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«Carnegie Mellon University Research Showcase CMU Department of Physics Mellon College of Science Structure and Interactions of Lipid Bilayers: Role ...»

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Carnegie Mellon University

Research Showcase @ CMU

Department of Physics Mellon College of Science

Structure and Interactions of Lipid Bilayers: Role of

Fluctuations

John F. Nagle

Carnegie Mellon University, nagle@cmu.edu

Stephanie Tristram-Nagle

Carnegie Mellon University, stn@cmu.edu

Follow this and additional works at: http://repository.cmu.edu/physics

Part of the Physics Commons

Published In Biological Physics Series: Lipid Bilayers, 1-23.

This Book Chapter is brought to you for free and open access by the Mellon College of Science at Research Showcase @ CMU. It has been accepted for inclusion in Department of Physics by an authorized administrator of Research Showcase @ CMU. For more information, please contact researchshowcase@andrew.cmu.edu.

Structure and Interactions of Lipid Bilayers:

Role of Fluctuations John F. Nagle and Stephanie Tristram-Nagle 1 Introduction The cell is the fundamental unit in biology. Each cell is spatially de ned by its cytoplasmic membrane. The structural basis for each membrane is lipid in bilayer form. Following this reductionist point of view, it is therefore not surprising that lipid bilayers have been much studied using a great variety of techniques.

What is surprising is the large uncertainty for simple structural quantities that has been generated by the di erent studies. Let us consider the most studied of all bilayers, the one composed of the lipid DPPC in the fully hydrated, biologically relevant phase (L = uid(F)=liquid-crystalline) at T = 50o C. Various di raction and NMR studies have given values for the interfacial area A per DPPC lipid that range from 56A2 to 72A2 1,2]. A most distinguished neutron di raction study suggested A = 58A2 3] while a much used x-ray method obtained A = 71A2 4]. The real uncertainty in these numbers is even larger than the nominal 24% obtained by dividing one result by the other because A for DPPC in the low temperature gel (G) phase is AG 2 DPPC = 48A 1,5,6]. Therefore, the e ect of uidizing the F DPPC bilayer (i.e., making it biologically relevant) should be de ned to be A ;AG. Using the above di erences for the uid phase area of DPPC yields an enormous uncertainty in AF G DPPC ; ADPPC - from 8A to 24A. Even though one does expect to achieve as good precision in biophysics as in the physical sciences, this 100% level of uncertainty is ridiculous!

Uncertainty in A is directly related to uncertainty in the bilayer thickness.

A common de nition of bilayer thickness is DB = 2VL =A, where VL is the volume of a lipid molecule in the bilayer VL has been measured accurately (0:2%) by a number of groups 7]. The thickness of lipid bilayers (vide infra for discussion of various de nitions of thickness) is an important structural quantityfor discussing the incorporation of intrinsic membrane proteins.

Molecular dynamics simulations give much insight into lipid bilayer structure at a level of detail not available experimentally, but uncertainty in A negatively impacts such simulations. Some simulations are done with lipids and water in a simulation box of xed size, in which case A is xed in the simulation. Results obtained from such simulations performed at the wrong A 2 Nagle and Tristram-Nagle will be misleading and could even lead the unwary simulator to vary interaction parameters in order to t other data, such as the NMR order parameters.

Many simulations are now done with constant lateral pressure 8{10]. It is then in principle possible for the simulation to nd the correct value of A, but the computer time necessary to equilibrate can be large if the starting A is far from the equilibrated value. Furthermore, even if the simulation can be equilibrated, experimental uncertainty in A reduces the ability to test the interaction parameters used in the simulation.

This chapter will review some of the e orts to obtain structural results for L phase lipid bilayers with an emphasis on recent work from our lab. To obtain some of these structural results we found that it was necessary to deal with the e ects of uctuations. This in turn led us to the issue of interactions between bilayers, which is the second topic that will be discussed in this chapter. Underlying both these e orts is the central role of uctuations.

