Consistency of encoding in monkey visual cortex.

Are different kinds of stimuli (for example, different classes of geometric images or naturalistic images) encoded differently by visual cortex, or are the principles of encoding the same for all stimuli? We examine two response properties: (1) the range of spike counts that can be elicited from a neuron in epochs representative of short periods of fixation (up to 400 msec), and (2) the relation between mean and variance of spike counts elicited by different stimuli, that together characterize the information processing capabilities of a neuron using the spike count code. In monkey primary visual cortex (V1) complex cells, we examine responses elicited by static stimuli of four kinds (photographic images, bars, gratings, and Walsh patterns); in area TE of inferior temporal cortex, we examine responses elicited by static stimuli in the sample, nonmatch, and match phases of a delayed match-to-sample task. In each area, the ranges of mean spike counts and the relation between mean and variance of spike counts elicited are sufficiently similar across experimental conditions that information transmission is unaffected by the differences across stimulus set or behavioral conditions [although in 10 of 27 (37%) of the V1 neurons there are statistically significant but small differences, the median difference in transmitted information for these neurons was 0.9%]. Encoding therefore appears to be consistent across experimental conditions for neurons in both V1 and TE, and downstream neurons could decode all incoming signals using a single set of rules.

Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex.

This paper is concerned with a striking visual experience: that of seeing geometric visual hallucinations. Hallucinatory images were classified by Klüver into four groups called form constants comprising (i) gratings, lattices, fretworks, filigrees, honeycombs and chequer-boards, (ii) cobwebs, (iii) tunnels, funnels, alleys, cones and vessels, and (iv) spirals. This paper describes a mathematical investigation of their origin based on the assumption that the patterns of connection between retina and striate cortex (henceforth referred to as V1)-the retinocortical map-and of neuronal circuits in V1, both local and lateral, determine their geometry. In the first part of the paper we show that form constants, when viewed in V1 coordinates, essentially correspond to combinations of plane waves, the wavelengths of which are integral multiples of the width of a human Hubel-Wiesel hypercolumn, ca. 1.33-2 mm. We next introduce a mathematical description of the large-scale dynamics of V1 in terms of the continuum limit of a lattice of interconnected hypercolumns, each of which itself comprises a number of interconnected iso-orientation columns. We then show that the patterns of interconnection in V1 exhibit a very interesting symmetry, i.e. they are invariant under the action of the planar Euclidean group E(2)-the group of rigid motions in the plane-rotations, reflections and translations. What is novel is that the lateral connectivity of V1 is such that a new group action is needed to represent its properties: by virtue of its anisotropy it is invariant with respect to certain shifts and twists of the plane. It is this shift-twist invariance that generates new representations of E(2). Assuming that the strength of lateral connections is weak compared with that of local connections, we next calculate the eigenvalues and eigenfunctions of the cortical dynamics, using Rayleigh-Schrödinger perturbation theory. The result is that in the absence of lateral connections, the eigenfunctions are degenerate, comprising both even and odd combinations of sinusoids in straight phi, the cortical label for orientation preference, and plane waves in r, the cortical position coordinate. 'Switching-on' the lateral interactions breaks the degeneracy and either even or else odd eigenfunctions are selected. These results can be shown to follow directly from the Euclidean symmetry we have imposed. In the second part of the paper we study the nature of various even and odd combinations of eigenfunctions or planforms, the symmetries of which are such that they remain invariant under the particular action of E(2) we have imposed. These symmetries correspond to certain subgroups of E(2), the so-called axial subgroups. Axial subgroups are important in that the equivariant branching lemma indicates that when a symmetrical dynamical system becomes unstable, new solutions emerge which have symmetries corresponding to the axial subgroups of the underlying symmetry group. This is precisely the case studied in this paper. Thus we study the various planforms that emerge when our model V1 dynamics become unstable under the presumed action of hallucinogens or flickering lights. We show that the planforms correspond to the axial subgroups of E(2), under the shift-twist action. We then compute what such planforms would look like in the visual field, given an extension of the retinocortical map to include its action on local edges and contours. What is most interesting is that, given our interpretation of the correspondence between V1 planforms and perceived patterns, the set of planforms generates representatives of all the form constants. It is also noteworthy that the planforms derived from our continuum model naturally divide V1 into what are called linear regions, in which the pattern has a near constant orientation, reminiscent of the iso-orientation patches constructed via optical imaging. The boundaries of such regions form fractures whose points of intersection correspond to the well-known 'pinwheels'. To complete the study we then investigate the stability of the planforms, using methods of nonlinear stability analysis, including Liapunov-Schmidt reduction and Poincaré-Lindstedt perturbation theory. We find a close correspondence between stable planforms and form constants. The results are sensitive to the detailed specification of the lateral connectivity and suggest an interesting possibility, that the cortical mechanisms by which geometric visual hallucinations are generated, if sited mainly in V1, are closely related to those involved in the processing of edges and contours.

