Stochastic effects for interacting microbial populations

1. Stochastic effects for interacting microbial populations Rosalind Allen School of Physics and Astronomy, Edinburgh University eSI “Stochastic effects in microbial infection” September 29th 2010

2. Andrew Free School of Biological Sciences Edinburgh University Eulyn Pagaling Fiona Strathdee Bhavin Khatri Jana Schwarz-Linek Richard Blythe Mike Cates Wilson Poon

3. Human bodies contain complex microbial communities • Eg intestine contains • ~1014 microbes, ~400 species • Various chemical niches • (fermentation, methanogenesis, sulphate reduction) • competition for resources • interaction with host • interaction with environment via immigration and washout • Infecting microbes must compete with normal flora Germ stories by Kornberg R. Ley et alCell 124, 837–848 (2006)

4. General questions about microbial communities • How do complex microbial communities get established? • How resilient are communities to disturbance (eg antibiotic treatment) • How likely are invaders to succeed? • How stochastic are these processes? Relevant to understanding infection?

5. O2 Aerobic water Anaerobic water Anaerobic sediment H2S Our model system: the Winogradsky column Carbon CycleSulphur Cycle Organic acids and Sulphur oxidisers CO2 fixed into SO42- <- H2S organic matter Cell death Organic acids and Sulphur reducers CO2 released by SO4 -> H2S decomposers Aim: use this system to learn about microbial community dynamics

6. Which microbes are present? Denaturing gradient gel electrophoresis (DGGE) • Extract DNA from the community • Use PCR to amplify 16S rRNA gene fragments ~200bp • Run on gel, gradient of denaturant • different sequences stop in different places • -> fingerprint of the community • “one band = one 16S rRNA gene fragment” • Also analyse community function from redox gradient top -> bottom

7. Loch Leven (6 sites) Trossachs Lochs Blackford pond Sample after 16 weeks 36 sterilised microcosms Inoculate with different communities in triplicate Blackford Pond sediment + nutrients 1. How do communities colonise new environments? Put different communities in the same environment. Do they develop differently or the same?

8. Results: the communities “remember” their origin Measure similarity between DGGE fingerprints (Bray-Curtis) -> similarity matrix -> cluster analysis (MDS) Microcosm communities tend to cluster according to geographical origin

9. 1 2 3 1 2 3 But identical communities can give different outcomes In function (redox) and community composition

10. In progress: Are some aspects of the community more stochastic than others? Are other aspects more strongly dependent on initial community?

11. Modelling interacting microbial populations Example: Cycling of carbon by methanogens and methanotrophs: Methanogens Carbon dioxide + hydrogen/acetate -> methane Methanotrophs Methane + oxygen -> carbon dioxide

12. A highly simplified model Waste product of microbe 1 is substrate for microbe 2 Waste product of microbe 2 is substrate for microbe 1 Variables Microbe population sizes n1 and n2 Substrate concentrations s1 and s2 Parameters Substrate inflow rates q1, q2 Growth parameters vmax,Km,f for both populations Death rates m1, m2 for the microbes

13. Results: “Boom-bust” cycles (only substrate 1 supplied) Microbe 1 Microbe 2 • Inflow of substrate 1 causes population boom of microbe 1 • Microbe 1 produces substrate 2 • This causes population boom of microbe 2, accompanied by microbe 1 • Eventually steady state is reached

14. What happens when we include noise? Deterministic equations is the vector (n1,n2,s1,s2) Equivalent stochastic equations is a Gaussian white noise vector zero mean, unit variance describes coupling between fluctuations of substrate and microbial populations (can derive from Master Equation)

15. Deterministic Stochastic Noise can cause persistent oscillations

16. To do: Develop more realistic models for microcosm communities Can we predict effects of changing environmental conditions? (eg cellulose)

17. Conclusions Microbial community development has significant stochasticity We’re trying to understand it better using model microcosms Modelling may help us track down the origin of the variability How to relate this to infection? Gut communities may be metabolically simpler than our microcosms Theoretical models for community dynamics in the gut? Connection with models of individual species growth and interactions? (eg phase variation + interspecies interactions…) Do suitable experimental “microcosm” systems exist?

18. The End

19. Growth of a microbial population Microbe population size n(t) Substrate concentration s(t) Waste product concentration w(t) Vmax = maximal substrate consumption rate / bacterium Km = substrate concentration for half maximal growth f = fraction of substrate carbon used for growth c = carbon / bacterium

20. Results: “Boom-bust” cycles (only substrate 1 supplied) • “Boom-bust” dynamics • Inflow of substrate 1 causes population boom of microbe 1 • Microbe 1 produces substrate 2 • This causes population boom of microbe 2, accompanied by microbe 1 • Eventually steady state is reached Microbe 1 Microbe 2 vmax,1 = 24.9 umoles carbon / bug / litre / day vmax,2 = 5.81 umoles carbon / bug / litre / day Km,1 = 6.24 umoles carbon / litre Km,2 = 2.49 umoles carbon / litre f1 = 0.76 f2 = 0.64 m1 = 0.1 X 109 bugs / litre / day m2 = 0.1 X 109 bugs / litre / day q1 = 10 umoles C / litre / day q2 = 0 Substrate 1 Substrate 2