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

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

Human bodies contain complex microbial communities Germ stories by Kornberg Eg intestine contains ~10 14 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 R. Ley et al Cell 124, 837–848 (2006)

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?

Carbon CycleSulphur Cycle Organic acids and Sulphur oxidisers CO 2 fixed into SO 4 2- <- H 2 S organic matter Cell death Organic acids andSulphur reducers CO 2 released by SO 4 -> H 2 S decomposers Our model system: the Winogradsky column O2O2O2O2 Aerobic water Anaerobic water Anaerobic sediment H2SH2S Aim: use this system to learn about microbial community dynamics

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

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

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

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

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

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

A highly simplified model Parameters Substrate inflow rates q 1, q 2 Growth parameters v max,K m,f for both populations Death rates  1,  2 for the microbes Waste product of microbe 1 is substrate for microbe 2 Waste product of microbe 2 is substrate for microbe 1 Variables Microbe population sizes n 1 and n 2 Substrate concentrations s 1 and s 2

Results: “Boom-bust” cycles (only substrate 1 supplied) 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

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)

Deterministic Stochastic Noise can cause persistent oscillations

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

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?

The End

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

Results: “Boom-bust” cycles (only substrate 1 supplied) v max,1 = 24.9 umoles carbon / bug / litre / day v max,2 = 5.81 umoles carbon / bug / litre / day K m,1 = 6.24 umoles carbon / litre K m,2 = 2.49 umoles carbon / litre f 1 = 0.76 f 2 = 0.64  1 = 0.1 X 10 9 bugs / litre / day  2 = 0.1 X 10 9 bugs / litre / day q 1 = 10 umoles C / litre / day q 2 = 0 Microbe 1 Microbe 2 Substrate 1 Substrate 2 “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