Imaging & Photomanipulation - Approaches

Force Imaging and Assays

Cell Traction Assays (CTA)

A crucial factor in cell migration is the system of forces generated during interactions of the cell with the substrate over which it moves. These interactions are influenced by surface chemistry, topology and overall substrate compliance. Several studies have indicated that focal adhesions (FAs) act as mechanosensors whose input feeds directly into the regulation of physiological processes. In order to propel itself, a cell exerts tractive forces on the substrate via its adhesion molecules. As a response, a mechanical stress is generated in the substrate. As cells probe their environment, their shape and adhesion, as well as their cytoskeletal organization and tension, are affected and regulated by the stress at the cell/substrate interface.

The cell traction assays have evolved out of attempts to quantify the direction and magnitude of these interfacial forces at desired locations and under various conditions, in order to correlate the forces with the observed cytoskeletal and FA dynamics in motile cells.

All the methods described in this section rely on Newton's Third Law: the action (of the cell on the substrate) is equal to the reaction (of the substrate on the cell) (Figure 11). The goal is to measure the former, but it is impossible to do so directly--instead, the cell tractions are determined from the deformation they cause in the substrate.

Figure 11. Schematic of a migrating cell and the tractions it generates on the substrate. The thick arrows are forces with which the cell acts upon the substrate (black) and the elastic substrate reaction forces that act upon the cell (green and purple). In case of the stuck cell presented here, the "propulsive" tractions act mainly on the cell front, while "frictional" tractions act at the cell rear. Only the forces along the direction of migration are presented here--the net force at each point on the substrate also has a component perpendicular to the direction of movement. The integral (over the total area of the substrate covered by the cell) of the net force and the net torque about an arbitrary origin has to be zero.

Biologists and engineers have been developing cell traction assays on elastic substrates for more than 20 years. According to the mechanics of probing, the existing methods can be divided into two conceptually different groups: continuum methods and discrete methods. A more intuitive division according to the substrate material (silicone, polyacrylamide, or other) is often used, but it is mentioned only parenthetically in the classification presented below.

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Classification of traction assays according to the mechanics of probing

Continuum methods. These methods of probing the cell tractions are based on recording the elastic response of the substrate as a continuum. The displacement of any point on the substrate is coupled with the displacements of neighboring points-- thus, the force sensor is the entire surface of the substrate.

The first elastic substrate was a thin silicone film formed on the surface of an uncured polymer resin (phenylmethyl polysiloxane, trimethyl-terminated) by gently flaming the surface (Harris et al., 1980). The silicone film wrinkles in response to the forces that cells generate while adhering or moving across the film. The wrinkles are easily detectable with a light microscope, but they develop slowly and are often larger than the cells, resulting in poor spatial resolution. Efforts to finely tune the mechanical properties of the silicone film for better quantification and versatility resulted in spatial resolution of 1 µm squared and force resolution of 10 nN, within 10 nN - 1 µN range (Burton & Taylor, 1997). Because the non-linear relationship between the forces and the wrinkle geometry is too complex for facile quantitative analysis, the wrinkling substrate assays remain a qualitative tool.

Adequate quantitative description of the elastic substrate response to cell tractions is provided by continuum mechanics--in particular, the theory of elasticity. Micah Dembo (Biomedical Engineering, Boston University) has used this theory to develop a method of converting the substrate displacements to cell tractions (Dembo et al., 1996; Dembo & Wang, 1999). Under the small-strain plane-stress conditions, the theory yields a transform expressing the displacement field of the elastic substrate as an integral over the discretized traction field. The integral equation does not have an analytic solution--it can only be solved numerically (with the aid of computers). The tractions are calculated by transform inversion and using the method of Bayesian likelihood. All the calculations--from deformation image processing, through transform inversion, to rendering of traction maps--are provided by Dembo's software package LIBTRC (independently developed and available, by a limited conditional license requested from the author, for nonprofit academic installation on a single LINUX workstation).

