Annals of Biomedical Engineering, Vol. 24, pp. 595-605, 1996 0090-6964/96 $10.50 + .00 Printed in the USA. All rights reserved. Copyright 1996 Biomedical Engineering Society A Piconewton Force Transducer and Its Application to Measurement of the Bending Stiffness of Phospholipid Membranes VOLKMAR HEINRICH and RICHARD E. WAUGH Department of Biophysics, University of Rochester School of Medicine and Dentistry, Rochester, NY Abstract--The bending stiffness of a phospholipid bilayer (k~) was measured by forming thin bilayer cylinders (tethers) from giant phospholipid vesicles. Based on the balance of forces, the tether force was expected to be proportional to the square root of the membrane tension, with a constant of proportionality con- taining kc. The membrane tension was controlled via the aspira- tion pressure in a micropipette used to hold the vesicle. The force on the tether was generated by an electromagnet acting on a paramagnetic bead attached to the vesicle surface. The magni- tude of the force was determined from measurements of the magnet current, which was adjusted to maintain the position of the bead. Measurements were performed on vesicles composed of stearoyl-oleoyl-phosphatidylcholineplus 5% (by mole) bioti- nylated phosphatidylethanolaminc to mediate adhesion to streptavidin-coated beads. From each vesicle, tethers were formed repeatedly at different values of the membrane tension. The expected relationship between membrane tension and tether force was observed. The mean value of k~ for 10 different ves- icles was 1.17 x 10 19j (SD = 0.0g X 10-19 J). The preci- sion of these data demonstrates the reliability of this approach, which avoids uncertainties of interpretation and measurement that may be associated with other methods for determining k~. Keywords--Magnetic particles, Bilayer membrane, Mechanics, Micromanipulation, Curvature elasticity INTRODUCTION To a large extent progress in the biomechanics of cells and subcellular structures such as biomembranes has been confined by the small number of experimental approaches that are available. The method that has accounted for our most detailed knowledge of mechanical properties of cells Acknowledgment--The authors thank Richard G. Bauserman and James Butler for technical assistance, Dr. C. Jeffrey Wang of Sphero- tech, Inc., for his generosity with bead samples and technical advice, and Philippe M616ardfor patiently supplying us with hints for the setup of the vesicle electroformation method. This work was supported in part by a postdoctoral fellowship of the Deutsche Forschungsgemeinschaft,and by the U.S. Public Health Service under NIH grants HL 18208 and HL 31524. Address correspondence to Dr. Richard E. Waugh, Department of Biophysics, University of Rochester School of Medicine and Dentistry, 601 Elmwood Ave., Rochester, NY 14642. (Received 22Dec95, Accepted 31Jan96) and membranes is micropipette aspiration. In recent years, the need for alternative approaches to cellular microme- chanics has been mainly met by the "optical tweezers" technique employing laser-generated optical traps (2). This technique has provided the possibility of imposing forces in the range of piconewtons, a task that arises in numerous physical and biological applications. Yet op- tions for applying well-known and well-controlled small forces are rather limited (e.g., Ref. 9). In this paper we present an adaptation of a magnetic force transducer de- veloped by Guilford and Gore (14) to apply and measure small forces in a range down to piconewtons. For many experimental purposes, this force transducer provides a low-cost and flexible alternative to optical tweezers. The main application of magnetic particles in biological research has been their use in magnetic separators. Guil- ford and coworkers (15) have introduced a technique in which single magnetic beads were attached to leukocytes, and forces generated during cell locomotion were mea- sured. Combining this original work with micromanipu- lation techniques has provided the basis for the develop- ment of our force transducer. Any objects like soft micro- particles, biological cells, or even small tissue samples are potentially suitable subjects of study with the apparatus. A general overview of the experimental setup is the following. The object of investigation is held in a micropi- pette or otherwise fixed to a micromanipulator on the stage of a microscope. Using antibodies or other adhesive mol- ecules, a paramagnetic bead of spherical shape is attached to it. An electromagnet designed to fit on the microscope stage is positioned with its tip close to the optical path, i.e., the point of observation. In connection with an ap- propriate force calibration, well-defined forces can be ap- plied to the magnetic bead. The deformation of the spec- imen at known force is observed microscopically and provides the information needed to characterize the me- chanical properties of the material. In the present paper, the operation of the force trans- ducer is demonstrated with giant phospholipid vesicles. These are artificial, closed bilayer membranes of given lipid composition that form spontaneously in aqueous so- 595