Mostly from x-ray from bent (hexagonal) phases

http://link.springer.com/protocol/10.1007%2F978-1-59745-519-0_24

although their is a newer indirect method using fluorescence

http://www.pnas.org/content/106/52/22245.full

Note that fluorescent lipids flip between much less frequently then natural lipids. Without looking into it in detail, I don't know how this affect their results.

Changes in the spontaneous membrane curvature can be approximated much easier by measuring the change in the phase transition temperature to the hexagonal (positive curvature) or inverted hexagonal (negative curvature) lipid phase by DSC or NMR, although this method does not really distinguish between changes in the bilayer elasticity or changes in the spontaneous curvature.

https://www.researchgate.net/publication/24172897_Determining_the_effects_of_lipophilic_drugs_on_membrane_structure_by_solid-state_NMR_spectroscopy_the_case_of_the_antioxidant_curcumin?ev=srch_pub

Article Determining the Effects of Lipophilic Drugs on Membrane Stru...

thanks so much, Jeffrey!

Hi, we happen to have just got a paper accepted on this issue. Please check out http://pubs.rsc.org/en/content/articlelanding/2013/sm/c3sm51829a#!divAbstract.

If you have further questions, please let me know.

Cheers, Georg

Dear Zheng,

The paper by Michael Kozlov that Jeffrey pointed you to is an excellent place to start. I also believe Michael published another paper on this elsewhere but I don't recall exactly where. Additionally I suggest you look at the original works by Peter Rand who is the main author on most of the spontaneous curvature papers. The 1989 paper by Peter and Adrian Parsegian is also a good place to start for an idea of the interactions between bilayers (http://www.sciencedirect.com/science/article/pii/0304415789900105). The fluorescent method is not something I recommend. Although I have to admit I have not read that paper. Issues of lipid flip-flop indeed make the analysis somewhat dubious perhaps.

Now, Peter retired about a decade ago but if you have any specific questions about his method than please do not hesitate to ask. If you are interested in determining the spontaneous curvature there are some details you should know that you might not be able to glance from these papers. I can assist if need be (look me up at Kent State).

Best.

Edgar

After having worked on this problem ourselves I have to say that literature on spontaneous curvatures J0 is quite misleading in many cases, especially if one enters this subject. There is a fine but important difference how the curvature is defined. Peter Rand and coworkers, Richard Templer's group and also others determine J0 from the pivotal plane of inverted hexagonal phases. This is the plane were the area does not change upon bending. However, ideally, the spontaneous curvature is determined at the neutral plane (plane were bending and stretching modes are decoupled). It is possible to estimate the neutral plane from the pivotal plane, but you need to know a few elastic parameters. If you really want to get deeply into this I recommend a book chapter by M. Kozlov (M. M. Kozlov, Methods in Membrane Lipids, Springer, 2007, pp. 355–366) as starter.

In our new paper, we derive the neutral plane from electron density maps with a simple analysis. We derived estimates for spontaneous curvatures for a series of membrane lipids, i.e. we extend the list of known values and we also add the temperature dependence.

Thanks, Georg and Edgar! These are very nice advices and papers. I'm not really planning to measure the spontaneous curvature of lipids. But I got interested in this question because I wantted to know how does specific lipids (PE for example), influece the overall physical properties of a bilayer. I think the spontaneous curvature of the bilayer won't be altered as long as composition of the two leaflets remains the same. Then the relatively large negative spontaneous curvature of PE will provide a large number of packing defects for the bilayer. I'm wondering if there are other roles that PE is playing..

Other than visualizing via transmissional electron microscopy is almost impossible and only speculative and very indirect. Yes, you may expect that incorporation of conical phospholipids into outer leaflet will curve membrane, but what radius of curavature it will produce is a big question. If you have a chance to make a slice of presumably curved membrane and look at it under TEM, it will be most precise way to get what you want, I think. Whatever estimation you do, a lot of has to be taken into account - compositional asymmetry of bilayer, ratio of long- short- tailed fatty acids, temperature, you count on, will affect for sure you want to measure

Hi, this is a nice discussion that you have initiated

You might also want to look at some of the work by Michael Brown et al on measurements of curvature using 2H NMR.

E.g. http://www.ncbi.nlm.nih.gov/pubmed/8499443

Thanks, Evgeny! I was actually wondering, in artificial bilayers such as GUVs, to what extent should we consider the compositional assymetry of two leafleats? Do you know if there are people who measured/estimated this?

