DIELECTRIC PROPERTIES O F NORMAL A N D ABNORMAL LIPOPROTEINS IN AQUEOUS SOLUTION C. G. Essex, E. H. Grant, R. J . Sheppard, G. P. South, M. S. Symonds Physics Department Queen Elizabeth College London W8 7A H , United Kingdom
G . L. Mills Courtauld Institute of Biocheniistry Middlesex Hospilal Medical School London WI P S P R . United Kingdom Joan Slack M R C Clinical Genetics Unit Institute of Child Health London WCI N I E H . United Kingdotti
Dielectric dispersion techniques have been in use for nearly forty years’ as a means of characterizing the molecular properties of protein^^-^ and smaller biological moleculess.6 in aqueous solution. More recently dielectric measurements have been made on larger biological molecules such as DNA,’ and this has been paralleled by investigations on polypeptides and artificial biopolymers.’*’ By contrast, very little dielectric work appears to have been carried out on natural lipoproteins (apart from a small pilot study”), although there have been some recent studies on phospholipid vesicles and similar systems.”*’2 In this paper we report dielectric measurements made on aqueous solutions of human and bovine serum low-density lipoproteins (LDL). Permittivity and conductivity measurements were made over the frequency range 0.15-1000 MHz and as a function of temperature, concentration, ionic conductivity, and solution pH. Particular emphasis was placed on determinations carried out at 800 MHz, it having been shown in previous work” that this is in the optimum frequency region for locating any differences in hydration that may exist between the various forms of lipoprotein. The dielectric decrement at 800 M H z was measured for samples of LDL isolated from the sera of patients with familial hyperbetalipoproteinaemia and compared with that determined for LDL obtained from the controls. Analysis of the results shows the presence of three separate dispersion regions in the range 0.15-1000 MHz, which, in order of ascending frequency, may be ascribed to counterion relaxation, Maxwell-Wagner effects arising from the heterogeneous nature of the lipoprotein particle, and bound water. These three dispersions may be respectively termed the a,@, and 6 regions, and they exist in addition to the y dispersion which is due to the relaxation of free water molecules
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and which occurs at frequencies i n the region of I 100 G H z . Of particular interest in the present work is the &dispersion, where i t is shown that the magnitude and relaxation frequency are compatible with the structure of the lipoprotein molecule comprising a conducting core surrounded by an insulating shell. Thus the dielectric data are consistent with a lipid bilayer model but are inconsistent with a lipid core model. The results at 800 MHz suggest an association between permittivity and clinical condition. The most likely explanation of the observed dilrerences in permittivity is that the quantity of bound water (water of hydration) associated with the lipoproteins arising from the patients with hyperbetalipoproteinaemia is larger than that present in the controls. ND MErtiom M A T E R I A LA S
LDL is usually defined as that group of lipoproteins having a density range 1.006~1.063 and a flotation rate ( S , ) 0~20 Svedberg units. (Flotation rate is equivalent to velocity/acceleration and I Svedberg u n i t equals I O - ” s ) . I n human plasma LDL is the most abundant lipoprotein and is normally present in a concentration of about 350 mg/100 ml of plasma. The isolation of the lipoproteins was carried out as described by Grant el d..” with the following modification. After the crude lipoprotein concentrate obtained by precipitation had been dialysed against 0. I5 M NaCl solution for 48 hours, i t was added to one fifth of its volume of NaCl solution of density 1.079 g/ml. This raised the density of the solvent phase to 1.019 g/ml. Six ml of this solution were added to each o f an appropriate number of centrifuge tubes, and 3 ml of NaCl solution of density. 1.019 g/ml layered on top. The prepared tubes were then centrifuged for 16 hours at 12°C in the 30.2 Spinco ultracentrifuge rotor at 30 000 rev/min (79420 g), aftcr which the supernatant lipoproteins were aspirated OH‘ i n I ml and discarded. The next three ml were also removed separately. Four ml of NaCl solution of density 1.0955 g/ml were added to each tube, and thoroughly mixed. After centrifugation under the same conditions as before, the supernatant lipoprotein layers were aspirated off in a combined volume of about 6 ml and dialyzed for 48 hours against a solution containing 0.17 x 10-4M K H l P 0 4 and 3.17 x 1 0 - 4 M N a l H P 0 4 . Before determining the permittivity, the samples were tiltered to prevent any sedimentatipn occurring during the measurement procedure. Since the filtration could slightly alter the concentration. a small amount of the final solution ( - I ml) was set aside for concentration determination. To eliminate decomposition. all the measurements were made within two days of preparation. a trial r u n having shown that consistent values of permittivity are obtained over this period of time. The relative permittivity c ’ and conductivity (c)were determined for the LDL solutions by three experimental techniques. In the frequency range 0.15 9 MHz, a Wayne Kerr B201 admittance bridge was used with a cell design and calibration procedure described p r e v i ~ u s l y .At ~ ~frequencies ’~~ between I and I00 MHr. measurements were made with a Boonton 3314 admittance bridge15 and in the high frequency range (300- 1000 MHz), an automated coaxial line system was em-
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p l ~ y e d . ' ~ , 'A' few confirmatory measurements were made in other laborat ~ r i e s l * at " ~frequencies below and above the range covered by our apparatus.
