Interactions between lipid membranes

Horia I. PetracheDepartment of Physics

Indiana University Purdue University Indianapolis, USA

www.iupui.edu/~lab59

Support:

IUPUI Biomembrane Signature Center IUPUI Integrated Nanosystems Development Institute Alpha 1 Foundation NIH Generous student volunteering

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oily tails

Lipid molecules have two parts

dipolar head

15- 25 Å

5- 7 Å

Lipids aggregate and form bilayers (membranes)

Visible by X-ray depending on electron density.

~ 40 Å

liquid water

Zero net density contrast but...

10𝑒30 𝐴3=0.333𝑒 /Å3

lipid400𝑒

1200 𝐴3 =0.333𝑒 /Å 3

Electron densities at T = 300 K

lipid headgroup160𝑒

320 𝐴3=0.5𝑒 / 𝐴3

lipid tails9𝑒

50 𝐴3 =0.18𝑒 / 𝐴3

compared to 0.333 e/ Å3 for water

Electron densities at T = 300 K

=> can see them!

X-ray scattering from unoriented lipid membranes

X-ray scattering from oriented lipid membranes

Biophys. J. 2005, J. Lipid Research, 2006

2q1Incident beam

MLV sample

Bragg rings seen on the detector

2q2Scattered beam(s)

X-ray scattering from multilayers (1D randomly oriented lattice)

q hD sin2Bragg’s Law

q hD sin2Bragg’s Law

With D = 60 Å, = 1.54 Å, and h = 1, obtain

q = 0.74o (small angle)

=> Need a small x-ray machine

angle

x-ray source (tube)

detectorsample chamber

Wavelength = 1.54 Å (Cu source)

Sample-to-detector distances: 0.15 m, 0.6 m, and 1 m

Lattice spacings: 8 Å to 900 Å

Fixed anode Bruker Nanostar U, 40 kV x 30 mA.

Electron density of a typical lipid bilayer

0.333 e/Å3

Note: broad distributions (no sharp lipid-water interface)

Higher spatial resolution from oriented samples

J. Lipid Research 2006

(DLPC: a lipid we like)

Cryo-EM, Dganit Danino, Technion, Israel

Electron microscopy of lipids in water

Equilibrium distance means

attractive force + repulsive force = 0

F1

F2

D-spacing

=> Any measured change in distance means a change in membrane forces.

+ water => + more water =>

=> Can control spacing by hydration/dehydration (osmotic stress)

+ electrolyte =>

... or by adding ions/electrolytes

1 Molar = a pair of ions for each 55 water molecules.

100 mM = 10 times less ions or 10 times more water.

Debye screening lengths for electrostatic interactions in solution:

10 Å in 100 mM monovalent ions3 Å in 1M

q (Å-1)

Example: D-spacing increases in KBr

DLPC/water20mM KBr

40mM

60mM

80mM100mM

200mM400mM

600mM

q (Å-1)

DLPC/water20mM KBr

40mM

60mM

80mM100mM

200mM400mM

600mM

Example: D-spacing increases in KBr

Equilibrium distances depend on polarizabilities (as expected)

Numbers indicate polarizability ratios .

Szymanski, Petrache, J. Chem. Phys. 2011

KCl

KBr

Water spacing

...but need to explain a curiously large difference between the effects of KBr and KCl

screening length

D

2DKClW

KBrW DD

Looks like electrostatics but distances are large

...112 2

WDH

van der Waals

Hamaker, Parsegian, Ninham, Weiss,...

Attractive interactions between lipid bilayers

With Hamaker parameter H ~ 1-2 kBT

hydration repulsion

Repulsion #1

Empirical exponential form with two adjustable parameters: Ph ~ 1000 – 3000 atm ~ 2 – 3 A

/WDh eP

(lipids don’t want to give water away)

Rand, Parsegian, Marcelja, Ruckenstein, ...

shape fluctuation

Repulsion #2

2

2 12 C

B

KTk

KC=bending modulus = fluctuation amplitude

Helfrich, de-Gennes, Caillé

(membranes bend and undulate)

electrostatics: some analytical forms, mostly numerical calculations

Repulsion #3

Main parameters:

membrane surface charge

Debye screening length (of the electrolyte)

Poisson-Boltzmann, Debye-Huckel, Gouy-Chapman, Andelman, ...

