competition and cooperation in spatial expansion of yeast colonies
TRANSCRIPT
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Harvard UniversityFAS Center for Systems Biology
Competition and cooperationin
microbial spatial expansions
Melanie JI MüllerDavid R Nelson, Andrew W Murray
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Range expansions• Range expansion = species conquer new territory• Species - expand from where they evolved - migrate in response to environmental change - invade when brought to new territory
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Life on surfaces• Microbes grow in a variety of habitats
• Many are surfaces: - leaves, bark, fruits, rocks - animal epithelial surfaces - man-made surfaces
• Different species grow together, can compete, cooperate
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Life on surfaces• What is the impact of spatial structure on
- growth patterns? - population dynamics? - species interactions? - evolution?
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Grow microbes in the lab
well-mixed population structured population
• shaken liquid culture • colonies on agar surface
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12mm2mm
Day 0 Day 6
1mm
1) Mix yellow and blue strains
2) Inoculate drop on agar surface
→ observe pattern3) Colony expands
• Range expansion assay:
Microbial range expansions
Hallatschek & Nelson, Theoret. Pop. Biol. 2008
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• Human migration
Neutral range expansions• Yeast migration
1week
Ramachadran et al, PNAS 2005Distance [km] from Addis Ababa, Ethiopia
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Outline
• Competition: Spatial growth with selection
• Cooperation: Spatial growth with cooperative interaction
• Basic effects of spatial growth: - spatial demixing - reduced genetic diversity
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Spatial growth without and with selection• Yellow and blue with same growth rate
• Yellow grows faster than blue
curved sector boundary
bulge
Homeland yellow:blue 1:1 Homeland yellow:blue 1:500
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Sector shape • Assume: - fixed for either blue or yellow - constant radial velocities v1, v2
→ Sector angle = logarithmic spiral
• Theory
2 2
2 1
( ) ( )dr rddrtv v
• Equate time increments:
relative fitness
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Spatial versus well-mixed fitness
1.4
1.2
1.0
1.0 1.2 1.4
• Sectors spatial relative fitness = ratio of velocities
• Yeast not motile spatial = well-mixed fitness
fitness in well-mixed culture
fitne
ss o
n pl
ate
• Well-mixed culture relative fitness = ratio of growth rates
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Outline
• Competition: Spatial growth with selection
• Cooperation: Spatial growth with cooperative interaction
• Basic effects of spatial growth
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Mutualistic yeast• want: yeast cross-feeding
→ (almost) no growth
Leu–Trp+
Leu+Trp–
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Mutualistic yeast• How to make yeast secrete an amino acid? → overproduction
chorismate
anthranilate
Trp2
tryptophan
other amino acids
• Tryptophan biosynthesis
…
…
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Mutualistic yeast• How to make yeast secrete an amino acid? → overproduction using feedback resistance (FBR)
chorismate
anthranilate
• Tryptophan biosynthesis
…
Trp2FBR
TRYPTOPHAN
other amino acids
…
• Similar feedback-resistance for leucine biosynthesis
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Mutualistic yeast• want: yeast cross-feeding
→ robust growth
Leu–TrpFBR
LeuFBRTrp–
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Range expansion patterns
1mm
1mm
Mutualism
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Range expansion patterns
→ inhibited demixing → spatial demixing1mm1mm
Mutualism No mutualism
Mutualists grow slower (50%)
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Mutualist patch size
100μm
L
Spatial expansion demixed patches
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Mutualist patch size
Leu diffuses into leu-consumer patch:
leucine diffusion
~ 700 μm
→ Length scale
leucine uptake by cells
100μm
L = 50μm
Spatial expansion demixed patches
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Mutualist patch sizeDiffusion of patch boundaries due to cell division pushing
~ 1 μm
100μm
L = 50μm
cell size ~ 5μm → diffusion ~ 25μm2/generation
growth velocity ~ 20μm/generation
~ 50 μm
Patch size
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Mutualist patch size
100μm
ξ║
L=ξ┴
growthdirection
Correlation lengths: - in expansion direction: ξ║ = 110 μm- perpendicular: ξ┴ = 52 μm
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Theory
diffusion selection genetic drift
• time development with selection:
• What is the selection?
