Effect of cell and microvillus mechanics on the transmission of applied loads to single bonds in dynamic force spectroscopy

COMPUTATIONAL DETERMINATION OF THE DETACHMENT TIME OF THE LEUKOCYTE UNDER DIFFERENT KINETIC DISSOCIATION RATE PARAMETERS

Three-dimensional simulation of the leukocyte detachment subjected to blood flow is presented. The initially captured leukocyte is modeled as a sphere adhered to the bottom wall of a cylindrical vessel via receptor/ligand bonds (P-selectin/PSGL-1). Ansys Parametric Design Language is used to create the geometrical model and couple the Navier–Stokes flow solver with structural equations and the Monte Carlo equation to define the stochastic breakage of the bonds. The assumption of equal forces on bonds has been ignored and the force on each bond is obtained from the balance between hydrodynamic forces and cellular viscoelasticity at every time step. In this model, catch-slip behavior of the P-selectin/PSGL-1 is considered by using the two-pathway dissociation model instead of the Bell model to define the rate of dissociation of each bond. Detachment time of the leukocyte is the time elapsed until all the bonds break. The effects of various values of blood inlet velocities, bond stiffness and kinetic properties of the catch bonds on the detachment time of the leukocyte are studied.

Yielding elastic tethers stabilize robust cell adhesion

Many bacteria and eukaryotic cells express adhesive proteins at the end of tethers that elongate reversibly at constant or near constant force, which we refer to as yielding elasticity. Here we address the function of yielding elastic adhesive tethers with Escherichia coli bacteria as a model for cell adhesion, using a combination of experiments and simulations. The adhesive bond kinetics and tether elasticity was modeled in the simulations with realistic biophysical models that were fit to new and previously published single molecule force spectroscopy data. The simulations were validated by comparison to experiments measuring the adhesive behavior of E. coli in flowing fluid. Analysis of the simulations demonstrated that yielding elasticity is required for the bacteria to remain bound in high and variable flow conditions, because it allows the force to be distributed evenly between multiple bonds. In contrast, strain-hardening and linear elastic tethers concentrate force on the most vulnerable bonds, which leads to failure of the entire adhesive contact. Load distribution is especially important to noncovalent receptor-ligand bonds, because they become exponentially shorter lived at higher force above a critical force, even if they form catch bonds. The advantage of yielding is likely to extend to any blood cells or pathogens adhering in flow, or to any situation where bonds are stretched unequally due to surface roughness, unequal native bond lengths, or conditions that act to unzip the bonds.

Cells adhere to surfaces and each other in the presence of forces that would easily overpower the individual noncovalent receptor-ligand bonds that mediate this adhesion, raising the question as to how these bonds cooperate to withstand such high forces. Here we show that cooperation and robust adhesion depends on the elastic properties of the bonds. A type of nonlinear elasticity referred to as elastic yielding ensures that the total force is distributed equally across the individual bonds regardless of geometry. In contrast, with linear or strain-hardening elasticity, the bonds that are stretched the most are exposed to higher forces, which cause them to fail sequentially. This work explains why elastic yielding is found in structurally and evolutionarily diverse adhesive complexes.

Rupture of single receptor-ligand bonds: a new insight into probability distribution function

Single molecule force spectroscopy is widely used to determine kinetic parameters of dissociation by analyzing bond rupture data obtained via applying mechanical force to cells, capsules, and beads that are attached to an intermolecular bond. The current analysis assumes that the intermolecular bond force is equal to the externally applied mechanical force. We confirm that viscous drag alone or in combination with cellular deformation resulting in viscoelasticity modulates bond force so that the instantaneous intermolecular bond force is not equivalent to the applied force. The bond force modulation leads to bond rupture time and force histograms that differ from those predicted by probability distribution function (PDF) using the current approach. A new methodology that accounts for bond force modulation in obtaining PDF is presented. The predicted histograms from the new methodology are in excellent agreement with the respective histograms obtained from Monte Carlo simulation.

Effect of viscoelasticity on the analysis of single-molecule force spectroscopy on live cells

Single-molecule force spectroscopy is used to probe the kinetics of receptor-ligand bonds by applying mechanical forces to an intermediate media on which the molecules reside. When this intermediate media is a live cell, the viscoelastic properties can affect the calculation of rate constants. We theoretically investigate the effect of media viscoelasticity on the common assumption that the bond force is equal to the instantaneous applied force. Dynamic force spectroscopy is simulated between two cells of varying micromechanical properties adhered by a single bond with a constant kinetic off-rate. We show that cell and microvilli deformation, and hydrodynamic drag contribute to bond forces that can be 28-90% lower than the applied force for loading rates of 10(3)-10(7) pN/s, resulting in longer bond lifetimes. These longer bond lifetimes are not caused by changes in bond kinetics; rather, they are due to the mechanical response of the intermediate media on which the bonds reside. Under the assumption that the instantaneous bond force is equal to the applied force--thereby ignoring viscoelasticity--leads to 14-39% error in the determination of off-rates. We present an approach that incorporates viscoelastic properties in calculating the instantaneous bond force and kinetic dissociation parameter of the intermolecular bond.

Effect of viscous drag on multiple receptor-ligand bonds rupture force

Monte Carlo simulation of the rupture of multiple receptor-ligand bonds between two PMN cells suspended in a Newtonian fluid is performed. We demonstrate via micro-mechanical model of two cells adhered by multiple receptor-ligand bonds that viscous drag caused by relative motion of cell suspended in a Newtonian fluid modulates transmission of an applied external load to bonds. Specifically, it is demonstrated that at any time the intermolecular bond force is not equivalent to the instantaneous applied force. The difference in the instantaneous applied force and the intermolecular bond force depends on the viscosity of fluid, the size of cell, the applied loading rate, and the number of bonds at any instant of time. Viscous drag acting on cell reduces average bond rupture forces.

A theoretical method to determine unstressed off-rate from multiple bond force spectroscopy

Using dynamic force spectroscopy to measure the kinetic off-rates of intermolecular bonds currently requires the isolation of single molecules. This requirement arises in part because no tractable analytic method for determining kinetic off-rates from the rupture of a large number of bonds under dynamic forces is currently available. We introduce a novel method for determining the unstressed off-rate from dynamic force spectroscopy experiments involving a large number of bonds. Using both the Bell and Dembo models we show that the unstressed off-rate calculated using the proposed method is in good agreement with the prescribed unstressed off-rate used in Monte-Carlo simulations of multiple bond dynamic force spectroscopy experiments given initial number of bonds (50-500) and loading rate 10(3)-10(6)pN/s.