Experimental support for tilt-dependent theory of biomembrane mechanics

Recent simulations have indicated that the traditional model for topographical fluctuations in biomembranes should be enriched to include molecular tilt. Here we report the first experimental data supporting this enrichment. Utilizing a previously posited tilt-dependent model, a height-height correlation function was derived. The x-ray scattering from a liquid crystalline stack of oriented fluid phase lipid bilayers was calculated and compared with experiment. By fitting the measured scattering intensity, both the bending modulus K(c)=8.3±0.6×10⁻²⁰ J and the tilt modulus K(θ)=95±7  mN/m were determined for DOPC lipid bilayers at 30 °C.

Anomalous swelling in phospholipid bilayers is not coupled to the formation of a ripple phase

Aligned stacks of monomethyl and dimethyl dimyristoyl phosphatidylethanolamine (DMPE) lipid bilayers, like the much studied dimyristoyl PC (DMPC) bilayers, swell anomalously in a critical fashion as the temperature is decreased within the fluid phase towards the main transition temperature, T(M). Unlike DMPC bilayers, both monomethyl and dimethyl DMPE undergo transitions into a gel phase rather than a rippled phase below T(M). Although it is not fully understood why there is anomalous swelling, our present results should facilitate theory by showing that the formation of the phase below T(M) is not related to critical phenomena above T(M).

The thermotropic phase behavior of cationic lipids: calorimetric, infrared spectroscopic and X-ray diffraction studies of lipid bilayer membranes composed of 1,2-di-O-myristoyl-3-N,N,N-trimethylaminopropane (DM-TAP)

The thermotropic phase behavior of lipid bilayer model membranes composed of the cationic lipid 1,2-di-O-myristoyl-3-N,N,N-trimethylaminopropane (DM-TAP) was examined by differential scanning calorimetry, infrared spectroscopy and X-ray diffraction. Aqueous dispersions of this lipid exhibit a highly energetic endothermic transition at 38.4 degrees C upon heating and two exothermic transitions between 20 and 30 degrees C upon cooling. These transitions are accompanied by enthalpy changes that are considerably greater than normally observed with typical gel/liquid--crystalline phase transitions and have been assigned to interconversions between lamellar crystalline and lamellar liquid--crystalline forms of this lipid. Both infrared spectroscopy and X-ray diffraction indicate that the lamellar crystalline phase is a highly ordered, substantially dehydrated structure in which the hydrocarbon chains are essentially immobilized in a distorted orthorhombic subcell. Upon heating to temperatures near 38.4 degrees C, this structure converts to a liquid-crystalline phase in which there is excessive swelling of the aqueous interlamellar spaces owing to charge repulsion between, and undulations of, the positively charged lipid surfaces. The polar/apolar interfaces of liquid--crystalline DM-TAP bilayers are not as well hydrated as those formed by other classes of phospho- and glycolipids. Such differences are attributed to the relatively small size of the polar headgroup and its limited capacity for interaction with moieties in the bilayer polar/apolar interface.

Method for obtaining structure and interactions from oriented lipid bilayers

Precise calculations are made of the scattering intensity I(q) from an oriented stack of lipid bilayers using a realistic model of fluctuations. The quantities of interest include the bilayer bending modulus Kc, the interbilayer interaction modulus B, and bilayer structure through the form factor F(qz). It is shown how Kc and B may be obtained from data at large q(z) where fluctuations dominate. Good estimates of F(qz) can be made over wide ranges of q(z) by using I(q) in q regions away from the peaks and for q(r) not equal0 where details of the scattering domains play little role. Rough estimates of domain sizes can also be made from smaller q(z) data. Results are presented for data taken on fully hydrated, oriented DOPC bilayers in the L(alpha) phase. These results illustrate the advantages of oriented samples compared to powder samples.

Structure of lipid bilayers

The quantitative experimental uncertainty in the structure of fully hydrated, biologically relevant, fluid (L(alpha)) phase lipid bilayers has been too large to provide a firm base for applications or for comparison with simulations. Many structural methods are reviewed including modern liquid crystallography of lipid bilayers that deals with the fully developed undulation fluctuations that occur in the L(alpha) phase. These fluctuations degrade the higher order diffraction data in a way that, if unrecognized, leads to erroneous conclusions regarding bilayer structure. Diffraction measurements at high instrumental resolution provide a measure of these fluctuations. In addition to providing better structural determination, this opens a new window on interactions between bilayers, so the experimental determination of interbilayer interaction parameters is reviewed briefly. We introduce a new structural correction based on fluctuations that has not been included in any previous studies. Updated measurements, such as for the area compressibility modulus, are used to provide adjustments to many of the literature values of structural quantities. Since the gel (L(beta)') phase is valuable as a stepping stone for obtaining fluid phase results, a brief review is given of the lower temperature phases. The uncertainty in structural results for lipid bilayers is being reduced and best current values are provided for bilayers of five lipids.

