Applications of graphene to cell biology 3

Appendix A Cell migration analysis framework In this section, I present the cell migration analysis framework that I developed to analyze cell motility on various substrates. A.1 Segmentation and tracking The first step in the process is to segment cells. Since it is challenging, if not impossible, to segment cells from bright field images, cell nuclei are stained with a Hoechst dye. I then implemented, in C++, the gradient flow tracking algorithm presented in [70]. This implementation allows fast and parallelized processing on CBIS’ computer cluster. A large number of cells is required for reliable statistics, so images are acquired using the 10x objective, which allows for approximately 1000 cells per image in a confluent monolayer. This number is further multiplied by acquiring several locations per substrate using a motorized stage, and by repeating experiments. 139 I am interested in cell motion, so time-lapse experiments are run, taking an image every minutes. Tracking of cells in this context is fairly easy, as the motion between the frames is little. Experiments are run for 8h or more, so a single experiment can easily lead to millions of position and velocity vectors (1000 cells per image × 12 frames per hour × hours × 20 different locations), good enough for serious statistical analysis. Figure A.1: Example of cell tracking using nuclei staining. A.2 Motion analysis From the segmentation and tracking, a set of positions (xi (t), yi (t)) is obtained, where i is an arbitrary index identifying each cell, and t is the time step. I can then compute easily compute velocity vectors (vxi (t), vyi (t))), and speed vi (t). 140 This statistical analysis is performed using R [94]. I am interested in several descriptors, commonly found in the literature: Cell density. The simplest descriptor is the number of cells per frame: densityavg = N (t) Average speed. Another simple descriptor is the average speed of cell motion. I simply take the average speed of all cells, at all times: vavg = vi (t) This speed can be taken at different time intervals: I have found that computing cell motion over hour, rather than minutes, gives numbers that are less sensitive to noise and nucleus motion inside the cell. I can also compute the average speed for each timepoint, to see if the speed is changing during the experiment. Mean-squared-displacement. The MSD is a useful and commonly used tool to describe persistence of motion [45]. It is function of a time interval ∆t: ρ2 (∆t) = (xi (t0 + ∆t) − xi (t0 ))2 + (yi (t0 + ∆t) − yi (t0 ))2 This function is usually plotted on a log-log scale (see Figure A.2), where it shows up as a straight line (especially at longer time-scales: shorter time scales are more sensitive to random noise and nucleus motion), hence it 141 can be fitted to a power law: ρ2 (∆t) ∝ ∆tα The coefficient α is usually between and 2: indicates a purely Brownian motion (random, memory-less behavior), while indicates a ballistic motion (the cell goes straight at a constant speed). 100 50 MSD ((microns)^2) 200 500 PDMS 1:80 control alpha=1.25 PDMS 1:20 control alpha=1.41 ● ● ● ● ● ● ● ● ● 10 20 ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ●● ● ●● ●● ●● ●●● ● ● ●● ● ●● ● ●● ● ● ●● ● ●● ● ● ●● ● ● ● ●● ● ● ●● ● ● ● ● ● ●● ● ● ● ●● ●● ●● ● ● ● ● ● ● 10 20 50 100 200 Time (minutes) Figure A.2: Example of Mean Square Displacement curve, with a power law fit. The red curve corresponds to IEC-6 cells on a relatively hard PDMS substrate (1:20 curing agent/prepolymer ratio), while the yellow curve corresponds to a much softer, viscoelastic PDMS substrate (1:80). The fit is usually done at longer time scale (e.g. more than hour), as shorter time scales are more sensitive to noise. For cells on PDMS 1:20 and 1:80: α is fitted to respectively 1.41 and 1.25. 