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] sec^-1

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} \times pol }[/math]

Estimating how quickly the output signal responds...

• Entering cell and completing transcription takes about 20 seconds
• RNA pol ~50 bp/sec

Diff eq for what the protein is doing over time

[math]\displaystyle{ \frac{dP}{dt} = F_{pops} - k_d\left(P\right) }[/math]

If we choose t_1/2=10', k_d=0.07/min
If we choose this to be at steady state,

[math]\displaystyle{ \frac{dP}{dt} = 0 = F_{pops} - k_d\left(P\right) }[/math]

[math]\displaystyle{ P_{ss} = \frac{F_{pops}}{k_d} = \frac{70 per min}{0.07} = 1000 P }[/math]

Doing analysis, it will take about 10 to 15 minutes to get to 1000P
Time constant ([math]\displaystyle{ \Delta T }[/math]) is therefore about 10 or 15
Total latency is about 20 minutes (back o' envelope calc)

What about F_pops?

• No time to go over in class
• Term is defined by interaction of repressor or activator with other proteins at the site
• Endy will make it available in written form

Summary

Genetic devices

• more than one type
• don't have to be logic functions
• slow
• could make a large number
• could think of them as physical systems