Interpretation of small angle X-ray measurements guided by molecular dynamics simulations of lipid bilayers

https://doi.org/10.1016/j.chemphyslip.2003.08.001Get rights and content

Abstract

Reconstruction and interpretation of lipid bilayer structure from X-ray scattering often rely on assumptions regarding the molecular distributions across the bilayer. It is usually assumed that changes in head–head spacings across the bilayer, as measured from electron density profiles, equal the variations in hydrocarbon thicknesses. One can then determine the structure of a bilayer by comparison to the known structure of a lipid with the same headgroup. Here we examine this procedure using simulated electron density profiles for the benchmark lipids DMPC and DPPC. We compare simulation and experiment in both real and Fourier space to address two main aspects: (i) the measurement of head–head spacings from relative electron density profiles, and (ii) the determination of the absolute scale for these profiles. We find supporting evidence for the experimental procedure, thus explaining the robustness and consistency of experimental structural results derived from electron density profiles. However, we also expose potential pitfalls in the Fourier reconstruction that are due to the limited number of scattering peaks. Volumetric analysis of simulated bilayers allows us to propose an improved, yet simple method for scale determination. In this way we are able to remove some of the restrictions imposed by limited scattering data in constructing reliable electron density profiles.

Introduction

X-ray diffraction studies of lipid bilayers have been specifically geared towards elucidation of the electron density profile, from which structural parameters such as the bilayer thickness, DB, and the area per lipid, A, can be calculated (Nagle and Tristram-Nagle, 2000). Obtaining accurate estimates of these quantities is important for two main reasons. First, the close matching between the bilayer thickness and the hydrophobic part of membrane proteins appear to control protein function Huang, 1986, Bloom et al., 1991, Harroun et al., 1999. It has been hypothesized that structural matching is biologically regulated via selection of lipids with proper chain length and saturation (Bloom et al., 1999). Depending on the length and saturation, bilayer thicknesses can differ by 10–15 Å Rand and Parsegian, 1989, Nagle and Tristram-Nagle, 2000. Yet, significantly more subtle variations are known to influence ion channel lifetimes (Elliott et al., 1983) and conformations (Greathouse et al., 1994), as well as the orientations of hydrophobic helical peptides Killian and Heijne, 2000, Petrache et al., 2000, Petrache et al., 2002. Similarly, structural properties associated with the lipid cross-sectional area and lateral stress Gruner, 1989, Brown, 1994, Botelho et al., 2002 are known to modulate protein function, as well as membrane permeability.

Second, accurate measurements of structural parameters are needed for quantification of interbilayer interactions McIntosh and Simon, 1986a, Rand and Parsegian, 1989, Israelachvili, 1992, Leikin et al., 1993, Zimmerberg and Chernomordik, 1999. At small distances, interbilayer forces depend exponentially on the interbilayer separation, changing by 20% with a 1 Å change in separation McIntosh and Simon, 1986a, McIntosh and Simon, 1993, Marsh, 1989, Rand and Parsegian, 1989, Petrache et al., 1998a. Here the relevant structural parameter is the water spacing DW, which is calculated from the lamellar repeat D, as DW=DDB. The accuracy of DW then depends on the determination of DB.

Measuring structural parameters for soft, highly fluctuating materials such as the lipid membrane, is a difficult task. Structural descriptions are more readily obtained for the lower temperature states: gel Nagle and Wiener, 1989, Sun et al., 1996a, Tristram-Nagle et al., 2002, subgel Tristram-Nagle et al., 1994, Katsaras, 1995 and, obviously, crystal (Small, 1986), where lipid hydrocarbon chains are ordered. Both normal (thickness) and lateral (cross-sectional area) parameters can be determined directly from the low and the wide angle X-ray scattering, respectively. For the fluid (melted chain) phase, the apparent structural resolution is 5–10 Å, corresponding to the spatial extent of the molecular distributions, as presented by the electron density profiles Worthington, 1969, Blaurock et al., 1971, Wiener and White, 1992. However, by parsing the lipid bilayer into molecular components, such as the lipid headgroup and acyl chains, average structural parameters are commonly reported with a precision of 1 Å or less Rand and Parsegian, 1989, Nagle and Tristram-Nagle, 2000, Rawicz et al., 2000.

