A mathematical model for estimating muscle tension in vivo during esophageal bolus transport

We present a model of esophageal wall muscle mechanics during bolus transport with which the active and "passive" components of circular muscle tension are separately extracted from concurrent manometric and videofluoroscopic data. Local differential equations of motion are integrated across the esophageal wall to yield global equations of equilibrium which relate total tension within the esophageal wall to intraluminal pressure and wall geometry. To quantify the "passive" (i.e. inactive) length-tension relationships, the model equations are applied to a region of the esophagus in which active muscle contraction is physiologically inhibited. Combining the global equations with space-time-resolved intraluminal pressure measured manometrically and videofluoroscopic geometry data, the passive model is used to separate active and "passive" components of esophageal muscle tension during bolus transport. The model is of general applicability to probe basic muscle mechanics including the space-time stimulation of circular muscle, the relationship between longitudinal muscle tension and longitudinal muscle shortening, and the contribution of the collagen matrix surrounding muscle fibers to passive tension during normal human esophageal bolus transport and in pathology. Example calculations of normal esophageal function are given where active tone is found to extend only over a short intrabolus segment near the bolus tail and segmental regions of active muscle squeeze are demonstrated.     

Lattice shrinkage with increasing resting tension in stretched, single skinned fibers of frog muscle.

The 1,0 lattice spacing d1,0 in chemically and mechanically skinned single fibers of frog muscle was measured at various sarcomere lengths, L, in the range from L = 2.1 to 6.0 microns by an x-ray diffraction method. In chemically skinned fibers, d1,0 decreased with a similar slope to that of mechanically skinned fibers up to L congruent to 3 microns, but beyond this point d1,0 steeply decreased with further stretching. This steep decrease in d1,0 could be ascribed mainly to an increase in the compressing force associated with the longitudinal extension of a remnant of the sarcolemma. In mechanically skinned fibers, the gradual decrease in d1,0 continued beyond filament overlap (L greater than or equal to 3.5 microns) and was highly proportional to a resting tension. This decrease in d1,0 at L greater than or equal to 3.5 microns could be ascribed to an increase in the force exerted by lateral elastic components, which is proportional to the longitudinal resting tension. A conceptual model is proposed of a network structure of elastic components in a sarcomere.     

The mechanics of asymmetric retraction loops used in fixed appliance therapy

In order to move a tooth bodily without tipping, both a force P and an anti-tilt couple N of a suitable constant magnitude are required. Although many different spring components are available to orthodontists for this purpose, a comparison of the merits of different designs has not been possible because analytical solutions to the deformation behaviour have only been generally available for the atypical case in which the loop is centrally positioned. The asymmetric case, with two redundancies, for open and closed U-loops both with or without helices has been solved using the complementary (strain) energy method on the assumption that the effect of a longitudinal tension or compression on the bending of a cantilever beam by lateral forces (the tie-bar effect) is small. Unless the arms are of equal length it is then found that unequal couples M and N act at the posterior and anterior ends of the appliance, and in addition equal but oppositely directed forces Q are induced at either end. Check measurements were carried out on enlarged model components using a special jig utilizing a mixed dead-load and strain-gauge system. Agreement with theory was generally within the known errors of measurement. The main characteristics of these retraction components in the clinical situation can consequently be predicted. The characteristics examined are the lateral and vertical stiffnesses (S and dQ/dy, respectively), the N/P and Q/P ratios, the self-righting ability (SRA) and dN/d beta, the change in anti-tilt couple per degree change in gable angle (the angle of the mesial arm with respect of a horizontal in the unactivated appliance).     

Theoretical and electrophysiological evidence for axial loading about aortic baroreceptor nerve terminals in rats

