Biochemistry - The Chemical Reactions of Living Cells, Volume 1 - D. Metzler 1980

Membranes and Cell Walls
Membrane Structure
Physical Properties of Membranes Determined by Their Lipid Composition

A fully extended 18-carbon fatty acid chain (Fig. 5-1) has a length of approximately 2 nm. The cross-sectional area occupied by such a molecule viewed "end-on" is 0.20 nm². Consequently, the thickness of the hydrocarbon layer in a lipid bilayer containing such fatty acid chains should be ~4 nm. The experimentally measured thickness of myelin membranes turned out to be ~3.5 nm, whereas in the membranes of the retinal rod outer segment it did not exceed 1.8 nm, and in artificial black films completely devoid of solvent, it is 3.1 nm [15]. These and many other findings suggest that the hydrocarbon chains in the membrane are not fully stretched out; As a result, the area occupied by the membrane is somewhat larger than would be expected from the elementary model, which assumes that the fatty acid chains are fully extended. The prevalence of cis-isomers of Unsaturated Fatty acids and other molecules, such as sterols or Proteins, in the membrane promotes folding, thereby reducing membrane thickness. The hypothesis that the thickness of Introduction/36.html">Biological Membranes is greater than it should be if their Structure corresponded to the elementary model is supported by measurements of lipid monolayer thickness in Plasma Membranes. According to the data obtained, the cross-sectional area of a phospholipid molecule averages 0.52 nm², whereas for a compact packing it should be ~0.40 nm² (twice the cross-section of a single extended chain) [16].

At sufficiently low temperatures, lipid bilayers behave like solids. According to X-Ray Diffraction data, the bilayer thickness is 0.42 nm, which corresponds to a hexagonal packing of the fatty acid chains. At a Temperature exceeding the transition temperature (T_t), the bilayer thickness increases to 0.46 nm. The bilayer structure is preserved, but the fatty acids "melt," resulting in easier rotation and twisting of molecules compared to low temperatures [16a]. The melting of Membrane Lipids has been directly demonstrated by several Methods. For example, at temperatures above T_t, the hydrogen atoms of methyl and methylene groups in the fatty acid side chains give narrow signals in the proton and ¹³C-NMR spectra of membranes.

The sharp broadening of these bands at temperatures below T_t is due to the loss of mobility of the hydrocarbon chains (Supplement 5-A). Similar Conclusions were drawn from studies of spin-labeled bilayers containing covalently bound stable free radicals, whose unpaired electrons can be detected by electron paramagnetic Resonance (EPR, see Supplement 5-B).

The transition or "melting" temperature of lipid bilayers depends on the COMPOSITION OF THE fatty acids they contain. Long-chain saturated Fatty acids are characterized by high transition temperatures. Myelin is distinguished by a particularly high content of long-chain Sphingolipids and Cholesterol, which are known to increase the stability of artificial bilayers. In essence, the state of myelin membranes in The Human Body approaches that of a solid.

The transition temperature of bilayers can often be quite distinct. However, careful studies have shown that, as in the case of impure crystals, melting actually begins long before T_t. Thus, the higher solubility of paramagnetic 2,2,6,6-tetramethylpiperidine-1-oxyl in the liquid Regions of the bilayer compared to the solid ones makes it possible to study the bilayer melting process by heating the membrane directly in an EPR spectrometer through Changes in the solubility of this spin-labeled compound (Supplement 5-B). For dipalmitoylphosphatidylcholine (lecithin), the T_t value is 40.5 °C,

however, the first signs of melting can be noticed much earlier—at a temperature of 29.5 °C [17]. Similar data were obtained by the "fluorescent probe" method, which was used to measure the fluorescence intensity of N-phenylnaphthylamine, which depends on the polarity of its environment (Ch. 13, Sec. V.1). When this compound is incorporated into the membrane, its fluorescence intensity increases significantly. The data indicate that even at temperatures < T_t, liquid and solid regions coexist within the bilayer [17a]. This phenomenon is called lateral phase Separation [17]. The equilibrium between Solid and liquid states is dynamic and largely depends on the ionic composition of the medium surrounding the bilayer. There is reason to believe that lateral phase separation plays a fundamental role in Nerve Impulse propagation [18].