The most readily available parameter from the electron density profile is the spacing DHH between the electron rich headgroup peaks. By itself, DHH is not sufficient for a complete description of structure, because its relationship with lateral parameters (area per lipid, A) is complicated by the broad lipid–water interface. One needs to relate DHH to better defined, and thermodynamically relevant parameters such as the hydrocarbon thickness DC and the total bilayer thickness DB, which are related to A through molecular volumes. Therefore, it is necessary to combine electron density and volumetric analyses in order to describe fluid phase bilayer structure McIntosh and Simon, 1986b, Nagle et al., 1996, Petrache et al., 1997, Armen et al., 1998, Tristram-Nagle et al., 1998, Nagle and Tristram-Nagle, 2000.

Given the experimental scattering data, i.e. the form factor ratios rh=Fh/F1, there are two main methods to construct the electron density profile, ρ*(z). The first method is model-free and consists of direct Fourier reconstruction (Worthington, 1969), ρ*(z)−ρW*=1DF(0)+2DF1h=1hmaxαhrhcos2πhzD,where ρW* is the bulk water electron density, D is the lamellar repeat spacing, αh=±1 are form factor phases, and hmax is the number of observed diffraction orders. There are two quantities in Eq. (1) that are usually not available from X-ray. These are F1, which in this formalism sets ρ*(z) on an absolute scale, and F(0) which gives the total bilayer contrast (offset) relative to the water electron density ρ*W, AF(0)=2(nL*−ρW*VL)=2(ρL*−ρW*)VL,in which A, VL, and nL* denote the area, volume, and number of electrons per lipid molecule, respectively. Handling the scale has been an issue for the fluid phase, as this requires additional information or certain assumptions with regard to the shape of the electron density profile (Petrache et al., 1998b). The shape, however, is strongly influenced by the number of diffraction orders available, hmax, which truncate the sum in Eq. (1). Fourier truncates complicates comparison between lipid bilayers.

The second method for constructing electron density profiles is functional modeling. This is done by assuming a particular functional form for the bilayer profile, with a number of free parameters to be determined by fitting to scattering form factors. Several approaches have been undertaken, from simple step-function models (Worthington, 1969), to more realistic Gaussian models Nagle and Wiener, 1989, Wiener et al., 1989, Wiener and White, 1992 and to more detailed component models Wiener and White, 1992, Schalke and Losche, 2000. Each of these models attempt to breakdown the electron density into component distributions by integrating knowledge from other measurements, such as specific volume, to reduce the number of fitting parameters.

Atomic-level computer simulations provide a new perspective on bilayer structure. There are numerous valuable contributions to the field addressing the underlying molecular disorder and heterogeneity Chiu et al., 1995, Berger et al., 1997, Tieleman et al., 1997, Feller et al., 1997, Tobias et al., 1997, Smondyrev and Berkowitz, 1999, Huber et al., 2002. In the hierarchy of models just discussed, these in fact constitute the most elaborate. One consequence of such detail, however, is that molecular dynamics simulations cannot be cast as fitting procedures as with the models above, as tuning the force-field parameters to a particular scattering dataset is unfeasible. Of course, the aims of simulations are more ambitious than just modeling of electron density profiles, but in this work we will focus just on this aspect. Because simulated electron density profiles result from all-atom representations which implicitly obey volume conservation, they can be used to evaluate assumptions employed in structure determination from scattering data.

A “bootstrap” method has been used in the literature to obtain structural parameters for a new bilayer by comparison with a reference structure McIntosh and Simon, 1986b, Nagle and Tristram-Nagle, 2000. It is assumed that the difference in the hydrocarbon thickness ΔDC can be estimated from the shift of the headgroup peak, ΔDHH/2, if two lipids have the same headgroup. (A factor of 1/2 is needed because DC is conventionally defined as half-thickness.) Having estimated DC from the DHH shift, the area per lipid is then obtained as the ratio between hydrocarbon volume and thickness. DHH does not depend on F(0) or the density scale, but needs to be corrected for Fourier truncation effects Blaurock et al., 1971, Lesslauer et al., 1972. To minimize these effects, DHH values have customarily been compared at similar resolution, D/hmax McIntosh and Simon, 1986a, McIntosh and Simon, 1986b, McIntosh and Simon, 1993, Rawicz et al., 2000, and correction terms were estimated using functional modeling (Sun et al., 1996a). With the availability of detailed atomic simulations, this aspect calls for renewed attention.

