Mathematical Modeling of Stress Fiber Reorganization Induced by Cyclic Stretch
Arterial endothelial cells (ECs) are subjected to pulsatile strain due to pressure changes in the cardiac cycle and this may play a significant role in vascular function in health and disease. Further, ECs differentially respond to different patterns of strain. There is much evidence that cyclic uniaxial strain results in a perpendicular orientation of ECs and their stress fibers, while no such alignment occurs in response to cyclic equaibiaxial stretch. It is unclear how cells and their stress fibers determine their specific response to particular spatiotemporal changes in the matrix, however. Given that ECs located at regions in the arterial tree prone to atherogenesis are non-aglined, while ECs in relatively healthy regions are oriented perpendicular to the principal direction of cyclic stretch, it is important to understand the mechanisms which regulate stretch-induced stress fiber alignment. The focus of this thesis was to develop realistic models to describe the dynamic changes in the organization of stress fibers in response to diverse spatiotemporal patterns of stretch. The model is based on the premise that stress fibers are pre-stressed at a ?homeostatic? level so that stress fibers are extended beyond their unloaded lengths, and that perturbation in stress fiber length from the homeostatic level destabilizes the stress fibers. A deterministic model described experimentally measured time courses of stress fiber reorientation perpendicular to the direction of cyclic uniaxial stretch, as well as the lack of alignment in response to equibiaxial stretch. In the case of cyclic simple elongation with transverse matrix contraction, stress fibers oriented in the direction of least perturbation in stretch. Model analysis indicated the need for a time-dependent stress fiber mechanical property, however. Thus, a stochastic model was developed that incorporated the concept that stress fibers tend to self-adjust to an equilibrium level of extension when they are perturbed from their unload lengths with the turnover of stress fibers. The stochastic model successfully described experimentally measured time courses of stress fiber reorganization over a range of frequencies. At a frequency of 1 Hz, stress fibers predominantly oriented perpendicular to stretch, while at 0.1 Hz the extent of stress fiber alignment was markedly reduced and at 0.01 Hz there was no alignment at all. Both the deterministic and stochastic models accurately described the relationship between stretch magnitude and the extent of stress fiber alignment in endothelial cells subjected to cyclic uniaxial stretch. Parameter sensitivity analyses for each model were used to demonstrate the effects of each parameter on the characteristics of the system response. In summary, the mathematical models were capable of describing stress fiber reorganization in response to diverse temporal and spatial patterns of stretch. These models provide a theoretical framework to elucidate the mechanisms by which adherent cells sense the characteristics of matrix deformation and describe a mechanism by which the cells can then adapt to such deformations to maintain mechanical homeostasis.
Hsu, Hui-Ju (2009). Mathematical Modeling of Stress Fiber Reorganization Induced by Cyclic Stretch. Master's thesis, Texas A&M University. Available electronically from