Lipid membrane physics

4/27/2012
Lipid membrane physics Bert Nickel, 26.04.2012
lecture 2 (out of 9 + 3 guest lectures)
guest lectures:
Joachim Rädler
Erich Sackmann
liposomes, cationic phases (31. May, 05. July)
cell adhesion (towards end)
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Outline
• molecular
molecular structure of lipid molecules
structure of lipid molecules
chains, backbone, and tail
• lipid mixtures with water
low lipid concentration: micelles, vesicles
high lipid concentration: 3d phases
Lipids
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popular lipids
Phospholipids
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headgroups
net negative
(anionic)
zwitterionic
zwitterionic
sugar
(glycolipids)
C18:0
C18:1
C18:2
C18:3
omega‐3 (eat fish …)
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naming lipids
tail ‐ head
tail ‐ head
Fat (triglyceride)
=
+
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Outline
• molecular structure of lipid molecules
chains, backbone, and tail
,
,
• lipid mixtures with water
low lipid concentration: micelles, vesicles
high lipid concentration: 3d phases
diluted lipid phases
mass dominated by water
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hydrophilic / hydrophobic principle
alone or together ?
N monomers in solution
results from combination of entropy (S) and internal energy (H) change
equilibrium adjusts according to the mass action law, aggregate formation is driven by Gibbs free energy gain G (no aggregate formation without energy lowering)
suggested reading: E. Sackmann, Biophysics, chapter 3:Thermodynamics
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Cato Maximilian Guldberg (11 August 1836 –
14 January 1902) was a Norwegian mathematician and chemist. Guldberg worked at the Royal Frederick University. Together with his brother‐in‐law, Peter Waage, he proposed the law of mass action. This law attracted little attention until in 1877 Jacobus Henricus van attention until, in 1877, Jacobus
Henricus van
't Hoff arrived at a similar relationship and experimentally demonstrated its validity.
Jacobus Henricus van 't Hoff, Jr. (30 August 1852 – 1 March 1911) was a Dutch physical and organic chemist and the first winner of the Nobel Prize in chemistry. He is best known for his discoveries in chemical kinetics, chemical equilibrium, osmotic pressure, and stereochemistry Van 'tt Hoff
stereochemistry. Van Hoff'ss work in these work in these
subjects helped found the discipline of physical chemistry as it is today.
Delft – Leiden ‐ Bonn – Paris – Utrecht ‐ …
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the mass action law for aggregates
K eq  e
G
k BT
free energy gain from
aggregate formation
balance of concentrations
ctot  c1  N  cN
cN
K eq  N
c1
aggregate
concentration
monomer
concentration
Keq is ideally a concentration independent characteristic number of the reaction, which
depends only on temperature (kept constant during isothermal reactions). Then, the mass
action law defines equilibrium concentration of monomeric lipids and lipid aggregates for a
given total concentration.
what does this tell us?
•
•
•
•
•
•
cN
K eq  N
c1
K eq  e
G
k BT
example: G= 10 kT and N=10 (small micelle)
then K = 22000
c1= 0.10 then cN = 22000 x 0.1010= 2 10‐6
c1= 0.20 then cN = 22000 x 0.2010= 2 10‐3
c1= 0.30 then cN = 22000 x 0.3010= 0.1
c1= 0.35 then cN = 22000 x 0.3510= 0.6
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titration experiments: increase ctot
result of experiments: lipids don’t dissolve well in water, they form aggregates (lucky us, CMC is small)
example:
l
water droplet (1mm)3 : 1 micro liter
CMC of droplet = 10‐6 l x 10‐9 mol/l = 10‐15 mol = 1 atto mol
1 mol = 1023 molecules, i.e. a vesicle with 108 molecules would be dissolved, then solution is saturated. area per two lipids: ca 0.5 nm2, CMC corresponds to a membrane equivalent patch of 2.5 107 nm2 which is a vesicle (A=4 pi r2) of 1.4 micron radius – a single giant vesicle or cell (r = 10 micron) can in principle survive in a microliter drop (ignoring osmosis effect). a single large unilamelar vesicle (r=0.1 micron) will be dissolved.
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relation between K and CMC (defined as maximal concentration for c1)
CMC  (N K ) – 1/N or
K  1/N x (CMC 1/N)
example before : N=10, K= 22000 then CMC = 0.29, true value slightly bigger, only approximation, i.e. terms such as (ln n) / n ignored
( pp
(approximation)
)
problem set (mass action law)
Membrane signaling. Assume a cell with 10.000 membrane receptors sitting in a 1 microliter drop. How much antigen concentration is needed for 50 % or 99 % bound receptors for K = 3 1013 (Biotin‐Strepatvidin) and for K = 6 107 (Calponin‐
actin) ? The mass action law also dictates the sensitivity of sensors based on recognition of molecules by binding. 11
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concentrated lipid solutions
concentrated lipid solutions
water and lipid concentration similar order of magnitude
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The plumbers nightmare: a bi‐continuous cubic phase, two continuous water phases separated by a bilayer. These are infinite periodic minimal surfaces, theorists like that. Structure determination by diffraction.
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Small angle scattering
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phase diagram of a mixture with water and
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