S4 in the Supporting Material)

S4 in the Supporting Material).Assumption 3. the duration of ligand-receptor contacts imposed by the bead movement. We quantitatively predict the reduction of adhesion probability measured for shorter tether length of the ligand or if a repulsive hyaluronan layer is added onto the surface. To account for our results, we propose that bond formation may occur in our system by crossing of a diffusive plateau in the energy landscape, around the timescale of 5?ms and an energy barrier of 5 as may be required to form a bond, writing the binding probability (14) as for binding. In contrast, a binding efficiency proportional to the ML241 encounter duration, as classically assumed for soluble molecules by the use of on-rate and in presence of adsorbed hyaluronan molecules acting as a repulsive layer. (was estimated to vary between 60 and 76?nm in ML241 DL configuration (three antibodies?+ Fc-ICAM-1) (14) and between 44 and 60?nm for the SL configuration (two antibodies?+ Fc-ICAM-1) (Fig.?1). Additionally, antibody molecules possess a central hinge allowing full rotation between the Fab and the Fc fragments, which are themselves relatively rigid (20); rotation is also possible between the Fc tag and the ICAM-1 fragment of the chimera (see the Supporting Material). Measurements of single-molecule mediated bead arrests in circulation The frequency of arrests was measured using a circulation chamber as already explained in the literature (14,19). The shear rate was varied between 10 and 85 s?1. Briefly, beads carried by the circulation were observed on a fixed field of view under the microscope at 20 magnification. Images were recorded with 20-ms time resolution. A bead was considered as arrested if its position did not switch by more than was obtained with the correction C 2is the most probable velocity of the beads (19). The detachment curve was built by plotting the portion of arrests exceeding the duration as a function of the gap between the bead and the wall. Numerical simulation The goal of the simulation is usually to determine the number and duration of encounters between the reactive site of individual receptors immobilized around the microbeads’ surface and the reactive site of individual ligands immobilized around the circulation chamber floor surface, according to our experimental situation (Fig.?1 move in a low Reynolds shear flow which obeys Navier-Stokes equations in their linear approximation. Movements in each spatial direction (vertical perpendicular or parallel to the circulation) are then uncoupled. The wall boundary condition around the circulation contributes as an additional friction TPOR pressure that slows down the movement of the bead at the vicinity of the wall (23). Translational invariance along the horizontal directions, combined with the absence of coupling between the spatial directions, limits the contribution of the wall to an altitude dependence. We compute the displacement of the bead by including the convective pressure of the fluid around the bead, between the bead and the wall in absence of ligands, given by ? 0.43 (23,24). We therefore focus on the calculation of the velocity of the center of mass of the bead, by its expression from Newton’s law, Eq. 1, the velocity of the center of mass of a hard sphere of radius reads (16,25) is the shear rate. The wall imposes an additional friction (23) accounted for by a damping of the diffusion coefficients, the gap between the wall and the bead. is the altitude-dependent correction to the shear velocity that originates from the increased friction of the bead near the wall. Writing the medium viscosity, one has the approximate formulas (24) the altitude-dependent prefactor of the stochastic terms in Eq. 2 should be calculated for its integration, leading to a nonunique result (26). A mathematical definition of the integration rule of Eq. 2 must be specified, and its relevance evaluated in the present physical context, for instance, by looking at the calculated vertical bead distribution under sedimentation. Here, we choose to work in the frame of ML241 the Stratonovitch interpretation, which consists of evaluating the stochastic space-dependent terms at time and (26). This integration rule indeed accounts for a Boltzmann sedimentation profile for the beads above a wall (16). The numerical integration of Eq. 2 is performed using the Euler algorithm at first order. This algorithm assumes that.