Mechanical Modelling Analysis Based On The Structure Of Adherent Cells

Cells are the basic unit of life activities of organisms.The structure,morphology,function,growth and development of cells are related to the cellular mechanical properties.The response rule of cellualr structure to the mechanical stimulation is the main aspect of cellular physiological functions,and the basis of all life activities.The cellular bio-mechanical properties play a key role in regulating their physiological and pathological functions,such as cell division,spreading and proliferation,which are closely related to their bio-mechanical properties.This paper combines theoretical calculation analysis and simulation to study the mechanical responses of the cellular main structures to the external stimuli based on the main constituent structure of cells,which are mainly composed of cytoplasm,cell membrane,nucleus,cytoskeleton(CSK)and nucleoskeleton(NSK).The main work and results are as follows:(1)Based on the method of tensegrity,the effects of different spreading degrees of cells on the overall stiffness of CSK are studied.The vertex coordinates and the centroid positions of CSK models(tensegrity models)are calculated theoretically under the different spreading degree.Two types of tensegrity models with and without intermediate filaments(IFs)with different spreading degree are established according to the theoretical calculations.Thereaction forces of tensegrity with different spreading degrees to the substrate are simulated by using the finite element method(FEM)models.The results show that the overall stiffness of CSK is related to the degrees of spreading.The greater the degree of spreading,the greater the reaction force to the substrate.Compared with the tensegrity without IFs,the reaction force of model including IFs to the substrate can increase in large strain(>20%),indicating that IFs can significantly increase the overall stiffness of CSK under large deformation.It provides a basis for a comprehensive and scientific understanding of the influence of the spreading degrees of CSK on the overall stiffness of cells.(2)The theoretical calculation method is used to study the changes of cell membrane tensions when cells are deformed under the action of gravity.Different shapes of vesicle models are used to represent suspended cells and adherent cells,respectively.The undeformed vesicle model is regarded as a sphere based on the shape of suspended cells.The deformed vesicle model is treated as a pseudo-ellipsoid,a pseudo-spherical cap or a spherical cap with a circle contact area,which is used to represent adherent cells.The equilibrium differential equations of the deformed vesicle models in radial and vertical directions and the corresponding boundary conditions are established according to the numerical model.The expressions of cell membrane tension are obtained by using the semi-inverse method and Gaussian fitting method.The results show that gravity has a certain effect on the cell membrane tension.The cell membrane tension is no longer a constant,and it is a function of cell height when gravity is considered.This study provides a new way for further understanding of the spreading of vesicle model under the action of gravity.(3)The surface elasticity modulus of Hela cells at different action sites are quantitatively studied under Atomic Force Microscopy(AFM).AFM was selected to observe the microstructure,surface morphology and corresponding geometric sizes of the cells.The force-displacement curves of the four sites of each cells are measured,and the surface elasticity modulus of different sites ofcells are obtained using the Sneddon model.The results show that the surface elasticity modulus of the cells has apparent positional differences,and the cell edges are greatly affected by the basal effect.This study provides a reference for exploring the single-cell surface elasticity modulus and subsequent study.(4)A single-cell finite element method(FEM)model is established to quantitatively study the effects of the main cellular components on the overall stiffness of cells based on the AFM experimental data.The FEM model is composed of cell membrane,cytoplasm,nucleus,CSK.To verify the rationality of the model,two action sites are chosen according to the AFM experiment,namely the cell center(point of action 1)and the application point closest to the substrate(point of action 4).After the rationality verification of the model,the cell center(point of action 1)is selected to measure the overall stiffness of the single-cell model under compression and to study the effects of IFs on the overall cellular stiffness in the range of small deformation.Parametric analysis is used to determine the main factors affecting the overall cellular stiffness.The results show that IFs have litter contribution to the overall cellular stiffness within small deformation.However,IFs can transfer external forces directly from the cell membrane to the nucleus when the single cell model contains IFs.Parametric analysis shows that both the material properties of CSK and continuum(cell membrane,cytoplasm and nucleus)can affect the overall cellular stiffness.However,CSK is the primary factor determining the overall cellular stiffness.This study provides a new ideas for measuring the mechanical properties of cells and promotes the study of the bio-mechanical properties of single cells.(5)Cell traction forces(CTFs)on the folded microplate are calculated.The folded microplate are simplified into pure curved beams by assuming that the adherent cells are spherical cap,the intracellular microfilaments and the tension of microfilaments are uniformly distributed.The relationships between CTFs and folding angle are obtained according to the relationship between foldingangle and moment.The rationality of the formula obtained in this paper is verified by comparison with the formula between CTFs and folding angle measured by micropillars force sensor array technology.This study provides a new approach for measuring CTFs in three dimensions(3D).(6)The FEM models of cell origami are firstly established based on the tensegrity,and the effects of CSK and NSK on the folding angle of the microplate are qualitatively analyzed.In order to study the effects of the degree of complexity of the tensegrity structure and NSK on the folding angle,four types of tensegrity(12-node CSK,24-node CSK,12-node CSK-NSK and24-node CSK-NSK)are constructed to simulate cell origami.In the FEM model,the folded microplate is assumed to be an isotropic linear-elastic solid with a flexible joint,which is connected with the cell tensegrity structure model by spring elements representing focal adhesion complexes(FACs).The results demonstrate that the increased complexity can reduce the overall stiffness of the tensegrity and lead to a decrease in the folding angle of the microplate,while the inclusion of the NSK can increase the folding angle of the microplate.The proposed models can visually simulate cell origami.This study can provide new ideas for the application of biotechnology and the analysis of the 3D structures of cells and the self-assembly of cell-based medical micro-devices.