The first quantitative traction assay utilizing this method was developed for silicone films similar to those used for wrinkling assays, but with latex beads (of the order of 1 µm) embedded at the film surface (Lee et al., 1994; Oliver et al., 1995; Dembo et al., 1996; Oliver et al., 1999). As the cell migrates over the substrate surface, the beads serve as fiduciary markers for two-dimensional imaging of the substrate displacement, which is then used to calculate the cell tractions (Figure 12.a and 12.b). The main substrate parameter featuring in this calculation is the Young's modulus-a measure of the substrate stiffness.

The silicone films are relatively compliant and they are successfully used for moderately-adhering and fast-moving cells, e.g., fish keratocytes. Regardless of the cell type, it is important to keep the marker displacements small in order to insure that no plastic deformation of the film occurred, i.e., the applied deformation should be reversible. This condition is achieved by adjusting the film compliance during the cross-linking phase to match the strength of the cell, but the adjustment requires some trial and error and is difficult to reproduce exactly. The main disadvantage of this type of substrate, however, is the uncertainty in determination of the exact location of the centroids of the latex beads from the phase-contrast images. The bead clustering and the reflections from the markers below the surface additionally affect the image processing and, consequently, the determination of tractions.

Figure 12. Traction maps obtained by continuum methods. a) phase-contrast image of the fish scale keratocyte, b) traction map for the same cell (adapted from Oliver et al., 1999); c) fluorescence image of a human foreskin fibroblast expressing GFP-vinculin that localizes to focal adhesions (inset: phase-contrast image of the upper part of the cell; the white dots are fluorescent markers and the green arrows represent their displacements). (adapted from Balaban et al., 2001).

Further developments along these lines resulted in the sheets of fully cross-linked PDMS, whose surface is micropatterned with a uniform grid of lines or fluorescent dots using soft lithography microfabrication techniques (Balaban et al., 2001). The pattern size (2 - 30 µm) is chosen according to the spatial resolution required for imaging displacements. In this case, there are no markers in the bulk of the substrate and, consequently, the images are clear and easier to analyze, especially those with fluorescent dots (Figure 12.c, inset). The substrate was modeled as the infinite half-space, in a similar way as in theory developed by Dembo. The tractions, however, were assumed to act as point-forces only at the FAs and are calculated from the displacement vectors using the Green function that maps the tractions into displacements. Zero-order regularization was used to solve for tractions (which is, again, an inverse problem). Although micropatterned silicone substrates are a welcome improvement regarding the imaging, their fabrication is costly and the roughness of their texture, if in some critical range, may in itself affect the adhesion.

One of the important disadvantages of silicone substrates is that they are not suitable for wide selection of cell types. Slow and strongly-adhering cells (fibroblasts) require stiffer substrates, while faster but weaker-adhering cells (keratocytes) require very compliant substrates--the available stiffness range of silicone films is too narrow to accommodate both and the possible applications are confined to more compliant substrates. Another disadvantage is related to cells that adhere poorly to uncoated silicone, for which it is necessary to conjugate the matrix proteins on the substrate surface. The matrix proteins have poor optical properties (Harris, 1988) and they may also undergo some irreversible deformation (Roy et al., 1997)--both problems could affect the overall accuracy of continuum methods.

In effort to improve a substrate for continuum traction assays, the silicone was replaced with polyacrylamide gel and the plain latex beads were replaced by the fluorescent ones for better displacement imaging. Polyacrylamide sheets have better mechanical and optical properties than the silicone films (Pelham & Wang, 1997) and they can be coated easily with ECM proteins such as type I collagen or laminin to provide surface properties that are physiologically acceptable to specific cell types. 0.2 µm beads were added to the entire polyacrylamide volume before cross-linking and a drop of the mixture was sandwiched between two coverslips (Dembo & Wang, 1999; Munevar et al., 2001; Beningo et al., 2001)--during cross-linking the beads slowly sink to the bottom coverslip, practically forming a monolayer at that surface that will be used as the top surface during the assays. To further reduce the background fluorescence from out-of-focus beads, a thin top layer of uncured polyacrylamide-bead mixture can be placed and cross-linked on top of a pre-cured bead-free layer (Bridgman et al., 2001). The current version of the LIBTRC package mentioned above, as used for silicone substrates, is used to calculate the tractions from the displacement maps on the polyacrylamide substrate. The post-processing now allows for plotting not only the displacement maps and distribution of tractions, but also stress contours and shear gradients (Figure 13).