RESULTSA N D ANALYSIS Typical dispersion curves in permittivity ( t ' ) and conductivity ( u ) are shown in FIGURES I and 2, the full data being given by Essex.20 The conductivity plotted in FIGURE 2 is the incremental value over and above the contribution due to ionic conductivity, which is assumed to be frequency-independent. The quantity S which is plotted as the ordinate in FIGURE 2 is equal to the measured conductivity ( u ) divided by the permittivity of free space (60). Use of S rather than u facilitates the calibration of the bridge.13 At the weaker concentrations the incremental conductivity is a small change in a large quantity, and for this reason the analysis was carried out with the permittivity data only. It is assumed that the permittivity curves can be described mathematically by
83
82 # #
81
80
B' 79 #
8
7E
# 0 0
# 0
7i
7f
7! 0 # #
P 1
1.0
10 100 Frequency MHz
1000
FIGURE I . Variation with frequency of the permittivity o f human LDL solution. (Concentration = 48.17 rng/ml; pH = 6.8; upper curve, 10°C; lower curve, 20°C.)
145
Essex et al.: Lipoproteins in Aqueous Solution 4
80-
...
,
60-
,, 40-
20-
---
1
----s-
0
-0.
1
1.0
0.1
10
Frequency MHr
FIGURE 2. Variation with frequency of incremental conductivity of h u m a n LDL solution. theoretical curve for t w o Debye dispersions: -- theoretical curve for one Debye dispersion.
- _ _ _ =-
n
$ = CI +Aiw i=l
2 2 + c , T,
where cj. is the permittivity of the solution at a frequency 1; Ai is the magnitude of the ith dispersion, w is the angular frequency ( w = 27rf), T~ is the relaxation time of the i l h dispersion and c m has its usual significance. The experimental curves were analyzed with the aid of a computer, and with a least mean squares minimization technique.*' T o correct for the effect of the y dispersion, which is caused by the relaxation of free water molecules having a relaxation frequency of about 20 G H z at 25"C?2 the following procedure was adopted. With use of Time Domain methods,23 measurements were made" at frequencies up to 10 G H z on a few samples to confirm the form of the y dispersion. As expected, the results indicated that the contribution of the y dispersion to changes in the permittivity with frequency is negligible below 400 MHz. At higher frequencies small corrections were made to the lipoprotein data with the Debye equations which are known to give an adequate description of the dielectric data of the y dispersion. After correction (O.I",, at 400 MHz and 0.5",,at 800 MHz) the values of permittivity of the lipoprotein solutions were fitted to Equation I . The data between 0.15 and 1000 MHz are found to be characterized by three dispersions with relaxation frequencies of 0.5 MHz, 4-6 M H z and 200-500 MHz, which, following previous c l a ~ s i f i c a t i o n ~may ~ ' ~ be ~ termed the a, p and 6 dis-
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A n n a l s New York A c a d e m y of Sciences
persions, respectively. The computer analysis predicts a leveling of the permittivity at frequencies below 0.15 MHz, and this was confirmed by measurements made" on a few samples with other apparatus. In using Equation I,various values of n were tried, and since, in general, an increase in the number of parameters will lead to a reduction in the error of fit, the values obtained were tested for statistical significance. N o parameter was introduced that did not yield a significant improvement in the fit at the 95",, level. With the computer technique used, it may be possible to fit too few parameters but difficult, if not impossible, to fit too many. I f an extra component is introduced the erect of which on the curve is not detectable, it will invariably result in a correlation coefficient near unity; i.e., the extra parameter will be found to be highly correlated with another parameter. Although three Debye dispersions have been assumed in the frequency range 0.15-1000 MHz, the possibility cannot be excluded that small additional dispersions may also be present or that one or more of the observed dispersion regions may have a distribution of relaxation times. With the experimental accuracy available in the present work. the introduction of any extra parameters does not result i n any significant improvement; i t . , additional components cannot be detected i n thc presence of the experimental error. Thus the three-component fit suggested is found to be the most appropriate analysis of the data. The results taken a t 800 MHz are shown in F I G U R E S 7 and 8 and will be discussed separately at the end o f t h e paper.
MOLECULAR 1NTERPRETATlON OF
RESUI.TS
As mentioned earlier in this paper, the dielectric measurements were carried out over a wide range of values of various physical parameters: temperature, concentration, and solution pH and ionic conductivity. The purpose of this was to establish the variation of the dielectric increment (Ai)and the relaxation frequency [ J = ( 2 r r i ) - ' ] with the physical parameters listed above. By this means it is possible to eliminate particular molecular processes from being responsible for the observed dispersions while at the same time narrowing down the number of acceptable possibilities. From the observed dielectric behavior we conclude that the best explanation for the origin of the a-dispersion is to attribute it to counterion relaxation of the type proposed by Schwarz.26 Full details of the observations and calculations that lead to this conclusion will appear in a subsequent publication,*' but the essential features of the argument can be summarized as follows. The linear dependence of the dielectric increment (A,) upon concentration (up to a certain critical concentration) is shown in FIGURE 3. Observations also show A, to be independent of pH and concentration and only slightly dependent on temperature. With regard to the relaxation frequency (fa) the experiments show that this is independent of concentration, conductivity, and pH. The relationship betweenfi and the inverse of absolute temperature is exponential, and a logarithmic plot gave an activation enthalpy of 4 kJ/mole. All these observations, coupled with a measured relaxation frequency of 0.5 M H z are compatible with a
Essex et af.: Lipoproteins in Aqueous Solution
147
counterion mechanism but are incompatible with any of the other processes that give rise to dielectric relaxation: 28 Debye rotation, proton tluctuation, MaxwellWagner effects, surface conductivity, ion atmosphere, and structured water. Moreover. the assumption of a counterion relaxation mechanism enables the charge on the lipoprotein molecule (eo) to be calculated from the dielectric data. Assuming a molecular radius o f I 1 nm the value of eo turns out to be 2 x C, which agrees well with the value obtained from electrophoretic studies.