142 A.2.1 Motion characterization Upadhyaya [111] provides a detailed analysis of how cell migration deviates from Brownian motion, and some of their findings are briefly summarized here. In Brownian motion, the velocity along a given axis (i.e. the velocity vector projected onto any base vector) is normally distributed with parameters N (0, σ ). The average velocity is 0, as the particles exhibit no preferred direction (i.e., no drift), and the parameter σ determines the average speed of the particles. For particles in gases, σ depends on the type of gas, and increases with temperature. Therefore, the speed, that is, the norm of the velocity, is distributed according to a Maxwell distribution Z = X12 + X22 + X32 in the dimen- sional case, where all the Xi are normal distributions N (0, σ ). Since the cells are constrained on a 2D plane, the speed distribution would be a 2D Maxwell distribution Z = X12 + X22 , also known as Rayleigh distribution. Additionally, the particles in Brownian motion are “memory-less”, and the angle between their velocities at consecutive intervals is uniformly distributed. That is, the fact that a particle is moving in a given direction at a time t does not play any role in the direction of the particle at a time t + 1. Figure A.3a shows the velocity distribution for a given observation point, along the X axis of the images. A log-likelihood minimizing Gaussian distribution fit is also shown (i.e. a Gaussian distribution with the same standard deviation as the data). Approximating the distribution by a Gaussian is acceptable as a first approximation, even though it is clear that the real distribution has heavy tails (one could fit a Gaussian around 143 1.5 1.0 0.0 0.5 Density −1.0 −0.5 0.0 0.5 1.0 Velocity (X axis) 1.5 0.010 45 90 135 180 0.5 1.0 Angle 0.0 Density 0.000 2.0 Density 2.5 (a) Distribution of velocity 0.0 0.2 0.4 0.6 0.8 Speed (microns/min) (b) Distribution of speed and angle Figure A.3: IEC-6 cells, graphene substrate 144 1.0 the peak, leaving outliers on each side of the distribution). Figure A.3b shows the speed distribution, with a 2D Maxwell distribution fit: as for the one-dimensional case, the fit is a rough approximation of the observed distribution. One can also look at the insert, showing the angle distribution between successive velocity observations: instead of a flat uniform distribution, cells usually continue along the same direction as they moved before. Finally, the general shape of the distribution of speed are consistent across observations: mean speed may vary, but the distribution always appears “Maxwell-like”. A.2.1.1 Average speed Speed distributions histograms not allow one to easily compare speed differences on various substrates, as shown in Figure A.4a. Therefore, I compute the mean, and obtain a confidence interval around that value. To compute this confidence interval, I first need to compute the standard error of the mean, which is defined as: σ SE = √ , M where σ is the standard deviation of the data, and M the number of measurements. In my experiments, I have M = N × T measurements: N cells over T time intervals. However, measurements are both auto-correlated, as cells are not Brownian particles, and cross-correlated, as the motion of one cell influences its neighbors. I can compensate for the correlation by multiplying SE by the 145 0.015 0.010 Density 0.005 Density Glass Graphene PDMS 45 90 135 180 Angle (°) 0.0 0.2 0.4 0.6 0.8 Speed (microns/min) (a) Distribution of speed and angle 0.20 0.15 0.10 0.05 0.00 Speed (microns/min) 0.25 0.30 Glass Graphene PDMS Glass Graphene PDMS (b) Average speed Figure A.4: IEC-6 speed for 14 points, on substrates 146 factor 1−ρ , 1+ρ k= where ρ is the the correlation between any pairs of measurements. If I know the average auto-correlation ρT and cross-correlation ρN , I can compute the average correlation: (N − 1) · ρN + (T − 1) · ρT + (T − 1) · (N − 1) · ρN · ρT T ·N −1 ρT ρN + + ρT · ρN ≈ T N ρ= ≈ ρT · ρN , where the approximation assumes large N and T . From my datasets, I have, at most, an average autocorrelation coefficient ρT ≈ 0.25, and the average cross-correlation across cells is very low, around ρN ≈ 0.001. Therefore, I obtain ρ ≈ 0, and k = 1. In other words, I have enough data to be able to ignore correlation in my datasets. Finally, from the standard error of the mean, I obtain a 95% confidence interval (i.e. ±1.96 · SE , assuming Gaussian distribution of the mean). Figure A.4b shows an example of average speed on different substrates. There is significant variability across points on the same substrate, that could be due, for example, to local differences in the substrate, or to variations in cell density. In an attempt to eliminate such local effect, I merge all points on any given substrate to a single value, and obtain the bar chart shown in Figure A.5. 