Lipid bilayer structure

Fluctuations, inherent in flexible and biologically relevant lipid bilayers, make quantitative structure determination challenging. Shortcomings in older methods of structure determination have been realized and new methodologies have been introduced that take fluctuations into account. The large uncertainty in literature values of lipid bilayer structural parameters is being reduced.

Clarification of the ripple phase of lecithin bilayers using fully hydrated, aligned samples

Aligned samples of lipid bilayers have been fully hydrated from water vapor in a different type of x-ray chamber. Our use of aligned samples resolves issues concerning the ripple phase that were ambiguous from previous powder studies. In particular, our x-ray diffraction data conclusively demonstrate that, on cooling from the L alpha to the P beta' phase, both chiral and racemic samples of dipalmitoyl phosphatidylcholine (DPPC) exhibit phase coexistence of long and short ripples with a ripple wavelength ratio lambda L/lambda S approximately 1.8. Moreover, the long ripple always forms an orthorhombic unit cell (gamma L = 90 degrees), strongly supporting the possibility that these ripples are symmetric. In contrast, gamma S for short ripples was consistently different from 90 degrees, implying asymmetric ripples. We continue to find no evidence that chirality affects the structure of rippled bilayers. The relative thermodynamic stability of the two types of ripples was investigated and a qualitative free energy diagram is given in which the long ripple phase is metastable. Finally, we suggest a kinetic mechanism, involving loss of water, that promotes formation of the metastable long ripple phase for special thermal protocols.

Re-analysis of magic angle spinning nuclear magnetic resonance determination of interlamellar waters in lipid bilayer dispersions

A recent method to obtain the number of water molecules of hydration of multilamellar lipid vesicles using magic angle spinning nuclear magnetic resonance has been re-examined. The previous interpretation divided the water into bulk and interlamellar water and ignored water in defects (lakes) that are intrinsic to multilamellar lipid vesicles; the result was inconsistent with x-ray results for the lipid DOPC. The new interpretation takes advantage of the reduction of lake water with increased spinning and it uses osmotic pressure measurements to determine the loss of interlamellar water. The new result for DOPC from magic angle spinning is consistent with x-ray results.

Polymorphism in myristoylpalmitoylphosphatidylcholine

This study focuses on the mixed-chain lipid myristoylpalmitoylphosphatidylcholine (MPPC) near full hydration. The lipid, synthesized according to the procedure of (Mason et al., 1981a, has a low degree of acyl chain migration. When MPPC is temperature-jumped (T-jumped) from the L alpha phase (T = 38 degrees C) to T = 20 degrees C or below, a subgel phase forms; this formation takes less than 1 h at a temperature below T = 12 degrees C. The subgel remains stable up to T = 29 degrees C. When MPPC is T-jumped from the L alpha phase to T = 24 degrees C or above, a ripple phase forms with coexisting ripple wavelengths of 240 A and 130 A. In contrast, when MPPC is melted from the subgel phase, the ripple phase is characterized by bilayers having a single ripple wavelength of 130 A. In agreement with earlier studies (Stumpel et al., 1983; Serrallach et al., 1984. Structure and thermotropic properties of mixed-chain phosphatidylcholine bilayer membranes. Biochemistry 23:713-720.), no stable gel phase was observed. Instead, an ill-defined low-angle X-ray pattern is initially observed, which gradually transforms into the subgel phase below 20 degrees C, or into the ripple phase above 24 degrees C. In the wide-angle X-ray diffraction, a single peak is observed, similar to the ripple phase wide-angle pattern, that either persists above 24 degrees C or transforms into a multi-peaked subgel wide-angle pattern below 20 degrees C. The absence of a gel phase can be understood phenomenologically as the relative dominance of the subgel phase in mixed-chain PCs compared to same-chain PCs. The subgel structure and molecular interactions responsible for this comparative behavior are interesting open issues.

Absence of a vestigial vapor pressure paradox

The enigmatic but much accepted vapor pressure paradox for oriented lipid bilayer samples was recently justified theoretically. Subsequently, recent experiments have shown that there is no vapor pressure paradox. The first result of this paper is to consider another degree of freedom that reverses the previous theoretical conclusion, so that theory and experiment are now in agreement that there is no vapor pressure paradox. However, this analysis also suggests the possibility of a vestigial vapor pressure paradox that would rationalize why the vapor pressure paradox was historically so persistent and that would have led to an improved protocol for obtaining bilayer structure. This vestigial vapor pressure paradox would involve a phase transition as a function of applied osmotic pressure. We test this possibility experimentally using combined neutron and x-ray scattering data. The conclusion from these experiments is that there is not even a vestigial vapor pressure paradox. However, this negative result validates an improved method for calibrating osmotic pressure in x-ray studies of oriented samples.

