Edge Detector Paper

The genetic edge detector paper just came out in Cell! Congratulations to Jeff and everyone else who worked on this paper. This is a project that we hatched about 3 or 4 years ago and it is finally out after a lot of hard work by everyone involved except me :-).

The project engineered bacteria to act as a communal signal processor implementing an "edge detector". You can think of the engineered bacteria as being like very simple computers, each running the following program: "Am I in the light? If so, shout to my neighbors. Otherwise, if I'm in the dark and I hear my neighbors shouting then raise my hand." Those that are in the dark and hear a neighbor must be near an edge. The "shout" is implemented by having the cells produce a small molecule which diffuses to their neighbors to be "heard" (actually, "smelled" is a better description). The "raise my hand" is implemented by having the cells produce a dark sugar which is visible to the naked eye when you look at the plate.

Interestingly, natural cells implement this edge-detection algorithm: the retina -- the first stages of image processing in the eye is to extract edges by a similar algorithm. The Nobel prize was awarded in 1967 to Hartline for this discovery in the retinas of the horseshoe crab.

Fountain spouts

Today I sculpted the spouts for the fountain on my back porch. The white boards under each are scaffolds supporting them until the dry at which time I will remove, glaze, and fire them. The firing should cause them to shrink so then I will be able to mortar them back into position.

Bed stain

Stained the bed today (not what you're thinking!). Almost done with this project! It's taken way too long.

Bed

I haven't been posting house progress for a while. My night-time project for the last week has been construction of a bed with a little bit of a floating cloud theme. I laminated four 4x8 sheets of maple plywood together and then cut out circles of various radii.


After Alex's sanding for many hours...


Here's the rough-cut end table before I cut out the circles...

Molecular model transfer function

Today I got around to trying out a simplified molecular version of the gate model that will replace my hyperbolic function.



The kinetics are all arbitrary for the model, but the shape of the transfer function looks even better than the made-up model from before. There's an almost perfectly linear section in the middle -- it looks more made-up than my made-up model! This is assuming that all three reactions have the same strength. Next, I need reasonable terms for the three reaction rates.

More parameter space of "standing" circuit

Using the parameter space maps made last time, I've set the "standing" circuit into a place where it has a nearly symmetric bi-stable steady-state at p1 =0.25 and p2=0.50.



The following is the derivative at a given concentration of standing. This dy/dt vs y plot (I don't know if there is a correct name for this find of plot) shows that there are two stable steady states at the zero crossings -5, and +5. There's also the unstable point near zero. It is not exactly at zero because the gate model functions do not cross at zero as seen below.






Now I continue the analysis with the "tired" half of the circuit. I'm interested in the response of "tired" when the "standing" input reaches 0, the point at which the tired circuit will charge fully.



Charging of the tired circuit when standing is 0 and tired starts at its steady-state value of -5


So, "tired" reaches 0 (the point at which the gate 5 is going to be fully on) within about 20 time units when standing = 0.

The following is a sampling of the parameter space for p1 and p2 given "standing" = 0. The steady-state value of tired changes as a function of p1, so for each graph I've started "tired" off at the appropriate steady-state and then watch the evolution when "standing" = 0. This demonstrates that I can delay both the onset of tired (when it hits zero) and how high tired gets at steady-state by adjusting these two parameters.


Next up, I put the circuit back together again...

Parameter space of "standing" circuit

I've been working on decomposing the traveling pulse circuit in order to understanding the parameter space. Today I've worked on the isolated "standing" circuit.



There's two parts. The "pull down" gate that is constantly trying to pull the system to a negative value against the action of the resistor which is trying to pull it to zero. The ratio of the pull down gate (1) to the resistor (RNAase) determines the steady-state level when the feedback gate 3 is not active. The RNAase resistor must be common to all nodes so I treat it as a fixed parameter; I picked the value 0.01 out of thin air for it.

For the following graphs, I pick different starting conditions for "standing" and let this circuit evolve. Each colored trace in the chart is one run of the circuit. Note that there are two steady states. One is about 28 and the other is about -1. If the "standing" value falls below about -0.5 then it goes to the low steady-state and above that it goes high. I like this chart in comparison to typical transform function plots because it lets you see both the kinetics and the steady-states in one place.


Here's the same chart but zoomed in around the origin so you can see that the critical point is about -0.5 which is determined by the gate model.

I varied the two parameters over a range and plotted the parameter space result (best viewed on large monitor).


From top to bottom p1 is increasing. From left to right p2 is increasing. Increasing p2 shifts the steady-state of the "standing" state upwards and thereby separates the two states more dramatically. As p1 is increased -- moving from top to bottom -- both the top and bottom steady-states shift downwards but the bottom one seems to move faster. In the lower left, the two states blur into each other and are poorly defined. So, in general you'd like to push p2 and p1 fairly high but this comes at the cost of slowing down the approach to steady-state as they are pushed further away. When the other half of the circuit is added, p2 value will have to be smaller than p5, so that will determine the upper bound of p2.