An inverse power-law distribution of molecular bond lifetimes predicts fractional derivative viscoelasticity in biological tissue

Self-Assembly of Lipid Molecules under Shear Flows: A Dissipative Particle Dynamics Simulation Study

The self-assembly of lipid molecules in aqueous solution under shear flows was investigated using the dissipative particle dynamics simulation method. Three cases were considered: zero shear flow, weak shear flow and strong shear flow. Various self-assembled structures, such as double layers, perforated double layers, hierarchical discs, micelles, and vesicles, were observed. The self-assembly behavior was investigated in equilibrium by constructing phase diagrams based on chain lengths. Results showed the remarkable influence of chain length, shear flow and solution concentration on the self-assembly process. Furthermore, the self-assembly behavior of lipid molecules was analyzed using the system energy, particle number and shape factor during the dynamic processes, where the self-assembly pathways were observed and analyzed for the typical structures. The results enhance our understanding of biomacromolecule self-assembly in a solution and hold the potential for applications in biomedicine.

Inertial artifact in viscoelastic measurements of striated muscle: Modeling and experimental results

Viscoelastic properties of striated muscle are often measured using length perturbation analysis and quantified as a complex modulus, whose elastic and viscous components reflect the energy-storage and energy-absorbing properties of the tissue, respectively. The energy stored as inertia is commonly ignored due to the small size of samples examined, typically <1 mm. Considering recent advances in tissue engineering to generate muscle tissues of larger sizes, we questioned whether ignoring the inertial artifact was still reasonable in these samples. To answer this question, we derived and solved the one-dimensional wave equation that describes the propagation of strain along the length of a sample. The inertial artifact was predicted to contaminate the elastic modulus with (2πf)2L02ρ/6, where f is perturbation frequency, L0 is muscle length, and ρ is muscle density. We then measured viscoelastic properties up to 500 Hz in mouse skeletal muscle fibers at long (4.8 mm) and short (<1 mm) lengths and up to 100 Hz in rat cardiac slices at long (10-12 mm) and short (<2 mm) lengths. We found the elastic modulus of long preparations was elevated as frequency increased and was about half the magnitude of that predicted by the model. While the prediction tended to overestimate the measured inertial artifact, these results provided some validity to the model. We used the predicted artifact as an overly conservative estimate of error that might arise in a mechanics assay of mammalian striated muscle, whose nominal resting stiffness is on the order 100 kN m-2. We found that muscle lengths of <1 mm resulted in negligible inertial artifact (<0.5% error) for perturbation frequencies under 250 Hz. Muscle samples longer than 5 mm, on the other hand, would result in >5% error at frequencies of 200 Hz and higher.

Enhancing diastolic function by strain-dependent detachment of cardiac myosin crossbridges

The force response of cardiac muscle undergoing a quick stretch is conventionally interpreted to represent stretching of attached myosin crossbridges (phase 1) and detachment of these stretched crossbridges at an exponential rate (phase 2), followed by crossbridges reattaching in increased numbers due to an enhanced activation of the thin filament (phases 3 and 4). We propose that, at least in mammalian cardiac muscle, phase 2 instead represents an enhanced detachment rate of myosin crossbridges due to stretch, phase 3 represents the reattachment of those same crossbridges, and phase 4 is a passive-like viscoelastic response with power-law relaxation. To test this idea, we developed a two-state model of crossbridge attachment and detachment. Unitary force was assigned when a crossbridge was attached, and an elastic force was generated when an attached crossbridge was displaced. Attachment rate, f(x), was spatially distributed with a total magnitude f₀. Detachment rate was modeled as g(x) = g₀+ g₁x, where g₀ is a constant and g₁ indicates sensitivity to displacement. The analytical solution suggested that the exponential decay rate of phase 2 represents (f₀ + g₀) and the exponential rise rate of phase 3 represents g₀. The depth of the nadir between phases 2 and 3 is proportional to g₁. We prepared skinned mouse myocardium and applied a 1% stretch under varying concentrations of inorganic phosphate (Pi). The resulting force responses fitted the analytical solution well. The interpretations of phases 2 and 3 were consistent with lower f₀ and higher g₀ with increasing Pi. This novel scheme of interpreting the force response to a quick stretch does not require enhanced thin-filament activation and suggests that the myosin detachment rate is sensitive to stretch. Furthermore, the enhanced detachment rate is likely not due to the typical detachment mechanism following MgATP binding, but rather before MgADP release, and may involve reversal of the myosin power stroke.

