Scale-invariance in miniature coarse-grained red blood cells by fluctuation analysis

To accurately represent the morphological and elastic properties of a human red blood cell, Fu et al. [Fu et al., Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS, 2017, 210, 193-203] recently developed a coarse-grained molecular dynamics model with particular detail in the membrane. However, such a model accrues an extremely high computational cost for whole-cell simulation when assuming an appropriate length scaling - that of the bilayer thickness. To date, the model has only simulated "miniature" cells in order to circumvent this, with the a priori assumption that these miniaturised cells correctly represent their full-sized counterparts. The present work assesses the validity of this approach, by testing the scale invariance of the model through simulating cells of various diameters; first qualitatively in their shape evolution, then quantitatively by measuring their bending rigidity through fluctuation analysis. Cells of diameter of at least 0.5 μm were able to form the characteristic biconcave shape of human red blood cells, though smaller cells instead equilibrated to bowl-shaped stomatocytes. Thermal fluctuation analysis showed the bending rigidity to be constant over all cell sizes tested, and consistent between measurements on the whole-cell and on a planar section of bilayer. This is as expected from the theory on both counts. Therefore, we confirm that the evaluated model is a good representation of a full-size RBC when the model diameter is ≥0.5 μm, in terms of the morphological and mechanical properties investigated.