Applications of graphene to cell biology 3

Since it is challenging,if not impossible, to segment cells from bright field images, cell nuclei arestained with a Hoechst dye.. A large number of cells is required for reliable statist

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 arestained with a Hoechst dye I then implemented, in C++, the gradientflow tracking algorithm presented in [70] This implementation allows fastand parallelized processing on CBIS’ computer cluster

A large number of cells is required for reliable statistics, so images areacquired using the 10x objective, which allows for approximately 1000 cellsper image in a confluent monolayer This number is further multiplied byacquiring several locations per substrate using a motorized stage, and byrepeating experiments

I am interested in cell motion, so time-lapse experiments are run, taking

an image every 5 minutes Tracking of cells in this context is fairly easy,

as the motion between the frames is little Experiments are run for 8h ormore, so a single experiment can easily lead to millions of position andvelocity vectors (1000 cells per image × 12 frames per hour × 8 hours ×

20 different locations), good enough for serious statistical analysis

Figure A.1: Example of cell tracking using nuclei staining

From the segmentation and tracking, a set of positions (xi(t), yi(t)) isobtained, where i is an arbitrary index identifying each cell, and t is the timestep I can then compute easily compute velocity vectors (vx i(t), vy i(t))),

This statistical analysis is performed using R [94] I am interested inseveral descriptors, commonly found in the literature:

Cell density The simplest descriptor is the number of cells per frame:

densityavg = hN (t)i

Average speed Another simple descriptor is the average speed of cellmotion I simply take the average speed of all cells, at all times:

vavg = hvi(t)i

This speed can be taken at different time intervals: I have found thatcomputing cell motion over 1 hour, rather than 5 minutes, gives numbersthat are less sensitive to noise and nucleus motion inside the cell

I can also compute the average speed for each timepoint, to see if thespeed is changing during the experiment

tool to describe persistence of motion [45] It is function of a time interval

∆t:

ρ2(∆t) = h(xi(t0+ ∆t) − xi(t0))2+ (yi(t0+ ∆t) − yi(t0))2i

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 timescales are more sensitive to random noise and nucleus motion), hence it

can be fitted to a power law:

ρ2(∆t) ∝ ∆tα

The coefficient α is usually between 1 and 2: 1 indicates a purely nian motion (random, memory-less behavior), while 2 indicates a ballisticmotion (the cell goes straight at a constant speed)

Figure A.2: Example of Mean Square Displacement curve, with a powerlaw fit The red curve corresponds to IEC-6 cells on a relatively hardPDMS substrate (1:20 curing agent/prepolymer ratio), while the yellowcurve corresponds to a much softer, viscoelastic PDMS substrate (1:80).The fit is usually done at longer time scale (e.g more than 1 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

A.2.1 Motion characterization

Upadhyaya [111] provides a detailed analysis of how cell migration viates from Brownian motion, and some of their findings are briefly sum-marized here

de-In Brownian motion, the velocity along a given axis (i.e the velocityvector projected onto any base vector) is normally distributed with pa-rameters N (0, σ2) The average velocity is 0, as the particles exhibit nopreferred direction (i.e., no drift), and the parameter σ determines the av-erage 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 distributedaccording to a Maxwell distribution Z =pX2

1 + X2

2 + X2

3 in the 3 sional case, where all the Xi are normal distributions N (0, σ2) Since thecells are constrained on a 2D plane, the speed distribution would be a 2DMaxwell distribution Z =pX2

dimen-1 + X2

2, also known as Rayleigh distribution.Additionally, the particles in Brownian motion are “memory-less”, andthe angle between their velocities at 2 consecutive intervals is uniformlydistributed 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 observationpoint, along the X axis of the images A log-likelihood minimizing Gaus-sian distribution fit is also shown (i.e a Gaussian distribution with thesame standard deviation as the data) Approximating the distribution by

a Gaussian is acceptable as a first approximation, even though it is clearthat the real distribution has heavy tails (one could fit a Gaussian around

the peak, leaving outliers on each side of the distribution).

