1. Computational and Systems Biology
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Inferring genetic interactions from comparative fitness data

  1. Kristina Crona
  2. Alex Gavryushkin
  3. Devin Greene
  4. Niko Beerenwinkel  Is a corresponding author
  1. American University, United States
  2. ETH Zurich, Switzerland
  3. SIB Swiss Institute of Bioinformatics, Switzerland
Research Article
Cite this article as: eLife 2017;6:e28629 doi: 10.7554/eLife.28629
10 figures, 3 tables and 1 additional file

Figures

All 24 rank orders of the biallelic two-locus system, where the 16 colored rank orders imply epistasis.

Red (top row) indicates positive epistasis and blue (middle row) negative epistasis.

https://doi.org/10.7554/eLife.28629.002
(a) A partial fitness order of genotypes.

The rank orders that extend this partial order are orders (9 , 10 , 12 , 13 , 14), and (16) in Figure 1. All of them imply negative epistasis (ε2<0). (b) A partial order of genotypes with all its total extensions shown on the right. The first extension shown in red implies positive epistasis (ε2>0), while the second one in black does not.

https://doi.org/10.7554/eLife.28629.003
For a biallelic two-locus system where the genotype 00 has the lowest fitness, there are four fitness graphs.

The graph (a) is compatible with additive fitness, whereas the remaining graphs imply negative epistasis.

https://doi.org/10.7554/eLife.28629.004
The fitness graph (a) implies three way epistasis, the graph (b) implies epistasis, but not higher order epistasis, and (c) does not imply epistasis, since all arrows point up.
https://doi.org/10.7554/eLife.28629.005
Interactions detected from fitness summary statistics and from rank orders.

The horizontal axis is labeled by the four interaction coordinates u110, , u111 and twenty circuits a, , t. The boxplots show the distributions of the various interactions induced by the empirical fitness distribution. The red star indicates whether the interaction has been detected by our rank order method. Specifically, a star with vertical coordinate -1, 0, and one means negative, no, and positive interaction, respectively.

https://doi.org/10.7554/eLife.28629.006
The TEM-family of β-lactamase contributes to antibiotic resistance problems in hospitals.

The fitness graph shows a four-locus system consisting of the wild type, TEM-1, the quadruple mutant, TEM-50, and all intermediate mutants, including six clinically found mutants in the TEM family. The mutation M69L corresponds to 1000, E104K to 0100, G238S to 0010, and N276D to 0001. Growth rates were measured for the 16 genotypes under exposure to the antibiotic FEP Cefepime, and the fitness graph was determined accordingly (Mira et al., 2015). The graph reveals higher order epistasis.

https://doi.org/10.7554/eLife.28629.007
The fitness graph shows a four-locus system for the filamentous fungus Aspergillus Niger.

The system consists of all combinations of the four individually deleteriouis mutations fwnA1, leuA1, oliC2 and crnB12. The landscape has in total four peaks, labeled 0000,1100,0011 and 1001.

https://doi.org/10.7554/eLife.28629.008
The fitness graph is compatible with the two rank orders (5) and (6).
https://doi.org/10.7554/eLife.28629.009
An example of an isomorphism.

Here, the allele labels ‘0’ and ‘1’ in the first locus have been interchanged, as well as the second and third loci.

https://doi.org/10.7554/eLife.28629.010
All 54 fitness graph types.

Those depicted in red imply three-way epistasis.

https://doi.org/10.7554/eLife.28629.012

Tables

Table 1
Numbers and fractions of rank orders that imply n-way epistasis. 
https://doi.org/10.7554/eLife.28629.011
LociRank ordersImply epistasisFraction
224162/3
340,32016,1282/5
420,922,789,890,0004,649,508,864,0002/9
Table 2
Comparison of the rank order method with t-test.

The first column lists the four interaction coordinates and twenty circuits. The second column shows p-values returned by Student’s t-test based on fitness measurements. The third column shows which interactions are significant based on 0.03 threshold and their signs. For comparison, the last column displays the results obtained from rank order methods.

https://doi.org/10.7554/eLife.28629.013
Interactionp-valueResultFrom rank order
u0111.13e-31+0
u1012.67e-12-0
u1101.20e-24-0
u1111.50e-29++
a7.10e-16-+
b5.23e-32--
c7.62e-04++
d8.36e-68--
e1.39e-38++
f2.59e-0100
g3.10e-59-0
h2.22e-02-+
i7.97e-05+0
j2.20e-32--
k1.96e-05+0
l7.50e-51--
m4.88e-07-0
n9.87e-37+0
o8.83e-03+0
p7.18e-19++
q1.94e-0100
r5.02e-50++
s7.10e-27-0
t8.49e-61--
Table 3
Data from (Franke et al., 2011) on a 5-locus system determined by the mutations fwnA1, argH12, pyrA5, leuA1, and pheA1.

We consider 5-way epistasis for the system. The first column lists the ranking of the genotypes, where ”?” means missing measurement. The eighth column indicates whether the genotype is odd or even. The ninth and tenth columns show the cumulative number of o’s and e’s, respectively. The last column indicates whether the number of o’s exceeds the number of e’s (-) or vice versa (+). We see that if genotype 11101 has higher fitness than genotype 10011, genotypes 11000,10010 are ranked arbitrarily, the missing genotype 10111 has rank 1-15, and 11010 rank 20-32, then the last column would change to all +’s, so the rank order would imply u11111>0.

https://doi.org/10.7554/eLife.28629.014
Rankfwnargpyrleuphe#mutationso/
e
#o cumul.#e cumul.neg. vs
pos.
1000000e01+
2100012e02+
3010113o12+
4010012e13+
5110114e14+
6 (or 7)110002e15+
7 (or 6)100102e16+
8000011o26+
9111003o36+
10010001o46+
11011013o56+
12101002e57+
13000101o67+
14100001o77+
15110013o87-
16011002e88+
17001113o98-
18 (or 19)111014e99+
19 (or 18)100113o109-
20000112e1010+
21010102e1011+
22001012e1012+
23001001o1112+
24011114e1113+
25011103o1213+
26001102e1214+
27101013o1314+
28111104e1315+
29111115o1415+
30101103o1515+
?110103o???
?101114e???

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