147 0.30 0.20 0.15 0.10 0.05 0.00 Speed (microns/min) 0.25 Glass Graphene PDMS IEC−6 Figure A.5: Average speed on substrates 148 158 Appendix C Effect of localized forces on cells This appendix shows results of a research direction inspired by reversing the experiment I attempted to perform in Chapter 3: instead of measuring forces applied by cells, this design looked into applying forces on cells, in a localized area. This is a natural extension of the reversible piezoelectric effect, described in Section 3.4. I first planned to use a PVDF film to apply forces on cells: applying a voltage perpendicular to the film using a pair of gold electrodes would, in theory, generate a force that the cells would sense. However, I found that only very high frequency signals would cause a deformation of the film. A likely explanation for this was Joule heating of the electrodes, deforming the film. I then moved on to a new design, making full use of Joule heating. Both designs, to be presented, were able to kill cells on the electrodes, with healthy cells from unaffected areas covering back the affected area, 159 leading to an innovative way of generating a wound assay. This kind of wound assay might be more realistic than existing techniques: one method prevents cells from covering an area, then release the area for cells to cover; another common method scraps cells with a mechanical tool [74]. In our case, wounded cells are still present, that may be able to produce biochemical signals to nearby, healthy cells. However, it was not readily possible to separate the contributions of mechanical and thermal effects on the cells, and killing cells by heat shock was considered to be less interesting and further away from the scope of this thesis. However, some of the techniques, mainly in terms of device fabrication and wiring, proved useful in the making of the device presented in Chapter 4. C.1 First device design Our first device layout is shown in Figure C.1: gold electrodes are patterned on either sides of a µm PVDF film. The film is then attached to a piece of PDMS, with a hole localized at the intersection of the electrodes, so as to promote strong vibration of the film. The whole device is glued to the bottom of a Petri dish, coated with Fibronectin (PVDF is hydrophobic), and cells are seeded on the surface. A function generator (Stanford Research Systems DS345) is connected to both electrodes of the device, and various voltages/frequencies could be applied. No noticeable movement of the device was observed with DC signals. However, for reasons that were unclear at the time, the device 160 moves down by up to µm, in the center area, when a 30 Mhz signal is applied (the highest frequency available on the signal generator). I then performed amplitude modulation of this 30 Mhz signal with a Hz square signal, leading to an on-off pattern (half a second on, half a second off). To evaluate the motion of the film, I put 15 µm fluorescent beads on the PVDF film, and imaged the beads with an upright microscope (15 µm beads sink rapidly on the surface of the film, and are hard to dislodge, unlike smaller beads). First, a z-stack is acquired, then, a fast time-lapse video is acquired, with the signal generator on, so that I can observe the film going up and down. From the center position of the bead, I can evaluate the lateral motion, while the motion in the Z-axis can be evaluated by comparing the beads radius to the z-stack acquired previously (the bead appears smaller, at a given threshold, when it goes out of focus). An example of such motion in Z is shown in Figure C.2. Finally, data is collected and analyzed over a set of points (Figure C.3), showing that most of the Z displacement is concentrated near the center of the device. I not show X/Y displacement here, as it is less significant. Figure C.1: First design of PVDF device to apply forces on cells. A 9µm PVDF film, with gold electrodes patterned on either sides, is attached to a piece of PDMS, with a hole localized at the intersection of the electrodes. 161 21 Bead Z position 20.5 Z position (µm) 20 19.5 19 18.5 18 17.5 Time (s), approximate Figure C.2: Computed Z position of a bead near the center of the device, showing the amplitude of displacement, with time. Figure C.3: Stitched image of the actual device. Red arrows show the computed Z amplitude over a few positions on the device: Most of the amplitude is concentrated near the center of the device, reaching around 2µm in some places (scale bar at the bottom left). 