Figure 13. Traction microscopy of migrating NIH 3T3 fibroblast on polyacrylamide substrate: A) the cell and the fluorescent microspheres embedded in polyacrylamide substrates (image was recorded with simultaneous illumination for phase contrast and epi-fluorescence); arrow indicates the direction of cell migration; B) deformation vectors, plotted over the phase image of the cell; C)map of tractions, shown as arrows within the boundary of the cell; D) map of tractions, rendered as a color image after mapping the magnitude of stress into different colors that range from violet (9.20 × 10² dyncm^-2) to red ( 3.60 × 10⁵ dyncm^-2); the segmented scheme of pseudo-color mapping, as shown along the right edge, allowed the visualization of both the stress magnitude as function of position and the stress contour plot; E) normalized "shear of traction" (measure of shear gradient) that ranges from violet (2.02 × 10²cm^-1) to red (5.53 × 10⁴cm^-1), reflecting the local complexity of traction forces (scale bar, 20 µm). (adapted from Munevar et al., 2001).

The compliance of the polyacrylamide gel depends on the proportion of the acrylamide and BIS-acrylamide (cross-linker), which can be optimized for wide variety of cell types to give measurable bead motions due to the applied cell tractions. The method for measuring the substrate stiffness (as shown on Figure 14) is simpler and more accurate than pinch-tests and microneedles used previously on silicone substrates. Suitable mix proportions were first found for fibroblasts and other slow-migrating cells, but further investigation has shown that very compliant gels (for fast-migrating cells with weak tractions, e.g. keratocytes) can also be fabricated by lowering the acrylamide while increasing BIS concentration (Beningo et al., 2002).

CTA Figure 4. Material characterization of polyacrylamide substrate. Identically sized strips of polyacrylamide with various acrylamide/bis-acrylamide ratios were fixed at one end and stretched at the other end with a downward force of 0.103 N. The lengths between the dashed lines represent the resulting stretch, which is inversely proportional to the stiffness, i.e., Young's modulus (adapted from Pelham & Wang, 1997).

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Discrete methods. These methods are based on probing the cell tractions at discrete points at the cell/substrate interface--thus the designation "discrete" in classification of the method.
The first notable substrate of the discrete kind was based on micro-electro-mechanical system (MEMS) devices (Galbraith & Sheetz, 1997), micromachined from a silicon wafer and coated with laminin. The substrate contains arrays of micro-cantilevers each tipped with a 4-25 µm² pad. Each cantilever is deflected by the cell as it sweeps over the pad and the magnitude of deflection, as well as the direction in which the cell moved are recorded (Figure 15). As described in Figure 15.d, the Beam Theory, with its simple algebraic equation of proportionality between the force and cantilever deflection, is then used to calculate the force that cell exerts on the pad. Each cantilever deflects independently of its neighbors and allows the measurement of tractions at single adhesion sites.

The main disadvantage, as for the micropatterned substrate, is the high cost of fabrication of MEMS substrate. Also, the tractions can be measured only at the positions that the cell "chooses" to cross--unless the point of interest on the cell moves over one of the pads, the traction at that location on the cell/substrate interface cannot be calculated. Therefore, the continuum methods have an advantage over this discrete method in that they allow for calculation of tractions at any point of the cell/substrate interface. However, this method is impervious to the degradation of extracellular matrix (ECM) proteins conjugated to the surface, so it can be used for a wide selection of cell types.

Figure 15. Different magnifications of the MEMS substrate: a) a cut-away drawing showing the lever, the pad, and the well (bar = 10 µm); b) two neighboring pads (bar = 10 µm); c) arrays of beams (bar = 1 mm); the white square indicates the region shown in b; d) force diagram explaining how the cell force is calculated; e) micrographs (in 10 min intervals) and traction force generated at or near the leading edge. (adapted from Galbraith & Sheetz, 1997).

