Phase transitions of phospholipid single-wall vesicles and multilayers. Measurement by vibrational raman spectroscopic frequency differences

Raman spectroscopic frequency differences between selected carbon-carbon stretching modes of lipid hydrocarbon chains were determined as a function of temperature for use in monitoring lipid phase transition behavior and acyl chain disorder in both multilamellar and single-wall vesicles. Transition temperatues detected by this procedure for pure dipalmitoyl phosphatidylcholine and dimyristoyl phosphatidylcholine multilayers were observed at $\text{39±1 °}\text{C}$ and $\text{23±1 °}\text{C}$, respectively. Although the phase transition for unilamellar vesicles of dipalmitoyl phosphatidylcholine occurred at nearly the same temperature as the multilayers, the crystal-liquid crystalline transition for the single-shell vesicles appeared to span a slightly broader temperature range, a characteristic consistent with irregularities in the packing arrangement of the hydrocarbon chains. Within the precision of the Raman spectroscopic method, however, the temperature behavior of both the multilamellar and the unilamellar dimyristoyl phosphatidylcholine assemblies appeared nearly identical. The temperature profile for the Raman frequency differences of an excess water sonicate of 25 mol percent cholesterol in dipalmitoyl phosphatidylcholine served as an example of the effect upon lipid phase transition characteristics of a bilayer component intercalated between the acyl chains. For this particular cholesterol-lipid system the phase transition was broadened over a 30 °C temperature range, in contrast to the narrow 5?4 °C range observed for pure multilayer and single-shell vesicle particles.     

Interactions of proteins and cholesterol with lipids in bilayer membranes

Mixtures of lipids and proteins, the ATPase from rabbit sarcoplasmic reticulum, were studied by freeze-fracture electron microscopy and by measurement of the amount of fluid lipid with the spin label 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO). In dimyristoyl phosphatidylcholine vesicles the protein molecules were randomly distributed above the transition temperature, $\text{T}{}_{\mathrm{<mtext>t</mtext>}}$, of the lipid and aggregated below $\text{T}{}_{\mathrm{<mtext>t</mtext>}}$. For mixtures af dimyristoyl and dipalmitoyl phosphatidylcholine the existence of fluid and solid domains was shown in the temperature interval predicted from earlier TEMPO measurements. When protein was incorporated into this lipid mixture, freeze-fracture particles were randomly distributed in fluid lipids, or aggregated when only solid lipids were present.In mixtures of dimyristoyl phosphatidylcholine with cholesterol the protein was distributed randomly above the transition temperature of the phosphatidylcholine. Below that transition temperature the protein was excluded from a banded phase of solid lipid in the case of 10 mol% cholesterol. In mixtures containing 20 mol% cholesterol, protein molecules formed linear arrays, 50–200 nm in length, around smooth patches of lipid.Phase diagrams for lipid/cholesterol and lipid/protein systems are proposed which account for many of the available data. A model for increasing solidification of lipid around protein molecules or cholesterol above the transition temperarture of the lipid is discussed.     

Mode of binding of cytochrome b5 to phospholipid bilayers in lamellar structure

X-ray diffraction studies were made on the multilamellar systems produced by incubation of phospholipid bilayers and the membrane protein, cytochrome b₅, or non-membrane proteins (albumin, ovalbumin and β-lactoglobulin A) at pH 8.1 in aqueous 5 mM CaCl₂ solutions.Detergent-extracted cytochrome b₅ (soluble aggregate) forms two types of lamellar phase with dipalmitoyl phosphatidylcholine bilayers, depending upon the incubation temperature. One type, which has a repeat distance of 114Å, is formed above 34°C, where the binding of cytochrome b₅ to the bilayers is hydrophobic. The other type, with a repeat distance of 153 Å, is formed below 34°C, where the binding is electrostatic. It is also suggested that cytochrome b₅ is monomeric in the former phase but remains aggregated in the latter phase.When dimyristoyl phosphatidylcholine is used, the boundary temperature for the two types shifts to 12°C. These boundary temperatures coincide with the thermal pretransition points of hydrated dipalmitoyl phosphatidylcholine and dimyristoyl phosphatidylcholine, respectively.Trypsin-treated cytochrome b₅ (monomeric) and the three non-membrane proteins exhibit only binding of the electrostatic type to the bilayers, independently of the incubation temperature. The observed repeat distances suggest that in these cases two layers of protein molecules are incorporated between the bilayers.     

