Competing aggregation and iso-density equilibrium lead to band pattern formation in density gradients

Abstract: Centrifugation of biological matter in density gradient solutions is a standard method for separating cell types or components. It is also used to separate red blood cells (RBCs) by age, as they lose water and become denser over their lifespan. When the density gradient is prepared with Percoll, discrete bands of RBCs are systematically observed along the gradient, despite the continuous density distribution of RBCs. Early studies suggested that cell aggregation might influence spatial distribution, but it remains debated whether a continuous density population can form discrete bands. We developed a continuity equation incorporating cell aggregation to describe the macroscopic evolution of RBC volume fraction in a density gradient, considering a continuous RBC density distribution. Numerical solutions demonstrate that the competition between isodensity distribution and aggregation is sufficient to create band patterns. Our model reproduces the temporal evolution observed in experiments, but also predicts several types of bifurcation-like behaviors for the steady-state patterns in constant gradients, depending on RBC volume fraction and aggregation energy. This demonstrates that the competition between RBC aggregation and iso-density distribution is a novel mechanism driving pattern formation.