Local Contraction Research Articles

Fixed-point for local contractions: applications to recursive utility

Fixed-point for local contractions: applications to recursive utility

Effect of Isoproterenol on Local Contractile Behaviors of Rat Cardiomyocytes Measured by Atomic Force Microscopy

Inotropic agents induce changes in the contraction amplitude and frequency of cardiomyocytes (CMs). However, it is unknown how local contractions of CMs treated by inotropic agents behave spatiotemporally. In this study, the effect of isoproterenol, a positive inotropic agent, on local contractions of isolated neonatal rat CMs was explored by atomic force microscopy (AFM). We observed that changes in local contraction amplitude of CM in the presence of isoproterenol were heterogeneous; they were unchanged or increased, at different positions, with respect to the amplitude of untreated CMs. Interestingly, spatial heterogeneities of local contraction amplitude of CM in the presence of isoproterenol did not obviously correlate with the local elasticity, indicating that the local contractions were facilitated by cooperative dynamics of the cytoskeletal structure in relatively large regions, rather than those just under AFM indentation. Moreover, local contraction amplitude of CM in the presence of isoproterenol was not proportional to that in the control condition, showing that the former change was no longer additive in local scales.

Displacement Spectra Under Isometric Muscle Contraction

The purposes of this work were to detect the microscopic displacements accompanying isometric muscle tissue contraction under different external loads, to explore their spectral characteristics, and to develop physical models capable of explaining the experimental data obtained. By means of a spectral Doppler musculoskeletal ultrasound method, spectral characteristics of local isometric skeletal muscle tissue contraction were studied. In this method, the phased fluctuation (Doppler) algorithm is used to estimate tissue displacements within the given sample volume in real time, and the spectral characteristics of recorded displacements are determined. Observation of local isometric muscle contraction was conducted in the brachioradial muscle of the flexor digitorum profundus. Data obtained from 6 healthy volunteers during observation of muscle contraction in a relaxed state and under different static loads (2, 5, and 10 kg) were processed. The main difference in recorded displacements under different loads was in the displacement fluctuation values, whereas spectral characteristics were almost constant. Differences in the numbers and values of spectral maxima were also observed. These results are explained by a developed physical model assuming that the mechanochemical characteristics of crossbridges between actin and myosin filaments are the main factors influencing the spectral peculiarities of the Doppler response. Both the developed model of the Doppler response and the proposed dynamic model of sarcomere movement establish a link between macroscopic Doppler measurements and the biomechanical processes and behavior of sarcomeres at a subcellular level. The results of these pilot experiments demonstrate the suitability of this spectral Doppler method for a more detailed spectral study of biomechanical processes that occur under muscle contraction. The stability of the spectral characteristics under different loads also testifies to the value of this method as a reliable and valid diagnostic tool for diagnosing neuromuscular disorders.

The role of asymmetric thickening of the uterine myometrium during pregnancy

This study aimed to examine the role of local uterine contractions during pregnancy depicted as asymmetric thickening of the myometrium ultrasonographically. 419 pregnant women at 12-21 weeks of gestation who visited our outpatient department were studied. These subjects visited either for regular antenatal examinations or because of ill-defined subjective symptoms. Ultrasonographic examination was conducted to detect asymmetric thickening of the uterine myometrium. Blood flow in the region of myometrial thickening was studied by color Doppler imaging. Among 419 subjects, 27.38 % (112/419) patients visited our outpatient department showed asymmetric thickening of myometrium. Since cervical changes or progression to labor occurred in none of the subjects, the reviewed symptoms were considered to be benign contractions. Many women with ill-defined symptoms showed asymmetric thickenings of the myometrium (73.75 % sensitivity and 84.32 % specificity). Myometrial thickening under the placenta tended to be associated with abundant blood flow (88.46 % sensitivity and 87.21 % specificity). This different pattern of the blood flow was considered to correlate to arcuate artery resistance but did not correlate to the severity of ill-defined symptoms. Among those patients having no clinical symptoms, 53 exhibited asymmetric thickening of the myometrium. This phenomenon might be the caution of ill-defined symptoms. Asymmetric thickening of the uterine myometrium during pregnancy represented the ill-defined symptoms. Different patterns of blood flow images at this local contraction did not correlate to the severity of these symptoms.

