Computer Assisted Image Analysis.

Hey everyone! I am Maham Zia and this summer I worked as a post-bacc for Anna Ritz (primary advisor) and Derek Applewhite (co-advisor). I graduated from Reed in May 2020 with a degree in Physics, but during my undergraduate career I worked in a cell biology and cellular biophysics lab. I am interested in how physics interacts with other disciplines such as biology and chemistry. I believe that interdisciplinary research transcends boundaries and aids the scientific community to think about a variety of problems in creative ways.  

This summer I put my coding skills to use by working on a computational project that involved analyzing images of cells. For her senior thesis, Madelyn O’ Kelley-Bangsberg  ’19 used the punctate/diffuse index to measure the distribution of phosphorylated NMII Sqh. Punctate/diffuse index is widely used to measure the spread of cytochrome c in cells during apoptosis. Measuring this index involves determining standard deviation of the average brightness of the pixels using time lapse microscopy [1]. O’Kelley-Bangsberg’19 used the same idea to determine whether the cell has punctate phosphorylated myosin (high pixel intensity standard deviation) or diffuse phosphorylated myosin (low pixel intensity standard deviation). She did this in ImageJ by outlining each cell, obtaining an X-Y plot of the intensity and finally calculating the relative standard deviation ((standard deviation/mean pixel intensity) x 100 ) by setting the highest intensity value to 1 and lowest intensity value to 0. She used relative standard deviation instead of the absolute standard deviation to draw comparisons because she observed that mean pixel intensity values changed significantly between treatments [1]. Under Anna’s guidance I worked on automating this process in MATLAB by making use of image processing techniques which made the entire process a lot more time efficient.

I was working with images that each had two channels:

  1. An actin channel that shows the distribution of actin- a double helical polymer that aids in cell locomotion and gives the cell its shape. Since actin is distributed throughout the cell, staining it allows us to see the entire cell [2].
  2. A channel showing the distribution of phosphorylated NMII Sqh.

The general idea was to use the actin image to detect/outline the cells and somehow use that information to plot the cell outline on the second image which has the distribution of the phosphorylated NM II Sqh. Plotting them would allow me to obtain the intensity values of the pixels within each cell and determine the standard deviation of the pixel intensity values for each cell.

Initially, my code read in the image with the actin staining and used the inbuilt imfindcircles function in MATLAB to detect cells in the actin image. One of the input arguments of the function is radiusRange which can be used to detect circles with radii within a certain range. However, the function doesn’t work well for ranges bigger than approximately 50 pixels which means it doesn’t work well for images with both small and large cells. Moreover, the function has an internal sensitivity threshold used for detecting the cells. Sensitivity (number between 0 and 1) can be modified by putting it in as an optional argument when calling the function, but increasing it too much leads to false detections [3]. Using imfindcircles function is not a robust way to detect cells and therefore I decided to switch to the drawfreehand function in MATLAB 2020 that allows the user to interactively create a region of interest (ROI) object.

After creating the ROI object (in simple terms that means outlining the cell) as shown in the figure above, I created a binary mask and used regionprops to get the centroid and the equivalent diameter of the object.
The code then read in the second image as shown in image below with the distribution of the phosphorylated NMII Sqh and used outputs from regionprops and the impixel function to get the pixel intensity values for each cell. This image mostly looks dark because it is only showing the distribution of phosphorylated NMII Sqh which is the small cluster of bright pixels we see.

Impixel function takes the column and row indices of the pixels to be sampled and gives their pixel intensity values. However, lengths of column and row vectors need to be the same and since I was approximating the cells as circles, the only way to extract the intensity values of the pixels was to think of the circle as enclosed in a square. So, I used the center coordinates and radii of the circles to get coordinates of the top left corner of the square and used the linspace function to get equally spaced vectors for column and row. Finally, std2 and insertText functions were used for calculating the standard deviation values and displaying them on the image showing the actin distribution respectively.

