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Kristina Crona

Alex Gavryushkin

Devin Greene

Niko Beerenwinkel

(2017)
Inferring genetic interactions from comparative fitness data

eLife 6:e28629.

https://doi.org/10.7554/eLife.28629
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Figures
Tables
Additional files

10 figures, 3 tables and 1 additional file

Figures

Figure 1

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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

Figure 2

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(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 ( $ε_{2} < 0$ ). (b) A partial order of genotypes with all its …
https://doi.org/10.7554/eLife.28629.003

Figure 3

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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

Figure 4

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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

Figure 5

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Interactions detected from fitness summary statistics and from rank orders.

The horizontal axis is labeled by the four interaction coordinates $u_{110}$ , $\dots$ , $u_{111}$ and twenty circuits $a$ , $\dots$ , $t$ . The boxplots show the distributions of the various interactions induced by the empirical …
https://doi.org/10.7554/eLife.28629.006

Figure 6

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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. …
https://doi.org/10.7554/eLife.28629.007

Figure 7

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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

Figure 8

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

Figure 9

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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

Figure 10

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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

Loci	Rank orders	Imply epistasis	Fraction
2	24	16	$2 / 3$
3	40,320	16,128	$2 / 5$
4	20,922,789,890,000	4,649,508,864,000	$2 / 9$

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 …

https://doi.org/10.7554/eLife.28629.013

Interaction	p-value	Result	From rank order
$u_{011}$	1.13e-31	$+$	$0$
$u_{101}$	2.67e-12	$-$	$0$
$u_{110}$	1.20e-24	$-$	$0$
$u_{111}$	1.50e-29	$+$	$+$
$a$	7.10e-16	$-$	$+$
$b$	5.23e-32	$-$	$-$
$c$	7.62e-04	$+$	$+$
$d$	8.36e-68	$-$	$-$
$e$	1.39e-38	$+$	$+$
$f$	2.59e-01	$0$	$0$
$g$	3.10e-59	$-$	$0$
$h$	2.22e-02	$-$	$+$
$i$	7.97e-05	$+$	$0$
$j$	2.20e-32	$-$	$-$
$k$	1.96e-05	$+$	$0$
$l$	7.50e-51	$-$	$-$
$m$	4.88e-07	$-$	$0$
$n$	9.87e-37	$+$	$0$
$o$	8.83e-03	$+$	$0$
$p$	7.18e-19	$+$	$+$
$q$	1.94e-01	$0$	$0$
$r$	5.02e-50	$+$	$+$
$s$	7.10e-27	$-$	$0$
$t$	8.49e-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. …

https://doi.org/10.7554/eLife.28629.014

Rank	fwn	arg	pyr	leu	phe	#mutations	$o$ / $e$	# $o$ cumul.	# $e$ cumul.	neg. vs pos.
1	0	0	0	0	0	0	$e$	0	1	+
2	1	0	0	0	1	2	$e$	0	2	+
3	0	1	0	1	1	3	$o$	1	2	+
4	0	1	0	0	1	2	$e$	1	3	+
5	1	1	0	1	1	4	$e$	1	4	+
6 (or 7)	1	1	0	0	0	2	$e$	1	5	+
7 (or 6)	1	0	0	1	0	2	$e$	1	6	+
8	0	0	0	0	1	1	$o$	2	6	+
9	1	1	1	0	0	3	$o$	3	6	+
10	0	1	0	0	0	1	$o$	4	6	+
11	0	1	1	0	1	3	$o$	5	6	+
12	1	0	1	0	0	2	$e$	5	7	+
13	0	0	0	1	0	1	$o$	6	7	+
14	1	0	0	0	0	1	$o$	7	7	+
15	1	1	0	0	1	3	$o$	8	7	$-$
16	0	1	1	0	0	2	$e$	8	8	+
17	0	0	1	1	1	3	$o$	9	8	$-$
18 (or 19)	1	1	1	0	1	4	$e$	9	9	$+$
19 (or 18)	1	0	0	1	1	3	$o$	10	9	$-$
20	0	0	0	1	1	2	$e$	10	10	+
21	0	1	0	1	0	2	$e$	10	11	+
22	0	0	1	0	1	2	$e$	10	12	+
23	0	0	1	0	0	1	$o$	11	12	+
24	0	1	1	1	1	4	$e$	11	13	+
25	0	1	1	1	0	3	$o$	12	13	+
26	0	0	1	1	0	2	$e$	12	14	+
27	1	0	1	0	1	3	$o$	13	14	+
28	1	1	1	1	0	4	$e$	13	15	+
29	1	1	1	1	1	5	$o$	14	15	+
30	1	0	1	1	0	3	$o$	15	15	+
?	1	1	0	1	0	3	$o$	?	?	?
?	1	0	1	1	1	4	$e$	?	?	?

Additional files

Transparent reporting form: https://doi.org/10.7554/eLife.28629.015
Download elife-28629-transrepform-v1.docx

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Figures

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

(a) A partial fitness order of genotypes.

For a biallelic two-locus system where the genotype $00$ has the lowest fitness, there are four fitness graphs.

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.

Interactions detected from fitness summary statistics and from rank orders.

The TEM-family of $β$ -lactamase contributes to antibiotic resistance problems in hospitals.

The fitness graph shows a four-locus system for the filamentous fungus Aspergillus Niger.

The fitness graph is compatible with the two rank orders (5) and (6).

An example of an isomorphism.

All 54 fitness graph types.

Tables

Numbers and fractions of rank orders that imply $n$ -way epistasis.

Comparison of the rank order method with t-test.

Data from (Franke et al., 2011) on a 5-locus system determined by the mutations fwnA1, argH12, pyrA5, leuA1, and pheA1.

Additional files

Transparent reporting form

Download links

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All 24<math id="inf28"><mn>24</mn></math> rank orders of the biallelic two-locus system, where the 16<math id="inf29"><mn>16</mn></math> colored rank orders imply epistasis.

(a) A partial fitness order of genotypes.

For a biallelic two-locus system where the genotype 00<math id="inf37"><mn>00</mn></math> has the lowest fitness, there are four fitness graphs.

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.

Interactions detected from fitness summary statistics and from rank orders.

The TEM-family of β<math id="inf84"><mi>β</mi></math>-lactamase contributes to antibiotic resistance problems in hospitals.

The fitness graph shows a four-locus system for the filamentous fungus Aspergillus Niger.

The fitness graph is compatible with the two rank orders (5) and (6).

An example of an isomorphism.

All 54 fitness graph types.

Numbers and fractions of rank orders that imply n<math id="inf323"><mi>n</mi></math>-way epistasis.

Comparison of the rank order method with t-test.

Data from (Franke et al., 2011) on a 5-locus system determined by the mutations fwnA1, argH12, pyrA5, leuA1, and pheA1.

Transparent reporting form

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

For a biallelic two-locus system where the genotype $00$ has the lowest fitness, there are four fitness graphs.

The TEM-family of $β$ -lactamase contributes to antibiotic resistance problems in hospitals.

Numbers and fractions of rank orders that imply $n$ -way epistasis.