Figure A.3b shows the speed distribution, with a 2D Maxwell tion fit: as for the one-dimensional case, the fit is a rough approximation

distribu-of the observed distribution One can also look at the insert, showing theangle distribution between successive velocity observations: instead of aflat uniform distribution, cells usually continue along the same direction asthey moved before

Finally, the general shape of the distribution of speed are consistentacross observations: mean speed may vary, but the distribution alwaysappears “Maxwell-like”

Speed distributions histograms do not allow one to easily compare speeddifferences on various substrates, as shown in Figure A.4a Therefore, Icompute the mean, and obtain a confidence interval around that value

To compute this confidence interval, I first need to compute the dard error of the mean, which is defined as:

stan-SE = √σ

M,where σ is the standard deviation of the data, and M the number of mea-surements In my experiments, I have M = N × T measurements: N cellsover T time intervals

However, measurements are both auto-correlated, as cells are not nian particles, and cross-correlated, as the motion of one cell influences itsneighbors I can compensate for the correlation by multiplying SE by the

(b) Average speedFigure A.4: IEC-6 speed for 14 points, on 3 substrates

k =r 1 − ρ

1 + ρ,where ρ is the the correlation between any 2 pairs of measurements

If I know the average auto-correlation ρT and cross-correlation ρN, Ican compute the average correlation:

where the approximation assumes large N and T

From my datasets, I have, at most, an average autocorrelation cient 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,

coeffi-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% confidenceinterval (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, thatcould be due, for example, to local differences in the substrate, or to vari-ations in cell density

In an attempt to eliminate such local effect, I merge all points on anygiven substrate to a single value, and obtain the bar chart shown in Fig-ure A.5

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 cell-substrate interactions of tissue cells (∼ 20 µm2 in area) In all approaches,

we were far from being able to create such a high-resolution device, so asimple workaround is to use larger cells

Several options were considered (Amoeba Proteus, Chaos sis, Dictyostelium Discoideum), and I performed experiments with ChaosCarolinensis, as it was available in NUS

Carolinen-Chaos Carolinensis is a large amoeba (∼1 mm in length), that is grown

at 22◦C, in a mixed culture with paramecium It is visible without scope, and can be easily picked with a fine-tip glass pipette

micro-B.1 Motility and substrate affinity

Some imaging of the amoeba was performed using the Perkin ElmerUltraview Even using the 4x objective, cells are moving so fast that theytend to exit the field of view within a few minutes To track cell for alonger time, a stitched 3x3 image was acquired, and later reconstructedusing ImageJ [96]

I tried “seeding” cells on 3 different substrates Some sample imagesare shown in Figure B.1 As expected, amoeba prefer hydrophilic surfacessuch as glass and treated plastic dishes, and do not seem to spread a lot

on PDMS 1:10

However, further experiments (not shown here) showed some cells thatseemed to attach to untreated PDMS 1:40 The “healthiness” of the cellseems to play a role in its behavior Also, the number of amoeba is very lim-ited (I usually put 1 or 2 amoeba in one dish), which makes it complicated

to gather enough data to draw conclusions

I also acquired some images with the 20x objective (Figure B.2) thatshow very fast movement in the cytoplasm, called cytoplasmic streaming

or cyclosis Organelles (probably mitochondria), and vacuoles can clearly

be seen

(a) Plastic bottom

Figure B.1: Images of Chaos cells on 3 different substrates

Figure B.2: Images of a Chaos cell, using the 20x objective, some areas

are blurred because of fast cytoplasmic streaming

B.2 Forces exerted on the surface

For the purpose of this work, the first thing to confirm is whether theamoeba actually presses on its substrate The amoeba is seeded on an un-treated 1:80 PDMS, mixed with 1 µm polystyrene fluorescent beads (Invit-rogen) Z-stacks, both in fluorescence, and bright field, are acquired usingthe Ultraview Spinning Disk with the high-sensitivity camera, leading tothe image shown in Figure B.3

