Interaction forces between red cells agglutinated by antibody. I. Theoretical

Abstract

A general method of calculating forces, torques, and translational and rotational velocities of rigid, neutrally buoyant spheres suspended in viscous liquids undergoing a uniform shear flow has been given by Arp and Mason (1977). The method is based on the matrix formulation of hydrodynamic resistances in creeping flow by Brenner and O'Neill (1972). We describe the solution of the Brenner-O'Neill force-torque vector equation in terms of the particle and external flow field coordinates and derive expressions for the normal force acting along, and the shear force acting perpendicular to, the axis of the doublet of spheres, the latter explicitly given for the first time. The equations consist of a term comprising force and torque coefficients obtained from the matrices of the hydrodynamic resistances (functions of the distance h between sphere surfaces which have been computed), and terms comprising the orientation of the doublet axis relative to the coordinates of the external flow field and the shear stress (which can be experimentally determined). We have applied the theory to a system of doublets of sphered, hardened human red cells of group A or B antigenic type cross-linked by the corresponding antibody at a fixed interparticle distance. Working from studies of the breakup of doublets of red cells in an accelerating Poiseuille flow, given in the succeeding paper, we are able to compute the hydrodynamic force required to separate the two spheres. Previous work has shown that the theory can be applied to doublets in a variable shear, Poiseuille flow, provided the ratio of particle to tube diameter is small. In calculating the force-torque coefficients it was assumed that the cells are crosslinked by antibody with h = 20 nm.

Probabilistic Modeling of Platelet Aggregation: Effects of Activation Time and Receptor Occupancy

“…In future studies of platelet aggregation, the progression of the reaction between solution fibrinogen and gpIIb-IIIa should be considered. Tha & Goldsmith (1986 When the normal force is negative, the hydrodynamic forces are acting to move the particles closer together. Assuming that crossbridges need not counter this compressive force, the force experienced by cross-bridges between the doublet is…”

“…During the collision, the force acting on the bonds changes as the particles move relative to each other. Tha & Goldsmith (1986) derive expressions for the fluid force acting on two equal-sized spherical particles as a function of their size, their relative positions, the viscosity of the fluid, and the shear rate. For platelets of radius 1:4 mm; a viscosity of 1:3 cP; and a shear rate of 300 s À1 the maximum magnitude of the force on a bond is about 14:7 pN; and the mean, taken over all configurations, is 5:3 pN; ignoring compression.…”

United States Air Force Summer Research Program -- 1995. High School Apprenticeship Program Final Reports. Volume 12A. Armstrong Laboratory

“…Adhesion strength is defined as the minimum force needed to separate bound cells. Tha and Goldsmith (1988) report that the force required to separate red blood cell doublets is approximately 1.43 nano-Newtons (nN). In addition, Bell (1978) suggests that the force per bond is 0.04 nN.…”

Characterization of Antibodies against Human Red Blood Cell Antigens with a Rheo-Optical Approach

“…With this technique, they measured the force required to disrupt two erythrocytes that were agglutinated. Tees et al [14] and Tha et al [15,16] described a method to measure hydrodynamic forces to separate doublets of fixed swollen erythrocytes adhered by specific antibodies. Optical methods have been also developed to study cell aggregation because transmitted or scattered light intensity depends on the scattering area of particles in suspension and, consequently, on the level of adhesion.…”