Myosin cross-bridge kinetics slow at longer muscle lengths during isometric contractions in intact soleus from mice

Muscle contraction results from force-generating cross-bridge interactions between myosin and actin. Cross-bridge cycling kinetics underlie fundamental contractile properties, such as active force production and energy utilization. Factors that influence cross-bridge kinetics at the molecular level propagate through the sarcomeres, cells and tissue to modulate whole-muscle function. Conversely, movement and changes in the muscle length can influence cross-bridge kinetics on the molecular level. Reduced, single-molecule and single-fibre experiments have shown that increasing the strain on cross-bridges may slow their cycling rate and prolong their attachment duration. However, whether these strain-dependent cycling mechanisms persist in the intact muscle tissue, which encompasses more complex organization and passive elements, remains unclear. To investigate this multi-scale relationship, we adapted traditional step-stretch protocols for use with mouse soleus muscle during isometric tetanic contractions, enabling novel estimates of length-dependent cross-bridge kinetics in the intact skeletal muscle. Compared to rates at the optimal muscle length (L_o), we found that cross-bridge detachment rates increased by approximately 20% at 90% of L_o (shorter) and decreased by approximately 20% at 110% of L_o (longer). These data indicate that cross-bridge kinetics vary with whole-muscle length during intact, isometric contraction, which could intrinsically modulate force generation and energetics, and suggests a multi-scale feedback pathway between whole-muscle function and cross-bridge activity.

Omecamtiv Mecarbil Slows Myosin Kinetics in Skinned Rat Myocardium at Physiological Temperature

Heart failure is a life-threatening condition that occurs when the heart muscle becomes weakened and cannot adequately circulate blood and nutrients around the body. Omecamtiv mecarbil (OM) is a compound that has been developed to treat systolic heart failure via targeting the cardiac myosin heavy chain to increase myocardial contractility. Biophysical and biochemical studies have found that OM increases calcium (Ca²⁺) sensitivity of contraction by prolonging the myosin working stroke and increasing the actin-myosin cross-bridge duty ratio. Most in vitro studies probing the effects of OM on cross-bridge kinetics and muscle force production have been conducted at subphysiological temperature, even though temperature plays a critical role in enzyme activity and cross-bridge function. Herein, we used skinned, ventricular papillary muscle strips from rats to investigate the effects of [OM] on Ca²⁺-activated force production, cross-bridge kinetics, and myocardial viscoelasticity at physiological temperature (37°C). We find that OM only increases myocardial contractility at submaximal Ca²⁺ activation levels and not maximal Ca²⁺ activation levels. As [OM] increased, the kinetic rate constants for cross-bridge recruitment and detachment slowed for both submaximal and maximal Ca²⁺-activated conditions. These findings support a mechanism by which OM increases cardiac contractility at physiological temperature via increasing cross-bridge contributions to thin-filament activation as cross-bridge kinetics slow and the duration of cross-bridge attachment increases. Thus, force only increases at submaximal Ca²⁺ activation due to cooperative recruitment of neighboring cross-bridges, because thin-filament activation is not already saturated. In contrast, OM does not increase myocardial force production for maximal Ca²⁺-activated conditions at physiological temperature because cooperative activation of thin filaments may already be saturated.

