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

## 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

- Volume of one e. coli is about 10

- [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