7
6
5
4
Aa 3
2
1
0
I
20
40 60 80 100 LDL concentration (mg/ml)
120
FIGUKI.3 . Variation with concentration 01' the dielectric incrcmcnt of t h e m-dispersion ( T = 20°C: pH = 6 . 8 ) .A = bovine L D L . 0 = h u m a n LDL.
The abrupt change in shape of the increment-concentration curve at such a low concentration of 30 mgm/ml is a very unusual kind of phenomenon and is presumably due to the formation o f micellular structure.29 The dielectric behavior o f the @-dispersion is very similar to that observed for the a-dispersion, except that the increment ( A a ) is smaller and the relaxation frequency is about ten times as high. The variation of A, with concentration i s approximately linear ( F I G U R E 4), but there is little dependence on conductivity,
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5
4
*P 2
1
0
1
20
40
60 80 100 LD L concentration (mg/rnl)
120
FIGURE 4. Variation with concentration of the dielectric increment of the &dispersion ( T = 20°C; pH = 6.8). (Measurements for h u m a n LDL.) - - - - - - - = theoretical curve predicted by Pauly-Schwan Equations.
pH or temperature. The relaxation frequency (b) is independent of concentration, pH and conductivity and its variation with temperature predicts an activation enthalpy of about 4 kJ/mole. The best explanation (full mathematical details will appear later2’) for the origin of the P-dispersion is to attribute it to a Max~ e l l ~ ~ - W a g n type e r ” of mechanism. The LDL molecule is a highly complicated entity, but it is known to have a spherical shape and it may be assumed that the protein and lipid constituents tend to concentrate in different specific regions. For the purpose of interpreting the P-dispersion, it is necessary to employ a model for the LDL molecule that arranges the lipid and protein regions so that the electrical properties of the overall structure would predict the existence of a dielectric dispersion region of appropriate dielectric increment and relaxation frequency of about 5 MHz. To satisfy these conditions the requirements are that the LDL molecule should have a conducting core surrounded by an insulated shell. Of the various models proposed for the structure of a LDL molecule, one that complies with the above requirements is a lipid bilayer model such as the one proposed by Mateu et in which the lipoprotein molecule is considered t o consist of a protein core 4.6 nm in radius surrounded by a lipid shell 3.5 nm in width. Outside the shell are further protein subunits that are sufficiently spaced so as not to make a continuous shell. For the purpose of discussing electrical behavior the model can be represented by FIGURE5 , where CL and g,,, are the permittivity and con-
Essex et al.: Lipoproteins in A q u e o u s Solution
149
ductivity of the water continuum, and c,!, I J ~and , E ; , us refer to the protein interior and lipid shell, respectively. Assuming realistic values for these six parameters and using the above values of R and d , we have calculated the dielectric increment (A,) and the relaxation frequency (f,) by using the Pauly-Schwan equations.33 The agreement between theory and experiment was found to be very satisfactory, and F I G U R4E shows the predicted dependence of increment on concentration. The capacitance/unit area (C,) of the bilayer was calculated from the dielectric results, and the value obtained is 4.4 + 1 . 1 pF/cmZ. This is in good agreement with the figure of 3.3-4.2 pF/cm2 obtained for phospholipid vesicles by Redwood et al.” Typical values for other biological membranes are 0.5-5 p F / ~ m ’ . ~ ~ The amplitude of the d dispersion is small but significant, and, following previous proposal^,^ may be interpreted as being due to the relaxation of bound water of an amount in the range of about 0.02 to 0.14 g/g lipoprotein. The properties of the &dispersion will be more fully discussed s u b s e q ~ e n t l y ,and ~ ~ the question of lipoprotein hydration as deduced from measurements at a single frequency will be discussed now. PERMITTIVITY MEASUREMENTS AT 800 M H z The relationship between relativity permittivity and frequency for an aqueous solution of biological macromolecules is shown i n FIGURE6. At frequencies in excess of 10 MHz the permittivity of the solution is seen to be less than that of pure water, and for a solution of unit concentration this fall in permittivity below
---
- ------------------------ - - - - - ---FICUHE5 . Simple three-layer model o f a lipoprotein molecule in water. R = radius of = thickness of shell. ti, e l , tb = permittivity of core, shell, and solvent, respectively; uj, o,, u w - conductivity of core, shell, and solvent, respectively,
core; d
150
Annals New York Academy of Sciences 80
-
70
-
c' 60-
0.01
0.1
i
10
Frequency GHz
F I G U R 6. F Permittivity o f a biological solution of u n i t concentration, showing decrement = permittivity o r p u r e water.