162 C.1.1 Experiments with cells The next step was to observe the effects of such displacement on cells. First, I coated the device with Fibronectin (20µg/ml, 1hr incubation), and seeded Hela cells at a confluent density. After letting the cells settle for a few hours, I applied the 30Mhz signal, with an amplitude modulation of 1Hz, for 15 minutes. Figure C.4 shows the effect of the shock. Cells round up within 1-2 hours, possibly die, and healthy cells from the unaffected area start spreading in the area. 163 Figure C.4: HeLa cells on PVDF device. Time, in hours, is shown in the top-left corner of each image. The shock lasts for 15 minutes, starting at time 2:35. One can see that some cells take more than an hour to react to the shock. And that cells from “safe” area fill up the area left empty by dead cells. 164 C.2 Second device design The most likely explanation for the phenomenon in the first design is that the gold electrodes are heating up: as the frequency increases, the impedance of the capacitor formed by the intersection of the gold electrode decreases, leading to a higher current, and therefore larger Joule dissipation in the gold electrodes. From there, I decided to go for another design, that makes full use of Joule heating to actuate the PVDF film. Gold electrodes are patterned using toner transfer lithography [99]. The design shown is Figure C.5 is achieved using the following process: • A thick film of PDMS is spun on a glass slide, then cured. • parallel lines are cut in the PDMS using a scalpel blade, then the PDMS is peeled off the glass slide, creating a hole. • The required gold electrode design is printed with an office laser printer on some non-stick paper (I used the plastic support of sticky labels). Media+cells Gold electrode PVDF Hole PDMS Figure C.5: Second design of PVDF device. gold electrodes are patterned on one side of a 25µm PVDF film. The film is then attached to a piece of PDMS, with a hole underneath the electrodes, so as to promote strong vibration of the film. The whole device is glued to the bottom of a Petri dish, coated with Fibronectin (PVDF is hydrophobic), and cells are seeded on the surface. 165 • I cut a small piece of 25 µm PVDF, with gold/chromium pre-deposited on one side. • The toner is heat-transferred to the gold side of the PVDF sheet. • The PVDF sheet is then put in a gold etchant solution [117]: the toner protects selected areas, and the rest is etched. • The toner is removed with acetone, revealing the gold pattern. • A very thin film of Hexane/PDMS is spun on the gold side of the PVDF, then cured (the PDMS film helps bonding the PVDF layer to the PDMS/glass slide base, as PVDF does not react to oxygen plasma). • Both the PDMS on the glass slide and the PVDF film (coated with PDMS) are treated with a plasma cleaner, then bonded together. • Electrodes are connected using conductive epoxy. • Finally a hole is drilled in a Petri dish, and stuck to the top of the device. I chose a design with electrode widths (∼200 µm and ∼300 µm). Then, using a Arduino and a simple circuit with a MOSFET (Figure C.6), I apply short pulses of current to the device, at regular interval (typical 12V MOSFET Figure C.6: Circuit used to actuate the PVDF film. A short pulse is sent from an Arduino, through a MOSFET to increase the available voltage (12V) 166 parameters are 500 µs pulses of 12 volts, every second): This causes the gold to heat up, leading to an expansion of the PVDF film, and the device bends down. Longer pulses, or continuous currents, easily destroy the device. C.2.1 Experiments with cells Figure C.7 shows part of the device, with HeLa cells seeded on it: the gold/chromium layer is so thick that is it impossible to see through. I typically include a Nuclei stain (Hoechst 33342), and well as a dead cell stain (SYTOX green). Several pulse parameters were tried, but only extreme cases seems to be able to kill the cells. Figure C.8 shows dead cells near the electrode, after applying 500µs pulses of 12 volts, 100 times per second, for 15 minutes. Figure C.7: HeLa cells seeded on the second PVDF device design, showing the electrodes (the gold layer provided by the PVDF supplier is so thick that one cannot see through). 