Cell traction forces are vital for many biological processes, including angiogen

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 8 pN.

Explanation / Answer

Though, i'm not seeing any diagrams:

I'll be proceeding by some assumptions.

Let K1 = 7.7 pN/nm and K2 = 2 pN/nm are two spring constants in series

So, Equivalent spring constant= Keq = K1K2 / K1+K2 = 7.7*2 / 7.7+2 = 1.5876  pN/nm

So, Total Force ,F = Keq X

then , X = F/Keq = 8pN/1.5876  pN/nm = 5.04 nm

So, Energy stored , U = 1/2 Keq X2 = 0.5*1.5876*25.4 = 20.156 J

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