Arterial baroreceptors are essential for neurocirculatory control, providing rapid hemodynamic feedback to the central nervous system. The pressure-dependent discharge of carotid and aortic baroreceptor afferents has been extensively studied. A common assumption has been that circumferential deformation of the arterial wall is the predominant mechanical force affecting baroreceptor discharge. However, in vivo the arterial tree is under significant longitudinal tension, leading to the hypothesis that axially directed forces may contribute to baroreceptor function. To test this hypothesis, we utilized a combination of finite element modeling methods and an in vitro rat aortic arch preparation. Model formulation utilized traditional analytic constructs available in the literature followed by refinement of model material parameters through direct comparison of computationally and experimentally generated pressure-diameter curves. The numerical simulations strongly indicated a functional role for axial loading within the region of the baroreceptive nerve terminal. This prediction was confirmed through single-fiber recording of baroreceptor nerve discharge under conditions with and without longitudinal tension in the vessel preparation. The recordings (n = 5) demonstrated that longitudinal tension significantly (P < 0.02) lowered both the pressure threshold (P(th), mmHg) for baroreceptor discharge and sensitivity (S(th), Hz/mmHg). The effect was nearly instantaneous and sustained; i.e., under longitudinal tension average P(th) was 84 +/- 3 mmHg and S(th) was 0.71 +/- 0.15 Hz/mmHg, which immediately increased to a P(th) of 94 +/- 4 mmHg and a S(th) of 1.20 +/- 0.32 Hz/mmHg with loss of axial tension. Possible explanations of how an abrupt change in axial loading could result in a synchronized increase in afferent drive of the baroreceptor reflex, and the potentiating effect this could have on neurogenically mediated orthostatic intolerance are discussed.     

Longitudinal tension variation in collapsible channels: a new mechanism for the breakdown of steady flow.

There are several mechanisms potentially involved in the breakdown of steady fluid flow in a collapsible tube under external pressure. Here we investigate one that has received little attention in the past: the fact that the longitudinal tension in the tube wall, T, decreases with distance downstream as a consequence of the viscous shear stress exerted by the fluid. If the tube is long enough, or the initial tension small enough, T may fall to zero before the end of the collapsible tube, and unsteady motion would presumably then ensue; this is what we mean by "breakdown." We study the phenomenon theoretically, when the flow Reynolds number is of order one, using lubrication theory in a symmetric two-dimensional channel in which the collapsible tube is replaced by membranes occupying a segment of each wall. The resulting nonlinear ordinary differential equations are solved numerically for values of the dimensionless parameters that cover all the qualitatively different types of solution (e.g., in which the channel is distended over all its length, collapsed over all its length, or distended in the upstream part and collapsed downstream). Reducing the longitudinal tension has a marked effect on the shape of the collapsible segment, causing it to become much more deformed for the same flow rate and external pressure. Indeed, the wall slope is predicted to become very large when the downstream tension is very small, so the model is not self-consistent then. Nevertheless, the parameter values for which T becomes zero are mapped out and are expected to be qualitatively useful.(ABSTRACT TRUNCATED AT 250 WORDS)     

The effect of mepyramine on the development of morphine tolerance and physical dependence in mice.

Latency relaxation (LR) as well as resting tension and twitch tension of frog toe muscles are studied in an isotonic solution (= 1 T) and in solutions made hypotonic by leaving out the appropriate amounts of NaCl and KCl (0.54 T and 0.76 T). In hypotonic solutions there is an increase in peak twitch tension as well as a decrease in the depth of the LR: the resting tension is increased at sarcomere lengths which are greater than 2.8 μm and is decreased at sarcomere lengths which are less than this value. The behaviour of twitch tension is discussed with respect to the influence of the sarcoplasmic ionic strength on the interaction between the contractile filaments. Concerning the decrease in both the LR and the resting tension, it is assumed that these effects are induced osmotically, the tension of the membranes of the longitudinal sarcoplasmic reticulum being the particular parameter which is influenced.     

Effects of tension and transmural stimulation on prostaglandin production by estrous rabbit oviductal isthmus

The effect of longitudinal and circular stretch on the amounts of Prostaglandin F (PGF) and Prostaglandin E (PGE) found in the fluid bathing rabbit oviductal isthmus has been investigated. It was found that the amounts of PGE nad PGF measured in the bathing fluid of longitudinally or circularly stretched tissues were negatively correlated to the maturity of the animal. Prostaglandin E increased with time in the tissues under longitudinal and circular tension. Prostaglandin F also increased with time under longitudinal tension but remained fairly constant under circular tension. Increasing the load from 0.5 to 2.0 g had no significant effect on PGE found under longitudinal or circular tension or on PGF found under longitudinal tension. Under circular tension, PGF found increased. Transmural stimulation at 20 Hz increased PGE 8-fold over control values while PGF increased only 1 to 3-fold. It is suggested that distension of the rabbit oviductal isthmus results in increased PGF production, which could be important in ovum transport.     

