(226c) Hydrodynamic Interactions during AFM Imaging of Biological Cells: Can AFM Truly Resolve Lipid Membrane Position?

We investigate physical processes taking place during the atomic force microscope (AFM) imaging of soft biological membranes in liquid environment. Mechanical properties of the cell membranes are typically deduced by generating an applied force versus distance curve as the AFM tip scans the surface, and then fitting the experimental results into a simple Hertz model for the maximum distance between two elastically deformed surfaces. It is well established that due to softness of the cellular membrane its position cannot be resolved accurately by traditional methods of AFM imaging of living cells. The AFM image shows not the true position of a cell membrane (i.e., to define cell topology) but rather its underlying rigid structures such as cytoskeleton or organelles. An ability to accurate predict the membrane position and measure local properties of living cell would enable investigations into biochemistry of membrane processes and surface distributions of membrane proteins and structures. In other words, a significant question is whether or not the AFM can ever see the cell membrane, and if yes, then under what conditions? Recent progress in the field of AFM instrumentation brought to life a new generation of sensors with much higher sensitivity, dynamic range, and capable of measuring AFM forces and tip displacement independently(1). With this in mind, the aim of our work is to theoretically consider the possibility of accurate cell membrane imaging by AFM and what instrument parameters and operating mode could possibly lead to such an outcome. We approach this problem through rigorous modeling of the dynamics of a complex viscoelastic biosystem in which AFM imaging process is intimately coupled to the membrane biomechanics. In our analysis we take into account motion of the AFM tip, induced viscous effects in fluid outside and inside of the cell, as well as viscous and elastic effects in the lipid bilayer of the membrane. We simplify the analysis by considering axisymmetric system in which fluid mechanics is described in the limit of the Stokes creeping flow. We also use the Helfrich's quasi-equilibrium theory for the elastic energy associated with the membrane shape (2) enhanced by the Evans' treatment of viscous effects in the membrane subjected to fast deformations (3). The boundary integral method (BIM) is used to solve the resulting quasi-steady Stokes system of conservation equations coupled via the sheer stress jump condition at the membrane interface between the extra- and intra-cellular domains. The effects of the AFM tip geometry and dimensions, the amplitude and frequency of the AFM probing motion, elastic and viscous properties of the membrane, as well as viscosity ratio of the intracellular to extracellular fluid media are investigated in detail to establish the structure and evolution of the fluid field and dynamics of membrane deformation. In integral sense, this leads to rigorous prediction of the force-vs-distance diagram for the AFM imaging process and local tension variation in the cell membrane. In turn, the latter allows us to formulate the optimal strategy for lipid membrane imaging by AFM as well as to define dimensions of the AFM tip that would yield the sensitivity needed for successful, high resolution detection of cellular membrane.

1. Onaran, A. G., Balantekin, M., Lee, W., Hughes, W. L., Buchine, B. A., Guldiken, R. O., Parlak, Z., Quate, C. F., and Degertekin, F. L. A new atomic force microscope probe with force sensing integrated readout and active tip. Review of Scientific Instruments, 77:023501-1-7,2006. 2. Zhongcan, O. Y. and Helfrich, W. Bending Energy of Vesicle Membranes - General Expressions for the 1st, 2nd, and 3rd Variation of the Shape Energy and Applications to Spheres and Cylinders. Physical Review A, 39: 5280-5288, 1989. 3. Evans, E. and Yeung, A. Hidden Dynamics in Rapid Changes of Bilayer Shape. Chemistry and Physics of Lipids, 73: 39-56, 1994.