Future goals could involve analyzing a number of images to determine reasonable standard deviation values and finding a way to extract pixel intensity values for pixels only within the ROI object instead of a square enclosing the object to calculate standard deviation values.

Now that I am done with this project, for this upcoming year I will be working as a research assistant in a lab part of the department of Genetics, Cell Biology, and Development at the University of Minnesota.

References:

[1] M. O’Kelley-Bangsberg, Reed undergraduate thesis (2019) 

[2] J. Wilson and T. Hunt, Molecular Biology of the Cell: The Problems Book (Gar- land Science, New York, NY, 2008), 5th ed., ISBN 978-0-8153-4110-9, oCLC: 254255562.
[3] MathWorks, “Detect and Measure Circular Objects in an Image”, https://www.mathworks.com/help/images/detect-and-measure-circular-objects-in-an-image.html

Microbe Machine

Molecular cloning with Gibson Assembly

Molecular cloning is a technique established in the early 1970s that made introducing specific genes into a host possible [1]. This significantly advanced research because it allowed us to isolate and study individual genes. One method cloning has made possible is protein purification. By introducing a gene to a bacterial vector, the encoding protein is able to be overexpressed and then subjected to biochemical analyses such as crystallization or enzymatic assays to elucidate the function of the protein [2].

I am using this exact technique in my senior thesis at Reed College to study CG11811, a protein novelly indicated as a non-muscle myosin II (NMII) regulator. NMII is an actin binding protein that when activated, constricts actin filaments to change cell shape [3]. Our previous studies found that when CG11811 was depleted using RNAi, there were decreased contractility events. However, we do not know how exactly CG11811 regulates NMII. Therefore, I am cloning CG11811 into a strain of E. coli designed to mass produce proteins in order to purify it and run enzymatic assays to reveal some of its biochemical properties. The first step of this cloning process is creating the recombinant DNA plasmid to transform into the bacteria.

A very efficient technique for this purpose is Gibson Assembly, designed by Dr. Daniel Gibson in 2009 [4]. With Gibson cloning, any two sequences (the gene of interest and the vector) can be joined together without the need for restriction enzyme sites (Figure 1A). The basis of this technique is to design two sets of primers that overlap the gene and the vector (Figure 1B). When these sets of primers are used in PCR, the vector has a section at the end that is complementary to the insert and the insert has a section at the end that is complementary to the vector (Figure 1B). These two PCR products are then combined in the Gibson reaction with an exonuclease that will chew back the overlaps to create “sticky” ends that will anneal to each other, polymerase to fill in any gaps in base pairs in the overlaps, and ligase to join the fragments together (Figure 2). The resulting product is a contiguous plasmid that can then be transformed into the protein expression E. coli to get mass quantities of CG11811.

Figure 1. Primers with overlaps sections produces a PCR product with ends that can anneal the insert and vector together. By designing primers with added end portions of the insert or vector is supposed to join, “sticky” ends are created that can be annealed in a Gibson Assembly reaction.

Figure 2. Gibson Assembly creates complementary ends that anneal to each other to create a contiguous plasmid. In the reaction, an exonuclease chews up the ends that then anneal to the complementary sequences of the other fragment ends. A polymerase then fills in any missing bases and then the ligase completes the plasmid.








Citations

1. Jackson, D. A., Symons, R. H., & Berg, P. (1972). Biochemical method for inserting new genetic information into DNA of Simian Virus 40: circular SV40 DNA molecules containing lambda phage genes and the galactose operon of Escherichia coli. Proceedings of the National Academy of Sciences of the United States of America, 69(10), 2904–2909. doi:10.1073/pnas.69.10.2904
2. Rosano, G. L., & Ceccarelli, E. A. (2014). Recombinant protein expression in Escherichia coli: advances and challenges. Frontiers in microbiology, 5, 172. doi:10.3389/fmicb.2014.00172
3. Martin, A. C., Kaschube, M., & Wieschaus, E. F. (2009). Pulsed contractions of an actin–myosin network drive apical constriction. Nature, 457(7228), 495–499. https://doi.org/10.1038/nature07522
4. Gibson, D. G., Young, L., Chuang, R.-Y., Venter, J. C., Hutchison, C. A., & Smith, H. O. (2009). Enzymatic assembly of DNA molecules up to several hundred kilobases. Nature Methods, 6(5), 343–345. https://doi.org/10.1038/nmeth.1318

