Stress Analysis of Bacteria Submitted to Extrusion Loading
Bacteria are known to sense and respond to mechanical signals. To examine bacterial mechanics and their relation to biological responses, we used a microfluidic device to apply a mechanical loading condition we refer to as extrusion loading to individual Escherichia coli. Extrusion loading was generated by flowing bacteria in liquid media into tapered constrictions. A difference in fluid pressure across the bacteria and the frictional and normal forces from the channel walls generate loads and deformations on the bacteria. The recent experimental findings in our group suggests that extrusion loading can influence growth rates and the performance of cell membrane proteins involved in the resistance to toxins. Mechanical models of bacteria under extrusion loading were developed to determine the stress state and Young’s modulus of the cell envelope. Here I used analytical and finite element models to characterize the stresses in the cell envelope of bacteria submitted to extrusion loading. The analytical model was derived based on a force balance and transversely isotropic constitutive laws. An axisymmetric nonlinear finite element model was developed using solid elements with transversely isotropic material properties. As many aspects of bacteria material properties are not known, a parametric analysis was performed to determine the combinations of material properties that yielded finite element simulations consistent with experimental results. We found that extrusion loading led to increases in tensile axial stress, shear stress, and compressive radial stress, and decreases in tensile hoop stress. Besides, the internal pressure on bacteria (the “turgor pressure”) increased during extrusion loading. Additionally we used a series of analytical and finite element models to determine the cell envelope Young’s modulus. The analytical model provided a closed form solution for Young’s modulus. An axisymmetric nonlinear finite element model was developed using solid elements with isotropic material properties to identify the cell envelope Young’s moduli that were consistent with experimental observations. The analytical analysis was extremely sensitive to experimental measurements suggesting that small errors in measurement would have large effects on the predicted Young’s modulus. The parametric finite element analysis showed resulting deformations insensitive to the tested range of Young’s moduli, preventing us from iteratively determining a Young’s modulus. Proposed future approaches to determine the cell envelope Young’s modulus are discussed.
Cell mechanics; Mechanical modeling; Microfluidic device; Elasticity; Mechanical engineering; Biomechanics; Finite element method; Continuum mechanics
Hernandez, Christopher J.
M.S., Mechanical Engineering
Master of Science
dissertation or thesis