Bacterial export takes its Tol.

The recent crystal structure of TolC elegantly indicates its function and provides insight into its mechanism for export of a wide range of molecules across the periplasmic space and outer membrane of Gram-negative bacteria. The structure is compared to those of other proteins that are embedded in bacterial outer membranes or that traverse the periplasmic space.

Mesoscopic surfactant organization and membrane protein crystallization.

The paucity of detailed X-ray crystallographic structures of integral membrane proteins arises from substantive technical obstacles in the overexpression of multimilligram quantities of protein, and in the crystallization of purified protein-detergent complexes (PDCs). With rare exception, crystal contacts within the lattice are mediated by protein-protein interaction, and the detergent surrounding the protein behaves as a disordered solvent. The addition and use of surfactants that display mesoscopic self-assembly behavior in membrane protein crystallization experiments presents a novel alternative strategy. Well-ordered crystals of the water channel human aquaporin-1 (hAQP1) that diffract to 4 A resolution have been obtained with this approach.

Expression, purification, and initial structural characterization of YadQ, a bacterial homolog of mammalian ClC chloride channel proteins.

YadQ of Escherichia coli is a homolog of the mammalian chloride channels of the ClC family. The yadQ gene was cloned as a fusion protein with a hexahistidine tag and tobacco etch virus protease site for the removal of the tag. The protein was expressed in the membrane of E. coli and extracted with decylmaltoside. Purification was achieved by metal affinity chromatography followed by cation exchange. Circular dichroism revealed a high alpha-helical content. Size exclusion chromatography suggests that YadQ forms dimers. The similarity in primary, secondary, and quaternary structure and the ability to recombinantly express YadQ in the cell membrane make the protein a good candidate for the structural study of ClC chloride channels.

Using response models to estimate channel capacity for neuronal classification of stationary visual stimuli using temporal coding.

Both spike count and temporal modulation are known to carry information about which of a set of stimuli elicited a response; but how much information temporal modulation adds remains a subject of debate. This question usually is addressed by examining the results of a particular experiment that depend on the specific stimuli used. Developing a response model allows us to ask how much more information is carried by the best use of response strength and temporal modulation together (that is, the channel capacity using a code incorporating both) than by the best use of spike count alone (the channel capacity using the spike count code). This replaces dependence on a particular data set with dependence on the accuracy of the model. The model is constructed by finding statistical rules obeyed by all the observed responses and assuming that responses to stimuli not presented in our experiments obey the same rules. We assume that all responses within the observed dynamic range, even if not elicited by a stimulus in our experiment, could be elicited by some stimulus. The model used here is based on principal component analysis and includes both response strength and a coarse (+/-10 ms) representation of temporal modulation. Temporal modulation at finer time scales carries little information about the identity of stationary visual stimuli (although it may carry information about stimulus motion or change), and we present evidence that, given its variability, it should not be expected to do so. The model makes use of a linear relation between the logarithms of mean and variance of responses, similar to the widely seen relation between mean and variance of spike count. Responses are modeled using truncated Gaussian distributions. The amount of stimulus-related information carried by spike count in our data are 0.35 and 0.31 bits in primary visual and inferior temporal cortices, respectively, rising to 0.52 and 0.37 bits for the two-principal-component code. The response model estimates that the channel capacity is 1.1 and 1.4 bits, respectively, using the spike count only, rising to 2.0 and 2.2 bits using two principal components. Thus using this representation of temporal modulation is nearly equivalent to adding a second independent cell using the spike count code. This is much more than estimated using transmitted information but far less than would be expected if all degrees of freedom provided by the individual spike times carried independent information.

