Two-dimensional numerical study of flow dynamics of a nucleated cell tethered under shear flow

• We developed a model to study the dynamics of a nucleated cell tethered under flow.
• Properties of nucleus significantly affect the flow dynamics of tethered cells.
• Presence of nucleus leads to leukocyte tether dynamics different from platelets.
• Varied internal viscosity leads to the variation in tether dynamics of leukocytes.

When blood components (e.g., leukocytes and platelets) adhere to a surface (e.g., blood vessel wall), shear flow causes the elongation of the non-adherent part of the cell membrane forming a long thin cylinder shape (i.e., cell tether). The formation of cell tether is important for regulation of cell adhesion strength and stabilization of cell rolling, and may significantly affect the flow dynamics inside the vessel, as well as the motion of other cells and bioactive molecules. Although significant efforts have been made to reveal mechanisms underlying cell tether formation, the role of nucleus, nucleus/cell volume ratio, nucleus/plasma viscosity ratio and cytoplasm/plasma viscosity ratio remains unknown. As such, we developed a two-dimensional mathematical model, in which leukocytes are regarded as compound viscoelastic capsules with a nucleus. We investigated the effects of several factors on flow dynamic characteristics of tethered cells, including the cell length, the inclination angle, the drag and lift forces acting on the cell. The presence of a nucleus (with nucleus/cell volume ratio of 0.44) led to a decrease of 33.8% in the cell length and an increase of 152%, 113% and 43.6% in the inclination angle, the drag force and lift force respectively compared to those of a cell without nucleus. For a cell with nucleus/cell volume ratio of 0.2, a 10-fold increase in cytoplasm/plasma viscosity ratio resulted in a decrease of 19.3% in the cell length and an increase of 93.9%, 155% and 131% in the inclination angle, the drag force and lift force respectively. These results indicate that nucleus and cytoplasm play a significant role in flow dynamics of nucleated cells tethered under shear flow. The developed mathematical model could be used to further understand the mechanisms of cell-adhesion related bioprocesses and to optimize the conditions for cell manipulation in microfluidics.