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 FreeSchool of Biological SciencesEdinburgh University

Eulyn PagalingFiona Strathdee

Bhavin Khatri

Jana Schwarz-LinekRichard BlytheMike CatesWilson Poon

Human bodies contain complex microbial communities

Germ stories by Kornberg

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

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 Cycle Sulphur Cycle

Organic acids and Sulphur oxidisersCO2 fixed into SO4

2- <- H2Sorganic matter

Cell death

Organic acids andSulphur reducersCO2 released by SO4 -> H2Sdecomposers

Our model system: the Winogradsky column

OO22

Aerobicwater

Anaerobicwater

Anaerobicsediment

H2S

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 microcosmsInoculate with different communities in triplicate

Sample after 16 weeks

Blackford Pondsediment + 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

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 q1, q2

Growth parameters vmax,Km,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 n1 and n2

Substrate concentrations s1

and s2

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?

XAdt

Xd

Deterministic equations

is the vector (n1,n2,s1,s2)

WXAdt

Xd

X

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)

W

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)

ConclusionsMicrobial 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

)(

)(/)( max

tsK

tsvcftn

dt

dn

m

Vmax = maximal substrate consumption rate / bacterium

Km = 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)

)(

)()( max

tsK

tsvtn

dt

ds

m

dt

dsf

dt

dw 1

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

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

1 = 0.1 X 109 bugs / litre / day

2 = 0.1 X 109 bugs / litre / day

q1 = 10 umoles C / litre / day

q2 = 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