Outer membrane protein A of E. coli folds into detergent micelles, but not in the presence of monomeric detergent.

Outer membrane protein A (OmpA) of Escherichia coli is a beta-barrel membrane protein that unfolds in 8 M urea to a random coil. OmpA refolds upon urea dilution in the presence of certain detergents or lipids. To examine the minimal requirements for secondary and tertiary structure formation in beta-barrel membrane proteins, folding of OmpA was studied as a function of the hydrophobic chain length, the chemical structure of the polar headgroup, and the concentration of a large array of amphiphiles. OmpA folded in the presence of detergents only above a critical minimal chain length of the apolar chain as determined by circular dichroism spectroscopy and a SDS-PAGE assay that measures tertiary structure formation. Details of the chemical structure of the polar headgroup were unimportant for folding. The minimal chain length required for folding correlated with the critical micelle concentration in each detergent series. Therefore, OmpA requires preformed detergent micelles for folding and does not adsorb monomeric detergent to its perimeter after folding. Formation of secondary and tertiary structure is thermodynamically coupled and strictly dependent on the interaction with aggregated amphiphiles.

Stochastic nature of precisely timed spike patterns in visual system neuronal responses.

It is not clear how information related to cognitive or psychological processes is carried by or represented in the responses of single neurons. One provocative proposal is that precisely timed spike patterns play a role in carrying such information. This would require that these spike patterns have the potential for carrying information that would not be available from other measures such as spike count or latency. We examined exactly timed (1-ms precision) triplets and quadruplets of spikes in the stimulus-elicited responses of lateral geniculate nucleus (LGN) and primary visual cortex (V1) neurons of the awake fixating rhesus monkey. Large numbers of these precisely timed spike patterns were found. Information theoretical analysis showed that the precisely timed spike patterns carried only information already available from spike count, suggesting that the number of precisely timed spike patterns was related to firing rate. We therefore examined statistical models relating precisely timed spike patterns to response strength. Previous statistical models use observed properties of neuronal responses such as the peristimulus time histogram, interspike interval, and/or spike count distributions to constrain the parameters of the model. We examined a new stochastic model, which unlike previous models included all three of these constraints and unlike previous models predicted the numbers and types of observed precisely timed spike patterns. This shows that the precise temporal structures of stimulus-elicited responses in LGN and V1 can occur by chance. We show that any deviation of the spike count distribution, no matter how small, from a Poisson distribution necessarily changes the number of precisely timed spike patterns expected in neural responses. Overall the results indicate that the fine temporal structure of responses can only be interpreted once all the coarse temporal statistics of neural responses have been taken into account.

Response features determining spike times.

Interpreting messages encoded in single neuronal responses requires knowing which features of the responses carry information. That the number of spikes is an important part of the code has long been obvious. In recent years, it has been shown that modulation of the firing rate with about 25 ms precision carries information that is not available from the total number of spikes across the whole response. It has been proposed that patterns of exactly timed (1 ms precision) spikes, such as repeating triplets or quadruplets, might carry information that is not available from knowing about spike count and rate modulation. A model using the spike count distribution, the low-pass filtered PSTH (bandwidth below 30 Hz), and, to a small degree, the interspike interval distribution predicts the numbers and types of exactly-timed triplets and quadruplets that are indistinguishable from those found in the data. From this it can be concluded that the coarse (< 30 Hz) sequential correlation structure over time gives rise to the exactly timed patterns present in the recorded spike trains. Because the coarse temporal structure predicts the fine temporal structure, the information carried by the fine temporal structure must be completely redundant with that carried by the coarse structure. Thus, the existence of precisely timed spike patterns carrying stimulus-related information does not imply control of spike timing at precise time scales.