Heterotrimeric G protein signaling governs the cortical stability during apical constriction in Drosophila gastrulation

During gastrulation in Drosophila melanogaster, coordinated apical constriction of the cellular surface drives invagination of the mesoderm anlage. Forces generated by the cortical cytoskeletal network have a pivotal role in this cellular shape change. Here, we show that the organisation of cortical actin is essential for stabilisation of the cellular surface against contraction. We found that mutation of genes related to heterotrimeric G protein (HGP) signaling, such as Gβ13F, Gγ1, and ric-8, results in formation of blebs on the ventral cellular surface. The formation of blebs is caused by perturbation of cortical actin and induced by local surface contraction. HGP signaling mediated by two Gα subunits, Concertina and G-iα65A, constitutively regulates actin organisation. We propose that the organisation of cortical actin by HGP is required to reinforce the cortex so that the cells can endure hydrostatic stress during tissue folding.

The size, shape, and dynamics of cellular blebs

A cellular bleb grows when a portion of the cell membrane detaches from the underlying cortex under the influence of a cytoplasmic pressure. We develop a quantitative model for the growth and dynamics of these objects in a simple two-dimensional setting. In particular, we first find the minimum cytoplasmic pressure and minimum unsupported membrane length for a stationary bleb to nucleate and grow as a function of the membrane-cortex adhesion. We next show how a bleb may travel around the periphery of the cell when the cytoplasmic pressure varies in space and time in a prescribed way and find that the traveling speed is governed by the speed of the pressure change induced by local cortical contraction while the shape of the traveling bleb is governed by the speed of cortical healing. Finally, we relax the assumption that the pressure change is prescribed and couple it hydrodynamically to the cortical contraction and membrane deformation. By quantifying the phase space of bleb formation and dynamics, our framework serves to delineate the range and scope of bleb-associated cell motility.

Following nature's challenges

Following nature's challenges

Cardiomyocyte-driven gel network for bio mechano-informatic wet robotics

This paper reports on a cellular mechano-informatics network gel robot which was powered by culturing cardiomyocytes in the micro gel structure. Contraction activities propagated through the cardiomyocyte gel network will transmit a spatial mechanical wave as information about the chemical and mechanical responses to environmental changes. The cardiomyocyte gel network robot transmits electrically excited potential and mechanical stretch-induced contractions as information carried on the gel network. The cardiomyocyte gel network robot was fabricated from a mixture of primary cardiomyocytes and collagen gel and molded in a PDMS casting mold, which could produce serial, parallel lattice, or radial pattern networks. Fluorescent calcium imaging showed that the calcium activity of the cardiomyocytes in the gel network was segmented in small domains in the gel network; however, the local contraction that started on one branch of the gel network was propagated to a neighboring branch, and the propagation velocity was increased with increasing concentration of adrenaline. This increase was limited to ~20 mm/s. This proposed mechano-informatics kineticism will provide not only mechano-informatics for cardiomyocyte powered wet robotics but will also help show how cardiac disease occurs in activity propagation systems.

Deformation associated with ghost craters and basins in volcanic smooth plains on Mercury: Strain analysis and implications for plains evolution

Since its insertion into orbit about Mercury in March 2011, the MESSENGER spacecraft has imaged most previously unseen regions of the planet in unprecedented detail, revealing extensive regions of contiguous smooth plains at high northern latitudes and surrounding the Caloris basin. These smooth plains, thought to be emplaced by flood volcanism, are populated with several hundred ghost craters and basins, nearly to completely buried impact features having rims for which the surface expressions are now primarily rings of deformational landforms. Associated with some ghost craters are interior groups of graben displaying mostly polygonal patterns. The origin of these graben is not yet fully understood, but comparison with numerical models suggests that the majority of such features are the result of stresses from local thermal contraction. In this paper, we highlight a previously unreported category of ghost craters, quantify extensional strains across graben‐bearing ghost craters, and make use of graben geometries to gain insights into the subsurface geology of smooth plains areas. In particular, the style and mechanisms of graben development imply that flooding of impact craters and basins led to substantial pooling of lavas, to thicknesses of ∼1.5 km. In addition, surface strains derived from groups of graben are generally in agreement with theoretically and numerically derived strains for thermal contraction.

