1
What Makes a Membrane
Stablization of Bilayer
• Intra-leaflet hydrogen bonding
• Headgroup replusion
• Intra-leaflet alkyl chain interaction
• Balance areas
Israelachvili, J. N., Intermolecular and Surface Forces, Elsevier Inc.(2011),
1.1
Curved Surface as a Membrane Model
Curvature as Basis for the Study of Membrane Forces
1
Definitions
• parameterized as
1
R
=c
• Total curvature J = c1 + c2
• Gaussian curvature K = c1 · c2
• Intrinsic Curvature vs Imposed Curvature
First Connection with Chemistry
2
1.2
Polymorphism of Lipid Structures
Generic Lipid Packing Forms
1.3
Membrane Curvature and Energy Content of Membranes
Membrane Curvature
The Radius of Curvture and Forces
Fb =
kR
2 A (Hc + Hd
− Hm )2 dA k bending rigidity Hc and Hd principle curvatures
Hm intrinsic Curvature
2
Molecular Basis for Shape
Molecular Basis for Shape
3
• Φ angle
Crystal Structures H–bonds
Carbons
12
14
lyso
Σ
39
38
19
S
39
45
34
Φ
0
33
55
Φ = cos−1 ( nS∑ )
• Θ3 and Θ4
• Θ1 Parallel to Membrane Normal
• Generation of curvature
4
5
• Hydrocarbon Packing
• Elastic Bending
• Hydration
• Electrostatic
6
3
3.1
First Consideration of Membrane Thermodynamics
Two Component Lipid Phases
Analysis of Thermal Behavior
• Lipids have Characteristic Thermal Behavior
• Membrane melting disorders but does not destroy bilayer
• Thermal behavior of membrane can be studied as suspension in water
• Phase – A region of Material that is Chemically Identical but Physically
Distinct.
7
3.2
Analysis of Phase Diagrams for Membranes
Lipid Phases
• Ideal Mixing ∆G = 0 for A+B mixing.
• Tm,A 6= Tm,B ∆HA 6= ∆HB
−−
*
• gel )
−
− liquid
• Mole Fraction
• Lipid is the “Standard State”
• Transition Range Temperatures
• Since xg + x f = 1
g
xf =
xB − xB
f
xB − xB
(1)
and
xg = 1 − x f
8
(2)
• Heat Capacity
cp =
d∆H(T )
dT
•
g
∆H(T ) =
xB − xB
f
xB − xB
·
f
f
xB · ∆HB + (1 − xB )·
∆HA
9
• Lo and Ld
• Gibbs Phase Rule
• Degrees of Freedom
F = C − P + 1∗
10
(3)
3.3
Complex Phase Relationships
Complex Phase Behavior
11
Temperature level is 37◦ C Phases that include Lo are prominent
12
Condensing Effect of cholesterol Membrane Rafts
4
Analysis of Membrane Dynamics
4.1
Dynamic Model of Membrane Structure
Fluid Mozaic Model of Membranes
Fluid Mozaic Model – Singer & Nicolson Science (1972) Detailed analysis of movement in
membranes
13
4.2
Time Domains of Membrane Dynamics
Membrane Dynamics
Membrane dynamics encompass many time domains
4.3
Motion and Order Within Lipid Atoms
Dynamics within Lipid Structure
14
Glycerol backbone
Alignment with Membrane Normal
15
Alkane Chain Conformation
POPC Chains
Summary of bilayer Structure
16
Chain Order Summary cyan – phospholipid, blue – +cholesterol
Distribution of Membrane Components
Periodic Boundry Simulation
17
5
Phase Transitions of Membranes
Phase–Behavior of Membranes (II)
• Membranes are polymorphic
– Their amphipathic and varied structure guarantees that they will display
complex thermal behavior
– It also provides a complex relation to hydration, ionic and osmotic
strength, pH
– Many of these vary in the environments where membranes function
– Therefore they are a legitimate subject to characterize membrane function
• Differential Scanning Calorimetry
– Determine the heat flow, dE/dt, to maintain a constant temperature
increase, dT /dt
– Sample and reference must be equilibrated throught the measurement
– A thermal transition will cause the sample to diverge from the reference
– Membrane components undergo phase changes at common temperatures
• Analysis of a Temperature Transition
– The peak is a direct measure of the enthalpy of the transiton (∆Hcal )
– At the midpoint, Tm , the ∆G = 0 so that
∆S = ∆Hcal /Tm
18
(4)
• DPPC Thermal Transitions
– Equilibration of the sample
– Three transitons
Tm
18.4
35.1
41.1
• DPPC Thermal Transitions
Revisit the membrane structure for each phase.
19
∆T1/2
3.0
1.8
0.18
∆Hcal
3.23
1.09
6.9
∆S
11
3.5
11.0
• Pseudocrystalline
Lc
20
Extended aliphatic chains with Φ angle and packing similar to that seen in
available crystals of similar phsopholipids
• Gel
21
Lβ
Increased hydration of the headgroup (2 to 15), decreases packing in alkyl
chains and some increase in cross sectional area
• Ripple
22
Pβ
At these temperatures long axis rotation dramatically increases but the tilt is
retained producing the “ripple”
• Fluid
23
Lα
This generates internal rotation in the alkane chains producing “kinks” that
shorten the chains producing thinner and more spread membranes
5.1
Fractors Affecting Phase transitions
Factors that influence phase behavior
• Non-biological factors
Degree of hydration Barotropic effects
• Vesicle size
The curvature of vesicles affects the order of the chain packing and the
interaction of the head groups.
• Alkane chain length
– Linear relationship with carbons in the alkane chains
– Indicates a co-operative threshold at 4 to 5 carbons
– Use of chain length to respond to environmental changes
• Alkane chain chemistry
– Linear, branched, cyclohexal substituted chains
– Mono-unsaturated 4
– Position of unsaturation (opt at 9-10)
– Position of unsaturated chain
24
• Interdigitation
– Structural, acyl asymmetry, sphingolipids
– Head group–chain area asymmetry
– Interdigitation decreases void potential
– Consequence: Thickness, charge density, coupling loss of midplane
• Head group chemistry
– Size, polarity, charged groups
– Isolation of components for study
– Small, uncharged etc that let alkane chains dominate
25
– Charged groups pH, ionic strength
– Ion layers at the membrane surface
• Interfacial Chemistry
– Acyl to ether change reduce the Tm (phase destabilization)
– Amide groups, sphingolipids, increase Tm (phase stabilization)
26