Mechanism Behind the Beauty: The Golden Ratio Appeared in the Shape of Red Blood Cells (Communications in Computational Physics, 2018)
In the past two decades, a rigorous solution for the shape of human redblood cell (RBC) with a negative spontaneous curvature $c_0$ has been derived with theHelfrich model under the condition that both the osmotic pressure ∆$p$ and tensile stress $λ$ are equal to zero. By fitting the experimentally observed shape of RBC, $c_0$$R_0$ has beenpredicted to be −1.62, the minus golden ratio, where $R_0$ is the radius of a sphere whichhas the same surface area as RBC. In this paper, we verify this prediction by comparingexperimental data with an analytical equation describing the relation between volumeand surface area. Furthermore, it is also found $ρ$max /$ρ_B$ ≈ 1.6 with $ρ$max the maximalradius and $ρ_B$ the characteristic radius of RBC, showing an approximate beautifulgolden cross section of RBC. On the basis of a complete numerical calculation, wepropose a mechanism behind the beauty of the minus golden ratio that $c_0$$R_0$ resultsfrom the balance between the minimization of the surface area and the requirementof adequate deformability of RBC to allow it passing through the spleen, the so called"physical fitness test".