Asymmetric antagonistic effects of an inhalation anesthetic and high pressure on the phase transition temperature of dipalmitoyl phosphatidic acid bilayers

The phase transition temperature ($\text{T}{}_{\mathrm{<mtext>t</mtext>}}$) of dipalmitoyl phosphatidic acid multilamellar liposomes is depressed 10°C by the inhalation anesthetic methoxyflurane at a concentration of 100 mmol/mol lipid. Application of 100 atm of helium pressure to pure phosphatidic acid liposomes increased $\text{T}{}_{\mathrm{<mtext>t</mtext>}}$ only 1.5°C. However, application of 100 atm helium pressure to dipalmitoyl phosphatidic acid lipsomes containing 100 mmol methoxyflurane/mol lipid almost completely antagonized the effect of the anesthetic. A nonlinear pressure effect is observed. In a previous study, a concentration of 60 mmol methoxyflurane/mol dipalmitoyl phosphatidylcholine depressed $\text{T}{}_{\mathrm{<mtext>t</mtext>}}$ only 1.5°C, exhibiting a linear pressure effect. The completely different behavior in the charged membrane is best explained by extrusion of the anesthetic from the lipid phase.     

Transient and linear dichroism studies on bacteriorhodopsin: determination of the orientation of the 568 nm all-trans retinal chromophore

The orientation of the 568 nm transition dipole moment of the retinal chromophore of bacteriorhodopsin has been determined in purple membranes from Halobacterium halobium and in reconstituted vesicles. The angle between the 568 nm transition dipole moment and the normal to the plane of the membrane was measured in two different ways.In the first method the angle was obtained from transient dichroism measurements on bacteriorhodopsin incorporated into large phosphatidylcholine vesicles. Following flash excitation with linearly polarized light, the anisotropy of the 568 nm ground-state depletion signal first decays but then reaches a time-independent value. This result, obtained above the lipid phase transition, is interpreted as arising from rotational motion of bacteriorhodopsin which is confined to an axis normal to the plane of the membrane. It is shown that the relative amplitude of the time-independent component depends on the orientation of the 568 nm transition dipole moment. From the data an angle of 78 ° ± 3 ° is determined.In the second method the linear dichroism was measured as a function of the angle of tilt between the oriented purple membranes and the direction of the light beam. The results were corrected for the angular distribution of the membranes within the oriented samples, which was determined from the mosaic spread of the first-order lamellar neutron diffraction peak. In substantial agreement with the results of the transient dichroism method, linear dichroism measurements on oriented samples lead to an angle of 71 ° ± 4 °.No significant wavelength dependence of the dichroic ratio across the 568 nm band was observed, implying that the exciton splitting in this band must be substantially smaller than the recently suggested value of 20 nm (Ebrey et al., 1977).The orientation of the 568 nm transition dipole moment, which coincides with the direction of the all-trans polyene chain of retinal, is not only of interest in connection with models for the proton pump, but can also be used to calculate the inter-chromophore distances in the purple membrane.     

Functional group contributions to the partitioning of phenols between liposomes and water

The temperature dependency of the partitioning of p-alkylphenols and p-halophenols has been determined between dimyristoyl phosphatidylcholine liposomes and 0.15 M NaCl. Partition coefficients increased as a function of temperature below the endothermic phase transition temperature (T_c) of the phospholipid but decreased above this temperature. The transfer process was found to be entropy-dominated below and enthalpy-dominated above the T_c, although large negative entropy changes were observed. Regular changes in the thermodynamic functions, partition coefficients and functional group free energies occurred as a function of the alkyl chain length or size of the halogen substituent below but not above the T_c. This has tentatively been attributed to increased phenol-phospholipid interaction at the higher temperatures. The partitioning of p-fluorophenol behaved in a manner expected of fluorinated compounds, yielding relatively low partition coefficients, but it produced an additional effect of markedly lowering the T_c of dimyristoyl phosphatidylcholine. Good correlations of the partition coefficients in liposomes with those in bulk organic solvents and with molecular size of the solute have been obtained.     

