Positive feedback by a potassium-selective inward rectifier enhances tuning in vertebrate hair cells.

Titin (also known as connectin) is a muscle-specific giant protein found inside the sarcomere, spanning from the Z-line to the M-line. The I-band segment of titin is considered to function as a molecular spring that develops tension when sarcomeres are stretched (passive tension). Recent studies on skeletal muscle indicate that it is not the entire I-band segment of titin that behaves as a spring; some sections are inelastic and do not take part in the development of passive tension. To better understand the mechanism of passive tension development in the heart, where passive tension plays an essential role in the pumping function, we investigated titin's elastic segment in cardiac myocytes using structural and mechanical techniques. Single cardiac myocytes were stretched by various amounts and then immunolabeled and processed for electron microscopy in the stretched state. Monoclonal antibodies that recognize different titin epitopes were used, and the locations of the titin epitopes in the sarcomere were studied as a function of sarcomere length. We found that only a small region of the I-band segment of titin is elastic; its contour length is estimated at approximately 75 nm, which is only approximately 40% of the total I-band segment of titin. Passive tension measurements indicated that the fundamental determinant of how much passive tension the heart develops is the strain of titin's elastic segment. Furthermore, we found evidence that in sarcomeres that are slack (length, approximately 1.85 microns) the elastic titin segment is highly folded on top of itself. Based on the data, we propose a two-stage mechanism of passive tension development in the heart, in which, between sarcomere lengths of approximately 1.85 microns and approximately 2.0 microns, titin's elastic segment straightens and, at lengths longer than approximately 2.0 microns, the molecular domains that make up titin's elastic segment unravel. Sarcomere shortening to lengths below slack (approximately 1.85 microns) also results in straightening of the elastic titin segment, giving rise to a force that opposes shortening and that tends to bring sarcomeres back to their slack length.     

Mechanical properties of pore-spanning lipid bilayers probed by atomic force microscopy

We measure the elastic response of a free-standing lipid membrane to a local indentation by using an atomic force microscope. Starting point is a planar gold-coated alumina substrate with a chemisorbed 3-mercaptopropionic acid monolayer displaying circular pores of very well defined and tunable size, over which bilayers composed of N,N,-dimethyl-N,N,-dioctadecylammonium bromide or 1,2-dioleoyl-3-trimethylammonium-propane chloride were spread. Centrally indenting these "nanodrums" with an atomic force microscope tip yields force-indentation curves, which we quantitatively analyze by solving the corresponding shape equations of continuum curvature elasticity. Since the measured response depends in a known way on the system geometry (pore size, tip radius) and on material parameters (bending modulus, lateral tension), this opens the possibility to monitor local elastic properties of lipid membranes in a well-controlled setting.     

Cell motility and local viscoelasticity of fibroblasts

Viscoelastic changes of the lamellipodial actin cytoskeleton are a fundamental element of cell motility. Thus, the correlation between the local viscoelastic properties of the lamellipodium (including the transitional region to the cell body) and the speed of lamellipodial extension is studied for normal and malignantly transformed fibroblasts. Using our atomic force microscopy-based microrheology technique, we found different mechanical properties between the lamellipodia of malignantly transformed fibroblasts (H-ras transformed and SV-T2 fibroblasts) and normal fibroblasts (BALB 3T3 fibroblasts). The average elastic constants, K, in the leading edge of SV-T2 fibroblasts (0.48 +/- 0.51 kPa) and of H-ras transformed fibroblasts (0.42 +/- 0.35 kPa) are significantly lower than that of BALB 3T3 fibroblasts (1.01 +/- 0.40 kPa). The analysis of time-lapse phase contrast images shows that the decrease in the elastic constant, K, for malignantly transformed fibroblasts is correlated with the enhanced motility of the lamellipodium. The measured mean speeds are 6.1 +/- 4.5 microm/h for BALB 3T3 fibroblasts, 13.1 +/- 5.2 microm/h for SV-T2 fibroblasts, and 26.2 +/- 11.5 microm/h for H-ras fibroblasts. Furthermore, the elastic constant, K, increases toward the cell body in many instances which coincide with an increase in actin filament density toward the cell body. The correlation between the enhanced motility and the decrease in viscoelastic moduli supports the Elastic Brownian Ratchet model for driving lamellipodia extension.     

Time-dependent recovery of passive neutrophils after large deformation.

