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Single-cell mechanics: The parallel plates technique
CHAPTER
Single-cell mechanics: The parallel plates technique
11
Nathalie Bufi, Pauline Durand-Smet, Atef Asnacios1 Laboratoire Matie`res et Syste`mes Complexes, Universite´ Paris-Diderot/CNRS, Sorbonne Paris Cite´, Paris, France 1
Corresponding author: E-mail: [email protected]
CHAPTER OUTLINE Introduction ............................................................................................................ 188 1. Experimental Setup ............................................................................................ 189 2. Microplates ....................................................................................................... 191 2.1 Microplate Fabrication ......................................................................... 192 2.1.1 Materials .......................................................................................... 192 2.1.2 Equipment ....................................................................................... 192 2.1.3 Method ............................................................................................ 192 2.2 Microplate Calibration ......................................................................... 193 2.2.1 Materials .......................................................................................... 194 2.2.2 Method ............................................................................................ 194 2.3 Microplate Cleaning ............................................................................ 194 2.3.1 Materials .......................................................................................... 194 2.3.2 Equipment ....................................................................................... 195 2.3.3 Method ............................................................................................ 195 2.4 Microplate Coating .............................................................................. 196 2.4.1 Materials .......................................................................................... 196 2.4.2 Equipment ....................................................................................... 196 2.4.3 Method ............................................................................................ 196 2.4.4 Possible modifications for different coatings ...................................... 196 3. Cell Preparation ................................................................................................. 197 3.1 Materials ............................................................................................ 197 3.2 Equipment ......................................................................................... 197 3.3 Method .............................................................................................. 197 4. Experimental Protocols....................................................................................... 198 4.1 Cell Capture........................................................................................ 198 4.2 Calibration of the Optical Sensor .......................................................... 199 4.3 Single-Cell Traction Force Measurements .............................................. 199 Methods in Cell Biology, Volume 125, ISSN 0091-679X, http://dx.doi.org/10.1016/bs.mcb.2014.11.002 © 2015 Elsevier Inc. All rights reserved.
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4.3.1 Simple traction ................................................................................. 199 4.3.2 Real-time single-cell response to stiffness ......................................... 200 4.4 Single-Cell Rheology............................................................................ 200 4.4.1 Dynamic mechanical analysis ........................................................... 200 4.4.2 Creep experiment ............................................................................. 205 4.4.3 Relaxation experiment ...................................................................... 205 5. Discussion ......................................................................................................... 206 Supplementary Data ................................................................................................ 208 References ............................................................................................................. 209
Abstract We describe here the parallel plates technique which enables quantifying single-cell mechanics, either passive (cell deformability) or active (whole-cell traction forces). Based on the bending of glass microplates of calibrated stiffness, it is easy to implement on any microscope, and benefits from protocols and equipment already used in biology labs (coating of glass slides, pipette pullers, micromanipulators, etc.). We first present the principle of the technique, the design and calibration of the microplates, and various surface coatings corresponding to different cellesubstrate interactions. Then we detail the specific cell preparation for the assays, and the different mechanical assays that can be carried out. Finally, we discuss the possible technical simplifications and the specificities of each mechanical protocol, as well as the possibility of extending the use of the parallel plates to investigate the mechanics of cell aggregates or tissues.
INTRODUCTION The mechanical properties of cells and tissues are involved in many physiological processes, and their alteration leads to impaired biological functions and diseases (Suresh, 2007). For instance, in sickle cell anemia, increased rigidity of red blood cells induces obstruction of small capillaries and hypoxia. This example illustrates the importance of the passive mechanical behavior of cells, i.e., their ability to deform under external forces (“rheological” features). Beyond deformability, cells are also mechanically active, applying traction forces on their environment either to migrate (morphogenetic movements, transmigration, wound healing) or to maintain homeostatic tension in tissues (Wozniak & Chen, 2009). Passive and active mechanical behaviors of cells are often related. For example, cancer cells display modified rigidity and migratory phenotype. However, experimental techniques are usually adapted to the characterization of only one of these properties. For instance, on the one hand, micropipette aspiration (Hochmuth, 2000), magnetic twisting cytometry (Fabry et al., 2001), and optical stretchers (Guck et al., 2005) are used to determine the rheological behavior. On the other hand, actively generated traction forces are measured through the deformation of compliant gels (Munevar, Wang, & Dembo, 2001) or 2D arrays of micropillars (Tan et al., 2003). Three main techniques are generally used to quantify both passive
1. Experimental setup
and active mechanical properties of cells. Optical tweezers (OT) (Balland, Richert, & Gallet, 2005) (Allioux-Gue´rin et al., 2009), using micrometric beads as probes, are dedicated to local, subcellular mechanics. Atomic force microscopy (AFM) (Alcaraz et al., 2003) (Webster, Crow, & Fletcher, 2011) can investigate cell mechanics from the subcellular to the whole-cell scales depending on the size of the probe, ranging from a few tens of nanometers (“sharp tips,” usually pyramidal) to tens of microns (tipless cantilevers) (See also Braybrook and Gautier et al. [Chapter 13 of this volume] on the use of AFM, respectively in plant and animal cells mechanics). Eventually, the parallel plates technique (Nicolas Desprat, Richert, Simeon, & Asnacios, 2005) (Mitrossilis et al., 2009), based on springlike glass plates of calibrated stiffness, allows one to investigate the mechanics of isolated single cells, as well as of cell aggregates or even millimeter-sized tissues and organisms, depending on the shape and dimensions of the flexible plate used as force probe. Compared to OT and AFM, the parallel plates technique is certainly the cheapest and the easiest to implement on a regular cell biology microscope. Based on glass plates, it readily benefits from well-known protocols established for coverslips coatings in order to ensure various cellesubstrate adhesion conditions. Moreover, for microplates fabrication, one can rely on methods and setups usually used for patch clamp and similar techniques (micropipette pullers, microforge). Indeed, while the parallel plates technique is in principle similar to using a tipless AFM, a first advantage here is that the microplates fabrication process is completely controlled and their bending stiffness and geometry can be finely tuned according to the experimental needs, in particular, the size and overall rigidity of the sample to be studied. Moreover, the geometry of the setup allows one to image the cell shape while carrying out mechanical measurements, which is not obvious, if at all possible, with AFM. Eventually, since the parallel plates setup is custom-made, the mechanical measurements by themselves may be carried out at different levels of technical refinements (Mitrossilis et al., 2010), and coupled to specific imaging protocols (Fouchard et al., 2014). For instance, single-cell traction force can be measured through simple image analysis of microplate bending, thus requiring no specific or additional equipment. In contrast, more sophisticated assays like creep measurements or real-time control of stiffness imply automated plate position detection and control. In the following, we detail the methods and protocols necessary for various parallel plates-based mechanical measurements.
1. EXPERIMENTAL SETUP The parallel plates setup is aimed at manipulating cells to access their mechanical properties, in a cell-by-cell manner. Various experiments can be conducted through this device, but they all rely on a very simple principle: the cell is caught between two parallel plates, one flexible, of calibrated bending stiffness k, and the other one rigid, in practice often 1000 times stiffer than the flexible plate. The microplates are mounted on an inverted microscope, placed parallel to each other, their edges
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parallel to the focal plane of the objective of the microscope, so that a side view of the cell caught between the plates can be imaged through a camera (Figure 1). For the simplest protocols (measurements of the cell Young’s modulus or traction force at constant plate stiffness), the bright-field image is used simultaneously to measure the flexible plate deflection (force measurements) and to determine cell shape and deformation. For more advanced mechanical tests (measure of creep function under constant stress, real-time stiffness control), a fast, real-time detection of the flexible plate deflection, i.e., independent of the image acquisition rate of the camera, is needed. In this case, the side view of the cell and plate tips is imaged on two different ports of the microscope. One port is hosting a camera for imaging of cell shape or even fluorescence monitoring of intracellular structures. The second optical port of the microscope is fitted with a photosensitive detector (PSD, S3931, Hamamatsu, Japan). The signal from the PSD is processed with an electronic board (C3683, 10 to þ10 V output range, Hamamatsu, Japan) delivering a voltage proportional to the flexible plate tip displacement. In all cases, once the displacement of the flexible plate tip is measured, the force exerted by/on the cell can be derived trivially from the flexible plate deflection d, F ¼ kd (Figure 1). The microplates are controlled via piezoelectric micromanipulators, enabling friction-less displacement of the plates with submicron resolution. Therefore, we can carry out a wide variety of rheological tests, which are always about applying a force (either
(A) base position
retro-acting loop
(B)
tip position
190
Flexible plate
k Rigid plate
FIGURE 1 Principle of the parallel plates setup. (A) The setup is composed of a rigid and a flexible plate calibrated in stiffness. The deflection of the flexible plate is proportional to the force applied to or by the cell at its tip. An optical sensor detects the displacement of the tip of the flexible plate, and this information can be used in return to act on both the flexible plate and the rigid plate according to the desired test performed. (B) Image of a cell undergoing single-cell parallel plates assay (scale bar 10 mm).
2. Microplates
through traction or compression) and measuring a deformation, or the opposite, in order to derive the response function of the sample tested.
2. MICROPLATES The microplates are manufactured in situ by stretching glass lamellae. The lamellae are then cut and fused to glass capillaries, and then calibrated to identify their bending stiffness (Figure 2). This manual process enables us to control the geometric and mechanical properties of the microplates. Thus, as shown in Figure 2, the angle between the lamella and the capillary tube can be modulated, but more importantly, the length of the lamella can be adapted to reach the desired bending stiffness. Indeed, basic strength of material theory tells us that the deflection d at the tip of a cantilever can be expressed by means of the force applied:
FIGURE 2 Microplate fabrication and calibration. (A) Steps to follow to manufacture the microplates. A heating filament melts a glass lamella (1, 2), that is then cut in order to get two microplates (3). The microplates are then sealed onto a capillary tube (4), which is in return bent (5) to achieve the desired shape (6). (B) Each manufactured microplate is calibrated against a reference microplate of known bending stiffness. The graph represents an example of calibration curve.
