Mean first passage times for bond formation for a Brownian particle in linear shear flow above a wall

Korn, Christian; Schwarz, Ulrich S.

doi:10.1063/1.2464080

Cited by 29 publications

(64 citation statements)

References 41 publications

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“…Cell deformations in free flow should become relevant only at shear rates well above 100 Hz [22]. In adhesion, cell deformation depends also on the number and strength of adhesion bonds.…”

Section: Discussionmentioning

confidence: 99%

“…A more detailed description of our algorithm is given in Refs. [22,37]. In order to obtain accurate results when simulating the motion of the sphere it is essential to properly calculate the mobility matrix M and the shear force F S .…”

Section: A Stokesian Dynamicsmentioning

confidence: 99%

“…Using this approach, we were able to predict the efficiency of initiating cell adhesion in shear flow as a function of the density and geometry of the receptor and ligand patches [21,22]. A large modeling effort has also been spent on the role of cell deformability [23,24,25,26,27] and the interaction between multiple particles [27,28,29].…”

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Dynamic states of cells adhering in shear flow: From slipping to rolling

2008

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Motivated by rolling adhesion of white blood cells in the vasculature, we study how cells move in linear shear flow above a wall to which they can adhere via specific receptor-ligand bonds. Our We also investigate the effect of non-molecular parameters. In particular, we find that an increase in viscosity of the medium leads to a characteristic expansion of the region of stable rolling to the expense of the region of firm adhesion, but not to the expense of the regions of free or transient motion. Our results can be used in an inverse approach to determine single bond parameters from flow chamber data on rolling adhesion.

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“…Cell deformations in free flow should become relevant only at shear rates well above 100 Hz [22]. In adhesion, cell deformation depends also on the number and strength of adhesion bonds.…”

Section: Discussionmentioning

confidence: 99%

Section: A Stokesian Dynamicsmentioning

confidence: 99%

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Dynamic states of cells adhering in shear flow: From slipping to rolling

2008

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“…The efficiency with which cells or beads in flow can bind to a substrate depends crucially on the spatial distribution of receptors and ligands [12]. Previously, we proposed a model based on a Langevin equation for a spherical particle in linear shear flow above a wall which allows to numerically compute MFPTs for different ligand and receptor distributions and flow parameters both for two-dimensional (2D) and three-dimensional (3D) movements [7,13]. Due to the complex geometry arising from the receptor and p-1 ligand distributions and the complexity of the positiondependent mobility functions arising from the hydrodynamic equations, exact analytic results for the MFPT cannot be obtained in this general case.…”

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confidence: 99%

Mean encounter times for cell adhesion in hydrodynamic flow: Analytical progress by dimensional reduction

Korn

Schwarz

2008

Europhys. Lett.

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in biological systems PACS 47.15.G--fluid dynamics, low-Reynolds-number flows PACS 05.10.Gg -stochastic analysis methods (FokkerPlanck, Langevin, etc.) Abstract. -For a cell moving in hydrodynamic flow above a wall, translational and rotational degrees of freedom are coupled by the Stokes equation. In addition, there is a close coupling of convection and diffusion due to the position-dependent mobility. These couplings render calculation of the mean encounter time between cell surface receptors and ligands on the substrate very difficult. Here we show for a two-dimensional model system how analytical progress can be achieved by treating motion in the vertical direction by an effective reaction term in the mean first passage time equation for the rotational degree of freedom. The strength of this reaction term can either be estimated from equilibrium considerations or used as a fit parameter. Our analytical results are confirmed by computer simulations and allow to assess the relative roles of convection and diffusion for different scaling regimes of interest.Introduction. -Biological function is often based on the formation of a specific binding complex between receptor and ligand [1]. However, in order for binding to occur, a physical transport process must exist which brings the binding partners to sufficiently close proximity [2]. In many cases of interest, this transport process is rather complex. Usually it contains several coupled degrees of freedom, like a cell surface receptor moving laterally on a membrane which fluctuates in the vertical direction [3]. The efficiency of biological transport processes often can be framed as mean first passage time (MFPT) problems, for example for the gating of ion channels [4] or the arrival of a virus at the nucleus [5]. Another example of a complex transport process of large biological relevance is the receptor-mediated adhesion of cells which are carried over a ligand-coated substrate by hydrodynamic flow [6]. Here the mean encounter time between receptors and ligands is a measure for the efficiency of cell adhesion under the conditions of hydrodynamic flow [7]. For this system, additional complications arise from the presence of multiple length scales. For the micron-sized cell, the hydrodynamic equations result in coupling of the translational and rotational degrees of freedom. Even for high shear rates, Brownian motion is relevant because receptors and ligands are nanometer-sized objects, thus even small movements for the cell result in a large effect on the molecular level.

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“…These require an additional Brownian equation of motion for the orientation of the symmetry axis of the rod, while the rotations around this axis are ignored. The rotations of anisotropic colloids, which represent the most generalised class of rigid particles, is more difficult to simulate by the Brownian Dynamics approach and has hardly been explored in the literature [41,78,84,101,127,135,140,169,171]. One difficulty arises from the degeneracy, and the resulting strong singularities in the equation of motion, attached to the commonly used rotational coordinate systems, such as the Euler angles [74].…”

Section: Introductionmentioning

confidence: 99%

Chameleon behaviour of a-synuclein : brownian dynamics simulations of protein aggregation

Ilie

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Mean first passage times for bond formation for a Brownian particle in linear shear flow above a wall

Cited by 29 publications

References 41 publications

Dynamic states of cells adhering in shear flow: From slipping to rolling

Dynamic states of cells adhering in shear flow: From slipping to rolling

Mean encounter times for cell adhesion in hydrodynamic flow: Analytical progress by dimensional reduction

Chameleon behaviour of a-synuclein : brownian dynamics simulations of protein aggregation

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