Rank Epistasis
A new metric for measuring epistatic interactions in the absence of quantifiable fitness interactions
Acacia Ackles*, Austin Ferguson, Connor Grady, & Charles Ofria
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Michigan State University
Acknowledgements
People
Clifford Bohm
Wolfgang Banzhaf
Christoph Adami
FUNDING
land
Land acknowledgement? What's that?
bit.do/why-land
Michigan State University, where this work was conducted, resides on the ancestral, traditional, and contemporary Lands of the Anishinaabeg - Three Fires Confederacy of Ojibwe, Odawa, and Potawatomi peoples.
bit.do/alife2020-ackles
What is epistasis?
We have some naive idea that genetic effects should "stack on top of each other" in some simple way.
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Epistasis is the deviation from that baseline expectation.
What is epistasis?
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A
B
AB
A
B
AB
A
AB
B
Positive epistasis creates a more beneficial effect than expected.
Negative epistasis creates a more deleterious effect than expected.
No epistasis is our expectation of the fitness effect of two mutations in combination.
Multiple genes must lose normal function before cells become cancerous
What is epistasis?
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buffer
instability
reduced generality
unstable specificity
stable specificity
https://www.genome.gov/genetics-glossary/Cancer
who cares?
Epistatic interactions form the basis of complex genetic structures.
If we want to understand complex structures, we need to first understand which sites are interacting epistatically.
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current measures
number of mutations
average fitness of genotypes with k mutations
effect of mutations alone
effect of mutations combined
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Limitations
What is our baseline expectation?
What number do we assign to fitness?
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A
B
AB
Rank Epistasis
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We developed a rank-based measure of epistasis inspired by non-parametric statistics.
Rank Epistasis
1. Rank all single-mutation variants in a population in order of decreasing fitness.
1 1 1 0 1 0
0 0 1 0 1 0
0 1 0 0 1 0
0 1 1 1 1 0
0 1 1 0 0 0
0 1 1 0 1 1
1 1 1 0 1 0
0 0 1 0 1 0
0 1 0 0 1 0
0 1 1 1 1 0
0 1 1 0 0 0
0 1 1 0 1 1
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0 1 1 0 1 0
0.3
0.5
0.7
0.3
0.2
0.9
0.9
0.7
0.5
0.2
0.3
0.3
1
2
3
4.5
4.5
6
Rank Epistasis
2. Select a target site, and mutate that site in combination with all single-mutation variants from (1). Rank this list.
bit.do/alife2020-ackles
0 1 1 0 1 0
0 0 1 0 1 0
1 0 1 0 1 0
0 0 1 0 1 0
0 0 0 0 1 0
0 0 1 1 1 0
0 0 1 0 0 0
0 0 1 0 1 1
1.8
1.3
1.0
1.0
0.2
1.0
1 1 1 0 1 0
0 0 1 0 1 0
0 1 0 0 1 0
0 1 1 1 1 0
0 1 1 0 0 0
0 1 1 0 1 1
0.3
0.5
0.7
0.3
0.2
0.9
1
2
3
4.5
4.5
6
Rank Epistasis
2. Select a target site, and mutate that site in combination with all single-mutation variants from (1). Rank this list.
bit.do/alife2020-ackles
0 1 1 0 1 0
0 0 1 0 1 0
1 0 1 0 1 0
0 0 1 0 1 0
0 0 0 0 1 0
0 0 1 1 1 0
0 0 1 0 0 0
0 0 1 0 1 1
1.8
1.3
1.0
1.0
0.2
1.0
1 0 1 0 1 0
0 0 1 0 1 0
0 0 0 0 1 0
0 0 1 1 1 0
0 0 1 0 0 0
0 0 1 0 1 1
1.8
1.3
1.0
1.0
0.2
1.0
4
6
2
1
4
4
Rank Epistasis
3. Compare the two ranked lists to determine the degree of epistatic activity at the target site.
bit.do/alife2020-ackles
0 1 1 0 1 0
0 0 1 0 1 0
1 0 1 0 1 0
0 0 1 0 1 0
0 0 0 0 1 0
0 0 1 1 1 0
0 0 1 0 0 0
0 0 1 0 1 1
1 1 1 0 1 0
0 0 1 0 1 0
0 1 0 0 1 0
0 1 1 1 1 0
0 1 1 0 0 0
0 1 1 0 1 1
1
2
3
4.5
4.5
6
4
6
2
1
4
4
Rank Epistasis
3. Compare the two ranked lists to determine the degree of epistatic activity at the target site.
bit.do/alife2020-ackles
0 1 1 0 1 0
0 0 1 0 1 0
1
2
3
4.5
4.5
6
Wilcoxon's W
4
6
2
1
4
4
NK Landscapes
0 1 1 0 1 0
| 0 | 1 | 2 | 3 | 4 | 5 | |
| 0 0 | 0.5 | 0.0 | 0.3 | 4.2 | 0.5 | 0.1 |
| 0 1 | 4.2 | 1.2 | 0.2 | 1.2 | 2.4 | 0.1 |
| 1 0 | 2.0 | 3.1 | 2.0 | 3.4 | 3.4 | 9.3 |
| 1 1 | 1.4 | 4.0 | 4.0 | 2.1 | 1.1 | 2.0 |
Increasing k leads to increasing interaction between sites (increased epistasis)
N
K
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NK Landscapes
0 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 . . . .
N
K
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2
200
4
9
Modular agent based evolver
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Recap
We are testing our rank-based epistasis metric on NK fitness landscapes to see whether it has viability as measure of epistasis without assumptions of interactivity.
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We expect...
Sites with higher degrees of epistatic activity (higher K) will score higher on this metric.
We will see this result regardless of any a priori assumptions about which genes are interacting with each other or how they interact.
bit.do/alife2020-ackles
K (number of sites each site interacts with)
W (Wilcoxon Signed Rank Sum)
one target site, one organism
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W (Wilcoxon Signed Rank Sum)
one target site, all organisms
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K (number of sites each site interacts with)
W (Wilcoxon Signed Rank Sum)
average across All loci
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Locus
K=2
K=4
K=9
we found...
Expectation 1: Sites with higher degrees of epistatic activity (higher K) will score higher on this metric.
True! Higher K led to higher rank epistasis.
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we found...
True! We saw higher rank epistasis on average even though we did not specify which sites were interacting.
Expectation 2: We will see this result regardless of any a priori assumptions about which genes are interacting with each other or how they interact.
bit.do/alife2020-ackles
future directions
-
Tuning of the metric for more fine-grained differences between levels of epistatic activity
-
Comparison with other metrics of epistasis to see old information in a new light
-
Experimentation on digital landscapes with more complex genetic architectures.
- Application to wet lab data
bit.do/alife2020-ackles
http://cse.msu.edu/~dolsonem/
Questions?
Main Result
Locus
W
future directions
Fine-tuning the metric
Comparison to other metrics
More complex digital landscapes
Application to wet lab work
bit.do/alife2020-ackles
K=2
K=4
K=9