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FL3 3EI where L is the length of the plate and I its second moment of area (for a rectangular cross-section beam, I ¼ bh3/12, where b and h are the width and height of the beam, respectively). Here we see that force and deflection are linked by a constant, the bending stiffness modulus: d¼
3EI L3 This bending stiffness decreases with the cube of the length, meaning that a small variation of length has a big impact on the bending stiffness of the plate. The microplates are fabricated from glass lamellae with a rectangular cross-section. Although they keep a rectangular cross-section after stretching, the cross-sectional area is not constant along the stretched plate, and the microplates bending stiffness therefore needs to be systematically measured through a calibration process. A plate of a 1 0.1 mm initial section when stretched over about 1 cm will typically display a tip with a 50 5 mm and a stiffness of a few nN/mm. k¼
2.1 MICROPLATE FABRICATION 2.1.1 Materials •
Glass lamellae We use glass lamellae of 100 2mm with 0.1, 0.2, and 0.3 mm thicknesses alternatively, depending on the range of desired stiffness (lamellae were manufactured on demand by Lecordier-Siverso, France). The rigid plate can be either pulled out of 0.2 or 0.3 mm original thickness, but must be kept short. • Glass capillaries • Tweezers • Protection glasses
2.1.2 Equipment •
Micropipette puller (in our case, Narishige PB-7, Japan)
2.1.3 Method 1. 2. 3. 4. 5.
Slide the lamella in the holders of the pipette puller Switch on the heating resistor Wait for the lamella to melt and to be stretched by the stretcher Cut the two parts of the stretched lamella in the middle Cut the base of the lamella with precision scissors into approximately 5-mm length 6. Place the lamella in secure environment on a gum
2. Microplates
7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
17.
18.
We usually use a capillary sealing paste from Vitrex, but for this step any kind of modeling clay can be used Place the capillary tube so that one extremity lies in the middle of the heating resistor Turn on the heat Wait for partial melting and clamp together the extremity This step is important to ensure impermeability of the tube Seize the lamella with the tweezers and fuse it into the melting tip of the capillary Switch the heat off Turn the capillary into a handy position Switch the heat on Turn the lamella into the desired angle with the capillary Turn the heat off and wait for complete cooling down Check under the microplate experiment microscope for good alignment of a pair of rigid þ flexible microplates Tip and angle can be finely tuned with a microforge if necessary (MF-900 from Narishige in our case). Please refer to chapter Dual Pipette Aspiration: A Unique Tool For Studying Intercellular Adhesion by Biro and Maitre for details about microforging. Adjust the geometry of the plates if necessary. Fine tuning can be obtained by using a microforge equipped with a binocular, although this is not necessary for most applications. Take the microplates and store them by pair into safe environment We keep our plates by pair (1 rigid þ 1 flexible) planted in gum material (Vitrex paste) and kept in glass tubes filled with ethanol to avoid bacterial propagation An alternative to steps 9e10 would be: 90 . Enlarge the fusing extremity of the capillary with the tips of the tweezers. 100 . Insert the lamella inside the capillary. 110 . Clamp the enlarged extremity of the capillary around the lamella, melting them together and sealing the capillary.
2.2 MICROPLATE CALIBRATION Once the microplates are manufactured, one must operate a calibration to determine the bending stiffness of the plate. This calibration is done by using a microplate of known bending stiffness k0 as a reference. The bending stiffness of the reference microplate has been itself determined by stacking copper micro-wires at the extremity of the plate, as described in Desprat, Guiroy, and Asnacios (2006), but this method is too time consuming to be performed routinely in the lab. The comparative method described below is much lighter to implement, while still providing good accuracy. The two microplates are placed one against the other as shown in Figure 2(B). A controlled displacement D is applied to the reference microplate, and the
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displacement of the contact point d is measured via imaging. The momentum equations at the contact point gives: F ¼ kd ¼ k0 ðD dÞ And therefore we can express k in terms of k0, D, and d: D 1 k ¼ k0 d Therefore, if we measure different pairs (D,d), we can access the slope of the curve a ¼ D/d and access k (Figure 2(B)).
2.2.1 Materials • • •
Reference microplate Piezoelectric micromanipulator Microscope
2.2.2 Method 1. 2. 3. 4. 5. 6. 7.
Place the two microplates in contact as represented in Figure 2(B) Note the localization of the contact point Increment the position of the reference plate of a known displacement D Measure the position of the contact point d and note D and d Perform steps (3) and (4) about 10 times Plot D ¼ f(d) and get the slope value Extract the bending stiffness value
2.3 MICROPLATE CLEANING Once the microplates are calibrated, you need to clean them and coat them to ensure good adhesion of the cells. Although basic glass cleaning can be performed (hot water, dishwashing soap, ethanol), a deep cleaning is necessary for controlled adhesion conditions, and at least once a month to get rid of any cellular remains that can accumulate on the plates. The microplates can thus be used indefinitely. If they happen to break, recalibration is necessary, and if they break too short, they can still be used as rigid plates. Cleaning is done using a piranha solution (70% H2SO4 þ 30% H2O2), very abrasive that ensures the digestion of any organic component.
2.3.1 Materials • • • •
Sulfuric acid solution, pure Hydrogen peroxide solution, pure Graduating cylinder Erlenmeyer flasks For security reasons, use two flasks, the one receiving the piranha solution fitting inside of a bigger one
2. Microplates
• • •
• • •
•
Glass lid Lid must be big enough to cover up the biggest Erlenmeyer flask Swiss Boy Microplate holder Here we use an articulated arm finished by a platform where we deposit gum in order to plant the microplates by the capillary side Security glasses Lab coat Acid-proof gloves Any type of nitrile gloves can be used. Simple latex gloves can also be used if they are doubled, but it may increase the risk of mismanipulation. The most important here is to ensure continuity of protection between the glove and the lab coat (lab coat can be tucked inside the gloves and fixed with an elastic). Deionized water
2.3.2 Equipment •
Chemistry aspirating hood
2.3.3 Method Be careful as piranha solution is very dangerous. Check out with your security lab manager to ensure good practice before you try. 1. Prepare the setup by placing the small Erlenmeyer inside the big one. 2. Take your microplates out of their tubes and place them on the gummed platform of the holder. Holder should be placed on top of the Swiss Boy 3. Adjust the Swiss Boy and the holder so that the microplates hang with flexible tip facing down, high enough to pass above the Erlenmeyer containers. Place this setup in safe area under the hood (far from your movements). 4. Check that no part of your skin is exposed and put your protection glasses on. 5. Prepare the piranha solution by adding first 30% of hydrogen peroxide and second 70% of sulfuric acid. The solution should start boiling. Be careful here as the addition of hydrogen peroxide over acid will lead to projections that can cause very severe burns. 6. Place the microplates above the Erlenmeyer and lower them with the Swiss Boy so that they dip into the solution until the base of the capillary. 7. Leave the microplates in solution for 20e30 min. 8. Take the microplates out using the Swiss Boy. 9. Put the lid over the piranha solution and place in a corner of the hood. 10. Dip the microplates into fresh milli-Q water for 30 min. 11. Rinse and change water. 12. Dip the microplates again in fresh milli-Q water overnight.
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13. Get the microplates back in their tubes and discard the piranha into appropriate container. Here, be sure that the container is not tightly closed. The solution will keep creating gas and a sealed bottle would explode.
2.4 MICROPLATE COATING Once the plates are clean, it is time to coat them with your protein of interest. To study specific adhesion effects on cell mechanics, traction forces and physics of the cell with involvement of integrins and focal adhesion complexes, we used fibronectin (Sigma-Aldrich F1141, Saint Louis, US); for nonspecific adhesion, poly-L-Lysin (multiple charge interaction, P4707, Sigma-Aldrich, Germany) and glutaraldehyde (covalent bonds, G6403, Sigma-Aldrich, Germany) can be used.
2.4.1 Materials • • •
Roswell Park Memorial Institute (RPMI) medium Protein of interest 5 mL hemolysis tubes
2.4.2 Equipment • •
Sterile hood Incubator
2.4.3 Method 1. Rinse the microplates individually under deionized water to ensure elimination of all acid traces 2. Prepare a solution of fibronectin at 5 mg/mL in RPMI medium Here RPMI is used as a solvent because it provides a pH color indicator to monitor eventual remaining traces of acid. Deionized water or phosphatebuffered saline (PBS) can be used instead. 3. Fill the tubes with 3 mL of solution 4. Place the microplates pair-by-pair in each of the tubes 5. Leave at 37 C for 30 min
2.4.4 Possible modifications for different coatings For nonspecific adhesion based on electrostatic interactions, replace the fibronectin solution in step 2 by a solution of poly-L-Lysin (Sigma-Aldrich, P4707) at 0.01% in water. For nonspecific irreversible adhesion, one can coat the microplates with glutaraldehyde by replacing steps 2e5 by the following steps: 1. Prepare a solution of ethanol 90%, (3-Aminopropyl) triethoxysilane (SigmaAldrich 440140) 2%, deionized water 8%
3. Cell preparation
2. Filter this solution on a 0.22 mm filter in the tubes to reach a final volume of 3 mL of solution per tube Here you need as many tubes as pair of microplate you want to coat 3. Place the microplates pair-by-pair in each of the tubes 4. Leave at room temperature for 2 h 5. Prepare a solution of 2% glutaraldehyde (Sigma-Aldrich G6403) 6. Filter the glutaraldehyde solution on a 0.22 mm filter in the tubes (3 mL of solution per tube) 7. Take cautiously the microplates out of the silane tubes 8. Rinse with ethanol 9. Leave to dry for a couple of minutes The gum used to seal the microplates into the tube can be fixed on the lab bench, so that the microplates dry with the tip facing up 10. Once the microplates are dry, dip them into the glutaraldehyde-filled tubes 11. Leave for 30 min at room temperature 12. Wash with deionized water
3. CELL PREPARATION Most cell types are adherent. If it is the case, detaching the cells is necessary to enable individual testing. In this protocol, the cells are detached with trypsin and suspended in medium in 3 mL tubes. Cells are then left for 2 h under agitation to ensure the recovery of trans-membrane proteins while avoiding readhesion on the tube wall.