Coding strategies in monkey V1 and inferior temporal cortices.

We would like to know whether the statistics of neuronal responses vary across cortical areas. We examined stimulus-elicited spike count response distributions in V1 and inferior temporal (IT) cortices of awake monkeys. In both areas, the distribution of spike counts for each stimulus was well described by a Gaussian distribution, with the log of the variance in the spike count linearly related to the log of the mean spike count. Two significant differences in response characteristics were found: both the range of spike counts and the slope of the log(variance) versus log(mean) regression were larger in V1 than in IT. However, neurons in the two areas transmitted approximately the same amount of information about the stimuli and had about the same channel capacity (the maximum possible transmitted information given noise in the responses). These results suggest that neurons in V1 use more variable signals over a larger dynamic range than IT neurons, which use less variable signals over a smaller dynamic range. The two coding strategies are approximately as effective in transmitting information.

Using response models to study coding strategies in monkey visual cortex.

Usually the conditional probabilities needed to calculate transmitted information are estimated directly from empirically measured distributions. Here we show that an explicit model of the relation between response strength (here, spike count) and its variability allows accurate estimates of transmitted information. This method of estimating information is reliable for data sets with nine or more trials per stimulus. We assume that the model characterizes all response distributions, whether observed in a given experiment or not. All stimuli eliciting the same response are considered equivalent. This allows us to calculate the channel capacity, the maximum information that a neuron can transmit given the variability with which it sends signals. Channel capacity is uniquely defined, thus avoiding the difficulty of knowing whether the 'right' stimulus set has been chosen in a particular experiment. Channel capacity increases with increasing dynamic range and decreases as the variance of the signal (noise) increases. Neurons in V1 send more variable signals in a wide dynamic range of spike counts, while neurons in IT send less variable signals in a narrower dynamic range. Nonetheless, neurons in the two areas have similar channel capacities. This suggests that variance is being traded off against dynamic range in coding.

The CHIP28 water channel visualized in ice by electron crystallography.

Electron crystallography of frozen-hydrated two-dimensional crystals of deglycosylated human erythrocyte CHIP28 reveals an aqueous vestibule in each monomer leading to the water-selective channel that is enclosed by multiple transmembrane alpha-helices.

Purification and structure-function analysis of native, PNGase F-treated, and endo-beta-galactosidase-treated CHIP28 water channels.

CHIP28 occurs naturally in glycosylated and nonglycosylated forms. The purpose of this study was to determine the role of glycosylation in CHIP28 structure and function. A new purification procedure based on phenylboronic acid-agarose (PBA) affinity chromatography was developed to isolate CHIP28. In purified native CHIP28 from erythrocytes, approximately 50% of CHIP28 molecules were glycosylated; each mole of glycosylated CHIP28 contained 5.4 kDa of monosaccharides consisting of 2 mol of Fuc, 8 mol of Gal, 1 mol of GalN, 13 mol of GlcN, 3 mol of Man, and 1 mol of Neu5Ac. The proportions of each monosaccharide and the sensitivity to endo-beta-galactosidase indicated that CHIP28 contained polylactosaminyl oligosaccharides. Glycosylated and nonglycosylated CHIP28 remained tightly associated when solubilized in octyl beta-D-glucoside (OG) and could not be separated by conventional chromatographic procedures. To remove the sugar moiety, CHIP28 was enzymatically deglycosylated by PNGase F and purified by Q-Sepharose anion-exchange and Erythrina cristagalli lectin chromatography. High-performance size-exclusion chromatography revealed that native CHIP28 eluted as an apparent dimer, whereas deglycosylated CHIP28 eluted as an apparent monomer. In reconstituted proteoliposomes, deglycosylated CHIP28 had a single channel water permeability (pf) of 3.1 x 10(-14) cm3/s (10 degrees C), not different from that of 3.2 x 10(-14) cm3/s for native CHIP28. Circular dichroism of native and deglycosylated CHIP28 in OG revealed 45% and 48% alpha-helix, respectively; intrinsic tryptophan fluorescence showed no effects of glycosylation on tryptophan environment. Freeze-fracture electron microscopy with rotary shadowing indicated that native and deglycosylated CHIP28 assembled as tetramers in reconstituted proteoliposomes.(ABSTRACT TRUNCATED AT 250 WORDS)

