User:Yeem/BE.180 notes/3-16

AND gate diagram

Repressors

So far, we've been talking about repressors.

• Can't replace a computer with it, as it isn't quite fast enough.
• Defined NOT, AND, FOR, etc., devices
• Can use sender/receiver devices, not just boolean logic
• Start to think about sensors/actuators, etc.

Characteristics

What do we want to know about the physics/biology of our inverters?

• Toxicity
• Speed
• Signal levels
• Transfer function
• Load placed on cell

Do we care about the relation between the input and the output?

• We care about the range of the input signal
• How the output changes (transfer function)

How are we going to come up with answers?

Let's look at an inverter. Say the repressor controls something called [math]\displaystyle{ \lambda }[/math] cI.

• Model depends on physics of system
• Also going to encounter the science/biology of system
  • [math]\displaystyle{ \lambda }[/math] is a phage that does such & such...
  • [math]\displaystyle{ \lambda }[/math] repressor doesn't turn off in all instances, blah blah

Connection to BE.320

[math]\displaystyle{ A + B = AB \ }[/math]

[math]\displaystyle{ \frac{d(AB)}{dt} = k_{on}^{AB}-k_{off}^{AB} }[/math]

How quickly will our sample device work?

• Whereas the input signal is a discrete square wave, the output wave lags behind (latency) with a slightly rounded curve. [math]\displaystyle{ \Delta T }[/math] is the latency between the time between otherwise max & min.

[math]\displaystyle{ k_{on} = 10E9 }[/math] molecules per second

[math]\displaystyle{ k_{off} = 1 }[/math] sec¹

How dense is our DNA?

• Genome is often present in one copy
• E.coli:

[math]\displaystyle{ \frac{1 molecule of DNA}{cell} }[/math]

• • Volume of one e. coli is about 10^-15 L

[math]\displaystyle{ \frac{1 molecule}{10^{-15} L} = \frac{10^{15}}{1 L} \times \frac{1 mole}{10^24} = 10^{-9} moles = 1 nM }[/math]

Back to 320

[math]\displaystyle{ \frac{d(AB)}{dt} = k_{on}^{AB}-k_{off}^{AB} }[/math]

[math]\displaystyle{ = 10^9 \times 10^{-9} \times pol - 0 }[/math]

[math]\displaystyle{ = \frac{1}{sec} }[/math] (something)