PIPs, Pattern Formation, and the Regulation of the Cytoskeleton

William Foster, PhD, MD

Department of Physics

University of Houston

How Cells Crawl

Some reasons why this problem is medically important

human polymorphonuclear leukocyte (neutrophil) on a blood film, crawling among red blood cells and "chasing" Staphylococcus aureus microorganisms

C. Cunningham, MD

Listeria

An INTRAcellular organism.Triggers actin polymerization at its trailing edge

Melanoma

Usually grows slowly but kills patients because it can spread to the liver, brainand other parts of the body.

Human plateletsChanges in cell shape are due to changes in

the cytoskeleton

What is the cytoskeleton?

• The “skeleton” of a cell

• Made up of actin– a protein– Simplified in this

talk

Regulation of the cytoskeleton

• Actin monomers “G-actin” are added to the growing end of an actin filament “F-actin”

• Monomers fall off of the other end

• This process is driven by ATP

J. Käs, PhD

What is happening at the membrane?

• Proteins (gelsolin and profilin) cap actin filaments and prevent further grown

• Removal of these proteins allows elongation of filaments

• These proteins are regulated by CLUMPS of highly charged lipids

What is happening at the membrane?

How is actin regulated?• The cell membrane plays a critical role both in the

regulation of the actin cytoskeleton as well as many other processes

• The actin polymers elongate at the membrane– Wouldn’t want them to elongate in the middle of the nucleus or

near the DNA

T Stossel, MD

Not part of this talk!

What do we know about how the cytoskeleton works?

F-actin (polymerized actin) in the lamellipodia is (fluorescence labeled) GFP-Actin.

Intermediate Summary

• Actin is a protein that polymerizes to form much of the cytoskeleton.

• Some proteins that regulate the cytoskeleton are regulated in part by lipids (PIP) in the cell membrane.

• We want to understand the effect of these highly charged lipids (PIP) on cell membranes.

• We will now talk about some soft condensed matter concepts and techniques that will allow us to study this problem.

Lipids

PCPI PI(4,5)P2

Why PIP

• Usually a few % of total lipid in biological membranes

• In vitro, several proteins require 10 mole%

• Specialized regions of the plasma membrane (caveoli or lipid rafts) may be highly enriched (>20%) in PI’s

• This clumping of PIs may be important

Imaging MembranesLens

1 mm

Inject solublefactors intoaqueous phase

PC Texas Red - PE NBD-PIP2

PA Janmey, PhD

What is the effect of these highly charged lipids (PIP) on cell

membranes?• Start with a lipid film

– contains varying quanties of PIP– Contains 1% fluorescent probe

• Image the lipid film

Line Tension

• There can be domains of different phases– say, differently ordered

phases

• Domains have line tension– The 2 dimensional analog of

surface tension

• Domains in a film are round because that lowers the energy of the system

• The bar is 100 microns

Changes in line tension with PIP concentration (0%, 10%, 50%, 90%)

Addition of NaCl to screen electrostatic interactions

The labeled lipid in the prior slides also contains PIP

Line tension no longer dominates the shape of lipid domains

The free energy of the system is:

'

'

2'

'

2

2

3

2

rr

dAdA

rr

dAdAdrF

Where:=the line tension is the dipole density is the charge density DJ Keller, JP Korb, HM McConnell, J

Phys Chem 91 (1987).DJ Keller, HM McConnell, VT Moy, J Phys Chem 90 (1986).HM McConnell, VT Moy, J Phys Chem 92 (1988).

Consider evaluating this equation on an ellipse

• Using Green’s theorem:

'

'

2'

'

2)(

222

rr

dAdA

rr

drdrdrAF

Where:= the electrostatic energy/unit area= the line tension = the dipole density = the charge density

Evaluating the energy in terms of the complete elliptical integrals

)(43

4

'

'

2)()(

222 kaKab

rr

drdrkEAF

where 12

a

bk

K(k) is the complete ellipital integral of the first kindE(k) is the complete ellipital integral of the second kind

Expand in powers of =ln(b/a)• F=e0+e22+e44+…• e4>0, otherwise the system is unstable.• If e2>0, the minimum is at =0• If e2<0, the minima are at +e2/2e4

• The system undergoes a second order phase transition from a phase where round domains minimize the energy to a phase where distorted domains are favored.

de

abababe

3/10

2/12

22

2/1

2

)(4ln2

2

)()(3

16

)(20

Summary

• The cytoskeleton is a rich topic for biological physics research.

• Powerful techniques have been developed to study this system.

• We can quantatively understand the effect of different constituents to the structure of cell membranes

Thank you

• Paul Janmey, PhD (U. Penn)

• Josef Käs, PhD (U. Leipzig)