Effects of gaseous anaesthetics and inert gases on the phase transition in smectic mesophases of dipalmitoyl phosphatidylcholine

The phase transition in smectic mesophases of dipalmitoyl phosphatidylcholine was studied under high pressures of helium (340 atm), nitrogen (340 atm), nitrous oxide (43 atm), cyclopropane (4.4 atm) and $\text{n-}\text{propane}$ (8.2 atm), using a turbidimetric technique. Helium and nitrogen increased the transition temperature by 0.021 and 0.006°C/atm, respectively, compared with 0.024°C/atm for hydrostatic pressure. Nitrous oxide reduced the transition by 0.58°C/atm. The hydrocarbon gases spread the transition width and lowered the transition temperature with increasing effect at higher doses. Comparisons with other membrane probes are made and the concentration of gases in the bilayer which lower the transition temperature by 1°C are estimated, in mol%: He, 10.2; N₂, 13.2; N₂O, 9.04; $\text{n-}\text{C}{}_3\text{H}{}_8$, 6.3 and cyclopropane, 12.8.     

Characterization of mixed micelles of phospholipids of various classes and a synthetic,homogeneous analogue of the nonionic detergent triton X-100 containing nine oxyethylene groups

The synthesis and high-pressure liquid chromatographic purification of the homogeneous nonionic surfactant $\text{p-}\text{(1,1,3,3-tetramethylbutyl)phenoxynonaoxyethylene}$ glycol (OPE-9) in quantities suitable for membrane solubilization studies is reported. Micelles of OPE-9 and mixed micelles of OPE-9 with dimyristoyl and dipalmitoyl phosphatidylcholine as well as phosphatidylserine, phosphatidylethanolamine, lysophosphatidylcholine, sphingomyelin, and palmitic acid were characterized by column chromatography on 6% agarose. It was found that at 28°C OPE-9 micelles have a Stokes' radius of 32 Å, giving a molecular weight for a spherical micelle of about half that of micelles of the polydisperse nonionic surfactant Triton X-100 under the same conditions. The micelle size is temperature dependent: at 40°C the OPE-9 micelles have a Stokes' radius of 44 Å, giving a molecular weight for a spherical micelle of about twice that of the OPE-9 micelles at 28°C. The size of the mixed micelles varies linearly (as measured by $\text{K}{}_{\mathrm{<mtext>av</mtext>}}$) with the mole fraction of phospholipid. The mixed micelle size was found to be relatively independent of the absolute concentration of surfactant over a four-fold range if the mole fraction of phospholipid is kept constant. The usefulness of the OPE-9/phospholipid mixed micelle system for lipolytic enzyme substrates and membrane-related studies is considered.     

Lipid-protein interactions in membrane models fluorescence polarization study of cytochrome b5-phospholipids complexes

According to previous authors, cytochrome $\text{b}{}_5$, when extracted from bovine liver by a detergent method, is called cytochrome $\text{d-b}{}_5$. On the other hand, the protein obtained after trypsin action, which eliminates an hydrophobic peptide of about 54 residues, is called cytochrome $\text{t-b}{}_5$.Fluorescence polarization of the dansyl phosphatidylethanolamine probe inserted into phospholipid vesicles is very senstive to the binding of proteins, and so is a useful method to study lipid-protein interactions.The chromophore mobility, $\text{R}$, decreases markedly when dipalmitoyl phosphatidylcholine vesicles are incubated with cytochrome $\text{d-b}{}_5$, whereas $\text{R}$ does not change for cytochrome $\text{c}$ and cytochrome $\text{t-b}{}_5$. This can be interpreted as a strengthening of the bilayer, only due to the interaction of the hydrophobic peptide tail.Interaction of dipalmitoyl phosphatidylcholine vesicles with cytochrome $\text{d-b}{}_5$ occurs either below or above the melting temperature of the aliphatic chains (41 °C). Even for a high protein to lipid molar ratio (1 molecule of protein for 40 phospholipid molecules), the melting temperature is apparently unaffected.Phosphatidylserine and phosphatidylinositol do not interact at pH 7.7 with cytochrome $\text{d-b}{}_5$, because electrostatic forces prevent formation of complexes. At low pH, the interaction with the protein occurs, but the binding is mainly of electrostatic nature.     