of 800 M H L ( 6 8 ~ ) .-------
the pure-water value is termed the dielectric decrement (6). At frequencies around 800 MHz, it has been customary to assume that the solute molecules contribute to the overall permittivity in respect of their atomic and electronic polarization only. However, it was established by Buchanan ef a / . 3 5in 1952, and by others more r e ~ e n t l y . 4that . ~ ~ for protein solutions the value of dso0 is too large t o be accounted for by the effect of the solute molecules alone. and that the reason for this is that the water molecules tightly bound to the protein (water of hydration) d o not contribute fully to the polarization. Thus by measuring the dielectric decrement at frequencies around 500-1000 MHz and adopting a suitable dielectric mixture formula. estimates of the water of hydration for various proteins have been published .4*'0*35.36 The weakness with this approach is that the value of hydration obtained from the dielectric data is critically dependent on the choice of mixture formula and is very sensitive to the value assumed for the partial specific volume of the solute. The shape of the solute molecule also figures in the calculation, and this may not be known accurately. For these reasons it has been considered preferable to calculate the hydration from the amplitude of the b - d i ~ p e r s i o n , ~rather . ~ ~ than from the dielectric decrement. I n the present work, however, we are concerned with comparing the values of hydration for various types of lipoprotein of similar molecular shape and partial specific volume; therefore the disadvantages normally associated with the method disappear and the advantages of a measurement at one frequency only become immediately apparent. The relative permittivity at 800 MHz was measured for aqueous solutions of lipoproteins isolated from the sera of sixteen normal subjects and fifteen patients with type I 1 familial hyperbetalipoproteinaemia (FH), a condition characterized by high concentrations of LDL and associated with an increased risk of ischaemic heart disease.38 Of the fifteen patients considered in this particular study, seven were homozygotes and eight heterozygotes, although in general the proportion of
Essex ef al.: Lipoproteins in Aqueous Solution
151
homoLygotes is very much smaller than that of the heterozygotes. Patients in the latter group are prone to develop ischaemic heart disease at an early age, the expectation ofcoronary death for heterozygous men being about 50",, before the age of 55.39The much rarer homozygotes are likely to die in their late teens or early twenties. The results obtained for the controls are shown in F I G U R7,~ where the expected linearity between relative permittivity and solute concentration is seen. The dielectric decrements for the normals and for both categories of patient are 8. shown i n FIGUKF A statistical analysis of the decrements was carried out in two stages. First, an analysis of variance was performed on the data and the value of the F ratio (variance between the samples/variance within the samples) gave F = 8.82. Tabulated
79-
ITypical error 6'
707776-
7574 *
7372
-
71-
70 I 0
20
40 60 LDL concentration(mg/ml)
a0
FIGURI.7. Variation with concentration of permittivity of norniiil h u m a n LDL. solution a t 800 M H L .
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values4' of F with (2.28) degrees of freedom at the 997, level give F = 5.45. 95:" confidence intervals then evaluated, using a l-distribution, showed the following mean values and upper and lower 95';" confidence limits for GSoO: Normal, 105.9 < 107.4 < 109.0; heterozygote, 109.8 < 112.2 < 114.7; homozygote, 110.8 < 115.6 < 120.4. Hence there is strong evidence that GSoO depends upon the clinical condition of the patient and, in particular, that abnormals can be distinguished from nor-
t
A
161 A
A
m
A A A
.
0
.
. . . .... 8 .
0
.
0
,105 *
,100
. ..
-
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Sample Number
8. Values of 6800 for aqueous solutions of LDL. homozygotes.
FIGURE A =
0
0 =
normals;
=
heterozygotes;
mals. Following the analysis of variance, a subsequent t-test carried out between the means of the normals and heterozygotes gave a value of t = 4.03, as compared with a value of 2.84 for 22 degrees at the 997; confidence level obtained from statistical tables. The statistically significant differences in dsoO may be interpreted at a molecular level as follows. For a suspension of macroscopic spheroids of relative permittivity tp in a con-
Essex et al.: Lipoproteins in Aqueous Solution
153
tinuum of relative permittivity c, the relative permittivity of the mixture is given4' by t , where t
-= t
-
t,
+ Xt,
P-.
tp
tp
-
tw
+ Xt,
I n this equation p is the volume concentration of the spheroids and equals two if the particle is a sphere, but is greater than two for either a prolate or an oblate spheroid. In the present context to refers to a hydrated particle and the numerator of the left-hand side of Equation 2 is the product of the decrement and the solute concentration expressed as a fraction by weight. In general, cp is some assumed function of the relative permittivity ( c h ) of the bound water (water of hydration) and the relative permittivity ( t L ) of the solute core, the precise nature of the function depending upon the assumed model for the hydrated particle. In the present work, however, we are concerned with measuring differences in hydration (absolute values being relatively unimportant). and so the approximation t p N t h N tL E 5 at a frequency of 800 MHz can be made. Using the fact that all solutions are dilute ( p < 0.08). Equation 2 can be reduced'0337to the following convenient approximation ii+
w =
k K
(31
-66800
where wis the water of hydration expressed as a weight fraction. K = ( I + x ) / x and k is a constant of value 13.5 for the concentrations being considered in the present work. The partial specific volume (psv) of the solute particle is represented by Eand takes a value of 0.97 for LDL. Using Equation 3 . the values of hydration can be calculated for the three categories of LDL investigated. The shape of the LDL molecules as judged from electron micrographs appeared to deviate from spherical to a negligible extent, in which case K = 1.5 and the values of hydration are 0.04 0.02 (Normal), 0.09 j= 0.02 (heterozygote) and 0.12 + 0.04 (homozygote). The errors are the 95% confidence intervals, which, as seen from Equation 3, are directly proportional to the 95",, confidence intervals obtained for the values of dS00. Since Gsoo is dependent on iiand K as well as w , the question arises whether the dielectric results could be explained by a change either in shape or in partial specific volume, between the three forms of LDL. The first proposition can be rejected by noting that ultracentrifuge experiments show3xthat the abnormal lipoprotein has an increased S, (flotation rate) over that of the normal. which would require a change of shape in the opposite direction to that needed to explain the dielectric data. Therefore the observed differences in GSoo must mean that the quantity (ij + w ) varies between the three categories of LDL studied, and since appreciable variations in fi appear unthe best interpretation of the dielectric measurements is that the lipoprotein hydration depends on whether the LDL originates from normal serum or whether it is produced by the gene responsible for hyperbetalipoproteinaemia. This further supports the hypothesis proposed previously in a pilot study" carried out on the dielectric properties of normal and abnormal LDL.
