Interactions between lipid membranes Horia I. Petrache Department of Physics Indiana University Purdue University Indianapolis, USA Support: IUPUI Biomembrane Signature Center IUPUI Integrated Nanosystems Development Institute Alpha 1 Foundation NIH Generous student volunteering

o More (better) theory o Applications You can contribute with:

oily tails Lipid molecules have two parts dipolar head 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... lipid Electron densities at T = 300 K

lipid headgroup lipid tails compared to e/ Å 3 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

22 Incident beam MLV sample Bragg rings seen on the detector 22 Scattered beam(s) X-ray scattering from multilayers (1D randomly oriented lattice) Bragg’s Law

With D = 60 Å, = 1.54 Å, and h = 1, obtain  = 0.74 o (small angle) => Need a small x-ray machine angle

x-ray source (tube) detector sample 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 e/ Å 3 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 F1F1 F2F2 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 ions 3 Å in 1M

q (Å -1 ) Example: D-spacing increases in KBr DLPC/water 20mM KBr 40mM 60mM 80mM 100mM 200mM 400mM 600mM

q (Å -1 ) DLPC/water 20mM KBr 40mM 60mM 80mM 100mM 200mM 400mM 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 DD Looks like electrostatics but distances are large

van der Waals Hamaker, Parsegian, Ninham, Weiss,... Attractive interactions between lipid bilayers With Hamaker parameter H ~ 1-2 k B T

hydration repulsion Repulsion #1 Empirical exponential form with two adjustable parameters: P h ~ 1000 – 3000 atm ~ 2 – 3 A (lipids don’t want to give water away) Rand, Parsegian, Marcelja, Ruckenstein,...

shape fluctuation Repulsion #2 K C =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)

vdW shape fluctuation hydration Additivity/separability model of membrane interactions + elec Fitting parameters: P h,, H, K C Also need  (D W ) Parsegian, Nagle, Petrache

Long story short:  (D W ) from X-ray line shape analysis (DOPC and DOPS are two popular lipids) Petrache et al., Phys. Rev. E 1998

Osmotic pressure 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 35 o C hydration vdW Example of interaction analysis giving P h,, H, K C (no electrostatics)

Practical method: use well calibrated reference lipid to investigate salt/electrolyte effects on membrane interactions Koerner et al., Biophys. J Danino et al. Biophys. J Rostovtseva et al. Biophys. J Petrache et al., PNAS 2006 Kimchi et al., J. Am. Chem. Soc Main results: Screening of vdW interactions Electrostatic charging due to affinity of polarizable ions to lipids Some interesting complications at the water/lipid interface

KClKBrwater Fluid DLPC at 30 o C 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 Water spacing Expect Cl Br (according to Ninham, Parsegian)

Functional form OK but needs empirical correction Petrache et al., PNAS 2006

Detect electrostatic charging due to zwitterions Koerner et al., Biophys. J 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 KoernerZwitterions Luis Palacio, Matt JusticeX-ray Torri Roark Lithium salts Johnnie WrightExclusion measurements Visit us at Acknowledgements

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.)