Models of cytoskeletal biopolymer networks: Modes of deformation and force transmission
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$398 Journal of Biomechanics 2006, Vol. 39 (Suppl 1) contact area between receptor-expressing cell and ligand reconstituted glass- supported planar lipid bilayer. Applying the mathematical model to the contact area FRAP experiment enables in situ measurements of two dimensional kinetic rates of the adhesion molecules and their retarded diffusion in such a stable immunological synapse. 6926 Mo, 11:00-11:30 (P9) Cells feel matrix stiffness - Simple models and computational insights S. Sen, A.J. Engler, D.E. Discher. Pennsylvania Muscle Institute and Biophysical Engineering Lab, University of Pennsylvania; Philadelphia, PA, USA Normal tissue cells - including stem cells - are generally not viable when suspended in a fluid and are therefore said to be anchorage dependent. Such cells must adhere to a solid, but a solid can be as rigid as glass or softer than a baby's skin. The behavior of some cells on soft materials is characteristic of important phenotypes; for example, cell growth on soft agar gels is used to identify cancer cells. However, an understanding of how tissue cells sense matrix stiffness is just emerging with quantitative studies of cells adhering to gels (or to other cells) with which elasticity can be tuned to approximate that of tissues. Key roles in molecular pathways are played by adhesion complexes and the actin-myosin cytoskeleton, whose contractile forces are transmitted through transcellular structures. The feedback of local matrix stiffness on cell state increasingly appears to have important implications for development, differentiation, disease, and regeneration. We will present simple equilibrium type models and computations for the balance of forces. 5234 Mo, 11:30-11:45 (P9) Dynamics of a polymer chain under tension as a model of rheology of the cytoskeleton N. Rosenblatt 1, A.M. Alencar 2, A. Majumdar 1, B. Suki 1, D. Stamenovi~e 1. 1Department of Biomedical Engineering, Boston University, Boston, MA, USA, 2 Department of Environmental Health, Harvard School of Public Health, Boston, MA, USA Cellular biological responses to mechanical stress are governed by rheological properties of the cytoskeleton (CSK), a molecular network composed of different types of biopolymers. Biophysical measurements on cultured adherent cells have revealed that rheology of the CSK is regulated through the agency of preexisting mechanical tensile stress ("prestress") borne by the CSK. The physical basis for this influence, however, remains an open question. Here we report a model of dynamics of a semiflexible polymer chain under tension as a basis for understanding the effect of the prestress on rheology of the CSK. The chain is modeled as a two-dimensional elastically jointed system comprised of elastic bonds connected by flexible joints of finite stiffness. The chain was built inside a very long, straight, rigid tube of a constant diameter. Chain's dynamics was driven by fluctuations of its joints searching for the most probable configuration with probability determined by an energy barrier assuming the Gaussian distribution. The chain was stretched along the tube's axis by a pair of stepwise increasing forces of the same magnitude and opposite sense, acting at the endpoints of the chain. At each force step, the chain's creep response was calculated using a Monte Carlo sampling method. Model predictions are consistent with previously reported data from rheological measurements on living cells. The model reveals that nonlinear elasticity of the chain is critical for bringing forth the effect of the prestress on cell rheology and that it can be directly tied to the contributions of the internal energy to the chain's free energy. 5352 Mo, 11:45-12:00 (P9) Models of cytoskeletal biopolymer networks: Modes of deformation and force transmission F.C. MacKintosh. Department of Physics and Astronomy, Vrije Universiteit, Amsterdam, The Netherlands Networks of filamentous proteins play a crucial role in cell mechanics. These cyteskeletal networks, together with various crosslinking and other associated proteins largely determine the (visco)elastic response of cells. In contrast to common flexible polymer materials, recent studies have suggested that these unique materials of cell exhibit distinct regimes of elastic behavior that depend sensitively on binding/crosslinking proteins and network density. We discuss theoretical models and experimental studies of the elastic response in these filamentous protein networks. Oral Presentations 5497 Mo, 12:00-12:15 (P9) Finite-element model of the adhesion-cytoskeleton-nucleus mechanotrasnduction pathway in endothelial cells A.A. Spector 1, R.P. Jean 1, C.S. Chen 2. 