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Mechano-chemical interaction is very common in many important biological processes,such as cell division,differentiation and migration.Cell migration plays a big role in a series of biological phenomena,such as embryonic development,wound healing and cancer metastasis.During cell migration,it first polarizes,i.e.,the cell goes to a state with an asymmetric distribution of specific molecules and organelles along a geometric axis(front to back)in morphology,then it deforms to form protrusion,adheres to the substrate,moves the main body and finally releases the attachments of rear end [1].This process involves cytoskeleton,surface receptors and polarity proteins.Besides chemical factors,physical factors,such as topography and rigidity of substrate [2],collisions between cells [3],and fluid shear stress,influence the cell migration process.Usually,the chemical system is coupled with mechanical factors in this process,but most existing mathematical models only focus on the chemical process or physical process.Considering that membrane tension has been shown to act as a long-range inhibitor of cell polarization [4],we had previously proposed a cell polarization model incorporating the interplay between Rac GTPase,filamentous actin(F-actin),and cell membrane tension [5].This model is the first to recapitulate the experimental results described by Houk et al.,revealing that aspiration(elevation of tension)and release(reduction of tension)result in a decrease in and recovery of the activity of Rac-GTP,respectively,and that the relaxation of tension induces new polarity of the cell body when a cell with the pseudopod-neck-body morphology is severed.However,other experiments suggest that elevation of tension could enhance cell polarity to a certain extent,and then enhance the migration ability [6].Therefore,the role of tension in the regulation of cell migration may not be monotonic.Here,we further develop our cell polarization model to describe cell deformation and migration by introducing Myosin and protrusion force.In the present of noise,our simulations successfully recapitulate the random and persistent migration.On the other hand,we use a wide field fluorescence microscope to measure the deformation,movement and intracellular PI3K signaling of MDA-MB-231 cells and MCF7 cells that are free to move in the two-dimensional environment when cell tension is adjusted by changing osmotic pressure of solution or adding deoxycholate.The preliminary results suggest that higher cell tension leads to slower migration.The understanding of mechano-chemical mechanism for cell polarity and deformation during cell migration will facilitate developing new therapeutic strategy against tumor metastasis by targeting the signaling of the membrane tension modulation of tumor cells.