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  .
The macroscopic properties, the properties of individual components and how those components interact with each other are three important aspects of a composited structure. An understanding of the interplay between them is essential in the study of complex systems. Using axonal cytoskeleton as an example system, here we perform a theoretical study of slender structures that can be coarse-grained as a simple smooth 3-dimensional curve. We first present a generic model for such systems based on the fundamental theorem of curves. We use this generic model to demonstrate the applicability of the well-known worm-like chain (WLC) model to the network level and investigate the situation when the system is stretched by strong forces (weakly bending limit). We specifically studied recent experimental observations that revealed the hitherto unknown periodic cytoskeleton structure of axons and measured the longitudinal fluctuations . Instead of focusing on single molecules, we apply analytical results from the WLC model to both single molecule and network levels and focus on the relations between extensions and fluctuations. We show how this approach introduces constraints to possible local dynamics of the spectrin tetramers in the axonal cytoskeleton and finally suggests simple but self-consistent dynamics of spectrins in which the spectrins in one spatial period of axons fluctuate in-sync .
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complex structure. Knowing two of them will provide us information of the third. Here
composited structure. An understanding of the interplay between them is essential in the study of complex systems. Using axonal cytoskeleton as an example system, here
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a composited system that is slender and
slender structures that
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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
We first present a generic model for such systems based on the fundamental theorem of curves. We use this generic model to demonstrate the applicability of the well-known
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. 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
to the network level and investigate the situation when the system is stretched by strong forces (weakly bending limit). We specifically studied
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, and show how the comparison between our results and experiments limits possible local configurations and
. Instead of focusing on single molecules, we apply analytical results from the WLC model to both single molecule and network levels and focus on the relations between extensions and fluctuations. We show how this approach introduces constraints to possible local
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and finally suggests simple but self-consistent dynamics of spectrins in which the spectrins in one spatial period of axons fluctuate in-sync