Chap. 5. Biomembranes 林宙晴. Composition of Biomembranes Amphiphile Mesogenes (ex. Liquid...
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Transcript of Chap. 5. Biomembranes 林宙晴. Composition of Biomembranes Amphiphile Mesogenes (ex. Liquid...
Chap. 5. Biomembranes
林宙晴
Composition of Biomembranes
• Amphiphile• Mesogenes (ex. Liquid crystal) – mesophase
– Form a variety of condensed phases with properties in between those of solids and isotropic fluids
• Single-chain vs Double chain fatty acid– Single-chained molecules assembles into bilayers only at
high concentration (> 50%)
Phospholipids
• Single vs. Double bond
Chain Length of Fatty Acids
• Too short: hard to form bilayers at low concentration
• Too long: too viscous and lateral diffusion within bilayer is restricted
• ~0.1 nm/CH2 & C ~=15-18 bilayer: 4-5 nm
• Mean cross-sectional area of a single chain is 0.2 nm2, surface area occupied is 0.4-0.7 nm2
Favored Phases
• The phase favored by a particular amphiphile partly reflects its molecular shape.
ratio of head group area to cross sectional area of hydrocarbon region
Forming a hole
• Bending a bilayer needs energy
• Hole formation– Forming a hole needs to overcome edge tension
– Effective edge tension is temperature-dependent and vanishes at sufficiently high temperature.
Self-Assembly of Amphiphiles
• CMC: critical micelle concentration
• Competition between hydrophobic region to contact with water and reduction of entropy
• Ebind is defined as the energy required to create the new water/hydrocarbon interface
Ebind = 2ncRhclcc
Sgas = kB{5/2-ln(. [h/{wmkBT}1/2]3}
Fsol ~ Ebind - T Sgas
nclcc
Rhc
: surface tensionSgas: entropy/moleculeFsol: free energy/molecule: molecule density
Aggregation Density (agg)
• Aggregation (agg) occurs at Fsol = 0
agg. [h/{wmkBT}1/2]3 = exp(5/2- Ebind /kB
T)• Estimates from above formula for 10 carbons
– agg(single) 0.3 molar≒
– agg(double) 2≒ . 10-5 molar
• Experimental values– agg(single) 10≒ -2 - 10-3 molar
– agg(double) 10≒ -3 - 10-5 molar?? CMC == agg
Dependence of CMC on Chain Length• Single chains have uniformly higher CMCs than d
ouble chains• Experimental values (-slope)
– [single double] = [1.15 1.8]
• Theoretical prediction– [single double] = [2 3]
• Selection of values for (surface tension) may produce more compatible values.
• A more rigorous approach (dropping the assumption of two-phase aggregates) produced similar
results.
Effective Cross Sectional Area
• For hydrocarbon part– vhc = 27.4 + 26.9ncx10-3 nm3
– lhc = 0.154 + 0.126nc nm
ahc = vhc/lhc = 0.21 nm2
• For head group– a0 ~ 0.5 nm2
• In the following, packing in several shapes will be discussed.
Shape Factor (vhc/a0lhc or ahc/a0)
• For spherical micelles– 4R2/a0 = (4R3/3)/vhc
R = 3vhc/a0
∵ R l≦ hc vhc/a0lhc 1/3≦• For cylindrical micelles
– 2Rt/a0 = R2t/3/vhc
R = 2vhc/a0
1/3 < vhc/a0lhc 1/2≦
Shape Factor (continued)
• For bilayers– vhc = a0lhc vhc/a0lhc = 1
1/2 < vhc/a0lhc 1≦• For inverted micelles
– vhc/a0lhc > 1
• For amphiphiles in the cell (real situation)– Single chain: ahc/a0 ~ 0.21/0.5 0.4 ≒ micelles
– Double chain: ahc/a0 ~ 0.42/0.5 0.8≒ bilayers
Another advantage of forming bilayers with double chain fatty acids are a low CMC.
