Tethered cells in fluid flows—beyond the Stokes' drag force approach

Johan Zakrisson, Krister Wiklund, Ove Axner and Magnus Andersson

Simulations of tethered cells in viscous sub-layers are frequently performed using the Stokes' drag force, but without taking into account contributions from surface corrections, lift forces, buoyancy, the Basset force, the cells' finite inertia, or added mass. In this work, we investigate to what extent such contributions, under a variety of hydrodynamic conditions, influence the force at the anchor point of a tethered cell and the survival probability of a bacterium that is attached to a host by either a slip or a catch bond via a tether with a few different biomechanical properties. We show that a consequence of not including some of these contributions is that the force to which a bond is exposed can be significantly underestimated; in general by ~32–46%, where the influence of the surface corrections dominate (the parallel and normal correction coefficients contribute ~5–8 or ~23–26%, respectively). The Basset force is a major contributor, up to 20%, for larger cells and shear rates. The lift force and inertia contribute when cells with radii >3 μm have shear rates >2000 s−1. Buoyancy contributes significantly for cells with radii >3 μm for shear rates <10 s−1. Since the lifetime of a bond depends strongly on the force, both the level of approximation and the biomechanical model of the tether significantly affect the survival probability of tethered bacteria. For a cell attached by a FimH–mannose bond and an extendable tether with a shear rate of 3000 s−1, neglecting the surface correction coefficients or the Basset force can imply that the survival probability is overestimated by more than an order of magnitude. This work thus shows that in order to quantitatively assess bacterial attachment forces and survival probabilities, both the fluid forces and the tether properties need to be modeled accurately.

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