Analysis of simulated NMR order parameters for lipid bilayer structure determination

The conventional formula for relating CD2 average order parameters <Sn> to average methylenic travel <Dn> is flawed when compared to molecular dynamics simulations of dipalmitoylphosphatidylcholine. Inspired by the simulated probability distribution functions, a new formula is derived that satisfactorily relates these quantities. This formula is used to obtain the average chain length <LC>, and the result agrees with the direct simulation result for <LC>. The simulation also yields a hydrocarbon thickness 2<DC>. The result <LC> = <DC> is consistent with a model of chain packing with both early chain termination and partial interdigitation of chains from opposing monolayers. The actual simulated area per lipid <A> is easily obtained from the order parameters. However, when this method is applied to NMR order parameter data from dimyristoylphosphatidylcholine, the resulting <A> is 10% larger than the currently accepted value.

Structure and interactions of fully hydrated dioleoylphosphatidylcholine bilayers

This study focuses on dioleoylphosphatidylcholine (DOPC) bilayers near full hydration. Volumetric data and high-resolution synchrotron x-ray data are used in a method that compares DOPC with well determined gel phase dipalmitoylphosphatidylcholine (DPPC). The key structural quantity obtained is fully hydrated area/lipid A0 = 72.2 +/- 1.1 A2 at 30 degrees C, from which other quantities such as thickness of the bilayer are obtained. Data for samples over osmotic pressures from 0 to 56 atmospheres give an estimate for the area compressibility of KA = 188 dyn/cm. Obtaining the continuous scattering transform and electron density profiles requires correction for liquid crystal fluctuations. Quantitation of these fluctuations opens an experimental window on the fluctuation pressure, the primary repulsive interaction near full hydration. The fluctuation pressure decays exponentially with water spacing, in agreement with analytical results for soft confinement. However, the ratio of decay length lambda(fl) = 5.8 A to hydration pressure decay length lambda = 2.2 A is significantly larger than the value of 2 predicted by analytical theory and close to the ratio obtained in recent simulations. We also obtain the traditional osmotic pressure versus water spacing data. Our analysis of these data shows that estimates of the Hamaker parameter H and the bending modulus Kc are strongly coupled.

Effect of substrate roughness on D spacing supports theoretical resolution of vapor pressure paradox

The lamellar D spacing has been measured for oriented stacks of lecithin bilayers prepared on a variety of solid substrates and hydrated from the vapor. We find that, when the bilayers are in the L(alpha) phase near 100% relative humidity, the D spacing is consistently larger when the substrate is rougher than when it is smooth. The differences become smaller as the relative humidity is decreased to 80% and negligible differences are seen in the L(beta') phase. Our interpretation is that rough substrates frustrate the bilayer stack energetically, thereby increasing the fluctuations, the fluctuational repulsive forces, and the water spacing compared with stacks on smooth surfaces. This interpretation is consistent with and provides experimental support for a recently proposed theoretical resolution of the vapor pressure paradox.

DMSO produces a new subgel phase in DPPC: DSC and X-ray diffraction study

Equilibrium phases and the kinetics of subgel phase transformation of dipalmitoylphosphatidylcholine (DPPC) hydrated with mixtures of dimethylsulfoxide (DMSO)/water have been studied using differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The rate of gel-to-subgel transformation is decreased with a small increase in X, the DMSO/water mole fraction, but then speeds up and becomes faster than in pure water by X = 0.16. The DSC scans show multiple subgel peaks, some of which can be attributed to impacted domain growth. For X greater than 0.10, XRD shows that there is a new, stable subgel phase, S, which also accounts for some of the multiplicity of DSC peaks. Our electron density profiles show that the thickness of the bilayer in the S phase is greater than in the usual C subgel phase. We suggest that the S subgel phase is characterized by different headgroup ordering and smaller chain tilt angle than in the C subgel phase. Electron density profiles show that increasing X decreases the water space between bilayers in all phases, subgel, gel and fluid (L alpha). For X = 0.20, a different gel phase is also observed that may be due to subtle changes in the orientation of chain tilt first observed in partially dehydrated DMPC. The dehydrating effect of DMSO explains the results of a previous study, confirmed in this study, that increasing the concentration of DMSO raises the main transition temperature and eliminates the ripple phase.

