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

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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 λ cI.

• Model depends on physics of system
• Also going to encounter the science/biology of system
• λ is a phage that does such & such...
• λ repressor doesn't turn off in all instances, blah blah

Connection to BE.320

$A + B = AB \$

$\frac{d(AB)}{dt} = k_{on}^{AB}-k_{off}^{AB}$

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. ΔT is the latency between the time between otherwise max & min.
kon = 10E9 molecules per second
koff = 1 sec-1

How dense is our DNA?

• Genome is often present in one copy
• E.coli:
$\frac{1 molecule of DNA}{cell}$
• Volume of one e. coli is about 10-15 L
$\frac{1 molecule}{10^{-15} L} = \frac{10^{15}}{1 L} \times \frac{1 mole}{10^24} = 10^{-9} moles = 1 nM$

Back to 320

$\frac{d(AB)}{dt} = k_{on}^{AB}-k_{off}^{AB}$
$= 10^9 \times 10^{-9} \times pol - 0$
$= \frac{1}{sec} \times pol$

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

$\frac{dP}{dt} = F_{pops} - k_d\left(P\right)$

If we choose t1/2=10', kd=0.07/min
If we choose this to be at steady state,

$\frac{dP}{dt} = 0 = F_{pops} - k_d\left(P\right)$
$P_{ss} = \frac{F_{pops}}{k_d} = \frac{70 per min}{0.07} = 1000 P$

Doing analysis, it will take about 10 to 15 minutes to get to 1000P
Time constant (ΔT) is therefore about 10 or 15
Total latency is about 20 minutes (back o' envelope calc)

What about Fpops?

• 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