Projection structure of the CHIP28 water channel in lipid bilayer membranes at 12-A resolution.

Osmotic water transport across plasma membranes in erythrocytes and several epithelial cell types is facilitated by CHIP28, a water-selective membrane channel protein. In order to examine the structure of CHIP28 in membranes, large (1.5-2.5-microns diameter), highly ordered, two-dimensional (2-D) crystals of purified and deglycosylated erythrocyte CHIP28 were generated by reconstitution of detergent-solubilized protein into synthetic lipid bilayers via detergent dialysis. Fourier transforms computed from low-dose electron micrographs of such crystals preserved in negative stain display order to 12-A resolution. The crystal lattice is tetragonal (a = b = 99.2 +/- 1.4 A) with plane group symmetry p4g. A projection density map at 12-A resolution defines the molecular boundary and organization of the CHIP28 monomers in the membrane plane. The unit cell contains four CHIP28 dimers, each composed of two oblong-shaped (37 x 25 A ) monomers with opposite orientations. The CHIP28 monomers associate to form tetrameric structures around the 4-fold axes normal to the membrane plane where stain is excluded. The 2-D crystals of CHIP28 display order extending beyond the limit typically achieved by negative staining and therefore may be amenable to high-resolution structure analysis by cryo-electron microscopy.

Structure of a fluid dioleoylphosphatidylcholine bilayer determined by joint refinement of x-ray and neutron diffraction data. II. Distribution and packing of terminal methyl groups.

We continue in this paper the presentation of theoretical and experimental methods for the joint refinement of neutron and x-ray lamellar diffraction data for the analysis of fluid (L alpha phase) bilayer structure (Wiener, M. C., and S. H. White. 1991 a, b, c. Biophys. J. 59:162-173 and 174-185; Biochemistry. 30:6997-7008; Wiener, M. C., G. I. King, and S. H. White. Biophys. J. 60: 568-576). We show how to obtain the distribution and packing of the terminal methyls in the interior of a fluid dioleoylphosphatidylcholine bilayer (66% RH) by combining x-ray and neutron scattering-length transbilayer profiles with no a priori assumptions about the functional form of the distribution. We find that the methyls can be represented by a Gaussian function with 1/e-halfwidth of 2.95 +/- 0.28 A situated at the bilayer center. There is substantial mixing of the methyls and methylenes in the bilayer center. The Gaussian representation of the methyl distribution is narrower and has a different shape than predicted by several simulations of fluid bilayers (Gruen, D. W. R., and E. H. B. de Lacey. 1984. Surfactants in Solution, Vol. 1. Plenum Publishing Corp., New York. 279-306; de Loof, H., et al. 1991. Biochemistry. 30:2099-2133) but this may be due to the smaller area/lipid of our experiments and the presence of the double-bonds. Determination of the absolute specific volume of DOPC and an analysis of bulk alkane volumetric data over a range of hydrostatic pressures lead to estimates of methylene and methyl volumes at the bilayer center of 27 +/- 1 A3 and 57.2 +/- 3.6 A3, respectively. This result provides direct confirmation of the common assumption that the molecular packing of methyl and methylene groups in bilayers is the same as in bulk liquid alkanes.

