report3.tex

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\usepackage{tikz}               % Drawings in Methods section.
\usepackage{xr}                 % References to external reports.
\usepackage{tabularx}           % Wrap multiple lines in a table.
\usepackage{minted}             % Source code highlighting.
\usepackage{epstopdf}           % Convert .TIF to .PNG
\usepackage{xcolor,colortbl}    % Color table cells.
\usepackage{multirow}           % Span multiple table rows.

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\bibliographystyle{biochem}
\externaldocument[r1-]{report1}
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% Convenience macros
\newcommand{\dicty}{\emph{Dictyostelium discoideum}\xspace}
\newcommand{\uM}{\textmu M\xspace}
\newcommand{\ul}{~\textmu l\xspace}
\newcommand{\um}{~\textmu m\xspace}

\title{\vspace{-4.5ex}Methotrexate inhibition reveals differential chemokine sensing mechanism in \dicty}
\author[1,2]{\small{Pariksheet Nanda}}
\author[1]{Michael Lemieux}
\author[1]{Sara McAnulty}
\author[1]{David Knecht}
\affil[1]{Department of Cell Biology}
\affil[2]{Department of Biomedical Engineering}

\begin{document}
\maketitle

\begin{abstract}
  \noindent
  Observations of \dicty in uniformy distributed folate chemotractant show highly directional cell movement.
  Specifically, cells leave their well containing media and folate to move under agarose which has been mixed with folate at an equal concentration as the well.
  Such directed movement suggests that chemotaxis, surprisingly, occurs even in a uniform folate gradient.
  \dicty break down the folate chemoattractant with folate deaminase to create a local gradient.
  However, the above behavior also occurs in methotrexate which \dicty has no known mechanism of breaking down.
  In this report, we investigate the characteristics of \dicty breakdown of folate and compare our results with  methotrexate.
\end{abstract}

\section{Introduction}
\label{sec:intro}

In education settings, we observe cells under agarose in the arrangement shown in Fig.~\ref{fig:dish:classic}, where cells leave a set of wells (or troughs) to chemotax to the center well containing the chemoattractant of 0.1~mM folate.
The cells are at a high concentration and create a high density ``wave'' grouping as they migrate towards the chemotactic chemical.

\begin{figure}[h]
  \centering
  \begin{tikzpicture}[
    well/.style={draw, inner sep = 0mm, minimum width=40mm, minimum height=5mm}
    ]
    \draw (3,3) circle [radius=3];
    % Bottom
    \draw
    (3,4) node [well] {cells monolayer}
    (3,3) node [well] {0.1~mM folate}
    (3,2) node [well] {cells monolayer};
  \end{tikzpicture}

  \caption{Classic arrangement, to scale, of wells cut using full-length razor into agarose in p60 dish to observe chemotaxis in MCB2225L class.}
  \label{fig:dish:classic}
\end{figure}

The cells following this initial wave display reduced chemokinetic motion, which is assumed to be due to depletion of the chemical concentration due to folate deaminase break down by the first wave.

Chemokinetic motion has previously been observed even in uniform chemical presence, by infusing the chemotactic chemical into the agar medium itself.
Given this surprising chemokinetic observation, we hypothesize that \dicty cells, break down chemokines using folate deaminase to differentially generate a motility signal, without an external chemotactic gradient.
The presence of a chemical that cannot be broken down should, therefore, reduce the effectiveness of the chemotactic machinery.
Such a folate analogue that cannot be broken down is methotrexate.
Previous experiments with methotrexate and \dicty suggest that a similar concentration to folate induces the same level of chemotactic motility.

\begin{table}[h]
  \centering
  \caption{Notable chemotaxis definitions discussed in this report.}
  \begin{tabularx}{\linewidth}{lX} \hline
    Chemotaxis & Cell movement towards, or away from, a chemical compound.\\\hline
    \dicty & An amoeba used as a model organism.\\\hline
    Folate & Chemotactic chemical known to attract \dicty.\\\hline
    Folate deaminase & Enzyme that breaks down the \emph{folate} amino acid.\\\hline
    Methotrexate & Chemotactic chemical known to attract \dicty, like \emph{folate}, but cannot be broken down by \emph{folate deaminase}.\\\hline
    Motility & Full cell body movement.\\\hline
Persistence & The ratio of distance traveled to displacement travelled; a unitless number between 0 and 1.
    When measuring a given cell, average all such measurements.\\\hline
Directionality & The cosine of the angle subtended between the instantaneous and final positions; a unitless number between -1 and 1.
  When measuring a given cell, average all such measurements.\\\hline
  \end{tabularx}
  \label{tab:def}
\end{table}

\section{Results and Discussion}

A broad overview showing the goals and concerns of each experiment conducted during this independent project is presented in Fig.~\ref{fig:mindmap}.