*
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Annals New York Academy of Sciences A c K N Ow L E L)CME NTS
Thanks are due to the Wellcome Trust for supporting CGE, GPS and MSS during the investigations and for financing the purchase of apparatus. Acknowledgment is also due to the Central Research Fund of London University for an equipment grant. We are indebted to Dr. A. Suggett, Unilever Ltd, Colworth House, Sharnbrook, U.K.. and to M r . R. Lamote, of the Simon Stevin Instituut, Brugge, Belgium, for making the TDS measurements and low-frequency bridge determinations, respectively. REFF R E NC E s I.
ONCI-FY. J . L . 1943. In Proteins. Amino-Acids and Peptides. E. J . Cohn and J . T.
2. 3.
PI:NNOCK. B. t.& H . P. SCHWAN. 1969. J . Phys. Cheni. (Ithaca) 73: 2600 2610. MOSFR. P., P. Q. SOUIRI~& C . T. O'KONSKI.1966. J . Phys. Chem. (Ithaca) 7k7.14 755. GRANT, E. H.. BARBARA G. R. MITTON, G . P. SOUTH & R. J . SHEPPARD. 1974. Biocheni. J. 139: 375 380. AARON.MARGARET W . & E. H. GRANT. 1967.Trans. Faraday Soc.63:2177 2180. S t i w k i t : m . J . C. W . & E. H . GRANT. 1968. Proc. R . Soc. Lond. A307: 3 3 5 ~357. MANI)PI.M. This volume. S T O C K M A YWL.RH, . This volume. M A R C H A I . . E. This volume. GRANT-. E. H . , R. J . SIiFPPAm, G . L . MII.I.S & J O A N S I A C K . 1972. Lancet i : l 159 1161. SCIIWAN,H . P., S. TAKASIIIMA. V . K . MIYAMOTO & W . STOKh1:NIC.S. 1970. Biophys. J. 10: I102 I 119. R t u w o o u , W . R., S. TAKASIIIMA, H. P. SCHWAN & T. E. T l i o M w ) N . 1972. Biochim. Biophys. Acta 255: 557 566. SOUTH. G . P. 1970. Ph.D. Thesis. University o f London. London. England. G R A N TE.. H.. G . P. SOUTII, s. T A K A S H I M A & H. I C H I M U K A . 1971. Biochenl. J . 122: 691 699. E S S E X , G., ~ . G. P. SOUTH.K. J. SHEPPARD & E. H. GRANT.1975. J . Phys. E. 8:
Edsall. Eds.: Chapt. 22. Reinhold Publishing Corporation. N e w York. N.Y.
4.
5. 6.
7. X.
9. 10.
I I. 12. 13. 14.
15.
3x5 389. R. J . 1972. J . Phys. D. 5: 1576 87. 16. SHEPPARI). . J . Phys. E. 5 : 1208 12. 17. S H t P P A K I ) . R. J. & E. H . G R A N T1972. R . Private communication. (See A('KNoWl.eDc;MliNTS.) I X . LAMOTE. A . Private communication. (See ACKNOWIE D G M E N T S . ) 19. SUGGFTT, Esstx, C. G . 1976. Ph.D. Thesis. University of London. London. England. SHFPPARI). R. J. 1973. J . Phys. D. 6: 790-794. S C H W A N . H . P., R. J. S t I E P P A K I ) & E. H. G R A N T1976. . J . Cheni. Phys. 64:2257 2258. SUGGETT, A . & A . H. CLARK.1976. J . Solution Chem. 5 : I 15. SctiwAN, H. P. 1957. Advances in Medical and Biological Physics 5 : 147 209. 25. S c k i W A N . H. P. 1974. In Biological EKects and Health Haiards o f Microwave Radiation. P. Czerski, Ed.: 152-59. Polish Medical Publishers. Warsaw. Poland. 26. SCHWARZ, G. 1962. J . Phys. Chem. (Ithaca) 66: 2634-42. G. L. MIILS, R. J . S H ~ P P A RJ I. )SLACK . & G . P. SOL~TII. 27. E s s t x , C . G., E. H. GRANT, To be published. G . P. & E. H . G R A N T1972. . Proc. R. Soc. Lond. A328: 371-87. 28. SOUTH. & S. TAKASIIIMA. 1974. J . Colloid. Interface Science 29. B E A R DR, . B.. T. F. MCMASTFK 48:92 99.
20. 21, 22. 23. 24.
Essex e! a / . : Lipoproteins in Aqueous Solution
155
30.
M ~ X M ~JL . CL. ,1892. A Treatise on Electricity and Magnetism. Oxford Univ. Press.
31. 32,
WAGNtK.
Oxl'ord, tngland.
33. 34.
35. 36. 37. 38. 39. 40. 41. 42. 43.
M4TI.C.
K . 1913. Ann. Phys.40:817 29. L. A . TARIXI.L. V . LLZ/.A.II, L . AGGERRECK & A . M . SCANL. 1972. J . Mol.
Biol. 70: 105-1 16. PA01 1 , H . & H . P. S C H w A N . 1959. Z . Nuturforsch. 146: 125 38: 6:621 633. C o l I . K . S . 1968. Membranes. Ions and Impulses. University o f California Press. Berkeley. Calif. BL'CHANAS.T. J . . C. H. HAGGIS. J . B . HASTED & B. G . R O ~ I N S O S 1952. . Proc. R . Soc. Lond. A213:379 91. GXANT,E. H . 1957. Phys. Med. Hiol. 2: 17 28. GRAhr. E. H.. S. E. K ~ 1 : l . i .& S. TAKASHIMA. 1968. J . Phys. Chem. (Ithaca) 72:4373 XO. Si.Ach, J . & G . 1.MII-IS. 1970. Clinica Chim. Acla 29: 15 2.5. SLACK. J . 1969. Lancet ii: 1380-82. L I N D I F \ . 0. W . & J . C. P. M I [ I.I:R. 1964. Cambridge Elementary Statistical tableb. Cambridge Univ. f'ress. Cambridge, England. F R l ( . h b . H . 1924. Phks. Rev. 24: 575 88. T o R o - < i o Y c , o , t. l95X. Ph.D. Thesis. Harvard University. Cambridge. Mass. FISIII-K. W . K..M . G . HAMMOND & C. L. WARMKE.1972. Biochemistry ll:51Y 2 5 .