Here we consider previously reported MD simulations of fluid phase DMPC and DPPC bilayers as the basis for our discussion of structure determination from X-ray. We have focused on the Fourier reconstruction method and the calculation of the area per lipid from DHH and density measurements. The main goal is a comprehensive exercise with electron density profiles, and not necessarily simulation refinement. We have used simulated bilayers with structural parameters within the experimental uncertainty (1.5% or better), as a scaffolding for construction of self-consistent methodologies for structure determination from experiment. Because the bilayer form factors are the primary X-ray data, we have compared simulation and experiment in the Fourier space. We show an overall agreement, especially in the low q range, which seems to have the major influence on the main structural parameters. We process the simulated continuous transform by artificial sampling and cutoff at high q-values to mimic the measurement of head–head spacing DHH. We then compare DHH differences between DMPC and DPPC with differences in the hydrocarbon thicknesses DC to test the bootstrapping assumption. By analysis of Fourier truncation effects, we identify conditions for ΔDC≈ΔDHH/2 and estimate a possible deviation range.

By comparison of continuous transforms, we identify and fix a scale discrepancy between simulation and experiment. We propose an improved method for setting experimental electron density profiles on an absolute scale by using structural and volumetric parameters obtainable from unscaled profiles. While not directly relevant for measurements of DHH and subsequent determination of bilayer thicknesses, a correct absolute scale is critical for X-ray contrast (substitution) experiments (Franks et al., 1978).

Section snippets

Simulation setup

Simulations were performed using CHARMM software (Brooks et al., 1983) version 26 and were previously reported (Petrache et al., 2002). Periodic boundary conditions were used with constant number of atoms (N), temperature (T), lateral area (A), and normal pressure (PN) to generate NAPNT ensembles. Two lipids were considered: dimyristoylphosphatidylcholine (DMPC), and dipalmitoylphosphatidylcholine (DPPC). Simulation temperatures were 30°C for DMPC and 50°C for DPPC. For both lipids, bilayers

Fourier truncation and head–head spacing DHH

Simulated electron density profiles for DMPC at 30°C and DPPC at 50°C are shown in Fig. 1. Electrons were counted in bins of 0.1Å (in the z-direction normal to the bilayer) and averaged over the simulation. The most prominent features of the profiles are the headgroup peaks at the lipid–water interface and the methyl troughs at the bilayer center. The two profiles shown are similar in shape, with DPPC being broader by about 2–3 Å due to its longer hydrocarbon chains. Relative to the water

Discussion

Guided by molecular dynamics simulations of DMPC and DPPC, we have taken a critical look at the Fourier reconstruction method used to obtain structural parameters from X-ray. We have addressed two main aspects. First, we have estimated the effect of Fourier truncation on the headgroup peak location, and the uncertainty in measuring ΔDC using the headgroups peaks. We have used smoothed (4-order) electron density profiles corresponding to the typical resolution achievable by experiments. Between

Acknowledgements

We thank Dr. John F. Nagle for valuable discussions and comments on the manuscript, and Dr. Thomas Huber for discussions of continuous transforms and of his simulation results. J.N.S. thanks the Whitaker Foundation for Biomedical Engineering for graduate fellowship support.

References (62)

  • D. Marsh

    Water adsorption isotherms and hydration forces for lysolipids and diacyl phospholipids

    Biophys. J.

    (1989)
  • R.J. Mashl et al.

    Molecular simulation of dioleoylphophatidylcholine lipid bilayers at differing levels of hydration

    Biophys. J.

    (2001)
  • J.F. Nagle et al.

    Relations for lipid bilayers—connection of electron-density profiles to other structural quantities

    Biophys. J.

    (1989)
  • J.F. Nagle et al.

