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Lecture 17

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Western University

Biology

Biology 2581B

Susanne Kohalmi

Winter

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Genetics Lecture 17 Notes
Is it possible to examine at the transcription of genes in a quantitative manner?
(Can we put numbers on the amount of transcription?)
If so, what could this tell us about transcriptional regulatory networks?
Goal: mathematical model of 2 simple genetic regulatory networks
Y = the target gene
X = the transcriptional activator
“Quantifying” Gene Regulation:
Imagine the box (Y) – within the box represents the level of mRNA present within
a cell
There are 2 things that are going to affect the level of Y in the cell – the rate of
production and the rate of degradation
There is a source and a sink – the source is just transcription, while the sink has
to do with degradation
Any message has a certain half-life in the cell – nothing lasts forever
The double triangle thing represents the regulation of b and a, which control how
much Y you have
Why are the units for the rate of degradation different from the units of
production? o If the rate of degradation is 0.1/minute, it means that 10% of Y is being
degraded per minute at that instant in time
o If a = 0.1 nmoles/time, it means that 10% of Y is degraded every minute
o If you catch the system at this instant in time, at that instant, you have
1000 nmoles in the cell – that means that the degradation rate is going to
be 100 nmoles/minute
o If you catch the system at the instant when you have 100 nmoles in the
cell – means that the degradation rate is going to be 10 nmoles/minute
o 10nmoles/minute for every 100 nmoles that are present in the cell
cancel out nmoles and it just comes out to 0.1/unit time
The rate of change of Y is determined by the production rate minus the
degradation rate
Dy/dt = b-ay
o Dy/dt = 0 at steady state
Y steady state/a = production rate/degradation rate
To quantify amount of message, you only need to know the production rate and
the degradation rate
The transcription of a gene can be simulated with the help of specialized
computer programs…
It is possible to “create” a gene that transcribes with a given production and
degradation rate within a computer program
In this way, the computer can handle the calculations and you can focus on the
results
The levels of Y mRNA will reach a steady state level within a cell based solely on
production and degradation rates:
Tell the computer what the production rate (b) and degradation rate (a) is and
what the level of Y is at the start of the system
For the second one, decrease production rate by ½, while the degradation rate is
the same
Given enough time, each gene hits a steady state
Gene F hits a higher steady state that gene G, which has a higher steady state
than gene H
The initial levels of Y mRNA will not affect the final steady state levels of the
message:
No matter where you start, given enough time, the system is ALWAYS going to
go to steady state Describing Activation Mathematically:
Now you want to look at the actual activation part so add in the activator to our
model of transcription
Have gene Y with the polymerase binding site add in X binding site
Some signal Sx will convert S to the activator form S* now we get even more
transcription than before
X* = CRP bound to cAMP
X = CRP
Sx = cAMP
The rate of production (promoter activity) is a function of x* because the more X*
we have, the more transcription we have (Y promoterctivity is proportional to X*)
Describing Activation Mathematically – Hill Function for an Activator:
This function does a pretty good job of describing transcription

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