Determination of component volumes of lipid bilayers from simulations

An efficient method for extracting volumetric data from simulations is developed. The method is illustrated using a recent atomic-level molecular dynamics simulation of L alpha phase 1,2-dipalmitoyl-sn-glycero-3-phosphocholine bilayer. Results from this simulation are obtained for the volumes of water (VW), lipid (V1), chain methylenes (V2), chain terminal methyls (V3), and lipid headgroups (VH), including separate volumes for carboxyl (Vcoo), glyceryl (Vgl), phosphoryl (VPO4), and choline (Vchol) groups. The method assumes only that each group has the same average volume regardless of its location in the bilayer, and this assumption is then tested with the current simulation. The volumes obtained agree well with the values VW and VL that have been obtained directly from experiment, as well as with the volumes VH, V2, and V3 that require certain assumptions in addition to the experimental data. This method should help to support and refine some assumptions that are necessary when interpreting experimental data.

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

Systematic low-angle and wide-angle x-ray scattering studies have been performed on fully hydrated unoriented multilamamellar vesicles of saturated lecithins with even chain lengths N = 16, 18, 20, 22, and 24 as a function of temperature T in the normal gel (L beta') phase. For all N, the area per chain Ac increases linearly with T with an average slope dAc/dT = 0.027 A2/degree C, and the lamellar D-spacings also increase linearly with an average slope dD/dT = 0.040 A/degree C. At the same T, longer chain length lecithins have more densely packed chains, i.e., smaller Ac's, than shorter chain lengths. The chain packing of longer chain lengths is found to be more distorted from hexagonal packing than that of smaller N, and the distortion epsilon of all N approaches the same value at the respective transition temperatures. The thermal volume expansion of these lipids is accounted for by the expansion in the hydrocarbon chain region. Electron density profiles are constructed using four orders of low-angle lamellar peaks. These show that most of the increase in D with increasing T is due to thickening of the bilayers that is consistent with a decrease in tilt angle theta and with little change in water spacing with either T or N. Because of the opposing effects of temperature on area per chain Ac and tilt angle 0, the area expansivity alpha A is quite small. A qualitative theoretical model based on competing head and chain interactions accounts for our results.

Structure of the ripple phase in lecithin bilayers

The phases of the x-ray form factors are derived for the ripple (Pbeta') thermodynamic phase in the lecithin bilayer system. By combining these phases with experimental intensity data, the electron density map of the ripple phase of dimyristoyl-phosphatidylcholine is constructed. The phases are derived by fitting the intensity data to two-dimensional electron density models, which are created by convolving an asymmetric triangular ripple profile with a transbilayer electron density profile. The robustness of the model method is indicated by the result that many different models of the transbilayer profile yield essentially the same phases, except for the weaker, purely ripple (0,k) peaks. Even with this residual ambiguity, the ripple profile is well determined, resulting in 19 angstroms for the ripple amplitude and 10 degrees and 26 degrees for the slopes of the major and the minor sides, respectively. Estimates for the bilayer head-head spacings show that the major side of the ripple is consistent with gel-like structure, and the minor side appears to be thinner with lower electron density.

X-ray structure determination of fully hydrated L alpha phase dipalmitoylphosphatidylcholine bilayers

Bilayer form factors obtained from x-ray scattering data taken with high instrumental resolution are reported for multilamellar vesicles of L alpha phase lipid bilayers of dipalmitoylphosphatidylcholine at 50 degrees C under varying osmotic pressure. Artifacts in the magnitudes of the form factors due to liquid crystalline fluctuations have been eliminated by using modified Caillé theory. The Caillé fluctuation parameter eta 1 increases systematically with increasing lamellar D spacing and this explains why some higher order peaks are unobservable for the larger D spacings. The corrected form factors fall on one smooth continuous transform F(q); this shows that the bilayer does not change shape as D decreases from 67.2 A (fully hydrated) to 60.9 A. The distance between headgroup peaks is obtained from Fourier reconstruction of samples with four orders of diffraction and from electron density models that use 38 independent form factors. By combining these results with previous gel phase results, area AF per lipid molecule and other structural quantities are obtained for the fluid L alpha phase. Comparison with results that we derived from previous neutron diffraction data is excellent, and we conclude from diffraction studies that AF = 62.9 +/- 1.3 A2, which is in excellent agreement with a previous estimate from NMR data.

Anomalous phase behavior of long chain saturated lecithin bilayers

X-ray scattering has been performed on fully hydrated unoriented multilamellar vesicles of lecithins with even chain lengths n from 16 to 24 as a function of temperature in chain ordered phases. The longer chain lengths, n > or = 20, show anomalous behavior compared to the shorter chain lengths, n < 20. This report concentrates on n = 24. Although the history and time dependence shows that equilibrium was not always achieved, it appears that there is a second gel-like phase G2 below 40 degrees C. The G2 phase has a small tilt angle and opposite hexagonal symmetry breaking from the usual G1 gel phase. Also, as T is raised above 45 degrees C, the wide-angle data suggest the appearance of a phase with hexagonal chain packing and small chain tilt angle.