    Structure of lipid bilayers

    Biochim. Biophys. Acta

    (2000)
  • J.F. Nagle et al.

    X-ray structure determination of fully hydrated Lα phase dipalmitoylphosphatidylcholine bilayers

    Biophys. J.

    (1996)
  • H.I. Petrache et al.

    Determination of component volumes of lipid bilayers from simulations

    Biophys. J.

    (1997)
  • H.I. Petrache et al.

    Fluid phase structure of EPC and DMPC bilayers

    Chem. Phys. Lipids

    (1998)
  • H.I. Petrache et al.

    Modulation of glycophorin A transmembrane helix interactions by lipid bilayers: molecular dynamics calculations

    J. Mol. Biol.

    (2000)
  • R.P. Rand et al.

    Hydration forces between phospholipid-bilayers

    Biochim. Biophys. Acta

    (1989)
  • W. Rawicz et al.

    Effect of chain length and unsaturation on elasticity of lipid bilayers

    Biophys. J.

    (2000)
  • M. Schalke et al.

    Structural models of lipid surface monolayers from X-ray and neutron reflectivity measurements

    Adv. Coll. Int. Sci.

    (2000)
  • W.J. Sun et al.

    Structure of gel phase saturated lecithin bilayers: temperature and chain length dependence

    Biophys. J.

    (1996)
  • D.P. Tieleman et al.

    A computer perspective of membranes: molecular dynamics studies of lipid bilayer systems

    Biochim. Biophys. Acta

    (1997)
  • D.J. Tobias et al.

    Atomic-scale molecular dynamics simulations of lipid membranes

    Current Opin. Colloid Interf. Sci.

    (1997)
  • S. Tristram-Nagle et al.

    Kinetics of subgel formation in DPPC—X-ray-diffraction proves nucleation-growth hypothesis

    Biochim. Biophys. Acta

    (1994)
  • S. Tristram-Nagle et al.

    Structure and interactions of fully hydrated dioleoylphosphatidylcholine bilayers

    Biophys. J.

    (1998)
  • S. Tristram-Nagle et al.

    Structure of gel phase DMPC determined by X-ray diffraction

    Biophys. J.

    (2002)
  • M.C. Wiener et al.

    Structure of a fluid dioleoylphosphatidylcholine bilayer determined by joint refinement of X-ray and neutron-diffraction data. 3. Complete structure

    Biophys. J.

    (1992)
  • M.C. Wiener et al.

    Structure of the fully hydrated gel phase of DPPC

    Biophys. J.

    (1989)
  • C.R. Worthington

    Interpretation of low-angle X-ray data from planar and concentric multilayered structures—use of one-dimensional electron density strip models

    Biophys. J.

    (1969)
  • J. Zimmerberg et al.

    Membrane fusion

    Adv. Drug Deliv. Rev.

    (1999)
  • Cited by (52)

    • Investigating the nanostructure of a CER[NP]/CER[AP]-based stratum corneum lipid matrix model: A combined neutron diffraction & molecular dynamics simulations approach

      2022, Biochimica et Biophysica Acta - Biomembranes
      Citation Excerpt :

      At the current state of the art, the detailed nanostructure and many of the biophysical properties of the SC, have yet to be studied in detail. A combinatorial approach using detailed neutron diffraction experiments and molecular dynamics (MD) simulations provides a good opportunity to address the relation between lipid arrangements and skin barrier at a nanoscale, by studying their model systems [22–25]. The earlier studies of the SC focused mainly on the comparison of healthy and diseased skin.

    • Atomistic resolution structure and dynamics of lipid bilayers in simulations and experiments

      2016, Biochimica et Biophysica Acta - Biomembranes
      Citation Excerpt :

      As already discussed in Section 2.1, significant advantage of MD model is that the same model can be straightforwardly compared to both, NMR and scattering data. Several models, reviewed by Heberle et al. [182], are developed to give structural interpretation for the form factor data [183], while also MD simulations are used [169,184-187]. In these studies the area per molecule is often fixed to a value minimizing the differences between experimental and simulated form factors [169,184-187].

    View all citing articles on Scopus
    View full text