Curtis Bustos

Chem 3810-001 BIOCHEMISTRY                          Name: KEY

Breakout Problem: Membrane curvature

1. Match each lipid to its function (signaling, energy storage & insulation, structural support) and class (glycerolphospholipid, triacylglycerol, steroid).

Lipid	Function	Class
Cortisol	Signaling	Steroid
Tripalmitoylglycerol	Energy storage & insulation	Triacylglycerol (TAG)
Phosphatidylethanolamine	Structure	Glycerolphospholipid

Curvature of membranes may result from the shapes and Van der Waals envelopes of lipids. For example, relative sizes of polar head groups and non-polar fatty acid chains create a specific size and shape of a surrounding Van der Waals envelope. When lipids with these characteristics aggregate, their Van der Waals envelope will contribute toward a specific membrane curvature. Below are some examples of lipids that contribute toward membrane curvature.

2. Based on the molecular drawings below, all three lipids seem to have very comparable polar-heads. Why does PE have a smaller polar-head than PC and LPC?

The methyl-groups that are bonded to the nitrogen on PC & LPC are larger and have much greater Van der Waals repulsive forces than the hydrogen atoms that are bonded to the nitrogen on PE.

3. Draw the Van der Waals envelope for each lipid mentioned previously.

                                   PE                           PC                         LPC

4. Identify positive, negative and neutral membrane curvature from the model below:

5. What lipid(s) contribute toward negative curvature (PC, LPC, PE)?

PE

6. What lipid(s) contribute toward positive curvature (PC, LPC, PE)?

LPC

7. What lipid does NOT contribute toward positive or negative curvature (PC, LPC, PE)?

PC

8. In addition to membrane curvature, SNAREs facilitate the fusion of membranes by bringing them together. During this process, induced membrane-curvature may occur. Identify the membrane curvature of A, B, C from the blue-side of the membrane.

A = neutral

B = negative curvature toward the bottom, positive curvature on the top

C = positive curvature

Passage-based questions: membrane curvature and lipid-protein interactions.

The following is an excerpt taken from a 2012 paper in the Biochemistry Journal of ACS Publications. 

Curvature Forces in Membrane Lipid–Protein Interactions

Michael F. Brown *

Department of Chemistry and Biochemistry and Department of Physics, University of Arizona, Tucson, Arizona 85721, United States

Biochemistry, 2012, 51 (49), pp 9782–9795

DOI: 10.1021/bi301332v

Publication Date (Web): November 19, 2012

Copyright © 2012 American Chemical Society

Abstract

Membrane biochemists are becoming increasingly aware of the role of lipid–protein interactions in diverse cellular functions. This review describes how conformational changes in membrane proteins, involving folding, stability, and membrane shape transitions, potentially involve elastic remodeling of the lipid bilayer. Evidence suggests that membrane lipids affect proteins through interactions of a relatively long-range nature, extending beyond a single annulus of next-neighbor boundary lipids. It is assumed the distance scale of the forces is large compared to the molecular range of action. Application of the theory of elasticity to flexible soft surfaces derives from classical physics and explains the polymorphism of both detergents and membrane phospholipids. A flexible surface model (FSM) describes the balance of curvature and hydrophobic forces in lipid–protein interactions. Chemically nonspecific properties of the lipid bilayer modulate the conformational energetics of membrane proteins. The new biomembrane model challenges the standard model (the fluid mosaic model) found in biochemistry texts. The idea of a curvature force field based on data first introduced for rhodopsin gives a bridge between theory and experiment. Influences of bilayer thickness, nonlamellar-forming lipids, detergents, and osmotic stress are all explained by the FSM. An increased awareness of curvature forces suggests that research will accelerate as structural biology becomes more closely entwined with the physical chemistry of lipids in explaining membrane structure and function.

Power of Curvature

The idea of a balance of opposing forces is also embodied in an earlier explanation for the polymorphism of membrane lipids(123, 138, 139, 146) using a geometric theory for the self-assembly of amphiphiles.(73, 127) The studies of G. Lindblom and co-workers(45, 47) have led to a model in terms of optimal packing of lipids in membranes that is directly related to the curvature energy.(48) Such a view exemplifies the chemistry perspective,(147) whereby molecular packing is quantitatively related to curvature;(148) either the balance of lamellar and nonlamellar lipids(36) or packing constraints(45, 47) lead to similar conclusions.(48) Figure 4a shows a chemical view of phospholipids in terms of a molecular packing parameter. The packing of lipids within the aggregate manifests the attractive and repulsive forces acting upon the polar headgroups and the nonpolar acyl chains.(73) Amphiphiles with a greater headgroup size relative to that of the chains, such as gangliosides, lysophospholipids, or single-chain detergents, favor packing into a conical molecular shape on average (Figure 4a, top). They tend to form micelles or normal hexagonal H_I phases and are analogous to an oil-in-water dispersion.(123) Lipids with larger headgroups, for instance, phosphatidylcholine (PC) whose headgroup is methylated versus phosphatidylethanolamine (PE), tend to pack on average with a cylindrical molecular shape (Figure 4a, middle). They form a planar lipid bilayer (Figure 2), as abundantly depicted in standard biochemistry texts. Last, those lipids with relatively small headgroups compared to the chains, such as PE, prefer to pack into an inverted conical molecular shape on average (Figure 4a, bottom). They are able to form the reverse hexagonal H_II phase (Figure 2), which is analogous to a water-in-oil dispersion.(123, 147)

