Chapter 4
Measuring Cell (and molecular) Mechanics
(with acknowledgement to Bao & Suresh[1])
4.1 Overview
Testing mechanical properties of engineering materials such as metal, ceramics, or polymers is a straightforward and well established procedure: specimens are placed in an Instron machine and stretched or compressed it in various ways until it breaks. Testing cells is not so easy. Cells are soft, complex, non-linear, and changeable. Unlike inanimate objects, that possess static properties, cells behave. From previous chapters it should now be clear that cells (Eukaryotic) are like thin elastic shells filled with an incompressible fluid, whose fundamental properties can change with circumstance. The challenge of cell mechanical measurement has been met with many ingenious testing devices.
Figure 4.1 Testing Cell mechanical responses
The most straightforward tests involve directly poking the cell, although with much more refinement than the hammer shown above. A simple probe for applying small nanoNewton level poking forces to cells is a fine-tipped micropipette. When the tip bends as it pushes on the cell, the degree of bending is roughly proportional to the cell stiffness, over a range. So the probes used are more refined than a hammer, but the principle is the same: apply a small deformation to the specimen while measuring as accurately as possible both the force applied and the deformation as it evolves over time.
Mechanically probing single cells and even biomolecules is becoming increasingly sophisticated. Devices for applying and measuring forces < 1 pN and deformations < nM, are available now and getting better. Combining these devices with the latest imaging, molecular biology, and bioinformatics, including modeling and simulationhas led cytomechanists to revolutionize our view of the cell. These new techniques can illuminate like never before the processes responsible for operation of cellular machinery, the forces arising from molecular motors and the interactions between cells, proteins and nucleic acids.
4.2 Types of forces
Measuring mechanical properties of any material, including a cell, requires applying some kind of force to it and recording the deformation response. As depicted in the figure below, force can be applied in many modes: tension or compression (a), either uniaxial or biaxial, bending (b), twisting or torsion (c), and pure shear (d). Additionally, force can be applied with fluid or gas, both statically and dynamically.
For any of these modes, varying the timing of also helps characterize the material: for example force can be applied suddenly, slowly or rhythmically. Sudden impulse or steps of force, ramps, or sinusoids. The common waveforms used to test mechanical behaviors, both linear and non-linear, are depicted below.
Devices or procedures that apply these forces can be conveniently classified into three types (Fig. 1): Type A, whereby local probes load or stretch a portion of a single cell; type B, mechanical loading of an entire cell; and type C, simultaneous loading of a population of cells.
Several type A methods are available as depicted in Figure below:
4.2 Atomic Force Microscopy (AFM)
In AFM, a sharp tip at the free end of a flexible cantilever (below) generates a local deformation on the cell surface[2] . The resulting deflection of the cantilever tip can be calibrated to estimate the applied force. This is a high-resolution technique that traces the fine structure of nanometer level objects. The tip can be conjugated with an antibody that binds to the cell (‘functionalized’, and then it can be used to pull on it with calibrated force.
Alenghat, Fabry Tsai, Goldmann, Ingber
The figure at left is a computer model of the mechanical deformation of a cell by the tip of an AFM cantilever. The model is based on continuum mechanics, and it includes contributions from the elasticity of the cell membrane as well as the interior of the cell.
4.3 Magnetic Tweezers
Magnetic beads, a few microns diameter, can be either incorporated into cells, or attached to specific receptors[3-5]. An illustration of pulling on a cell with a magnet is shown below. In this case, the bead has been incorporated into the cell, and is pulled with an external magnetic field. Calibrated stretch of the membrane can be thereby done.
A more specific force can be applied to individual molecules using functionalized magnetic beads. These have been coated with antibodies for specific CSK components such as Integrin. For example, when coated with fibronectin, the beads will bind to Integrin[6]. When the beads bind, an external magnetic field can be applied to twist the bead, measuring the response of the CSK portion directly, as shown below[7]:
By using a magnet to pull and twist individual molecules on a cell, this technique represents ‘magnetic tweezers’.
These magnetic-twisting studies confirmed that mechanical forces are transmitted only over specific molecular paths, in particular the Integrin hooks. When the beads were bound to non- CSK receptors, they could not effectively convey force to the inside of the cell. Highly specific molecular "adhesives" to show that tugging on particular receptors at the surface of a living cell triggers nearly instantaneous rearrangements in the nucleus.
