Evolutionary Dynamics of Metabolic Systems

1. Evolutionary Dynamics of Metabolic Systems Thomas Pfeiffer, Program for Evolutionary Dynamics Math 243, 21.04.2009

2. Overview • Crossfeeding • Introduction • Partial vs. complete degradation of resources and the optimization of metabolic pathways • Population dynamical model for the evolution of crossfeeding • Rate vs. Yield • Background • Game theory • Experimental Evidence

3. Long-term evolution in chemostat • Long-term evolution for hundreds of generations • Evolution of stable polymorphisms! • Single limiting resource, homogeneous environment • Polymorphisms maintained by crossfeeding Helling et al., Genetics, 1987 Rosenzweig et al., Genetics, 1994 Treves et al., Mol. Biol. Evol, 1998

4. Crossfeeding What is the advantage of two crossfeeding strains over a single competitor that completely degrades the resource?

5. 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 minimized

6. Optimal pathway design • Optimization: JS max, Ei≤ E*,  Xi ≤ X* • Results: optimal enzyme expression E1= E*X*/(X* + Sm2) , Ei = SE*m/(X* + Sm2) • JS ~ E*X*S/(X* + Sm2) Heinrich & Schuster, 1996

7. Partial 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)1/2

8. Conclusions 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!

9. 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.

10. Extended pathway scheme • Reversible uptake/excretion of an intermediate Xk

11. Chemostat dynamics • Dynamics of resource, intermediate and populations: dS/dt = D (S0 – S) – ΣNi JiS dXex/dt = ΣNi JiX – DXex dNi/dt = (Wi – D)Ni • Growth rate of a strain: W = f(JATP) – ΣAiEi – ΣBiXi

12. Dynamics 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 invade

13. Simulation results

14. Conclusions II • Crossfeeding may result from pathway optimization • Expected at high dilution rates and high costs for intermediates Costa 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!

15. Trade-offs between ATP rate and yield Rate (JATP) – units of ATP per unit of time Yield (nATP) – units of ATP per unit of resource Trade-off between rate and yield: ATP production is slow and efficient or fast and inefficient

16. Free energy difference ∆GSP Drives reaction rate Conserved as ATP Thermodynamic trade-off Linear flux-force relation: JS ~ ∆G JATP~ nATP(∆GSP- nATP ∆GATP) Trade-off between rate and yield of ATP production

17. When is it favorable to produce ATP fast? When is it favorable to produce ATP efficiently?

18. sugar sugar fast efficient ATP ATP ATP ATP ATP ATP ATP ATP Efficient versus fast ATP production Success (ATP) of a population is determined by ATP yield

19. sugar ATP ATP ATP ATP Efficient versus fast ATP production Success in competition is determined by the ATP rate

20. Slow and efficient ATP production = cooperative behavior Fast and inefficient ATP production = selfish behavior Pfeiffer et al., Science, 2001 Evolutionary dilemma A population of efficient resource users has a high payoff Invaders with fast resource use have an even higher payoff Inefficient resource users increase in frequency Payoff for the population and each individual decreases

21. Evolution 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 use • Pfeiffer et al., Science, 2001

22. Experimental 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 possible

23. Yield and rate over time • Increase in rate • Initial increase in yield • No evidence for trade-off

24. Between population tradeoff No evidence for tradeoff

25. Within populations • Evidence for within population tradeoff in three populations Novak et al, AmNat 2006

26. Acknowledgements • 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 Fellowship