\begin{figure}[p]
  \centering
  \begin{tikzpicture}
    \path[mindmap, concept color=black!20]
    % Chemotaxis
    node[concept] {Under agarose chemotaxis}
    [clockwise from=180]
    child[concept] {
      node[concept] {Exploration}
      [clockwise from=-120]
      child {node[concept] (r1) {Optimize chemical conc.}}
      child {node[concept] (r2) {Cell kinetics}}
      child {node[concept] (r3) {Cell incubation}}
    }
    child[concept] {
      node[concept] {Method adjustment}
      [clockwise from=150]
      child {node[concept] (m1) {Brass cutters}}
      child {node[concept] (m2) {Multi-XY positions}}
    }
    child[concept] {
      node[concept] {Technique practice}
      [clockwise from=150]
      child {node[concept] (t1) {Agar minutiae}}
      child {node[concept] (t2) {Humidity control}}
      child {node[concept] (t3) {Gentle pipetting}}
    }
    child[concept] {
      node[concept] {Automated analysis}
      [clockwise from=60]
      child {node[concept] (a1) {Image stitching}}
      child {node[concept] (a2) {Tracking}}
      child {node[concept] (a3) {Skewness detection}}
    }
    % Experiments
    node[concept, concept color=violet!30] (e1) at (-7,9)
    {Exp.~1: 7~plate snapshots}
    node[concept, concept color=green!30!black!20] (e2) at (0,11)
    {Exp.~2: 1~plate validation}
    node[concept, concept color=blue!30] (e3) at (7,9)
    {Exp.~3: folate calibration}
    node[concept, concept color=red!30] (e4) at (-3,-5)
    {Exp.~4: 24~hr incubation}
    node[concept, concept color=orange!30] (e5) at (3,-5)
    {Exp.~5: 2~hr incubation}
    ;
    % node[concept] at (0,-10) {Experiments}
    % [clockwise from=180]
    % child[concept color=violet!30] {node[concept] (e1) {\#1: 8 plate snapshots}}
    % child[concept color=green!30!black!20, sibling angle=45] {node[concept] (e2) {\#2: 1 plate snapshot}}
    % child[concept color=blue!30, sibling angle=45] {node[concept] (e3) {\#3: folate calibration}}
    % child[concept color=red!30, sibling angle=45] {node[concept] (e4) {\#4: 24~hr incubation}}
    % child[concept color=orange!30, sibling angle=45] {node[concept] (e5) {\#5: 2~hr incubation}}
    % ;
    % Connections
    \begin{pgfonlayer}{background}
      \draw [concept connection, color=violet!30]
      (e1) edge (r1)
      (e1) edge (a1)
      (e1) edge (m1)
      ;
      \draw [concept connection, color=green!30!black!20]
      (e2) edge (r1)
      (e2) edge (a1)
      (e2) edge (m1)
      (e2) edge (m2)
      (e2) edge (t1)
      ;
      \draw [concept connection, color=blue!30]
      (e3) edge (r1)
      (e3) edge (r2)
      (e3) edge (m2)
      (e3) edge (t1)
      ;
      \draw [concept connection, color=red!30]
      (e4) edge (r2)
      (e4) edge (r3)
      (e4) edge (t1)
      (e4) edge (t2)
      (e4) edge (t3)
      (e4) edge (m2)
      ;
      \draw [concept connection, color=orange!30]
      (e5) edge (r2)
      (e5) edge (r3)
      (e5) edge (m2)
      (e5) edge (t1)
      (e5) edge (t2)
      (e5) edge (t3)
      (e5) edge (a2)
      (e5) edge (a3)
      ;
    \end{pgfonlayer}
  \end{tikzpicture}

  \caption{Mindmap showing experiment progression over the 4 week project timeframe.
    Experiments 1 and 2 were primarily meant to calibrate chemokinetic chemical concentration, while also attempting to improve the experimental method with the use of brass cutters and multi-XY stage scanning, respectively.
    However various assumptions and technique problems did not yield reliable chemotactic concentration results.
    Experiment 3 quantified folate chemotactic chemical concentration using cell kinetics.
    Experiments 4 and 5 captured chemotaxis after cell incubation.
  }
  \label{fig:mindmap}
\end{figure}

\subsection{Brass cutters to create troughs in agarose (Experiment 0)}
\label{sec:results:brass}

Brass cutters were tested in the hope of more consistently creating the 12 troughs in Fig.~\ref{fig:dish} than the razor blade.
The cutters themselves were previously fabricated by sectioning a rectangular brass tube into 1~inch pieces of various cross-section dimensions, as listed in Table~\ref{tab:brass}.

\begin{table}[h]
  \centering
  \caption{Outer cross-sections of rectangular brass tube fabricated to cut aragose wells.}
  \begin{tabular}{c} \hline
    Dimensions (mm) \\\hline
    $2 \times 2$ \\
    $3 \times 3$ \\
    $2 \times 4$ \\
    $3 \times 7$ \\
    $4 \times 9$ \\\hline
  \end{tabular}
  \label{tab:brass}
\end{table}

The cross-section outer perimeter affects the corresponding well size.
The brass cutters with tested on 1.5\% agarose, 30~minutes after pouring the molten agarose into the p100 dish.
In all cases, the cutter pushed down easily.
One problem encountered was agarose sticking to the cutter brass sides.
Only the largest two cross-sections of $3 \times 7$~mm and $4 \times 9$~mm cut cleanly without the agarose sticking from the cutter being removed.
These two largest cutter sizes were additionally notable in that they had thinner walls from sharpening.
The largest cross-section of $4 \times 9$~mm also produced the most consistent cuts and its 4~mm height matches the classic paper shown in Fig.~\ref{fig:dish:classic}.
The macroscopic photograph shown in Fig.~\ref{fig:cuts} illustrates the quality of the troughs created by the brass cutter.

