peak and submaximal voluntary and electrically-elicited torque output, and accurately simulated the metabolic perturbations associated with voluntary contractions. This novel, comprehensive model could be used to better understand impact of global effectors such as age and disease on various components of the neuromuscular system, and ultimately, voluntary torque output.