Curvature stress

Odijk, T. (1998) Flexagonally packed DNA within bacteriophage T7 stabilized by curvature stress. Biophys. J., 75, 1223-1227. 

Bilayers are ideal for cylindrically shaped lipids, where the hydrocarbon tails are the same size as the head groups (see Fig. 7). The tails of many lipids prefer to occupy a larger area, however, giving these lipids an inherent tendency to curve. The flattening of these lipids into a planar bilayer causes a curvature stress, in which the center of the bilayer... 

Curvature stress could play an important role not only in the lipid phase but also in membrane protein stability. A membrane protein might... 

A different type of curvature in bilayers can also result from the unequal distribution of lipids between the two monolayers, with one mono-layer having more lipid molecules than the other. This curvature is different from the curvature stress described above in that it originates from the total number of lipids on each side of the membrane and not from an inherent curvature in each lipid molecule. This curvature could be important in the budding of lipid vesicles (Huttner and Zimmerberg, 2001) and would be expected to influence and be influenced by the curvature stress described above. 

The entire thermodynamic system of the membrane and TM protein must be considered to understand how the protein and bilayer achieve their native state. We have summarized four of the mechanisms, hydrophobic matching, tilt angles, and specific protein/lipid and protein/protein interactions that are important in determining the stability (Fig. 5). Other important factors, such as the stability of lipid/lipid interactions, have been left out of our protein-centric view. We describe a hydrophobic mismatch as an unfavorable interaction that can be relieved by the other three processes, but we would expect all these properties of the system to interact. We could easily describe the same equilibria by saying that a strain in curvature is relieved by a hydrophobic mismatch or that strong protein/protein packing interactions might help relieve the hydrophobic mismatch or curvature stress. The complex interplay between all these interactions is at the heart of what determines membrane protein stability and will no doubt be difficult to quantify. 

A biologic reason for the abundance of nonlamellar lipids in membranes is that they possess the ability to modulate the activities of membrane proteins (15, 16). It has been recognized that membranes exist in a state of curvature frustration, which may be sufficiently large to have significant effect on certain protein conformations (17). Many examples show that the lipid bilayer elastic curvature stress indeed couples to conformational changes of membrane proteins (15, 18, 19). Protein kinase C is one such example of an enzyme activated by lipids that exhibit a propensity for nonlamellar phase formation (20). The activity of Ca " -ATPase from sarcoplasmic reticulum membranes also strongly correlates with the occurrence of nonbilayer lipids in the membrane and increases with the increase of their amount. It is noteworthy that the protein activity does not depend on the chemical structure of the lipids but only on their phase propensity thus specific binding interactions are ruled out. The list of proteins with activities that depend on the phase properties... 

The La-//ii transition may be considered a result of competition between the spontaneous tendency of the lipid layers to bend and the resulting hydrocarbon chain packing strain thus, membranes exist in a state of fmstrated curvature stress (17). Respectively, the La-Hn transition is believed to be driven by the relaxation of the curvature of the lipid monolayers toward their spontaneous curvature. Conversely to the Lp-Lc transition, the La-H II transition temperature decreases with the hydrocarbon chain length increase (Fig. 3a). At sufficiently long chains. 

The release profiles suggest that the lysoPPC and PA hydrolysis products, which are formed in a 1 1 molar ratio by SPLA2, are incorporated into the target membranes [51], leading to the increase in the permeability of the target liposomal membranes. These hydrolysis products, due to their non-bilayer forming molecular shapes, induce a curvature stress [52, 53] and/or form small-scale lipid domains [33, 36], which lead to membrane defects and consequently increased membrane... 

Furthermore, Brown (1994) listed the following properties as those that are important in determining the activation of rhodopsin average bilayer thickness see Dratz Subheading 6.2.) lateral compressibility see Litman and Mitchell, below) curvature stresses of the lipid-water and protein-lipid interfaces and electrostatic forces (determined by the charge of the headgroups). 

Curvature stress Stress generated by the presence of a nonlameUar lipid in a lamellar membrane. 

The simple theory put forward by Meinhardt et al. accounts in a unified manner for both ripple phases and raft states in membranes. The prerequisites for the formation of such modulated phases is local phase separation (e.g., in the ripple case, between a liquid and a gel phase, or in the raft case, between a liquid disordered and a liquid ordered phase) and curvature stress in at least one of the two phases (typically the ordered one), resulting, e.g., from a size mismatch between head group and tails. In order to reproduce rippled states or rafts, coarsegrained simulation models must meet these criteria. This is often not the case. For example, the standard version of the popular MARTINI model does not have a ripple phase, because the low-temperature gel phase of saturated phospholipids is until ted. 

Rukmini R, Rawat SS, Biswas SC, Chattopadhyay A. Cholesterol organization in membranes at low concentrations Effects of curvature stress and membrane thickness. Biophys ]. 2001 81(4) 2122-2134. 

Malinin, V.S. and Lentz, B.R. (2004) Energetics of vesicle fusion intermediates comparison of calculations with observed effects of osmotic and curvature stresses. Biophysical Journal. 86, 2951-64. 

The main advantage of particle-based models over continuum treatments is their capability of being able to describe simultaneously membrane curvature and lipid chemistry, as well as their interplay how do specific lipids promote/prevent curvature stresses And how do lipids respond to curvature stresses, for example by partitioning between the inner and the outer monolayer of highly curved vesicles ... 

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