Comparison of fluorescence energy transfer and quenching methods to establish the position and orientation of components within the transverse plane of the lipid bilayer. Application to the gramicidin A--bilayer interaction.

Fluorescence quenching and resonance energy transfer methods have been used to investigate the position of fluorophores in the lateral and transverse planes of the lipid bilayer. A series of n-(9-anthroyloxy) fatty acids (n = 2, 6, 9, and 12) have been used as energy-transfer acceptors so that apparent transfer distances from a membrane-bound donor (N-stearoyltryptophan) have a transverse as well as a lateral component. Both theory and experiment show that the energy-transfer method is not precise enough to discriminate between the positions of the fluorophores in the transverse plane of the bilayer. The n-(9-anthroyloxy) fatty acids are also susceptible to quenching by the indole moiety of tryptophan. The relative quenching efficiency can provide a semiquantitative measure of the position of quenching molecules in the lipid bilayer. The quenching techniques are applied to the determination of the orientation of gramicidin A in lipid bilayers. The tryptophan residues of gramicidin appear to be located near the membrane surface in agreement with the head-to-head dimeric structure proposed by D. W. Urry et al. [(1971) Proc. Natl. Acad. Sci. U.S.A. 68, 672--676].     

Membrane fluidity and lipid composition of rat small intestinal brush-border membranes during postnatal maturation

Fluidity and lipid composition of rat small intestinal brush-border membranes (BBM) were studied during maturation in five age groups: newborns, sucklings (1-3 weeks), weaned (4-6 weeks), juveniles (8-10 weeks), and adults (12 weeks). Brush-border membrane fluidity was measured by steady-state fluorescence polarization. Fluorescent probes used were: 1,6-diphenyl-1,3,5-hexatriene, 1-(4-trimethylammonium)phenyl)-6-phenyl-1,3,5-hexatriene, and a set of n-(9-anthroyloxy) fatty acids. Fluorescence anisotropy measured with all fluorophores was increased in adult versus newborn rats (P less than 0.004). The weight ratio of saturated to cis-unsaturated fatty acids increased from birth to the suckling age (P less than 0.0004). The cholesterol to phospholipid molar ratio increased from birth to the weaned age (P less than 0.0001). Cholesterol to protein ratio and phospholipid to protein ratio decreased after the weaned age (P less than 0.004). The results not only describe maturational changes of brush-border membranes but also give a better understanding of the correlations between biophysical and biochemical data in biological membranes.     

An assessment of the fluidity gradient of the lipid bilayer as determined by a set of n-(9-anthroyloxy) fatty acids (n = 2, 6, 9, 12, 16).

The rotational behavior of a set of n-(9-anthroyloxy) fatty acid fluorescent probes is examined in two liquid paraffins and in liposomes composed of dipalmitoyl phosphatidylcholine. As has been observed with other membrane fluorescent probes (Hare, F., and Lussan, C. (1977) Biochim. Biophys. Acta 467, 262-272), the degree of fluorescence depolarization for a given solvent viscosity is dependent on the solvent standard employed. In addition, when the anthroyloxy group is in the terminal position of the acyl chain, it has more rotational freedom than when it is conjugated to positions 6, 9, or 12 where the rotational motion of the fluorophore is similar. When incorporated into lipid bilayers, values of fluorescence polarization reflect the gradient of "fluidity" which extends from the surface to the center of the membrane. The nature of this polarization gradient is discussed in relation to the intrinsic differences between the probes and the anisotropic rotations responsible for depolarization.     

The use of n-(9-anthroyloxy) fatty acids to determine fluidity and polarity gradients in phospholipid bilayers

