Homework 10.3: Cell fate determination and hydrodynamic instabilities in the C. elegans gonad? (100 pts)

Data set download

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You can do either this problem, Homework 10.1, or Homework 10.2 for Homework 10. Do not do more than one.

# Colab setup ------------------
import os, sys
if "google.colab" in sys.modules:
    data_path = "https://s3.amazonaws.com/bebi103.caltech.edu/data/"
else:
    data_path = "../data/"
# ------------------------------

import pandas as pd

import bokeh.io
import bokeh.plotting
bokeh.io.output_notebook()

Loading BokehJS ...

The C. elegans gonad, pictured below in an image taken from Chartier, et al., bioRxiv, 2020, is lined with cells that will potentially become oocytes.

As you proceed along the gonad, the cells slowly grow large. Then, some of the cells shrink and undergo apoptosis, while other grow and become large oocytes. Chartier and coworkers did a very interesting study on the hydrodynamic instabilities that give rise to this phenomenon. I encourage you to read the paper.

In one of their studies, they carefully measured the volume of cells as a function of fractional position along the gonad. The result is shown below.

df = pd.read_csv(os.path.join(data_path, "chartier_cell_volume.csv"), comment="#")

p = bokeh.plotting.figure(
    x_axis_label="fractional position along gonad",
    y_axis_label="cell volume (fL)",
    frame_width=450,
    frame_height=250,
)
p.circle(source=df, x="fractional position", y="volume (fL)", alpha=0.2, size=2)

bokeh.io.show(p)

It is clear that at some point along the gonad, the cell populations diverge, with once set of cells heading toward a fate of apoptosis, with a few lucky ones proceeding to an oocyte fate. As part of their theory, Chartier and coworkers worked out that a hydrodynamic instability leads to this decision. To help interpret experimental results in the context of the theory, it is useful to determine when the cells start to split into two populations; those that grow and those that do not. Your task in this problem is to use whatever inference techniques you think appropriate to decide at what position along the gonad that split starts to occur. You should provide sounds arguments as to why you chose the technique(s) you did.