3.1 MATERIALS • • • •
Cells Trypsin (Life Technologies, 0.05% Trypsin-EDTA (1), phenol red 500 mg/mL) Cell medium PBS
3.2 EQUIPMENT • • • •
Sterile hood Incubator Agitator Centrifuge
3.3 METHOD 1. Rinse the cell flask with PBS 2. Cover the cells completely with trypsin solution 3. Leave for 5e10min at 37 C
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4. Centrifuge the cells þ trypsin at 1500 r/min for 5 min 5. Discard supernatant 6. Separate the cells into tubes at the desired concentration Final concentration in the microplate chamber should be such that it is enough to find cells easily but not too crowded (one cell/image) to avoid interference with the optical sensor 7. Place the tubes on the agitator at 37 C and wait for 2 h 8. Place culture medium at 37 C to warm up before experiments Add HEPES buffer at 1.5% in the culture medium to ensure pH stability during open-air experiments.
4. EXPERIMENTAL PROTOCOLS The microplates device is a very versatile tool to decipher microscale mechanics. Since we can simultaneously monitor force (therefore stress) and deformation (therefore strain), a wide variety of rheological tests can be performed, from the simplest to the more elaborated ones. In each of the tests whose principle is described below, the protocol is the same:
4.1 CELL CAPTURE 1. At least 1 h before the beginning of the experiment, turn on all the equipment, place the experiment chamber, and wait for temperature stabilization at 37 C 2. When 37 C is reached, pour culture medium in the experiment chamber 3. Take the microplates out of the incubator and place them onto their holder 4. Arrange the microplates so that they are parallel, and place them just in contact with the bottom of the chamber using the manual micromanipulator 5. Raise the microplates up (60e70 mm is enough) with the piezoelectric micromanipulator 6. Add some cells into the chamber and wait for them to seed to the bottom 7. With the stage manipulator, adjust the cell position so it can be caught in between the plates 8. With the piezoelectric micromanipulator, lower the microplates to the bottom of the chamber and catch the pre-positioned cell 9. Move the microplates with the cell in between up (60 mm from the bottom of the chamber) and focus on the microplates þ cell system 10. If needed, perform calibration of the optical sensor 11. Run the desired test 12. Clean up the experimental chamber and start again Here, according to the test and the type of cell-plate adhesion, it may or may not be necessary to change microplates for clean ones at each new cell testing (if the cells adhere and leave remains, the microplates must be changed. If the cells are nonadherent, they can be kept).
4. Experimental protocols
4.2 CALIBRATION OF THE OPTICAL SENSOR For experimental protocols demanding fast detection of the flexible microplate deflection that cannot be achieved by the camera frame rate, an optical sensor mounted on a specific microscope port can be used (please see section Experimental Setup). The flexible plate tip is then imaged on the (PSD) that delivers an output voltage proportional to the position of the flexible plate tip. Indeed, since the PSD is sensitive to the spatial distribution of light intensity over its surface area, plate tip displacements lead to spatial modulations of light intensity and specific modulations of the output signal (see Desprat et al., 2006 for details). Therefore the signal depends on the microplate positioning and on the focus and settings of the microscope lens. Thus, before each experiment where this sensor is involved, calibration must be performed. To do so, the flexible microplate is displaced in such a way that its image spans the entire sensor area. The plate displacement D(t) and the sensor output s(t) are monitored simultaneously. In the central zone, the sensor is linear (s(t) ¼ a D(t)) and we can therefore plot s(t) with respect to D(t) and get the calibration parameter a value (Figure 3).
4.3 SINGLE-CELL TRACTION FORCE MEASUREMENTS 4.3.1 Simple traction Just like liquid droplets, some cell types spread on their substrate while applying a force on it. One can characterize this force with the microplates setup. Here the protocol is really simple. Once the cell is seized between the microplates, just record the deflection d of the tip of the soft microplate, the traction force
Sensor output s(t) (V)
−14
−16
−18
−20
−22 −0.1
0 0.1 0.2 Displacement (μm) D(t)
0.3
FIGURE 3 Optical sensor calibration. Once the cells are placed in between the plates and lifted from the bottom of the chamber, the calibration of the optical sensor has to take place to determine the relationship between the sensor output in volts and the actual tip displacement in microns. This curve is an example of calibration performed.
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exerted by the cell being F ¼ kd. Whatever the cell type tested so far, force over time exhibited a sigmoidal form (Figure 4), while cell shape evolved with spreading (Movie M1).
4.3.2 Real-time single-cell response to stiffness The effective stiffness felt by a cell when pulling in between the parallel microplates can be controlled through a feedback loop acting both on the rigid and flexible microplates (Mitrossilis et al., 2010). Whatever the actual stiffness of the soft microplate, the cell is sensing an effective rigidity which is the ratio of the force F(t) it applies to its shortening DL(t) ¼ L0 L(t) when contracting: keff ¼ F(t)/DL(t). keff can be set by making DL(t) a function of F(t) through adapted feedback signals d(t) and D(t) on the positions of the soft and rigid plates, respectively. The effective bending stiffness is then keff ¼ k0d(t)/D(t) (Figure 5).
4.4 SINGLE-CELL RHEOLOGY 4.4.1 Dynamic mechanical analysis Dynamic mechanical analysis is a widely used method in viscoelastic material rheology. The principle is to apply a controlled sinusoidal stress or strain at different frequencies, while measuring the complementary variable. In these conditions,
FIGURE 4 Typical traction force curve. The simplest test consists in letting a cell spread between the two microplates and record the tip deflection (i.e., the force) along the time (Movie M1). The curves obtained typically show a sigmoid shape, with three distinct phases. The first phase is a phase of early spreading and onset of force generation, followed by a phase of high rate traction. The third phase corresponds to slow down of contraction and saturation.
Real-time stiffness tuning. The retroaction loop on both the flexible and the soft plate allows mimicking a stiffness range from zero to infinity. (A) With no feedback, the cell is experiencing the bending stiffness of the flexible plate K0. (B) If the tip of the flexible plate is maintained in a constant position, the cell is facing and nondeformable solid, of infinite stiffness. (C) If the deflection of the flexible plate is maintained zero (no force), by retroacting on the rigid plate, the cell is experiencing a system infinitely soft, equivalent to zero stiffness. (D) The relationship between the 0 dðt Þ deflection of the flexible plate d(t) and of the displacement of the rigid plate D(t) can be set to reach any effective stiffness value: Keff ¼ KDðt Þ.
4. Experimental protocols
FIGURE 5
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elastic-like behavior (storage of energy) leads to stress and strain signals in phase, while viscous-like response (dissipation) is characterized by a p/2 phase shift. In the general case of a viscoelastic sample like living cells, the phase shift lies in between 0 and p/2, and the passive mechanical behavior is characterized by a complex viscoelastic modulus with a real part and an imaginary part: G ðuÞ ¼ G0 ðuÞ þ iG00 ðuÞ The real part G0 , referred to as the storage modulus, characterizes the elastic part of the cell response, while the imaginary part G00 , or loss modulus, gives an information on the dissipative contribution to cell mechanics. These loss and storage moduli can be derived from the parallel plates measurements. Indeed, G* is defined as the stressestrain ratio: sðtÞ G t ¼ εðtÞ with s(t) and ε(t) being stress and strain, respectively. There are two ways to carry out dynamical measurements depending on which plate the sinusoidal excitation signal is applied. •
Flexible plate-based excitation
In this case, a sinusoidal displacement D(t) is imposed to the base of the flexible plate, and the resulting movement at the plate tip d(t), which depends on the cell mechanical behavior, is recorded via the optical sensor. This gives, in complex form: D t ¼ D0 eiut d t ¼ d0 eiutþ4 where D0 and d0 are the amplitudes of the two signals, u their frequency, and 4 their phase lag. The stress s(t) can be derived from the force applied at the tip of the microplate divided by the area S of the celleplate contact: kdðtÞ kðDðtÞ dðtÞÞ ¼ s t ¼ S S where d(t) ¼ D(t) d(t) is the flexible plate deflection and k its bending stiffness. The area of contact S is estimated from the apparent contact diameters ø1 and ø2 at the flexible and rigid plate (Figure 6), assuming an axisymmetrical shape of the p 2 p 2 cell: S ¼ 12 4 1 þ 4 2 . •
Rigid plate-based excitation
From the expressions of D(t) and d(t), s(t) becomes k s t ¼ eiut D0 d0 ei4 S
4. Experimental protocols
(A)
k (B)
(C)
10000
d1 L0
d2
′
G
′′
G
Moduli (Pa)
1000
100
10 0.01
0.1
1
10
f (Hz) FIGURE 6 Dynamic mechanical analysis. (A) Schematic description of the experiment. Oscillations are applied at the base of the microplate, and the cell reaction is recorded. (B) Cell geometry parameters are measured on bright-field images (scale bar 10 mm). (C) By extracting the phase shift and the amplitude ratio of the input D(t) and the output d(t), we can derive the storage and loss moduli of the cell G0 and G00 , respectively. For single cell, these moduli behave as a power law of frequency, as the fitted data show above.