A very straight-forward discrete method was developed for measuring the forces exerted by stationary cells using a silicone (PDMS) substrate with arrays of posts or microneedles fabricated using soft lithography (Tan et al., 2003). Again, the tractions can be calculated from the recorded deflection of the posts using simple Beam Theory (Figure 16.a,b) and displayed in much the same way as the other traction maps (Figure 16.d). All or some of the post tips (Figure 16.c) can be coated with ECM proteins, allowing for studies of confined spreading.

The main advantage of this type of substrate is the ability to control the compliance of the substrate geometrically instead of chemically--changing the height and diameter of the posts changes the stiffness. Another advantage is that there is no need for recording the unstressed state of the substrate, because the posts were manufactured with sufficient precision. Although the substrate was originally designed for studies of stationary cells, it could be used for migrating cells, but the elastic spring-back of the post after the cell has moved over it can be a problem for imaging.

Figure 16. Smooth muscle cell lying on a bed of microneedles (bar = 10 µm): a) sketch of the idea behind the method (d = 2-10 µm, L = 3-50 µm, spacing = 6-10 µm); b) SEM of the cell deforming the posts during adhesion; c) traction map overlaid with the confocal image of immunofluorescence staining of the cell, with FA protein vinculin stained green. (adapted from Tan et al., 2003).

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Other notable traction assays

Collagen matrices have also been explored as the 3-D substrate for cell traction imaging (Vanni et al., 2003). For the most cell types, a collagen hydrogel substrate provides a physiologically natural substrate. At the same time, the intrinsic collagen fiber structure visible in differential interference contrast images provides markers for in situ strain mapping, while the optical sections of fluorescent protein distribution in the cell capture the actin cytoskeleton kinematics. The tractions were calculated from the timelapse differential interference contrast images using a software package available on the Internet (http://dqa.web.cmu.edu). The substrate preparation is simple--the stock solution of cells in the gel is poured over Teflon strips, thus creating a thin film that does not adhere to the supporting coverslip, but is only supported around the perimeter. Although the method is computationally demanding, its main disadvantage is the degradation of the collagen hydrogel, limiting its range of applications.

One of the useful discrete methods is a micropipette method (Riveline et al., 2001). The micropipette is used as a single probe for measuring the force at the contact with cell. The cell is pushed sideways by the pipette and the force is calculated again from the recorded deflection of the pipette tip. This method was used to study formation of focal adhesions due to external load on stationary cells (Figure 17).

Another substrate for measuring the tractions generated by non-motile cells was developed (Wang et al., 2002) in combination with continuum methods of traction mapping for adhesion studies of cells that are physically constrained to the limited adhesive areas on the substrate. The adhesive islands of specific sizes and shapes were created on the polyacrylamide substrate using a membrane patterning technique (MEMPAT).

Figure 17. Local formation of focal contacts in response to the application of external force. GFP-vinculin-transfected SV-80 cells are shown before (A-B) and after (C-D) application of pulling force produced by micropipette shift. (A, A', C, and C') GFP fluorescence showing the distribution of vinculin; (B and D) phase image of the same cell. The photographs were taken 2 min before pipette shift (A-B), immediately after the shift (D), and 3 min 37 s after the shift (C and C'). (adapted from Riveline et al., 2001).

Traction assay section contributed by Vesna Damljanovic.

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Atomic Force Microscopy (AFM)

Principles: The atomic force microscope (AFM) is so named because it measures forces that are governed by the interaction potentials between atoms. Depending on the sample and tip material and the medium in between different interactions will be important. Always present are van der Waals interaction and very short range repulsive interaction, which are caused by the quantum mechanical exclusion principle*). Van der Waals forces are generally attractive (except for very rare cases) and can be sensed at distances of 10 Å and more. In biological samples many other interaction may also be present such as electrostatic interactions (attractive and repulsive), steric interaction (e.g. with polymers, always repulsive) and specific adhesion forces at molecular contact. All these forces are usually called colloidal forces (Israelachvili, 1992).