A set of n-(9-anthroyloxy) fatty acid probes (n = 2, 6, 9, 12) have been used to examine gradients in fluorescence polarization, lifetime (tau F), relative quantum yield (phi rel) and positions of emission maxima (lambda max) through bilayers composed of synthetic phospholipids. The fluorophores of these probes report the environment at a graded series of depths from the surface to the centre of the bilayer structure. 1. Polarizations decrease as the fluorophore is moved deeper into the bilayer indicating greater rotational motion of the fluorophore in the hydrocarbon core of the bilayer. 2. The different responses of the probe diphenylhexatriene and the anthroyloxy fatty acids to the action of cholesterol on lipid bilayers are discussed in terms of the orientation of these probes in the bilayer and the types of anisotropic rotational motions which result in depolarization of fluorescence. 3. Stearic acid derivatives which have the fluorophore in the 6-, 9- and 12-positions along the acyl chain have a similar response to solvent polarity as measured by values of lambda max and phi rel in a variety of organic solvents. 4. The position of the emission maximum has little dependence on solvent viscosity, but viscosity does change the degree of vibrational structure seen in the emission spectrum. The vibrational structure itself may be used as an indication of the 'mciroviscosity' gradient in the transverse plane of the bilayer. 5. Values of lambda max, tau F and phi rel indicate that a gradient of polarity exists from the surface to the centre of the bilayer. For dipalmitoyl phosphatidylcholine in the crystalline phase, cholesterol acts to make this polarity gradient shallower.     

Properties and the locations of a set of fluorescent probes sensitive to the fluidity gradient of the lipid bilayer

The synthesis and properties of a set of four fluorescent probes (n-(9-anthroyloxy) fatty acids, n = 2, 6, 9, 12) sensitive to the fluidity gradient of the lipid bilayer are described. Fluorescent quenching experiments show that the probes locate at a graded series of depths in the bilayer. A fifth probe, methyl-9-anthroate, locates near the bilayer centre. As an example of their application, the probes are used to study the phase transitions of dipalmitoyl phosphatidyl-choline. Changes in the rotational relaxation times of the probes across the transitions are more pronounced at the centre of the bilayer than at the surface.     

Time-dependent absorption anisotropy and rotational diffusion of proteins in membranes.

The decay of flash-induced absorption anisotropy, r(t), of a chromophore in a membrane protein is closely correlated with rotational diffusion of the protein in the membrane. We develop a theory of time-dependent absorption anisotropy which is applicable to both linear chromophores and planar chromophores which have two different absorption moments at right angles to one another. The theory treats two types of rotational diffusion of membrane proteins: one is rotation of the whole protein about the normal to the plane of the membrane, and the other is restricted wobbling of the whole or part of the protein molecule. In the former case, r(t) is determined by a rotational diffusion coefficient and an angle between the absorption moment(s) and the normal to the plane of the membrane. Rotation of rigid transmembrane proteins can be described by this treatment. In the latter case, r(t) is characterized by a wobbling diffusion coefficient and the degree of orientational constraint. This treatment may be applicable to independent wobbling of the hydrophilic part of membrane proteins. We further show that, for linear and circularly degenerate chromophores, the effect of the excitation flash intensity on r(t) can be accounted for by a constant scaling factor.     

Total internal reflection fluorescence. Measurement of spatial and orientational distributions of fluorophores near planar dielectric interfaces

The fluorescence collected from a fluorophore which is near a planar interface and is excited by a laser beam that is totally internally reflected at the interface depends on the direction of the absorption and emission transition dipole moments of the fluorophore with respect to the interface, on the distance from the fluorophore to the interface, on the angle of incidence and polarization direction of the exciting beam, and on properties of the collection optics. Expressions are derived for the excitation and subsequent emission and collection of fluorescence from a population of fluorophores near a planar interface. Presented is a general model-independent method of obtaining characteristic parameters of the spatial and orientational distribution of the population of fluorophores, from a measure of the fluorescence collected as a function of the polarization and the incidence angle of the totally internally reflected laser beam. The method is illustrated with several simulation calculations.     

Separation of translational and rotational contributions in solution studies using fluorescence photobleaching recovery

Although fluorescence photobleaching recovery (FPR) experiments are usually interpreted in terms of the translational motions of a fluorescently labeled species, rotational motions can also modulate recovery through the cosine-squared laws for dipolar absorption and emission processes. In a complex interacting system, translational and rotational contributions may both be simultaneously present. We show how these contributions can be separated in solution studies using an FPR setup in which (a) the linear polarization of the low-intensity observation beam and the high-intensity photobleaching pulse can be varied independently, and (b) all emitted fluorescent photons are counted equally. The fluorescence recovery signal obtained with the observation beam polarized at the magic angle, 54.7 degrees, from the bleach polarization direction is independent of label orientation, whereas the anisotropy function formed from a combination of parallel and perpendicular polarizations isolates the orientational recovery. The anisotropy function is identical to that in fluorescence correlation spectroscopy and, for rigid-body rotational diffusion, can be expressed as a sum of five exponential terms.     