• f = fraction of blue cells x = coordinate along front
2
2
( , ) (1 )( ) (1 ) ( , )2
f x t f f fD s f f f x tt x N
2
2
( , ) ( ) (1 ) ( , )2
f x t f dV f f fD x tt x df N
Intuition: noisy diffusion in potential V(f)
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Theory
diffusion selection genetic drift
• dynamics: f = fraction of blue cells, x = coordinate along front2
2
( , ) (1 )( ) (1 ) ( , )2
f x t f f fD s f f f x tt x N
2
2
( , ) ( ) (1 ) ( , )2
f x t f dV f f fD x tt x df N
Intuition: noisy diffusion in potential V(f)
stable fraction f*
• mutualism: growth depends on partner → frequency-dependent selection
f = fraction of blue cells0 1
V(f)
Lots of blue cellsyellow grows faster
Lots of yellow cells blue grows faster
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Mutualists expand together
6 : 1 1 : 1 1 : 6Day 0
Day 7, mutualism
100 : 1 1 : 100
1mm
1mm
2mm
Day 7, no mutualism
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Mutualists expand together
6 : 1 1 : 1 1 : 6Day 0
Day 7, no mutualism
Day 7, mutualism
100 : 1 1 : 100
1mm
1mm
2mm
…but so is their production/uptake!
Why preferred ratio ~ 1:1?Leu, trp very different…
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To expand together – or not
Mutualism→ frequency-dependent selection→ mixing at fraction f*
Small front population size→ genetic drift (noise) → local fixation = demixing
no leu, trp lots of leu, trp
Probe antagonism: vary amino acid concentrations in medium
f = fraction of blue cells0 1
V(f)
f*
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To expand together – or not
no leu, trp lots of leu, trp
vary amino acid concentrations
in medium
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[leu]
[trp]
Leu+Trp-
Leu-Trp+
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[leu]
[trp]
Leu+Trp-
Leu-Trp+
yellow dominates
blue dominates
demixed
mixed
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[leu]
[trp]
Leu+Trp-
Leu-Trp+
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[leu]
[trp]
Leu+Trp-
Leu-Trp+
mutualism strength
demixing strength ~1/Ne
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[leu]
Leu+Trp-
Leu-Trp+Antagonism of mutualism and genetic drift• Phase transition from mixing to demixing (theoretical physics: directed percolation)
• Demixing although mixing would be beneficial
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Theoretical phase diagram
Korolev & Nelson, PRL 2011
Benefit for blue
Ben
efit
for y
ello
w
blue wins
• demixing depends on - mutualism strength - symmetry
demix
Mutualism→ inhibited
demixing
yellowwins
• experiment: vary amino acid concentrations
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[leu]
[trp]
Leu+Trp-
Leu-Trp+
mutations
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Mutants in mutualistic colonies• Mutualistic colonies exhibit 0-5 mutation sectors Average: ca. 1 sector/colony Phenotypic mutation rate 10^-9 - 10^-6 /generation/cell)
• Compare: sector shape for pure selection
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The most common mutant
Blue cells from sector+ yellow ancestor
Yellow cells from sector+ blue ancestor
Isolate singlecells
Compare: sector shape for pure selection
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Mutants
• blue mutant & yellow ancestor• blue & yellow ancestors
- faster, thin-striped growth with ancestral yellow partner- better at sucking up leucine
up
Dlk c
Characteristic length scale
• Yellow cells behave like ancestor• Blue cells have heritable phenotype:
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Conclusions
• Spatial growth with selection: - relative fitness ↔ sector shape - can be used to measure fitness
• Spatial growth with mutualistic interaction: - inhibited spatial demixing - spatial expansion impedes mutualism - mutations change pattern
• Basic effects of spatial growth: - spatial demixing
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THEORYDavid Nelson
Oskar HallatschekKirill Korolev
EXPERIMENTAndrew Murray
Beverly NeugeborenDavid van Dyken
Thank you!…for your attention
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References•Genetic drift opposes mutualism during spatial population expansion MJI Müller, BI Neugeboren, DR Nelson, AW Murray Proceedings of the National Academy of Sciences 111 (3), 1037-1042, 2014
•Spatial population expansion promotes the evolution of cooperation in an experimental Prisoner’s Dilemma JD Van Dyken, MJI Müller, KML Mack, MM Desai Current Biology 23 (10), 919-923, 2013
•Selective sweeps in growing microbial colonies KS Korolev, MJI Müller, N Karahan, AW Murray, O Hallatschek, ... Physical Biology 9 (2), 026008, 2012
Thank you!…for your attention