4.4 Micropipet Aspiration
This technique involves sucking up a small portion (patch) of a cell into a micropipette, while measuring the deformation and pressure force[8]. The geometry and kinematics of the situation shown below have been worked out by E. Evans, and will be presented in Chapter 6.
Micropipette aspiration can either be type A or B (Figure 4.2), depending on conditions. If the micropipette is tightly sealed to the cell, there is no movement of the main body of cell into the pipette, and hence only the patch is deformed- this is type A. If there is no seal and no friction between the cell and the pipette, then the whole cell gets squeezed into the pipette, and it is a type B stimulus.
Note that the cartoon of Figure 4.7 shows a highly simplified view of what happens to the CSK during aspiration. The pressure clearly deforms it, and by measuring the force required to pull it up the tongue of cell a given length, a measure of stiffness can be obtained. It is also apparent that the deformation is complex, being neither uniform nor isotropic, and applies tension, compression, as well as shear simultaneously. Analysis of the results is therefore complex, and will be discussed in Chapter 7.
Micropipettes can even be used to probe into sub-cellular structures, such as the nucleus as shown below. This sequence of pictures shows the pipette drawing a single chromosome into the pipette and gradually pulling it out of the nucleus. This remarkable experiment revealed the surprising, and still unexplained, phenomenon that all the chromosomes and the nucleolis are connected together by strings of DNA.
Micropipettes have also been used to measure the strength of single chemical bonds that a cell makes with its matrix. The pipette grabs onto the cell like a leech, and then can pull with a calibrated force until the bond breaks (Evans). With a manually operated
micromanipulation device, the micropipette is moved "like a golf club" to move the beads about 10 micrometers a second, while monitoring the cell with the video microscope.
Micropipette aspiration can also be used to test the entire cell as depicted below. A direct porthole connection to the entire cell made when sufficient suction is applied to break the membrane and CSK break open. Thus the cell can be inflated with known forces, while its diameter is measured and its surface area estimated. The whole cell swelling technique is powerful because the micropipette can control the internal milieu, including both the cytosol composition and the electrical potential, as depicted in Figure 4.
The total osmolarity of the cell and its external environment is important since slight imbalance can cause large osmotic forces for swelling or shrinking. In fact, using van’Hoff’s formula for osmotic pressure (See Appendix) indicates that for every 1 mOsm difference in salt concentration across the cell membrane, there is a transmembrane pressure gradient of 16.7 mm Hg.
Note that the internal and external osmolarities are labeled, C, flows of water are labeled Q, and pressure P. Cell stretch can be applied by applying pressure from the pipette (panel A). Cells can also be stretched by exposing them to hypotonicity, as shown in panel B[9].
4.5 Optical Tweezers
Another type A or B method involves optical tweezers or a laser trap, in which an attractive force is created between a dielectric bead of high refractive index and a laser beam, pulling the bead towards the focal point of the trap[10]. To deform a single cell, 2 microbeads (typically 1 m to several micrometres in diameter) are attached to opposite sides of it and one or both beads are trapped by the lasers, and then pulled apart. (Fig. 4.4 d). This technique relies on a high power laser trapping the bead, which involves substantial heating of it. In order not to heat the cell also, the laser beam must be much smaller than the size of the bead. By ‘functionalizing’ the bead, it can bind to specific molecules, allowing the probe to apply force to specific bonds.
4.6 Shear flow
A variety of configurations can deliver precise amounts of shear force to groups of cells attached to surfaces. A cone-and-plate viscometer is depicted in (a), consisting of a stationary flat plate and a rotating inverted cone with which laminar and turbulent flows can be applied. A parallel-plate flow chamber (b) subjects cells to laminar flow[11, 12]. In both cases the shear stress applied to cells can be readily quantified. Many cellular responses can be measured as a function of shear during and after the force application, including attachment strength, growth, and biochemical responses. These tests are most appropriate for cells for whom shear is a way of life, such as blood cells, and endothelial cells.
4.7 Hydrostatic loading
Groups of cells can be pressurized with devices shown below. In (a) a piston (platen) pressurizes the fluid above the monolayer of cells. When cells are grown in a 3-dimensional matrix, pressure can be applied directly to them as in (b). Cells can be either
confined or without side support. This type of testing is valuable to understand behaviour of bone and cartilage cells, as well as cells that may be subjected to high pressures under abnormal conditions.
