Biofilm Dynamics

8/3/2019 Biofilm Dynamics

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The Dynamics of Growing Biofilm

J. P. Keener (Utah),

with lots of help from

Nick Cogan (Tulane), Jack Dockery (Montana SU)

and the NSF

U

U

The Power ofMathematics

The Excitement ofBiology


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Biofilms

Biofilm fouling of fiber filter

Placque on teeth

U

U

The Power ofMathematics

The Excitement ofBiology


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Some of the Interesting and Important Questions

P. Aeruginosa (on catheters, IV tubes, etc.)

How do gels grow?

Mucus secretion (bronchial tubes, stomach lining)

Colloidal suspensions of cells (cancer cell growth)

Gel Morphology (The cellular shape of sponges)

Why are gels important?

Protective capability

High viscosity (low washout rate) -for drugs, acid protection


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Biofilm formation inPseudomonas Aeruginosa

Wild type Biofilm mutant Mutant with autoinducer

Heterogeneous structures


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Quorum Sensing:

What is it?

How does it work?

Heterogeneous structures:

How do these cells use polymer gel (EPS) for locomotion?

What are the mechanisms of pattern (structure) formation?

Why is polymer gel so effective as a protective environment?


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Quorum Sensing inP. Aeruginosa

P. Aeruginosa

Major cause of hospital infection in the US.

Major cause of deaths in intubated CF patients, and IV fed patients.

Quorum Sensing: The ability of a bacterial colony to sense itssize and regulate its activity in response.

Examples: Vibrio fisheri, myxococcus, P. Aeruginasa

P. Aeruginosa in planktonic (non-colonized) form are non-toxic, but

as a biofilm, they are highly toxic and well protected by the polymer

gel in which they reside. However, they do not become toxic or beginto form polymer gel until the colony is of sufficient size to overwhelm

the immune system. Before this, they cannot be detected by

the immune system.


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Quorum sensing inP. Aeruginosa

Planktonic

Loosely Bound EPS secreting


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Wall Sensing inP. Aeruginosa

Wall Sensing: The ability of bacteria to differentiate in response toContact with a wall (the substratum).

Planktonic Loosely Bound EPS secreting


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Quorum Sensing:

What is it?

How does it work?


How do these cells use polymer gel for locomotion?




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The Biochemistry of Quorum Sensing

ALasR

lasR

lasI

LasR LasIA

3-oxo-C12-HSL

rsaL LasR

B

C4-HSL

RhrR B

RhlI

rhlI

GacA

Vfr

rhlR

RhlR


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An ODE Model

Variable Concentration

R LasR

A 3-oxo-C12-HSL

P Dimer complex

L LasI

S RsaL

r lasR mRNA

l lasI mRNA

s rsaL mRNA

lasI

LasI

ALasR

lasRLasR A

3-oxo-C12-HSL

rsaL LasR


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Modeling Biochemical Reactions with ODEs

dP

dt k

AR

Rate of production

kP

Rate of degradation

dL

dt kll

Rate of production

KLL

Rate of degradation

dl

dt

VmaxP

Kl Pk

ll

l LProduction of enzyme from mRNA

lasI

LasI

A R PBimolecularreaction

ALasR

LasR A3-oxo-C12-HSL

P lProduction of mRNA


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dP

dt kRARA kPP,

dR

dt kRARA kPP kRR k1r,

dA

dt kRARA kPP k2L kAA,

dL

dt k3l klL,

dS

dt k4s kSS,

ds

dt

VsP

KsP

kss,

dr

dt Vr

P

Kr P krr r0,

dl

dtVl

P

Kl P

1

KS S kll l0.

The full system of differential equations for the biochemistry:

lasI

LasI

ALasR

lasRLasR A

3-oxo-C12-HSL

rsaL LasR


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Modeling diffusion across cell membrane

Does this model exhibit quorum sensing?

Two ways to proceed:

1) Numerical simulation (but few of the 22 parameters are known)

2) Qualitative analysis

dA

dt kRARA kPP k2L kAA

dE

dt kEE

A

E

where is the cell volume fraction.

( )

(1)( )

1 (E A)

(A E)


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Quasi-steady state analysis: Assume that all fast variables are in quasi-steady state

dR

dtVR

P

KR P kRR R0,

dA

dtVA

P

KA P A0 d()A,

PkRARA

kP, d() kA

(

kE(1)

kE(1)).


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An even simpler model

Set R=A (which is not correct), to find

dA

dtVA

A2

KA A2 A0 d()A, d() kA

(

kE(1)

kE(1)).


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A Simple Model for Wall Sensing

V

t G(V,A), V

7

A

t F(A,V) d(E(x L) A),

E

t DE

2E

x2 kEE d(x L)(A E)( 0)

Cells are immobile, so internal variables A and V do not diffuse,

but extracellular autoinducer E diffuses (rapidly) so

L

E

x


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A Simple Model for Wall Sensing - contd

V

t G(V,A), V

7

A

tF(A,V)

d

p

1 pA,

pD

d(1 tanh(

DL))

We can solve for E(x=L) assuming a quasi-equilibrium, to find

Since p decreases as L 0, this has a chance of up-regulating for small L.