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Supplement 5-A

Relaxation Times in Magnetic Resonance Spectroscopy

In modern literature on The Study of membranes, Enzymes, and the conformation of small molecules, terms such as longitudinal and transverse relaxation time and correlation time are frequently encountered. To understand the meaning of these terms, one must consult the original papers^a-e; the text below should be viewed merely as a brief introduction.

The initial goal of NMR spectroscopy was to obtain a high-resolution spectrum in which the magnetic moment of each Nucleus would be recorded as a distinct absorption signal or signals. The minimum signal width is limited by the Heisenberg uncertainty principle, according to which ΔE∙Δt = h/2π, where h is Planck's constant, ΔE is the energy uncertainty, and Δt is the lifetime of the excited magnetic state. Since E = hν for electromagnetic radiation, ΔE is directly proportional to the signal width. A nucleus possessing a magnetic moment is well shielded from external influences, and its lifetime in the excited state can be relatively long. It follows that Δν must be small, often less than 0.2 Hz. This circumstance facilitates the successful

use of high-resolution proton magnetic resonance (see, for example, Figs. 2-40 and 2-41).

If a very powerful pulse of electromagnetic radiation is applied to a sample in an NMR spectrometer, practically all nuclei can be driven into the excited magnetic state. If another pulse is applied immediately afterward, the energy absorption will be small because the system is saturated. In the most widely used NMR spectrometers, low-intensity radiofrequency fields are employed to reduce the saturation effect. However, in pulsed Fourier-transform NMR spectrometers, The Use of powerful pulses leads to a high degree of saturation. Repeated pulsing does not yield useful information unless the excited nuclei relax sufficiently fast into a state characterized by thermal equilibrium of energy distribution. Relaxation occurs through the interactions of nuclei with fluctuating magnetic fields of their environment. The relaxation of organic molecules in solution occurs mainly due to fluctuations caused by the motion of electric dipoles in close proximity. Nevertheless, even with such interactions, proton relaxation times in Water can be measured in seconds.

The relaxation of nuclear magnetic states is characterized by two times. The longitudinal relaxation time, or spin-lattice relaxation time T₁, determines The rate of relaxation of the total magnetic vector of the nuclei along the spectrometer magnetic field (H₀). The transverse, or spin-spin relaxation time T₂, characterizes relaxation in the plane perpendicular to the H₀ direction. Under certain conditions, the two relaxation times can be measured independently. In general, T₂ ≤ T₁. For solids, the time T₂ is short (approximately 10^-5 s), whereas for solutions, as already mentioned, it can be measured in seconds. Such a significant increase in the lifetime of the excited state upon transition from the solid to the liquid state leads to a narrowing of absorption lines, which plays a crucial role in NMR spectroscopy. This explains why NMR signals, which are normally narrow for liquids, broaden when the viscosity increases or membrane fluidity decreases.

How can T₂ and T₁ be measured? As a first approximation for liquids, T₂ is often estimated from the signal width Δν at half-height:

However, special pulsed NMR methods are usually employed for this purpose. The easiest way to measure T₁ is using a Fourier-transform spectrometer in the presence of the ¹³C isotope. Often, T₁ and T₂ times are used to obtain information about the dynamic CHARACTERISTICS OF THE system. In this case, the relationship between T₁ or T₂ on the one hand, and the correlation time τ_c for the nuclei under study on the other, is determined. The parameter τ_c is a time constant characterizing the exponential decay of fluctuations in the medium responsible for the relaxation of magnetic nuclei. In general, 1/τ_c can be considered as a rate constant representing the sum of all rate constants for various independent processes leading to relaxation. The most important of these processes is molecular reorientation, for which 1/τ = (3kT)/(4πηr³). Note the similarity of this equation to the equation describing rotational diffusion [Equation (6-32)]. Another parameter is the reciprocal of the residence time τ_m, which characterizes the average time during which a pair of dipoles remains close enough to each other for relaxation to occur.

