HAL Id: tel-02438077
https://tel.archives-ouvertes.fr/tel-02438077
Submitted on 14 Jan 2020
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The genotype-phenotype relationship across different scales
Henry Kemble
To cite this version:
Henry Kemble. The genotype-phenotype relationship across different scales. Molecular biology. Uni-
versité Sorbonne Paris Cité, 2018. English. �NNT : 2018USPCC178�. �tel-02438077�
β
β
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α β
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β
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genotype genotype genotype
phenotype phenotype phenotype Development
Heredity
Generation n n + 1 n + 2
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12
13 AUGCGAUGCUAG Met-Arg-Cys
DNA RNA Protein
TACGCTACGATC ATGCGATGCTAG
Transcription Translation
Replication
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KEGG PATHWAY
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Phage display library Bind
and wash
Immobilised surface
Elute and amplify
Sequence
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FACS
Deep-sequence
…
…
Cell library Fluorescence bins
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Illumina flow cell
Illumina-sequence;
Strip and re-synthesise second-strand with unmodifieddNTPs
Flow low concentration of fluorescently-tagged DNA-binding protein;
Image
Flow higher concentration of fluorescently-tagged
DNA-binding protein;
Image
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38 Propagate Propagate
Deep- sequence
Deep-
sequence
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-6 -4 -2 0 2 4 6
0.20.40.60.81.00.0
ΔG
[Nati v el y f ol de d protei n] Mutant dens ity
Wildtype stability
[Natively folded protein] relative to wildtype
Mutant f requenc y
0.0 0.2 0.4 0.6 0.8 1.0
0.00.10.20.30.4
Δ 𝑃 𝑛𝑎𝑡 =
1 1+ 𝑒 𝛥𝐺/𝑘𝑏𝑇
Δ Δ
Δ
Δ
Δ
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50 e = 0
e < 0 e > 0
magnitude
magnitude simple
sign
reciprocal sign reciprocal
sign none
Log phenotype
P
BP
AP
A+ P
B0
A
+B
+WT A
B
AB
A
-B
-A
+B
-simple sign
e < 0 e = 0 e > 0
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Lo g ph en oty pe E pi s tas is
ΔG
-6 -4 -2 0 2 4 6
-2 -1 0 1 2
Δ
Δ
Δ
Δ Δ
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Encapsulate single cells in droplets;
Ligate barcodes with
mutated regions Deep-sequence
Selection experiment
Deep-sequence
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Γ
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Γ
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0 0,2
0,4
0,6 0,8 1Rela tiv e f itn e ss
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α
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0.00 0.25 0.50 0.75
Growth rate (doub/hr)
crp-[pBC-crp+] crp-[pBC-crp-]
0.00 0.25 0.50 0.75 1.00
0.00 0.25 0.50 0.75
- cAMP - NaCl + cAMP - NaCl - cAMP + NaCl + cAMP + NaCl
Growth rate (doub/hr) Growth rate (doub/hr)
- NaCl + NaCl
[cAMP] (mM)
A B
C
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87
0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 2 4 6 8 10 12
Occu rr e n ce s (x 1 0
4)
log
10counts at t
0log
10counts at t
0Occu rr e n ce s (x 1 0
2)
0 1 2 3 4 5 6
0 2 4 6 8 10 12
WT
0 1 2 3 4 5
0 2 4 6 8 10 12 14 Occu rr e n ce s (x 1 0
2)
log
10# barcodes/genotype WT
A B C
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β
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α
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μ
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α
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μ
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α
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𝑃(𝑐𝑜𝑢𝑛𝑡𝑠 𝑡 1 | 𝑐𝑜𝑢𝑛𝑡𝑠 𝑡 2 , 𝜆)
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𝑃(𝑐𝑜𝑢𝑛𝑡𝑠 𝑡 2 | 𝑐𝑜𝑢𝑛𝑡𝑠 𝑡 1 , 𝜆) 𝜆
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γ
λ
β
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α
β
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∆ ∆∆
𝑃𝑛𝑎𝑡 = 1+𝑒 ∆𝐺0+∆∆𝐺 1
𝑙𝑜𝑔( 𝑊0 𝑊 ) = 𝑙𝑜𝑔(1 + 𝑒 ∆𝐺 0 ) − 𝑙𝑜𝑔(1 + 𝑒 ∆𝐺 0 +∆∆𝐺 ) ∆∆
∆∆
∆∆
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∆∆
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∆∆
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150
151
∆∆
152 α
λ
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λ
154
α
155
156
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162
163 𝐾 𝑗 = ( ∑ 𝐵𝐶 𝑊𝑡 𝑖 1 𝑖𝑗 1 𝑊𝑡 0
∑ 𝐵𝐶 𝑖 𝑖𝑗 0 ) 𝐵𝐶 𝑖𝑗 1 𝑊𝑡 1
𝐵𝐶 𝑖𝑗 0
𝐾 𝑖𝑗 = ( 𝐵𝐶 𝑖𝑗 1 𝑊𝑡 1
𝑊𝑡 0
𝐵𝐶 𝑖𝑗 0 ) = 𝐾 𝑗 .
𝐵𝐶 𝑖𝑗 1 ∑ 𝐵𝐶 𝑖 𝑖𝑗 1
∑ 𝐵𝐶 𝑖 𝑖𝑗 0 𝐵𝐶 𝑖𝑗 0
164
𝐺
𝑖𝑡𝑊𝑡
𝑡= 𝐺
𝑖0𝑊𝑡
0(𝑓 𝑖 ) 𝑡 𝑙𝑜𝑔 ( 𝑊𝑡 𝐺 𝑖 𝑡 𝑡 ) = 𝑡 𝐹 𝑖 + 𝑙𝑜𝑔 ( 𝑊𝑡 𝐺 𝑖 0 0 ) 𝐹 𝑖 = log(𝑓 𝑖 ).