\begin{figure}[h]
  \centering
  \includegraphics[width=0.4\textwidth]{data/ind_brass-cutter-holes-test.tif}
  \caption{Brass cutter holes in 1.5\% agarose.  Two cuts were made using each size listed in Table~\ref{tab:brass}.}
\label{fig:cuts}
\end{figure}

The brass cutters reduced the trough volume from 175\ul to 90\ul, using even the largest $4 \times 9$~mm brass cutter cross-section size.
This reduces the required volume of chemoattractant, and number of cells to form the mono layer.
However the resulting brass cut troughs also exhibited less precise agarose interfaces, and in many cases cells ``leaked'' into the surrounding agarose quickly after plating, which is detrimental to motility analysis.
An alternative to the brass cutters would be fabricating a mould with troughs, and transferring the moulded agarose into the experimental dish.

\subsection{Small plate, static chemotaxis snapshots (Experiment 1)}
\label{sec:results:chemoindiv}

\begin{figure}[h]
  \centering
  \begin{tikzpicture}[
    well/.style={draw, inner sep = 0mm, minimum width=9mm, minimum height=4mm},
    arr/.style={lightgray,line width=0.5mm,->},
    ann/.style={align=left, text width=4.5cm}
    ]
    \draw (3,3) circle [radius=3];
    % Bottom
    \draw
    (3,3) node [well] {}
    ++(3,0) node [ann] {cells}
    (3,4) node [well] {}
    ++(3,0) node [ann] {conc. $x$}
    (3,2) node [well] {}
    ++(3,0) node [ann] {conc. $x/10$};
  \end{tikzpicture}

  \caption{Modified classic arrangement, to scale, of wells cut using brass cutters into agarose in p60 dish to observe post-chemotactic cells.
  Concentrations of chemokine on each plate were set 1 magnitude apart, as represented by $x$ and $x/10$.}
  \label{fig:dish:retro}
\end{figure}

To determine the concentrations of folate and methotrexate at which chemotaxis occurs, 3 dishes were prepared for each chemokine using the configuration shown in Fig.~\ref{fig:dish:retro}.
The 3 plates therefore allowed 6 concentrations of each chemokine to be tested, as described in Protocol~\ref{sec:proto:conc}.
As a control, a separate plate with only SM media was created with cells in the center well and media in the top and bottom wells.
After the cells were left for 16~hours to chemotax, between 2 and 5 overlapping static images were collected per chemotactic well, from the edge of the cell well up to the farthest cell of wave front.

The images were stitched and thresholded as shown in Fig.~\ref{fig:isolated} to obtain the measurements listed in Table~\ref{tab:static}.
A bug in the stitching plugin causes bottom-to-top collected images to fail stitching, so all images were rotated to show cell movement from top-to-bottom.
The Center of Mass measurement was thus simply noting the calibrated Y-coodinate of the Center of Mass measurement in ImageJ, with the intention of indicating how far away all the cells moved from the cell trough.
Distance is the length traveled by the third farthest cell, measured by hovering the mouse cursor over such a cell and noting the calibrated Y-coordinate.
The yellow highlighted cell count of 368 in Table~\ref{tab:static} indicates the control threshold considered for non-chemotactic motility.
The green highlighted cell counts of 732 and 631 for folate and methotrexate, respectively, indicate the closest cell movement count over the threshold considered to correspond to chemotactic motility.
The corresponding concentrations of folate and methotrexate at these two indicators is 0.01~mM for both chemicals.

\begin{figure}[h]
  \centering
  \includegraphics[width=0.4\textwidth]{data/figj_indep_exp1/JpegCompressed_figj_indep_exp1.jpg}
  \caption{
    (A) Images captured using non-motorized microscope by eyeballing the overlap between fields and stitching.
    Top edge shows the cell trough boundary.
    Bottom, gray, trough contains 1~mM mtx.
    Middle phase-dark segment is the mtx trough edge.
    Stepped black left and right edges are due to  the camera being at an angle to the stage.
    (B) Cells isolated inverting intensity and thresholding.
  }
  \label{fig:isolated}
\end{figure}

There were a few problems with this experiment:
\begin{enumerate}
\item Some of the wells exhibited ``leaking'', where a few cells appeared outside of the wells as bright objects (phase-bright) using phase contrast.
There were many more of the expected phase-dark cells that chemotaxed, but the ``leaking'' phase-bright cells raise the concern about whether the integrity and consistency of the agarose-liquid interface in sufficient to observe reliable cell chemotactic behavior.
\item At the end of the 16~hours, all of the liquid inside the wells had dried up.
The cells were sitting on the laboratory workbench counter, and, in spite of the petri dish lids, airflow and low humidity from the room was suspected to have dried out the wells.
Drying out was suspected since there was condensation on the dish lids, and so liquid loss from diffusing under the agarose is assumed to be less significant.
One way to remedy the liquid loss is to observe the cells after a shorter time period less than 16~hours.
\end{enumerate}