In ordinary Solvents at room temperature, τ_c is 10^-12 s. Consequently, relaxation rates in solution are significantly higher than the frequencies of radiation absorbed in an NMR spectrometer (~10⁸ s^-1). Under these conditions, relaxation is relatively inefficient, and the times T₁ and T₂ are long and in most cases equal to each other. The signals thus remain narrow. As the correlation time increases (e.g., with increasing viscosity), the times T₁ and T₂ decrease; time T₁ reaches a minimum when τ_c^-1 equals the frequency of the absorbed radiation ν. Under these conditions, signals broaden, and hyperfine lines (due to magnetic spin interactions between different nuclei) merge and cannot be resolved. As τ_c increases further, time T₂ decreases and reaches a constant minimum value, whereas time T₁ increases again. NMR measurements can be carried out in the region where τ_c^-1 is greater than ν. This capability is realized in high-frequency spectrometers, which constitutes their advantage. At the same time, liquids are normally studied under the condition of extreme narrowing associated with high mobility at low values of τ_c^-1. As molecular mobility increases, The values of both T₁ and T₂ increase.

A serious limitation in using NMR methods to study proteins is associated with the increase in the correlation time of molecular reorientation for large molecules. Since 1/τ_r usually makes the largest contribution to the relaxation rate constant, narrow signals in the NMR spectrum appear only when studying small proteins whose molecular weight does not exceed 20,000^b.

A practical difficulty encountered in ¹³C NMR studies, associated with slow relaxation (a long T₁ value), is caused by partial saturation. As a result, carbon atoms for which relaxation is particularly inefficient exhibit signals of lower intensity. Relaxation times can be measured separately for each carbon atom in the molecule. Proper interpretation of the obtained data yields valuable information about the mobility of specific fragments and groups within the molecule. It should be noted that the relationships between relaxation times and intramolecular motions are complex, but the situation is often simplified by using ¹³C NMR. Since carbon atoms are usually surrounded by bonded hydrogen atoms, nuclear relaxation is largely determined by dipole-dipole interactions with these atoms. For a carbon atom bonded to N equivalent protons characterized by very rapid molecular reorientation,

where ħ = h/2π, and γ_c and γ_h are the gyromagnetic ratios of carbon and hydrogen nuclei, respectively. This relationship makes it possible to calculate the effective correlation time τ for each carbon atom.

An example of this kind of interpretation is the work of Goodman et al.^g. Some problems related to the interpretation of signal widths in membrane NMR spectra are discussed in the paper by Seiter and Chan^h.

^a Bovey F. A., Nuclear Magnetic Resonance Spectroscopy, Academic Press, New York, 1969.

^b Farrar T. C., Becker E. D., Pulse and Fourier Transform NMR, Academic Press, New York, 1971.

^в Swift J. T., Tech. Chem., 6, Part II, 521—563 (1974).

^г Lyerla J. R., Jr., Grant D. M. In: Magnetic Resonance, (McDowell C. A, ed.), MTP Int. Rev. Sсi. No. 4, pp. 155—200, Butterworth, London, and Univ. Park Press, Baltimore, 1972.

^д Lee A. G., Birdsall N. J. M., Metcalfe C. In: Methods in Membrane Biology (Korn E. D., ed.), Vol. 2, pp. 1—156, Plenum, New York, 1974.

^e Gray G. A., CRC Crit. Rev. Biochem., 1, 247—364 (1973).

^ж Goodman R. A., Oldfield E., Allerhand A., JACS, 95, 7553—7558 (1973).

³ Selter C. H. A., Chan S. I., JACS, 95, 7541—7553 (1973).

