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