One can see that after 62 s, the beads in the center of the image, wherethe amoeba contacts with the substrate, are clearly deflected compared

to their original position (the blue color beads show the position at time

62 s, while the red ones show their original position), clearly indicating asubstrate deformation I can also plot the displacement of one of the beadwith time, shown in Figure B.4 This gives an insight on the frequency andscale of the signal that I would like to measure

Figure B.3: Chaos Carolinensis on 1:80 PDMS with fluorescent beads.Z-stacks acquired using the Ultraview Spinning Disk microscope, with the20x objective, and the high-sensitivity The bright field channel displayedhere is acquired 15µm above the fluorescent beads The red beadsindicate the positions of the beads at time 0, while the blue beads showtheir current position (i.e at time 62 s here) Beads appear violet

(blue+red) when beads do not move

Figure B.4: Displacement of a single bead, near the center of Figure B.3,

due to substrate deformation cause by Chaos Carolinensis

Finally, I also performed some fixed staining of the amoeba, to get anidea if protocols used for tissue cells may be used with this cell type.The process is not straightforward, as the amoeba is not adherent tothe substrate, but I managed to obtain the images in Figure B.5 DAPIstains the nuclei in blue, while the actin is stained in red using phalloidin

As expected, the Chaos Carolinensis has many nuclei Also, interestingly,the actin seems to forms spherical shapes around areas that are clearly notnuclei (which would be stained in red, otherwise)

(a) Overall 3D image.

(b) Close-up.

Figure B.5: Nuclei (DAPI) + actin staining (phalloidin) on ChaosCarolinensis Z-stacks acquired using the Ultraview Spinning disk

B.4 Future work

Chaos Carolinensis does apply forces on its substrate, so it could be used

as a model organism to validate larger sized sensor However, its mobilityhas not been the topic of many studies, and may differ a lot compared toanimal cells, for which developing a better understanding of mobility hasmore potential applications

This is a natural extension of the reversible piezoelectric effect, scribed in Section 3.4 I first planned to use a PVDF film to apply forces

de-on cells: applying a voltage perpendicular to the film using a pair of goldelectrodes would, in theory, generate a force that the cells would sense.However, I found that only very high frequency signals would cause adeformation 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,

leading to an innovative way of generating a wound assay This kind ofwound assay might be more realistic than existing techniques: one methodprevents cells from covering an area, then release the area for cells to cover;another common method scraps cells with a mechanical tool [74] In ourcase, wounded cells are still present, that may be able to produce biochem-ical signals to nearby, healthy cells.

However, it was not readily possible to separate the contributions ofmechanical and thermal effects on the cells, and killing cells by heat shockwas considered to be less interesting and further away from the scope ofthis thesis

However, some of the techniques, mainly in terms of device tion and wiring, proved useful in the making of the device presented inChapter 4

Our first device layout is shown in Figure C.1: 2 gold electrodes arepatterned on either sides of a 9 µm PVDF film The film is then attached

to a piece of PDMS, with a hole localized at the intersection of the 2electrodes, 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 ishydrophobic), 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

moves down by up to 2 µm, in the center area, when a 30 Mhz signal isapplied (the highest frequency available on the signal generator) I thenperformed amplitude modulation of this 30 Mhz signal with a 1 Hz squaresignal, 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 onthe PVDF film, and imaged the beads with an upright microscope (15 µmbeads 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-lapsevideo is acquired, with the signal generator on, so that I can observe the filmgoing up and down From the center position of the bead, I can evaluatethe lateral motion, while the motion in the Z-axis can be evaluated bycomparing the beads radius to the z-stack acquired previously (the beadappears 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 thatmost of the Z displacement is concentrated near the center of the device I

do 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 9µmPVDF film, with gold electrodes patterned on either sides, is attached to

a piece of PDMS, with a hole localized at the intersection of the 2

electrodes