On the other hand, the strain ε(t) is defined as the ratio between the instantaneous cell elongation DL(t) ¼ L0 L(t) ¼ d(t) and its initial length L0: dðtÞ d0 eiutþ4 ¼ ε t ¼ L0 L0 This, all in all, gives an expression of the complex viscoelastic modulus: s kL0 D0 i4 G ¼ ¼ e 1 S d0 ε
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And the storage and loss moduli are therefore respectively 8 kL0 D0 > 0 > G ¼ cos 4 1 > < S d0 > kL0 D0 > 00 > : G ¼ sin 4 S d0 Here we see that we can access G0 and G00 by knowing k, L0, and S and monitoring D0, d0, and 4. While L0 and S are estimated from the bright-field images (Figure 6(B)), D0, d0, and 4 are extracted from analysis of the sine wave signals measured from the output of the piezoelectric device controlling the flexible plate displacement on the one hand (base movement D(t)) and from the optical tip position sensor (tip movement d(t)) on the other hand. It has been shown and is now widely accepted that G0 and G00 behave as a power law of frequency (Fabry et al., 2001) (Figure 6(C)). An alternative way to measure the cell complex modulus is to apply the sinusoidal displacement D(t) ¼ D0eiut to the rigid plate (and not to the base of the flexible plate as described above). The movement of the tip of the flexible plate remains of the form d(t) ¼ d0eiut, but the expressions of the stress and strain become k d0 eiutþ4 s t ¼ S D0 d0 ei4 iut e ε t ¼ L0 And the storage and loss moduli therefore write 8 kL0 D0 > 0 > ! >G ¼ cos 4 þ 1 > > d0 > D20 > > S 2 1 > > < d0 > kL0 D0 > 00 > ! > G ¼ sin 4 > > d0 > D20 > > S 1 > : 2 d0 This protocol is not fundamentally different from the previous one where the sinusoidal perturbation is applied through the flexible plate, but allows one to carry out the measurements only through image analysis since the rigid and flexible plate tips are visualized in the field of view (in the previous protocol, one needs to compare the displacements of the tip and the basis of the flexible plate which cannot both be visualized through the objective, implying a more tricky synchronization between image analysis and basis position command signal to ensure a proper phase shift determination). For instance, working at a typical frequency of 1 Hz, one can get 25 images with a regular camera, for each compression/traction cycle; each one giving a measurement of D(t) and d(t). The sine waves retrieved from image analysis can then be
4. Experimental protocols
fitted, and D0, d0, and 4 are determined. A fast camera can of course be used for measurements at higher frequencies.
4.4.2 Creep experiment The creep experiment consists in submitting the cell to a constant stress. The experiment is initiated by applying a step displacement to the base of the soft plate, leading to an initial plate deflection d0, and a stress s0 t ¼ kdS0 , where k is the plate stiffness and S is the cell-plate contact area defined as in the previous section. Then, the deflection is held constant by the feedback loop which applies a correction D(t) to the position of the rigid plate in order to maintain the tip of the flexible plate in its initial position. Therefore, if the surface area does not vary, the stress imposed to the cell remains constant. The creep function can be expressed as εðtÞ J t ¼ s0 Since the cell elongation is directly given by the feedback loop correction on the rigid plate DL(t) ¼ L0 L(t) ¼ D(t), the strain ε(t) defined as the ratio between the instantaneous cell elongation and its initial length L0, writes DðtÞ ε t ¼ L0 And the cell creep function is finally given by DðtÞS J t ¼ kd0 L0 Consistently with dynamical measurements in the frequency domain (previous section), the creep function of cells follows a power law of time (Figure 7).
4.4.3 Relaxation experiment The relaxation experiment follows the same principle as the creep experiment, but instead of applying a constant stress, here the strain is maintained constant and the stress evolution is measured. In the microplates setup, this is achieved by maintaining the rigid plate position fixed while feeding back on the base of the flexible plate. Initially, the flexible plate tip is moved over a distance d0 to a target position corresponding to the desired cell elongation (phase of strain rise up). Then, as the cell relaxes, the position of the flexible plate basis is modified (displacement D(t)) so that the tip remains at the target position. This second phase of the experiment, where the strain is constant and the stress decreasing, corresponds to the true relaxation regime. The strain is given by d0 ε t ¼ L0
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−1
10
−2
10
J(t) (Pa –1)
206
−3
10
−4
10
0.01
0.1
1
time (s)
10
100
1000
FIGURE 7 Creep experiment. A displacement step is applied to the base of the flexible plate, while the tip is maintained at the same position. The cell is therefore submitted to a step of force. This force is maintained constant across the experiment by retroacting on the position of the rigid plate to compensate for cell elongation. The creep function J is a weak power law of the time, as the fitted data illustrate above.
where L0 is the initial cell length. The stress is directly related to the feedback signal D(t): kðDðtÞ d0 Þ s t ¼ S where k is the flexible plate stiffness and S is the cell-plate contact area. A set of sðtÞ relaxation data is shown in Figure 8. The relaxation modulus G t ¼ ε0 then writes kðDðtÞ d0 Þ G t ¼ ε0 S Here again, the cell response is a power law of the time (Figure 8).
5. DISCUSSION The mechanical measurements described above present different levels of technical difficulty depending on the need or not of fast detection of the flexible plate deflection (real-time force measurement), and feedback on the positions of both flexible and rigid plates. From this point of view, the simple single-cell traction force assay
5. Discussion
stress (Pa)
10000
1000
100 0.1
1
10
100
time (s)
FIGURE 8 Relaxation experiment. While the rigid plate is at a fixed position all over the experiment, the tip of the flexible plate is initially shifted to a target position and then maintained immobile thanks to a feedback correction applied to its base. The cell is therefore submitted to a step strain and the stress necessary to compensate for tension relaxation in the cell structure is recorded all along the experiment. The relaxation modulus G is a decreasing weak power law of the time, as illustrated in this particular example.
is certainly the easiest. As shown in Figure 4, the characteristic timescale of force evolution is of about 10e20 min. Thus, the measurement of the flexible plate deflection (and consequently of force) can be done through image analysis after the experiment. Similarly, as already mentioned in the section dedicated to dynamical single-cell rheology, the storage and loss moduli (G0 and G00 ) can also be measured through image analysis, provided the experiments are run through the “rigid plate-based excitation” protocol, and the image sampling rate high enough compared to the excitation frequency. Conversely, stiffness control, creep, and relaxation assays require real-time detection of the flexible plate deflection, and feedback on both flexible and rigid plate positions. We achieved that using a position-sensitive detector with dedicated electronics to ensure that the rates of the detection and feedback loops are independent of the frequency of image acquisition (Desprat et al., 2006). However, the detection could easily be carried out, in real time, through image analysis for those who are familiar with particle tracking methods, which are now widespread in research labs. One of the advantages of the parallel plates technique is that it can be coupled to fluorescence microscopy since the setup can be implemented on any regular inverted
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microscope. In particular, simple traction force measurements are really easy to synchronize with fluorescence since no real-time detection is needed and timescales of force and cell shape evolution are quite long. Concerning the choice between the different rheology protocols, there are a few rules one has to keep in mind. If cell deformation is kept low (less than 10% typically), the three rheological protocols described in this chapter give equivalent information. In fact, cells, like many viscoelastic materials, exhibit different mechanical behaviors depending on the particular timescale over which they are tested. This can directly be achieved in creep or relaxation experiment where one monitors the time evolution of the corresponding mechanical response function. When performing dynamical tests, one has to run experiments at different frequencies to test cell behavior at different timescales, high frequencies corresponding to short times, and vice versa. Eventually, when working in the time domain, creep experiments are easier to analyze than relaxation ones. Indeed, applying a step stress (or force) is something trivial since it implies bending of an elastic microplate, which can be made instantaneously. In contrast, applying a step strain (or elongation) is not possible since it corresponds to an instantaneous deformation of a viscoelastic material (here the cell) which should necessitate an infinite applied force (for a viscous media, force is proportional to the rate of deformation). Thus, in any relaxation experiment, there is an initial phase of setting up of the target strain which does not correspond to true relaxation conditions of constant strain. This initial regime can be analyzed, but this is not straightforward. One generally analyzes the second regime where the strain is maintained constant, but then there is some uncertainty on the time “zero” at which this true relaxation regime is initiated. As a consequence, when cells can be made adherent to the plates, one should always perform creep tractions. If cells are not adherent, then relaxation in compression is the adapted solution, because creep in compression leads to increasing celleplates contact area, and thus to a decreasing applied stress even though force is maintained constant. Finally, it is noteworthy that the parallel plates technique could easily be adapted to study cell aggregates or even millimeter-sized organisms. Indeed, the stiffness of the flexible plate, used as a force sensor, can be tuned by adapting its shape and size (see section Microplates above), while the analysis of the geometry and deformation of samples bigger than single cells can be achieved with low-magnification objectives. For instance, we are currently using the parallel plates technique to study single plant cell mechanics (almost the same size as animal cells but necessitating plates with a 1000-fold increased stiffness) (Durand-Smet et al., 2014), as well as plant hypocotyls (plates 1000 times stiffer and 100 times bigger than those used for single animal cell measurements).
SUPPLEMENTARY DATA Supplementary data related to this article can be found online at http://dx.doi.org/10. 1016/bs.mcb.2014.11.002.
