Biophys J, July 2001, p. 25-42, Vol. 81, No. 1

Diffusion of Microspheres in Shear Flow Near a Wall: Use to Measure Binding Rates between Attached Molecules

Anne Pierres,^* Anne-Marie Benoliel,^* Cheng Zhu, and Pierre Bongrand^*

 ^*Laboratoire d'Immunologie, Hôpital de Sainte-Marguerite, 13274 Marseille Cedex 09, France and  George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 USA

The rate and distance-dependence of association between surface-attached molecules may be determined by monitoring the motion of receptor-bearing spheres along ligand-coated surfaces in a flow chamber (Pierres et al., Proc. Natl. Acad. Sci. U.S.A. 95:9256-9261, 1998). Particle arrests reveal bond formation, and the particle-to-surface distance may be estimated from the ratio between the velocity and the wall shear rate. However, several problems are raised. First, data interpretation requires extensive computer simulations. Second, the relevance of standard results from fluid mechanics to micrometer-size particles separated from surfaces by nanometer distances is not fully demonstrated. Third, the wall shear rate must be known with high accuracy. Here we present a simple derivation of an algorithm permitting one to simulate the motion of spheres near a plane in shear flow. We check that theoretical predictions are consistent with the experimental dependence of motion on medium viscosity or particle size, and the requirement for equilibrium particle height distribution to follow Boltzman's law. The determination of the statistical relationship between particle velocity and acceleration allows one to derive the wall shear rate with 1-s¹ accuracy and the Hamaker constant of interaction between the particle and the wall with a sensitivity better than 10²¹ J. It is demonstrated that the correlation between particle height and mean velocity during a time interval t is maximal when t is about 0.1-0.2 s for a particle of 1.4-µm radius. When the particle-to-surface distance ranges between 10 and 40 nm, the particle height distribution may be obtained with a standard deviation ranging between 8 and 25 nm, provided the average velocity during a 160-ms period of time is determined with 10% accuracy. It is concluded that the flow chamber allows one to detect the formation of individual bonds with a minimal lifetime of 40 ms in presence of a disruptive force of ~5 pN and to assess the distance dependence within the tens of nanometer range.

Biophys J, July 2001, p. 25-42, Vol. 81, No. 1
© 2001 by the Biophysical Society   0006-3495/01/07/25/18  $2.00

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