Physically-based structural modeling of a typical regenerative tissue analog bridges material macroscale continuum and cellular microscale discreteness and elucidates the hierarchical characteristics of cell-matrix interaction.

This paper presents a comprehensive physically-based structural modelling for the passive and active biomechanical processes in a typical engineered tissue - namely, cell-compacted collagen gel. First, it introduces a sinusoidal curve analog for quantifying the mechanical response of the collagen fibrils and a probability distribution function of the characteristic crimp ratio for taking into account the fibrillar geometric entropic effect. The constitutive framework based on these structural characteristics precisely reproduces the nonlinearity, the viscoelasticity, and fairly captures the Poisson effect exhibiting in the macroscale tensile tests; which, therefore, substantially validates the structural modelling for the analysis of the cell-gel interaction during collagen gel compaction. Second, a deterministic molecular clutch model specific to the interaction between the cell pseudopodium and the collagen network is developed, which emphasizes the dependence of traction force on clutch number altering with the retrograde flow velocity, actin polymeric velocity, and the deformation of the stretched fibril. The modelling reveals the hierarchical features of cellular substrate sensing, i.e. a biphasic traction force response to substrate elasticity begins at the level of individual fibrils and develops into the second biphasic sensing by means of the fibrillar number integration at the whole-cell level. Singular in crossing the realms of continuum and discrete mechanics, the methodologies developed in this study for modelling the filamentous materials and cell-fibril interaction deliver deep insight into the temporospatially dynamic 3D cell-matrix interaction, and are able to bridge the cellular microscale and material macroscale in the exploration of related topics in mechanobiology.

Stress relaxation and stress-strain characteristics of porcine amniotic membrane.

BACKGROUND: Recently, amniotic membrane (AM) as scaffold is accumulating much more attention in tissue engineering. It is well-known that the mechanical properties of the scaffold inevitably affect the biological process of the incorporated cells. OBJECTIVE: This study investigates the stress relaxation and stress-strain characteristics of AM, which have not been sufficiently elucidated before. METHODS: Porcine AM samples were prepared at four different AM regions and at three different directions. Ramp-and-hold and stretch-to-rupture tests were conducted on a uniaxial tensile apparatus. A nonlinear viscoelastic model with two relaxation coefficients is proposed to fit the ramp-and-hold data. Rupture strain, rupture stress, and elastic modulus of the linear portion of the stress-strain curve are used to characterize the strength properties of the AM. RESULTS: Sample direction has no significant effect on the mechanical properties of the AM. Samples at the ventral region has the maximum rupture strength and elastic modulus, respectively, 2.29±0.99MPa and 6.26±2.69MPa. The average of the relaxation coefficient for the fast and slow relaxation phases are 12.8±4.4s and 37.0±7.7s, respectively. CONCLUSIONS: AM is a mechanically isotropic and heterogeneous material. The nonlinear viscoelastic model is suitable to model the AM viscoelasticity and potential for other biological tissues.

A fibril-based structural constitutive theory reveals the dominant role of network characteristics on the mechanical behavior of fibroblast-compacted collagen gels.

In this paper, we present a general, fibril-based structural constitutive theory which accounts for three material aspects of crosslinked filamentous materials: the single fibrillar force response, the fibrillar network model, and the effects of alterations to the fibrillar network. In the case of the single fibrillar response, we develop a formula that covers the entropic and enthalpic deformation regions, and introduce the relaxation phase to explain the observed force decay after crosslink breakage. For the filamentous network model, we characterize the constituent element of the fibrillar network in terms its end-to-end distance vector and its contour length, then decompose the vector orientation into an isotropic random term and a specific alignment, paving the way for an expanded formalism from principal deformation to general 3D deformation; and, more important, we define a critical core quantity over which macroscale mechanical characteristics can be integrated: the ratio of the initial end-to-end distance to the contour length (and its probability function). For network alterations, we quantitatively treat changes in constituent elements and relate these changes to the alteration of network characteristics. Singular in its physical rigor and clarity, this constitutive theory can reproduce and predict a wide range of nonlinear mechanical behavior in materials composed of a crosslinked filamentous network, including: stress relaxation (with dual relaxation coefficients as typically observed in soft tissues); hysteresis with decreasing maximum stress under serial cyclic loading; strain-stiffening under uniaxial tension; the rupture point of the structure as a whole; various effects of biaxial tensile loading; strain-stiffening under simple shearing; the so-called "negative normal stress" phenomenon; and enthalpic elastic behaviors of the constituent element. Applied to compacted collagen gels, the theory demonstrates that collagen fibrils behave as enthalpic elasticas with linear elasticity within the gels, and that the macroscale nonlinearity of the gels originates from the curved fibrillar network. Meanwhile, the underlying factors that determine the mechanical properties of the gels are clarified. Finally, the implications of this study on the enhancement of the mechanical properties of compacted collagen gels and on the cellular mechanics with this model tissue are discussed.

The mechanisms of fibroblast-mediated compaction of collagen gels and the mechanical niche around individual fibroblasts.