(electric charges exist)

2

2

2/ 1

212

C

B

W

Dh K

TkD

HeP W

vdW shape fluctuationhydration

Additivity/separability model of membrane interactions

+ elec

Fitting parameters: Ph, , H, KC

Also need (DW)

Parsegian, Nagle, Petrache

Long story short: (DW) from X-ray line shape analysis

(DOPC and DOPS are two popular lipids)

Petrache et al., Phys. Rev. E 1998

Osmotic pressure

𝑃𝑜𝑠𝑚=− 𝑑𝐹𝑑𝑉𝑊

It can be measured with an osmometer.

Rand and Parsegian, 1979

Lipid

PEG

Reduce inter-membrane spacing by using osmolytes (e.g. polyethylene glycol, PEG)

Zero pressure

fluctuations

di(14:0)PC (DMPC) at 35oC

hydration

vdW

Example of interaction analysis giving Ph, , H, KC (no electrostatics)

Practical method: use well calibrated reference lipid to investigate salt/electrolyte effects on membrane interactions

Koerner et al., Biophys. J. 2011Danino et al. Biophys. J. 2009Rostovtseva et al. Biophys. J. 2008Petrache et al., PNAS 2006Kimchi et al., J. Am. Chem. Soc. 2005

Main results: Screening of vdW interactions Electrostatic charging due to affinity of polarizable ions to lipidsSome interesting complications at the water/lipid interface

KCl KBrwater

FluidDLPC at 30oC

1M salts

Water spacing (Å)

Fit with ~50% vdW reduction (no elec.)

J. Lipid Res. 2006

Detect Br- binding from data in 100 mM salt

Binding constant

Obtain vdW strength (H) vs. salt concentration

Waterspacing

ExpectDW /λD

DW )eλ/DH~( 221

Cl

Br

(according to Ninham, Parsegian)

Functional form OK but needs empirical correction

DWDDW eDH /2)/21(~

DWD /Petrache et al., PNAS 2006

Detect electrostatic charging due to zwitterions

Koerner et al., Biophys. J. 2011

Common pH buffers

Our calibrated lipid

(Koerner et al., BJ 2011)

Zwitterions (e.g. MOPS buffer) swell multilayers really well

Expect reduction of vdW attraction of membranes

weaker vdW

...and electrostatic charging

(at total 200 mM concentration)

Measure charging by competition with calibrated KBr

+¿−

neutral point: 75% MOPS, 25% KBr

% MOPS replacing KBr(at total 200 mM concentration)

Lipid multilayers are found around nerve axons

source: Public domain (Wiki)

Lipid multilayers are found around nerve axons

source: Public domain (Wiki)

Conclusions

[3] Water, mobile charges, and membrane fluctuations complicate calculations of interactions. Huge room for improvement.

[1] X-ray scattering measurements on well calibrated membrane systems provide experimental parameters for vdW and electrostatics. Experiments show larger screening length (reduced screening power of salt ions) than predicted theoretically.

[2] Can detect weak electrostatic interactions by competition measurements (e.g. MOPS vs. KBr).

Ryan Lybarger Buffers, mixtures

Jason Walsman E. coli (adaptation to ionic sol.)

Megan Koerner Zwitterions

Luis Palacio, Matt Justice X-ray

Torri Roark Lithium salts

Johnnie Wright Exclusion measurements

Visit us at www.iupui.edu/~lab59Acknowledgements

John Nagle (Carnegie Mellon Univ., USA)

Stephanie Tristram-Nagle (Carnegie Mellon Univ., USA)

Daniel Harries (Hebrew Univ., Israel)

Luc Belloni (Saclay, France)

Thomas Zemb (formerly at Saclay, France)

Adrian Parsegian (Univ. of Massachusetts, formerly at NIH)

Rudi Podgornik (University of Ljubljana, Slovenia)

Tanya Rostovtseva (NIH, USA)

Philip Gurnev (NIH, USA)

Acknowledgements (cont.)