4.8 Cell Stretching
When attached to a flexible substrate, cell populations can be stretched by pulling on the substrate[13]. A commercial device, Flexercell, has been extensively used for this purpose . A variety of configurations and actuator types are available as shown below. The procedure involves culturing cells on a thin-sheet polymer substrate, such as silicone, which is coated with ECM molecules for cell adhesion. The substrate is then mechanically deformed while maintaining the cell's viability in vitro. In this manner, the effects of mechanical loading on cell morphology, phenotype and injury can be examined. Furthermore, by systematically altering the mechanical properties of the substrate material through, for example, changing the degree of crosslink in the polymeric gel, the individual and collective interactions of the cells with the substrate can be studied2. Such studies have been performed to investigate the propensity for migration of a group of cells towards or away from the region of localized tension or compression in the substrate.
4.9 Microelectromechanical systems (MEMS)
Substrate topography can be micropatterned so that cells are induced to grow onto tiny elastic platforms that can be moved to apply or measure force[14]. This is a powerful technique, since the platforms can be precisely controlled, and can be functionalized with specific cellular matrix targets. Thus the micropattern can test and perturb cell-matrix interactions in a highly controlled environment. For example, the strength and behaviour of specific focal adhesions can be studied. The contractile forces generated by cells during locomotion and mitosis can also been measured with a deformable-substrate method.
Examples of MEMS cell testing systems are shown below. Two configurations are a cluster of microneedles (Fig. 4.13, a, b or a cantilever beam (Fig. 4.13, c). The device in part d can apply mechanical force or deformation at several points on a cell in the center.
4.11 Exercises
- In testing micropipette aspiration of cell patches, what modes of force application are applied? Use sketch.
- Describe a valid protocol for testing the time-dependent behaviour of cell mechanical properties.
- In the whole cell inflation test shown in Figure 4.9, how would the CSK respond to pressurization, based on what you know of its properties?
- In the hydrostatic loading test (4.9) describe the effects of adding side constraints to the cells.
- Find wall stress for cylinder.
- Calculate stress for a foraminifera not assuming a thin wall. Assume a diameter of 1 micrometer, and it is living in the Deep Challenger.
4.12 References
1.Bao, G. and S. Suresh, Cell and molecular mechanics of biological materials. Nature Materials, 2003. 2(11): p. 715-725.
2.Solletti, J.M., et al., Atomic-Force and Scanning Electron-Microscopy of Xenopus-Laevis Oocytes. Journal of Vacuum Science & Technology B, 1994. 12(3): p. 1535-1538.
3.Matthews, B.D., et al., Mechanical properties of individual focal adhesions probed with a magnetic microneedle. Biochemical and Biophysical Research Communications, 2004. 313(3): p. 758-764.
4.Overby, D.R., et al., Magnetic cellular switches. Ieee Transactions on Magnetics, 2004. 40(4): p. 2958-2960.
5.Alenghat, F.J., et al., Analysis of cell mechanics in single vinculin-deficient cells using a magnetic tweezer. Biochemical and Biophysical Research Communications, 2000. 277(1): p. 93-99.
6.Wang, N., J.P. Butler, and D.E. Ingber, Mechanotransduction across the cell surface and through the cytoskeleton. Science, 1993. 260(5111): p. 1124-7.
7.Wang, N. and D.E. Ingber, Control of Cytoskeletal Mechanics by Extracellular-Matrix, Cell-Shape, and Mechanical Tension. Biophysical Journal, 1994. 66(6): p. 2181-2189.
8.Hochmuth, R.M., Micropipette aspiration of living cells. Journal of Biomechanics, 2000. 33(1): p. 15-22.
9.Craelius, W., et al., Rheological behavior of rat mesangial cells during swelling in vitro. Biorheology, 1997. 34(6): p. 387-403.
10.Dao, M., C.T. Lim, and S. Suresh, Mechanics of the human red blood cell deformed by optical tweezers. Journal of the Mechanics and Physics of Solids, 2003. 51(11-12): p. 2259-2280.
11.Helmke, B.P., Shear stress-induced deformation of the endothelial cytoskeleton. Faseb Journal, 2002. 16(4): p. A519-A519.
12.Helmke, B.P. and P.F. Davies, The cytoskeleton under external fluid mechanical forces: Hemodynamic forces acting on the endothelium. Annals of Biomedical Engineering, 2002. 30(3): p. 284-296.
13.Brown, T.D., Techniques for mechanical stimulation of cells in vitro: a review. Journal of Biomechanics, 2000. 33(1): p. 3-14.
14.Singhvi, R., et al., Engineering cell shape and function. Science, 1994. 264(5159): p. 696-8.