Experiments are performed in which a passive human neutrophil is deformed into an elongated "sausage" shape by aspirating it into a small glass pipette. When expelled from the pipette the neutrophil recovers its natural spherical shape in approximately 1 minute. This recovery process is analyzed according to a Newtonian, liquid-drop model in which a variational method is used to simultaneously solve the hydrodynamic equations for low Reynolds-number flow and the equations for membrane equilibrium with a constant membrane tension. The theoretical model gives a good fit to the experimental data for a ratio of membrane cortical tension to cytoplasmic viscosity of approximately 1.7 x 10(-5) cm/s (0.17 micron/s). However, when the cell is held in the pipette for only a short time period of 5 s or less, and then expelled, the cell undergoes an initial, rapid elastic rebound suggesting that the cell behaves in this instance as a Maxwell viscoelastic liquid rather than a Newtonian liquid with constant cortical tension.     

Mechanical Response of Single Plant Cells to Cell Poking： A Numerical Simulation Model

Cell poking is an experimental technique that is widely used to study the mechanical properties of plant cells. A full understanding of the mechanical responses of plant cells to poking force Is helpful for experimental work. The aim of this study was to numerically investigate the stress distribution of the cell wall, cell turgor, and deformation of plant cells in response to applied poking force. Furthermore, the locations damaged during poking were analyzed. The model simulates cell poking, with the cell treated as a spherical, homogeneous, isotropic elastic membrane, filled with incompressible, highly viscous liquid. Equilibrium equations for the contact region and the non-contact regions were determined by using membrane theory. The boundary conditions and continuity conditions for the solution of the problem were found. The forcedeformation curve, turgor pressure and tension of the cell wall under cell poking conditions were obtained. The tension of the cell wall circumference was larger than that of the meridian. In general, maximal stress occurred at the equator around. When cell deformation increased to a certain level, the tension at the poker tip exceeded that of the equator. Breakage of the cell wall may start from the equator or the poker tip, depending on the deformation. A nonlinear model is suitable for estimating turgor, stress, and stiffness, and numerical simulation is a powerful method for determining plant cell mechanical properties.     

Bandpass filtering of DNA elastic modes using confinement and tension

During a variety of biological and technological processes, biopolymers are simultaneously subject to both confinement and external forces. Although significant efforts have gone into understanding the physics of polymers that are only confined, or only under tension, little work has been done to explore the effects of the interplay of force and confinement. Here, we study the combined effects of stretching and confinement on a polymer's configurational freedom. We measure the elastic response of long double-stranded DNA molecules that are partially confined to thin, nanofabricated slits. We account for the data through a model in which the DNA's short-wavelength transverse elastic modes are cut off by applied force and the DNA's bending stiffness, whereas long-wavelength modes are cut off by confinement. Thus, we show that confinement and stretching combine to permit tunable bandpass filtering of the elastic modes of long polymers.     

Kinetic characteristics of cross bridges in the heart muscles by a temperature jump method]

Experiments were performed on rat skinned trabecular muscles dissected from the right ventricles. They were activated (pCa = 5.9) at 10 C, 2.3 nm sarcomere length. The temperature jump induced the biexponential tension rise. The rate constant of the fast tension rise (k1) was 3-4.5 ms and that of the slow tension rise (k2) was about 15 ms. These values were slower (3 times) comparing with those of a single skeletal fibre. The discrepancy can be explained by different kinetic properties of heart and skeletal myosin or presents a well developed connection tissue (series elastic element) in the heart muscle.     

Cytomechanics of axonal development

Mechanical tension is a robust regulator of axonal development of cultured neurons. We review work from our laboratory, using calibrated glass needles to measure or apply tension to chick sensory neurons, chick forebrain neurons, and rat PC12 cells. We survey direct evidence for two different regimes of tension effects on neurons, a fluid-like growth regime, and a nongrowth, elastic regime. Above a minimum tension threshold, we observe growth effects of tension regulating four phases of axonal development:

1. Initiation of process outgrowth from the cell body;
2. Growth cone-mediated elongation of the axon;
3. Elongation of the axon after synaptogenesis, which normally accommodates the skeletal growth of vertebrates; and
4. Axonal elimination by retraction.

Significantly, the quantitative relationship between the force and the growth response is suprisingly similar to the simple relationship characteristic of Newtonian fluid mechanical elements: elongation rate is directly proportional to tension (above the threshold), and this robust linear relationship extends from physiological growth rates to far-above-physiological rates. Thus, tension apparently integrates the complex biochemistry of axonal elongation, including cytoskeletal and membrane dynamics, to produce a simple “force input/growth output” relationship. In addition to this fluid-like growth response, peripheral neurons show elastic behaviors at low tensions (below the threshold tension for growth), as do most cell types. Thus, neurites could exert small static forces without diminution for long periods. In addition, axons of peripheral neurons can actively generate modest tensions, presumably similar to muscle contraction, at tensions near zero. The elastic and force-generating capability of neural axons has recently been proposed to play a major role in the morphogenesis of the brain.     