Fibronectin fiber creep under constant force loading

Viscoelasticity is a fundamental property of virtually all biological materials, and proteinaceous, fibrous materials that constitute the extracellular matrix (ECM) are no exception. Viscoelasticity may be particularly important in the ECM since cells can apply mechanical stress resulting from cell contractility over very long periods of time. However, measurements of ECM fiber response to long-term constant force loading are scarce, despite the increasing recognition that mechanical strain regulates the biological function of some ECM fibers. We developed a dual micropipette system that applies constant force to single fibers for up to 8 h. We utilized this system to study the time dependent response of fibronectin (Fn) fibers to constant force, as Fn fibers exhibit tremendous extensibility before mechanical failure as well as strain dependent alterations in biological properties. These data demonstrate the Fn fibers continue to stretch under constant force loading for at least 8 h and that this long-term creep results in plastic deformation of Fn fibers, in contrast to elastic deformation of Fn fibers under short-term, but fast loading rate extension. These data demonstrate that physiologically-relevant loading may impart mechanical features to Fn fibers by switching them into an extended state that may have altered biological functions. STATEMENT OF SIGNIFICANCE: Measurements of extracellular matrix (ECM) fiber response to constant force loading are scarce, so we developed a novel technique for applying constant force to single ECM fibers. We used this technique to measure constant force creep of fibronectin fibers since these fibers have been shown to be mechanotransducers whose functions can be altered by mechanical strain. We found that fibronectin fibers creep under constant force loading for the duration of the experiment and that this creep behavior resembles a power law. Furthermore, we found that constant force creep results in plastic deformation of the fibers, which suggests that the mechanobiological switching of fibronectin can only occur once after long-term loading.

Active Viscoelasticity of Sarcomeres

The perturbation response of muscle is important for the versatile, stable and agile control capabilities of animals. Muscle resists being stretched by developing forces in the passive tissues and in the active crossbridges. This review focuses on the active perturbation response of the sarcomere. The active response exhibits typical stress relaxation, and thus approximated by a Maxwell material that has a spring and dashpot arranged in series. The ratio of damping to stiffness in this approximation defines the relaxation timescale for dissipating stresses that are developed in the crossbridges due to external perturbations. Current understanding of sarcomeres suggests that stiffness varies nearly linearly with neural excitation, but not much is known about damping. But if both stiffness and damping have the same functional (linear or not) dependence on neural excitation, then the stress relaxation timescale cannot be varied depending on the demands of the task. This implies an unavoidable and biologically unrealistic trade-off between how freely the crossbridges can yield and dissipate stresses when stretched (injury avoidance in agile motions) vs. how long they can maintain perturbation-induced stresses and behave like a solid material (stiffness maintenance for stability). We hypothesize that muscle circumvents this trade-off by varying damping in a nonlinear manner with neural excitation, unlike stiffness that varies linearly. Testing this hypothesis requires new experimental and mathematical characterization of muscle mechanics, and also identifies new design goals for robotic actuators.

Dependence of Tensional Homeostasis on Cell Type and on Cell-Cell Interactions

INTRODUCTION

The ability to maintain a homeostatic level of cell tension is essential for many physiological processes. Our group has recently reported that multicellularity is required for tensional homeostasis in endothelial cells. However, other studies have shown that isolated fibroblasts also maintain constant tension over short time scales without the need of cell-cell contacts. Therefore, in this study, our aim was to determine how different cell types regulate tension as isolated cells or in small clustered groupings and to investigate the role of cell-cell adhesion molecules, such as E-cadherin, in this system.

METHODS

Micropattern traction force microscopy was used to determine how bovine aortic endothelial cells, bovine vascular smooth muscle cells, mouse embryonic fibroblasts, and human gastric adenocarcinoma cells, with or without cell-cell interactions due to E-cadherin, maintain tensional homeostasis over time. Tension temporal fluctuations in single cells and cell clusters were evaluated.

RESULTS

We found that only endothelial cells require clustering for tensional homeostasis. The same was not verified in fibroblasts or vascular smooth muscle cells. Of relevance, in adenocarcinoma cells, we verified that tensional homeostasis was dependent on the competence of the adhesion molecule E-cadherin at both the single cells and multicellular levels.

CONCLUSION

These findings indicate that cell-cell contacts may be critical for tensional homeostasis and, potentially, for barrier function of the endothelium. Furthermore, the cell-cell adhesion molecule E-cadherin is an important regulator of tensional homeostasis, even in the absence of cadherin engagement with neighboring cells, which demonstrates its relevance not only as a structural molecule but also as a signaling moiety.

