evolutionary dynamics of metabolic systems
DESCRIPTION
Evolutionary Dynamics of Metabolic Systems. Thomas Pfeiffer, Program for Evolutionary Dynamics Math 243, 21.04.2009. Overview. Crossfeeding Introduction Partial vs. complete degradation of resources and the optimization of metabolic pathways - PowerPoint PPT PresentationTRANSCRIPT
Evolutionary Dynamics of Metabolic Systems
Thomas Pfeiffer, Program for Evolutionary Dynamics
Math 243, 21.04.2009
Overview
1. Crossfeeding• Introduction
• Partial vs. complete degradation of resources and the optimization of metabolic pathways
• Population dynamical model for the evolution of crossfeeding
2. Rate vs. Yield • Background
• Game theory
• Experimental Evidence
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
Crossfeeding
What 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 minimized
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
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
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!
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 Xk
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
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
Simulation results
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!
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
Trade-offs between ATP rate and yield
Thermodynamic trade-off
Trade-off between rate and yield of ATP production
Linear flux-force relation: JS ~ ∆GJATP~ nATP(∆GSP- nATP ∆GATP)
Conserved as ATP
Drives reaction rate
Free energy difference ∆GSP
When 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
sugar
fast
ATP
ATP
ATP
ATP
sugar
efficient
ATP ATP
ATP ATP
Efficient versus fast ATP production
Success in competition is determined by the ATP rate
sugar
ATP ATP
ATP ATP
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
Slow and efficient ATP production = cooperative behavior
Fast and inefficient ATP production = selfish behavior
Pfeiffer et al., Science, 2001
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
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
Yield and rate over time
• Increase in rate
• Initial increase in yield
• No evidence for trade-off
Between population tradeoff
No evidence for tradeoff
Within populations
• Evidence for within population tradeoff in three populations
Novak et al, AmNat 2006
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