# HW 5 Due 1/11

1. Simulate the repressilator in gro using chemostat mode. Show a few representative trajectories that oscillate and a few that don't. You might want figure out a way to track a single cell for the entire duration of the simulation, which would require keeping track of the cell ids in a clever way.

2. Slide 16 of lecture 13 says you can get a PCR machine for \$195-1000. (a) Find used PCR machines online in this price range and compare their features. (b) Describe five protocols that are essential to synthetic biology that require PCR (you can Google this or interview the denizens of a local synthetic biology lab).

3. The following system, in polar coordinates, is the simplest description of a stable oscillator you can find:

Convert this pair of differential equations into cartesian coordinates and simulate it from a variety of initial conditions, plotting x and y as a function of time. Compute the Jacobian (in cartesian coordinates) and find its eigenvalues. What can you conclude about the dynamics of the system about the origin?

4. Find five iGEM projects that use quorum sensing in some way. Describe each (briefly).

5. Make a gro simulation with two cells A and B each with zero growth rate placed some distance apart. Have the cells send a signal back and forth as follows. Each cell has three modes: SEND, RECV, WAIT. In mode RECV, the cell senses the signal concentration. When the concentration goes higher than some threshold, it goes into mode SEND. In mode send, it briefly produces a lot of signal and then goes into mode WAIT. In mode WAIT, it does nothing for some short period of time, and then goes into mode RECV again (this is so it does not receive its own signal). Cell A starts out in mode SEND and B starts out in mode RECV. Make each mode produce a different fluorescent color. Plot the results in a way that shows the mode of each cell and the concentration of signal at each cell versus time.

6. Extra credit: make the cells communicate in Morse code: Cell A repeatedly chooses one of several coded messages to send. Cell B fluoresces in a different color depending on what message is received.