𝐺 𝑖 𝑡 𝑊𝑡 𝑡
𝑛𝑏𝑝 𝑖 =
𝑐𝑒𝑖𝑙𝑖𝑛𝑔 ( 5
1+ 𝑉𝑖 (𝑀𝑖) 2
)
𝐺 𝑖 𝑡 𝑊𝑡 𝑡
𝐺 𝑖 𝑡
𝑊𝑡 𝑡
165 𝑀 ≈ 𝑋/5
𝑉 ≈ 𝑋 5 2 − 𝑋 25 2 = 4𝑋 25 2 𝑛𝑏𝑝 𝑖 = 5
1+ 𝑉𝑖 (𝑀𝑖) 2
= 1
5 1+ 𝑉𝑖
(𝑀𝑖) 2
> 1 𝑛𝑏𝑝 𝑖 = 2.
𝑀 ≈ 𝑋 𝑉 = 0 𝑛𝑏𝑝 𝑖 = 5.
166 𝑀𝐼𝐶 𝑖 = 6
1+
𝑉𝑖(𝑀𝑖)2
.
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168
169
∆∆
∆ ∆
∆
∆∆
∆∆
∆∆
∆∆
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∆∆
∆∆
∆∆
∆
∆∆
𝐹 𝑖 = 𝐿𝑜𝑔 ( 1 + 𝑒 ∆𝐺 𝑅𝑇 0 1 + 𝑒 ∆𝐺 0 𝑅𝑇 +∆∆𝐺 𝑖
) = 𝑔(∆∆𝐺 𝑖 )
171 𝐹 𝑖𝑗 = 𝐿𝑜𝑔 ( 1 + 𝑒 ∆𝐺 𝑅𝑇 0
1 + 𝑒 ∆𝐺 0 +∆∆𝐺 𝑅𝑇 𝑖 +∆∆𝐺 𝑗
) = 𝑔(∆∆𝐺 𝑖 + ∆∆𝐺 𝑗 ).
𝐹 𝑖 = ℎ 𝑖 + 𝐿𝑜𝑔 ( 1 + 𝑒 ∆𝐺 𝑅𝑇 0 1 + 𝑒 ∆𝐺 0 𝑅𝑇 +∆∆𝐺 𝑖
) = ℎ 𝑖 + 𝑔(∆∆𝐺 𝑖 )
𝐹 𝑖𝑗 = ℎ 𝑖 + ℎ 𝑗 + 𝐿𝑜𝑔 ( 1 + 𝑒 ∆𝐺 𝑅𝑇 0 1 + 𝑒 ∆𝐺 0 +∆∆𝐺 𝑅𝑇 𝑖 +∆∆𝐺 𝑗
) = ℎ 𝑖 + ℎ 𝑗 + 𝑔(∆∆𝐺 𝑖 + ∆∆𝐺 𝑗 ).
∆∆
∆∆
𝐹 𝑗 𝐹 𝑖𝑗 − 𝐹 𝑗 − ℎ 𝑖 𝐹 𝑖𝑗 − 𝐹 𝑗
𝐹 𝑖 − ℎ 𝑖 𝐹 𝑖𝑗 − 𝐹 𝑗 − ℎ 𝑖
172
∆∆
𝜎 𝑖𝑗
𝐿𝑜𝑔(𝐿𝑘(𝜎 𝑚 ))~ − ∑ 𝐿𝑜𝑔(𝜎 𝑖𝑗 2 + 𝜎 𝑚 2 )
𝑖,𝑗,𝑖≠𝑗
− ∑ (𝐹 𝑖𝑗 − 𝑔(∆∆𝐺 𝑖 + ∆∆𝐺 𝑗 )) 2 𝜎 𝑖𝑗 2 + 𝜎 𝑚 2 .
𝑖,𝑗,𝑖≠𝑗
𝐿𝑜𝑔(𝐿𝑘(𝜎 𝑚𝑝, 𝜎 𝑚𝑑 ))~ − ∑ 𝑖,𝑗,𝑖≠𝑗 𝐿𝑜𝑔(𝜎 𝑖𝑗 2 + 𝜎 𝑚𝑝 2 𝛿 𝑖𝑗 + 𝜎 𝑚𝑑 2 (1 − 𝛿 𝑖𝑗 )) − ∑ (𝐹
𝑖𝑗−𝑔(∆∆𝐺
𝑖+∆∆𝐺
𝑗))
2
𝜎
𝑖𝑗2+𝜎
𝑚𝑝2𝛿
𝑖𝑗+𝜎
𝑚𝑑2(1−𝛿
𝑖𝑗)
𝑖,𝑗,𝑖≠𝑗 ,
𝛿 𝑖𝑗 = 1
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β
Log araAexpression
Log araB expression
Env2[aTc]2, [IPTG]2
Env3 [aTc]3, [IPTG]2
AraA AraB
L-arabinose L-ribulose L-ribulose-5-P
GrowthPPP
A
B C
aTc IPTG DaraBA
PLtetO-1
PLlacO-1
…AATTGACATTGTGATCGGATAACAAGATACTGA…
…GATTGACATCCCTATCAGTGATAGAGATACTGA…
-35 -10
Env1 [aTc]1, [IPTG]1
D
ATP ADP
H+
e = 0 e < 0 e > 0
magnitude
magnitude simple
sign reciprocal
sign reciprocal
sign none
ln fitness
FrelaB FrelAb FrelAb+ FrelaB
0
A+B+
ab Ab
aB AB
A-B- A+B-
simple sign
e < 0 e = 0 e > 0