Measurements of these forces are made by means of the AFM probe, a sharp tip that interacts with the sample surface. Typical forces between the tip and the sample are within the range of 10 p - 10 nN in liquids although this also depends on the size of the tip used. The tip is mounted on the end of a soft, silicon nitride cantilever spring and it's position in relation to the sample is controlled with high precision in X, Y and Z using tube-shaped piezoceramics. Where optical setups are combined with the AFM it is the cantilever which translocates, alternatively the whole sample is mounted on a piezoelectric scanner and moved with respect to the probe.

Figure 18. Principle of AFM. The sample is positioned by a xyz piezo scanner while the AFM tip is in contact. The deflection of the cantilever is detected by an optical lever, a laser beam focused on to the very end of the cantilever and reflected onto a position sensitive detector

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The AFM comprises an instrument with combines very high spatial resolution (depending on sample nanometers or less), high force sensitivity (10's of pN) and the possibility to investigate biological samples under physiological conditions without fixation or other invasive sample preparation. This makes it possible to follow dynamics and processes on the molecular and cellular scale directly.

Figure 19. The spontaneous beating of live myocyte cells can be monitored directly by AFM. The bottom most spindle like cell is a myocyte, the neighboring cell above with prominent cytoskeletal structures is a fibroblast. When positioning the AFM tip to a given location (yellow dots) we can follow the height of the cell as a function of time (red traces). (from: Domke et al., 1999.)

Modes of operation and their applications:

Contact/DC Imaging Mode: In the most simple mode of operation (contact mode imaging at constant height) the tip raster-scans across the surface of the sample while the deflection of the cantilever is measured at each point and image is generated from this information (deflection image). Measurement of this deflection at each point leads to an * image of either surface topology or material properties of the sample. The deflection information is collected by directing a laser beam onto the gold-coated top surface of the cantilever, which reflects the beam into a position sensitive diode (PSD) that can detect changes of 1nm. However in this constant height mode the loading force of the tip on the sample is also changing when the deflection is changing since the cantilever acts as a spring ( F = k * d, where d is the deflection, k is the spring constant of the cantilever and F will be the force). For delicate samples, like biological molecules or cells, a feedback mechanisms is employed which adjusts the piezo height such that the cantilever deflection stays constant. Thus the loading force will also be constant and can be minimized by adjusting the set point of the deflection. In this mode the height information will be constructed from the voltage applied to the z-piezo (height image). As a matter of fact, since a feedback mechanism will never perform perfectly there will be some residual fluctuations in the deflection signal, which can be very helpful especially when imaging rather high samples like cells.

* No two fermions can be in exactly the same state, that is, have the same spin, angular momentum, and location. Atoms thus behave like hard spheres. (Hard-wall repulsion)

Figure 20. Contact mode images of life 3T3 cells in medium. On the left the height images is shown, on the right the deflection image. Although a feedback is used to keep the deflection constant due to limited response time of the electronics and the positioner, some residual fluctuations are still visible in the deflection image. However, the z-scale of the two images is very different, in the height image the range between black and white corresponds to 3 µm, whereas in the deflection image the range is only about 100 nm.

For cell biological applications most important is the fact that the AFM can be operated at physiological conditions allowing the investigation of dynamic processes like the activation of platelets (Fritz et al.,1994), cytoskeletal rearrangement (Henderson et al.,1992) (Schoenenberger & Hoh, 1994), protrusion of lamellipodia (Rotsch et al.,1999), or exocytosis (Schneider et al.,1997).

Tapping Mode: In tapping mode, the frequency of cantilever vibration is set near its resonant frequency, so that the amplitude of oscillation is much larger than in simple non-contact mode. The distance between the tip and sample is adjusted such that there is light contact when the cantilever is at the lowest point of its oscillation. This amplitude is maintained, as in contact mode, via an electronic feedback loop with input from the PSD and used to generate a topographical map of the sample surface. The difference here being that it is changes in the oscillation amplitude of the cantilever, rather than static deflection of it, that produce the signal. Tapping mode can be operated in liquids and has been proven to be very useful for imaging single protein molecules (Hansma et al., 1994) and follow activity of single molecules (Radmacher et al., 1994), like enzymatic activity or degradation of DNA (Bezanilla et al.,1994).