Scratch-wound Assays

The scratch-wound assay is a common method for assessing protein distribution and directionality in collectively migrating cells (Cory, 2011). This method is advantageous because it does not require chemical attractants in order to induce migration. Instead, the scratch-wound assay procedure typically involves culturing a sheet of cells on top of extracellular matrix. The matrix operates like tracks that allow the cells to migrate. A needle with a fine filamentous tip is then used to etch a wound onto the sheet of tissue. The wound is then left to heal via cellular proliferation and migration, and the direction of migration can be inferred as into the wound.

Figure 1. Shot depleted RasV12;WTSRNAi epithelial sheet with scratched wound at 0 min. Wound is outlined in yellow. Image was taken with Phase-contrast microscopy at Western blot analysis of acetylated and alpha tubulin Cell lysates of 40x.

For my thesis, I will be using scratch-wound assays in order to study orientation of microtubule growth in migrating Drosophila cells. I am currently culturing sheets of sheets of RasV12;WTSRNAi cells. Some of the cultures have depleted levels of either the protein Short-stop (Shot) or Pickled eggs (Pigs), both of which crosslink actin and microtubules. Into all of these cultures, I have transfected in a DNA construct that expresses a protein called Eb1, which marks the growing ends of microtubule filaments, that is tagged with a red fluorescent molecule. After performing a scratch-wound assay, I can take three minute timelapses of the migrating cells using Total Internal Reflection Fluorescence (TIRF) microscopy. TIRF microscopy essentially uses a laser to excite the red fluorescent molecule attached to the Eb1 proteins on the growing ends of microtubules. The results are short movies in which we can see red comets marking microtubule growth. One of the goals of my thesis is to calculate the angles at which the microtubules are growing relative to the line of the wound and see if there is a difference in orientation of growth between conditions in which proteins have been depleted in cells.

References:

Cory, Giles. “Scratch-wound assay.” Cell Migration. Humana Press, 2011. 25-30.

Culturing Primary Drosophila Neurons

Though there has been great progress with understanding actin and microtubule dynamics, and their relationship to cell motility, the scientific community is still working to try to better define these interactions, and their associated proteins, that allow this movement to happen. Many neurodevelopmental disorders and degenerative diseases are linked to genes associated with the cytoskeleton (Prokop et. al., 2013), making impaired motility of neurons a possible cause. Therefore, further information on growth and motility dynamics could help lead potential treatments for these disorders.

Neurons are understood to develop an axon, their outwardly-signaling appendage, by the elongation of a neurite via microtubule recruitment. The growth cone at the tip of this developing axon is actin-rich, and forms focal adhesions with the substrate to facilitate movement and network development (Prokop et. al., 2013), making the growth cone the leading edge in neurons.  Interestingly, there have been some indications that these growth cones may move at different rates on some substrates than others. Because of the substrate-dependency lead, it may be possible to utilize different substrates to characterize some of the proteins present in the extracellular matrix that contribute to efficient movement of neurons. For my thesis project I’m attempting to look at growth cone dynamics on two substrates: extracellular matrix (ECM) and concanavalin A (ConA, a plant lectin often used to plate cells) using neurons extracted from Drosophila 3rd instar larvae.