Numerical study of spontaneous ignition in pressurized hydrogen release through a length of tube with local contraction

Numerical investigations have been conducted on the effect of the internal geometry of a local contraction on the spontaneous ignition of pressurized hydrogen release through a length of tube using a 5th-order WENO scheme. A mixture-averaged multi-component approach was used for accurate calculation of molecular transport. The auto-ignition and combustion chemistry were accounted for using a 21-step kinetic scheme. It is found that a local contraction can significantly facilitate the occurrence of spontaneous ignition by producing elevated flammable mixture and enhancing turbulent mixing from shock formation, reflection and interaction. The first ignition kernel is observed upstream the contraction. It then quickly propagates along the contact interface and transits to a partially premixed flame due to the enhanced turbulent mixing. The partially premixed flames are highly distorted and overlapped with each other. Flame thickening is observed, which is due to the merge of thin flames. The numerical predictions suggested that sustained flames could develop for release pressure as low as 25 bar. For the release pressure of 18 bar, spontaneous ignition was predicted but the flame was soon quenched. To some extent this finding is consistent with Dryer et al.'s experimental observation in that the minimum release pressure required to induce a spontaneous ignition for the release through a tube with internal geometries is only 20.4 bar.

A Kinematic Approach for Efficient and Robust Simulation of the Cardiac Beating Motion

Computer simulation techniques for cardiac beating motions potentially have many applications and a broad audience. However, most existing methods require enormous computational costs and often show unstable behavior for extreme parameter sets, which interrupts smooth simulation study and make it difficult to apply them to interactive applications. To address this issue, we present an efficient and robust framework for simulating the cardiac beating motion. The global cardiac motion is generated by the accumulation of local myocardial fiber contractions. We compute such local-to-global deformations using a kinematic approach; we divide a heart mesh model into overlapping local regions, contract them independently according to fiber orientation, and compute a global shape that satisfies contracted shapes of all local regions as much as possible. A comparison between our method and a physics-based method showed that our method can generate motion very close to that of a physics-based simulation. Our kinematic method has high controllability; the simulated ventricle-wall-contraction speed can be easily adjusted to that of a real heart by controlling local contraction timing. We demonstrate that our method achieves a highly realistic beating motion of a whole heart in real time on a consumer-level computer. Our method provides an important step to bridge a gap between cardiac simulations and interactive applications.

Analysis of spontaneous and nerve-evoked calcium transients in intact extraocular muscles in vitro

Extraocular muscles (EOMs) have unique calcium handling properties, yet little is known about the dynamics of calcium events underlying ultrafast and tonic contractions in myofibers of intact EOMs. Superior oblique EOMs of juvenile chickens were dissected with their nerve attached, maintained in oxygenated Krebs buffer, and loaded with fluo-4. Spontaneous and nerve stimulation-evoked calcium transients were recorded and, following calcium imaging, some EOMs were double-labeled with rhodamine-conjugated alpha-bungarotoxin (rhBTX) to identify EOM myofiber types. EOMs showed two main types of spontaneous calcium transients, one slow type (calcium waves with 1/2max duration of 2–12s, velocity of 25–50μm/s) and two fast “flash-like” types (Type 1, 30–90ms; Type 2, 90–150ms 1/2max duration). Single pulse nerve stimulation evoked fast calcium transients identical to the fast (Type 1) calcium transients. Calcium waves were accompanied by a local myofiber contraction that followed the calcium transient wavefront. The magnitude of calcium-wave induced myofiber contraction far exceeded those of movement induced by nerve stimulation and associated fast calcium transients. Tetrodotoxin eliminated nerve-evoked transients, but not spontaneous transients. Alpha-bungarotoxin eliminated both spontaneous and nerve-evoked fast calcium transients, but not calcium waves, and caffeine increased wave activity. Calcium waves were observed in myofibers lacking spontaneous or evoked fast transients, suggestive of multiply-innervated myofibers, and this was confirmed by double-labeling with rhBTX. We propose that the abundant spontaneous calcium transients and calcium waves with localized contractions that do not depend on innervation may contribute to intrinsic generation of tonic functions of EOMs.

