User:Yeem/BE.180 notes/3-16: Difference between revisions
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:<math>k_{on} = 10E9</math> molecules per second | :<math>k_{on} = 10E9</math> molecules per second | ||
:<math>k_{off} = 1 </math> sec<sup>1</sup> | :<math>k_{off} = 1 </math> sec<sup>-1</sup> | ||
How dense is our DNA? | How dense is our DNA? | ||
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:<math>\frac{d(AB)}{dt} = k_{on}^{AB}-k_{off}^{AB}</math> | :<math>\frac{d(AB)}{dt} = k_{on}^{AB}-k_{off}^{AB}</math> | ||
:<math> = 10^9 \times 10^{-9} \times pol - 0</math> | :<math> = 10^9 \times 10^{-9} \times pol - 0</math> | ||
:<math> = \frac{1}{sec}</math> ( | :<math> = \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>\frac{dP}{dt} = F_{pops} - k_d\left(P\right)</math> | |||
If we choose t<sub>1/2</sub>=10', k<sub>d</sub>=0.07/min<br> | |||
If we choose this to be at steady state,<br> | |||
:<math>\frac{dP}{dt} = 0 = F_{pops} - k_d\left(P\right)</math> | |||
:<math>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<br> | |||
Time constant (<math>\Delta T</math>) is therefore about 10 or 15<br> | |||
Total latency is about 20 minutes (back o' envelope calc) | |||
What about F<sub>pops</sub>? | |||
*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 |
Revision as of 11:00, 16 March 2006
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 t1/2=10', kd=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 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