Lateral and transversal diffusion and phase transitions in erythrocyte membranes. An excimer fluorescence study

The lateral diffusion of the excimer-forming probe pyrene decanoic acid has been determined in erythrocyte membranes and in vesicles of the lipid extracts. The random walk of the probe molecules is characterized by their jump frequency, v_j, within the lipid matrix. At T = 35°C a value of v_j = 1.6 · 10³ s^?1 is found in erythrocyte membranes. A somewhat slower mobility is determined in vesicles prepared from lipid extracts of the erythrocyte membrane. Depending on structure and charge of the lipids we obtain jump frequencies between 0.8 · 10⁸ s^?1 and 1.5 · 10⁸ s^?1 at T = 35°C. The results are compared with jump frequencies yielded in model membranes.The mobility of molecules perpendicular to the membrane surface (transversal diffusion) is investigated. Erythrocyte ghosts doped with pyrene phosphatidylcholine were mixed with undoped ghosts in order to study the exchange kinetics of the probe molecule. A fast transfer between the outer layers of the ghost cells ($\text{τ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 1.6}\text{min at}\text{T = 37°}\text{C}$) is found. The exchange process between the inner and the outer layer of one erythrocyte ghost (flip-flop process) following this fast transfer occurs with a half-life time value of $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 100}\text{min at}\text{T = 37°}\text{C}$.The application of excimer-forming probes presumes a fluid state of the membrane. Therefore we investigated the phase transition behaviour using the excimer technique. Beside a thermotropic phase transition at T = 23°C and T = 33°C we observed an additional fluidity change at T = 38°C in erythrocyte ghosts. This transition is attached to a separation of the boundary lipid layer from the intrinsic proteins. No lipid phase transition is observed in liposomes from isolated extracts of the erythrocyte membrane with our methods.     

Transmembrane orientation of α-helices in the thylakoid membrane and in the light-harvesting complex. A polarized infrared spectroscopy study

The structure and orientation of the major protein constituent of photosynthetic membranes in green plants, the chlorophyll $\text{a}\text{b}$ light-harvesting complex (LHC) have been investigated by ultraviolet circular dichroism (CD) and polarized infrared spectroscopies. The isolated purified LHC has been reconstituted into phosphatidylcholine vesicles and has been compared to the pea thylakoid membrane. The native orientation of the pigments in the LHC reconstituted in vesicles was characterized by monitoring the low-temperature polarized absorption and fluorescence spectra of reconstituted membranes. Conformational analysis of thylakoid and LHC indicate that a large proportion of the thylakoid protein is in the α-helical structure (56 ± 4%), while the LHC is for 44 ± 7% α-helical. By measuring the infrared dichroism of the amide absorption bands of air-dried oriented multilayers of thylakoids and LHC reconstituted in vesicles, we have estimated the degree of orientation of the α-helical chains with respect to the membrane normal. Infrared dichroism data demonstrate that transmembrane α-helices are present in both thylakoid and LHC with the α-helix axes tilted at less than 30° in LHC and 40° in thylakoid with respect to the membrane normal. In thylakoids, an orientation of the polar C=O ester groups of the lipids parallel to the membrane plane is detected. Our results are consistent with the existence of 3–5 transmembrane α-helical segments in the LHC molecules.     

Temperature dependence of active K+ transport in cation dimorphic sheep erythrocytes

Arrhenius diagrams of K⁺ pump fluxes measured between 15°C and 41°C were discontinuous in high K⁺ but not in low K⁺ sheep red cells. Exposure of low K⁺ cells to anti-L caused a bimodal temperature response of K⁺ pump flux with a transition temperature, $\text{T}\text{c}$, similar to that found in high K⁺ cells but with comparatively higher activation energies above $\text{T}\text{c}$.     