1Department ef Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland, USA, 2Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania, USA Endothelial cells possess a network that connects adhesions on the basal surface, the cytoskeleton, and the nucleus. Force transmission along this pathway contributes to cellular changes generated in the nucleus, including the alteration of gene expression and cell proliferation. We study this pathway by analyzing the endothelial cell rounding. We previously did an experiment where we perturbed endothelial cell adhesions and measured the resulting changes in the cell and nucleus shape. Here, we use the obtained experimental data to reconstruct the transmitted forces and the stress field inside the nucleus and along its surface. In our model, we consider different scenarios of the cytoskelal fiber arrangement, including a set of discrete fibers and an effective homogeneous layer. In the initial (spread) state, the cytoskeletal fibers hold the nucleus in an elongated configuration. The narrowing of the apparent adhesion area of the cell is assumed to be accompanied by loss of tension in a part of the cytoskeletal fibers. This effect is modeled by the application of reactive forces deforming the nucleus and causing its rounding. The material of the nucleus is considered as nonlinear elastic, and the whole problem is solved computationally by using the finite-element method. For the nucleus and other cellular components, we use the elastic moduli reported in the literature, and we control our computational results by checking the strains in and the shape of the nucleus against our experimental data. The computed stresses in the nucleus are significant enough to affect the function of DNA molecules and chromatin fibers. Thus, the obtained results can be important for a better understanding of the mechanisms of mechanotransduction in cells. 6189 Mo, 12:15-12:30 (P9) Mechanics and mechanisms of nuclear deformation A. Vaziri 1, H. Lee 2, R.D. Kamm 3, M.R. Kaazempur Mofrad 3. 1Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA, 2Departments of Mechanical and Biological Engineering, MIT, Cambridge, MA, USA, 3Department of Bioengineering, University of California, Berkeley, CA The nucleus is delineated from the cytoplasm by the nuclear envelope, which comprises an outer nuclear membrane, inner nuclear membrane, nuclear pore complexes and nuclear lamina. The inner and outer membranes are each a lipid bi-layer separated by a small, electron transparent region of approximately 10-40 nm. Lamins are the major components of the nuclear lamina, which appears as a meshwork structure underneath the inner nuclear membrane. Lamina is thought to play a critical role in maintaining the structural integrity of the nucleus, organizing the nuclear envelope by recruiting proteins to the inner nuclear membrane and providing anchorage sites for chromatin. Each of the abovementioned nuclear elements has a distinct structure, which should be distinguished when studying the nucleus response to mechanical stimuli. We have developed a computational model based on finite element methods interwoven with the fundamentals of solid mechanics and materials engineer- ing, to simulate the response of the isolated nuclei to mechanical stimuli. In constructing this structural model for the nucleus, each of the three distinct structural elements was considered: the double lipid bilayer, the cortical layer comprised largely of lamin (nuclear lamina), and the nucleoplasm. All the nuclear elements have both solid- and fluid-like dual characteristics. Indeed, a purely solid model would not capture functions like motility. Similarly, a purely fluid model would fail in describing the nucleus ability to maintain its structural integrity. In this research, depending on the dynamic time scale of interest, we will use elastic or viscoelastic continuum description of the nuclear elements by implementing finite element-based descriptions of the nucleus compromising separate compartments for nuclear envelope and nucleoplasm. To the extent that such continuum models can capture experimentally-derived rheological properties and the stress/strain patterns within the nucleus, it can help us relate biological influences of various types of force application and dynamics under different geometrical configurations of nuclei. This continuum finite element-based model is able to separate the structural role of the indi- vidual nuclear elements, which is vital to understanding the nuclear mechanics and for functional insight. We will use this proposed computational model in order to gain insight into the mechanisms driving the nucleus response and stress transition throughout the nuclear elements in two common nuclear experiments: micropipette aspiration and atomic force microscopy.