Peroxynitrite irreversibly decreases diastolic and systolic function in cardiac muscle

Much of the damaging action of nitric oxide in heart may be due to its diffusion-limited reaction with superoxide to form peroxynitrite. Direct infusion of peroxynitrite into isolated perfused hearts fails to model the effects of in situ formation because the bulk of peroxynitrite decomposes before reaching the myocytes. To examine the direct effects of peroxynitrite on the contractile apparatus of the heart, we exposed intact and skinned rat papillary muscles to a steady state concentration of 4-microM peroxynitrite for 5 min, followed by a 30-min recovery period to monitor irreversible effects. In intact muscles developed force fell immediately to 26% of initial force, recovering to 43% by 30 min. Resting tension increased by 600% immediately, and was still elevated 500% by 30 min. Nitrotyrosine immunochemistry showed that peroxynitrite can induce tyrosine nitration at low concentrations and is capable of penetrating 200-380 microm into the papillary muscle after a 5-min infusion. Decomposed peroxynitrite had no effect on either intact or skinned muscle developed force or resting tension. Our results show that peroxynitrite directly damages both developed force and resting tension of isolated heart muscle, which can be extrapolated to systolic and diastolic injury in intact hearts.     

Governing equations of motion for the otolith organs and their response to a step change in velocity of the skull

The otolith organs are the linear motion sensors of the inner ear. They comprise an overdamped second-order system and respond to gravity and skull acceleration. The governing equations of motion which describe the relative displacement of the mass with respect to the skull are developed. When these equations are non-dimensionalized they indicate that the elastic term is almost negligible with respect to the viscous and inertial terms. For a step change in skull velocity an analytic solution is given for the elastic term equal to zero and numeric solutions are given for small values of the elastic term.     

Geometrical aspects of surface morphogenesis

This paper is concerned with the morphogenesis of structures which form thin deformable sheets. A general formalism is presented for the deformation of a sheet in the presence of an isotropic local body stress. This formalism leads to a set of equations, based on the theory of shells, in which corrections are made in the geometry due to large deformations. Under certain conditions the equations may be solved to give the surface metric tensor as a function of the local tension. A numerical example based on a simple "threshold" model is also presented.     

Estimation of evolutionary distances from protein spatial structures

New equations are derived to estimate the number of amino acid substitutions per site between two homologous proteins from the root mean square (RMS) deviation between two spatial structures and from the fraction of identical residues between two sequences. The equations are based on evolutionary models, analyzing predominantly structural changes and not sequence changes. Evolution of spatial structure is treated as a diffusion in an elastic force field. Diffusion accounts for structural changes caused by amino acid substitutions, and elastic force reflects selection, which preserves protein fold. Obtained equations are supported by analysis of protein spatial structures. Received: 21 September 1995 / Accepted: 19 May 1997     

On the effects of residual stress in microindentation tests of soft tissue structures

Microindentation methods are commonly used to determine material properties of soft tissues at the cell or even sub-cellular level. In determining properties from force-displacement (FD) data, it is often assumed that the tissue is initially a stress-free, homogeneous, linear elastic half-space. Residual stress, however, can strongly influence such results. In this paper, we present a new microindentation method for determining both elastic properties and residual stress in soft tissues that, to a first approximation, can be regarded as a pre-stressed layer embedded in or adhered to an underlying relatively soft, elastic foundation. The effects of residual stress are shown using two linear elastic models that approximate specific biological structures. The first model is an axially loaded beam on a relatively soft, elastic foundation (i.e., stress-fiber embedded in cytoplasm), while the second is a radially loaded plate on a foundation (e.g., cell membrane or epithelium). To illustrate our method, we use a nonlinear finite element (FE) model and experimental FD and surface contour data to find elastic properties and residual stress in the early embryonic chick heart, which, in the region near the indenter tip, is approximated as an isotropic circular plate under tension on a foundation. It is shown that the deformation of the surface in a microindentation test can be used along with FD data to estimate material properties, as well as residual stress, in soft tissue structures that can be regarded as a plate under tension on an elastic foundation. This method may not be as useful, however, for structures that behave as a beam on a foundation.     

Bend propagation in flagella. I. Derivation of equations of motion and their simulation.