Interaction of small molecules with phospholipid bilayer membranes: permeability studies

The passage of a phospholipid through the gel to liquid crystal phase transition is associated with an increase in the motional freedom of its fatty acyl chains as measured by spectroscopic techniques and an essentially isothermal absorption of heat as measured by differential scanning calorimetry (DSC). In addition, bilayers formed from that phospholipid display a permeability maximum for both non-electrolytes and electrolytes in the temperature region of the phase transition. In this study the sodium (and in some cases glucose) permeabilities of liposomes composed of either dimyristoyl or dipalmitoyl phosphatidylcholine plus dicetylphosphate were measured in the presence of a group of benzene and adamantane derivatives known to increase fatty acyl chain motion below the lipid transition temperature (T_c) and in the case of the adamantanes to also lower the T_c as measured by DSC. None of these compounds change the temperature at which the permeability maximum occurs despite their lowering of the phospholipid T_c. That is, in the presence of these additives there is observed an apparent dissociation between the phase transition and the permeability maximum. It is proposed that the permeability maximum normally observed in the temperature region of the T_c is associated with the completion of the ‘melting’ process. Hence a compound could cause early ‘melting’ of the bilayer but not change its permeability properties if the temperature at which the ‘melting’ process neared completion was not changed.     

Influence of membrane lipids on the photochemistry of bacteriorhodopsin in the purple membrane of Halobacterium halobium

Purple membrane fragments from Halobacterium halobium were reconstituted with the native lipids replaced by dipalmitoyl phosphatidylcholine and by egg lecithin. In parallel studies the temperature dependence of bacteriorhodopsin phototransient lifetime and absorption dichroism and of in situ lipid microviscosity were determined; the former two by, respectively, conventional and polarization flash photometry, and the latter by observation of emission depolarization of an embedded fluorescent dye, 1,6-diphenyl-1,3,5-hexatriene. Discontinuities in lipid microviscosity profiles in native and egg lecithin purple membrane were reflected in both the photochemical cycle frequency and bacteriorhodopsin chromophore rotational mobility. The influence exerted by membrane-lipid viscosity appears to be a secondary effect, and points to the bacteriorhodopsin chromophoric group being situated in the protein interior.     

Seasonal and temperature-related changes in mitochondrial membranes associated with torpor in the mammalian hibernator Spermophilus richardsonii

Seasonal variations in the thermal response of liver mitochondrial membranes from Richardson's ground squirrels (Spermophilus richardsonii) were determined by measuring succinate-cytochrome $\text{c}$ reductase activity and spin label motion over a temperature range of 2 °C to 35 °C. For seven summer animals from the field the Arrhenius-type plots for enzyme activity and spin label motion were biphasic indicating a transition in structure and function at $\text{22 + 2.3°C}\text{and}\text{23 ± 1.9°C}$, respectively; typical of homeothermic mammals. For 12 winter animals maintained at 19°C, the transition in structure and function was lowered to $\text{12 ± 1.1°C}$ and $\text{13 ± 1.4°C}$, respectively. The transition for 5 of 11 winter animals which were kept at 4°C and maintained normal activity and body temperature was similar to animals maintained at 19°C, while for the other six the transition was further lowered to less than 4°C. The transition for seven winter animals which were in deep hibernation was less than 4°C. The results for liver mitochondria show that lowering of the transition in membrane structure and function occurs as a two-stage process of about 10 deg. C for each stage and that the lowering is a requisite for hibernation rather than a response to the low-body temperatures experienced during hibernation.     

Effect of fluorescamine modification of purple membranes on exciton coupling and light-to-dark adaptation

Purple membranes of $\text{Halobacterium}\text{,}\text{halobium}$ were modified with fluorescamine. At pH 8.8, with a molar ratio of fluorescamine to bacteriorhodopsin of 170, about 6 residues of lysine were modified while the arginines were not affected at all. Except for the appearance of the fluorescamine peak at 394 nm and some broadening of the chromophore peak at 570 nm, the absorption spectrum of bacteriorhodopsin was not significantly changed after modification. After fluorescamine modification, circular dichroism studies indicated loss of exciton coupling between bacteriorhodopsin molecules in the purple membrane. Rotational diffusion studies suggested enhanced mobility of the chromophore after modification. However, the spectral changes accompanying the light-to-dark adaptation of purple membranes were not prevented by fluorescamine modification. The implications of these findings are that exciton coupling between neighboring bacteriorhodopsin molecules in the purple membrane is not required for light-to-dark adaptation.     