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A Proper (PDE) Model

V

t G(V,A), V

7

A

tF(A,V)

(EA),

E

t

2E kEE

1(A E),

Cells are immobile, so internal variables A and V do not diffuse,

but extracellular autoinducer E diffuses so

on the domain , subject to the (Robin) boundary condition

nDEE0, on


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Autoinducer with fixed colony size, variable density


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Autoinducer concentration; fixed density, variable

size colony

QuickTime and aAnimation decompressor

are needed to see this picture.


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Heterogeneous Structures





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A Hydrogel Primer

What is a hydrogel?A tangled polymer network in solvent

Examples of biological hydrogels:

Micellar gels

Jello (a collagen gel ~ 97% water)

Extracellular matrixBlood clot

Mucin - lining the stomach, bronchial tubes, intestines

Gycocalyx - lining epithelial cells of blood vessels

Sinus secretions

Other examples of gel-like structures

Cell colonies - colloidal suspensions

Gel morphology - sponges, jellyfish


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A Hydrogel Primer - II

Function of a biological hydrogelDecreased permeability to large molecules

Structural strength (for epithelial cell walls)

Capture and clearance of foreign substances

Decreased resistance to sliding/gliding

High internal viscosity (low washout)

Important features of gels

Usually comprised of highly polyionic polymers

Often exhibit large volumetric changes

eg. Highly compressed in secretory vessicle and expand rapidly

and dramatically on release

Can undergo volumetric phase transitions in response to ionicconcentrations (Ca++, H+), temperature, ..

Volume is determined by combination of attractive and

repulsive forces:

-- repulsive electrostatic, hydrophobic

-- attractive, hydrogen binding, cross-linking


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How gels grow

Polymerization/deposition

(blood clots)

Secretion

High Ca++

Ca++ Na+

Highly condensedDecondensed (swelled)

Interesting facts:

- Diffusion coefficient can vary substantially as a function of Ca++

- Expansion does not occur in distilled water.


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Modeling Biofilm Growth

A two phase material with polymer volume fraction

t (Vn) gn Network Phase

(EPS)

(1)

t (Vs(1)) 0 Solute Phase

b

t (Vnb) gb Bacterial Concentration

(1)u

t ((1)(VsuDu) gu Resource


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Force Balance

Solute phase hf(1)(Vn Vs)(solute-network friction)

(

n(V

n V

n

T))

(viscosity)

(pressure)

(1)p 0

Network phase

(pressure)

p0

(solute-network friction)

hf

(1)(Vn

Vs

)

(osmosis)

()

Incompressibility

(VnVs(1)) gnt (Vn) gn (1

)

t (Vs(1)) 0

Remark: Models of this form for the network phase have been used by lots of people

(Dembo and He, Lubkin and Jackson, Wolgemuth, Oster, Mogilner, )

Remark 2: A better model might keep track of Ca++ and Na+ concentrations as well


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Osmotic Pressure

What is the meaning of the term

In some formulations

(osmosis)

() ?

()F'() where F()

F() ()

is the Free Energy

'()> 0 gives expansion (swelling)

< 0 gives contraction (deswelling){() kT(k1(1)ln(1)(1)) From Flory-Huggins theory


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Phase Separation

Double-welled potentials give phase transitions and phase separation, similar to Cahn-Hilliard

()

(x)

x

To maintain an edge, () must be of the form ()2G()

()

0

0

0

(x)

x

(This is a theorem)


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Movement by Swelling

QuickTime and a

Animation d ecompressorare needed to see this picture.


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Propulsion by Swelling

QuickTime and a

Animation decompressorare needed to see this picture.


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No gel; no swell

QuickTime and a

Animation decompressorare needed to see this picture.


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Heterogeneous Structures





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Limited Resource Instability

Remark: This instability does not occur in a resource rich environment.


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Channeling

A Pouiseille flow


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Channeling


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Channeling


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Conclusions

Quorum Sensing:

What is it? A biochemical switch

How does it work? Extracellular autoinducer fails to diffuse away.


How do these cells use polymer gel for locomotion? Expansion byswelling

What are the mechanisms of pattern (structure) formation? Limited resource fingering Friction driven channeling

Others?(Is sloughing related to a Kelvin-Helmholz instability?)

Why is EPS so effective as a protective environment? Restricted pore size, chemical reactivity???


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More Questions (than answers)

Why does P.Aeruginosa attack only immune-compromised individuals?

(burn victims, post-surgery)

Why does P.Aeruginosa find a ready host in CF patients? (Decreased diffusion???)

What is it about the CFTR mutation in CF patients that makes their mucin so thick?

Is there cross talk between P. Aeruginaosa and other pathogens and if so, how?

Biofilm Dynamics

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