Thanks Deborah!

There are also some quick-and-dirty methods available to determiln

e spontaneous curvature with SAXS, if you don't want to go too much into detail like Rand and coworkers. However, these methods are based on the original in-depth studies of DOPE. Some articles on that are:

Doi: 10.1016/j.chemphyslip.2008.03.007

Doi: DOI: 10.1039/C3SM51829A

Zheng Shi,

> to what extent should we consider the compositional

> assymetry of two leafleats? Do you know if there are

> people who measured/estimated this?

If you have prepared your GUVs with different phospholipids (polar heads, degree of saturation of fatty acids of tails), you may expect that molecules with larger heads and thinner hydrophobic part will be pushed to outer leaflet, especially in small GUVs. Termodinamically it will be more stable configuration. Honestly, I'd be happy too to see someone who could perform direct measurement of membrane curvature formation due to incorporation of conical lipids into one leaflet. You may have a look at some papers by Martinac B and Kloda A, in particular,

http://www.ncbi.nlm.nih.gov/pubmed/12172537

Where you'll see how curved bilayer deforms body of mechanosensitive channel.

Zheng

Hi, On my researchgate page, you may find a number research articles on interpretation of lipid curvature based lamellar, micellar, reverse hexagonal phases of plant chloroplast thylakoid membranes using tansmission electron microscopy, 13-NMR and spin label ESR techniques.

Hi Zheng,

regarding PE: The negative J0 of PEs adds considerable strain to lipid bilayers stored in form of elastic energy in flat bilayers. You may release this energy, e.g. upon partially inserting a compound (peptide, protein, ...). This may then lead to a globally curved bilayer. This energy may also couple to protein function, e.g. transmembrane proteins that undergo conformational changes that lead to shape changes in the plane of the membrane (e.g. ion channels). These ideas are quite old and have been brought up by Sol Gruner (http://onlinelibrary.wiley.com/doi/10.1111/j.1749-6632.1991.tb33902.x/abstract) and later worked out in detail by Robert Cantor (see e.g. http://www.ncbi.nlm.nih.gov/pubmed/9054538). We have also been working on this mechanism recently.

regarding some other contributions to this nice discussion: Be aware that there is a difference between membrane curvature and spontaneous curvature of single lipids.

Thanks, Evgeny! It makes a lot of sense that highly curved vesicles will prefer to put the more cone shape lipids into outer leaflet.

Hi Georg,

Thanks again, I read your recent soft matter paper yesterday, it's a really nice work and quite enlightening to me. I was aware of the difference between lipid and monolayer spontaneous curvature (that will be eq.4 of your paper, right?) In the case of bilayer, I guess the overall curvature should be simply the sum of two leaflets?

Unfortunately it is not that easy. Eq (4) calculates the monolayer spontaneous curvature of a lipid mixture assuming linear additivity (which seems to be given in many cases). For a bilayer curvature additional factors come into play (elasticity). In many cases the membrane curvature is zero although the constituent lipids have a nonzero spontaneous curvature. An extreme case is given for PEs, which have J0

Hi, Thank you all for the kind help! I learnt a lot from the answers you posted and the papers you pointed to me. However, one remaining question I have is about the spontanesous curvature of PIP2, it seems to me that no one has measured this value. Given the importance of PIP2, especially PI4,5P2, it would be surprising if no one is interested in its spontaneous curvature... So, are you guys aware of any literature talking about this issue? (the value for PIP2 spontaneous cuarvature and if indeed no such value exsit, what is reason for that)

Thanks again!

Zheng

Dear Evgeny,

We have indeed produced GUVs with a negatively curved lipid only in the outer leaflet (i.e. ceramide), by enzymatic digestion.

https://www.researchgate.net/publication/5543512_Ceramide_triggers_budding_of_exosome_vesicles_into_multivesicular_endosomes?ev=prf_pub

My lab specializes in creating asymmetric GUVs and we are currently working on connecting curvature to trans-leaflet asymmetry.

For symmetric GUVs, I would not worry about curvature effects. We observed them only with vesicle radius 10 µm).

Best regards

Article Ceramide Triggers Budding of Exosome Vesicles into Multivesi...

You might want to follow the articles published by these researcher-

R. P. Rand https://brocku.ca/researchers/peter_rand/cv/rprcv.html

Jens Coorssen

N. L. Fuller

Regards

Deepti