The Dynamics of Growing Biofilm: 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 of Mathematics The Excitement of Biology


Biofilms: Biofilms Biofilm fouling of fiber filter Placque on teeth U U The Power of Mathematics The Excitement of Biology


Some of the Interesting and Important Questions : 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


Biofilm formation in Pseudomonas Aeruginosa: Biofilm formation in Pseudomonas Aeruginosa Wild type Biofilm mutant Mutant with autoinducer Heterogeneous structures


The Dynamics of Growing Biofilm : The Dynamics of Growing Biofilm 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?


Quorum Sensing in P. Aeruginosa : Quorum Sensing in P. 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 its size 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 begin to 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.


Quorum sensing in P. Aeruginosa : Quorum sensing in P. Aeruginosa Planktonic Loosely Bound EPS secreting


“Wall Sensing” in P. Aeruginosa : “Wall Sensing” in P. Aeruginosa Wall Sensing: The ability of bacteria to differentiate in response to Contact with a wall (the substratum). Planktonic Loosely Bound EPS secreting


The Dynamics of Growing Biofilm : The Dynamics of Growing Biofilm Quorum Sensing: What is it? How does it work? Heterogeneous structures: How do these cells use polymer gel for locomotion? What are the mechanisms of pattern (structure) formation? Why is polymer gel so effective as a protective environment?


The Biochemistry of Quorum Sensing: The Biochemistry of Quorum Sensing


An ODE Model: An ODE Model lasI LasI A 3-oxo-C12-HSL rsaL LasR


Modeling Biochemical Reactions with ODE’s: Modeling Biochemical Reactions with ODE’s


Slide13: The full system of differential equations for the biochemistry:


Slide14: 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


Slide15: Quasi-steady state analysis: Assume that all “fast” variables are in quasi-steady state


An even simpler model: An even simpler model Set R=A (which is not correct), to find


A Simple Model for Wall Sensing: A Simple Model for Wall Sensing Cells are immobile, so internal variables A and V do not diffuse, but extracellular autoinducer E diffuses (rapidly) so L E x


A Simple Model for Wall Sensing - cont’d: A Simple Model for Wall Sensing - cont’d 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.


A Proper (PDE) Model: A Proper (PDE) Model 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 on


Autoinducer with fixed colony size, variable density: Autoinducer with fixed colony size, variable density


Autoinducer concentration; fixed density, variable size colony: Autoinducer concentration; fixed density, variable size colony


Heterogeneous Structures: Heterogeneous Structures How do these cells use polymer gel for locomotion? What are the mechanisms of pattern (structure) formation? Why is polymer gel so effective as a protective environment?


A Hydrogel Primer: 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 matrix Blood 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


Fibrin Network (Blood Clot): Fibrin Network (Blood Clot)


A Hydrogel Primer - II: A Hydrogel Primer - II Function of a biological hydrogel Decreased 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 ionic concentrations (Ca++, H+), temperature, .. Volume is determined by combination of attractive and repulsive forces: -- repulsive electrostatic, hydrophobic -- attractive, hydrogen binding, cross-linking


How gels grow: How gels grow Polymerization/deposition (blood clots) Secretion High Ca++ Ca++ Na+ Highly condensed Decondensed (swelled) Interesting facts: - Diffusion coefficient can vary substantially as a function of Ca++ - Expansion does not occur in distilled water.


Modeling Biofilm Growth: Modeling Biofilm Growth


Force Balance: Force Balance Solute phase Network phase Incompressibility 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


Osmotic Pressure: Osmotic Pressure What is the meaning of the term In some formulations ? where is the Free Energy From Flory-Huggins theory


Phase Separation: Phase Separation Double-welled potentials give phase transitions and phase separation, similar to Cahn-Hilliard To maintain an edge, must be of the form 0 0 0 (This is a theorem)


Movement by Swelling: Movement by Swelling


Propulsion by Swelling: Propulsion by Swelling


No gel; no swell: No gel; no swell


Heterogeneous Structures: Heterogeneous Structures How do these cells use polymer gel for locomotion? What are the mechanisms of pattern (structure) formation? Why is polymer gel so effective as a protective environment?


“Limited Resource” Instability: “Limited Resource” Instability Remark: This instability does not occur in a resource rich environment.


Channeling: Channeling A Pouiseille flow


Slide37: Channeling


Channeling: Channeling


Conclusions : Conclusions Quorum Sensing: What is it? A biochemical switch How does it work? Extracellular autoinducer fails to diffuse away. Heterogeneous structures: How do these cells use polymer gel for locomotion? Expansion by swelling 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???


More Questions (than answers): 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?