Fluctuations are important in biology. The fact that the biologically relevant uid phase of lipid bilayers is the one with the largest uctuations supports this paradigm. Bilayers with greater uidity can seal leaks and tears more readily. Local uctuations in the lipid molecules a ect passive permeability of solutes through the membrane and can facilitate the function of intrinsic membrane proteins by transiently reducing activation energy barriers 11]. In addition to uctuations at the molecular length scale, there are also longer length scale uctuations that can be adaptive for cell shape changes. Longer wavelength uctuations give rise to an additional force between membranes, and these are the uctuations that degrade di raction data necessary to obtain structure. This chapter will focus upon these longer length scale uctuations.

–  –  –

We will nish this general introduction with Fig. 1 which shows one key piece of structural information from our lab 12,13], the volume per lipid VL.

The temperature dependence in Fig. 1 indicates the various thermodynamic phases of DPPC. This chapter will focus on the most biologically relevant phase, identi ed in di raction studies as the L phase. There will be some use made of results for the gel phase, which we believe is the best characterized of all the phases 5]. The chapter of Katsaras and Raghunathan 14] complements this chapter by focussing on the lower temperature phases, especially the subgel and the ripple phases.





2 Structure

2.1 Levels of Description of Structure It is important to appreciate that it makes no sense to contemplate an atomic level structure at the sub{A level for lipid bilayers. This is not because of poor di raction technique or sample preparation. Lipid bilayers have biologically vital uctuations. This means that atoms are not inherently localized. The proper description for the positions of atoms in the lipid molecule is that of broad statistical distribution functions. Fig. 2a shows simulations for distribution functions for several of the component groups of the lipid molecule along the direction of the bilayer normal 15]. The widths in this direction are of order 5A. In contrast, in the `in-plane' direction the distribution functions for the L phase are just constants because the lipid molecules are in a twodimensional uid phase. (Of course, one can still consider pair correlation functions, which are important for di use wide angle scattering, but this is a little explored area.) In contrast, for the lower temperature phases there is interesting and valuable in-plane structure 14,5].

Fluctuations in biologically relevant fully hydrated uid phase bilayers mean that x-ray di raction data can only yield electron density pro les like the one shown in Fig. 2b. The peaks in such electron density pro les are associated with the electron dense phosphate group and the lower electron density in the center is associated with the hydrocarbon region and especially with the low electron density of terminal methyl groups of the fatty acids. Therefore, electron density pro les con rm the usual picture of bilayer structure and they give another measure of the bilayer thickness, namely, the head{ head thickness, DHH. However, electron density pro les do not yield the z coordinate of molecular groups along the bilayer normal. Such information has been obtained using neutron di raction, either with selective deuteration of various component groups (DPPC at 98% RH 3]), or combined with x-ray di raction (DOPC at 67% RH 16]).

The transverse description of the bilayer as a set of distribution functions along the z axis is valuable, but it does not include other important information, such as A in the lateral direction, or volumes. Therefore, a complementary description of bilayer structure, shown in Fig. 2c, is appropriate 4 Nagle and Tristram-Nagle

–  –  –

7]. The simplest description on the left of Fig. 2c divides the volume VL of the lipid into two regions. The tail region is essentially a hydrophobic hydrocarbon chain region by de nition, it includes only the methylenes and terminal methyls on the fatty acid chains. The head region is essentially a hydrophilic region, which includes the remainder of the lipid molecule (carbonyls, glycerol, phosphate and choline). An average structure is depicted by drawing two sharp boundaries, one between chains and heads and one between heads and water, as shown on the left side of Fig. 2c. In view of the uctuations shown in Fig. 2a, such sharp boundaries with all the chains on one side and the heads on the other are clearly arti cial, but it is still a valid representation in the sense that the sharp lines can be justi ed as Gibbs dividing surfaces 17]. Nevertheless, in the case of the interface between the headgroups and the water, it is useful to consider a re nement to the simple description on the left side of Fig. 2c. This re nement, shown on the right side of Fig. 2c, explicitly mixes the heads and water in the polar, interfacial region. This gives better correspondence with the distribution function description in Fig. 2a in particular, it gives a better representation of the steric thickness, de ned to be DB.0