G . L. Mills Courtauld Institute of Biocheniistry Middlesex Hospilal Medical School London WI P S P R . United Kingdom Joan Slack M R C Clinical Genetics Unit Institute of Child Health London WCI N I E H . United Kingdotti
Dielectric dispersion techniques have been in use for nearly forty years’ as a means of characterizing the molecular properties of protein^^-^ and smaller biological moleculess.6 in aqueous solution. More recently dielectric measurements have been made on larger biological molecules such as DNA,’ and this has been paralleled by investigations on polypeptides and artificial biopolymers.’*’ By contrast, very little dielectric work appears to have been carried out on natural lipoproteins (apart from a small pilot study”), although there have been some recent studies on phospholipid vesicles and similar systems.”*’2 In this paper we report dielectric measurements made on aqueous solutions of human and bovine serum low-density lipoproteins (LDL). Permittivity and conductivity measurements were made over the frequency range 0.15-1000 MHz and as a function of temperature, concentration, ionic conductivity, and solution pH. Particular emphasis was placed on determinations carried out at 800 MHz, it having been shown in previous work” that this is in the optimum frequency region for locating any differences in hydration that may exist between the various forms of lipoprotein. The dielectric decrement at 800 M H z was measured for samples of LDL isolated from the sera of patients with familial hyperbetalipoproteinaemia and compared with that determined for LDL obtained from the controls. Analysis of the results shows the presence of three separate dispersion regions in the range 0.15-1000 MHz, which, in order of ascending frequency, may be ascribed to counterion relaxation, Maxwell-Wagner effects arising from the heterogeneous nature of the lipoprotein particle, and bound water. These three dispersions may be respectively termed the a,@, and 6 regions, and they exist in addition to the y dispersion which is due to the relaxation of free water molecules
142
Essex rf al.: Lipoproteins in Aqueous Solution
143
and which occurs at frequencies i n the region of I 100 G H z . Of particular interest in the present work is the &dispersion, where i t is shown that the magnitude and relaxation frequency are compatible with the structure of the lipoprotein molecule comprising a conducting core surrounded by an insulating shell. Thus the dielectric data are consistent with a lipid bilayer model but are inconsistent with a lipid core model. The results at 800 MHz suggest an association between permittivity and clinical condition. The most likely explanation of the observed dilrerences in permittivity is that the quantity of bound water (water of hydration) associated with the lipoproteins arising from the patients with hyperbetalipoproteinaemia is larger than that present in the controls. ND MErtiom M A T E R I A LA S
LDL is usually defined as that group of lipoproteins having a density range 1.006~1.063 and a flotation rate ( S , ) 0~20 Svedberg units. (Flotation rate is equivalent to velocity/acceleration and I Svedberg u n i t equals I O - ” s ) . I n human plasma LDL is the most abundant lipoprotein and is normally present in a concentration of about 350 mg/100 ml of plasma. The isolation of the lipoproteins was carried out as described by Grant el d..” with the following modification. After the crude lipoprotein concentrate obtained by precipitation had been dialysed against 0. I5 M NaCl solution for 48 hours, i t was added to one fifth of its volume of NaCl solution of density 1.079 g/ml. This raised the density of the solvent phase to 1.019 g/ml. Six ml of this solution were added to each o f an appropriate number of centrifuge tubes, and 3 ml of NaCl solution of density. 1.019 g/ml layered on top. The prepared tubes were then centrifuged for 16 hours at 12°C in the 30.2 Spinco ultracentrifuge rotor at 30 000 rev/min (79420 g), aftcr which the supernatant lipoproteins were aspirated OH‘ i n I ml and discarded. The next three ml were also removed separately. Four ml of NaCl solution of density 1.0955 g/ml were added to each tube, and thoroughly mixed. After centrifugation under the same conditions as before, the supernatant lipoprotein layers were aspirated off in a combined volume of about 6 ml and dialyzed for 48 hours against a solution containing 0.17 x 10-4M K H l P 0 4 and 3.17 x 1 0 - 4 M N a l H P 0 4 . Before determining the permittivity, the samples were tiltered to prevent any sedimentatipn occurring during the measurement procedure. Since the filtration could slightly alter the concentration. a small amount of the final solution ( - I ml) was set aside for concentration determination. To eliminate decomposition. all the measurements were made within two days of preparation. a trial r u n having shown that consistent values of permittivity are obtained over this period of time. The relative permittivity c ’ and conductivity (c)were determined for the LDL solutions by three experimental techniques. In the frequency range 0.15 9 MHz, a Wayne Kerr B201 admittance bridge was used with a cell design and calibration procedure described p r e v i ~ u s l y .At ~ ~frequencies ’~~ between I and I00 MHr. measurements were made with a Boonton 3314 admittance bridge15 and in the high frequency range (300- 1000 MHz), an automated coaxial line system was em-
Annals New York Academy of Sciences
144
p l ~ y e d . ' ~ , 'A' few confirmatory measurements were made in other laborat ~ r i e s l * at " ~frequencies below and above the range covered by our apparatus.
