HARVARD MATH 243 - Evolutionary Dynamics of Metabolic Systems

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Evolutionary Dynamics of Metabolic SystemsOverviewLong-term evolution in chemostatCrossfeedingHypothesisOptimal pathway designPartial vs. complete resource degradationConclusions IEvolution of crossfeeding: extended modelExtended pathway schemeChemostat dynamicsDynamics of evolutionSimulation resultsConclusions IITrade-offs between ATP rate and yieldThermodynamic trade-offSlide 17Efficient versus fast ATP productionSlide 19Evolutionary dilemmaEvolution of cooperationExperimental EvidenceYield and rate over timeBetween population tradeoffWithin populationsAcknowledgementsEvolutionary Dynamics of Metabolic SystemsThomas Pfeiffer, Program for Evolutionary DynamicsMath 243, 21.04.2009Overview1. Crossfeeding•Introduction•Partial vs. complete degradation of resources and the optimization of metabolic pathways•Population dynamical model for the evolution of crossfeeding2. Rate vs. Yield •Background•Game theory•Experimental EvidenceLong-term evolution in chemostat•Long-term evolution for hundreds of generations•Evolution of stable polymorphisms!•Single limiting resource, homogeneous environment•Polymorphisms maintained by crossfeedingHelling et al., Genetics, 1987Rosenzweig et al., Genetics, 1994Treves et al., Mol. Biol. Evol, 1998CrossfeedingWhat is the advantage of two crossfeeding strains over a single competitor that completely degrades the resource?Hypothesis•Crossfeeding results from optimization of three properties of ATP-producing pathways:–Rate of ATP production is maximized –Enzyme concentrations are minimized–Intermediate concentrations are minimizedOptimal pathway design•Optimization: JS  max,  Ei ≤ E*,  Xi ≤ X* •Results: optimal enzyme expressionE1= E*X*/(X* + Sm2) , Ei = SE*m/(X* + Sm2) •JS ~ E*X*S/(X* + Sm2) Heinrich & Schuster, 1996Partial vs. complete resource degradation•ATP-producing pathway: JATP = nATP JS ~ nATP E*X*S/(X* + Sm2)•If nATP increases with increasing pathway length m, an optimal pathway length exists: motp=(X*/S)1/2Conclusions I•Partial degradation may be of advantage•Low resource concentration  long pathways•High resource concentration  short pathways•(Trade-off between rate and yield!)•Important pre-condition for the evolution of crossfeeding•Extended model required!Evolution of crossfeeding: extended model •Extended pathway scheme– excretion/uptake of intermediate•Dynamics of populations, resource and intermediate–Chemostat dynamics•Dynamics of evolution–Strain characteristics–Mutations –etc.Extended pathway scheme•Reversible uptake/excretion of an intermediate XkChemostat dynamics•Dynamics of resource, intermediate and populations:dS/dt = D (S0 – S) – ΣNi JiSdXex/dt = ΣNi JiX – DXex dNi/dt = (Wi – D)Ni •Growth rate of a strain:W = f(JATP) – ΣAiEi – ΣBiXiDynamics of evolution•Start with a initial strain (characterized by E1…Em)•Calculate steady state concentrations and population size•Repeatedly:–Allow the best mutant to invade–Calculate new steady state (mutant coexists or can outcompetes resident strains)•Evolution ends if no novel strain can invadeSimulation resultsConclusions II•Crossfeeding may result from pathway optimization•Expected at high dilution rates and high costs for intermediatesCosta et al, Trends in Microbiol 2006 Katsuyama et al, JTB 2009•Threshold behavior: small changes may trigger large changes in population structure•Mechanism of sympatric speciation in microbial populations!Rate (JATP) – units of ATP per unit of timeYield (nATP) – units of ATP per unit of resourceTrade-off between rate and yield: ATP production is slow and efficient or fast and inefficientTrade-offs between ATP rate and yieldThermodynamic trade-off Trade-off between rate and yield of ATP productionLinear flux-force relation: JS ~ ∆GJATP~ nATP(∆GSP- nATP ∆GATP)Conserved as ATPDrives reaction rateFree energy difference ∆GSPWhen is it favorable to produce ATP fast?When is it favorable to produce ATP efficiently?Efficient versus fast ATP production Success (ATP) of a population is determined by ATP yield sugarfastATPATPATPATPsugarefficientATPATPATPATPEfficient versus fast ATP production Success in competition is determined by the ATP ratesugarATPATPATPATPEvolutionary dilemmaA population of efficient resource users has a high payoffInvaders with fast resource use have an even higher payoffInefficient resource users increase in frequencyPayoff for the population and each individual decreasesSlow and efficient ATP production = cooperative behaviorFast and inefficient ATP production = selfish behaviorPfeiffer et al., Science, 2001Evolution of cooperation•Non-cooperative resource use evolve in homogeneous environments•Cooperative resource use evolves in heterogeneous environments, where cells of the same type tend to be clustered•Spatial clustering drives the evolution of cooperative resource usePfeiffer et al., Science, 2001Experimental Evidence•How to measure a tradeoff?–Selection for one property leads to the decline of the other one–Between species (or populations): Negative correlation between the two properties across different populations–Within one population: Negative correlation between the two properties between individuals with a population•System: E. coli from Rich Lenski’s long term evolution experiment–12 lines of E. coli that evolved for 20000 generations in glucose-limited batch culture–all three tests possibleYield and rate over time•Increase in rate•Initial increase in yield•No evidence for trade-offBetween population tradeoffNo evidence for tradeoffWithin populations•Evidence for within population tradeoff in three populationsNovak et al, AmNat 2006Acknowledgements•Sebastian Bonhoeffer, ETH Zurich•Maja Novak, ETH Zurich•Uwe Sauer, ETH Zurich•Stefan Schuster, U Jena•Rich Lenski, U Michigan•Martin Nowak and the Program for Evolutionary Dynamics•Society in Science / The Branco Weiss


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HARVARD MATH 243 - Evolutionary Dynamics of Metabolic Systems

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