E3: Diffusion and tracking

Week 7. Due Wed 24 Feb 23:59, reviewed Thu 25 Feb

About 2 hours. This exercise feeds directly into milestone M2 of P1.

1. Nelson

Nelson: Your Turn 4b, 4c, 4d and 4e.

2. Diffusion times in the cell

Estimate the time \(t\sim L^2/(2D)\) it takes to diffuse a distance \(L\) for:

  1. a protein (\(D\approx 10\) µm²/s) across a bacterium (1 µm) and across a eukaryotic cell (20 µm);
  2. a neurotransmitter (\(D\approx 300\) µm²/s) across a synaptic cleft (20 nm);
  3. the same protein along a 1 m long nerve axon.

What do the numbers tell you about where cells can rely on diffusion and where they need active transport?

3. Test a tracking pipeline on synthetic data

Run synthetic_brownian.py. It makes a movie of beads with known \(D\), tracks them with trackpy and prints the true and fitted \(D\).

  1. Run it with --D 0.5. How close is the fitted value?
  2. In track_and_fit, set search_range=5 and run again. What happens to \(D\), and why? Estimate the per-axis step in pixels per frame and compare it with the search range.
  3. Set minmass=None. What happens now, and why?
  4. In one sentence: why must you test your own pipeline on synthetic data before you trust it on the lab data?