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".