The next experiment attempted timelapse video microscopy to observe chemotactic behavior in a more timely manner.

\begin{table}[h]
  \centering
  \caption{Analysis of post-chemotaxis static stitched images spanning the cell well to the chemokine well.}
  \begin{tabular}{lrrrr}\hline
    Chemokine & Conc (\uM) & Count & Center of Mass (mm) & Distance (mm)\\\hline
    \multirow{4}{*}{SM media (control)} & \multirow{4}{*}{N/A} & \cellcolor{yellow!50} 368 & 1.5 & 2.6\\
         & & 194 & 0.8 & 2.1\\
         & & 7 & 0.7 & 1.4\\
         & & 69 & 1.2 & 1.5\\\hline
    \multirow{6}{*}{Folate} & 1000 & 1495 & 1.1 & 5.6\\
         & 100 & 875 & 1.5 & 6.1\\
         & 10 & \cellcolor{green!50} 732 & 2.4 & 3.6\\
         & 1 & 237 & 0.8 & 2.4\\
         & 0.1 & 235 & 1.0 & 2.6\\
         & 0.01 & 118 & 1.7 & 3.3\\\hline
    \multirow{6}{*}{Methotrexate} & 1000 & 745 & 1.3 & 2.7\\
         & 100 & 467 & 2.0 & 4.7\\
         & 10 & \cellcolor{green!50} 631 & 6.4 & 8.4\\
         & 1 & 170 & 3.2 & 5.9\\
         & 0.1 & 51 & 1.0 & 1.3\\
         & 0.01 & 11 & 2.9 & 0.1\\\hline
  \end{tabular}
  \label{tab:static}
\end{table}

\subsection{Multi position imaging (Experiment 2)}
\label{sec:results:p100}

The goal of this experiment was to simultaneously image chemotaxis toward all the chemoattractant wells using a motorized XY stage.
Repeating the previous experiment using video microscopy would require imaging 13 single fields of view in successive timelapse experiments.
As it is not possible to fit 7 p60 dishes on a typical XY stage, two possible solutions are to either use a multi-well plate large enough to accomodate the a number of agarose wells, or, per Dr.~Knecht's suggestion, the larger p100 growth plate.
A standard 6 well multi-well plate that Dr.~Carol Norris uses for testing was evaluated, and confirmed to fit in the multi-XY stage.
In hindsight, a multi-well plate may yield better video images, since it is designed for image quality, but for cost and availability reasons this experiment was done using a p100 plate, this time with the standard half-length razor cutter, in the configuration shown in Fig.~\ref{fig:dish}.

A second experimental goal was to quickly iterate between the image acquisition and final numerical processing steps.
Sometimes, in research imaging, scientists spend weeks and months acquiring data sets and then, with great disappointment, discover insurmountable difficulties when analyzing them that should have been prevented at acquisition.
Therefore this experiment consisted of capturing multi position data, and then conducing all motility analysis that be would finally required of this project.

\begin{figure}[h]
  \centering
  \includegraphics[width=\textwidth]{data/figj_indep_exp2/JpegCompressed_figj_indep_exp2.jpg}
  \caption{
    (A) Image stitching plugin of a single timepoint resulted in a 2.9~GB image having about 33,000 pixels on each side.
    (B-E) Cropped phase images of $5 \times 5$ tiles from (A) showing ``leaking'' of cells under the agarose just 30 minutes after plating.
    The cells are the clusters of phase-bright dots.
    The center third of each image is the cell trough, with the edges of the SM liquid media meniscus appearing as black areas, and the agarose-liquid boundary is the thin white surrounding line.
    The gray cloudiness at the center of each image is the meniscus minimum height, or center.
    Varying concentrations of folate were placed at either side of (B) and (C), and varying concentrations of methotrexate at either side of (D) and (E).
  }
  \label{fig:3gb}
\end{figure}

This acquisition-analysis iteration was fruitful in uncovering 4 challenges:
\begin{enumerate}
\item The multi-well acquisition plugin of Micro-Manager only aligns to the well centers.
While it can be set to acquire a grid of images at the center, out of the box, it does not support a per-well offset or multiple grids per well.
Our need is to acquire a bimodal set of two chemokinetic areas per well; between the center cell trough and each of the chemokine wells.
\item It was desirable to acquire as many overlapping images as feasible to observe more cells to reduce the $p^2$ value.
The time duration for acquiring images in this manner over the entire area between wells was close to 5~minutes with a 4x objective.
Motion analysis of these cells should at most be only 1 minute apart, otherwise it would not be possible to uniquely identify individual cells to automate track reconstruction analysis. 
\item Stitching a single timepoint of overlapped images resulted in a 2.9~GB image with each edge having about 33,000~pixels, as the Grid/Collection Stitching plugin of FIJI, having no concept of positional grouping, includes all the ``black'' zero value areas between images instead of separating positions into hyperstack position slices.
\item The phase-bright cell ``leaking'' was still visible in the images ahead of the chemotactic wave.
Discussion at the lab meeting suggested gentler pipetting to not upset the agarose interface.
\end{enumerate}

As the stitched file size challenge was insurmountable, the advice at the lab meeting was to not do the stitching, but to simply acquire a single field of view along each chemotactic axis.
Following this advice, the rotational script included in Supplement~\ref{sec:rotation} was created.

