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Matrix viscoplasticity and its shielding by active mechanics in microtissue models: experiments and mathematical modeling

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ABSTRACT

The biomechanical behavior of tissues under mechanical stimulation is critically important to physiological function. We report a combined experimental and modeling study of bioengineered 3D smooth muscle microtissues that reveals a previously unappreciated interaction between active cell mechanics and the viscoplastic properties of the extracellular matrix. The microtissues’ response to stretch/unstretch actuations, as probed by microcantilever force sensors, was dominated by cellular actomyosin dynamics. However, cell lysis revealed a viscoplastic response of the underlying model collagen/fibrin matrix. A model coupling Hill-type actomyosin dynamics with a plastic perfectly viscoplastic description of the matrix quantitatively accounts for the microtissue dynamics, including notably the cells’ shielding of the matrix plasticity. Stretch measurements of single cells confirmed the active cell dynamics, and were well described by a single-cell version of our model. These results reveal the need for new focus on matrix plasticity and its interactions with active cell mechanics in describing tissue dynamics.

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Model for the mechanical response of a microtissue.A microtissue is shown schematically at top, and the model is shown below. The model includes a passive elastic element Es (blue) that accounts for internal cell stiffness (black), and cell-cell contact stiffness and aligned regions of ECM between cells (dashed blue). Es is in series with an active cellular contractile element (red) that obeys a Hill-like stress vs. strain-rate relation, with constant maximum active contractile stress  and active viscosity ηa. Passive model elements (green) act in parallel to the active elements and represent the behavior of the majority of the ECM, which is under compression in the native state (green dashed lines), and include stiffness Ep and a viscoplastic element with tensile and compressive yield stresses  and , and plastic viscosity ηp. σ and ε denote the total stress and strain of the microtissue, and the subscripts a, s, and, p delineate the stresses and strains of the active, series, and parallel elements, respectively. The quantities indicated in brackets are the material parameters of the model.
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f3: Model for the mechanical response of a microtissue.A microtissue is shown schematically at top, and the model is shown below. The model includes a passive elastic element Es (blue) that accounts for internal cell stiffness (black), and cell-cell contact stiffness and aligned regions of ECM between cells (dashed blue). Es is in series with an active cellular contractile element (red) that obeys a Hill-like stress vs. strain-rate relation, with constant maximum active contractile stress and active viscosity ηa. Passive model elements (green) act in parallel to the active elements and represent the behavior of the majority of the ECM, which is under compression in the native state (green dashed lines), and include stiffness Ep and a viscoplastic element with tensile and compressive yield stresses and , and plastic viscosity ηp. σ and ε denote the total stress and strain of the microtissue, and the subscripts a, s, and, p delineate the stresses and strains of the active, series, and parallel elements, respectively. The quantities indicated in brackets are the material parameters of the model.

Mentions: To describe the observed behavior and to determine quantitatively the material parameters of our constructs, we developed a three-element model for the biomechanical response to applied force, and used it to fit the data from our tissue and single cell experiments. This model, shown in Fig. 3, builds upon our previous work on active mechanics17, but adds additional features to account for the potential effects of ECM plasticity. Our model includes an active contractile element to describe the force generation of the cellular actomyosin system, and a passive elastic element in series with the active element to model the stiffness of the cellular actin filaments and cell-cell contacts, and the stiffness of ECM regions between the cells, which may be aligned and under tension18. In parallel with these is an elastic viscoplastic element that models the majority of the ECM, which is compressed as the microtissues form. (The elastic component of this element also accounts for any cellular components that act in parallel to the cellular active element). The reference configuration of the microtissue is after contractile stress activation and the corresponding compaction of the ECM, but before the application of magnetic force. (Compaction is defined as the state where the ECM has yielded under compressive stress). All the elements’ stresses and strains are variables under uniaxial loading. The total strain of the microtissue ε is decomposed into active contractile and passive series components, εa and εs. Further, since the viscoplastic element deforms in parallel with the cells, its strain εp is equal to the total strain, and thus


