Cytoskeleton is known as an important part of animal cells that supports various cellular functions while maintains the integrity of cells. Due to their diverse functions, different types of cells may have distinct cytoskeleton structures. Recent development in stochastic optical reconstruction microscopy (STORM) revealed the hitherto unknown periodic cytoskeleton structureof axons, which consists of co-axile actin rings connected by multiple parallel spectrins (Xu et al. Science 2013). In this experiment, the average spacing between adjacent actin rings, as well as the variance of the spacing, are measured. In this paper, we model the spectrins in this actin-spectrin network as worm-like chains(WLCs), which are stretched to lengths close to their contour lengths. The result attained shows that the observed variance in the separation between actin rings is consistent with the thermal fluctuation of spectrins predicted by the WLC model . The analytical result can be used as an alternative method to infer the contour length and persistence length of polymers by measuring their average extension and longitudinal fluctuations along the stretching (force ) direction. It also provides an additional criterion to check the region of validity of the WLC model .
The macroscopic properties, the properties of individual components, and how those components arrange themselves are three important aspects of a complex structure. Knowing two of them will provide us information of the third. Here we perform a theoretical study of a composited system that is slender and can be coarse-grained as a simple smooth 3-dimensional curve. Focusing on biological systems, especially the cytoskeletal networks, we show how the combination of the properties of the network and the individual components puts constraints on the local configurations and dynamics. When the network can be modeled as a single linear chain, similar as single polymer chains, its overall conformation is dominated by the competition between the internal energy and the thermal agitations. The conformational fluctuations of a composited chain reveal not only its elastic properties but also the local arrangements and dynamics of its components. We first show a general form of the internal energy of a coarse-grained composited chain, and discuss briefly how it is related to existing models and may contribute to building new models. Under certain limits this general expression of energy is reduced to the worm-like chain (WLC) model. Using this simplified energy in the strong-stretching limit, we obtain analytical solutions for all the cumulants of the end-to-end distance projected to the force direction . Finally we apply our results to recent experimental observations that revealed the hitherto unknown periodic cytoskeleton structure of axons and measured the longitudinal fluctuations, and show how the comparison between our results and experiments limits possible local configurations and dynamics of the spectrin tetramers in the axonal cytoskeleton .
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Cytoskeleton is known as an important part of animal cells that supports various cellular functions while maintains the integrity of cells. Due to their diverse functions, different types of cells may have distinct cytoskeleton structures. Recent development in stochastic optical reconstruction microscopy (STORM) revealed the hitherto unknown periodic cytoskeleton structureof axons, which consists of co-axile actin rings connected by multiple parallel spectrins (Xu et al. Science 2013). In this experiment,
The macroscopic properties, the properties of individual components, and how those components arrange themselves are three important aspects of a complex structure. Knowing two of them will provide us information of the third. Here we perform a theoretical study of a composited system that is slender and can be coarse-grained as a simple smooth 3-dimensional curve. Focusing on biological systems, especially the cytoskeletal networks, we show how the combination of the properties of the network and the individual components puts constraints on the local configurations and dynamics. When the network can be modeled as a single linear chain, similar as single polymer chains, its overall conformation is dominated by the competition between the internal energy and the thermal agitations. The conformational fluctuations of a composited chain reveal not only its elastic properties but also the local arrangements and dynamics of its components. We first show a general form of the internal energy of a coarse-grained composited chain, and discuss briefly how it is related to existing models and may contribute to building new models. Under certain limits this general expression of energy is reduced to the worm-like chain (WLC) model. Using this simplified energy in the strong-stretching limit, we obtain analytical solutions for all the cumulants of
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average spacing between adjacent actin rings, as well as the variance of the spacing, are measured. In this paper, we model the spectrins in this actin-spectrin network as worm-like chains(WLCs), which are stretched to lengths close to their contour lengths. The result attained shows that the observed variance in the separation between actin rings is consistent with the thermal fluctuation of spectrins predicted by the WLC model
end-to-end distance projected to the force direction
R
The analytical result can be used as an alternative method to infer the contour length and persistence length of polymers by measuring their average extension and longitudinal fluctuations along the stretching (force ) direction. It also provides an additional criterion to check the region of validity of the WLC model
Finally we apply our results to recent experimental observations that revealed the hitherto unknown periodic cytoskeleton structure of axons and measured the longitudinal fluctuations, and show how the comparison between our results and experiments limits possible local configurations and dynamics of the spectrin tetramers in the axonal cytoskeleton