Bilayer Compression Resistance
• First model: a homogeneous rigid sheet, such as a thin metallic plate in air
uxx = uyy = S(2/9Kv + 1/6)
= KA(uxx + uyy) =Sdp
KA = dpKv/(4/9 + Kv/3) (uniform rigid plate)
for many materials, Kv ~ 3
KA increases linearly with plate thickness
Kv & : volume compression and shear moduli
KA: area compression modulusuxx + uyy: relative area change
More on KA
ij = ij Kv tru + 2 (uij- ij tru/3)
Under isotropic pressure, ij = -P ij
P = -Kv tru
3D ii = Kv (uxx + uyy + uzz)
2D (plane strain) ii = KA (uxx + uyy)
1D ii = KL (uxx)
• Unrealistic• Both ii uii are defin
ed differently
Bilayer Compression Resistance
• Second model:• E = /a + a
= 2a0 + (/a)(a – a0)2
• E/a0 at a0 ~ [(a – a0)/ a0]2
also = (KA/2)(uxx + uyy)2
KA = 2 (monolayer)
KA = 4 (bilayer)
experimentally, = 0.02-0.05 J/m2
KA = 0.08-0.2 J/m2
E: interface energy/moleculea: mean interface area: surface tension/a: repulsive energy
uxx + uyy = 2 (a – a0)/ a0
Experimentally Measured KA and Kv
• Experimentally,
KA = 0.1-0.2 J/m2
• When carbon number increases,
KA only increases mildly,
KA is independent of dp
• KA vs. cholesterol content
• Kv ~ 2-3x109 J/m3, about the same as water (Kv = 1.9x109 J/m3)
Model 2 is more likely
Bilayer Bending Resistance
• For a given molecular composition, the energy per unit surface area to bend a bilayer increases with the curvature.
• F = (kb/2)(1/R1 + 1/R2)2 + kG/(R1R2)
• E = 4(2kb + kG) (sphere)
• E = kbL/R (cylinder)
F:
F: energy densityE: bending energy
kb: bending rigidity
kG : Gaussian bending rigidity
Experimental Measurements of kb
• Kb is about 10x of kBT
undulate readily
(please refer to p. 28)
• Thus, measurement of bending modulus needs to control undulation.
• KA, app = KA/[1 + KAkBT/(8kb)]
: applied tensionLow T or high : KA Low : 8kb/kBT
kb also rises with cholesterol content
Interpretation of kb
• Many models predict how kb depends on the bilayer thickness dbl.
kb = KAdbl2/
where = 12, 24 or 48.
• If KA is proportional to dbl, then
kb is proportional to dbl3
• Otherwise
kb is proportional to dbl2
From the plot, KA is independent of dbl
There is little experimental support for the rigid-plate prediction
Edge Energy
• : penalty energy for creating a free edge
• No documented results of curvature on • is assumed to be independent of curvature
• Esphere = 4(2kb + kG)
• Edisk = 4Rv
• When Rv begin to > (2kb + kG)/
sphere configuration is favor
(Bending energy)
Estimating • At T> 0, membrane boundary fluctuates,
larger is needed to seal the edge.
• Simulation show that
* = 1.36kBT/b
• Free energy for N plaquettes
open: F 2N≒ b - kBTNln(12.8)
closed: F -k≒ BTNln(1.73)
* = 1.0kBT/b
b: a length scale from the simulation
Membrane Rupture
• At T = 0,
H = E – A
H = 2R – R2
• At the peak, R* = R < R* holes shrink
R > R* holes expand
• When T increases, the energy barrier lowers.
• For planar membranes in two dimensions,
Edge-tensionmin (*) = 1.66kBT/b
R: radius of a hole: two-dimensional tension
Measured Edge Tensions
• For pure lecithin bilayers
= 4x10-11 J/m
• By exp. (shown)
for SOPC (p. 154)
= 0.9x10-11 J/m
for SOPC+30% cholesterol
= 3.0x10-11 J/m
It is estimated that must > 4x10-12 J/m to make the membrane resistant against rupture at ambient temperature.
R