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

We present in this paper the complete structure of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) in the L alpha phase (66% RH, 23 degrees C) obtained by the joint refinement of neutron and x-ray lamellar diffraction data. The structural details obtained have previously required a large number of neutron diffraction experiments, using numerous specifically-deuterated phospholipid isomorphs (Büldt et al., 1978. Nature (Lond.). 271:182-184). The joint-refinement approach minimizes specific deuteration by utilizing independent neutron and x-ray data sets. The method yields a quasimolecular structure consisting of a series of multiatomic fragments that are each represented by one or several Gaussian distributions whose positions and widths can be determined to within 0.06 to 0.52 A exclusive of the methylene region. The image of DOPC at 66% RH (5.36 +/- 0.08 waters per lipid) is consistent with many aspects of bilayer structure previously determined by structural and spectroscopic studies. The most striking feature of the structure is the large amount of transbilayer thermal motion suggested by the widths and overlaps of the Gaussian envelopes of the quasimolecular fragments. We discuss the "dynamic bilayer thickness" which describes the minimum effective thickness of the hydrocarbon permeability barrier in terms of the thermal motion of the water. A gradient of thermal motion exists that increases in either direction away from the glycerol backbone which is the most constrained portion of the bilayer. The steric interactions between headgroups of apposed bilayers, expected at the hydration level of our experiments, are clearly revealed. A useful consequence of the quasimolecular structure is that average boundaries within bilayers calculated using composition and volumetric data and ad hoc assumptions can be related to the positions of the principal structural groups. Several measures of "bilayer thickness" in common use can be identified as the positions of the cholines for Luzzati's d1 (Luzzati and Husson. 1962. J. Cell Biol. 12:207-219) and the glycerols for Small's dL (Small. 1967. J. Lipid Res. 8:551-556). We do not know if these relations will be true at other hydrations or for other lipids. Of particular interest is the fact that the position of the carbonyl groups marks the average hydrocarbon/headgroup boundary. It must be emphasized, however, that this region of the bilayer must be generally characterized as one of tumultuous chemical heterogeneity because of the thermal motion of the bilayer.

Structure of a fluid dioleoylphosphatidylcholine bilayer determined by joint refinement of x-ray and neutron diffraction data. I. Scaling of neutron data and the distributions of double bonds and water.

We described in two previous papers a method for the joint refinement of the structure of fluid bilayers using neutron and x-ray diffraction data (Wiener, M. C., and S. H. White 1991a, b. Biophys. J. 59: 162-173 and 174-185). An essential part of the method is the appropriate scaling of the diffraction data. Here we describe the scaling of the neutron data and the determination of the transbilayer distribution of double bonds in liquid-crystalline (L alpha phase) phospholipid bilayers of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). The distribution was determined by neutron diffraction of oriented multilayers (66% RH) of DOPC specifically deuterated at the 9- and 10-position of both acyl chains. The double-bond distribution is described accurately by a pair of Gaussian functions each located at a position Zcc = 7.88 +/- 0.09 A from the bilayer center with 1/e-halfwidths of Acc = 4.29 +/- 0.16 A. Previously, we determined the transbilayer distribution of bromine atoms in a specifically halogenated lipid, 1-oleoyl-2-9,10-dibromostearoyl-sn-glycero-3-phosphocholine (OBPC), and showed it to be an isomorphous replacement for DOPC (Wiener, M. C., and S. H. White, 1991c. Biochemistry. In press). A comparison of the double-bond and bromine profiles indicates that the positions of the centers of the deuterated double bond and the brominated methylene Gaussian distributions are equal within experimental error and that each label undergoes similar average thermal motions with respect to the bilayer normal. The observation that the average position of a label on both acyl chains (the deuterated double bonds) is similar to the average position of a label on the 2-chain alone (the brominated methylenes) indicates that the maximum separation along the bilayer normal between the double bonds of the acyl chains is 1 A or less. The fully-resolved transbilayer water distribution, previously determined at lower resolution (Jacobs, R. E., and S. H. White. 1989. Biochemistry. 28:3421-3437), was obtained from the analysis of neutron diffraction data of DOPC hydrated with a D20/H20 mixture. The water distribution is described accurately by a pair of Gaussian functions each located at a position Zw = 22.51 +/- 0.77 A from the bilayer center with 1/e-half widths of Aw = 4.63 +/- 0.48A. We present the relative absolute neutron and x-ray structure factors of DOPC at 66% RH that will be used to solve the complete structure of DOPC which will be presented in a later paper of this series.

