Genetics Lecture No. 16: Quantitating Gene Regulation
th
Monday March 11 , 2013
Introduction:
-So far, we have examined gene regulation in a strictly qualitative manner (e.g. the
transcriptional levels of the lac operon were either high or low; the presence of glucose in the
growth media decreased transcription of the lac operon). Is it possible to examine the
transcription of genes in a quantitative manner? If so what could this tell us about transcriptional
regulatory networks?
Quantitating Gene Regulation:
-The goal of quantitating gene regulation is to create working
mathematical models of two very simple genetic networks. Here
is a model we can use for a given gene Y:
Activation: Repression:
X -> (+) Y
X -> (-) Y
X = activator X =
repressor Y = target gene
Y = target gene
-Using this model, we can quantify the rate of mRNA production and degradation for gene Y
using a “source and sink” model:
Source Sink
The Y mRNA is being accumulated in
box Y in nmoles: dY/dt = b - aY
1) When production rate >
degradation rate, accumulation of Y mRNA in the box. 2) When production
rate < degradation rate, loss of Y mRNA in the box. 3) When
production rate = degradation rate, levels of Y mRNA stay the same.
The level of Y mRNA is dependent on two things:
1) How much Y mRNA is produced through transcription of the source (rate of production)
2) How much Y mRNA is degraded through degradation by nucleases
(rate of degradation) Spigots (a and b) control the flow of Y mRNA into the box:
1) When spigot b is open, there is a high production rate of
Y mRNA (in nmoles/min) 2) When spigot a is open, there is a high
degradation rate of Y mRNA (1/min) Degradation rate depends on the amount of Y
mRNA that is present: • If a = 0.1/min, 10% of Y mRNA is
degraded every minute • If at an instant in
time, there are 1000 nmoles, the rate of degradation is 100 nmol/min • If at another instant in time, there are 100 nmoles, the rate of degradation is 10 nmol/min
• a = 10 nmoles / min x 100 nmole = 0.1/min
Simulating Gene Transcription:
-The transcription of a gene can be simulated with the help of specialized computer programs.
For example, it is possible to “create” a gene that is transcribed 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 (in order to quantitate the
amount of Y mRNA, you need to know
production
Steady State Level: Gene F: b = 10 nmoles/min; a = 0.1/min; Yinit
and
degradation -A concentration of
Y mRNA reached over time
rates): where the rate of change is
zero; calculated by dividing
dY/dt = b – a Y
the production rate by the
degradation rate of the gene.
0 = b – a Y st Gene G: b = 5 nmoles/min; a = 0.1/min; Y init
[Y mRNA] (nmol)
-b = -a Y st Gene H: b = 5 nmoles/min; a = 0.2/min; Y = 0 init
Y stb / a
Time (min)
The initial levels of Y mRNA
will not affect the final steady
state levels of the message Gene F: b = 10 nmoles/min; a = 0.1/min

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