Fibroblast-mediated compaction of collagen gels attracts extensive attention in studies of wound healing, cellular fate processes, and regenerative medicine. However, the underlying mechanism and the cellular mechanical niche still remain obscure. This study examines the mechanical behaviour of collagen fibrils during the process of compaction from an alternative perspective on the primary mechanical interaction, providing a new viewpoint on the behaviour of populated fibroblasts. We classify the collagen fibrils into three types - bent, stretched, and adherent - and deduce the respective equations governing the mechanical behaviour of each type; in particular, from a putative principle based on the stationary state of the instantaneous Hamiltonian of the mechanotransduction system, we originally quantify the stretching force exerted on each stretched fibrils. Via careful verification of a structural elementary model based on this classification, we demonstrate a clear physical picture of the compaction process, quantitatively elucidate the panorama of the micro mechanical niche and reveal an intrinsic biphasic relationship between cellular traction force and matrix elasticity. Our results also infer the underlying mechanism of tensional homoeostasis and stress shielding of fibroblasts. With this study, and sequel investigations on the putative principle proposed herein, we anticipate a refocus of the research on cellular mechanobiology, in vitro and in vivo.

Expression of microRNA-1, microRNA-133a and Hand2 protein in cultured embryonic rat cardiomyocytes.

In this study, we investigated the expression of the pathway, SRF-microRNA-1/microRNA-133a-Hand2, in the Wistar rat embryonic ventricular cardiomyocytes under conventional monolayer culture. The morphological observation of the cultured cardiomyocytes and the mRNA expression levels of three vital constituent proteins, MLC-2v, N-cadherin, and connexin43, demonstrated the immaturity of these cultured cells, which was featured by less myofibril density, immature sarcomeric structure, and significantly lower mRNA expression of the three constituent proteins than those in neonatal ventricular samples. More importantly, results in this study suggest that the change of SRF-microRNA-1/microRNA-133a-Hand2 pathway results into the attenuation of the Hand2 repression in cultured cardiomyocytes. These outcomes are valuable to understand the cellular state as embryonic cardiomyocytes to be in vitro model and might be useful for the assessment of engineered cardiac tissue and cardiac differentiation of stem cells.

Viscoelastic characteristics of contracted collagen gels populated with rat fibroblasts or cardiomyocytes.

The viscoelastic characteristics of contracted collagen gels populated with rat fibroblasts or cardiomyocytes were investigated by uniaxial tensile testing. Rat type I collagen-Dulbecco's modified Eagle's medium solution (each 2 ml in volume, 0.5 mg/ml collagen concentration) containing 2.0 million rat fibroblasts or cardiomyocytes were cast in a circular shape. After gelation and culture for 10 days the contracted gels were first stretched to a tensile strain of approximately 0.20 at 4.6 × 10(-3)/s strain rate, and then the strain was kept unchanged for 3 min. The tensile stress in the gels was recorded. The results were regressed against the equations of the Kelvin viscoelastic model. It was found that the two elastic coefficients in the model were 6.5 ± 1.7 and 10.2 ± 3.2 kPa, respectively, for gels with cardiomyocytes and 5.1 ± 1.6 and 4.5 ± 0.9 kPa for those with fibroblasts; the values for gels with cardiomyocytes were significantly higher than those for gels with fibroblasts. The viscous coefficient was 169.6 ± 60.7 kPa s for the cardiomyocytes and 143.6 ± 44.7 kPa s for the fibroblasts. The relaxation time constant for gels with cardiomyocytes was 19.6 ± 10.6 s, significantly smaller than for gels with fibroblasts (36.4 ± 13.3 s). This study is the first to obtain viscoelastic data for living cell-contracted collagen gels. These data show that the viscous effect has a vital effect on the mechanical behavior of the gels and cannot be neglected in the culture and function of artificial substitutes based on contracted collagen gels. Furthermore, the data may imply that viscous coefficient of the gels might be closely related to collagen density rather than to cross linking among collagen fibrils.

Mechanics of curved plasma membrane vesicles: resting shapes, membrane curvature, and in-plane shear elasticity.

Highly curved cell membrane structures, such as plasmalemmal vesicles (caveolae) and clathrin-coated pits, facilitate many cell functions, including the clustering of membrane receptors and transport of specific extracellular macromolecules by endothelial cells. These structures are subject to large mechanical deformations when the plasma membrane is stretched and subject to a change of its curvature. To enhance our understanding of plasmalemmal vesicles we need to improve the understanding of the mechanics in regions of high membrane curvatures. We examine here, theoretically, the shapes of plasmalemmal vesicles assuming that they consist of three membrane domains: an inner domain with high curvature, an outer domain with moderate curvature, and an outermost flat domain, all in the unstressed state. We assume the membrane properties are the same in these domains with membrane bending elasticity as well as in-plane shear elasticity. Special emphasis is placed on the effects of membrane curvature and in-plane shear elasticity on the mechanics of vesicle during unfolding by application of membrane tension. The vesicle shapes were computed by minimization of bending and in-plane shear strain energy. Mechanically stable vesicles were identified with characteristic membrane necks. Upon stretch of the membrane, the vesicle necks disappeared relatively abruptly leading to membrane shapes that consist of curved indentations. While the resting shape of vesicles is predominantly affected by the membrane spontaneous curvatures, the membrane shear elasticity (for a range of values recorded in the red cell membrane) makes a significant contribution as the vesicle is subject to stretch and unfolding. The membrane tension required to unfold the vesicle is sensitive with respect to its shape, especially as the vesicle becomes fully unfolded and approaches a relative flat shape.