Assessing composition and structure of soft biphasic media from Kelvin-Voigt fractional derivative model parameters

Kelvin-Voigt fractional derivative (KVFD) model parameters have been used to describe viscoelastic properties of soft tissues. However, translating model parameters into a concise set of intrinsic mechanical properties related to tissue composition and structure remains challenging. This paper begins by exploring these relationships using a biphasic emulsion materials with known composition. Mechanical properties are measured by analyzing data from two indentation techniques - ramp-stress relaxation and load-unload hysteresis tests. Material composition is predictably correlated with viscoelastic model parameters. Model parameters estimated from the tests reveal that elastic modulus E₀ closely approximates the shear modulus for pure gelatin. Fractional-order parameter α and time constant τ vary monotonically with the volume fraction of the material's fluid component. α characterizes medium fluidity and the rate of energy dissipation, and τ is a viscous time constant. Numerical simulations suggest that the viscous coefficient η is proportional to the energy lost during quasi-static force-displacement cycles, E_A . The slope of E_A versus η is determined by α and the applied indentation ramp time T_r. Experimental measurements from phantom and ex vivo liver data show close agreement with theoretical predictions of the η - E_A relation. The relative error is less than 20% for emulsions 22% for liver. We find that KVFD model parameters form a concise features space for biphasic medium characterization that described time-varying mechanical properties.

Myosin MgADP release rate decreases at longer sarcomere length to prolong myosin attachment time in skinned rat myocardium

Cardiac contractility increases as sarcomere length increases, suggesting that intrinsic molecular mechanisms underlie the Frank-Starling relationship to confer increased cardiac output with greater ventricular filling. The capacity of myosin to bind with actin and generate force in a muscle cell is Ca(2+) regulated by thin-filament proteins and spatially regulated by sarcomere length as thick-to-thin filament overlap varies. One mechanism underlying greater cardiac contractility as sarcomere length increases could involve longer myosin attachment time (ton) due to slowed myosin kinetics at longer sarcomere length. To test this idea, we used stochastic length-perturbation analysis in skinned rat papillary muscle strips to measure ton as [MgATP] varied (0.05-5 mM) at 1.9 and 2.2 μm sarcomere lengths. From this ton-MgATP relationship, we calculated cross-bridge MgADP release rate and MgATP binding rates. As MgATP increased, ton decreased for both sarcomere lengths, but ton was roughly 70% longer for 2.2 vs. 1.9 μm sarcomere length at maximally activated conditions. These ton differences were driven by a slower MgADP release rate at 2.2 μm sarcomere length (41 ± 3 vs. 74 ± 7 s(-1)), since MgATP binding rate was not different between the two sarcomere lengths. At submaximal activation levels near the pCa50 value of the tension-pCa relationship for each sarcomere length, length-dependent increases in ton were roughly 15% longer for 2.2 vs. 1.9 μm sarcomere length. These changes in cross-bridge kinetics could amplify cooperative cross-bridge contributions to force production and thin-filament activation at longer sarcomere length and suggest that length-dependent changes in myosin MgADP release rate may contribute to the Frank-Starling relationship in the heart.

Molecular determinants of force production in human skeletal muscle fibers: effects of myosin isoform expression and cross-sectional area

Skeletal muscle contractile performance is governed by the properties of its constituent fibers, which are, in turn, determined by the molecular interactions of the myofilament proteins. To define the molecular determinants of contractile function in humans, we measured myofilament mechanics during maximal Ca(2+)-activated and passive isometric conditions in single muscle fibers with homogenous (I and IIA) and mixed (I/IIA and IIA/X) myosin heavy chain (MHC) isoforms from healthy, young adult male (n = 5) and female (n = 7) volunteers. Fibers containing only MHC II isoforms (IIA and IIA/X) produced higher maximal Ca(2+)-activated forces over the range of cross-sectional areas (CSAs) examined than MHC I fibers, resulting in higher (24-42%) specific forces. The number and/or stiffness of the strongly bound myosin-actin cross bridges increased in the higher force-producing MHC II isoforms and, in all isoforms, better predicted force than CSA. In men and women, cross-bridge kinetics, in terms of myosin attachment time and rate of myosin force production, were independent of CSA, although women had faster (7-15%) kinetics. The relative proportion of cross bridges and/or their stiffness was reduced as fiber size increased, causing a decline in specific force. Results from our examination of molecular mechanisms across the range of physiological CSAs explain the variation in specific force among the different fiber types in human skeletal muscle, which may have relevance to understanding how various physiological and pathophysiological conditions modulate single-fiber and whole muscle contractility.