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Abstract A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load‐bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure‐based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets and simulating the tip‐anchored optical tweezer experiment on our computational model, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium‐length‐dependent, we found the mechanical properties of the cilium are also highly deformation‐dependent. More important, we found that the cilium membrane near the base is not under pure in‐plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure‐based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging‐informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base.
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Fluid-structure interaction modelling of neighboring tubes with primary cilium analysis
We have developed a numerical model of two osculating cylindrical elastic renal tubules to investigate the impact of neighboring tubules on the stress applied to a primary cilium. We hypothesize that the stress at the base of the primary cilium will depend on the mechanical coupling of the tubules due to local constrained motion of the tubule wall. The objective of this work was to determine the in-plane stresses of a primary cilium attached to the inner wall of one renal tubule subject to the applied pulsatile flow, with a neighboring renal tube filled with stagnant fluid in close proximity to the primary tubule. We used the commercial software COMSOLⓇ to model the fluid-structure interaction of the applied flow and tubule wall, and we applied a boundary load to the face of the primary cilium during this simulation to produces a stress at its base. We confirm our hypothesis by observing that on average the in-plane stresses are greater at the base of the cilium when there is a neighboring renal tube versus if there is no neighboring tube at all. In combination with the hypothesized function of a cilium as a biological fluid flow sensor, these results indicate that flow signaling may also depend on how the tubule wall is constrained by neighboring tubules. Our results may be limited in their interpretation due to the simplified nature of our model geometry, and further improvements to the model may potentially lead to the design of future experiments.
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- Award ID(s):
- 1951568
- PAR ID:
- 10536872
- Publisher / Repository:
- AIMS press
- Date Published:
- Journal Name:
- Mathematical Biosciences and Engineering
- Volume:
- 20
- Issue:
- 2
- ISSN:
- 1551-0018
- Page Range / eLocation ID:
- 3677 to 3699
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3934/mbe.2023172
