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