Mesoscopic superelasticity, superplasticity, and superrigidity

Atomic-undercoordination-induced local bond contraction, bond strength gain, and the associated temperature (T)-dependent atomic-cohesive-energy and binding-energy-density are shown to originate intrinsically the exotic paradox of superplasticity, superelasticity, and superrigidity demonstrated by solid sizing from monatomic chain to mesoscopic grain. The paradox follows these relationships: $$\left. \begin{gathered} \varepsilon (K,T) \hfill \\ y(K,T) \hfill \\ \sigma (K,T) \hfill \\ \end{gathered} \right\} \propto \left\{ \begin{gathered} \exp \left( {{B \mathord{\left/ {\vphantom {B {\Delta T}}} \right. \kern-\nulldelimiterspace} {\Delta T}}_{mk} } \right), (Plastic strain) \hfill \\ \left( {\eta _1 \Delta T_{mk} } \right)d^{ - 3} , (Elastic modulus) \hfill \\ \left[ {1 + AK^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \exp \left( {{{\Delta T_{mk} } \mathord{\left/ {\vphantom {{\Delta T_{mk} } T}} \right. \kern-\nulldelimiterspace} T}} \right)} \right]\Delta T_{mk} d^{ - 3} , (Yield stress, IHPR) \hfill \\ \end{gathered} \right. $$ where A, B, η 1, d and ΔT mk = T m (K)−T are size (K)-dependent physical parameters. T m(K) is the melting point. Mechanical work hardening during compressing and self-heating during stretching modulate the measured outcome extrinsically. Superplasticity dominates in the solid-quasimolten-liquid transition state. The competition between the accumulation and annihilation of dislocations activates the inverse Hall-Petch relationship. Therefore, it is essential for one to discriminate the intrinsic competition between the local bond energy density gain and the atomic cohesive energy loss from the extrinsic factors of pressure and temperature in dealing with atomistic mechano-thermo dynamics.

A potential role for differential contractility in early brain development and evolution

Differences in brain structure between species have long fascinated evolutionary biologists. Understanding how these differences arise requires knowing how they are generated in the embryo. Growing evidence in the field of evolutionary developmental biology (evo-devo) suggests that morphological differences between species result largely from changes in the spatiotemporal regulation of gene expression during development. Corresponding changes in functional cellular behaviors (morphogenetic mechanisms) are only beginning to be explored, however. Here we show that spatiotemporal patterns of tissue contractility are sufficient to explain differences in morphology of the early embryonic brain between disparate species. We found that enhancing cytoskeletal contraction in the embryonic chick brain with calyculin A alters the distribution of contractile proteins on the apical side of the neuroepithelium and changes relatively round cross-sections of the tubular brain into shapes resembling triangles, diamonds, and narrow slits. These perturbed shapes, as well as overall brain morphology, are remarkably similar to those of corresponding sections normally found in species such as zebrafish and Xenopus laevis (frog). Tissue staining revealed relatively strong concentration of F-actin at vertices of hyper-contracted cross-sections, and a finite element model shows that local contraction in these regions can convert circular sections into the observed shapes. Another model suggests that these variations in contractility depend on the initial geometry of the brain tube, as localized contraction may be needed to open the initially closed lumen in normal zebrafish and Xenopus brains, whereas this contractile machinery is not necessary in chick brains, which are already open when first created. We conclude that interspecies differences in cytoskeletal contraction may play a larger role in generating differences in morphology, and at much earlier developmental stages, in the brain than previously appreciated. This study is a step toward uncovering the underlying morphomechanical mechanisms that regulate how neural phenotypic differences arise between species.