\subsection{Folate calibration using video microscopy (Experiment 3)}
\label{sec:results:folate}

Following the advice from the previous lab meeting, observing all the cells between the cell well and chemokine well was abandoned in favor of single, representative fields of view per chemokine concentration.
As the methotrexate quantity was relatively low, in anticipation of further problems, only the plentiful folate was used for imaging.
Protocol~\ref{sec:proto:conc} was followed and the imaging done using the same trough arrangement of Fig.~\ref{fig:dish}.
During imaging, the chemokine wells on either side of the cell trough contained identical sets of concentrations of folate as listed in Table~\ref{tab:conc}; the 2 replicates of each concentrations were to gain confidence in the measurement.

The expectation was to simply visually observe the cell motility and classify the motion as appearing to be chemotactic or not.
Visual observation confirmed the previous observation that at least 0.01~mM folate concentration is required for chemokinetic cell behavior.
At lower concentrations, cells still left the wells, but exhibited poorly directed movement.

New challenges discovered were:
\begin{enumerate}
\item Many of the image fields were out of focus.
  As there are no cells outside of the cell trough, one has to estimate where the plastic-agar boundary is to image phase-dark, under-agar, cell movement.
  Having the high contrast phase-dark cells is necessary to automate segmentation of the cells from other artifacts in the agar.
\item Over the course of several hours, cells were observed moving on top of the agar.
  The large depth of focus of the 4x objective saw these cells appear as wide, round spots, which interfered with segmenting the under-agarose cells.
  The top moving cells were a result of overflow while filling the cell trough.
  The overflowed may have been a result of:
  \begin{enumerate}
  \item Too much media containing the cells being filled into the trough.
  \item Fast, high pressure pipetting technique.
  \end{enumerate}
\item The motorized XY stage drifted along the Y-axis for the first field of view, only.
  This is assumed to be due to the stage joystick being not returning to the neutral center position.
  This type of mechanical sticking can often be fixed simply by using a plastic-safe lubricant.
\end{enumerate}

\subsection{Incubation for 24 hours (Experiment 4)}
\label{sec:results:24hrs}

Nearly all the methotrexate was consumed in Experiments 1 and 2.
Thus this first iteration of the degredation assay was, again, like Experiment 3, run only with folate.
To more efficiently run the experiment, instead of collecting supernatant from cells at different timepoints, different concentrations of cells were used to breakdown the chemokine and the supernatants were harvested all at once.
Cells were incubated as described in Protocol~\ref{sec:proto:xyprep} in a multiwell slide along with the chemokine, and the supernatant was harvested after 24~hours.
As the calibration experiment showed that at least 0.01~mM folate concentration was necessary to induce chemotaxis, that same concentration was used in each well.

Imaging for 16~hours revealed that just $5 \times 10^4$~cells were sufficient to impede chemokinetic activity after 24~hour incubation, and that the higher incubation quantities of $2 \times 10^6$ and $5 \times 10^5$~cells showed no discernable chemotactic activity.

There were fewer new problems from this experiment.
In fact, the XY stage drift of the first stage position did not occur.
However, the run was still affected by previous known challenges:

\begin{enumerate}
\item As with Experiment~1, the media from all the wells had evaporated; this time, at the end of 16~hours.
\item Condensation appearing on the cover of the dish made thresholding the cells at the latter third of time points increasingly difficult.
  This effect is not as bad as cells crawling on top of the agar, but can still introduce artifacts into the cell segmentation.
  To deal with this and the evaporation, the dish type will be switched to one with a bottom lip that should reduce thermal conduction from the XY stage to the plastic dish bottom.
  The new p100 dish should improve imaging quality by reducing artifacts from the plastic.
\item Many of the image fields were out of focus, like Experiment~3.
  The lower concentration meant that no cells appeared under agarose even after waiting for 3~hours.
This time the different focal planes were setup using the microscope motorized Z~drive for each position based on contamination under the agar.
However some of the focal plane guesses were significantly off.
\end{enumerate}

To make use of the higher range of cell incubation quantities of $2 \times 10^6$ and $5 \times 10^5$, the incubation time for next experiment will be reduced.
Additionally a higher chemical concentration will be used to try and induce chemotaxis earlier and, thus, reduce the image acquisition time.