References
REFERENCES Alcaraz, J., Buscemi, L., Grabulosa, M., Trepat, X., Fabry, B., Farre´, R., et al. (2003). Microrheology of human lung epithelial cells measured by atomic force microscopy. Biophysical Journal, 84(3), 2071e2079. Allioux-Gue´rin, M., Icard-Arcizet, D., Durieux, C., He´non, S., Gallet, F., Mevel, J.-C., et al. (2009). Spatiotemporal analysis of cell response to a rigidity gradient: a quantitative study using multiple optical tweezers. Biophysical Journal, 96(1), 238e247. Balland, M., Richert, A., & Gallet, F. (2005). The dissipative contribution of myosin II in the cytoskeleton dynamics of myoblasts. European Biophysics Journal, 34(3), 255e261. Desprat, N., Guiroy, A., & Asnacios, A. (2006). Microplates-based rheometer for a single living cell. Review of Scientific Instruments, 77(055111), 1e9. Desprat, N., Richert, A., Simeon, J., & Asnacios, A. (2005). Creep function of a single living cell. Biophysical Journal, 88(3), 2224e2233. Durand-Smet, P., Chastrette, N., Guiroy, A., Richert, A., Berne-Dedieu, A., Szecsi, J., et al. (2014). A Comparative Mechanical Analysis of Plant and Animal Cells Reveals Convergence across Kingdoms. Biophysical journal, 107, 2237e2244. Fabry, B., Maksym, G., Butler, J., Glogauer, M., Navajas, D., & Fredberg, J. J. (2001). Scaling the Microrheology of living cells. Physical Review Letters, 87(14), 1e4. http://dx.doi.org/ 10.1103/PhysRevLett.87.148102. Fouchard, J., Bimbard, C., Bufi, N., Durand-Smet, P., Proag, A., Richert, A., et al. (2014). Three-dimensional cell body shape dictates the onset of traction force generation and growth of focal adhesions. Proceedings of the National Academy of Sciences, 111(36), 13075e13080. Guck, J., Schinkinger, S., Lincoln, B., Wottawah, F., Ebert, S., Romeyke, M., et al. (2005). Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence. Biophysical Journal, 88(5), 3689e3698. Hochmuth, R. M. (2000). Micropipette aspiration of living cells. Journal of biomechanics, 33(1), 15e22. Mitrossilis, D., Fouchard, J., Guiroy, A., Desprat, N., Rodriguez, N., Fabry, B., et al. (2009). Single-cell response to stiffness exhibits muscle-like behavior. Proceedings of the National Academy of Sciences, 106(43), 18243e18248. Mitrossilis, D., Fouchard, J., Pereira, D., Postic, F., Richert, A., Saint-Jean, M., et al. (2010). Real-time single-cell response to stiffness. Proceedings of the National Academy of Sciences, 107(38), 16518e16523. Munevar, S., Wang, Y., & Dembo, M. (2001). Traction force microscopy of migrating normal and H-ras transformed 3T3 fibroblasts. Biophysical Journal, 80(4), 1744e1757. Suresh, S. (2007). Biomechanics and biophysics of cancer cells. Acta Materialia, 55(12), 3989e4014. Tan, J. L., Tien, J., Pirone, D. M., Gray, D. S., Bhadriraju, K., & Chen, C. S. (2003). Cells lying on a bed of microneedles: an approach to isolate mechanical force. Proceedings of the National Academy of Sciences, 100(4), 1484e1489. Webster, K. D., Crow, A., & Fletcher, D. A. (2011). An AFM-based stiffness clamp for dynamic control of rigidity. PLoS One, 6(3), e17807. Wozniak, M. A., & Chen, C. S. (2009). Mechanotransduction in development: a growing role for contractility. Nature Reviews Molecular Cell Biology, 10(1), 34e43.
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11
Nathalie Bufi, Pauline Durand-Smet, Atef Asnacios1 Laboratoire Matie`res et Syste`mes Complexes, Universite´ Paris-Diderot/CNRS, Sorbonne Paris Cite´, Paris, France 1
Corresponding author: E-mail: [email protected]
CHAPTER OUTLINE Introduction ............................................................................................................ 188 1. Experimental Setup ............................................................................................ 189 2. Microplates ....................................................................................................... 191 2.1 Microplate Fabrication ......................................................................... 192 2.1.1 Materials .......................................................................................... 192 2.1.2 Equipment ....................................................................................... 192 2.1.3 Method ............................................................................................ 192 2.2 Microplate Calibration ......................................................................... 193 2.2.1 Materials .......................................................................................... 194 2.2.2 Method ............................................................................................ 194 2.3 Microplate Cleaning ............................................................................ 194 2.3.1 Materials .......................................................................................... 194 2.3.2 Equipment ....................................................................................... 195 2.3.3 Method ............................................................................................ 195 2.4 Microplate Coating .............................................................................. 196 2.4.1 Materials .......................................................................................... 196 2.4.2 Equipment ....................................................................................... 196 2.4.3 Method ............................................................................................ 196 2.4.4 Possible modifications for different coatings ...................................... 196 3. Cell Preparation ................................................................................................. 197 3.1 Materials ............................................................................................ 197 3.2 Equipment ......................................................................................... 197 3.3 Method .............................................................................................. 197 4. Experimental Protocols....................................................................................... 198 4.1 Cell Capture........................................................................................ 198 4.2 Calibration of the Optical Sensor .......................................................... 199 4.3 Single-Cell Traction Force Measurements .............................................. 199 Methods in Cell Biology, Volume 125, ISSN 0091-679X, http://dx.doi.org/10.1016/bs.mcb.2014.11.002 © 2015 Elsevier Inc. All rights reserved.
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4.3.1 Simple traction ................................................................................. 199 4.3.2 Real-time single-cell response to stiffness ......................................... 200 4.4 Single-Cell Rheology............................................................................ 200 4.4.1 Dynamic mechanical analysis ........................................................... 200 4.4.2 Creep experiment ............................................................................. 205 4.4.3 Relaxation experiment ...................................................................... 205 5. Discussion ......................................................................................................... 206 Supplementary Data ................................................................................................ 208 References ............................................................................................................. 209
Abstract We describe here the parallel plates technique which enables quantifying single-cell mechanics, either passive (cell deformability) or active (whole-cell traction forces). Based on the bending of glass microplates of calibrated stiffness, it is easy to implement on any microscope, and benefits from protocols and equipment already used in biology labs (coating of glass slides, pipette pullers, micromanipulators, etc.). We first present the principle of the technique, the design and calibration of the microplates, and various surface coatings corresponding to different cellesubstrate interactions. Then we detail the specific cell preparation for the assays, and the different mechanical assays that can be carried out. Finally, we discuss the possible technical simplifications and the specificities of each mechanical protocol, as well as the possibility of extending the use of the parallel plates to investigate the mechanics of cell aggregates or tissues.
INTRODUCTION The mechanical properties of cells and tissues are involved in many physiological processes, and their alteration leads to impaired biological functions and diseases (Suresh, 2007). For instance, in sickle cell anemia, increased rigidity of red blood cells induces obstruction of small capillaries and hypoxia. This example illustrates the importance of the passive mechanical behavior of cells, i.e., their ability to deform under external forces (“rheological” features). Beyond deformability, cells are also mechanically active, applying traction forces on their environment either to migrate (morphogenetic movements, transmigration, wound healing) or to maintain homeostatic tension in tissues (Wozniak & Chen, 2009). Passive and active mechanical behaviors of cells are often related. For example, cancer cells display modified rigidity and migratory phenotype. However, experimental techniques are usually adapted to the characterization of only one of these properties. For instance, on the one hand, micropipette aspiration (Hochmuth, 2000), magnetic twisting cytometry (Fabry et al., 2001), and optical stretchers (Guck et al., 2005) are used to determine the rheological behavior. On the other hand, actively generated traction forces are measured through the deformation of compliant gels (Munevar, Wang, & Dembo, 2001) or 2D arrays of micropillars (Tan et al., 2003). Three main techniques are generally used to quantify both passive
1. Experimental setup
and active mechanical properties of cells. Optical tweezers (OT) (Balland, Richert, & Gallet, 2005) (Allioux-Gue´rin et al., 2009), using micrometric beads as probes, are dedicated to local, subcellular mechanics. Atomic force microscopy (AFM) (Alcaraz et al., 2003) (Webster, Crow, & Fletcher, 2011) can investigate cell mechanics from the subcellular to the whole-cell scales depending on the size of the probe, ranging from a few tens of nanometers (“sharp tips,” usually pyramidal) to tens of microns (tipless cantilevers) (See also Braybrook and Gautier et al. [Chapter 13 of this volume] on the use of AFM, respectively in plant and animal cells mechanics). Eventually, the parallel plates technique (Nicolas Desprat, Richert, Simeon, & Asnacios, 2005) (Mitrossilis et al., 2009), based on springlike glass plates of calibrated stiffness, allows one to investigate the mechanics of isolated single cells, as well as of cell aggregates or even millimeter-sized tissues and organisms, depending on the shape and dimensions of the flexible plate used as force probe. Compared to OT and AFM, the parallel plates technique is certainly the cheapest and the easiest to implement on a regular cell biology microscope. Based on glass plates, it readily benefits from well-known protocols established for coverslips coatings in order to ensure various cellesubstrate adhesion conditions. Moreover, for microplates fabrication, one can rely on methods and setups usually used for patch clamp and similar techniques (micropipette pullers, microforge). Indeed, while the parallel plates technique is in principle similar to using a tipless AFM, a first advantage here is that the microplates fabrication process is completely controlled and their bending stiffness and geometry can be finely tuned according to the experimental needs, in particular, the size and overall rigidity of the sample to be studied. Moreover, the geometry of the setup allows one to image the cell shape while carrying out mechanical measurements, which is not obvious, if at all possible, with AFM. Eventually, since the parallel plates setup is custom-made, the mechanical measurements by themselves may be carried out at different levels of technical refinements (Mitrossilis et al., 2010), and coupled to specific imaging protocols (Fouchard et al., 2014). For instance, single-cell traction force can be measured through simple image analysis of microplate bending, thus requiring no specific or additional equipment. In contrast, more sophisticated assays like creep measurements or real-time control of stiffness imply automated plate position detection and control. In the following, we detail the methods and protocols necessary for various parallel plates-based mechanical measurements.
1. EXPERIMENTAL SETUP The parallel plates setup is aimed at manipulating cells to access their mechanical properties, in a cell-by-cell manner. Various experiments can be conducted through this device, but they all rely on a very simple principle: the cell is caught between two parallel plates, one flexible, of calibrated bending stiffness k, and the other one rigid, in practice often 1000 times stiffer than the flexible plate. The microplates are mounted on an inverted microscope, placed parallel to each other, their edges
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parallel to the focal plane of the objective of the microscope, so that a side view of the cell caught between the plates can be imaged through a camera (Figure 1). For the simplest protocols (measurements of the cell Young’s modulus or traction force at constant plate stiffness), the bright-field image is used simultaneously to measure the flexible plate deflection (force measurements) and to determine cell shape and deformation. For more advanced mechanical tests (measure of creep function under constant stress, real-time stiffness control), a fast, real-time detection of the flexible plate deflection, i.e., independent of the image acquisition rate of the camera, is needed. In this case, the side view of the cell and plate tips is imaged on two different ports of the microscope. One port is hosting a camera for imaging of cell shape or even fluorescence monitoring of intracellular structures. The second optical port of the microscope is fitted with a photosensitive detector (PSD, S3931, Hamamatsu, Japan). The signal from the PSD is processed with an electronic board (C3683, 10 to þ10 V output range, Hamamatsu, Japan) delivering a voltage proportional to the flexible plate tip displacement. In all cases, once the displacement of the flexible plate tip is measured, the force exerted by/on the cell can be derived trivially from the flexible plate deflection d, F ¼ kd (Figure 1). The microplates are controlled via piezoelectric micromanipulators, enabling friction-less displacement of the plates with submicron resolution. Therefore, we can carry out a wide variety of rheological tests, which are always about applying a force (either
(A) base position
retro-acting loop
(B)
tip position
190
Flexible plate
k Rigid plate
FIGURE 1 Principle of the parallel plates setup. (A) The setup is composed of a rigid and a flexible plate calibrated in stiffness. The deflection of the flexible plate is proportional to the force applied to or by the cell at its tip. An optical sensor detects the displacement of the tip of the flexible plate, and this information can be used in return to act on both the flexible plate and the rigid plate according to the desired test performed. (B) Image of a cell undergoing single-cell parallel plates assay (scale bar 10 mm).