167 Figure C.8: HeLa cells, after applying 500µs pulses of 12 volts, 100 times per second, for 15 minutes. Green cells are dead (stained with SYTOX green). C.2.2 AFM characterization Finally, I did some characterization the device, using an AFM. because of technical constraints, one cannot operate the AFM within a small Petri dish, therefore the characterisation has to be performed before the last step of the fabrication process described earlier. The Z servo actuator is disabled, as it may not be fast enough to react to the device motion. Instead, I simply press down a soft tip on the substrate, and observe the deflection. Using this method, I can only observe motion 168 of a micron or so before the position sensitive photo detector (PSPD) saturates, so I repeat measurements by pushing the tip further down (i.e. saturating at the beginning of the process, but picking up information as the device goes down). Data is acquired using an oscilloscope, measuring both current applied to the device, and tip deflection. A sample data is shown in Figure C.9a. I can then assemble the curves together to obtain a full picture of the deflection (Figure C.9b). I can observe a delay of around 50 µs between the start of the pulse, and the onset of the motion. Part of this delay may be explained by a lag in the PSPD readout, but, more likely, it is due to the time required for the heat in the gold electrode to transfer to the PVDF film. At longer timescale, I can observe that the film “bounces” up after the initial downward motion (Figure C.10). Finally, by computing the second derivative of the tip position, I can obtain a rough estimate of the acceleration cells are subjected to. Figure C.11 shows that most of the acceleration occurs less than 50µs after the start of the pulse, with a maximum around 200g. Considered that cells are routinely centrifuged around this kind of acceleration, it seems unlikely that the motion alone would kill cells. 169 Current (mA) −0.5 0.0 Deflection (um) 0.5 92 1.0 Current Z: −0.15um Z: −0.3um Z: −0.6um Z: −0.8um 200 400 600 800 Time (us) (a) Raw data. Current (mA) −3 −2 −1 Deflection (um) 92 Current Z: −0.15um Z: −0.3um Z: −0.6um Z: −0.8um 200 400 600 800 Time (us) (b) Reconstructed data, showing the full motion of the PVDF film. Figure C.9: Deflection of the AFM tip, at different Z positions, as well as current going through the device (in black), acquired with an oscilloscope. 500µs pulses are applied to the device. 170 1.0 Current (mA) 88 −0.5 0.0 Deflection (um) 0.5 Current Z position −100 100 200 300 400 Time (ms) Figure C.10: Deflection of the AFM tip, as well as current going through the device (in black), at longer time scale, showing the film “bounces” back up after the initial drop. 171 Current (mA) 0.0 −0.6 −0.4 −0.2 Deflection (um) 92 0.2 0.4 Current Z position −100 −50 50 100 Current (mA) 2000 1000 −1000 −2000 Deflection acceleration (m/s^2) 3000 Current Z position 92 4000 Time (us) −100 −50 50 Time (us) Figure C.11: Deflection and acceleration in the first 100µs of a 200µs pulse, where most of the acceleration is concentrated. 172 C.3 Conclusion and future work From results in this appendix, I observe that pulses longer than 100 to 200 µs not introduce additional acceleration, and therefore only generate additional heat, rather than more force. Also, the measured acceleration is relatively small, compared to what cells undergo routinely when centrifuged. Since effects only seem to happen with frequent pulses, it may indicate that cells die because of heat shock, and not mechanical stresses. This setup could still be used as a wound assay, as cells are killed over a specific area. We could even imagine using graphene thermal properties to replace the gold electrodes, to facilitate imaging. However, the fact that cells die because of heat shock made it less interesting in the context of this thesis, and this project was left aside. 173 [...]