Matrix viscoplasticity and its shielding by active mechanics in microtissue models: experiments and mathematical modeling
Model for the mechanical response of a microtissue.A microtissue is shown schematically at top, and the model is shown below. The model includes a passive elastic element Es (blue) that accounts for internal cell stiffness (black), and cell-cell contact stiffness and aligned regions of ECM between cells (dashed blue). Es is in series with an active cellular contractile element (red) that obeys a Hill-like stress vs. strain-rate relation, with constant maximum active contractile stress  and active viscosity ηa. Passive model elements (green) act in parallel to the active elements and represent the behavior of the majority of the ECM, which is under compression in the native state (green dashed lines), and include stiffness Ep and a viscoplastic element with tensile and compressive yield stresses  and , and plastic viscosity ηp. σ and ε denote the total stress and strain of the microtissue, and the subscripts a, s, and, p delineate the stresses and strains of the active, series, and parallel elements, respectively. The quantities indicated in brackets are the material parameters of the model.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037370&req=5

f3: Model for the mechanical response of a microtissue.A microtissue is shown schematically at top, and the model is shown below. The model includes a passive elastic element Es (blue) that accounts for internal cell stiffness (black), and cell-cell contact stiffness and aligned regions of ECM between cells (dashed blue). Es is in series with an active cellular contractile element (red) that obeys a Hill-like stress vs. strain-rate relation, with constant maximum active contractile stress and active viscosity ηa. Passive model elements (green) act in parallel to the active elements and represent the behavior of the majority of the ECM, which is under compression in the native state (green dashed lines), and include stiffness Ep and a viscoplastic element with tensile and compressive yield stresses and , and plastic viscosity ηp. σ and ε denote the total stress and strain of the microtissue, and the subscripts a, s, and, p delineate the stresses and strains of the active, series, and parallel elements, respectively. The quantities indicated in brackets are the material parameters of the model.
Mentions: To describe the observed behavior and to determine quantitatively the material parameters of our constructs, we developed a three-element model for the biomechanical response to applied force, and used it to fit the data from our tissue and single cell experiments. This model, shown in Fig. 3, builds upon our previous work on active mechanics17, but adds additional features to account for the potential effects of ECM plasticity. Our model includes an active contractile element to describe the force generation of the cellular actomyosin system, and a passive elastic element in series with the active element to model the stiffness of the cellular actin filaments and cell-cell contacts, and the stiffness of ECM regions between the cells, which may be aligned and under tension18. In parallel with these is an elastic viscoplastic element that models the majority of the ECM, which is compressed as the microtissues form. (The elastic component of this element also accounts for any cellular components that act in parallel to the cellular active element). The reference configuration of the microtissue is after contractile stress activation and the corresponding compaction of the ECM, but before the application of magnetic force. (Compaction is defined as the state where the ECM has yielded under compressive stress). All the elements’ stresses and strains are variables under uniaxial loading. The total strain of the microtissue ε is decomposed into active contractile and passive series components, εa and εs. Further, since the viscoplastic element deforms in parallel with the cells, its strain εp is equal to the total strain, and thus

View Article: PubMed Central - PubMed

ABSTRACT

The biomechanical behavior of tissues under mechanical stimulation is critically important to physiological function. We report a combined experimental and modeling study of bioengineered 3D smooth muscle microtissues that reveals a previously unappreciated interaction between active cell mechanics and the viscoplastic properties of the extracellular matrix. The microtissues’ response to stretch/unstretch actuations, as probed by microcantilever force sensors, was dominated by cellular actomyosin dynamics. However, cell lysis revealed a viscoplastic response of the underlying model collagen/fibrin matrix. A model coupling Hill-type actomyosin dynamics with a plastic perfectly viscoplastic description of the matrix quantitatively accounts for the microtissue dynamics, including notably the cells’ shielding of the matrix plasticity. Stretch measurements of single cells confirmed the active cell dynamics, and were well described by a single-cell version of our model. These results reveal the need for new focus on matrix plasticity and its interactions with active cell mechanics in describing tissue dynamics.

No MeSH data available.


Related in: MedlinePlus