2.2 Problem with the Gravimetric Method A popular method for obtaining structural information 4,6] is most easily explained from the description shown on the left side of Fig. 2c. The total volume VL of one lipid molecule and its associated nw water molecules is AD=2, where D is the repeat distance that is easily and accurately measured by di raction on stacks of lipid bilayers. (Using synchrotron x-rays and a high resolution setup, we have measured D with accuracy of 0:01A, though reproducibility with nominally identical samples is usually not so good.) Therefore, AD = 2(VL + nw Vw ) (1) where VL is the measured lipid volume 12], VW is the volume of water and nw is the number of water molecules/per lipid. The gravimetric method simply weighs the amount of water and the amount of lipid to obtain nw. Then, A is obtained as a function of nw from Eq. 1. The procedure is then to vary nw and measure D. In principle, as nw increases towards full hydration, D increases until an excess water phase forms at the fully hydrated value of nw. Increasing nw further just adds to the excess water phase and D should remain constant.

While the concept of the gravimetric method is simple and elegant, it has been criticized and a number of studies have obtained di erent results 1,18{21]. So let us elucidate the aw. The gravimetric method assumes that all the water added to the system goes between the lipid bilayers that are neatly stacked in regular one-dimensional arrays. In fact, gravimetric experiments are performed on lipid dispersions consisting of multilamellar vesicles 6 Nagle and Tristram-Nagle (MLVs). Such samples have many defect regions. For example, it is customary to visualize MLVs as consisting of spheres of about 10 m diameter composed of stacks of nearly a thousand bilayers. As is well known, packing of spheres leaves defect volumes between the spheres that amount to about 26% of the total volume (for a nice schematic see Fig. 3 in 21]). Such defect volumes, which must be lled with water, escape detection by di raction, which focusses on the more ordered structure. Therefore, the value of nw that should be used in Eq. 1 should be smaller than the gravimetric value of nw because the total weighed water includes defect water that is invisible to di raction.

This artifact suggests that the gravimetric method will tend to overestimate A. Direct veri cation of this tendency for the gravimetric method to overestimate nw and A was given for the gel phase of DPPC, for which inplane chain-packing and tilt angle were measured directly from wide angle di raction. This gave AG 2 DPPC = 48A and nw = 12 1,5]. The results of the most recent gravimetric studies 4,22] gave nw in the range 17:5 ; 19 which would require AG DPPC to be in the range 52 ; 54A 1]. The only exception we know to this tendency of the gravimetric method to overestimate is for EPC where 23] obtained AF = 64A2 using the gravimetric method which EPC is smaller than our best value of AF = 69:4A2 24].

EPC The gravimetric method also indicated that A increases strongly as the limit of full hydration is approached 6,21]. Indeed, A should increase in this limit. Recall that less than full hydration is equivalent to exerting osmotic pressure P on the water. The major e ect of osmotic pressure is to decrease the water space Dw and thereby the D space. However, osmotic pressure also decreases A because this too extracts water from stacks of bilayers. The appropriate formula to describe this second e ect is 25]

A = A0 ; ADw P=KA (2)

where A0 is the fully hydrated area when P = 0 and KA is the phenomenological area modulus. However, while A should increase as full hydration is approached, Rand and Parsegian 25] realized that the changes in A obtained from the unadulterated gravimetric method became much too large near full hydration for the measured values of KA 26]. They then used gravimetric values of A obtained under osmotic pressure at 10 atmospheres and they used Eq. 2 to extrapolate to fully hydrated P = 0. This reduced the estimate of AF 2 DPPC from 71A obtained from the unadulterated gravimetric method to 68:1A2 25]. However, this is still larger than the value obtained by an alternative method that we now proceed to discuss.

Bilayers and Fluctuations 7

2.3 Electron Density Pro le Method The electron density pro le (z) for symmetric bilayers with a lamellar repeat spacing D is 2 hX F cos 2 hz max (z) ; W = D F(0) + D (3) hh D h=1 where for the di erent orders h 0, h is the phase factor which can only assume values of +1 or ;1. Fh is the bilayer form factor which is routinely obtained from the intensity Ih = Fh =Ch under the di raction peak. Ch is the Lorentz polarization correction factor for low angle scattering Ch is nearly proportional to h2 for unoriented MLV samples and to h for oriented samples.



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