... not been the topic of many studies, and may differ a lot compared to animal cells, for which developing a better understanding of mobility has more potential applications 157 158 Appendix C Effect of localized forces on cells This appendix shows results of a research direction inspired by reversing the experiment I attempted to perform in Chapter 3: instead of measuring forces applied by cells, this design... method prevents cells from covering an area, then release the area for cells to cover; another common method scraps cells with a mechanical tool [74] In our case, wounded cells are still present, that may be able to produce biochemical signals to nearby, healthy cells However, it was not readily possible to separate the contributions of mechanical and thermal effects on the cells, and killing cells by heat... B.4: Displacement of a single bead, near the center of Figure B .3, due to substrate deformation cause by Chaos Carolinensis B .3 Fixed staining Finally, I also performed some fixed staining of the amoeba, to get an idea if protocols used for tissue cells may be used with this cell type The process is not straightforward, as the amoeba is not adherent to the substrate, but I managed to obtain the images... intersection of the 2 electrodes, so as to promote strong vibration of the film The whole device is glued to the bottom of a Petri dish, coated with Fibronectin (PVDF is hydrophobic), and cells are seeded on the surface A function generator (Stanford Research Systems DS345) is connected to both electrodes of the device, and various voltages/frequencies could be applied No noticeable movement of the device... deformation of the film A likely explanation for this was Joule heating of the electrodes, deforming the film I then moved on to a new design, making full use of Joule heating Both designs, to be presented, were able to kill cells on the electrodes, with healthy cells from unaffected areas covering back the affected area, 159 leading to an innovative way of generating a wound assay This kind of wound assay...Appendix B Large cells: Amoeba Amoeba provided by Ketpin Chong, Cubic Membrane Research Laboratory (A/P Yuru Deng), NUS School of Medicine As seen in Chapter 3, the target is to obtain an force-sensing “pixel” area of 1 µm2 , that should give high enough resolution to understand cellsubstrate interactions of tissue cells (∼ 20 µm2 in area) In all approaches, we were far from being able to create such... that show very fast movement in the cytoplasm, called cytoplasmic streaming or cyclosis Organelles (probably mitochondria), and vacuoles can clearly be seen 150 (a) Plastic bottom (b) Glass (c) PDMS 1:10 Figure B.1: Images of Chaos cells on 3 different substrates 151 Figure B.2: Images of a Chaos cell, using the 20x objective, some areas are blurred because of fast cytoplasmic streaming 152 B.2 Forces... paper (I used the plastic support of sticky labels) Media+cells Gold electrode PVDF Hole PDMS Figure C.5: Second design of PVDF device 2 gold electrodes are patterned on one side of a 25µm PVDF film The film is then attached to a piece of PDMS, with a hole underneath the 2 electrodes, so as to promote strong vibration of the film The whole device is glued to the bottom of a Petri dish, coated with Fibronectin... up, leading to an expansion of the PVDF film, and the device bends down Longer pulses, or continuous currents, easily destroy the device C.2.1 Experiments with cells Figure C.7 shows part of the device, with HeLa cells seeded on it: the gold/chromium layer is so thick that is it impossible to see through I typically include a Nuclei stain (Hoechst 33 342), and well as a dead cell stain (SYTOX green) Several... forces applied by cells, this design looked into applying forces on cells, in a localized area This is a natural extension of the reversible piezoelectric effect, described in Section 3. 4 I first planned to use a PVDF film to apply forces on cells: applying a voltage perpendicular to the film using a pair of gold electrodes would, in theory, generate a force that the cells would sense However, I found that only . 0.010 0 45 90 135 180 (b) Distribution of speed and angle Figure A .3: IEC-6 cells, graphene substrate 144 the peak, leaving outliers on each side of the distribution). Figure A.3b shows the speed. School of Medicine. As seen in Chapter 3, the target is to obtain an force-sensing “pixel” area of 1 µm 2 , that should give high enough resolution to understand cell- substrate interactions of tissue. not seem to spread a lot on PDMS 1:10. However, further experiments (not shown here) showed some cells that seemed to attach to untreated PDMS 1:40. The “healthiness” of the cell seems to play