Drosophila lend themselves as an excellent model for examining the role of proteins in neuronal movement. Not only are the proteins affecting actin and microtubule dynamics well-conserved, making the findings generalizable across species, but the genetics are simplified in drosophila as well, with little redundancy in the genome. This attribute makes it so that a single knockout is capable of almost completely eliminating the function of a protein, whereas in other animals, such as mice, the knockout of multiple genes may be required to silence a protein due to redundancy (Prokop et. al., 2013). Additionally, existing knowledge about their genome makes it so that we can easily and time-efficiently make genetically altered strains for experimentation. This makes knockdown studies easy and efficacious, and desirable crosses quick to generate. Their neurons have been found to grow well in cultures, even forming networks and displaying similar electrical properties to in-vivo functioning neurons when in proper media (Küppers-Munther et. al., 2004). This allows easy visualization and analysis of neuronal movement, further contributing to their experimental value, which is why drosophila were chosen by our lab for these studies.

In a typical experiment, I extract 6-10 brains from the drosophila larvae and apply liberase to break apart the cell-cell contacts. These neurons are then plated in rich cell media on either an ECM- or a ConA-coated glass slide in a dish and allowed to attach to the bottom of the slide. After the neurons have attached, I visualize their movement by taking videos under a microscope. Additional visualization of proteins can be achieved with staining.

Sources:

Küppers-Munther, B., Letzkus, J. J., Lüer, K., Technau, G., Schmidt, H., & Prokop, A. (2004). A new culturing strategy optimises Drosophila primary cell cultures for structural and functional analyses. Dev Biol, 269(2), 459-478.

Prokop, A., Beaven, R., Qu, Y., & Sánchez-Soriano, N. (2013). Using fly genetics to dissect the cytoskeletal machinery of neurons during axonal growth and maintenance. J Cell Sci, 126(Pt 11), 2331-2341.

Actin Microtubule Crosslinking

Studies have shown that the cytoskeletal elements in the cell (actin, microtubules and intermediate filaments) engage in extensive crosstalk. This crosstalk is an important part of the regulation of the cytoskeleton, as well as a number of other biological processes. For this blog post, I will be focusing on actin-microtubule cross linking, since that is most relevant to my thesis research. Before I get into specifics about how this is related to my thesis, I’m going to give a brief, general overview of actin microtubule crosstalk and the various roles it can play within a cell.

Actin is a highly conserved protein in cells that switches between G-actin and filamentous F-actin. Actin is one of the most abundant proteins in eukaryotic cells and plays an important role in muscle contraction, cell signalling and regulation of cell shape. Microtubules are dynamic, polar and are made up of alpha & beta tubulin. The tubulin polymerizes to form microtubule filaments.  Key to microtubules ability to perform their functions in the cell is dynamic instability and polarity. Dynamic instability is characterized by periods of rapid growth followed by periods of depolymerization. This allows microtubules to rapidly alter their configuration in order to fit the needs of the cell. Microtubules and actin play important roles in cell division, cell migration and other important cellular processes.

Actin Microtubule crosstalk is mainly defined through the physical mechanisms by which it occurs. This means that usually what happens is a physical linkage between parts of actin and parts of microtubules that lead to stabilization or nucleation etc. One of the main forms of actin microtubule crosstalk is crosslinking. This occurs when proteins link microtubules to actin. This linkage is enabled by large protein complexes that can also interact with microtubule plus end binding proteins. This linkage connects the plus ends of microtubules to actin bundles which can result in a redirection of microtubule growth.

One of the proteins that plays a role in actin microtubule cross linking is Short Stop (Shot). Short stop is a spectraplakin that has been shown to bind microtubules & actin filaments and has also been localized in growth cones. In my thesis, I’m looking at microtubules in Drosophila melanogaster neuroblasts, specifically at what happens when you knock down shot thus inhibiting crosslinking. I’m studying the effect of knocking down this crosslinking protein on microtubule dynamics in 3 different parts of the neuron.

