Effect of divalent cations on the adhesion rate of cellular surfaces with ionizable groups

The adhesion rate of cells under charge regulation onto a rotating disc with constant potential is investigated theoretically in this paper. In particular, the effect of the presence of divalent carions in the suspension medium on adhesion rate of cells is discussed. By using sheep leucocytes as an illustrative example, it is shown that the presence of divalent cations in the suspension medium has the effect of decreasing the adhesion rate of cells. At a fixed level of ionic strength, the adhesion rate decreases with the increase of the concentration of divalent cations in the suspension medium for the various values of Peclet number andAd parameter given in this paper. For a fixed concentration of cations, the adhesion rate increases with the increase of ionic strength. At high ionic strength, the effect of increasing the concentration of cations on decreasing the adhesion rate of cells is not as high as that at low ionic strength. Applying the concept of Donnan potential, it is found that the magnitude of the electrostatic force between an ion-penetrable cell membrane and a solid surface is much smaller than that for the ion-impenetrable cell membrane.Nomenclature a cell radius (cm) - A Hamaker's constant (erg) - Ad A/kT - C dimensionless cell concentration - D cell diffusion coefficient (cm²/s) - e magnitude of electron charge (statcoul) - F dimensionless interaction force between cell and rotating disc pernkT - h minimum separation distance between cell surface and disc surface (cm) - H dimensionless separation distance between cell surface and disc surfaceh/a - H ⁺] _r hydrogen ion concentration in the suspension medium (mole dm^–3) - H ⁺] _s hydrogen ion concentration on the cell surface (mole dm^–3) - Boltzmann's constant (erg K^–1) - K _a dissociation equilibrium constant for acid groups on cell surface (mole dm^–3) - K _b dissociation equilibrium constant for base groups on cell surface (mole dm^–3) - n ionic strength in the suspension medium (ions cm^–3 - Pe Peclet number - q valence of cations - Sa the reciprocal of acidic density on the cell surface (cm²/group) - S _b the reciprocal of basic density on the cell surface (cm²/group) - Sh Sherwood number - T absolute temperature (K) - the fraction of cationic electrolyte in the suspension medium, 01 - reciprocal of Debye length, (cm^–1) - fluid kinematic viscosity (cm²/s) - ×a - l distance between two plate surfaces in Derjuguin's model (cm) - dimensionless total interaction energy between cell surface and disc surface - _vdw dimensionless unretarded van der Waals potential between cell surface and disc surface - _DL dimensionless double-layer interaction potential between cell surface and disc surface - dimensionless electrostatic potential between cell surface and disc surface - rotating speed of the disc (rad/s)