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 $$\lambda$$ cI.
 * Model depends on physics of system
 * Also going to encounter the science/biology of system
 * $$\lambda$$ is a phage that does such & such...
 * $$\lambda$$ 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. $$\Delta T$$ is the latency between the time between otherwise max & min.


 * $$k_{on} = 10E9$$ molecules per second
 * $$k_{off} = 1 $$ 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 ($$\Delta T$$) 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