Tension Propagation Research Articles

Mapping the Energy Landscape of Biomolecules Using Single Molecule Force Correlation Spectroscopy: Theory and Applications

We present, to our knowledge, a new theory that takes internal dynamics of proteins into account to describe forced-unfolding and force-quench refolding in single molecule experiments. In the current experimental setup (using either atomic force microscopy or laser optical tweezers) the distribution of unfolding times, P( t), is measured by applying a constant stretching force f S from which the apparent f S-dependent unfolding rate is obtained. To describe the complexity of the underlying energy landscape requires additional probes that can incorporate the dynamics of tension propagation and relaxation of the polypeptide chain upon force quench. We introduce a theory of force correlation spectroscopy to map the parameters of the energy landscape of proteins. In force correlation spectroscopy, the joint distribution P( T, t) of folding and unfolding times is constructed by repeated application of cycles of stretching at constant f S separated by release periods T during which the force is quenched to f Q < f S. During the release period, the protein can collapse to a manifold of compact states or refold. We show that P( T, t) at various f S and f Q values can be used to resolve the kinetics of unfolding as well as formation of native contacts. We also present methods to extract the parameters of the energy landscape using chain extension as the reaction coordinate and P( T, t). The theory and a wormlike chain model for the unfolded states allows us to obtain the persistence length l p and the f Q-dependent relaxation time, giving us an estimate of collapse timescale at the single molecular level, in the coil states of the polypeptide chain. Thus, a more complete description of landscape of protein native interactions can be mapped out if unfolding time data are collected at several values of f S and f Q. We illustrate the utility of the proposed formalism by analyzing simulations of unfolding-refolding trajectories of a coarse-grained protein ( S1) with β-sheet architecture for several values of f S, T, and f Q = 0. The simulations of stretch-relax trajectories are used to map many of the parameters that characterize the energy landscape of S1.

High-Frequency Stress Relaxation in Semiflexible Polymer Solutions and Networks

We measure the linear viscoelasticity of sterically entangled and chemically cross-linked networks of actin filaments over more than five decades of frequency. The high-frequency response reveals rich dynamics unique to semiflexible polymers, including a previously unobserved relaxation due to rapid axial tension propagation. For high molecular weight, and for cross-linked gels, we obtain quantitative agreement with predicted shear moduli in both amplitude and frequency dependence.

Modeling the dynamics of pressure propagation and diameter variation in tree sapwood

A non-steady-state model of water tension propagation in tree stems was developed. The model is based on the cohesion theory and the assumption that fluctuating water tension driven by transpiration together with the elasticity of wood cause variations in the diameter of a tree stem. The change in xylem diameter can be linked to water tension in accordance with Hooke's law. The model was tested against field measurements of the diurnal change in xylem diameter at different heights in a 180-year-old Scots pine tree at Hyytiälä, southern Finland. Model predictions agreed well with measurements. The effect of tree dimensions on pressure propagation was examined with the model. The model outcomes were also consistent with results of several field measurements presented in the literature.

せん断変形下におけるポリマー材の局所不安定伝ぱ挙動―ポリカーボネートの表面微視構造の形成と成長―

Polymeric materials under large deformation exhibit localized instability propagation, such as neck propagation under tension and shear band propagation under shearing. In this study, formation and growth of micro-shear bands in a glassy polymeric material, polycarbonate (PC) deformed under simple shear, were observed using an Atomic Force Microscope (AFM). In the early stage of shear deformation, the first micro-shear bands along the shearing direction was formed, and they merged together with increase in its density, and then, resulted in the formation of the macro-shear band. In this process, crossing orthogonally to the first micro-shear band, the secondary micro-shear bands were formed. After the applied force reached its maximum, the macro-shear band propagation started in the perpendicular direction to the shearing direction. As the macro-shear band propagated, the rotation of the secondary micro-shear band was observed. In addition, hierarchical structure of the secondary micro-shear band was revealed in region right after the macro-shear band propagation.