A set of nonlinear differential equations describing flagellar motion in an external viscous medium is derived. Because of the local nature of these equations and the use of a Crank-Nicolson-type forward time step, which is stable for large deltat, numerical solution of these equations on a digital computer is relatively fast. Stable bend initiation and propagation, without internal viscous resistance, is demonstrated for a flagellum containing a linear elastic bending resistance and an elastic shear resistance that depends on sliding. The elastic shear resistance is derived from a plausible structural model of the radial link system. The active shear force for the dynein system is specified by a history-dependent functional of curvature characterized by the parameters m0, a proportionality constant between the maximum active shear moment and curvature, and tau, a relaxation time which essentially determines the delay between curvature and active moment.     

Investigating various many-body force fields for their ability to predict reduction in elastic modulus due to vacancies using molecular dynamics simulations

ABSTRACT

Molecular dynamics simulations are more frequently being utilised to predict macroscale mechanical properties as a result of atomistic defects. However, the interatomic force field can significantly affect the resulting mechanical properties. While several studies exist which demonstrate the ability of various force fields to predict mechanical properties, the investigation into which is most accurate for the investigation of vacancies is limited. To obtain meaningful predictions of mechanical properties, a clear understanding of force field parameterisation is required. As such, the current study evaluates various many-body force fields to demonstrate the reduction in mechanical properties of iron and iron–chromium due to the presence of vacancies while undergoing room temperature atomistic uniaxial tension. Reduction was normalised in each case with the zero-vacancy elastic modulus, removing the need to predict an accurate nominal elastic modulus. Comparisons were made to experimental data and an empirical model from literature. It was demonstrated that accurate fitting to vacancy formation and migration energy allowed for accurate predictions. In addition, bond-order based force fields showed enhanced predictions regardless of fitting procedure. Overall, these findings highlight the need to understand capabilities and limitations of available force fields, as well as the need for enhanced parameterisation of force fields.     

Physical properties of resistance vessel wall in peripheral blood flow regulation--I. Mathematical model

A mathematical model is introduced to investigate the influence of the physical properties of the resistance vessel wall on the metabolic and myogenic mechanisms. The resistance vessel wall is assumed to have an elastic property and the elastic modulus to be a function of pressure (myogenic) and flow (metabolic). Blood is Poiseuille's flow. The resulting mathematical equations for pressure-flow, pressure-diameter, pressure-wall tension and pressure-wall elastic modulus relationships introduced obey Laplace's law. Poiseuille's law and Hooke's law. In comparison with the experimental data (pressure diameter), the mathematical model is confirmed to explain well the dynamic behavior of the resistance vessel wall in vivo.     

Influence of thermally driven surface undulations on tethers formed from bilayer membranes

Tether formation is a powerful method to study the mechanical properties of soft lipid bilayer membranes. The force required to maintain a tether at a given length depends upon both membrane elastic properties and tension. In this report, we develop a theoretical analysis that considers the contribution of thermally driven surface undulations and the corresponding entropically driven tensions on the conformation of tethers formed from unaspirated lipid vesicles. In this model, thermal undulations of the vesicle surface provide the excess area required for tether formation. Energy minimization demonstrates the dependence of equilibrium tether conformation on membrane tension and provides an analytical relationship between tether force and radius. If the contributions of nonlocal bending are not considered, an analytical relationship between tether force and length can also be obtained. The predictions of the model are compared to recently reported experimental data, and a value for the initial vesicle tension is obtained. Since most analyses of tether formation from cells and unaspirated vesicles neglect the contributions of nonlocal bending, the appropriateness of this assumption is analyzed. The effect of surface microvesiculations on the tether force-length relation is also considered.     

A quantitative model of cellular elasticity based on tensegrity

A tensegrity structure composed of six struts interconnected with 24 elastic cables is used as a quantitative model of the steady-state elastic response of cells, with the struts and cables representing microtubules and actin filaments, respectively. The model is stretched uniaxially and the Young's modulus (E0) is obtained from the initial slope of the stress versus strain curve of an equivalent continuum. It is found that E0 is directly proportional to the pre-existing tension in the cables (or compression in the struts) and inversely proportional to the cable (or strut) length square. This relationship is used to predict the upper and lower bounds of E0 of cells, assuming that the cable tension equals the yield force of actin (approximately 400 pN) for the upper bound, and that the strut compression equals the critical buckling force of microtubules for the lower bound. The cable (or strut) length is determined from the assumption that model dimensions match the diameter of probes used in standard mechanical tests on cells. Predicted values are compared to reported data for the Young's modulus of various cells. If the probe diameter is greater than or equal to 3 microns, these data are closer to the lower bound than to the upper bound. This, in turn, suggests that microtubules of the CSK carry initial compression that exceeds their critical buckling force (order of 10(0)-10(1) pN), but is much smaller than the yield force of actin. If the probe diameter is less than or equal to 2 microns, experimental data fall outside the region defined by the upper and lower bounds.