2. Microplates
through traction or compression) and measuring a deformation, or the opposite, in order to derive the response function of the sample tested.
2. MICROPLATES The microplates are manufactured in situ by stretching glass lamellae. The lamellae are then cut and fused to glass capillaries, and then calibrated to identify their bending stiffness (Figure 2). This manual process enables us to control the geometric and mechanical properties of the microplates. Thus, as shown in Figure 2, the angle between the lamella and the capillary tube can be modulated, but more importantly, the length of the lamella can be adapted to reach the desired bending stiffness. Indeed, basic strength of material theory tells us that the deflection d at the tip of a cantilever can be expressed by means of the force applied:
FIGURE 2 Microplate fabrication and calibration. (A) Steps to follow to manufacture the microplates. A heating filament melts a glass lamella (1, 2), that is then cut in order to get two microplates (3). The microplates are then sealed onto a capillary tube (4), which is in return bent (5) to achieve the desired shape (6). (B) Each manufactured microplate is calibrated against a reference microplate of known bending stiffness. The graph represents an example of calibration curve.
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FL3 3EI where L is the length of the plate and I its second moment of area (for a rectangular cross-section beam, I ¼ bh3/12, where b and h are the width and height of the beam, respectively). Here we see that force and deflection are linked by a constant, the bending stiffness modulus: d¼
3EI L3 This bending stiffness decreases with the cube of the length, meaning that a small variation of length has a big impact on the bending stiffness of the plate. The microplates are fabricated from glass lamellae with a rectangular cross-section. Although they keep a rectangular cross-section after stretching, the cross-sectional area is not constant along the stretched plate, and the microplates bending stiffness therefore needs to be systematically measured through a calibration process. A plate of a 1 0.1 mm initial section when stretched over about 1 cm will typically display a tip with a 50 5 mm and a stiffness of a few nN/mm. k¼
2.1 MICROPLATE FABRICATION 2.1.1 Materials •
Glass lamellae We use glass lamellae of 100 2mm with 0.1, 0.2, and 0.3 mm thicknesses alternatively, depending on the range of desired stiffness (lamellae were manufactured on demand by Lecordier-Siverso, France). The rigid plate can be either pulled out of 0.2 or 0.3 mm original thickness, but must be kept short. • Glass capillaries • Tweezers • Protection glasses
2.1.2 Equipment •
Micropipette puller (in our case, Narishige PB-7, Japan)
2.1.3 Method 1. 2. 3. 4. 5.
Slide the lamella in the holders of the pipette puller Switch on the heating resistor Wait for the lamella to melt and to be stretched by the stretcher Cut the two parts of the stretched lamella in the middle Cut the base of the lamella with precision scissors into approximately 5-mm length 6. Place the lamella in secure environment on a gum
2. Microplates
7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
17.
18.
We usually use a capillary sealing paste from Vitrex, but for this step any kind of modeling clay can be used Place the capillary tube so that one extremity lies in the middle of the heating resistor Turn on the heat Wait for partial melting and clamp together the extremity This step is important to ensure impermeability of the tube Seize the lamella with the tweezers and fuse it into the melting tip of the capillary Switch the heat off Turn the capillary into a handy position Switch the heat on Turn the lamella into the desired angle with the capillary Turn the heat off and wait for complete cooling down Check under the microplate experiment microscope for good alignment of a pair of rigid þ flexible microplates Tip and angle can be finely tuned with a microforge if necessary (MF-900 from Narishige in our case). Please refer to chapter Dual Pipette Aspiration: A Unique Tool For Studying Intercellular Adhesion by Biro and Maitre for details about microforging. Adjust the geometry of the plates if necessary. Fine tuning can be obtained by using a microforge equipped with a binocular, although this is not necessary for most applications. Take the microplates and store them by pair into safe environment We keep our plates by pair (1 rigid þ 1 flexible) planted in gum material (Vitrex paste) and kept in glass tubes filled with ethanol to avoid bacterial propagation An alternative to steps 9e10 would be: 90 . Enlarge the fusing extremity of the capillary with the tips of the tweezers. 100 . Insert the lamella inside the capillary. 110 . Clamp the enlarged extremity of the capillary around the lamella, melting them together and sealing the capillary.
2.2 MICROPLATE CALIBRATION Once the microplates are manufactured, one must operate a calibration to determine the bending stiffness of the plate. This calibration is done by using a microplate of known bending stiffness k0 as a reference. The bending stiffness of the reference microplate has been itself determined by stacking copper micro-wires at the extremity of the plate, as described in Desprat, Guiroy, and Asnacios (2006), but this method is too time consuming to be performed routinely in the lab. The comparative method described below is much lighter to implement, while still providing good accuracy. The two microplates are placed one against the other as shown in Figure 2(B). A controlled displacement D is applied to the reference microplate, and the
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displacement of the contact point d is measured via imaging. The momentum equations at the contact point gives: F ¼ kd ¼ k0 ðD dÞ And therefore we can express k in terms of k0, D, and d: D 1 k ¼ k0 d Therefore, if we measure different pairs (D,d), we can access the slope of the curve a ¼ D/d and access k (Figure 2(B)).
2.2.1 Materials • • •
Reference microplate Piezoelectric micromanipulator Microscope
2.2.2 Method 1. 2. 3. 4. 5. 6. 7.
Place the two microplates in contact as represented in Figure 2(B) Note the localization of the contact point Increment the position of the reference plate of a known displacement D Measure the position of the contact point d and note D and d Perform steps (3) and (4) about 10 times Plot D ¼ f(d) and get the slope value Extract the bending stiffness value
2.3 MICROPLATE CLEANING Once the microplates are calibrated, you need to clean them and coat them to ensure good adhesion of the cells. Although basic glass cleaning can be performed (hot water, dishwashing soap, ethanol), a deep cleaning is necessary for controlled adhesion conditions, and at least once a month to get rid of any cellular remains that can accumulate on the plates. The microplates can thus be used indefinitely. If they happen to break, recalibration is necessary, and if they break too short, they can still be used as rigid plates. Cleaning is done using a piranha solution (70% H2SO4 þ 30% H2O2), very abrasive that ensures the digestion of any organic component.
2.3.1 Materials • • • •
Sulfuric acid solution, pure Hydrogen peroxide solution, pure Graduating cylinder Erlenmeyer flasks For security reasons, use two flasks, the one receiving the piranha solution fitting inside of a bigger one
2. Microplates
• • •
• • •
•
Glass lid Lid must be big enough to cover up the biggest Erlenmeyer flask Swiss Boy Microplate holder Here we use an articulated arm finished by a platform where we deposit gum in order to plant the microplates by the capillary side Security glasses Lab coat Acid-proof gloves Any type of nitrile gloves can be used. Simple latex gloves can also be used if they are doubled, but it may increase the risk of mismanipulation. The most important here is to ensure continuity of protection between the glove and the lab coat (lab coat can be tucked inside the gloves and fixed with an elastic). Deionized water
2.3.2 Equipment •
Chemistry aspirating hood
2.3.3 Method Be careful as piranha solution is very dangerous. Check out with your security lab manager to ensure good practice before you try. 1. Prepare the setup by placing the small Erlenmeyer inside the big one. 2. Take your microplates out of their tubes and place them on the gummed platform of the holder. Holder should be placed on top of the Swiss Boy 3. Adjust the Swiss Boy and the holder so that the microplates hang with flexible tip facing down, high enough to pass above the Erlenmeyer containers. Place this setup in safe area under the hood (far from your movements). 4. Check that no part of your skin is exposed and put your protection glasses on. 5. Prepare the piranha solution by adding first 30% of hydrogen peroxide and second 70% of sulfuric acid. The solution should start boiling. Be careful here as the addition of hydrogen peroxide over acid will lead to projections that can cause very severe burns. 6. Place the microplates above the Erlenmeyer and lower them with the Swiss Boy so that they dip into the solution until the base of the capillary. 7. Leave the microplates in solution for 20e30 min. 8. Take the microplates out using the Swiss Boy. 9. Put the lid over the piranha solution and place in a corner of the hood. 10. Dip the microplates into fresh milli-Q water for 30 min. 11. Rinse and change water. 12. Dip the microplates again in fresh milli-Q water overnight.
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13. Get the microplates back in their tubes and discard the piranha into appropriate container. Here, be sure that the container is not tightly closed. The solution will keep creating gas and a sealed bottle would explode.
2.4 MICROPLATE COATING Once the plates are clean, it is time to coat them with your protein of interest. To study specific adhesion effects on cell mechanics, traction forces and physics of the cell with involvement of integrins and focal adhesion complexes, we used fibronectin (Sigma-Aldrich F1141, Saint Louis, US); for nonspecific adhesion, poly-L-Lysin (multiple charge interaction, P4707, Sigma-Aldrich, Germany) and glutaraldehyde (covalent bonds, G6403, Sigma-Aldrich, Germany) can be used.
