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THE ROLE OF MOTILITY AND NUTRIENTS IN
BACTERIAL COLONY FORMATION AND
COMPETITION
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Silogini Thanarajah
Guest Lecture
OUTLINES
Introduction
Single
General model
competition
Mathematical theorems
Agar
Numerical simulation
Liquid
Conclusion
Extended model
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INTRODUCTION
Bacterial competition and colony formation are an important
part in medicine and plant roots colonization.
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Bacterial colonies.
Different colony shapes.
Many existing theoretical studies
assume that bacteria have to move
in the direction of nutrients.
“Random walk” movement observed
for bacteria in the absence of
chemotaxis .
Undirected motility must have
evolved before chemotaxis.
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Directed movement (chemotaxis)
and undirected movement.
The undirected motility was
thought to be not important.
Undirected motility can be more
important in resourcehomogeneous environments.
When the chemicals are not
chemotactic stimulus.
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Wei et al.
PDE model in the explicit consideration of nutrient and
different bacterial strains characterized by motility.
Two types of bacterial strains: motile and immotile
Agar vs liquid
Motile: Moving or having power to move spontaneously.
Immotile: Almost not moving or lacking the ability to move.
Agar media: A dried hydrophilic, colloidal substance
extracted from various species of red algae; used in
solid culture media for bacteria and other
microorganisms.
Liquid media:Chemically defined basal liquid media are
used to provide nutrients for cell growth in research.
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RANDOM VS BIASED RANDOM WALK
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Reaction - diffusion system
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OTHER BACTERIA MODELS

Lauffenburger model

Mimura model
Wei model
Tyson model
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EFFECT OF CHEMOTAXIS IN COMPETITIONCONFINED NONMIXED
Focusing on the influence of the random motility (μ) and the chemotaxis(Χ)
There is a minimum value of Χ necessary for a chemotactic population to
have a competitive advantage over an immotile population in a confined
nonmixed system.
Chemotaxis does not automatically provide a competitive advantage
Conclusion:
(1)Both die out; species 1 exist alone, species 2 exist alone; both coexist
(2) well-mixed: slower growing can coexist and even exist alone if it
possesses sufficiently superior motility and chemotaxis.
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EFFECT OF RANDOM MOTILITY IN
COMPETITION-CONFINED NONMIXED
Assumption:
 differing growth kinetic and motility properties
 Diffusible growth-rate-limiting chemical nutrient entering from the boundary
Conclusion:
(1)Species 1 survives, 2 dies out ; species 2 survives, 1 dies out;
both coexist
(2) Smaller maximum growth rate may grow to a larger population than he other
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AGAR METHOD VS LIQUID METHOD
(BRUCE LEVIN’S GROUP EXPERIMENT)
agar
day
motile
Non-motile
Observation from experiments results:
In agar, the motile strain has higher total density.
In liquid, both have the same total density.
The population dynamics of bacteria in physically structured habitats
and the adaptive virture of random motility, Wei et al., PNAS
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GENERAL MODEL- REACTION-DIFFUSION MODEL
Where hi(N)=αiN or αiN/(ki+N) satisfy hi(0)=0,hi’(t)>0 and hi’’(t)≤0
Bi – Density of bacterial strains;
N- Density of nutrient
Di –Diffusion coefficients;
δi – Mortality rates
Ϫi – The yield coefficients;
αi – resource uptake rate
Ki- Half-saturation constants (nutrient uptake efficiencies)
with initial and zero flux boundary conditions.
B1-motile strain
B2-immotile strain
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SINGLE BACTERIAL
SPECIES
Bacteria-Substrate model
without nutrient diffusion
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Spatially uniform steady states (1-D,2-D)
Spatially uniform steady states: independent of time and space
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MATHEMATICAL THEOREMS
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COMPETITION CASE - AGAR
(5)
These bacterial strains are genetically identical except
for their motility:
α1=α2, δ1=δ2, ϫ1=ϫ2, k1=k2 with D1>>D2
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COMPETITION CASE - LIQUID
(6)
These bacterial strains are genetically identical except
for their motility:
D3 – diffusion constant for nutrient.
α1=α2, δ1=δ2, ϫ1=ϫ2, k1=k2 with D3 >>D1>>D2
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Theorem III.4. The equilibrium line (0,0,ζ), where ζ is an
arbitrary, is globally attracting.
Theorem III.5. The necessary condition for existence of
traveling wave solutions for (5) is
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Numerical Simulations for 1-dimensional space-Agar
(Motile vs immotile)
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MOTILE STRAIN AND IMMOTILE STRAIN
TOTAL POPULATION OVER THE SPACE
о-motile
■-immotile
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Numerical Simulations for 1-dimensional space-Liquid
(Motile vs immotile)
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Motile strain and immotile strain total population
over the space
day
о-motile
■-immotile
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AGAR CASE VS LIQUID CASE
In agar, the density of the motile strain is high on
the boundary of the petri dish while the density of
the immotile strain is high in the middle of the petri
dish.
In liquid, bacterial motility is not that important
because liquid nutrient moves almost infinitely fast
compared to bacterial movement.
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Numerical simulations for 2-dimensional space-Agar
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CONCLUSION
Bacteria always go extinct due to lack of nutrient after a long time
while some nutrient will always be remaining.
From existence of traveling wave solutions:
As the motility of motile bacteria increases, traveling waves
propagate faster, thus it takes less time for motile bacteria to occupy
the non-center region of petri dish.
In agar media the motile strain is dominant in total density, while in
liquid media bacterial motility is not that important.
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In 2-D agar case motile strain is dominant in total density.
Simulation results are consistent with Bruce Levin’s group
experimental results.
Simulation and experimental results illustrate the advantage of
undirected motility in agar media and in absence of chemotaxis.
Undirected motility gives bacteria with a selective advantage at
which they compete in nutrient-limited enivironment.
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Competition of fast and slow movers
for renewable and diffusive resource
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INTRODUCTION
We extend the model to incorporate renewal
diffusive resource to discuss the competition of
slow and fast movers.
The environment is assumed to be continuous but
not homogeneous.
species are genetically identical except their
moving speeds.
The resource uptake functions are assumed to be
linear or nonlinear.
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THE MODEL
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OTHER RD MODELS


Gray-Scott Model
Tsoularis Model

Inkyung Inn Model

J Dockery et. Al model
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First we consider J.Dockery et.al model:
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Conclusion:
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Biologically, evolution always favors the slowest diffuser.
CONVERT OUR MODEL TO THEIR MODEL
FORMAT
Same as Dockery model
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SIMULATION RESULTS : LINEAR, NONLINEAR
h(N)=αN
h(N)=αN
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h(N)=αN/k+N
Red-fast
Black-slow
h(N)=αN/k+N
OBSERVATIONS
Linear case:
The fast mover goes extinct but the slow mover
survives at a positive constant level, or both
species go extinct.
Non-linear case: (New outcomes)
The fast mover goes extinct but the slow mover
survives at oscillations, or both species survive at
oscillations.
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BIFURCATION DIAGRAM
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α2
Nutrient uptake rate of fast mover (α1)
ACKNOWLEDGEMENTS
Dr.Hao Wang, Department of Mathemetics
& Statistical Sciences, University of Alberta
Dr.Bruce Levin, Emory University
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THANK YOU!
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