Small-angle x-ray scattering from lipid bilayers is well described by modified Caillé theory but not by paracrystalline theory

X-ray scattering data at high instrumental resolution are reported for multilamellar vesicles of L alpha phase lipid bilayers of 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine at 50 degrees C under varying osmotic pressure. The data are fitted to two theories that account for noncrystalline disorder, paracrystalline theory (PT) and modified Caillé theory (MCT). The MCT provides good fits to the data, much better than the PT fits. The particularly important characteristic of MCT is the long power law tails in the scattering. PT fits (as well as ordinary integration with no attempt to account for the noncrystalline disorder) increasingly underestimate this scattering intensity as the order h increases, thereby underestimating the form factors used to obtain electron density profiles.

Testing BR photocycle kinetics

An improved K absorption spectrum in the visible is obtained from previous photocycle data for the D96N mutant of bacteriorhodopsin, and the previously obtained M absorption spectrum in the visible and the fraction cycling are confirmed at 25 degrees C. Data at lower temperatures are consistent with negligible temperature dependence in the spectra from 5 degrees C to 25 degrees C. Detailed analysis strongly indicates that there are two intermediates in addition to the first intermediate K and the last intermediate M. Assuming two of the intermediates have the same spectrum and using the L spectrum obtained previously, the best kinetic model with four intermediates that fits the time course of the intermediates is rather unusual, with two L's on a cul-de-sac. However, a previously proposed, more conventional model with five intermediates, including two L's with the same spectra and two M's with the same spectra, also fits the time course of the intermediates nearly as well. A new criterion that tests an individual proposed spectrum against data is also proposed.

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

Wide-angle and low-angle X-ray diffraction data were obtained during the time course of the gel to subgel phase transformation in fully hydrated DPPC. When the system was kept close to equilibrium by following a T-jump protocol, the X-ray data unequivocally demonstrate the coexistence of growing subgel and shrinking gel domains. When the system was supercooled and held further from equilibrium as in previous studies, the kinetic behavior was more complicated. These data prove that the basic mechanism for the gel to subgel phase transformation is one of nucleation of subgel domains followed by growth of the domains.

Area/lipid of bilayers from NMR

Values of area per lipid A ranging from 56 to 72 A 2 have been reported from essentially the same SCD data from DPPC in the L alpha phase. The differences are due primarily to three separate binary choices in interpretation. It is argued that one particular combination is best; this yields A = 62 +/- 2 A 2 for DPPC at 50 degrees C. Each preceding interpretation agrees with at least one of the three present choices and disagrees with at least one.

Measurement of chain tilt angle in fully hydrated bilayers of gel phase lecithins

The tilt angle theta tilt of the hydrocarbon chains has been determined for fully hydrated gel phase of a series of saturated lecithins. Oriented samples were prepared on glass substrates and hydrated with supersaturated water vapor. Evidence for full hydration was the same intensity pattern of the low angle lamellar peaks and the same lamellar repeat D as unoriented multilamellar vesicles. Tilting the sample permitted observation of all the wide angle arcs necessary to verify the theoretical diffraction pattern corresponding to tilting of the chains towards nearest neighbors. The length of the scattering unit corresponds to two hydrocarbon chains, requiring each bilayer to scatter coherently rather than each monolayer. For DPPC, theta tilt was determined to be 32.0 +/- 0.5 degrees at 19 degrees C, slightly larger than previous direct determinations and considerably smaller than the value required by recent gravimetric measurements. This new value allows more accurate determinations of a variety of structural parameters, such as area per lipid molecule, A = 47.2 +/- 0.5 A2, and number of water molecules of hydration, nw = 11.8 +/- 0.7. As the chain length n of the lipids was increased from 16 to 20 carbons, the parameters A and nw remained constant, suggesting that the headgroup packing is at its excluded volume limit for this range. However, theta tilt increased by 3 degrees and the chain area Ac decreased by 0.5 A2. This behavior is explained in terms of a competition between a bulk free energy term and a finite or end effect term.

Evidence of partial rotational order in gel phase DPPC

It is shown how the dichroic ratio of the symmetric methylene stretching modes depends upon both the rotational order of hydrocarbon chains about their long axis and the tilting of the long chains with respect to the bilayer normal. Use of a recent determination of the tilt angle from x-ray measurements together with recent dichroic infrared data yields a rotational order parameter g = -0.30 compared to g = 0 for complete disorder and g = +/- 1 for complete order. The negative value of g corresponds to a preference for the plane defined by the chain carbons to be more perpendicular than parallel to the plane defined by the tilt direction and the bilayer normal.

