A Study On The Flexural Rigidity Of Cytoskeletal Filaments And Its Role In The Endocytosis

Cell is a highly coupled biochemical/biomechanical system.The maintenance of cell structure,endocytosis and cell adhesion/migration at the macroscopic scale,as well as perception and transduction of mechanical signals on the microscopic scale,are inseparable from the complex mechanical behaviors of the cytoskeletal filaments.Cytoskeletal filaments show both active and passive dynamic mechanical behaviors.Measuring the mechanical properties of individual filament can not only help us understand the mechanisms behind the complex dynamic behaviors,but also provide basis to calibrate biological piconewton forcemeters.Although many methods have been proposed about measuring the flexural rigidity of the cytoskeletal filaments,they all have some defects and the results in literature are still quite different.Thus,in order to reveal the main factors affecting the measurement of the flexural rigidity,it is necessary to study the dynamic bending behavior of the cytoskeletal filaments in-depth.In addition,endocytosis is a complex physiological process and provides a necessary pathway for the metabolism of cells and organisms.In recent years,the microscopic molecular mechanisms of endocytosis have been studied and many theoretical/computational models have been proposed to model the endocytosis behavior.Although,these models have shed some light on the process of endocytosis,the understanding of the role that actin network played during endocytosis is still limited.Besides,the tensile deformation of the membrane is also rarely considered in previous models.Thus,the bending properties of cytoskeletal filament and the influence of active forces of actin filament on the endocytosis process are studied in this thesis.The main results are given as follows:1.Based on the modal analysis method and the principle of virtual work,a linear static method has been proposed to measure the flexural rigidity of cytoskeletal filaments.Then,based on the experimental configurations of the filament in the literature and the simulated configurations of the filament by ABAQUS,the flexural rigidity of the corresponding filament has been calculated.The results are in good agreement with the given values.Further,the shortcomings of the traditional bending modal analysis method are discussed.For the first time,the proposed linear static method reveals the influences of the sampling time interval and hydrodynamic effect of the wall on the measured flexural rigidity of the filament.It can give a good estimation of the filament's flexural rigidity,especially for microtubule with a higher bending rigidity.2.From the view of the fluctuation-dissipation theorem,a nonlinear method for measuring the flexural rigidity of cytoskeletal filament has been established based on the modal analysis method and the principle of virtual work.The Finite Element Method-Brownian Dynamics(FEM-BD)method is used to simulate the Brownian motion of the cytoskeletal filament in solution.The experimental configuration of the filament in the literature and the simulated configuration of the filament are taken as samples to verify the validity and correctness of the proposed nonlinear method.Besides,the proposed nonlinear static/dynamic methods are compared with the linear method and the traditional bending modal analysis method.The influence of measuring error on the flexural rigidity of the filament is also discussed.For the first time,the viscous dissipation,sampling time interval and hydrodynamic effect of the wall are theoretically involved to measure the flexural rigidity of the cytoskeletal filament in our nonlinear dynamic method.The results show that the nonlinear dynamic method can measure the flexural rigidity of cytoskeletal filament more accurately and is much closer to the physical reality of the dynamic behaviors of the filament.The equipartition theorem used in the traditional bending modal analysis method,however,is not suitable for estimating the average bending energy stored in each mode of the filament.3.A generalized Canham-Helfrich model and a coarse-grained Canham-Helfrich model have been proposed.Firstly,based on the traditional Canham-Helfrich model,the governing equation and corresponding modal function solution of the endocytic behavior are developed and discussed,where both actin forces,osmotic pressure and membrane tension are included.Then,based on the co-rotation grid method,a coarse-grained Canham-Helfrich model,which involves both the tensile and bending energy of the membrane,is proposed.The simulation results of this model are consistent with the experimental results given in the literature.The results show that tensile deformation dominates near the neck position of the invaginated membrane and the tensile deformation of the membrane cannot be ignored.4.The effects of the actin forces on the endocytosis are studied.The critical loads of actin forces required for forming a closed vesicle are determined under different action positions,angles and asymmetrical conditions.It suggests that the actin force at the endocytic site is the main mechanism for driving the invagination of the membrane.Under certain conditions,actin force together with the osmotic pressure can promote the protrusion of the membrane,which provides a potential pathway for the macropinocytosis.