The Mechanism Behind Beauty: Golden Ratio Appears in Red Blood Cell Shape

Abstract

In the past two decades, under the conditions that both the osmotic pressure $\Delta p$ and tensile stress $\lambda$ equal zero, a rigorous solution (RS) of human red blood cell (RBC) with a minus spontaneous curvature $c_0$ has been derived with Helfrich model. And, by fitting with observed shapes of RBC, $c_0{R}_0$ has been predicted to be -1.62 as minus golden ratio, where $R_0$ is the radius of a sphere with the same area of RBC. In this Lett., it is also found ${\rho }_{max}$ /${\rho }_B\approx$ 1.6 shows a approximately beautiful golden cross section of RBC, where ${\rho }_{max}$ is the radius of RBC and ${\rho }_B$ is the radius at maximal thickness of RBC. With a complete numerical calculation, we find the mechanism behind the beauty that minus golden ratio of $c_0{R}_0$ is the balance between economical surface area and enough deformability to pass spleen, the so called "physical fitness test".

4pages, 5figures