Fatty acids specifically related to the anisotropic properties of plasma membrane from rat urothelium

Four different luminal surfaces of rat urothelium differing in their fatty acid composition were prepared by dietary induction. In order to induce lipid changes, each of four groups of rat received a basal diet rich in one of the unsaturated n-3, n-6 or n-9 fatty acid families and a commercial (control) diet. The effects of the dietary regime on the fatty acid composition of luminal urothelial membranes and their relation to the mobility of fluorescent probes were studied. In comparison with the control diet membrane, all three fatty acid-rich diets induced a decrease of the percentage amount of saturated fatty acid while that of the unsaturated fatty acids was increased. Accordingly, all three diets increased the unsaturation index in comparison with the control diet. The anisotropy across each membrane fraction was assessed using the n-(9-anthroyloxy) fatty acid fluorescent probes 3-AS, 7-AS and 12-AS, which locate at different depths in the membrane. Two different anisotropy profiles were observed. One profile showed the highest anisotropy at the C7 depth, whereas the other exhibited a continuous decrease of the anisotropy from the surface to the center of the bilayer. The molecular properties (isomerization) of 18:2n-9 fatty acid may account, at least in part, for the observed V-shaped profile (the ascending trend) of the membrane anisotropy values as a function of the respective 18:2n-9 fatty acid contents. Nevertheless, the minimum value of the profile did not correspond to the minimum 18:2n-9 fatty acid content, but rather to the higher amount of docosahexaenoic (22:6n-3) fatty acid. Thus, a modulating role of the 22:6n-3 fatty acid on the rigidifying effect of 18:2n-9 fatty acid is suggested, possibly mediated by relationships between fatty acid composition, saturated and unsaturated chain lengths, and freedom of motion of the phospholipid acyl chains.     

Shape of the fluidity gradient in the plasma membrane of living HeLa cells

The shape of the fluidity gradient of the outer hemi-leaflet of the plasma membrane of living HeLa cells was determined using a series of n-(9-anthroyloxy) fatty acid probes where n = 2, 3, 6, 7, 9, 10, 11, 12, and 16. Fluorescence uptake and steady-state anisotropy values were obtained with a flow cytometer capable of continuous recording over time of vertical and horizontal emission intensities, and of the output of these intensities as calculated anisotropy values. The fluorescence uptake of all of the membrane probes was rapid up to about 15 min. The magnitudes of the uptake of fluorescence were, for the n-(9-anthroyloxy) series, in the order 2 greater than 3 greater than 6 greater than 7 greater than 9 greater than 10 greater than 11 = 12 = 16. Anisotropy values were constant from 5 to 30 min after addition of the various probes, and the magnitudes were in the order 7 greater than 6 greater than 9 = 10 greater than 2 = 3 greater than 11 greater than 12 greater than 16, indicative of the shape of the fluidity gradient. No differences were noted between the values obtained with 12-(9-anthroyloxy) stearic acid and 12- (9-anthroyloxy) oleate. The kinetics of anisotropy exhibited by those probes with the anthroyloxy group in positions deeper than 9, where initially higher values declined until equilibrium was reached, were probably indicative of an energy barrier at the approximate depth sensed by 7 AS.     

Effect of fluorophore linkage position of n-(9-anthroyloxy) fatty acids on probe distribution between coexisting gel and fluid phospholipid phases

The quenching of probe fluorescence by spin-labeled phospholipid has been used to determine the distribution of a series of n-(9-anthroyloxy) fatty acids between coexisting gel and fluid liquid-crystal phases in multilamellar phospholipid vesicles. The phase distribution ratio in every case is found to favor the fluid lipid phase, but is much greater between fluid and Ca2+-induced gel than between fluid and thermal gel. For a given gel type, n-(9-anthroyloxy)stearic acids with n = 3, 6, 9 or 12 as well as 11-(9-anthroyloxy)undecanoic acid all exhibit similar behavior, favoring the fluid phase by about a factor of 4 over thermally-induced lipid gel phase and by 18 over Ca2+-induced gel phase. 16-(9-Anthroyloxy)palmitic acid, with the bulky probe at the terminus of the 16-carbon chain, favors the fluid phase less strongly, by a factor of 1.5 or 11 over thermally-induced or Ca2+-induced gel phase, respectively, indicating better packing of this probe in phospholipid gel phases.     