Fracture termination and step-over at bedding interfaces due to frictional slip and interface opening

Three types of fracture intersection with bedding contacts have been investigated within numerical experiments: fracture transection through bed contacts, termination (abutment) at contacts and step-over of fractures at bedding contacts. To evaluate the mechanisms responsible for different fracture intersections with bed contacts, the numerical experiments explored deformation associated with end-member conditions of sliding-only interfaces and opening-only interfaces. A third suite of models explored the combined influence of both sliding and opening, as a fracture approached the interface. In contrast to our initial supposition that interface sliding promotes fracture termination, the sliding-only interfaces encouraged propagation of fractures straight through the modeled interface. In contrast, the opening-only interfaces yielded either fracture termination or initiation of a new fracture near the ends of the open interface segment (several centimeters from parent fracture in these models). These results suggest that local interface opening near the tip of approaching fractures, rather than sliding, is responsible for fracture termination and step-over at bedding contacts. Combined sliding and opening yielded fracture termination in models with weak interfaces ( μ=0; c=0 MPa; T=0 MPa) and either fracture step-over or termination at moderate-strength interfaces ( μ=0.65; c=3.25 MPa; T=5 MPa). Fracture termination occurs at moderate-strength interfaces when the stresses along the interface are not great enough to initiate a new step-over fracture. Fracture termination is more likely under conditions of shallower burial depth, lower layer-parallel effective tension and fluid-driven fracture propagation rather than remote layer-parallel tension. Furthermore, thicker beds and greater layer-parallel effective tension may produce greater distances of fracture step-over than thinner beds and more compressive layers. These results may assist in the prediction of subsurface fracture networks and associated fluid flow paths.

Straightening of Thermal Fluctuations in Semiflexible Polymers by Applied Tension.

We investigate the propagation of a suddenly applied tension along a thermally excited semiflexible polymer using analytical approximations, scaling arguments, and numerical simulation. This problem is inherently nonlinear. We find subdiffusive propagation with a dynamical exponent of 1/4. By generalizing the internal elasticity, we show that tense strings exhibit qualitatively different tension profiles and propagation with an exponent of 1/2.

Elastic and viscous properties of resting frog skeletal muscle

The mechanical properties of the resting, whole semitendinosus muscle of the frog have been characterized as functions of both muscle length and temperature. Measurements were made of pseudorandom white noise (PRWN) displacements (less than 10 A/half-sarcomere) applied to the muscle and the force responses to these movements. Signal correlation techniques were then used to obtain the dynamic modulus function for the muscle in the frequency range 2.44-320 Hz. This function was represented by a series combination of a Voigt element and a time delay element for tension propagation along the muscle. A dynamic elastic modulus (E), coefficient of damping (B), and tension transmission velocity (V) were measured for resting muscle on the basis of this model. For each of these parameters, a marked variation with sarcomere length (s) was found. The mean values for E and B at LO (s=2.25 mum) were 1.84+/-0.24 X 10(5) N/m2 and 2.33+/-0.25 X 10(2) Ns/m2, respectively. Further, B demonstrated a negative temperature dependence, Q10=0.78 (P less than 0.05), in the range s=2.6-3.0 mum, while E was not significantly temperature dependent. The length-dependent variations of E and B are interpreted as deriving from both passive muscle elements and attached crossbridges. Velocity was calculated at a single displacing frequency for every experiment; the mean value at LO and all temperatures was v=11.7+/-0.6 m/s. Velocity was also calculated as a function of frequency within several experiments: the results indicate considerable variation of v with frequency.

Experimental investigation of the correspondence between quasistatic tension and longitudinal wave propagation in a polyethylene rod

The propagation of longitudinal waves created by the impact of a rigid mass against a polyethylene rod of finite length has been investigated. The experimental procedure is described and oscillograms of the process are presented. The relaxation spectrum is calculated from the experimental data on the mechanical behavior of the material over a broad range of strain rates. The results of the experiments are compared with a numberical solution of the problem of the impact of a rigid mass against a rod whose material is characterized by a relaxation spectrum.