A Mechanical Model Of Cytoskeleton Network Based On Form-finding Analysis

Cells are the basic unit of life. Living cells possess special structureand mechanical properties to undergo internal and external mechanicalstimuli. Research has shown that the change of cell structure andmechanical properties not only result in the cell morphology change, butalso lead to physiological dysfunction. Although the transmissionmechanism between mechanical force and biological signal in living cellsis still not clear, as primary task, the study of the responses of cells undermechanical force is of great importance. Therefore, it becomes a focalpoint in biomechanics to find out the cell structure, establish and improvethe mechanical models of cells.In this paper, a new cell mechanical model, form-finding model, isproposed based on the form-finding analysis, which is widely used in thedesigning of flexible structures, such as membrane structure and cablenetwork. Form-finding model simulate the structure morphology andmechanical characteristics of the network of actin filaments cross-linkedby actin cross-linking proteins. Actin filaments and cross-linking proteinsin form-finding model are modeled as beam and cable respectively, whoseinput parameters such as relative density, length and mechanical properties,are from the experiment data. The elements in form-finding model aregenerated by stochastic simulation method and the final shape is achievedafter form-finding analysis. The form-finding analysis is carried outthrough several equilibrium iterations after pre-stressed in cross-linkers.The form-finding model is not only similar to real cell cytoskeleton inmorphology, but also simulates the stress-strain relationship of cellcytoskeleton properly. Moreover, it can explain many cell experimental observations. The main research work using form-finding model coveredin this paper as follows:(1) The elastic modulus was predicted. The average elastic moduluscomputed by form-finding model is on the order of103Pa, that isconsistence with most cell experiment results.(2) The effects of relative density of actin filament, filament lengthand relative density of cross-links on cell stiffness were studied. Thestatistical results of a number of models show that relative density offilaments and cross-links positively correlated with cytoskeletal stiffness,and the relation is approximately linear. The average elastic modulus ofcytoskeleton is proportional to the length of actin filament. As the length ofactin filament increases, the elastic modulus approaches to a constant valuebecause of the limit of the size of model.(3) The mechanical property of network comprised of cross-linkedfilaments and filament bundles was explored. The results show thatparallel bundles in the extension direction can significantly increase cellrigidity and improve the ability of cells to resist external forces. As therelative density of filament bundles increases, the cell stiffness will have amaximum value, when the content of filaments is fixed in a model. Incontrast, randomly distributed bundles are of no effect on increasing cellstiffness.(4) Three-dimensional form-finding model was established based onthe planar model. The effects of actin filaments, cross-links and filamentbundles on cell stiffness were restudied. The computational results ofthree-dimensional model are in consistence with the planar model, thatindicates the form-finding model is capable to simulate the three-dimensional cellular cytoskeleton.