Cells test substrate rigidity by local contractions on submicrometer pillars

Cell growth and differentiation are critically dependent upon matrix rigidity, yet many aspects of the cellular rigidity-sensing mechanism are not understood. Here, we analyze matrix forces after initial cell-matrix contact, when early rigidity-sensing events occur, using a series of elastomeric pillar arrays with dimensions extending to the submicron scale (2, 1, and 0.5 μm in diameter covering a range of stiffnesses). We observe that the cellular response is fundamentally different on micron-scale and submicron pillars. On 2-μm diameter pillars, adhesions form at the pillar periphery, forces are directed toward the center of the cell, and a constant maximum force is applied independent of stiffness. On 0.5-μm diameter pillars, adhesions form on the pillar tops, and local contractions between neighboring pillars are observed with a maximum displacement of ∼60 nm, independent of stiffness. Because mutants in rigidity sensing show no detectable displacement on 0.5-μm diameter pillars, there is a correlation between local contractions to 60 nm and rigidity sensing. Localization of myosin between submicron pillars demonstrates that submicron scale myosin filaments can cause these local contractions. Finally, submicron pillars can capture many details of cellular force generation that are missed on larger pillars and more closely mimic continuous surfaces.

A New Method for Cardiac Computed Tomography Regional Function Assessment

Background— Quantitative assessment of regional myocardial function has important diagnostic implications in cardiac disease. Recent advances in CT imaging technology have allowed fine anatomic structures, such as endocardial trabeculae, to be resolved and potentially used as fiducial markers for tracking local wall deformations. We developed a method to detect and track such features on the endocardium to extract a metric that reflects local myocardial contraction. Methods and Results— First-pass CT images and contrast-enhanced cardiovascular magnetic resonance images were acquired in 8 infarcted and 3 healthy pigs. We tracked the left ventricle wall motion by segmenting the blood from myocardium and calculating trajectories of the endocardial features seen on the blood cast. The relative motions of these surface features were used to represent the local contraction of the endocardial surface with a metric we call Stretch Quantifier of Endocardial Engraved Zones (SQUEEZ). The average SQUEEZ value and the rate of change in SQUEEZ were calculated for both infarcted and healthy myocardial regions. SQUEEZ showed a significant difference between infarct and remote regions ( P <0.0001). No significant difference was observed between normal myocardium (noninfarcted hearts) and remote regions ( P =0.8). Conclusions— We present a new quantitative method for measuring regional cardiac function from high-resolution volumetric CT images, which can be acquired during angiography and myocardial perfusion scans. Quantified measures of regional cardiac mechanics in normal and abnormally contracting regions in infarcted hearts were shown to correspond well with noninfarcted and infarcted regions as detected by delayed enhancement cardiovascular magnetic resonance images.

Dependence of Forces and Ahdesion Structures of Primary Myocytes on Substrate Elasticity

Force generation is the main physiological function of primary heart muscle cells (myocytes). To study this experimentally, we cultivated primary myocytes from neonatal rat pups on silicone elastomer substrates of controlled elasticities. Young's moduli ranged from 1 to 500 kPa covering physiological and pathological heart tissue stiffnesses. Fluorescent microbeads embedded in the surface of these substrates served as markers for the displacements caused by spontaneously contracting cells. Forces of isolated cells were extracted from these displacements by the method of traction force microscopy (TFM). Transfection with GFP-α-actinin enabled visualization of cell adhesions simultaneously to TFM. By restricting the force application points chosen for the TFM algorithm to certain adhesion structures their mutual relevance for cellular traction force application was explored. Moreover, total cell forces clearly depended on substrate stiffness. These experiments were complemented by a quantification of myofiber contraction. Here, GFP-α-actinin containing z-bands of separate myofibers were imaged by fluorescence microscopy. Subsequent digital image processing was used to quantify the local contraction of individual fibers on different stiffnesses. In contrast to forces, fiber contraction appeared to depend little on substrate stiffness.

