title: Experimental and numerical investigations of stress fibre reorientation in biological cells
Creators: name: Keshavanarayana, Pradeep
Publisher: name: University of Glasgow
Year: 2019
Subjects: subject: Cell mechanics, stress fibres, focal adhesion, cell stretcher, stress fibre reorientation, bio-chemo-mechanical model, staggered coupling, monolithic coupling, calcium signalling, feedback loop.

description: Cells are the fundamental units of living organisms controlling the behaviour of tissues, organs and thereby the organ system. The mechanical stimuli has been found to contribute towards changes in mechanical properties of cells, sometimes resulting in diseases. In order to quantify the response of cells to mechanical stimuli, a variety of experiments have been carried out. They have helped us to understand the effects of different types of stimuli, responses in different length and time scales, effect of different environmental factors, and the relation between different components of the cell. Focal adhesions present on the cell membrane contain mechanosensitive proteins called integrins which can form a connection between the cell and the extra cellular matrix, and thus sense the properties of the substrate and thereby the external stimuli. This creates a chain of biochemical reactions within the cytoplasm, leading to a cross bridge between the actin and myosin proteins in the presence of calcium ions, forming stress fibres. In this regard, cyclic loading experiments have been performed to understand the nature of connection between the growth of focal adhesions and stress fibres. In this thesis, a novel DIY design of an uniaxial cell stretcher has been designed and the manufacturing process using 3D printing technology has been explained. The device has been used to apply uniaxial cyclic load with different amplitudes, keeping the frequency constant to study the response of cells to changing strains. The experiments have been performed on two types of cells, fibroblasts and osteoblasts. The results are analysed quantitatively and the stress fibre orientation is studied for varying loading conditions for each cell type. Since the experiments performed are in vitro, the numerical models are developed in order to apply in vivo type loading and study the response of cells. In this regard, a numerical model is developed wherein the already existing stress fibre and focal adhesion growth models are extended and coupled through a feedback loop involving cytoplasmic calcium concentration. Stress fibre is assumed to depend on the calcium concentration and the active stress, while focal adhesion is modelled by assuming that integrins which exist in two states are in thermodynamic equilibrium. The active stress is taken as a product of strain-rate and strain dependent functions. The focal adhesion forming a bond with the substrate, and the cell provides a traction force to the cell. To consider the variation of calcium concentration depending on the focal adhesion growth, a feedback loop is introduced. The effect of substrate stiffness on the response of cells is analysed. The model thus developed is used to obtain solutions to numerical problems simulating biological phenomenon including stress fibre reorientation due to changing amplitude of cyclic loading. The mathematical model developed results in a coupled system of equations, for which the solution scheme needs special consideration. Noting the limitation on the time step that could be used with the staggered coupling scheme, a monolithic coupling scheme is developed where the system of equations are solved simultaneously. The variational formulation of the constitutive equations have been derived along with the algorithmic aspects of the solution schemes. The solution is obtained by following the finite element method with large strain formulation. Numerical problems have been solved to compare the coupling schemes for space and time refinements, and for changing parameter values. The convergence behaviour of the solution schemes have been analysed. Finally, the solution obtained from the numerical scheme have been compared with the experimental observations, and the ways this project could be extended has been discussed. Some of the important results that could be drawn from this thesis are: 1) A novel compact 3D-printed cell stretcher which has the size of a standard 96-well plate. 2) Stress fibres are formed predominantly in directions away from the direction of loading, when cells are subjected to uni-axial cyclic stretch. 3) Reorientation is higher with increasing amplitude of the cyclic loading. 4) Mathematical model for stress fibre growth has been coupled with focal adhesions' and the cytoplasmic calcium is controlled through a feedback loop. 5) Feedback loop plays a crucial role in simulating experiments such as optical tweezers, and ROCK inhibition. 6) Uni-axial cyclic stretch simulation results could be qualitatively compared to the average results obtained from experiments. 7) Coupling the system of equations can be performed following either a staggered or a monolithic approach. 8) Monolithic approach allowed using higher time step values, while staggered approach had limitations in the time step, and the parameter values that could be used.