二价金属离子对嵌有线粒体H~+-ATP酶的脂酶体不同层次脂质流动性的影响

本文报道用荧光偏振及顺磁共振两种方法研究Mg~(2+)及其它二价金属离子对嵌有H~+-ATP酶的脂酶体不同层次脂质流动性的影响。 (1)顺磁标记探剂5-、12-、16-氮氧基硬脂酸测定结果表明Mg~(2+)和其它二价金属离子都能降低膜脂双分子层表层的流动性。降低流动性的顺序为Mg~(2+)=Ca~(2+)>Sr~(2+)>Cd~(2+)。较深层脂则无明显变化。 (2)荧光探剂7-、12-(9-蒽酰)硬脂酸及16-(9-蒽酰)棕榈酸的测定结果也表明Mg~(2+)和其它二价金属离子降低了膜脂表层的流动性,尤以Mn~(2+)、Ca~(2+)降低流动性最显著,流动性降低的顺序为;Mn~(2+) Ca>Sr~(2+) Mg~(2+) Cd~(2+)。除Mn~(2+)、Ca~(2+)还能影响膜脂深层的流动性外,其它与对照无明显差异。     

Orientation of cyanine fluorophores terminally attached to DNA via long, flexible tethers

Cyanine fluorophores are commonly used in single-molecule FRET experiments with nucleic acids. We have previously shown that indocarbocyanine fluorophores attached to the 5′-termini of DNA and RNA via three-carbon atom linkers stack on the ends of the helix, orienting their transition moments. We now investigate the orientation of sulfoindocarbocyanine fluorophores tethered to the 5′-termini of DNA via 13-atom linkers. Fluorescence lifetime measurements of sulfoindocarbocyanine 3 attached to double-stranded DNA indicate that the fluorophore is extensively stacked onto the terminal basepair at 15°C, with properties that depend on the terminal sequence. In single molecules of duplex DNA, FRET efficiency between sulfoindocarbocyanine 3 and 5 attached in this manner is modulated with helix length, indicative of fluorophore orientation and consistent with stacked fluorophores that can undergo lateral motion. We conclude that terminal stacking is an intrinsic property of the cyanine fluorophores irrespective of the length of the tether and the presence or absence of sulfonyl groups. However, compared to short-tether indocarbocyanine, the mean rotational relationship between the two fluorophores is changed by ∼60° for the long-tether sulfoindocarbocyanine fluorophores. This is consistent with the transition moments becoming approximately aligned with the long axis of the terminal basepair for the long-linker species.     

Membrane structural dynamics of plasma membranes of living human prostatic carcinoma cells differing in metastatic potential

Rigidity of the outer hemileaflet of the plasma membrane of two prostatic carcinoma cell lines with different metastatic potential, 1-LN and 1-LN-EMS-10, was assessed by steady-state anisotropy, using a battery of fluorescent probes. The "bulk" membrane rigidity sensed by diphenylhexatriene, trimethylammonio-DPH, 1-palmitoyl-2-[DPH-ethylcarbonyl]-phosphatidylcholine, and 10-pyrenedecanoic acid indicated slightly higher rigidity in the membrane of the highly metastatic line (1-LN). This was accompanied by 26% greater mole fraction of cholesterol and 9% lower phospholipid, resulting in 40% greater cholesterol/phospholipid ratio. Phosphatidylethanolamine was increased 12%, but corresponding decreases in phosphatidylserine and phosphatidylinositol resulted in no significant change in molar ratio of choline/noncholine phospholipids. Whereas unsaturation index was slightly higher in 1-LN, fatty acids of 1-LN plasma membranes contained 15% more 18:1, 43% more 20:4, 26% more 22:4, and 38% less 18:2. Anisotropy gradients were determined for the two cell lines using a series of n-(9-anthroyloxy) fatty acid probes with n = 2, 3, 6, 7, 9, 12, and 16. Gradients differed only in position of anisotropy maxima, which occurred with n = 6, in 1-LN, and n = 7, in 1-LN-EMS-10. Possible relationships between observed anisotropy gradients and differences in membrane cholesterol and fatty acid composition are discussed.     