Transcript of Models of cytoskeletal biopolymer networks: Modes of deformation and force transmission
$398 Journal o f Biomechanics 2006, Vol. 39 (Suppl 1)
contact area between receptor-expressing cell and ligand reconstituted glass- supported planar lipid bilayer. Applying the mathematical model to the contact area FRAP experiment enables in situ measurements of two dimensional kinetic rates of the adhesion molecules and their retarded diffusion in such a stable immunological synapse.
6926 Mo, 11:00-11:30 (P9) Cells feel matrix stiffness - Simple models and computational ins ights S. Sen, A.J. Engler, D.E. Discher. Pennsylvania Muscle Institute and Biophysical Engineering Lab, University of Pennsylvania; Philadelphia, PA, USA
Normal tissue cells - including stem cells - are generally not viable when suspended in a fluid and are therefore said to be anchorage dependent. Such cells must adhere to a solid, but a solid can be as rigid as glass or softer than a baby's skin. The behavior of some cells on soft materials is characteristic of important phenotypes; for example, cell growth on soft agar gels is used to identify cancer cells. However, an understanding of how tissue cells sense matrix stiffness is just emerging with quantitative studies of cells adhering to gels (or to other cells) with which elasticity can be tuned to approximate that of tissues. Key roles in molecular pathways are played by adhesion complexes and the actin-myosin cytoskeleton, whose contractile forces are transmitted through transcellular structures. The feedback of local matrix stiffness on cell state increasingly appears to have important implications for development, differentiation, disease, and regeneration. We will present simple equilibrium type models and computations for the balance of forces.
5234 Mo, 11:30-11:45 (P9) Dynamics of a po lymer chain under tension as a model of rheology of the cytoskeleton
N. Rosenblatt 1 , A.M. Alencar 2, A. Majumdar 1 , B. Suki 1 , D. Stamenovi~e 1 . 1Department of Biomedical Engineering, Boston University, Boston, MA, USA, 2 Department of Environmental Health, Harvard School of Public Health, Boston, MA, USA
Cellular biological responses to mechanical stress are governed by rheological properties of the cytoskeleton (CSK), a molecular network composed of different types of biopolymers. Biophysical measurements on cultured adherent cells have revealed that rheology of the CSK is regulated through the agency of preexisting mechanical tensile stress ("prestress") borne by the CSK. The physical basis for this influence, however, remains an open question. Here we report a model of dynamics of a semiflexible polymer chain under tension as a basis for understanding the effect of the prestress on rheology of the CSK. The chain is modeled as a two-dimensional elastically jointed system comprised of elastic bonds connected by flexible joints of finite stiffness. The chain was built inside a very long, straight, rigid tube of a constant diameter. Chain's dynamics was driven by fluctuations of its joints searching for the most probable configuration with probability determined by an energy barrier assuming the Gaussian distribution. The chain was stretched along the tube's axis by a pair of stepwise increasing forces of the same magnitude and opposite sense, acting at the endpoints of the chain. At each force step, the chain's creep response was calculated using a Monte Carlo sampling method. Model predictions are consistent with previously reported data from rheological measurements on living cells. The model reveals that nonlinear elasticity of the chain is critical for bringing forth the effect of the prestress on cell rheology and that it can be directly tied to the contributions of the internal energy to the chain's free energy.
5352 Mo, 11:45-12:00 (P9) Models of cytoskeletal biopolymer networks: Modes of deformation and force transmission F.C. MacKintosh. Department of Physics and Astronomy, Vrije Universiteit, Amsterdam, The Netherlands
Networks of filamentous proteins play a crucial role in cell mechanics. These cyteskeletal networks, together with various crosslinking and other associated proteins largely determine the (visco)elastic response of cells. In contrast to common flexible polymer materials, recent studies have suggested that these unique materials of cell exhibit distinct regimes of elastic behavior that depend sensitively on binding/crosslinking proteins and network density. We discuss theoretical models and experimental studies of the elastic response in these filamentous protein networks.
