Question

Cell traction forces are vital for many biological processes, including angiogenesis, inflammation, wound healing, and metastasis. The study of cell traction forces enables us to better understand the mechanisms of these biological processes at the cellular and molecular levels. A two-spring model has been successfully applied to capture the impact of cell type and substrate stiffness on cell traction. The first spring constant represents extracellular elasticity as perceived by the cell through the focal adhesion site. The second spring constant represents the mechanical properties of the intracellular structure. This model can be used to explain how some cell types tend to spread more efficiently on stiff substrates and the dependence of cell spreading on cell type. In the diagram, the arrows represent actin tensions with a spring constant of 7.7 pN/nm and the springs represent the extracellular elasticity with a spring constant of 2 pN/nm (these springs can be considered in series). Calculate the energy stored in a cellular interaction corresponding to a total applied force of 5 pN.

Answer 1

a) if the springs are in parallel arrange

Keq= K1+K2= 7.7 + 2= 9.7

F=-kx

x=-F/k= -5/9.7= -0.515

E= 1/2 * k*x ^2= (0,5)(9.7) (-0,515)^2= 1,28

a) if the springs are in serie arrange

Keq= 1/K1+1/K2= 1/7.7 + 1/2= 0.62

F=-kx

x=-F/k= -5/0.62= -7.9

E= 1/2 * k*x ^2= (0,5)(0.62) (-7.9)^2= 19.3