2.4.1 Materials • • •
Roswell Park Memorial Institute (RPMI) medium Protein of interest 5 mL hemolysis tubes
2.4.2 Equipment • •
Sterile hood Incubator
2.4.3 Method 1. Rinse the microplates individually under deionized water to ensure elimination of all acid traces 2. Prepare a solution of fibronectin at 5 mg/mL in RPMI medium Here RPMI is used as a solvent because it provides a pH color indicator to monitor eventual remaining traces of acid. Deionized water or phosphatebuffered saline (PBS) can be used instead. 3. Fill the tubes with 3 mL of solution 4. Place the microplates pair-by-pair in each of the tubes 5. Leave at 37 C for 30 min
2.4.4 Possible modifications for different coatings For nonspecific adhesion based on electrostatic interactions, replace the fibronectin solution in step 2 by a solution of poly-L-Lysin (Sigma-Aldrich, P4707) at 0.01% in water. For nonspecific irreversible adhesion, one can coat the microplates with glutaraldehyde by replacing steps 2e5 by the following steps: 1. Prepare a solution of ethanol 90%, (3-Aminopropyl) triethoxysilane (SigmaAldrich 440140) 2%, deionized water 8%
3. Cell preparation
2. Filter this solution on a 0.22 mm filter in the tubes to reach a final volume of 3 mL of solution per tube Here you need as many tubes as pair of microplate you want to coat 3. Place the microplates pair-by-pair in each of the tubes 4. Leave at room temperature for 2 h 5. Prepare a solution of 2% glutaraldehyde (Sigma-Aldrich G6403) 6. Filter the glutaraldehyde solution on a 0.22 mm filter in the tubes (3 mL of solution per tube) 7. Take cautiously the microplates out of the silane tubes 8. Rinse with ethanol 9. Leave to dry for a couple of minutes The gum used to seal the microplates into the tube can be fixed on the lab bench, so that the microplates dry with the tip facing up 10. Once the microplates are dry, dip them into the glutaraldehyde-filled tubes 11. Leave for 30 min at room temperature 12. Wash with deionized water
3. CELL PREPARATION Most cell types are adherent. If it is the case, detaching the cells is necessary to enable individual testing. In this protocol, the cells are detached with trypsin and suspended in medium in 3 mL tubes. Cells are then left for 2 h under agitation to ensure the recovery of trans-membrane proteins while avoiding readhesion on the tube wall.
3.1 MATERIALS • • • •
Cells Trypsin (Life Technologies, 0.05% Trypsin-EDTA (1), phenol red 500 mg/mL) Cell medium PBS
3.2 EQUIPMENT • • • •
Sterile hood Incubator Agitator Centrifuge
3.3 METHOD 1. Rinse the cell flask with PBS 2. Cover the cells completely with trypsin solution 3. Leave for 5e10min at 37 C
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4. Centrifuge the cells þ trypsin at 1500 r/min for 5 min 5. Discard supernatant 6. Separate the cells into tubes at the desired concentration Final concentration in the microplate chamber should be such that it is enough to find cells easily but not too crowded (one cell/image) to avoid interference with the optical sensor 7. Place the tubes on the agitator at 37 C and wait for 2 h 8. Place culture medium at 37 C to warm up before experiments Add HEPES buffer at 1.5% in the culture medium to ensure pH stability during open-air experiments.
4. EXPERIMENTAL PROTOCOLS The microplates device is a very versatile tool to decipher microscale mechanics. Since we can simultaneously monitor force (therefore stress) and deformation (therefore strain), a wide variety of rheological tests can be performed, from the simplest to the more elaborated ones. In each of the tests whose principle is described below, the protocol is the same:
4.1 CELL CAPTURE 1. At least 1 h before the beginning of the experiment, turn on all the equipment, place the experiment chamber, and wait for temperature stabilization at 37 C 2. When 37 C is reached, pour culture medium in the experiment chamber 3. Take the microplates out of the incubator and place them onto their holder 4. Arrange the microplates so that they are parallel, and place them just in contact with the bottom of the chamber using the manual micromanipulator 5. Raise the microplates up (60e70 mm is enough) with the piezoelectric micromanipulator 6. Add some cells into the chamber and wait for them to seed to the bottom 7. With the stage manipulator, adjust the cell position so it can be caught in between the plates 8. With the piezoelectric micromanipulator, lower the microplates to the bottom of the chamber and catch the pre-positioned cell 9. Move the microplates with the cell in between up (60 mm from the bottom of the chamber) and focus on the microplates þ cell system 10. If needed, perform calibration of the optical sensor 11. Run the desired test 12. Clean up the experimental chamber and start again Here, according to the test and the type of cell-plate adhesion, it may or may not be necessary to change microplates for clean ones at each new cell testing (if the cells adhere and leave remains, the microplates must be changed. If the cells are nonadherent, they can be kept).
4. Experimental protocols
4.2 CALIBRATION OF THE OPTICAL SENSOR For experimental protocols demanding fast detection of the flexible microplate deflection that cannot be achieved by the camera frame rate, an optical sensor mounted on a specific microscope port can be used (please see section Experimental Setup). The flexible plate tip is then imaged on the (PSD) that delivers an output voltage proportional to the position of the flexible plate tip. Indeed, since the PSD is sensitive to the spatial distribution of light intensity over its surface area, plate tip displacements lead to spatial modulations of light intensity and specific modulations of the output signal (see Desprat et al., 2006 for details). Therefore the signal depends on the microplate positioning and on the focus and settings of the microscope lens. Thus, before each experiment where this sensor is involved, calibration must be performed. To do so, the flexible microplate is displaced in such a way that its image spans the entire sensor area. The plate displacement D(t) and the sensor output s(t) are monitored simultaneously. In the central zone, the sensor is linear (s(t) ¼ a D(t)) and we can therefore plot s(t) with respect to D(t) and get the calibration parameter a value (Figure 3).
4.3 SINGLE-CELL TRACTION FORCE MEASUREMENTS 4.3.1 Simple traction Just like liquid droplets, some cell types spread on their substrate while applying a force on it. One can characterize this force with the microplates setup. Here the protocol is really simple. Once the cell is seized between the microplates, just record the deflection d of the tip of the soft microplate, the traction force
Sensor output s(t) (V)
−14
−16
−18
−20
−22 −0.1
0 0.1 0.2 Displacement (μm) D(t)
0.3
FIGURE 3 Optical sensor calibration. Once the cells are placed in between the plates and lifted from the bottom of the chamber, the calibration of the optical sensor has to take place to determine the relationship between the sensor output in volts and the actual tip displacement in microns. This curve is an example of calibration performed.
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exerted by the cell being F ¼ kd. Whatever the cell type tested so far, force over time exhibited a sigmoidal form (Figure 4), while cell shape evolved with spreading (Movie M1).
4.3.2 Real-time single-cell response to stiffness The effective stiffness felt by a cell when pulling in between the parallel microplates can be controlled through a feedback loop acting both on the rigid and flexible microplates (Mitrossilis et al., 2010). Whatever the actual stiffness of the soft microplate, the cell is sensing an effective rigidity which is the ratio of the force F(t) it applies to its shortening DL(t) ¼ L0 L(t) when contracting: keff ¼ F(t)/DL(t). keff can be set by making DL(t) a function of F(t) through adapted feedback signals d(t) and D(t) on the positions of the soft and rigid plates, respectively. The effective bending stiffness is then keff ¼ k0d(t)/D(t) (Figure 5).
4.4 SINGLE-CELL RHEOLOGY 4.4.1 Dynamic mechanical analysis Dynamic mechanical analysis is a widely used method in viscoelastic material rheology. The principle is to apply a controlled sinusoidal stress or strain at different frequencies, while measuring the complementary variable. In these conditions,
FIGURE 4 Typical traction force curve. The simplest test consists in letting a cell spread between the two microplates and record the tip deflection (i.e., the force) along the time (Movie M1). The curves obtained typically show a sigmoid shape, with three distinct phases. The first phase is a phase of early spreading and onset of force generation, followed by a phase of high rate traction. The third phase corresponds to slow down of contraction and saturation.
Real-time stiffness tuning. The retroaction loop on both the flexible and the soft plate allows mimicking a stiffness range from zero to infinity. (A) With no feedback, the cell is experiencing the bending stiffness of the flexible plate K0. (B) If the tip of the flexible plate is maintained in a constant position, the cell is facing and nondeformable solid, of infinite stiffness. (C) If the deflection of the flexible plate is maintained zero (no force), by retroacting on the rigid plate, the cell is experiencing a system infinitely soft, equivalent to zero stiffness. (D) The relationship between the 0 dðt Þ deflection of the flexible plate d(t) and of the displacement of the rigid plate D(t) can be set to reach any effective stiffness value: Keff ¼ KDðt Þ.
4. Experimental protocols
FIGURE 5
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elastic-like behavior (storage of energy) leads to stress and strain signals in phase, while viscous-like response (dissipation) is characterized by a p/2 phase shift. In the general case of a viscoelastic sample like living cells, the phase shift lies in between 0 and p/2, and the passive mechanical behavior is characterized by a complex viscoelastic modulus with a real part and an imaginary part: G ðuÞ ¼ G0 ðuÞ þ iG00 ðuÞ The real part G0 , referred to as the storage modulus, characterizes the elastic part of the cell response, while the imaginary part G00 , or loss modulus, gives an information on the dissipative contribution to cell mechanics. These loss and storage moduli can be derived from the parallel plates measurements. Indeed, G* is defined as the stressestrain ratio: sðtÞ G t ¼ εðtÞ with s(t) and ε(t) being stress and strain, respectively. There are two ways to carry out dynamical measurements depending on which plate the sinusoidal excitation signal is applied. •
Flexible plate-based excitation
In this case, a sinusoidal displacement D(t) is imposed to the base of the flexible plate, and the resulting movement at the plate tip d(t), which depends on the cell mechanical behavior, is recorded via the optical sensor. This gives, in complex form: D t ¼ D0 eiut d t ¼ d0 eiutþ4 where D0 and d0 are the amplitudes of the two signals, u their frequency, and 4 their phase lag. The stress s(t) can be derived from the force applied at the tip of the microplate divided by the area S of the celleplate contact: kdðtÞ kðDðtÞ dðtÞÞ ¼ s t ¼ S S where d(t) ¼ D(t) d(t) is the flexible plate deflection and k its bending stiffness. The area of contact S is estimated from the apparent contact diameters ø1 and ø2 at the flexible and rigid plate (Figure 6), assuming an axisymmetrical shape of the p 2 p 2 cell: S ¼ 12 4 1 þ 4 2 . •
Rigid plate-based excitation
From the expressions of D(t) and d(t), s(t) becomes k s t ¼ eiut D0 d0 ei4 S
4. Experimental protocols
(A)
k (B)
(C)
10000
d1 L0
d2
′
G
′′
G
Moduli (Pa)
1000
100
10 0.01
0.1
1
10
f (Hz) FIGURE 6 Dynamic mechanical analysis. (A) Schematic description of the experiment. Oscillations are applied at the base of the microplate, and the cell reaction is recorded. (B) Cell geometry parameters are measured on bright-field images (scale bar 10 mm). (C) By extracting the phase shift and the amplitude ratio of the input D(t) and the output d(t), we can derive the storage and loss moduli of the cell G0 and G00 , respectively. For single cell, these moduli behave as a power law of frequency, as the fitted data show above.