Aurora B kinase-dependent recruitment of hZW10 and hROD to tensionless kinetochores

The mitotic checkpoint ensures proper chromosome segregation by monitoring two critical events during mitosis. One is kinetochore attachment to the mitotic spindle, and the second is the alignment of chromosomes at the metaphase plate, resulting in tension across sister kinetochores (reviewed in [1, 2]). Mitotic-checkpoint proteins are known to accumulate at unaligned chromosomes that have not achieved proper kinetochore-microtubule attachments or established an adequate level of tension across sister kinetochores. Here, we report that hZW10 and hROD, two components of the evolutionarily conserved RZZ complex, accumulate at kinetochores in response to the loss of tension. By using live-cell imaging and FRAP, we showed that the accumulation of hZW10 at tensionless kinetochores stems from a 4-fold reduction of kinetochore turnover rate. We also found that cells lacking hZW10 escape loss-of-tension-induced mitotic-checkpoint arrest more rapidly than those arrested in response to the lack of kinetochore-microtubule attachments. Furthermore, we show that pharmacological inhibition of Aurora B kinase activity with ZM447439 in the absence of tension, but not in the absence of kinetochore-microtubule attachments, results in the loss of hZW10, hROD, and hBub1 from kinetochores. We therefore conclude that Aurora B kinase activity is required for the accumulation of tension-sensitive mitotic-checkpoint components, such as hZW10 and hROD, in order to maintain mitotic-checkpoint arrest.     

Internal forces, tension and energy density in tethered cellular membranes

We analyze tethered cellular membranes by considering the membrane resultants, tension and densities of two modes of energy, bending and adhesion. These characteristics are determined based on a computational (finite-difference) analysis of membrane shape. We analyze the relative contribution and distribution of the membrane characteristics in four typical zones of the membrane surface. Using an axisymmetric model, we found that the meridional and circumferential components of the resultant are different near the tether body and they converge to the value of membrane tension farther from the tether. At the beginning of the area of membrane detachment from the cytoskeleton, the density of bending energy is on the same order of magnitude as membrane tension (resultant). Away from the tether, the bending energy density quickly decreases and becomes of the same order as that of the adhesion energy in the membrane-cytoskeleton attachment area. In that area, both modes of energy are significantly smaller than the membrane tension. We also consider the effect of the membrane bending modulus on the distribution of the membrane characteristics. An increase in the bending modulus results in changing the length and position on the membrane surface of zone 1 characterized by significant evolution of the resultant components. It also results in shortening zone 2 that covers the rest of the area of membrane detachment. The obtained results can help in a better interpretation of the measurements of membrane mechanical properties as well as in analyses of proteins and channels in curved membranes.     

New insights into the behavior of muscle during active lengthening.

A muscle fiber was modeled as a series-connected string of sarcomeres, using an A. V. Hill type model for each sarcomere and allowing for some random variation in the properties of the sarcomeres. Applying stretches to this model led to the prediction that lengthening of active muscle on or beyond the plateau of the length tension curve will take place very nonuniformly, essentially by rapid, uncontrolled elongation of individual sarcomeres, one at a time, in order from the weakest toward the strongest. Such a "popped" sarcomere, at least in a single fiber, will be stretched to a length where there is no overlap between thick and thin filaments, and the tension is borne by passive components. This prediction allows modeling of many results that have previously been inexplicable, notably the permanent extra tension after stretch on the descending limb of the length tension curve, and the continued rise of tension during a continued stretch.     

A finite-element model of tracheal collapse

The trachea has been approximated by an appropriate finite-element model. The three-dimensional equilibrium problems set by the tracheal deformation under various stresses have been solved using a convenient augmented Lagrangian functional. The dimensions were obtained from human tracheae. Mechanical constants for the anatomic components were calculated from the stress-strain relationships. The compressive narrowing is essentially due to the invagination of the posterior membrane in the tracheal lumen for transmural pressures down to -7 kPa. A surface of contact between the membranous wall and the lateral walls appears when the transmural pressure equals -6 kPa. The transmural pressure-area relationship is sigmoidal with a compliance equal to 0.08 kPa-1 for a transmural pressure of -2 kPa. The tracheal collapse is greater when the material constants of the membranous wall decrease or when the tracheal segment is subjected to a longitudinal tension. A slight flexion of the trachea induces an asymmetric deformation.     