Figure 4. Phospholipid form and function involve molecular packing and spontaneous membrane curvature. (a) Schematic illustration of the older view characterized by a molecular packing parameter. Lipids with different headgroups and acyl chains are inscribed within their corresponding geometrical shapes. Molecular packing involves the optimal cross-sectional area of the headgroups vs the projected acyl chain length and the hydrocarbon volume. Either a frustum of a cone (top or bottom) or average cylindrical lipid shape (middle) accounts for the diversity of cellular lipids. (b) The new model entails mismatch of the optimal areas of the headgroups vs the cross-sectional chain area, thus giving a bending moment for the lipid monolayer. For a membrane bilayer, the spontaneous curvature compensates for the frustration of the acyl chain packing. Examples are shown where the spontaneous (intrinsic) monolayer curvature is positive (toward hydrocarbon), zero, or negative (toward water). As the optimal headgroup area becomes progressively smaller vis-à-vis the acyl chains, the spontaneous curvature follows a sequence from positive through zero to negative. The spontaneous monolayer curvature becomes more negative as the temperature increases or the level of hydration decreases, giving the sequence of microstructures in Figure 2 (figure redrawn from ref 1 courtesy of J. Kinnun).

Shape and Form in Membrane Lipid Function

Perhaps it is worth noting that the curvatures are not implicit; rather, they correspond to bending of a neutral (pivotal) plane running beneath the membrane aqueous interface, where the lateral area remains constant. For example, lipids that form nonlamellar phases, such as the H_II phase, have a negative spontaneous curvature H₀. When they are present in a planar bilayer, there is a mismatch of the geometric mean curvature H (which is zero) from the spontaneous curvature H₀. The two monolayers are held together by the hydrophobic effect and packing forces. Curvature mismatch involves the tendency of an individual monolayer of the bilayer to achieve its natural curvature, which is frustrated by the chain packing interactions with the other monolayer. Although a bilayer is flat on average, the two monolayers can still have an inherent tendency to curl. All of these aspects are discussed in several earlier review articles.(1, 123, 140)

With these basic precepts in mind, the polymorphism of membrane lipids can now be readily understood by applying the continuum flexible surface model. The spontaneous (intrinsic) monolayer curvature (H₀) can be positive (toward hydrocarbon), zero, or negative (toward water), as shown in Figure 4b. When the optimal headgroup separation exceeds the chains, there is a tendency to curl toward hydrocarbon; the headgroups have their greatest exposure to water, as in the case of single-chain surfactants (e.g., lysolipids), as well as glycolipids and gangliosides, as at the top of Figure 4b. The positive spontaneous curvature H₀ is expressed through formation of small micelles or the normal hexagonal H_I phase (or elongated wormlike micelles), with the headgroups outside and the chains inside the aggregate (oil-in-water dispersion) (not shown). By contrast, lipids with smaller headgroups or larger chains, as in the case of double-chain phospholipids, are less exposed to water. They favor a more condensed membrane surface, with a smaller interfacial area per lipid. If the optimal headgroup separation matches the chains, there is only a small inclination of a monolayer to curl, as in the case of PCs; the spontaneous curvature H₀ is now approximately zero. The planar lipid bilayer is formed as in the standard fluid mosaic model; see the middle of Figure 4b. Finally, lipids with small headgroups are even less hydrated, so they promote a further condensation of the membrane surface. Because the optimal polar headgroup separation is less than the chains, the lipid monolayer tends to curl toward water, e.g., as occurs in unsaturated and polyunsaturated PEs; now there is a negative spontaneous curvature. Hence, the reverse hexagonal H_II (or cubic) phases are formed (see the bottom of Figure 4b), with the headgroups inside and the chains outside the lipid aggregate (water-in-oil dispersion).

9. The section entitled “power of curvature” describes how PC, PE, and LPC (a lysophospholipid) contribute toward membrane curvature.  According to the article, does each of these lipids (PC, LPC, PE) contribute to positive, negative, or neutral curvature?  Does this agree with your reasoning in questions 5-7 above?

Answers should be the same as questions 5,6,7 above.

10. Spontaneous (intrinsic) curvature can be identified as  

A) Positive (toward hydrocarbon)

B) Neutral

C) Negative (toward water)

D) All of the above terms can be used to describe intrinsic curvature.