Harvard UniversityFAS Center for Systems Biology

Competition and cooperationin

microbial spatial expansions

Melanie JI MüllerDavid R Nelson, Andrew W Murray

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

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

Life on surfaces• What is the impact of spatial structure on

- growth patterns? - population dynamics? - species interactions? - evolution?

Grow microbes in the lab

well-mixed population structured population

• shaken liquid culture • colonies on agar surface

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

• Human migration

Neutral range expansions• Yeast migration

1week

Ramachadran et al, PNAS 2005Distance [km] from Addis Ababa, Ethiopia

Outline

• Competition: Spatial growth with selection

• Cooperation: Spatial growth with cooperative interaction

• Basic effects of spatial growth: - spatial demixing - reduced genetic diversity

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

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

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

Outline

• Competition: Spatial growth with selection

• Cooperation: Spatial growth with cooperative interaction

• Basic effects of spatial growth

Mutualistic yeast• want: yeast cross-feeding

→ (almost) no growth

Leu–Trp+

Leu+Trp–

Mutualistic yeast• How to make yeast secrete an amino acid? → overproduction

chorismate

anthranilate

Trp2

tryptophan

other amino acids

• Tryptophan biosynthesis

…

…

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

Mutualistic yeast• want: yeast cross-feeding

→ robust growth

Leu–TrpFBR

LeuFBRTrp–

Range expansion patterns

1mm

1mm

Mutualism

Range expansion patterns

→ inhibited demixing → spatial demixing1mm1mm

Mutualism No mutualism

Mutualists grow slower (50%)

Mutualist patch size

100μm

L

Spatial expansion demixed patches

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

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

Mutualist patch size

100μm

ξ║

L=ξ┴

growthdirection

Correlation lengths: - in expansion direction: ξ║ = 110 μm- perpendicular: ξ┴ = 52 μm

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)

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

Mutualists expand together

6 : 1 1 : 1 1 : 6Day 0

Day 7, mutualism

100 : 1 1 : 100

1mm

1mm

2mm

Day 7, no mutualism

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…

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*

To expand together – or not

no leu, trp lots of leu, trp

vary amino acid concentrations

in medium

[leu]

[trp]

Leu+Trp-

Leu-Trp+

[leu]

[trp]

Leu+Trp-

Leu-Trp+

yellow dominates

blue dominates

demixed

mixed

[leu]

[trp]

Leu+Trp-

Leu-Trp+

[leu]

[trp]

Leu+Trp-

Leu-Trp+

mutualism strength

demixing strength ~1/Ne

[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

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

[leu]

[trp]

Leu+Trp-

Leu-Trp+

mutations

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

The most common mutant

Blue cells from sector+ yellow ancestor

Yellow cells from sector+ blue ancestor

Isolate singlecells

Compare: sector shape for pure selection

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:

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

THEORYDavid Nelson

Oskar HallatschekKirill Korolev

EXPERIMENTAndrew Murray

Beverly NeugeborenDavid van Dyken

Thank you!…for your attention

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