Sequential Estimation of Structural Models With a Fixed Point Constraint

This paper considers the estimation problem of structural models for which empirical restrictions are characterized by a fixed point constraint, such as structural dynamic discrete choice models or models of dynamic games. We analyze a local condition under which the nested pseudo likelihood (NPL) algorithm converges to a consistent estimator, and derive its convergence rate. We find that the NPL algorithm may not necessarily converge to a consistent estimator when the fixed point mapping does not have a local contraction property. To address the issue of divergence, we propose alternative sequential estimation procedures that can converge to a consistent estimator even when the NPL algorithm does not.

A thermodynamic and mechanical model for formation of the Solar System via 3-dimensional collapse of the dusty pre-solar nebula

The fundamental and shared rotational characteristics of the Solar System (nearly circular, co-planar orbits and mostly upright axial spins of the planets) record conditions of origin, yet are not explained by prevailing 2-dimensional disk models. Current planetary spin and orbital rotational energies (R.E.) each nearly equal and linearly depend on gravitational self-potential of formation (Ug), revealing mechanical energy conservation. We derive −ΔUg≅Δ.R.E. and stability criteria from thermodynamic principles, and parlay these relationships into a detailed model of simultaneous accretion of the protoSun and planets from the dust-bearing 3-d pre-solar nebula (PSN). Gravitational heating is insignificant because Ug is negative, the 2nd law of thermodynamics must be fulfilled, and ideal gas conditions pertain to the rarified PSN until the objects were nearly fully formed. Combined conservation of angular momentum and mechanical energy during 3-dimensional collapse of spheroidal dust shells in a contracting nebula provides ΔR.E.≅R.E. for the central body, whereas for formation of orbiting bodies, ΔR.E.≅R.E.f(1−If/Ii), where I is the moment of inertia. Orbital data for the inner planets follow 0.04×R.E.f≅−Ug which confirms conservation of angular momentum. Significant loss of spin, attributed to viscous dissipation during differential rotation, masks the initial spin of the un-ignited protoSun predicted by R.E.=−Ug. Heat production occurs after nearly final sizes are reached via mechanisms such as shear during differential rotation and radioactivity. We focus on the dilute stage, showing that the PSN was compositionally graded due to light molecules diffusing preferentially, providing the observed planetary chemistry, and set limits on PSN mass, density, and temperature. From measured planetary masses and orbital characteristics, accounting for dissipation of spin, we deduce mechanisms and the sequence of converting a 3-d dusty cloud to the present 2-d Solar System, and infer the evolution of dust and gas densities. Duration of events is obtained from the time-dependent virial theorem. As the PSN slowly contracted, collapse of pre-solar dust in spheroidal shells simultaneously formed rocky protoplanets embedded in a dusty debris disk, creating their nearly circular co-planar orbits and upright axial spins with the same sense as orbital rotation, which were then enhanced via subsequent local contraction of nearby nebulae. Because rocky kernels at great distance out-competed the pull of the co-accreting star, gas giants formed in the outer reaches within ∼3Ma as PSN contraction hastened. This pattern repeated to form satellite systems. The PSN imploded, once constricted to within Jupiter’s orbit. Afterwards, disk debris slowly spiraled toward the protoSun, cratering and heating intercepted surfaces. Our conservative 3-d model, which allows for different behaviors of gas and dust, explains key Solar System characteristics (spin, orbits, gas giants and their compositions) and second-order features (dwarf planets, comet mineralogy, satellite system sizes).

Influence of elastic deformations on the supersolid transition

We study within the Ginzburg-Landau (GL) theory of phase transitions how elastic deformations in a supersolid lead to local changes in the supersolid transition temperature. The GL theory is mapped onto a Schr\"odinger-type equation with an effective potential that depends on local dilatory strain. The effective potential is attractive for local contraction and repulsive for local expansion. Different types of elastic deformations are studied. We find that a contraction (expansion) of the medium that may be brought about by either externally applied or internal strain leads to a higher (lower) transition temperature as compared to the unstrained medium. In addition, we investigate edge dislocations and illustrate that the local transition temperature may be increased in the immediate vicinity of the dislocation core. We remark on the effects of shear screening induced by dislocation motion. Our analysis is not limited to supersolidity. Similar strain effects should also play a role in superconductors. Non-uniformly strained superconductors may thus exhibit a similar distribution of smeared local transition temperatures.