Oral Presentations
5497 Mo, 12:00-12:15 (P9) Finite-element model of the adhesion-cytoskeleton-nucleus mechanotrasnduction pathway in endothelial cells
A.A. Spector 1 , R.P. Jean 1 , C.S. Chen 2. 1Department ef Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland, USA, 2Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania, USA
Endothelial cells possess a network that connects adhesions on the basal surface, the cytoskeleton, and the nucleus. Force transmission along this pathway contributes to cellular changes generated in the nucleus, including the alteration of gene expression and cell proliferation. We study this pathway by analyzing the endothelial cell rounding. We previously did an experiment where we perturbed endothelial cell adhesions and measured the resulting changes in the cell and nucleus shape. Here, we use the obtained experimental data to reconstruct the transmitted forces and the stress field inside the nucleus and along its surface. In our model, we consider different scenarios of the cytoskelal fiber arrangement, including a set of discrete fibers and an effective homogeneous layer. In the initial (spread) state, the cytoskeletal fibers hold the nucleus in an elongated configuration. The narrowing of the apparent adhesion area of the cell is assumed to be accompanied by loss of tension in a part of the cytoskeletal fibers. This effect is modeled by the application of reactive forces deforming the nucleus and causing its rounding. The material of the nucleus is considered as nonlinear elastic, and the whole problem is solved computationally by using the finite-element method. For the nucleus and other cellular components, we use the elastic moduli reported in the literature, and we control our computational results by checking the strains in and the shape of the nucleus against our experimental data. The computed stresses in the nucleus are significant enough to affect the function of DNA molecules and chromatin fibers. Thus, the obtained results can be important for a better understanding of the mechanisms of mechanotransduction in cells.
6189 Mo, 12:15-12:30 (P9) Mechanics and mechanisms of nuclear deformation A. Vaziri 1 , H. Lee 2, R.D. Kamm 3, M.R. Kaazempur Mofrad 3. 1Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA, 2Departments of Mechanical and Biological Engineering, MIT, Cambridge, MA, USA, 3Department of Bioengineering, University of California, Berkeley, CA
The nucleus is delineated from the cytoplasm by the nuclear envelope, which comprises an outer nuclear membrane, inner nuclear membrane, nuclear pore complexes and nuclear lamina. The inner and outer membranes are each a lipid bi-layer separated by a small, electron transparent region of approximately 10-40 nm. Lamins are the major components of the nuclear lamina, which appears as a meshwork structure underneath the inner nuclear membrane. Lamina is thought to play a critical role in maintaining the structural integrity of the nucleus, organizing the nuclear envelope by recruiting proteins to the inner nuclear membrane and providing anchorage sites for chromatin. Each of the abovementioned nuclear elements has a distinct structure, which should be distinguished when studying the nucleus response to mechanical stimuli. We have developed a computational model based on finite element methods interwoven with the fundamentals of solid mechanics and materials engineer- ing, to simulate the response of the isolated nuclei to mechanical stimuli. In constructing this structural model for the nucleus, each of the three distinct structural elements was considered: the double lipid bilayer, the cortical layer comprised largely of lamin (nuclear lamina), and the nucleoplasm. All the nuclear elements have both solid- and fluid-like dual characteristics. Indeed, a purely solid model would not capture functions like motility. Similarly, a purely fluid model would fail in describing the nucleus ability to maintain its structural integrity. In this research, depending on the dynamic time scale of interest, we will use elastic or viscoelastic continuum description of the nuclear elements by implementing finite element-based descriptions of the nucleus compromising separate compartments for nuclear envelope and nucleoplasm. To the extent that such continuum models can capture experimentally-derived rheological properties and the stress/strain patterns within the nucleus, it can help us relate biological influences of various types of force application and dynamics under different geometrical configurations of nuclei. This continuum finite element-based model is able to separate the structural role of the indi- vidual nuclear elements, which is vital to understanding the nuclear mechanics and for functional insight. We will use this proposed computational model in order to gain insight into the mechanisms driving the nucleus response and stress transition throughout the nuclear elements in two common nuclear experiments: micropipette aspiration and atomic force microscopy.