\subsection{Incubation for 2 hours (Experiment 5)}
\label{sec:results:2hrs}

\begin{figure}[h]
  \centering
  \begin{tikzpicture}[
    well/.style={draw, inner sep = 0mm, minimum width=20mm, minimum height=5mm},
    arr/.style={lightgray,line width=0.5mm,->},
    ann/.style={align=left, text width=4.5cm}
    ]
    % Dish
    \draw (5,5) circle [radius=5];
    % Bottom
    \draw
    (5,0.75) node [well] (fb) {folate}
    ++(0,1) node [well] {cells}
    ++(0,1) node [well] (mb) {mtx}
    ++(7.5,-1) node [ann] (lb) {$5 \times 10^5$ cells incubation};
    \draw
    [arr] (lb) -- ++(-6,0) -- ++(0,1) -- (mb);
    \draw
    [arr] (lb) -- ++(-6,0) -- ++(0,-1) -- (fb);
    % Top
    \draw
    (5,9.25) node [well] (ft) {folate}
    ++(0,-1) node [well] {cells}
    ++(0,-1) node [well] (mt) {mtx}
    ++(7.5,1) node [ann] (lt) {No cell incubation\\(control)};
    \draw
    [arr] (lt) -- ++(-6,0) -- ++(0,1) -- (ft);
    \draw
    [arr] (lt) -- ++(-6,0) -- ++(0,-1) -- (mt);
    % Left
    \draw
    (0.75,5) node (fl) [well, rotate=90] {folate}
    ++(1,0) node [well, rotate=90] {cells}
    ++(1,0) node (ml) [well, rotate=90] {mtx}
    ++(10,1.5) node [ann] (ll) {$2 \times 10^6$ cells incubation};
    \draw
    [arr] (ll) -| (fl);
    \draw
    [arr] (ll) -| (ml);
    % Right
    \draw
    (9.25,5) node (fr) [well, rotate=90] {folate}
    ++(-1,0) node [well, rotate=90] {cells}
    ++(-1,0) node (mr) [well,rotate=90] {mtx}
    ++(5.5,-1.5) node [ann] (lr) {$5 \times 10^4$ cells incubation};
    \draw
    [arr] (lr) -| (fr);
    \draw
    [arr] (lr) -| (mr);
  \end{tikzpicture}

  \caption{Arrangement, to scale, of wells cut using half-length razor into agarose in p100 dish.
  Cell incubation count is in decreasing order counter-clockwise starting from the top, control, position.}
  \label{fig:dish}
\end{figure}

In this final experiment, cells were incubated in both, methotrexate and folate, at concentrations of 1~mM.
Motility in the presence of mtx appeared random in the rose plots of Fig.~\ref{fig:rosexhist}.
The randomness measurement is approximated by the skewness of the track coordinates.
As a positive control, folate shows varying levels of chemotaxis for the same 1~mM incubation conditions.
Per the assay in report 2, a skewness close to zero is consistent with random motion.

\begin{figure}[hp]
  \centering
  \includegraphics[height=0.43\textheight,clip,trim = 4mm 2mm 20mm 0mm]{fig/indep_fol_rose_plots_with_x_histogram.eps}
  \includegraphics[height=0.43\textheight,clip,trim = 4mm 2mm 20mm 0mm]{fig/indep_mtx_rose_plots_with_x_histogram.eps}
  \caption{
    Supernatant chemotaxis after 2 hour incubation in cells of folate (top panel) and methotrexate (bottom panel).
    The first row of each panel shows the tracks as they appeared in in the original images, and their initial points re zeroed to form the rose plots.
    Only 150 of longest tracks are drawn in these plots to minimize clutter; however, the x-histograms, accurately, contain all the x-coordinates.
    The dashed line in each rose plot is the zero X-axis intercept.
    Incubation was done with cells at concentrations incremented by an order of magnitude: high represents $2 \times 10^6$ cells, medium: $5 \times 10^5$ cells, low: $5 \times 10^4$ cells, and control: no cells.
}
  \label{fig:rosexhist}
\end{figure}

This 2 hour degradation assay in Fig.~\ref{fig:rosexhist} shows that even highly degraded folate is as chemotactically as methotrexate.
Methotrexate chemotaxes similarly at the 3 different incubation cell concentrations and is consistent with the known biochemistry that it is not broken down by \dicty.
There was a problem acquiring good images with the folate control due to XY stage drift, and the small track lengths and x-histogram, in fact, indicates random motility even in full folate concentration.

This experiment shows cell motility in methotrexate is consistent with random motion.
This result, together with the folate supernatants, supports the hypothesis of the folate deaminase breakdown contributing to improved chemotactic movement.
It would be of great interest to either genetically engineer \dicty without folate deaminase, or knock down the folate deaminase capability, and compare motility against the wild type to further give weight to the local gradient hypothesis.

Challenges found from this experiment were:

