User:Yeem/BE.180/pset5

This model assumes an even spaced lawn of bacteria that do not replicate, die off, or move. Four chemical gradients ("A" through "D") are established as shown in "external inputs".

• To achieve the general pill shape of the design, cells are "activated" by chemical B and "repressed" by chemical "A". "B" diffuses radially outward from the center of the field, while two parallel lines of "A" run horizontally near the top and bottom. In the presence of "B", cells generate [math]\displaystyle{ \beta }[/math] protein, which forms a heterodimer with [math]\displaystyle{ \sigma }[/math] protein. [math]\displaystyle{ \sigma }[/math] is constantly produced by cells.
• For the alternating color scheme, cells sense the concentration of vertically dispersed chemical "D" as indicated in "processes". According to the relative amount of chemical "D" in the cell, the [math]\displaystyle{ \beta\sigma }[/math] complex signals the production of red, blue, or green pigment.
• For the "hollowed out" rectangle within the design, high amounts of chemicals "C" and "D" signal the production of the [math]\displaystyle{ \Delta }[/math] and [math]\displaystyle{ \gamma }[/math] proteins, which form a heterodimer that inactivates the [math]\displaystyle{ \beta\sigma }[/math] complex and prevents it from producing color. Chemicals "C" and "D" are placed as orthogonal lines, thus producing a squared-off rectangle shape.

External inputs

Chemical "A" gradient.	Chemical "B" gradient.	Yellow: cells "activated" by B, "repressed" by A.
Chemical "C" gradient.	Chemical "D" gradient.	Spectrum of colors dictated by D gradient.

Processes

Activation by B produces [math]\displaystyle{ \beta\sigma }[/math] heterodimer.	Repression by [math]\displaystyle{ \alpha }[/math] protein or [math]\displaystyle{ \Delta\gamma }[/math] heterodimer.
Set_color activated by [math]\displaystyle{ \beta\sigma }[/math] heterodimer produces blue pigment.

Chemical	Protein generated
A	[math]\displaystyle{ \alpha }[/math]
B	[math]\displaystyle{ \beta }[/math]
C	[math]\displaystyle{ \gamma }[/math]
D	[math]\displaystyle{ \Delta }[/math]

Concentration of D	Color generated
+++++	red
++++	blue
+++	red
++	blue
+	red
-	green

Delta-gamma inhibition

Output

Sample output from Matlab.