On the other hand, the strain ε(t) is defined as the ratio between the instantaneous cell elongation DL(t) ¼ L0 L(t) ¼ d(t) and its initial length L0: dðtÞ d0 eiutþ4 ¼ ε t ¼ L0 L0 This, all in all, gives an expression of the complex viscoelastic modulus: s kL0 D0 i4 G ¼ ¼ e 1 S d0 ε
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And the storage and loss moduli are therefore respectively 8 kL0 D0 > 0 > G ¼ cos 4 1 > < S d0 > kL0 D0 > 00 > : G ¼ sin 4 S d0 Here we see that we can access G0 and G00 by knowing k, L0, and S and monitoring D0, d0, and 4. While L0 and S are estimated from the bright-field images (Figure 6(B)), D0, d0, and 4 are extracted from analysis of the sine wave signals measured from the output of the piezoelectric device controlling the flexible plate displacement on the one hand (base movement D(t)) and from the optical tip position sensor (tip movement d(t)) on the other hand. It has been shown and is now widely accepted that G0 and G00 behave as a power law of frequency (Fabry et al., 2001) (Figure 6(C)). An alternative way to measure the cell complex modulus is to apply the sinusoidal displacement D(t) ¼ D0eiut to the rigid plate (and not to the base of the flexible plate as described above). The movement of the tip of the flexible plate remains of the form d(t) ¼ d0eiut, but the expressions of the stress and strain become k d0 eiutþ4 s t ¼ S D0 d0 ei4 iut e ε t ¼ L0 And the storage and loss moduli therefore write 8 kL0 D0 > 0 > ! >G ¼ cos 4 þ 1 > > d0 > D20 > > S 2 1 > > < d0 > kL0 D0 > 00 > ! > G ¼ sin 4 > > d0 > D20 > > S 1 > : 2 d0 This protocol is not fundamentally different from the previous one where the sinusoidal perturbation is applied through the flexible plate, but allows one to carry out the measurements only through image analysis since the rigid and flexible plate tips are visualized in the field of view (in the previous protocol, one needs to compare the displacements of the tip and the basis of the flexible plate which cannot both be visualized through the objective, implying a more tricky synchronization between image analysis and basis position command signal to ensure a proper phase shift determination). For instance, working at a typical frequency of 1 Hz, one can get 25 images with a regular camera, for each compression/traction cycle; each one giving a measurement of D(t) and d(t). The sine waves retrieved from image analysis can then be
4. Experimental protocols
fitted, and D0, d0, and 4 are determined. A fast camera can of course be used for measurements at higher frequencies.
4.4.2 Creep experiment The creep experiment consists in submitting the cell to a constant stress. The experiment is initiated by applying a step displacement to the base of the soft plate, leading to an initial plate deflection d0, and a stress s0 t ¼ kdS0 , where k is the plate stiffness and S is the cell-plate contact area defined as in the previous section. Then, the deflection is held constant by the feedback loop which applies a correction D(t) to the position of the rigid plate in order to maintain the tip of the flexible plate in its initial position. Therefore, if the surface area does not vary, the stress imposed to the cell remains constant. The creep function can be expressed as εðtÞ J t ¼ s0 Since the cell elongation is directly given by the feedback loop correction on the rigid plate DL(t) ¼ L0 L(t) ¼ D(t), the strain ε(t) defined as the ratio between the instantaneous cell elongation and its initial length L0, writes DðtÞ ε t ¼ L0 And the cell creep function is finally given by DðtÞS J t ¼ kd0 L0 Consistently with dynamical measurements in the frequency domain (previous section), the creep function of cells follows a power law of time (Figure 7).
4.4.3 Relaxation experiment The relaxation experiment follows the same principle as the creep experiment, but instead of applying a constant stress, here the strain is maintained constant and the stress evolution is measured. In the microplates setup, this is achieved by maintaining the rigid plate position fixed while feeding back on the base of the flexible plate. Initially, the flexible plate tip is moved over a distance d0 to a target position corresponding to the desired cell elongation (phase of strain rise up). Then, as the cell relaxes, the position of the flexible plate basis is modified (displacement D(t)) so that the tip remains at the target position. This second phase of the experiment, where the strain is constant and the stress decreasing, corresponds to the true relaxation regime. The strain is given by d0 ε t ¼ L0
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−1
10
−2
10
J(t) (Pa –1)
206
−3
10
−4
10
0.01
0.1
1
time (s)
10
100
1000
FIGURE 7 Creep experiment. A displacement step is applied to the base of the flexible plate, while the tip is maintained at the same position. The cell is therefore submitted to a step of force. This force is maintained constant across the experiment by retroacting on the position of the rigid plate to compensate for cell elongation. The creep function J is a weak power law of the time, as the fitted data illustrate above.
where L0 is the initial cell length. The stress is directly related to the feedback signal D(t): kðDðtÞ d0 Þ s t ¼ S where k is the flexible plate stiffness and S is the cell-plate contact area. A set of sðtÞ relaxation data is shown in Figure 8. The relaxation modulus G t ¼ ε0 then writes kðDðtÞ d0 Þ G t ¼ ε0 S Here again, the cell response is a power law of the time (Figure 8).
5. DISCUSSION The mechanical measurements described above present different levels of technical difficulty depending on the need or not of fast detection of the flexible plate deflection (real-time force measurement), and feedback on the positions of both flexible and rigid plates. From this point of view, the simple single-cell traction force assay
5. Discussion
stress (Pa)
10000
1000
100 0.1
1
10
100
time (s)
FIGURE 8 Relaxation experiment. While the rigid plate is at a fixed position all over the experiment, the tip of the flexible plate is initially shifted to a target position and then maintained immobile thanks to a feedback correction applied to its base. The cell is therefore submitted to a step strain and the stress necessary to compensate for tension relaxation in the cell structure is recorded all along the experiment. The relaxation modulus G is a decreasing weak power law of the time, as illustrated in this particular example.
is certainly the easiest. As shown in Figure 4, the characteristic timescale of force evolution is of about 10e20 min. Thus, the measurement of the flexible plate deflection (and consequently of force) can be done through image analysis after the experiment. Similarly, as already mentioned in the section dedicated to dynamical single-cell rheology, the storage and loss moduli (G0 and G00 ) can also be measured through image analysis, provided the experiments are run through the “rigid plate-based excitation” protocol, and the image sampling rate high enough compared to the excitation frequency. Conversely, stiffness control, creep, and relaxation assays require real-time detection of the flexible plate deflection, and feedback on both flexible and rigid plate positions. We achieved that using a position-sensitive detector with dedicated electronics to ensure that the rates of the detection and feedback loops are independent of the frequency of image acquisition (Desprat et al., 2006). However, the detection could easily be carried out, in real time, through image analysis for those who are familiar with particle tracking methods, which are now widespread in research labs. One of the advantages of the parallel plates technique is that it can be coupled to fluorescence microscopy since the setup can be implemented on any regular inverted
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microscope. In particular, simple traction force measurements are really easy to synchronize with fluorescence since no real-time detection is needed and timescales of force and cell shape evolution are quite long. Concerning the choice between the different rheology protocols, there are a few rules one has to keep in mind. If cell deformation is kept low (less than 10% typically), the three rheological protocols described in this chapter give equivalent information. In fact, cells, like many viscoelastic materials, exhibit different mechanical behaviors depending on the particular timescale over which they are tested. This can directly be achieved in creep or relaxation experiment where one monitors the time evolution of the corresponding mechanical response function. When performing dynamical tests, one has to run experiments at different frequencies to test cell behavior at different timescales, high frequencies corresponding to short times, and vice versa. Eventually, when working in the time domain, creep experiments are easier to analyze than relaxation ones. Indeed, applying a step stress (or force) is something trivial since it implies bending of an elastic microplate, which can be made instantaneously. In contrast, applying a step strain (or elongation) is not possible since it corresponds to an instantaneous deformation of a viscoelastic material (here the cell) which should necessitate an infinite applied force (for a viscous media, force is proportional to the rate of deformation). Thus, in any relaxation experiment, there is an initial phase of setting up of the target strain which does not correspond to true relaxation conditions of constant strain. This initial regime can be analyzed, but this is not straightforward. One generally analyzes the second regime where the strain is maintained constant, but then there is some uncertainty on the time “zero” at which this true relaxation regime is initiated. As a consequence, when cells can be made adherent to the plates, one should always perform creep tractions. If cells are not adherent, then relaxation in compression is the adapted solution, because creep in compression leads to increasing celleplates contact area, and thus to a decreasing applied stress even though force is maintained constant. Finally, it is noteworthy that the parallel plates technique could easily be adapted to study cell aggregates or even millimeter-sized organisms. Indeed, the stiffness of the flexible plate, used as a force sensor, can be tuned by adapting its shape and size (see section Microplates above), while the analysis of the geometry and deformation of samples bigger than single cells can be achieved with low-magnification objectives. For instance, we are currently using the parallel plates technique to study single plant cell mechanics (almost the same size as animal cells but necessitating plates with a 1000-fold increased stiffness) (Durand-Smet et al., 2014), as well as plant hypocotyls (plates 1000 times stiffer and 100 times bigger than those used for single animal cell measurements).
SUPPLEMENTARY DATA Supplementary data related to this article can be found online at http://dx.doi.org/10. 1016/bs.mcb.2014.11.002.
References
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