 

Works Cited

 

Applewhite, D.A., Grode, K.D., Keller, D., Zadeh, A.D., Slep, K.C., and Rogers, S.L. (2010). The Spectraplakin Short Stop Is an Actin–Microtubule Cross-Linker That Contributes to Organization of the Microtubule Network. Molecular Biology of the Cell 21, 1714–1724.

Dogterom, M., and Koenderink, G.H. (2018). Actin–microtubule crosstalk in cell biology. Nature Reviews Molecular Cell Biology.

Sanchez-Soriano, N., Travis, M., Dajas-Bailador, F., Goncalves-Pimentel, C., Whitmarsh, A.J., and Prokop, A. (2009). Mouse ACF7 and Drosophila Short stop modulate filopodia formation and microtubule organisation during neuronal growth. Journal of Cell Science 122, 2534–2542.

qRT-PCR to verify RNAi knockdown

As discussed in a recent blog post, RNAi is a common technique used in the Applewhite lab to observe the effects of a silenced gene. When preparing for RNAi, it is common practice to run a sample of the dsRNA template on a gel to make sure the resulting band is the same size as the target. However, is this sufficient practice to conclude your following results are due to the knockdown of the gene? Many publishers would say no. It is possible that the exogenous dsRNA was not in appropriate concentration, or was not an effective target to cleave the specific mRNA sequences. Real time quantitative polymerase chain reaction (qRT-PCR) is a supplementary method used to verify the successful knockdown of the gene of interest.

Quantitative PCR (qPCR) is accomplished by extracting endogenous RNA from your cells treated with RNAi, reverse transcribing the RNA to DNA, designing primers to amplify the gene of interest, and using intercalating dyes, such as SYBR Green, which bind to the DNA and fluoresce with greater intensity as the concentration of the target sequence increases. Important to note, in the presence of off-target dsDNA, sequence-specific probes can be used which rely on FRET for detection, and fluoresce only when the DNA polymerase separates the quencher from the emitter. These sequence-specific probes include Taqman, Molecular Beacons, and Scorpions, although require more complex and expensive implementations (1).

The real time element is essential to determining initial DNA template concentration. Since qPCR only measures the end concentration of target sequence, there is no way to calculate an initial concentration. qRT-PCR however, measures template concentration at an exponential stage of replication, which allows for calculation of an initial starting concentration. This in turn, enables analysis of initial gene expression, and if minimal, verification of RNAi success (2).

Figure 1. Relative qRT-PCR and qPCR measurements of target concentration in respect to duration of PCR.

Sources Cited

  1. The Basics: RT-PCR.Thermo Fisher Scientific – USAvailable at: https://www.thermofisher.com/us/en/home/references/ambion-tech-support/rtpcr-analysis/general-articles/rt–pcr-the-basics.html. (Accessed: 23rd October 2018)
  2. Bansal, R.et al.Quantitative RT-PCR Gene Evaluation and RNA Interference in the Brown Marmorated Stink Bug.Plos One11,(2016).

 

Mander’s Coefficient

One aspect of my thesis is exploring co-localization of Split Discs with other proteins in drosophila cells. In order to do this, not only does wet lab work need to be accomplished, but mathematical analysis (in this case using Mander’s coefficient).

Fluorescence microscopy does not have the ability to see whether or not two molecules are directly interacting. However, by looking to see if they co-localize in the cell, it can be determined whether they interact with the same complexes in the cell. The limit for fluorescence microscopy is the resolution of the images produced. Because of this, small numbers of puncta are not sufficient for determining whether or not the experimental molecules are actually co-localized. Multiple puncta from different regions within the cell must be used in analysis so the data is not limited to overlapping puncta which are a result of organelles that are close in proximity to one another.