Transbilayer distribution of bromine in fluid bilayers containing a specifically brominated analogue of dioleoylphosphatidylcholine.

We describe in this paper the transbilayer distribution of the bromines of the specifically halogenated phospholipid 1-oleoyl-2-(9,10-dibromostearoyl)-sn-glycero-3- phosphocholine (OBPC). The distribution was determined by X-ray diffraction of oriented multilayers of mixtures of OBPC and 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) at 66% relative humidity by the general approach of Franks et al. (1978) [Nature 276, 530-532]. The bromine distribution of OBPC in the fluid L alpha phase is described accurately by a pair of Gaussian functions located 7.97 +/- 0.27 A from the center of the bilayer with l/e half-widths of 4.96 +/- 0.62 A. We find that OBPC bilayers are accurately described as DOPC bilayers with an additional bromine distribution centered at the position of the double bond of DOPC and conclude that OBPC is an excellent structural isomorph for DOPC under the conditions of these experiments. The distribution obtained is the complete and fully resolved transbilayer image of the halogen label because the broad distribution of the bromines is due entirely to thermal disorder and not to experimental limitations [Wiener, M. C., & White, S. H. (1991a) Biophys. J. 59, 162-173]. The observed width of the bromine distribution indicates that virtually all of the hydrocarbon interior is accessible to the bromines. The distance between the bromine/double-bond position and the headgroup phosphate position was determined from one-dimensional Patterson maps and found to be approximately 12 A. The application of accurately determined bromine distributions to the quantitative interpretation of fluorescence quenching experiments is discussed. A method for the self-consistent global analysis of diffraction data from mixtures that permits the use of data sets with different instrumental scale factors is developed in an Appendix.

Fluid bilayer structure determination by the combined use of x-ray and neutron diffraction. I. Fluid bilayer models and the limits of resolution.

This is the first in a series of papers concerned with methods for the determination of the structures of fluid phospholipid bilayers in the liquid-crystalline (L alpha) phase. The basic approach is the joint refinement of quasimolecular models (King and White, 1986. Biophys. J. 49:1047-1054) using x-ray and neutron diffraction data. We present here (a) the rationale for quasimolecular models, (b) the nature of the resolution problem for thermally disordered bilayers, and (c) an analysis of the resolution of experiments in which Gaussian functions are used to describe the distribution of submolecular components. We show that multilamellar liquid-crystalline bilayers are best described by the convolution of a perfect lattice function with a thermally disordered bilayer unit cell. Lamellar diffraction measurements on such a system generally yield only 5-10 orders of diffraction data from which transbilayer profiles of the unit cell can be constructed. The canonical resolution of these transbilayer profiles, defined as the Bragg spacing divided by the index of the highest recorded diffraction order, is typically 5-10 A. Using simple model calculations, we show that the canonical resolution is a measure of the widths of the distributions of constituents of the unit cell rather than a measure of the spatial separation of the distributions. The widths provide a measure of the thermal motion of the bilayer constituents which can be described by Gaussian functions. The equilibrium positions of the centers of the distributions can be determined with a precision of 0.1-0.5 A based upon typical experimental errors.