It is generally believed that in all organisms at physiological temperatures, the Lipid Components of most membranes exist partially in a liquid state [19]. This liquid state of membrane lipids can be attributed to at least three factors. 1. Human organisms (as well as E. coli) contain unsaturated fatty acids that lower the melting point; E. coli mutants incapable of synthesizing unsaturated fatty acids cannot survive in media devoid of these compounds [20]. 2. In Bacillus subtilis grown at 37 °C, which lack unsaturated fatty acids, and in other Gram-positive Bacteria, over 70% of the membrane fatty acids contain additional methyl groups (Ch. 12, Sec. D) [21]. Similar to double bonds in the cis-configuration, these additional methyl groups contribute to a lowered melting point and a 1.5-fold increase in the surface area of the monolayer.

3. The lowering of the lipid melting point may also be due to the presence of cyclopropane-containing fatty acids in their composition (Ch. 12, Sec. D.1).

At the same time, the presence of cholesterol in membranes restricts molecular mobility and decreases the surface area occupied by phospholipid molecules [22].

Why must membrane lipids possess mobility? One of the reasons is likely related to the involvement of membranes in vital transport processes. Biological membranes exhibit a fairly high permeability to neutral molecules (including H₂O), and at temperatures exceeding T_t, the fatty acid chains can freely rotate around single bonds by 120°, transitioning from a trans- to a gauche-configuration. As a result of such rotation around adjacent or closely spaced bonds, "kinks" are formed in the fatty acid chains. If a kink forms near the bilayer surface (which is most often the case), a small molecule can easily slip into the resulting cavity. Since the kink easily moves along the bilayer, small molecules can freely penetrate the membrane [23]. It is also possible that these same factors facilitate The transport of larger molecules acting as carriers in membrane transport.

The lipid and protein molecules that make up membranes are capable of moving relative to one another. The rate of lateral diffusion of lipids in bilayers and of Antigens (proteins) on Cell surfaces is quite high. Assuming that phospholipid diffusion occurs through the mutual exchange of adjacent molecules, the frequency of such exchanges can reach 10⁷ s^-1 [24].

Experimental data obtained using NMR and EPR methods indicate that the outer regions of bilayers are in a somewhat more rigid state than the inner ones. It is presumably not by chance that the first double bond in polyunsaturated fatty acids typically occurs between the 9th and 10th carbon atoms. As a result, the double bonds in the fatty acids of galactosyl diglycerides in METABOLISM/14.html">Chloroplasts are located at the same distance from the membrane surface as the methyl groups of the phytol chains in chlorophyll. It is believed that the "molten" center of the bilayer contains regions with an irregular structure formed by the methyl groups of the phytol chains (Fig. 13-19), which are incorporated into chloroplast membranes [25] and anchor chlorophyll molecules there¹.

Supplement 5-B

Electron Paramagnetic Resonance (EPR) Spectra and Spin Labels

Because unpaired electrons possess magnetic moments, they serve as convenient objects for magnetic resonance spectroscopy. Its methodological framework is basically similar to NMR spectroscopy; however, EPR spectroscopy employs electromagnetic waves with frequencies of ~10¹⁰ Hz (microwave range), the energy of which is approximately 100 times greater than that of the waves used in NMR spectroscopy^a-c. Unpaired electrons are found in free radicals of organic molecules as well as in certain transition metals. Both classes of compounds are of great importance for A number of enzymatic processes. In addition, spin labels—stable organic radicals—can be attached to various sites of macromolecules. Using EPR or NMR methods, it is often possible to detect interactions between the unpaired electrons of such artificially incorporated radicals and the magnetic moments of unpaired electrons or nuclei.

¹ This viewpoint reflects only one of the proposed theories; other possible explanations are discussed in Ch. 3, Sec. D.3.

