QUANTITATIVE LAWS June 13 -June 24

1. Characteristic features:
large variability in gene expression
large variability in cell size
What is the effect of physiological variation on gene expression?
(So et al. Nat Genet 43:554-560)
Stochastic gene expression
in growing cell populations
Philipp Thomas

2. Common ways of quantification
proteinmRNA
km dilution
ks
k0
• Gillespie Algorithm:
reaction kinetics at constant cell size
• often not sufficient to describe the variability
observed within a population (extrinsic noise)
cell size
protein fluorescence (gene expression variability)

3. Gene expression
in growing and dividing cells
single cell
growth & gene expression
division
& partitioning of
molecules
low fluorescence high fluorescence
smaller cell larger cell
s(t)=s0eαt
Gillespie trajectory

4. single cell
growth & gene expression
division
& partitioning of
molecules
low fluorescence high fluorescence
model predicts cell size & gene expression
When is it equivalent
to constant population
at constant cell size?
sizevariability
gene expression
noise
cell size distribution
1.0 1.5 2.0 2.5
0.2
0.4
0.6
0.8
1.0
1.2
1.4
theory
simulation
size
protein count after cell sorting
cell size
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••••••••••••••••••••••••••••••••••••••••••••
•
1.0 1.5 2.0 2.5
50
100
150
200
on average
PopulationLevel

5. Mass action kinetics: the effective dilution model is exact
for networks containing only reactions of the form:
But not for translation!
When does population structure matter?
Fano[M|s]
•
•
•••••••••••••••••••••••••••••••••••••
•
•
•
1.0 1.5 2.0
cell size
0.6
0.8
1.0
1.2
1.4
•
••••••••••••••••••••••••••••••••••••••••••••
•
1.0 1.5 2.0 2.5
cell size
50
100
150
200
E[P|s]
CME only holds
on average here!
•
•••••••••••••••••••••••••••••••••••••
•••
•
•
•
•
1.0 1.5 2.0 2.5
0.01
0.02
0.03
0.04
0.05
0.06
simulation
CV2
[P|s]
effective
dilution model
conditional
mRNA distribution
is Poissonian
the effective
dilution model
holds on average
cell size
mRNApre-mRNA
proteinmRNA
+

6. • • • • • • • • • • • • • •
•
•
•
•
•
• • • • • • • • • • • • • •
0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
birth size
0.02
0.04
0.06
0.08
0.10
0.12
0.14
CV2
[P|s0]
•••
•••••••••••••••••••••••••••••••••••••
••
•••
•
•••••••••••••••••••••••••••••••••
•••
•••
•
•
1.0 1.5 2.0 2.5
cell size
0.035
0.040
0.045
0.050
0.055
0.060
CV2
[P|s]
Protein fluctuations depend on cell history
that can be quantified by size at birth.
theory vs simulation:
adder and sizer models