The transverse organisation of ubiquinones in mitochondrial membranes as determined by fluorescence quenching

The transverse organisation of ubiquinone in mitochondrial membranes was investigated by quenching a set of fluorescent fatty acids. We show that the fluorescent moiety of the probes is located at a graded series of depths in the mitochondrial membrane. The probes sense the characteristics of the lipid phase and do not significantly perturb mitochondrial function as measured by the respiratory control ratio and the ADP/O ratio. The anthroyloxy fatty acids are readily quenched by ubiquinone-10. A recently developed method in the analysis of quenching data was used to obtain the subvolume of the membrane within which the quenching interactions are confined. The results indicate that ubiquinone-10 is restricted to two sites in the transverse plane of the membrane: one near the surface and the other close to the bilayer centre. The implications of these findings for the two-pool model of ubiquinone organisation are discussed.Abbreviations n-AS n-(9-anthroyloxy) stearic acids (n=6,9,12) - n-AP n-(9-anthroyloxy) palmitic acids (n=2,16) - n-AF n-(9-anthroyloxy) fatty acids (n=2,6,9,12,16) - n nitroxide stearic acids (n=5,16) - UQ _n ubiquinone-n (n=4,6,10) - HBHM heavy beet heart mitochondria     

Effects of ethanol on the Escherichia coli plasma membrane.

The effects of ethanol on the fluidity of Escherichia coli plasma membranes were examined by using a variety of fluorescent probes: 1,6-diphenyl-1,3,5-hexatriene, perylene, and a set of n-(9-anthroyloxy) fatty acids. The anthroyloxy fatty acid probes were used to examine the fluidity gradient across the width of the plasma membrane and artificial membranes prepared from lipid extracts of plasma membranes. Ethanol caused a small decrease in the polarization of probes primarily located near the membrane surface. In comparison, hexanol decreased the polarization of probes located more deeply in the membrane. Temperature had a large effect on probes located at all depths. The effects of ethanol on E. coli membranes from cells grown with or without ethanol were also examined. Plasma membranes isolated from cells grown in the presence of ethanol were more rigid than those from control cells. In contrast to plasma membranes, artificial membranes prepared from lipid extracts of ethanol-grown cells were more fluid than those from control cells. These differences are explained by analyses of membrane composition. Membranes from cells grown in the presence of ethanol are more rigid than those from control cells due to a decrease in the lipid-to-protein ratio. This change more than compensates for the fluidizing effect of ethanol and the ethanol-induced increase in membrane C18:1 fatty acid which occurs during growth. Our results suggest that the regulation of the lipid-to-protein ratio of the plasma membrane may be an important adaptive response of E. coli to growth in the presence of ethanol.     

Tryptophan imaging of membrane proteins

A theoretical analysis of resonance energy transfer between protein tryptophan and the n-(9-anthroyloxy) (AO) fatty acid probes has been carried out to evaluate its potential use in determining the tryptophan distribution in membrane proteins. The F?rster theory for two-dimensional energy transfer was formulated to calculate multiple donor (tryptophan) transfer efficiencies to ensembles of AO probes at different depths in the bilayer. The variation of transfer efficiency with AO probe depth is found to be a sensitive function of tryptophan position and the protein radius but not the dipole-dipole orientation factor or the decay heterogeneity of the donor. For single tryptophan-containing proteins the model predicts that the tryptophan position can be determined with a precision of about 2 A. Although for multiple tryptophans there is appreciable deterioration in resolution, it is still possible to determine the essential features of the distribution such as its first two moments. The positions determined by this method are the projections of the tryptophan positions on a plane perpendicular to the membrane surface, since the probes distribute uniformly around the protein. To analyze the data, a Monte Carlo approach has been developed to search for tryptophan distributions compatible with the observed efficiencies and to display the results in terms of a tryptophan density map. It is shown that even for cases in which little is known about the quantum yield distribution, significant information can be determined about the tryptophan spatial distribution.     