Long tail kinetics in biophysics?

Long tail kinetics describe a variety of data from complex, disordered materials that cannot be described by conventional kinetics. It is suggested that the kinetics of diffusive motion in complex biological media, such as cytoplasm or biomembranes, might also have long tails. The effects of long tail kinetics are investigated for two standard biophysical measurements, fluorescence recovery after photobleaching (FRAP), and dynamic light scattering (DLS). It is shown that long tail kinetic data would yield significantly distorted and misleading results when analyzed assuming conventional kinetics.

Photocycle kinetics: analysis of Raman data from bacteriorhodopsin

A recently developed algorithm for analyzing photocycle kinetics was applied to recently obtained Raman data for the time course of bacteriorhodopsin (bR) and its intermediates, L, M, N and O. The algorithm allows all possible transitions between any of the intermediates in the kinetic model. The best fit to all the Raman data required the transitions L in equilibrium with M in equilibrium with N----O----bR and also the branch L in equilibrium with N. The rates are moderately well determined and smooth as a function of pH. From the ratios of forward and backward rates the differences in free energy of the L, M and N states are no larger than 1.5 kcal. The possibility that only the sum of the L and N concentrations is well determined, but not the individual L and N concentrations, was investigated. The model L in equilibrium with M in equilibrium with N----O----bR satisfactorily fitted condensed L + N data and gave predicted individual L and N concentrations considerably different than those measured individually. The possibility of Raman invisible states, such as two Ms or two Ns was also investigated. Models with two Ns were not successful and it cannot yet confidently be concluded which model with two Ms is best. However, the model, L in equilibrium with M1----M2----N----O----bR plus the branch L----N, fits the data better with the same number of parameters as the best model with only one M intermediate. This provides strong support for two Ms in the bR photocycle.

Solving complex photocycle kinetics. Theory and direct method

A direct nonlinear least squares method is described that obtains the true kinetic rate constants and the temperature-independent spectra of n intermediates from spectroscopic data taken in the visible at three or more temperatures. A theoretical analysis, which is independent of implementation of the direct method, proves that well determined local solutions are not possible for fewer than three temperatures. This analysis also proves that measurements at more than n wavelengths are redundant, although the direct method indicates that convergence is faster if n + m wavelengths are measured, where m is of order one. This suggests that measurements should concentrate on high precision for a few measuring wavelengths, rather than lower precision for many wavelengths. Globally, false solutions occur, and the ability to reject these depends upon the precision of the data, as shown by explicit example. An optimized way to analyze vibrational spectroscopic data is also presented. Such data yield unique results, which are comparably accurate to those obtained from data taken in the visible with comparable noise. It is discussed how use of both kinds of data is advantageous if the data taken in the visible are significantly less noisy.

Structure of the fully hydrated gel phase of dipalmitoylphosphatidylcholine

X-ray diffraction intensities for lamellar repeats, h = 1 to 7, and wide-angle x-ray scattering were measured for the gel phase of fully hydrated dipalmitoylphosphatidylcholine. A hybrid model, which represents the electron density along the lamellar repeat direction as a continuous function composed of constant strips and superimposed Gaussians, is defined. The data were used to determine the best parameters in hybrid models and also in the older strip models. The most successful results were obtained when the density of the methylene region was constrained to the value obtained from the wide-angle scattering. Further analysis utilized the lipid volume obtained from absolute specific volume measurements. Together with the fundamental relations derived in the previous paper, the electron density modeling yielded the headgroup volume (340 +/- 10 A3) and the methylene volume (25.3 +/- 0.2A3). The results were in agreement whether the hybrid model or the strip model was used and whether our data or the data of Torbet and Wilkins were used. Additional structural results, such as the area (45.9 +/- 2.0 A2) and the number of waters of hydration per lipid (10.6 +/- 2.0), required one additional piece of information, which we took to be the tilt angle theta, which is 30 +/- 3 degrees from other experiments in the literature. Absolute electron density profiles, which clearly indicate two features in the headgroup region, are presented. The analysis yielded an accurate value of F(0), which contributes to the continuous scattering transform F(X), which is also given.