The conditions for energy absorption in an EPR spectrometer are given by the equation , which is identical in form to the fundamental equation of NMR spectroscopy. Here, ß is a constant known as the Bohr magneton. The g-factor, or spectroscopic splitting factor, is one of the most important characteristics used in describing the EPR spectrum. For a free electron, the g-factor is 2.000; for radicals, it may differ slightly, and for transition Metal Ions, the deviation is sometimes quite significant. One of the factors causing the g-factor to depend on its environment is spin-Orbit coupling, which is associated with the Asymmetry of the p- and d-orbitals of atoms. For the same reason, the g-factor sometimes takes three discrete values for three different directions (g-factor anisotropy). In other cases, the g-factor value in the direction parallel to H₀ (g_‖) differs from its value in the perpendicular direction (g_⊥). Both of these values can be determined experimentally.

Another characteristic of the EPR spectrum is hyperfine structure, THE ORIGIN OF which is related to the interaction between the magnetic moments of the unpaired electron and nuclear spins. This interaction is analogous to spin-spin coupling in NMR (Ch. 2, Sec. 3). The hyperfine splitting constant A, much like the coupling constant J in NMR spectroscopy, is expressed in hertz. The splitting is caused by the presence of a magnetic moment in The Nucleus around which the electron orbits, or in a nearby nucleus, as well as by the presence of another unpaired electron. Sometimes the presence or absence of splitting allows for important chemical conclusions to be drawn. For example, in the EPR spectrum of a metal ion in a complex, splitting due to Ligand nuclei will be observed only if the ligand is covalently bound to the ion.

Typically, EPR spectroscopy utilizes the first derivative of the absorption curve rather than the absorption curve itself. For instance, in the case of an nitroxide spin label, the EPR spectrum consists of three evenly spaced lines. Their centers are located at the points where the derivatives of the absorption curves cross the horizontal axis. Interaction with the ¹⁴N nuclear spin leads to splitting into three lines, as shown in the figure below.

EPR spectrum of tetramethylpiperidine-1-oxide (Sec. A4) dissolved in an aqueous phospholipid emulsion. Top: at a temperature above T_t; center: between T_t and the pretransition temperature; bottom: at a temperature below the "pretransition"^г.

(Reprinted with permission from American Chemical Society Biochemistry, 12, 2553, 1973.)

The bottom of the three spectra approaches that of a spin label in water, whereas the other two are more complex spectra characteristic of states where a portion of the label is dissolved in the phospholipid bilayers.

Because the frequencies used in EPR spectroscopy are approximately 100 times higher than those in NMR spectroscopy, correlation times (Supplement 5-A) must not exceed 10^-9 s to obtain well-resolved spectra. Although clear spectra can be obtained for solutions, samples are generally frozen to slow down molecular motion, and measurements are conducted at very low temperatures. When investigating spin labels in lipid bilayers, line widths and shapes serve as sensitive Criteria for the nature of molecular motion, which can be either isotropic or anisotropic. To compare line shapes obtained under various conditions with those predicted by specific line-broadening theories, computers are frequently and successfully employed^d,e. Examples of spin labels incorporated into lipid bilayers include the following compounds:

The interpretation of Observed changes in the EPR spectra of spin labels is, in most cases, purely empirical in nature. For instance, when interpreting the spectra shown in the figure above, one may assume that a greater amount of the spin label dissolves in the lipid at high temperatures than at lower ones. The ratio indicated in the figure represents an empirical parameter whose temperature dependence can be evaluated from experiments conducted at various temperatures. Plots reflecting the dependence of f on T were used to determine the Transition Temperature and pretransition temperature in bilayers^г.

^а Knowles Р. F., Essays Biochem., 8, 79—106 (1972).

^б Chen К. S., Hirota N.. Tech. Chem., 6, Part II, 565—636 (1974).

^в Griffith О. H., Waggoner A. S., Acc. Chem. Res., 2, 17—24 (1969).

^г Shimshick E. I., McConnell H. M., Biochemistry, 12, 2351—2360 (1973).

^д Deraux P., McConnell H. M., JACS, 94, 4475—4481 (1972).

^e Sackmann E., Trouble H., JACS, 94, 4482—4498 and 4499—4510 (1972).