Probing Membrane Electrostatics with the Atomic Force Microscope

1

Probing Membrane Electrostatics with the Atomic
Force Microscope
Jason H. Hafner Dept. of Physics Astronomy Rice
University
2
Lipids in Biological Membranes - not just a
solvent!
Singer, Nicolson, Science 175, p720 (1972)
3
Membrane Electrostatics
DMPC
C
N
C
C
C
C
O
P
O
O
O
C
C
C
O
O
C
C
O
O
Complex Electrostatic Environment
-more than one atom (no Hamiltonian!)
-large density of charges and dipoles
-10s mV potential across 6 nm!
-large variation in dielectric constant
Review Cevc, Biochimica et Biophysica Acta v.1031
p.311 (1990)
C
C
4
Statistical Mechanical Molecular Simulations
Group - Stockholm
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Membrane Potentials
1. Transmembrane Potential
-The potential difference between two bulk
phases. -Membrane simply separates two
electrolytes. -Transmembrane potential
determined by the Nernst equation
c1
c2
y(x)
x
6
Membrane Potentials
2. Surface Potential
-Created by charges on lipids at the lipid-water
interface. -Surface potential can be described
by Gouy-Chapman double-layer theory (at large
distances from the interface) -Surface
potential controls protein adsorption and can
regulate membrane transport.
y(x)
x
7
Membrane Potentials
3. Dipole Potential
-Molecular dipoles of water and lipid create a
net moment into the bilayer. -Dipole potentials
observed by difference in translocation rate of
anionic and cationic hydrophobic ions. -Dipole
potentials not easily measured or calculated!
y(x)
x
8
Biological Atomic Force Microscopy
AFM provides nanometer-scale images of
biomolecules and biological interfaces in fluid
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Biological Atomic Force Microscopy
AFM provides nanometer-scale images of
biomolecules and biological interfaces in fluid
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AFM A Unique Probe of Membrane Electrostatics
Noninvasive
High Resolution
Quantitative?
Elucidate Molecular Details?
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Electrostatic Forces in the AFM
Gouy-Chapman Theory
e80
Assumptions
-surface charge is smeared in a thin plane.
-ions are point particles.
x
-water is a dielectric continuum
Start with the Poisson-Boltzmann Eqn
Counterions are attracted to the charged surface
to form the electric double layer.
Assume small potentials to linearize the equation
for a simpler solution
The potential falls off exponentially with a 1/e
distance called the Debye Length.
Although linear G-C theory only applies for ylt25
mv, it usually works up to 50 mV.
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Electrostatic Forces in the AFM
Parsegian and Gingell (1972)
Used linear G-C theory to calculate the pressure
between two dissimilarly charged plane
surfaces. ..this result is rigorous
at all distances as long as ionic energies at the
surfaces are small compared with thermal
energies. It is also a good approximation for
higher surface potentials when the separation
distances are large d/l gt 1.
s1
d
s2
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Electrostatic Forces in the AFM
H. J. Butt (1991)
Simplified P-G equation by assuming the
separation is larger than the Debye length
Next, integrated this plane-plane pressure over a
plane-sphere to get the tip-sample force. This
requires that the tip radius be larger than the
separation, which simplifies the solution to
To sum up R gtgt d gt l l 3 to 10 nm (for 1
to 10 mM electrolyte) The validity of this
expression has been confirmed by AFM measurements
on inorganic substrates.
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AFM of Lipid Bilayer Membranes
1. Prepare vesicles of the lipid or lipid
mixture.
3. Scan supported membranes by AFM.
2. Expose to mica to promote vesicle fusion.
The AFM measures the topography of supported
lipid membranes with 10s nm to 10s micron
diameter. gives an accurate height of 5
nm. does not resolve individual lipids since
they are too small and move too fast.
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Electrostatic Forces Over Lipid Membranes
PC
PS
C
N
C
C
Si3N4 (-)
Si3N4 (-)
C
C
O
TAP
P
O
O
O
C
C
C
O
O
C
C
O
Although G-C theory flattens the complex lipid
head-group region into a thin plane, force curves
over lipids exhibit simple exponential decay with
correct Debye length and polarity.
Anionic lipids
Tip-Sample Force
Cationic lipids
Tip-Sample Separation
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Quantitative Electrostatics
Butt
With AFM parameters
DV
Calibrated z-position
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Quantitative Electrostatics
Butt
With AFM parameters
Added-Mass Method
Cleveland et al, Rev. Sci. Inst. 64, p1868 (1993)
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Quantitative Electrostatics
Butt
With AFM parameters
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Quantitative Electrostatics
Butt
With AFM parameters
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Quantitative Electrostatics
Butt
With AFM parameters
Use a Known Reference Surface like alumina? You
will get an answer that is the right order of
magnitude but surface chemistry is highly
sensitive to chemical composition and history.
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Quantitative Electrostatics
Butt
With AFM parameters
Use an Identical Reference Surface!
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Quantitative Membrane Charge
Increasing PS
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Numerical Solution
Solve full Poisson Boltzmann Equation for 11
electrolyte in the tip sample region
stip, R
electrolyte
ssample
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Numerical Solution
Calculation yields the surface potentials for a
given tip and sample charge density
Changing tip force is due to change in osmotic
pressure
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Numerical Solution
Numerical solution matches Butts equation for
large separations and fits data to a smaller
separation.
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Quantitative Membrane Charge (Numerical)
Increasing PS
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Electrostatic Mapping with the AFM
- Fluid Electric Force Microscopy -
Johnson et al, Langmuir 19, p10007 (2003)
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Lipid Rafts
Liquid-disordered fluid phase (mostly DOPC)
111 DOPCSMChol
Liquid-ordered raft phase (rich in SM and Chol)
mica
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Electrostatic Mapping of Lipid Rafts
Liquid-disordered fluid phase (mostly DOPC)
Liquid-ordered raft phase (rich in SM and Chol)
Rafts are more positive than fluid phase. Why?
PC
SM
Chol
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Molecular Details
Stategy 1. Take a closer look.
DOPC
but at very close range Electrostatics vdW
hydration membrane fluctuation
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Molecular Details
Stategy 2. Study the effective surface
potential
DOPC
and how it varies with electrolyte conditions
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Dependence on Debye Length
Sources of Surface Potential 1. Charged
Impurities s constant 2. Selective Stern
Layer s determined by Langmuir Isotherms 3.
Dipole Potential s due to finite thickness of
dipole layer
Belaya et al, Langmuir 10, p2010 (1994)
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Dependence on Debye Length
Sources of Surface Potential 1. Charged
Impurities s constant 2. Selective Stern
Layer s determined by Langmuir Isotherms 3.
Dipole Potential s due to finite thickness of
dipole layer
0.05
DOPC
0.04
mica
0.03
Prefactor A
0.02
0.01
0
3
4
5
6
7
8
9
10
Debye Length nm
Belaya et al, Langmuir 10, p2010 (1994)
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Conclusions
The AFM is a unique probe of membrane
electrostatics! Expression derived for
tip-sample interactions based on G-C theory gives
correct dependence on charge density, Debye
length, and separation, but is not
quantitative. Numerical fits to AFM force curves
enable electrostatic analysis at higher surface
potentials, for smaller tip-sample separations,
and for sharper tips. The AFM can image the
surface potential of membranes and single
molecules at 40 nm resolution. AFM analysis
allows one to study Stern layer and dipole
potential effects with minimal perturbation of
the membrane.
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Acknowledgements Yi Yang Katie Mayer NSF Beckman
Foundation