Relations for lipid bilayers. Connection of electron density profiles to other structural quantities

Three relations are derived that connect low angle diffraction/scattering results obtained from lipid bilayers to other structural quantities of interest. The first relates the area along the surface of the bilayer, the measured specific volume, and the zeroth order structure factor, F(0). The second relates the size of the trough in the center of the electron density profile, the volume of the terminal methyl groups, and the volume of the methylene groups in the fatty acid chains. The third relates the size of the headgroup electron density peak, the volume of the headgroup, and the volumes of water and hydrocarbon in the headgroup region. These relations, which are easily modified for neutron diffraction, are useful for obtaining structural quantities from electron density profiles obtained by fitting model profiles to measured low angle x-ray intensities.

New phases of DPPC/water mixtures

Hydration of DPPC at low temperatures yielded two new phases, a non-lamellar C1 phase and a lamellar C2 phase, as well as the normal gel phase, depending upon the initial physical state of the dry lipid. From the results of wide-angle diffraction and calorimetry the C2 phase appears very similar to the normal C phase, but the D spacing is considerably larger, suggesting that the C2 phase is a C phase with untilted chains.

Structure of fully hydrated bilayer dispersions

A systemic formalism is developed that shows how the results for absolute specific volumes of multilamellar lipid dispersions may be combined with results from diffraction studies to obtain quantitative characterizations of the average structure of fully hydrated lipid bilayers. Quantities obtained are the area per molecule, the thickness and volumes of the bilayer, the water layer, the hydrocarbon chain layer and the headgroup layer, and where appropriate, the tilt angle of the hydrocarbon chains. In the case of the C phase of DPPC this formalism leads to the detection of inconsistencies between three data. Results for the G phases of DPPC and DLPE are in reasonable agreement with, though more comprehensive than, previous work that used fewer data and equations. Various diffraction data for the F phase of DPPC are in disagreement and it is shown how this disagreement affects results for the bilayer structure. A recent method of McIntosh and Simon for obtaining fluid phase structure utilizing gel phase structure is slightly modified to obtain results for the F phase of DLPE. Methods of obtaining the average methylene and methyl volumes in the fluid phases are critically examined.

Specific volumes of lipids in fully hydrated bilayer dispersions

The neutral buoyancy method of obtaining absolute specific volumes of lipid in multilamellar dispersions is critically investigated. Control experiments show that there is no preferential partitioning of 2H2O vs. H2O into the liposomes, and several thermodynamic properties of the samples, such as the enthalpy change and the volume change of the main transition, are changed very little with deuteration of the solvent. The assumption that the molecular volume of the solvent in the interlamellar space is essentially the same as in bulk solution is discussed; and it is shown to introduce rather small corrections. Previous procedures have been modified to avoid possible kinetic limitations in phases with low water permeability. It is concluded that the molecular volume of lipid in bilayers can be obtained to an accuracy better than 0.002 nm3 (2A3) which is less than 0.2% of typical molecular volumes of lipids.

Theory of passive proton conductance in lipid bilayers

The large permeability of lipid bilayers to protons compared to other small ions calls for a special proton transport mechanism. At the present time, only mechanisms involving transient hydrogen-bonded chains of water can account for the experimental result that the conductance is nearly independent of pH. Three models involving transient hydrogen-bonded chains are discussed, including an outline of the kinetic calculations that lead to predictions of current versus voltage drop and current versus pH differences. These calculations can be compared to experiment to determine which, if any, of these models pertains to lipid bilayers.

Kinetics of the subtransition in dipalmitoylphosphatidylcholine

The kinetics of the interconversions of the subgel and gel phases in dipalmitoylphosphatidylcholine have been studied by using differential dilatometry, differential scanning calorimetry (DSC), and neutral buoyancy centrifugation as a function of incubation temperature and deuteriation of the solvent. As seen by others, DSC scans show two peaks in the subgel transition region for incubation temperatures below 1 degree C. After incubation at 0.1 degree C, the DSC peak that occurs at the lower scanning temperature appears with an incubation half-time of 0.5 day and eventually converts into a peak at higher scanning temperature with an incubation half-time of 18 days. By varying the scanning rate, we show that these two peaks merge into one at slow scanning rates with a common equilibrium transition temperature of 13.8 degrees C, in agreement with equilibrium calorimetry and dilatometry (delta V = 0.017 +/- 0.001 mL/g). For incubation temperatures above 4.6 degrees C, only one peak appears in both scanning dilatometry and calorimetry. While the initial rate of subgel conversion is smaller at the higher incubation temperatures, after 300 h a higher percentage of the sample has converted to subgel than at the lower incubation temperatures. We suggest that higher incubation temperatures (near 5 degrees C) are preferable for forming the stable subgel phase, and we present a colliding domain picture that indicates why this may be so. Our results in D2O and the similarity of the kinetics of volume decrease with the kinetics of wide-angle diffraction lines also support the suggestion that the partial loss of interlamellar water plays a kinetic role in subgel formation.

