Public good diffusion limits microbial mutualism Zijnge V et al. PLoS ONE 2010:5 Rajita Menon Korolev Lab Kolenbrander et al. (2010) Menon, R & Korolev, KS, Phys. Rev. Lett. (2015)

Complex microbial networks do amazing things Global interaction network in human microbiome Individual dynamics to bigger picture : focus is shifting in microbial ecology studies. Example of public goods importance : Jim Collins paper here. Two-way interactions maintain the complexity of ecosystems. Metabolite exchange can allow coexistence of 50 species even. Faust K, Sathirapongsasuti JF, Izard J, Segata N, Gevers D, et al. Plos Comp. Biol. (2012)

Diffusible molecules mediate microbial interactions Public BADS (Antibiotics) Antibiotic simple example, ring of inhibition (s.aureus inhibited by penicillin), same thing with cross feeding (Daniel’s paper metabolic eclipse)- leads to non trivial effects like the eclipse. Segue from here, saying that selection of diffusivities is not often studied, but it was studied last year in THIS data set MODELING DIFFUSION IS VERY IMPORTANT textbookofbacteriology.net Antibiotic ring of inhibition

Is diffusivity of public goods under selection? How does nutrient diffusivity affect mutualism? Are nutrient diffusivities under selection? Recent example – siderophores. Remove paper figure with text. Maybe interaction are driven by cheaters cooperators (Allen, Gore, Nowak). But cross feeding is not explained by all this. In some context we know the effect of diffusion but nor for cross feeding Add data figure from figure Abergel et al., PNAS (2006)

Cross feeding : simple example of diffusive interaction Two-way cross feeding is the simplest microbial community species A species B Show petri dish pictures for Momeni. Picture of Shou who designed this system that has been studied extensively. Well mixed culture they coexist, but you have to grow them in a petri dish to see the coexistence and segregation Momeni et al., eLife (2013) Muller et al., PNAS (2014)

Cross feeding : simple example of diffusive interaction Two-way cross feeding is the simplest microbial community species A species B Show petri dish pictures for Momeni. Picture of Shou who designed this system that has been studied extensively. Well mixed culture they coexist, but you have to grow them in a petri dish to see the coexistence and segregation Momeni et al., eLife (2013) Muller et al., PNAS (2014) W. Shou

Coexistence and segregation in interacting yeast cultures Cooperative yeast partners intermix Competitive yeast partners segregate Show petri dish pictures for Momeni. Picture of Shou who designed this system that has been studied extensively. Well mixed culture they coexist, but you have to grow them in a petri dish to see the coexistence and segregation Scale bar = 100 micron Momeni et al., eLife (2013)

Coexistence is fragile in space Genetic drift causes demixing Mutualism opposes demixing First predicted by Korolev and Nelson. It’s well known that random effects create differences in species that persist over time and cause demixing. Mutualism counters this effect, but in space it’s fragile and lost easily. 2 aspects of space, demixing + diffusion. Demixing is well understood, but not diffusion. Without diffusion – mutualism is same as coexistence. With diffusion, benefit even in segregated domains i.e mutualism without coexistence Seen by Shou/ Momeni And Muller/Murray Muller et al., PNAS (2014) increasing benefit of cross feeding

High nutrient diffusivity promotes demixing extent of mutualism critical diffusivity public goods diffusivity

Domains grow much faster than diffusion length domain length length diffusion length Graph with diffusion distance + domain size on same plot. Here’s what is going on. Diffusion is root D (simple physics). Domain size grows because diffusion reduces the selection for mutualism. To see this => cartoon No equations, no exponents public goods diffusivity

Nutrient diffusion reduces selection for mutualism One by one, 2 plots. First one just species. Next whole thing without annotations. Bottom plot for selection, write the formula for s effective in words. No need for analytic expressions Hallatschek, Oskar, et al. PNAS (2007)

Nutrient diffusion reduces selection for mutualism selection = difference in public good concentration selection One by one, 2 plots. First one just species. Next whole thing without annotations. Bottom plot for selection, write the formula for s effective in words. No need for analytic expressions Hallatschek, Oskar, et al. PNAS (2007)

Effective selection near domain boundary is reduced species fractions selection public goods conc. One by one, 2 plots. First one just species. Next whole thing without annotations. Bottom plot for selection, write the formula for s effective in words. No need for analytic expressions selection

Now we can use the results of game theory Now use results of game theory to predict things

Critical diffusivity population size has the largest effect on critical diffusivity In words, critical diffusivity. Confirmed in simulations. Shows that mapping works. Using this we can also have a prediction for domain size which can be tested experimentally

Dynamics with different public good diffusivities Are DA and DB under selection?

Dynamics with different public good diffusivities Are DA and DB under selection? Expect selection because this is all important: then we saw that there was none! But found that was because of nonlinearity! Details gave us something new (biologist/phycisist joke)

Dynamics with different public good diffusivities Are DA and DB under selection? linear fitness profile fitness Simplistic function = linear fitness, biology doesn’t work this way. Add graphs for fitness function instead of nonlinearity formulae public goods concentration

Dynamics with different public good diffusivities nonlinearities are important Are DA and DB under selection? fitness public goods concentration

Dynamics with different public good diffusivities nonlinearities are important Are DA and DB under selection? fitness public goods concentration

Dynamics with different public good diffusivities nonlinearities are important Are DA and DB under selection? fitness public goods concentration Diminishing returns in fitness favor slow diffusion

Why nonlinearities matter? Consider small DA and large DB

Why nonlinearities matter? Consider small DA and large DB diminishing returns species A inside B domain fitness species A species A inside A domain public goods concentration

Summary nutrient diffusion destroys mutualism

Summary nutrient diffusion destroys mutualism nutrient diffusion rescales selection

Summary nutrient diffusion destroys mutualism nutrient diffusion rescales selection game theoretic model with diffusion

Summary nutrient diffusion destroys mutualism nutrient diffusion rescales selection nonlinearities select for slow or fast diffusion game theoretic model with diffusion

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