\begin{enumerate}
\item Unlike the low -0.3 skewness random measurement in  Fig.~\ref{r2-fig:xhist} of the previous report 2, the expected  random movement of folate attracted cells in this report ranged at  higher levels of skewness as high as 1.5, in Fig.~\ref{fig:rosexhist} of  this report from the effect of the cells diffusing into the field of view.
  This ``entry diffusion effect'' appears as false  directionality.
  The report 2 random measurement was done using  cells plated under agarose with no chemoattractant, which did not  have to overcome the agarose barrier in leaving their cells.
\item An  additional measurement problem is the chemokine break down, as  described in the Introduction.
  The breakdown makes cells following the initial wave have a lower magnitude chemotactic motility which affects the overall measurement.
  One possibility of correcting for both the entry diffusion effect,  and the initial wave chemokine breakdown effect, would be to isolate  the initial wave of cells and only apply motility measurements to  them.
  This would then allow normalizing chemotactic motion to the  initial wave of a negative control of cells weakly chemotaxing into  the field of view, say, using the 0.01~mM folate minimum value  calibrated.
  The degree of numerical analysis to mathematically  isolate the initial wave from subsequent random motion is beyond the  scope of this report.
\item The experiment design may also instead incorporate FRET measurement of folate in the agarose media to  differentiate between chemotactic and non-chemotactic motion by the  consumption of folate itself.
  The FRET sensor project is a future  direction of chemotactic motility analysis in the Knecht laboratory.
\item As with flow cytometry, creating large quantities of data from cell tracks also requires careful thought to gating the useful data from erroneous measurements.
  While the cell tracking algorithm itself works well for thresholding cells, one could only consider cells that have a minimum track length to consider higher quality, contiguous tracks.
\item One might consider widefield imaging of strongly fluorescently labelled cells to track the cells instead of transmitted light, to:
  \begin{enumerate}
  \item Eliminate the complications in segmenting the cells from the condensation and agarose artifacts.
  \item Reduce the shutter jitter seen in transmitted light images, which also contributed to broken cell tracks in the analysis.
  \end{enumerate}
  As the tracking was done with $4 \times 4$ binning of a 6.5\um pixel CCD and a 4x objective, one would get similar spatial resolution with a 16\um pixel EMCCD with $2 \times 2$ binning and the same 4x objective.
\item The standard growth plate fit into the standard multi-well XY stage insert better than the different p100 dish used for this experiment.
  The plastic bottom of the dish warped from pushing it into the insert which may have caused the focus shift seen during the the first 3 hours of the experiment.
  The difference in size may be due to a standardization difference in measuring the lid as 100~mm vs the bottom in the latter case.
\end{enumerate}

\section{Materials and Methods}
\label{sec:matmeth}

The motility imaging experiment was conducted using a standard p100 growth plate as shown in Fig.~\ref{fig:dish} and described in Protocol~\ref{sec:proto:null}.

Microscopy videos were captured using the Micro-Manager software \citep{ausubel_computer_2010,JBM36} version 1.4.20 controlling an Andor Clara CCD detector on a motorized Nikon Ti inverted microscope, and ASI MS-2000 linear encoded motorized XY stage.
A 4x phase objective was used to capture transmitted light phase images.
The halogen transmitted light source stabilized by operating it at high volage using neutral density and green interference filter.
The Micro-Manager configuration file is included in report 1, Supplement \ref{r1-sec:cfg}.
Additionally, a beanshell script was used to align the rotation axis of each XY position, included in Supplement~\ref{sec:rotation}.

Cell tracking was done in FIJI using the TrackMate plugin \citep{schindelin_fiji:_2012}, and XY stage drift was corrected using the Descriptor based registration plugin \citep{preibisch_software_2010}.
Numerical analysis of the TrackMate data was done using Python scripts run inside an IPython shell \citep{PER-GRA:2007} on Gentoo GNU/Linux \citep{stallman_gnu_2014}.
Graphs were created using Matplotlib \citep{Hunter:2007}.
All source files are released into the public domain on GitHub (\url{https://github.uconn.edu/pan14001/cell-bio-lab-2015}).

\bibliography{bib}

\section{Protocols}
\label{sec:proto}

\subsection{Multi-well timelapse of motility under agar}
\label{sec:proto:null}
\begin{enumerate}
\item Create 2 under agarose plates (Fisher $100 \times 20$~mm), and one practise plate (Fisher $60\times15$~mm) by pipetting 22~ml and 8~ml, respectively, of 1.5\% agar solution and waiting about 45~minutes for it to solidify.
\item Prepare 175\ul of cells at $500 \times 10^{4}$ cells/ml for each of 3 troughs, or $350 \times 10^{4}$ cells.
  Centrifuge the cells into from HL5 to SM media per Protocol~\ref{sec:proto:centrifuge}.
\item Fill plates.
  Create a trough on either side of the cell trough: a control with SM, and the other trough with either folate or methotrexate (mtx). % MTX is 50 mM, 1 ml. Folate is 1 mM, 1 ml.
  \begin{enumerate}
  \item Fill middle trough with 175\ul of cells in SM.
  \item Fill top trough with 175\ul of SM as control.
  \item Fill bottom trough with the chemotactic chemical.
    Use varying concentrations of folate in half of the wells and methotrexate chemoattractant in the other half of the wells.
  \end{enumerate}
\item Begin timelapse, multi-XY video microscopy using 4x objective.
  Acquire transmitted light phase images.
\end{enumerate}

\subsection{Incubation of cells in chemotactic media}
\label{sec:proto:xyprep}
\begin{enumerate}
\item Incubate 300\ul of different cell concentrations in fixed concentrations of fol or mtx in an 8 well dish (Lab-Tek).
% We could use higher concentrations of cells and a higher volume of media using 50~ml Falcon tubes.
% However we are limited by our already low concentrations of chemicals.
\item Use 0.01~\uM fol, or 0.5~\uM mtx in SM media for all wells.
\item Control well will have the chemical without any cells.
\item Add cells to reach concentrations per Table~\ref{tab:cellconc}.
  \begin{table}[h]
    \centering
    \caption{Number of cells in incubation wells.
      Each set of 4 wells will contain folate and methotrexate, respectively.}
    \begin{tabular}{r|c|c|c|c} \hline
      Well & 1 & 2 & 3 & 4 \\
      Cells $\times 10^{4}$ & 5 & 50 & 200 & 0 \\\hline
    \end{tabular}
    \label{tab:cellconc}
  \end{table}
\item To prevent drying out during incubation, place the 8 well dish (Lab-Tek) inside a growth plate (Fisher $100 \times 20$~mm) having 15~ml of water.
\item Incubate for 24 hours on bench top in a dark environment (light breaks down folate).
\item Spin down cells in Eppendorf tubes at 7,000~rpm for 15~seconds.
\item Add 175\ul of supernatant to wells of the agarose plate per Protocol~\ref{sec:proto:null}.
\end{enumerate}

