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, brain
and other parts of the body.
Human platelets
Changes 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 “Gactin” are added to
the growing end of an
actin filament “Factin”
• 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
What is happening at the
membrane?
• These proteins are
regulated by
CLUMPS of highly
charged lipids
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
PC
PI
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 Membranes
Lens
PC
Texas Red - PE
NBD-PIP2
1 mm
PA Janmey, PhD
Inject soluble
factors into
aqueous phase
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:
F    dr 

2
2

dA' dA

2
dA' dA

3

2
r  r'
r  r'
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
dr
'
dr

F  A  (   2 )  dr 


2
r  r' 2
Where:
 = the electrostatic energy/unit area
L = the line tension
 = the dipole density
 = the charge density
dA' dA
 r  r '
Evaluating the energy in terms of
the complete elliptical integrals
2
2
dr
'
dr
4

ab 4aK (k )
F  A  (   2 ) E (k ) 


2
r  r ' 3
2
where k   b   1
 
a
K(k) is the complete ellipital integral of the first kind
E(k) is the complete ellipital integral of the second kind
Expand in powers of D=ln(b/a)
•
•
•
•
•
F=e0+e2D2+e4D4+…
e4>0, otherwise the system is unstable.
If e2>0, the minimum is at D=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.
 4(ab)1/ 2 
2 (ab)1/ 2 
 2 (ab) 
2
2
 3(   ) 
  2 ln  10 / 3 
e2  0 
16
2 

 e d 
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)