RESULTSA N D ANALYSIS Typical dispersion curves in permittivity ( t ' ) and conductivity ( u ) are shown in FIGURES I and 2, the full data being given by Essex.20 The conductivity plotted in FIGURE 2 is the incremental value over and above the contribution due to ionic conductivity, which is assumed to be frequency-independent. The quantity S which is plotted as the ordinate in FIGURE 2 is equal to the measured conductivity ( u ) divided by the permittivity of free space (60). Use of S rather than u facilitates the calibration of the bridge.13 At the weaker concentrations the incremental conductivity is a small change in a large quantity, and for this reason the analysis was carried out with the permittivity data only. It is assumed that the permittivity curves can be described mathematically by
83
82 # #
81
80
B' 79 #
8
7E
# 0 0
# 0
7i
7f
7! 0 # #
P 1
1.0
10 100 Frequency MHz
1000
FIGURE I . Variation with frequency of the permittivity o f human LDL solution. (Concentration = 48.17 rng/ml; pH = 6.8; upper curve, 10°C; lower curve, 20°C.)
145
Essex et al.: Lipoproteins in Aqueous Solution 4
80-
...
,
60-
,, 40-
20-
---
1
----s-
0
-0.
1
1.0
0.1
10
Frequency MHr
FIGURE 2. Variation with frequency of incremental conductivity of h u m a n LDL solution. theoretical curve for t w o Debye dispersions: -- theoretical curve for one Debye dispersion.
- _ _ _ =-
n
$ = CI +Aiw i=l
2 2 + c , T,
where cj. is the permittivity of the solution at a frequency 1; Ai is the magnitude of the ith dispersion, w is the angular frequency ( w = 27rf), T~ is the relaxation time of the i l h dispersion and c m has its usual significance. The experimental curves were analyzed with the aid of a computer, and with a least mean squares minimization technique.*' T o correct for the effect of the y dispersion, which is caused by the relaxation of free water molecules having a relaxation frequency of about 20 G H z at 25"C?2 the following procedure was adopted. With use of Time Domain methods,23 measurements were made" at frequencies up to 10 G H z on a few samples to confirm the form of the y dispersion. As expected, the results indicated that the contribution of the y dispersion to changes in the permittivity with frequency is negligible below 400 MHz. At higher frequencies small corrections were made to the lipoprotein data with the Debye equations which are known to give an adequate description of the dielectric data of the y dispersion. After correction (O.I",, at 400 MHz and 0.5",,at 800 MHz) the values of permittivity of the lipoprotein solutions were fitted to Equation I . The data between 0.15 and 1000 MHz are found to be characterized by three dispersions with relaxation frequencies of 0.5 MHz, 4-6 M H z and 200-500 MHz, which, following previous c l a ~ s i f i c a t i o n ~may ~ ' ~ be ~ termed the a, p and 6 dis-
146
A n n a l s New York A c a d e m y of Sciences
persions, respectively. The computer analysis predicts a leveling of the permittivity at frequencies below 0.15 MHz, and this was confirmed by measurements made" on a few samples with other apparatus. In using Equation I,various values of n were tried, and since, in general, an increase in the number of parameters will lead to a reduction in the error of fit, the values obtained were tested for statistical significance. N o parameter was introduced that did not yield a significant improvement in the fit at the 95",, level. With the computer technique used, it may be possible to fit too few parameters but difficult, if not impossible, to fit too many. I f an extra component is introduced the erect of which on the curve is not detectable, it will invariably result in a correlation coefficient near unity; i.e., the extra parameter will be found to be highly correlated with another parameter. Although three Debye dispersions have been assumed in the frequency range 0.15-1000 MHz, the possibility cannot be excluded that small additional dispersions may also be present or that one or more of the observed dispersion regions may have a distribution of relaxation times. With the experimental accuracy available in the present work. the introduction of any extra parameters does not result i n any significant improvement; i t . , additional components cannot be detected i n thc presence of the experimental error. Thus the three-component fit suggested is found to be the most appropriate analysis of the data. The results taken a t 800 MHz are shown in F I G U R E S 7 and 8 and will be discussed separately at the end o f t h e paper.
MOLECULAR 1NTERPRETATlON OF
RESUI.TS
As mentioned earlier in this paper, the dielectric measurements were carried out over a wide range of values of various physical parameters: temperature, concentration, and solution pH and ionic conductivity. The purpose of this was to establish the variation of the dielectric increment (Ai)and the relaxation frequency [ J = ( 2 r r i ) - ' ] with the physical parameters listed above. By this means it is possible to eliminate particular molecular processes from being responsible for the observed dispersions while at the same time narrowing down the number of acceptable possibilities. From the observed dielectric behavior we conclude that the best explanation for the origin of the a-dispersion is to attribute it to counterion relaxation of the type proposed by Schwarz.26 Full details of the observations and calculations that lead to this conclusion will appear in a subsequent publication,*' but the essential features of the argument can be summarized as follows. The linear dependence of the dielectric increment (A,) upon concentration (up to a certain critical concentration) is shown in FIGURE 3. Observations also show A, to be independent of pH and concentration and only slightly dependent on temperature. With regard to the relaxation frequency (fa) the experiments show that this is independent of concentration, conductivity, and pH. The relationship betweenfi and the inverse of absolute temperature is exponential, and a logarithmic plot gave an activation enthalpy of 4 kJ/mole. All these observations, coupled with a measured relaxation frequency of 0.5 M H z are compatible with a
Essex et af.: Lipoproteins in Aqueous Solution
147
counterion mechanism but are incompatible with any of the other processes that give rise to dielectric relaxation: 28 Debye rotation, proton tluctuation, MaxwellWagner effects, surface conductivity, ion atmosphere, and structured water. Moreover. the assumption of a counterion relaxation mechanism enables the charge on the lipoprotein molecule (eo) to be calculated from the dielectric data. Assuming a molecular radius o f I 1 nm the value of eo turns out to be 2 x C, which agrees well with the value obtained from electrophoretic studies.