The three-dimensional structure of the central region in a synaptonemal complex: a comparison between rat and two insect species,Drosophila melanogaster andBlaps cribrosa

The highly ordered central region of the synaptonemal complex (SC) inBlaps cribrosa has recently been studied by electron microscope tomography (EMT), and a simple three-dimensional model presented. Using the same experimental approach we have now compared the central region inBlaps with the central regions inDrosophila melanogaster and rat. In all three species, the SCs exhibit a central element (CE) flanked by two lateral elements (LEs). The central region between the two LEs is crossed by transverse filaments (TFs). TheBlaps CE element is the most ordered one with a well-defined ladder-like structure with two longitudinal components bridged by a number of regularly spaced transverse components, the rungs of the ladder. At the junctions between the longitudinal and transverse components there are prominent dense structures. The CE is multi-layered with the ladders of the separate layers in approximate register. InDrosophila the transverse CE components are as distinct and well organized as inBlaps, while in rat they are present but are less frequent and less well ordered. The longitudinal CE components inDrosophila are often fragmented and even more so in rat. The tomographic analysis revealed that in all three species the central region contains the same structural units: a single TF associated with two short pillars (or globules), which correspond to the junction structures. A fibrous lattice connects the two pillars/globules on the same TF forming the transverse CE component and those on adjacent TFs forming the longitudinal CE component; fibers between pillars/globules also link consecutive CE layers together. In the longitudinal component the number of fibrous bridges between the pillars/globules is related to the conspicuousness of the longitudinal component, i.e.Blaps has most,Drosophila almost as many, and rat considerably fewer bridges. We conclude that the central region in rat,Drosophila andBlaps contains the same basic structural unit but the degree of order and concentration of the units differ: a higher density seems to be accompanied by a higher order within the CE.     

Structural and functional reconstitution of thin filaments in the contractile apparatus of cardiac muscle.

The muscle contractile apparatus has a highly ordered liquid crystalline structure. The molecular mechanism underlying the formation of this apparatus remains, however, to be elucidated. Selective removal and reconstitution of the components are useful means of examining this mechanism. In addition, this approach is a powerful technique for examining the structure and function of a specific component of the contractile system. In this study we have achieved the structural and functional reconstitution of thin filaments in the cardiac contractile apparatus. First, all thin filaments other than short fragments at the Z line were removed by treatment with gelsolin. Under these conditions no active tension could be generated. By incorporating exogenous actin into these thin filament-free fibers, actin filaments were reconstituted, and active tension, which was insensitive to Ca2+, was restored. The active tension after the reconstitution of thin filaments reached 135 +/- 64% of the original level. The augmentation of tension was attributable to the elongation of reconstituted filaments. As another possibility for augmented tension generation, we suggest the presence of an inhibitory system that was not reconstituted. In any case, the thin filaments of the cardiac contractile apparatus are considered to be assembled so as not to develop the highest degree of tension. Incorporation of the tropomyosin-troponin complex fully restored Ca2+ sensitivity without affecting maximum tension. The present results indicate that a muscle contractile apparatus with a higher order structure and function can be constructed by the self-assembly of constituent proteins.     

Evidence that myosin light chain phosphorylation regulates contraction in the body wall muscles of the sea cucumber

The Ca²⁺ activation mechanism of the longitudinal body wall muscles of Parastichopus californicus (sea cucumber) was studied using skinned muscle fiber bundles. Reversible phosphorylation of the myosin light chains correlated with Ca²⁺-activated tension and relaxation. Pretreatment of the skinned fibers with ATPγS and high Ca²⁺ (10^-5M) resulted in irreversible thiophosphorylation of the myosin light chains and activation of a Ca²⁺ insensitive tension. In contrast, pretreatment with low Ca²⁺ (10^-8M) and ATPγS results in no thiophosphorylation of the myosin light chains or irreversible activation of tension. These results are consistent with a Ca²⁺-sensitive myosin light chain kinase/phosphatase system being responsible for the activation of the muscle. Other agents known to have an effect upon the Ca²⁺-activated tension in skinned vertebrate smooth muscle fibers (trifluoperazine, catalytic subunit of the cyclic AMP-dependent protein kinase, and calmodulin) did not have an effect on myosin light chain phosphorylation or Ca²⁺-activated tension. These results suggest a different type of myosin light chain kinase than is found in vertebrate smooth muscle is responsible for the activation of parastichopus longitudinal body wall muscle.     

A novel method for measuring tension generated in stress fibers by applying external forces

The distribution of contractile forces generated in cytoskeletal stress fibers (SFs) contributes to cellular dynamic functions such as migration and mechanotransduction. Here we describe a novel (to our knowledge) method for measuring local tensions in SFs based on the following procedure: 1), known forces of different magnitudes are applied to an SF in the direction perpendicular to its longitudinal axis; 2), force balance equations are used to calculate the resulting tensions in the SF from changes in the SF angle; and 3), the relationship between tension and applied force thus established is extrapolated to an applied force of zero to determine the preexisting tension in the SF. In this study, we measured tensions in SFs by attaching magnetic particles to them and applying known forces with an electromagnetic needle. Fluorescence microscopy was used to capture images of SFs fluorescently labeled with myosin II antibodies, and analysis of these images allowed the tension in the SFs to be measured. The average tension measured in this study was comparable to previous reports, which indicates that this method may become a powerful tool for elucidating the mechanisms by which cytoskeletal tensions affect cellular functions.     