In order to quantitatively determine the correlation of co-localization in the cell, mathematical analysis of the data is employed. For my thesis, I am employing Mander’s Overlap Coefficient (MOC) for this analysis because it does not require distinguishing fluorescence as being the result of a fluorescent protein or background noise. MOC is able to do this because it only compares the co-occurrence of fluorescence among pixels. MOC = ∑i(Ri×Gi) / √(∑iR2i×∑iG2i) where Ri and Gi are the average level of grey from the red and green fluorescence respectively (Manders et al., 1993). MOC has a range of 0 – 1 and Ri and Gi have a range of -1 – +1. The limitation to this equation is that the ratio of values can result in ambiguous numbers. Therefore, the numerator and denominator can be split up in such a way to account for the ambiguity.  From this we get two coefficients: M1 (fraction of red fluorescence in areas with green fluorescence) and M2 (fraction of green fluorescence in areas with red fluorescence)  (Manders et al., 1993). M1 = (∑iRi,colocal) / ∑iRi where Ri,colocal = Ri if Gi > 0 and Ri,colocal = 0 if Gi = 0 and M2 = (∑iGi,colocal) / ∑iGi where Gi,colocal = Gi if Ri > 0 and Gi,colocal = 0 if Ri = 0 (Manders et al., 1993). The larger MOC, M1, and M2 are the stronger the evidence for co-localization of the proteins within a cell. In my thesis, MOC, M1, and M2, will be gathered for each cell to determine whether or not Split Discs are co-localizing with other specific proteins.

 

References:

 

Dunn, K. W., Kamocka, M. M., & McDonald, J. H. (2011). A practical guide to evaluating colocalization in biological microscopy. American Journal of Physiology – Cell Physiology, 300(4), C723–C742. http://doi.org/10.1152/ajpcell.00462.2010

Manders, E. M., Verbeek, F. J. & Aten, J. A. (1993). Measurement of co‐localization of objects in dual‐colour confocal images. Journal of Microscopy, 169, 375-382. doi:10.1111/j.1365-2818.1993.tb03313.x

BioID of SPECC1L

BirA is biotin protein ligase in E. coli that selectively adds biotin to a subunit of acetyl-CoA carboxylase. Roux et al. created a mutant BirA that isn’t selective to its native substrate and will instead biotinylate any proteins that are close-by. This allows for identification of protein-protein interactions in eukaryotic cells by creating a fusion protein of BirA and a protein of interest that will biotinylate proximal proteins, which can then be captured and identified. Protein identification utilizes the strong association of biotin and streptavidin (or avidin) to capture proteins that have been biotinylated by BirA, followed by mass spectroscopy to identify biotinylated proteins.

 

Figure 1. Schematic of BioID assay from Roux et al. 2012.

I am investigating the protein interactions of an actin-microtubule crosslinking protein coded by the gene SPECC1L (with an ortholog known as “split discs” in Drosophila). Mutations in SPECC1L have been identified in a number of diverse cases of orofacial cleft, and thus knowledge of protein-protein interactions by the product of SPECC1L is particularly important to understanding the developmental basis of this set of conditions.

To this end, I am using a BirA-split discs construct to investigate what proteins split discs interacts with in vivo in Drosophila. This construct will ideally biotinylate proteins that split discs typically interacts with, without excessive non-target biotinylation and without affecting the behavior or split discs. I will then capture biotinylated proteins using the biotin-streptavidin interaction and identify using mass spectrometry.

 

References:

Roux KJ, Kim DI, Raida M, Burke B. A promiscuous biotin ligase fusion protein identifies proximal and interacting proteins in mammalian cells. The Journal of Cell Biology. 2012;196(6):801.

CG and Flapwing: Knockouts, Knockdowns, and RNA Interference

When attempting to understand a protein’s function in a cell, the effects of removing that protein can be very telling. As such, knockdowns and knockouts, techniques which remove a targeted protein from acting in the cell, are widely used to identify how a cell behaves without the functions performed by said target protein.