Flash spectroscopy of purple membrane

Flash spectroscopy data were obtained for purple membrane fragments at pH 5, 7, and 9 for seven temperatures from 5 degrees to 35 degrees C, at the magic angle for actinic versus measuring beam polarizations, at fifteen wavelengths from 380 to 700 nm, and for about five decades of time from 1 microsecond to completion of the photocycle. Signal-to-noise ratios are as high as 500. Systematic errors involving beam geometries, light scattering, absorption flattening, photoselection, temperature fluctuations, partial dark adaptation of the sample, unwanted actinic effects, and cooperativity were eliminated, compensated for, or are shown to be irrelevant for the conclusions. Using nonlinear least squares techniques, all data at one temperature and one pH were fitted to sums of exponential decays, which is the form required if the system obeys conventional first-order kinetics. The rate constants obtained have well behaved Arrhenius plots. Analysis of the residual errors of the fitting shows that seven exponentials are required to fit the data to the accuracy of the noise level.

Dilatometric studies of isobranched phosphatidylcholines

Absolute apparent specific volumes have been obtained for phosphatidylcholine lipids with saturated, isobranched hydrocarbon chains with ni = 15 to 20 carbons, with an emphasis upon phase transition behavior, both equilibrium and kinetic. The temperature of the chain-melting transition extrapolates with increasing chain length to the melting temperature of polyethylene with a small odd/even alternation. There are also odd/even alternations in the volume of transition and in the hysteresis of the chain-melting transition, but with the odd and even reversed when compared with the larger odd/even alternation in the lower solid-solid transition that occurs in the longer chain ni lipids. A phenomenological picture is given for the coalescence of the two transitions for shorter ni lipids and this picture is used to sharpen the discussion of the kinetic mechanism of melting. A temperature-reversal experiment shows that the melting from the lowest temperature crystal or C phase to the fluid F phase does not proceed via the metastable gel G phase for 16i. The dilatometric results are combined with recent X-ray structural results for the C and G phases of 17i and 20i to deduce various structural information, including the hydration numbers and the volume of the headgroup, VH = 341 A3, which agrees very well with VH for straight-chain phosphatidylcholines. For the chain-melted F phase the assumption that the methylene volumes of the different ni lipids should be the same at the same temperature is used to obtain the volumes of the methylene and the methyl groups.

Thermodynamic studies of purple membrane

Differential dilatometric and differential scanning calorimetric measurements have been made of purple membrane with an emphasis upon the temperature range 5 degrees C less than T less than 45 degrees C. The coefficient of thermal expansion alpha is about 7 X 10(-4)/Cdeg up to 30 degrees C and decreases at higher temperatures. The specific heat increases rapidly with temperature with absolute values in the range 0.30-0.45 cal/Cdeg per g. A nearly constant alpha juxtaposed with a rapidly increasing specific heat is similar to the properties of lipid bilayers in the gel phase and alkanes in the solid phase. This behavior is explained by the concept of hindered vibrations which would now appear to apply to at least one integral membrane protein. There may also be a small broad transition centered near 20-25 degrees C that would correspond to the melting of less than 25 degrees of freedom per bacteriorhodopsin molecule and associated lipids. Using our measured apparent specific volume the average thickness of purple membrane is calculated to be 43.5 A. The specific volume of interaction of lipids and proteins is estimated, using the amino acid sequence of bacteriorhodopsin and average amino acid volumes from structural studies of other proteins, to be about 11% of the specific volume of the purple membrane lipids or 4% of the volume of the bacteriorhodopsin protein. A positive volume of interaction is consistent with lipid-protein interactions being an important determinant of the thermodynamic properties of purple membrane.

Metastability in the phase behavior of dimyristoylphosphatidylethanolamine bilayers

A new subgel phase is demonstrated to occur in hydrated dimyristoylphosphatidylethanolamine ( DMPE ) by using dilatometric and calorimetric techniques. The formation of the subgel phase takes place very slowly at temperatures near 0 degree C, but it can still be observed at 25 degrees C. Once formed, the subgel phase melts (delta Hh = 16.0 +/- 0.6 kcal/mol and delta V = 0.085 +/- 0.014 mL/g) directly into the liquid-crystalline phase at a temperature, Th = 56.3 degrees C, that is higher than the gel to liquid-crystalline transition temperature, Tm = 49.6 degrees C. Thus, the gel phase appears to be metastable over its entire temperature range. In this regard, DMPE behaves differently from dipalmitoylphosphatidylcholine and distearoylphosphatidylcholine but similarly to dilaurylphosphatidylethanolamine . This unusual long-lived metastability provides cells an additional option in determining the properties of membranes.