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.