Image resolution

Imaging resolution will depend on the size of the tip apex, which is anywhere between a few nanometers to tens of microns, sample roughness and sample stiffness. Atomic resolution is only really possible with flat, periodic samples such as inorganic crystals. High resolution with biological samples can be achieved with well adsorbed two dimensional arrays of proteins (Engel et al., 1997). When imaging single proteins molecules will look broadened, whereas the height of the molecules will be detected accurately. In imaging cells, the softness of the sample will often result in resolutions on the order of 50 nm (Braet et al.,1997). However, in special cases very high resolution on cells has also been achieved (Le Grimellec et al.,1998).

Figure 21. Comparison of real width of proteins and apparent width in topographic images. The width is greatly over estimated, nevertheless the height can be measured very accurately.

Figure 22.. Simple model explaining the tip broadening effect. A pyramidal AFM tip with a spherical tip at its end (diameter 70 nm) will result in apparent images of microtubules (real diameter 25 nm) with 85 nm

Force Curves

In addition to topographic imaging it is possible to measure interaction forces between the AFM tip and the sample under investigation. In a force curve the deflection is monitored while the sample is moved only in z-direction. The sample is cycled vertically with respect to the tip, and cantilever deflection is measured relative to sample position. There are three basic steps to the cycle, each one yielding information on different tip-sample interaction forces in the nN range.

1. As the tip approaches the sample, deflection is caused by forces due to electrostatics or steric repulsion.
2. While in contact, the tip and sample deform one another, giving rise to elasticity measurements.

As the sample is pulled away from the tip, deflection will be due to binding or tip-sample adhesion forces.

Depending on the sample information on sample elasticity (Young's modulus), electrostatic interaction, adhesion etc. can be obtained. With very soft cantilevers (spring constant 10-30 mNm^-1) very high force sensitivity is achieved which allows even to measure specific interaction forces between single molecules, like ligand receptor pairs.

Figure 23. Example of measuring electro static interaction forces by AFM. Bilayer of the positively charged amphiphile DODAB were adsorbed on genatively charged mica. In the topographic image these bilayer patches of 5 nm height are clearly visible. Force curves taken on the bilayer or the mica support will show attractive or repulsive electrostatic interaction due to negative charges on the silicon nitride tip. (From: Rotsch & Radmacher, 1997)

AFM tips coated with different molecules have been used to study receptor-ligand interactions both in vitro (eg. biotin-avidin, cadherin-cadherin) (Florin et al.,1994), and in vivo (eg. integrin distribution on osteoclasts). Single molecule unfolding has been studied by anchoring one end of the molecule to the surface, and the other end to the tip and pulling them apart (eg titin, single DNA, bacteriorhodopsin, elastin) (Rief et al., 1997).

Force Mapping; In force mapping mode (or force volume mode) (Radmacher et al.,1994a), these force curves are gathered at many points on the sample surface, to map out properties such as elasticity (Rotsch & Radmacher, 2000) (Radmacher, 2002) and dynamic changes in elasticity during migration (Rotsch et al., 1999) and cell division (Matzke et al., 2001).

Figure 24. Topographic image of a osteoblast cells shows prominent cytoskeletal structures (left). In the region of interest marked by a white square in the left image, 64 by 64 force curves were taken (force mapping). From these force curves the local elastic modulus was calculated and is displayed in the elasticity map on the right. (from: Domke et al, 2000)

Outlook

Since its invention (Binnig et al., 1986) the AFM has been developed along different lines to suit it to several areas of biological research, from single molecule binding interactions to whole-cell studies. Along with the need for very little sample preparation, the combination of nanometer resolution with the capability to operate in physiological conditions, gives it a special niche for investigating molecular details in vitro and in vivo. Simultaneous imaging and measuring of forces under physiological conditions allow global mechanics to be linked to the visualized dynamics, which will invaluable in deepening our understanding of such a complex process as cell motility.

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