Simulation of structure, orientation, and energy transfer between AlexaFluor molecules attached to MscL

Measurements of time-resolved fluorescence anisotropy and fluorescence resonance energy transfer are finding many applications in the study of biological macromolecules as they enable structural properties of the host molecules to be determined in their natural environment. A difficulty in interpreting these experiments is that they both require knowledge of the relative orientation of the fluorophores, a property that is almost impossible to measure. Here we conduct simulations of AlexaFluor488 and AlexaFluor568 attached to two sites on the membrane channel MscL to provide an alternative mechanism for determining the likely configurations and orientational freedom of the fluorophores, as well as the most likely value of the orientation factor κ² for energy transfer between them. The fluorophores are relatively mobile, and are found to be more so when immersed in bulk water than when they interact with the lipid membrane. The fluorophores never insert deeply into the lipid, despite their hydrophobic linkers and aromatic headgroup structures. Properties such as the fluorescence anisotropy decay can be predicted from simulations of the fluorophores in bulk water that closely match experimental data. In contrast, when the fluorophores were attached to the large MscL protein it was difficult to sample all the possible configurations of the fluorophores due to the computational time required. While this approach is likely to provide useful data on solvent-accessible fluorophores attached to small proteins, simulations lasting >50 ns or the use of biasing forces are required to accurately predict orientation factors for use in energy transfer experiments on larger membrane-bound proteins.     

Mechanism and kinetics of merocyanine 540 binding to phospholipid membranes

The physicochemical mechanism for merocyanine 540 (M540) binding to unilamellar phosphatidylcholine (PC) vesicles was examined by steady-state and dynamic fluorescence and fluorescence stopped-flow methods. At 530-nm excitation, aqueous M540 has an emission peak at 565 nm, which red shifts to 580 nm with formation of membrane-bound monomers (M); bound dimers (D) are nonfluorescent. Equilibrium fluorescence titrations show that 50% of total M540 partitions into the membrane to form D at [M540]/[PC] (Rm/p)_approximately 0.6. M and D concentrations are equal at Rm/p approximately 0.05. For Rm/p less than 0.1, M540 has a single fluorescence lifetime (tau), which decreases with Rm/p [tau-1 (ns-1) = 0.48 + 3.3Rm/p], indicating a rapid collisional rate between M to form D. Dynamic depolarization studies show that hindered rotation of M (r infinity = 0.13 at Rm/p = 0.006) becomes more rapid (rotational rate 0.2-1.9 ns-1) with increasing Rm/p (0.006-0.075). The efficiencies of energy transfer between n-(9-anthroyloxy) fatty acid probes (n = 2, 6, 9, 12, 16) and bound M540 suggest that M is oriented parallel to the phospholipids near the membrane surface; studies of efficiencies of n-AF quenching by D are consistent with an orientation of D perpendicular to the phospholipids. In stopped-flow fluorescence measurements in which M540 is mixed with PC vesicles, there is a rapid (1 ms) followed by a slower (10-50 ms) concentration-dependent fluorescence increase.(ABSTRACT TRUNCATED AT 250 WORDS)     

Response of rat heart membranes and associated ion-transporting ATPases to dietary lipid

The effects of different dietary fat intake on the lipid composition and enzyme behaviour of sarcolemmal (Na+ + K+)ATPase and sarcoplasmic reticulum Ca2+-ATPase from rat heart were investigated. Rat diets were supplemented with either sunflower seed oil (unsatd./satd. 5.6) or sheep kidney fat (unsatd./satd. 0.8). Significant changes in the phospholipid fatty acid composition were observed in both membranes after 9 weeks dietary lipid treatment. For both membranes, the total saturated/unsaturated fatty acid levels were unaffected by the dietary lipid treatment, however the proportions of the major unsaturated fatty acids were altered. Animals fed the sunflower seed oil diet exhibited an increase in n-6 fatty acids, including linoleic (18:2(n-6] and arachidonic (20:4(n-6] while the sheep kidney fat dietary rats were higher in n-3 fatty acids, principally docosahexaenoic (22:6), with the net result being a higher n-6/n-3 ratio in the sunflower seed oil group compared to sheep kidney fat dietary animals. Fluorescence polarization indicated that the fluidity of sarcoplasmic reticular membrane was greater than that of sarcolemmal membrane, with a dietary lipid-induced decrease in fluidity being observed in the sarcoplasmic reticular membrane from sheep kidney fat dietary animals. Despite these significant changes in membrane composition and physical properties, neither the specific activity nor the temperature-activity relationship (Arrhenius profile) of the associated ATPases were altered. These results suggest that with regard to the parameters measured in this study, the two ion-transporting ATPases are not modulated by changes which occur in the membrane lipid composition as a result of the diet.