 

A knockout is an irreversible procedure that removes the target protein from the cell permanently, often by editing the genome itself to either deactivate or directly remove the target protein’s coding sequence. This can be achieved by selective breeding when dealing with whole organisms, but when working with cell cultures, knockouts are typically accomplished by means such as the gene-editing kit TALEN or, in recent years, by use of the tool CRISPR-cas9.
A knockdown, on the other hand, is a repeated procedure which removes the target protein from the cell temporarily. By treating cells on a regular basis, the target protein is disrupted from its usual function, and the cells can be observed without its influence. If the treatment ceases, the target protein will no longer be disrupted and the cell will return to normal function, if mildly worse for wear. The distinction between these two procedures can be likened to ending a fight (knockout) as opposed to temporarily ‘gaining advantage’ or suspending the fight (knockdown).

 

In our experiment, we have performed a RNA interference (RNAi) knockdown of our target proteins flw and CG. This is achieved first by the transformation of genomic DNA (gDNA) that codes for the target protein into double stranded RNA (dsRNA), and then by simply exposing cultured cells to the dsRNA on a sustained and regular basis.
The reason this apparently simple method (which requires more pipetting and tube shuffling than that short sentence might imply) works and removes the target protein from action is due to the cell’s own inherent defensive mechanisms. When exposed to free floating dsRNA in solution, some dsRNA is naturally taken up into the cell, where it is recognized as foreign and chopped to pieces. Ironically, this causes the fragmented dsRNA to bind to messenger RNA (mRNA) already in the cell that matches its sequence, whereupon the entire dsRNA-fragment-mRNA amalgamation is recognized as foreign and chopped to pieces.

 

Figure 1. dsRNA suspended in cell media is taken into a cell, recognized as a foreign component, and cut into pieces by the appropriate enzymes. The cut pieces of dsRNA attach to pieces of mRNA naturally present in the cell, which are subsequently tagged for sheering due to their binding with a foreign component.

 

When the dsRNA is in sufficient concentration, this defensive response results in the cell being unable to translate the appropriate mRNA into the target protein, since it is instead destroying that mRNA as fast as it can. Once depleted of the target protein, cells can be treated, fixed, stained, or any combination thereof, and the effects of the knockdown can be observed to extrapolate the target protein’s function.

Team Force: Data Analysis Techniques

In the previous post we described how the data is collected using Traction Force Microscopy (TFM). The process of imaging outputs several “movies,” which display the cells exerting forces and moving the beads embedded in the compliant gel matrix.

The data analysis algorithm is threefold: 1) tracking, 2) low-pass filtering, and 3) calculating traction stresses.

To calculate the displacements of the beads, a reference image of the beads on a plain compliant matrix is compared to an image of the beads on a compliant matrix with the cell on top of it which then pulls on the substrate near its edges. Using an array containing the tracked particle data for each frame of the movie, the displacements are extrapolated with stochastic drift taken into account. These data are then output onto an XY grid at each time interval.

Then, a low pass-filter is added to remove the high-frequency noise from the displacement data.

Next, the displacement data is correlated to the traction stresses through an algorithm derived by Style et. al. (2014) along with the elasticity theory, which states that the properties of the compliant matrix such as thickness, stiffness, and compressibility must be taken into account when considering traction stresses, which are continuous distributions of forces (Abidi, 2016). Modeling the gel as a “spring,” we can use Hooke’s Law, F=-kx, where k is the elasticity constant, x is displacement, and F is the force.

Finally, once the traction stresses have been computed, we will overlay a plot of the displacement and traction stress vectors on top of an image of the cell, as shown in Figure 1 (Abidi, 2016).

Figure 1: A force vector field calculated by Abidi (2016) using example data from Style et. al. (2014)

 

References

Abrar A. Abidi. Quantifying cellular mechanotransduction in morphogenesis and cancer. Reed College, 2016.

Robert W Style, Rotislav Boltyanskiy, Guy K German, Callen Hyland, Christopher W MacMinn, Aaron F Mertz, Larry A Wilen, Ye Xu, and Eric R Dufresne. Traction force microscopy in physics and biology. Soft Matter, 10(23):4047-4055, 2014.