Laser Raman spectroscopy of lipid-protein systems Differences in the effect of intrinsic and extrinsic proteins on the phosphatidylcholine Raman spectrum

Laser Raman spectroscopy is used to examine the interactions of intrinsic and extrinsic proteins with the lipid layer structure. The interactions of cytochrome c and cytochrome c oxidase with lipids have been well established by others using a variety of techniques. Cytochrome c is thought to act as an extrinsic membrane protein while cytochrome c oxidase is thought to act as an intrinsic membrane protein. The lipid-cytochrome c and lipid cytochrome c oxidase systems are used to assist in interpreting the spectral changes due to extrinsic and intrinsic protein interactions. The two types of proteins examined produced differential changes in the lipid hydrocarbon CH stretch Raman modes for both dimyristoyl and dipalmitoyl phosphatidylcholine. The plasma proteins albumin and fibrinogen were also found to differentially affect the lipid hydrocarbon CH stretch Raman modes. These proteins appear to interact with lipids in an extrinsic manner different from that of cytochrome c.     

Effect of the phase transition on the transbilayer movement of dimyristoyl phosphatidylcholine in unilamellar vesicles

Dimyristoyl phosphatidylcholine rapidly exchanges between vesicles at 37°C without vesicle fusion.The rate of the transbilayer movement of dimyristoyl phosphatidylcholine in sonicated vesicles has been measured employing ¹³C NMR using N-¹³CH_3? labeled lipids which are introduced into the outer monolayer of non-labeled vesicles by a phosphatidylcholine exchange protein. The rate of transbilayer movement of dimyristoyl phosphatidylcholine shows a distinct maximum (halftime 4 h) in the temperature range at which the hydrocarbon phase transition occurs.The activation energy of the flip-flop rate above the phase transition is 23.7 ± 2.0 kcal/mol.     

Kinetic parameters for the binding of p-nitrophenyl alpha-d-mannopyranoside to concanavalin A.

Binding of the chromogenic ligand p-nitrophenyl α-d-mannopyranoside to concanavalin A was studied in a stopped-flow spectrometer. Formation of the protein-ligand complex could be represented as a simple one-step process. No kinetic evidence could be obtained for a ligand-induced change in the conformation of concanavalin A, although the existence of such a conformational change was not excluded. The entire change in absorbance produced on ligand binding occurred in the monophasic process monitored in the stopped-flow spectrometer. The value of the apparent second-order rate constant (k_a) for complex formation (k_a = 54,000 s^?1m^? at 25 °C, pH 5.0, Γ/2 0.5) was independent of the protein concentration when the protein was in the range of 233–831 μm in combining sites and in excess of the ligand. The apparent first-order rate constant (k_?a) for dissociation of the complex was obtained from the rate constant for the decomposition of the complex upon the addition of excess methyl α-d-mannopyranoside (k_?a = 6.2 s^?1 at 25 °C, pH 5.0, Γ/2 0.5). The ratio $\text{k}{}_{\mathrm{<mtext>a</mtext>}}{}_{\mathrm{<mtext>?</mtext><mtext>a</mtext>}}$ (0.9 × 10₄m^?1) was in reasonable agreement with value of 1.1 ± 0.1 × 10⁴m^?1 determined for the equilibrium constant for complex formation by ultraviolet difference spectrometry. Plots of ln($\text{k}{}_{\mathrm{<mtext>a</mtext>}}\text{T}$) and ln($\text{k}{}_{\mathrm{<mtext>a</mtext>}}\text{T}$) vs $\text{1}\text{T}$ were linear (T is temperature) and were used to evaluate activation parameters. The enthalpies of activation for formation and dissociation of the complex are 9.5 ± 0.3 and 16.8 ± 0.2 kcal/mol, respectively. The unitary entropies of activation for formation and dissociation of the complex are 2.8 ± 1.1 and 1.3 ± 0.7 entropy units, respectively. These entropy changes are much less than those usually associated with substantial changes in the conformation of proteins.     

Increase in temperature induces the Z to B transition of poly[d(G-C)] in water-ethanol solution

An increase in temperature from 20 to 50° C results in the complete transition from the Z to B form of poly(d(G-C)], dissolved in a 55% ethanol-water solution. The transition is fully reversible and displays a slow kinetics. The transition profiles for the free polynucleotide and for that in the presence of ethidium bromide, which is known to stabilize the B form, are obtained by circular dichroism. Based on these data the enthalpy value for the B-Z transition in our conditions is estimated to be ΔH_BZ = ?0.7 $\text{kcal}\text{mol}$.