Experimental Set-Ups to Measure Cellular Forces

Cellular forces have been shown to be of importance in various biological pro-cesses such as cell migration [69], proliferation and differentiation [28]. To measure the cellular forces during these processes, different methods have been developed, both from an experimental as well as from an analytical point of view.

One of the earliest methods to visualise forces exerted by adherent cells was the imaging of soft elastic substrates. If cells located on the substrate contracted, the gel was deformed, resulting in a wrinkly surface [41]. To be able to quantify the forces corresponding to the degree of ’wrinkling’, more accurate imaging tech-niques had to be found. Generally, four different methods for force measuring experiments have developed over time: atomic force microscopy (AFM) measure-ments (e.g.[58, 78]), micro-post arrays (e.g.[29, 57, 65, 116, 120]), continuous elastic substrates containing markers (e.g.[17, 20, 43, 74, 89, 107, 122]) and, most recently, fluorescent, spring-like force sensor molecules (e.g.[31, 125, 127]). A sketch of all methods may be found in Fig. 2.4.

To measure the force exerted along an axis, atomic force microscopy or similar set-ups can be used (e.g.[58, 78], Fig. 2.4A). The cell is grown between a substrate and a flexible microplate [78] or cantilever [58]. By changing the stiffness of the flexible part of the set-up, the response of the cell to the stiffness can be deter-mined. Also, detachment forces from the cell to the substrate may be measured by actively applying an external force. However, as already mentioned, this approach measures the forces along a one-dimensional axis.

A two-dimensional tool to measure the contractile forces is the so called micro-post array (e.g. [29, 57, 65, 116, 120], Fig. 2.4 B). A micro-post array consists of a number of elastic, deformable posts positioned close to each other. The single posts are usually cast from Poly(dimethylsiloxane) (PDMS) and vary in post size, density and stiffness [120]. They are regularly distributed to facilitate easy tracking of deformation. Further, the posts are coated with adhesion proteins such as fibrin to facilitate attachment. By micro-contact printing the adhesive proteins to the posts in defined geometries, the cell’s shape and cytoskeletal organisation can be actively controlled [57]. Contracting cells seeded on the array deflect the underlying micro-posts, enabling the observer to directly re-calculate the exerted force. These assays are either conducted on ensembles of cells [29, 65] or on a

Chapter 2 STATE OF THE ART

F

F

F

F

A B

C D

Figure 2.4.: Four dierent methods to study the force F generated by a cell (orange). The direction of force measurement is given by the black arrows. A AFM measurements are conducted by determining the deection in a cantilever upon cell contraction. To facilitate this kind of measurement, adhesive proteins (green) are often used on the surface and cantilever. B Cells can be grown on micro-post arrays and the deection of the single post reects the contraction.

Contrary to AFM, this is done in two dimensions. C Also measured in two dimensions is the deformations of elastic substrates underneath a cell (TFM). The beads within the substrate (green) are displaced accordingly to the exerted force above them (green arrows). D A localised force measurement technique involves the use of molecular force sensors (blue-red spheres). Upon pulling on the molecule, it is stretched, thus increasing the distance between the active parts (both spheres). Following, either the change in energy transfer is measured (two uorophores) or the direct change in uorescent intensity (one uorophore and one quencher).

single-cell basis [57, 116, 120]. Note that this approach yields a measurement at discrete locations, namely the positions of the micro-posts.

Instead of using the discrete, two-dimensional set-up of micropost arrays, con-tinuous substrates can be used, a technique called traction force microscopy (TFM, e.g.[17, 20, 43, 74, 89, 107, 122], Fig. 2.4C). These substrates are cast from PDMS [17, 43] or, most commonly, polyacrylamide (PAA, [81, 89, 107, 122]). Within the strate, fluorescent markers are embedded to visualise the deformation of the sub-strate during cell contraction. Contrary to the micropost array, each fluorescent marker within the continuous gel yields a contribution to the measurement of the entire deformation field. Keeping in mind that the size of the fluorescent beads in general varies between a few tens to hundreds of nanometres in diameter, this gives a much higher resolution of the force field. The resolution in force mea-surement is limited by the density of beads, the imaging resolution as well as the employed analysis algorithm. At the same time, as all previously described force measurement tools, the stiffness of the substrate can be varied, here in terms of the degree of cross-linking in the polymer gels. The fabrication of PAA gels have

Force Measurements of Contractile Cells 2.2 been adapted to also include micro-contact printed proteins as for the micro-post

arrays [74, 81, 89, 122] as well as force measurement in three dimensions [21, 62].

Using this experimental set-up, keep in mind that due to the continuity of the substrate, deformations are not only observed at the point of force transduction on the gel but also in its direct neighbourhood.

To measure the forces at the actual point of force transmission, in recent years, so called tension sensor molecules have been developed (e.g.[31, 125, 127], Fig. 2.4 D). Simplified, these sensors consist of two fluorescent molecules connected by a spring-like molecule. When the two fluorophores are close together (= the "spring"

is relaxed), an active energy exchange occurs between them and can be measured by using Förster resonance energy transfer (FRET). The further the molecules are apart, less energy transfer is seen. Depending on the folding properties of the connecting molecule, different force ranges can be covered with a single sensor, often spanning an interval of some piconewtons [31], contrary to the nanonewtons measured in the methods described above. Alternatively to two fluorophores, one can be exchanged by a gold particle to quench the flourescence of the other [105, 127]. Developing these sensors is still an ongoing research topic as it has to be guaranteed that advert effects such as hysteresis do not occur during multiple stretching cycles.

In the presented work, the most common force measurement technique, TFM in combination with continuous PAA substrates, is used. This allows us to study the force development of a single platelet both in a two-dimensional space as well as in time. PAA substrates have the advantage of being well tunable in stiffness between 100 Pa and 100 kPa [115] which corresponds to the elasticity range found in the human body [28]. It has previously been demonstrated that platelets adhere well to these substrates when coated with fibrinogen [93, 107].

In TFM, one interesting point apart from the experimental set-up is the way to analyse the given data. Independent of the dimensionality of the set-up, the initial point of analysis is a given set of images of beads changing their position.

To re-calculate the forces exerted by the cell on the gel from the bead positions, a multitude of algorithms have been developed and are presented in the following.

Chapter 2 STATE OF THE ART