\subsection{Calibration curve of chemotactic motility at various concentrations}
\label{sec:proto:conc}
\begin{enumerate}
\item Create 6 under agarose plates (Fisher $60\times15$~mm) per Protocol~\ref{sec:proto:agar}.
  Use cutting device for center trough and 3 outer troughs. % Make drawing in tikz?
\item Prepare 75\ul of cells at $500 \times 10^{4}$ cells/ml for each of the 8 troughs, or about $300 \times 10^{4}$ cells. %Titer was 800 e4 cells/ml and 8ml solution = 6400 e4 cells50~ml Falcon tubes.
  Centrifuge the cells into from HL5 to SM media per Protocol~\ref{sec:proto:centrifuge}.
\item Fill plates.
  As described in Protocol~\ref{sec:proto:agar}, create 5 agar plates; 1 control with SM, 2 with folate, and 2 with methotrexate (mtx). % MTX is 50 mM, 1 ml. Folate is 1 mM, 1 ml.
  \begin{enumerate}
  \item Fill middle trough with 100\ul of cells in SM.
  \item Add a set of 2 chemotactic concentrations to each plate per Table~\ref{tab:conc}.
    It's easiest to create using successive dilutions.
    Each chemoattractant will require 3 plates.
    The 7th plate will be the control.
    An additional 8th plate of double size with 1~\uM folate was tested to find the cross-talk distance.
    \begin{table}[h]
      \centering
      \caption{Concentrations of chemotactic chemicals added to plate troughs.}
      \begin{tabular}{r|c|c|c|c|c|c} \hline
        Trough & 1 & 2 & 3 & 4 & 5 & 6 \\
        Conc. (\uM) & 100 & 10 & 1 & 0.1 & 0.001 & 0.0001 \\\hline
      \end{tabular}
      \label{tab:conc}
    \end{table}
  \item Wear gloves and googles when handling mtx.
  \item Dispose all mtx contacted materials into spearate toxic container. % Cite Nandini-Kishore 1981 for MTX conc.
  \end{enumerate}
\item After 6~hours, image each dish with transmitted light.
\end{enumerate}

\subsection{Centrifuge HL5 cells to SM media}
\label{sec:proto:centrifuge}
\begin{enumerate}
\item Put cells in 15 ml tube.
\item Centrifuge cells for 5~min at 1000~rpm at 4~\degree C, and discard HL5 media.
\item Resuspend in Sorenson's buffer (Sor), recentrifuge, and discard Sor.
\item Resuspend in SM media.
\end{enumerate}

\subsection{Agarose plate layer preparation}
\label{sec:proto:agar}
\begin{enumerate}
\item Create 1.5\% or 1~g/66~ml agar in 66~ml SM media.
\item Melt agarose in SM in 125~ml flask in the microwave in 6 second bursts with the flask cap loose.
\item We are looking for a 3~mm height of agarose in the plate.
  Using the cylinder volume equation we obtain the required volumes in Table~\ref{tab:vol}.
  \begin{table}[h]
    \centering
    \caption{Calculated volumes for plates (diameter $\times$ height) to reach 3~mm agarose height.}
    \begin{tabular}{r|r} \hline
      Plate (mm $\times$ mm) & Agar (ml) \\
      $60 \times 15$ & 8.5 \\
      $100 \times 20$ & 23.5 \\\hline
    \end{tabular}
    \label{tab:vol}
  \end{table}
\item Allow 45~minutes to solidify.
\item After cutting out wells, rotate agar around for 1 circle.
  Otherwise agar adhesion can prevent cells from moving out at all.
\item Use one agarose plate for practise.
\end{enumerate}

\subsection{Typical  ImageJ processing to isolate cells for tracking}
\label{sec:proto:improcess}
\begin{enumerate}
\item \emph{Invert} to make dark cells bright.
\item Create background image using \emph{Z project...} with ``Median'' processing.
\item Subtract background using ``Difference'' (not ``Subtract'', as it clips) with \emph{Image Calculator}.
  \emph{Threshold...} using ``Yen'' algorithm and ``Stack Histogram''.
\item \emph{TrackMate} with 0.1 ``Threshold''.
\item \emph{Save} TrackMate XML file from the plugin.
\item Run Python script on the XML files to create graphs.
\end{enumerate}
\section{Source Code}
\label{sec:src}

\subsection{Camera rotation per XY field in Micro-Manager}
\label{sec:rotation}
\inputminted[linenos]{java}{data/chemotaxisRotation.bsh}

\end{document}