Available online at http://www.idealibrary.com on doi:10.1006/bulm.2002.0289 Bulletin of Mathematical Biology (2002) 64, 531–563 Motion of Nanobeads Proximate to Plasma Membranes During Single Particle Tracking DAVID M. BRODAY Faculty of Agricultural Engineering, Technion, Israel Institute of Technology, Haifa, 32000, Israel E-mail: dbroday@tx.technion.ac.il Drag and torque on nanobeads translating within the pericellular layer while atta- ched to glycolipids of the plasma membrane are calculated by a novel hydrody- namic model. The model considers a bead that translates proximate to a rigid planar interface that separates two distinct Brinkman media. The hydrodynamic resistance is calculated numerically by a modified boundary integral equation for- mulation, where the pertinent boundary conditions result in a hybrid system of Fredholm integrals of the first and second kinds. The hydrodynamic resistance on the translating bead is calculated for different combinations of the Brinkman screening lengths in the two layers, and for different viscosity ratios. Depending on the bead–membrane separation and on the hydrodynamic properties of both the plasma membrane and the pericellular layer, the drag on the bead may be affected by the properties of the plasma membrane. The Stokes–Einstein relation is applied for calculating the diffusivity of probes (colloidal gold nanobeads attached to gly- colipids) in the plasma membrane. This approach provides an alternative way for the interpretation of in vitro observations during single particle tracking procedure, and predicts new properties of the plasma membrane structure. c  2002 Society for Mathematical Biology. Published by Elsevier Science Ltd. All rights reserved. 1. I NTRODUCTION The slow motion of particles in a porous medium near a confining boundary is a common problem encountered in chemical and biomedical engineering, and in fields such as biomembrane physics (Yechiel and Edidin, 1987; Edidin et al., 1991; Zhang et al., 1991; Janson et al., 1996; Kucik et al., 1999), DNA gel- sequencing (Doktycz et al., 1992), and microcirculation in the perfusing blood vessels (Weinbaum, 1998). For example, in a single particle tracking (SPT) pro- cedure the motion of individual nanobeads, presumably attached firmly to mem- brane glycoproteins or glycolipids, is tracked by a nanovid microscopy technique. Specifically, diffusion coefficients of the complexes are calculated by analyzing video images of trajectories of the beads. This common tool is used to study properties of the plasma membrane (Sheetz et al., 1989; Lee et al., 1993), the structure of the underlying actin cytoskeleton (Sako and Kusumi, 1995; Kusumi 0092-8240/02/030531 + 33 $35.00/0 c  2002 Society for Mathematical Biology. Published by Elsevier Science Ltd. All rights reserved.