Nanotopographical stimulation of mechanotransduction and changes in interphase centromere positioning

We apply a recently developed method for controlling the spreading of cultured cells using electron beam lithography (EBL) to create polymethylmethacrylate (PMMA) substrata with repeating nanostructures. There are indications that the reduced cell spreading on these substrata, compared with planar PMMA, results from a reduced adhesivity since there are fewer adhesive structures and fewer of their associated stress fibres. The reduced cell spreading also results in a reduced nuclear area and a closer spacing of centrosomes within the nucleus, suggesting that the tension applied to the nucleus is reduced as would be expected from the reduction in stress fibres. In order to obtain further evidence for this, we have used specific inhibitors of components of the cytoskeleton and have found effects comparable with those induced by the new substrata. We have also obtained evidence that these subtrata result in downregulation of gene expression which suggests that this may be due to the changed tension on the nucleus: an intriguing possibility that merits further investigation.     

Effects of pressure on equatorial x-ray fiber diffraction from skeletal muscle fibers.

When skeletal muscle fibers are subjected to a hydrostatic pressure of 10 MPa (100 atmospheres), reversible changes in tension occur. Passive tension from relaxed muscle is unaffected, rigor tension rises, and active tension falls. The effects of pressure on muscle structure are unknown: therefore a pressure-resistant cell for x-ray diffraction has been built, and this paper reports the first study of the low-angle equatorial patterns of pressurized relaxed, rigor, and active muscle fibers, with direct comparisons from the same chemically skinned rabbit psoas muscle fibers at 0.1 and 10 MPa. Relaxed and rigor fibers show little change in the intensity of the equatorial reflections when pressurized to 10 MPa, but there is a small, reversible expansion of the lattice of 0.7 and 0.4%, respectively. This shows that the order and stability of the myofilament lattice is undisturbed by this pressure. The rise in rigor tension under pressure is thus probably due to axial shortening of one or more components of the sarcomere. Initial results from active fibers at 0.1 MPa show that when phosphate is added the lattice spacing and equatorial intensities change toward their relaxed values. This indicates cross-bridge detachment, as expected from the reduction in tension that phosphate induces. 10 MPa in the presence of phosphate at 11 degrees C causes tension to fall by a further 12%, but not change is detected in the relative intensity of the reflections, only a small increase in lattice spacing. Thus pressure appears to increase the proportion of attached cross-bridges in a low-force state.     

Nonlinear tensile properties of bovine articular cartilage and their variation with age and depth

Tensile stiffness of articular cartilage is much greater than its compressive stiffness and plays an essential role even in compressive properties by increasing transient fluid pressures during physiological loading. Recent studies of nonlinear properties of articular cartilage in compression revealed several physiologically pertinent nonlinear behaviors, all of which required that cartilage tensile stiffness increase significantly with stretch. We therefore performed sequences of uniaxial tension tests on fresh bovine articular cartilage slices using a protocol that allowed several hours to attain equilibrium and measured longitudinal and transverse tissue strain. By testing bovine cartilage from different ages (6 months to 6 years) we found that equilibrium and transient tensile modulus increased significantly with maturation and age, from 0 to 15 MPa at equilibrium and from 10 to 28 MPa transiently. Our results indicate that cartilage stiffens with age in a manner similar to other highly hydrated connective tissues, possibly due to age-dependent content of enzymatic and nonenzymatic collagen cross links. The long relaxation period used in our tests (5-10 hours) was necessary in order to attain equilibrium and avoid a very significant overestimation of equilibrium modulus that occurs when much shorter times are used (15-30 minutes). We also found that equilibrium and transient tensile modulus increased nonlinearly when cartilage is stretched from 0 to 10% strain without any previous tare load. Although our results estimate a nonlinear increase in tensile stiffness with stretch that is an order of magnitude lower than that required to predict nonlinear properties in compression, they are in agreement with previous results from other uniaxial tension tests of collagenous materials. We therefore speculate that biaxial tensile moduli may be much higher and thereby more compatible with observed nonlinear compressive properties.