7
6
5
4
Aa 3
2
1
0
I
20
40 60 80 100 LDL concentration (mg/ml)
120
FIGUKI.3 . Variation with concentration 01' the dielectric incrcmcnt of t h e m-dispersion ( T = 20°C: pH = 6 . 8 ) .A = bovine L D L . 0 = h u m a n LDL.
The abrupt change in shape of the increment-concentration curve at such a low concentration of 30 mgm/ml is a very unusual kind of phenomenon and is presumably due to the formation o f micellular structure.29 The dielectric behavior o f the @-dispersion is very similar to that observed for the a-dispersion, except that the increment ( A a ) is smaller and the relaxation frequency is about ten times as high. The variation of A, with concentration i s approximately linear ( F I G U R E 4), but there is little dependence on conductivity,
Annals New York Academy of Sciences
148
5
4
*P 2
1
0
1
20
40
60 80 100 LD L concentration (mg/rnl)
120
FIGURE 4. Variation with concentration of the dielectric increment of the &dispersion ( T = 20°C; pH = 6.8). (Measurements for h u m a n LDL.) - - - - - - - = theoretical curve predicted by Pauly-Schwan Equations.
pH or temperature. The relaxation frequency (b) is independent of concentration, pH and conductivity and its variation with temperature predicts an activation enthalpy of about 4 kJ/mole. The best explanation (full mathematical details will appear later2’) for the origin of the P-dispersion is to attribute it to a Max~ e l l ~ ~ - W a g n type e r ” of mechanism. The LDL molecule is a highly complicated entity, but it is known to have a spherical shape and it may be assumed that the protein and lipid constituents tend to concentrate in different specific regions. For the purpose of interpreting the P-dispersion, it is necessary to employ a model for the LDL molecule that arranges the lipid and protein regions so that the electrical properties of the overall structure would predict the existence of a dielectric dispersion region of appropriate dielectric increment and relaxation frequency of about 5 MHz. To satisfy these conditions the requirements are that the LDL molecule should have a conducting core surrounded by an insulated shell. Of the various models proposed for the structure of a LDL molecule, one that complies with the above requirements is a lipid bilayer model such as the one proposed by Mateu et in which the lipoprotein molecule is considered t o consist of a protein core 4.6 nm in radius surrounded by a lipid shell 3.5 nm in width. Outside the shell are further protein subunits that are sufficiently spaced so as not to make a continuous shell. For the purpose of discussing electrical behavior the model can be represented by FIGURE5 , where CL and g,,, are the permittivity and con-
Essex et al.: Lipoproteins in A q u e o u s Solution
149
ductivity of the water continuum, and c,!, I J ~and , E ; , us refer to the protein interior and lipid shell, respectively. Assuming realistic values for these six parameters and using the above values of R and d , we have calculated the dielectric increment (A,) and the relaxation frequency (f,) by using the Pauly-Schwan equations.33 The agreement between theory and experiment was found to be very satisfactory, and F I G U R4E shows the predicted dependence of increment on concentration. The capacitance/unit area (C,) of the bilayer was calculated from the dielectric results, and the value obtained is 4.4 + 1 . 1 pF/cmZ. This is in good agreement with the figure of 3.3-4.2 pF/cm2 obtained for phospholipid vesicles by Redwood et al.” Typical values for other biological membranes are 0.5-5 p F / ~ m ’ . ~ ~ The amplitude of the d dispersion is small but significant, and, following previous proposal^,^ may be interpreted as being due to the relaxation of bound water of an amount in the range of about 0.02 to 0.14 g/g lipoprotein. The properties of the &dispersion will be more fully discussed s u b s e q ~ e n t l y ,and ~ ~ the question of lipoprotein hydration as deduced from measurements at a single frequency will be discussed now. PERMITTIVITY MEASUREMENTS AT 800 M H z The relationship between relativity permittivity and frequency for an aqueous solution of biological macromolecules is shown i n FIGURE6. At frequencies in excess of 10 MHz the permittivity of the solution is seen to be less than that of pure water, and for a solution of unit concentration this fall in permittivity below
---
- ------------------------ - - - - - ---FICUHE5 . Simple three-layer model o f a lipoprotein molecule in water. R = radius of = thickness of shell. ti, e l , tb = permittivity of core, shell, and solvent, respectively; uj, o,, u w - conductivity of core, shell, and solvent, respectively,
core; d
150
Annals New York Academy of Sciences 80
-
70
-
c' 60-
0.01
0.1
i
10
Frequency GHz
F I G U R 6. F Permittivity o f a biological solution of u n i t concentration, showing decrement = permittivity o r p u r e water.
of 800 M H L ( 6 8 ~ ) .-------
the pure-water value is termed the dielectric decrement (6). At frequencies around 800 MHz, it has been customary to assume that the solute molecules contribute to the overall permittivity in respect of their atomic and electronic polarization only. However, it was established by Buchanan ef a / . 3 5in 1952, and by others more r e ~ e n t l y . 4that . ~ ~ for protein solutions the value of dso0 is too large t o be accounted for by the effect of the solute molecules alone. and that the reason for this is that the water molecules tightly bound to the protein (water of hydration) d o not contribute fully to the polarization. Thus by measuring the dielectric decrement at frequencies around 500-1000 MHz and adopting a suitable dielectric mixture formula. estimates of the water of hydration for various proteins have been published .4*'0*35.36 The weakness with this approach is that the value of hydration obtained from the dielectric data is critically dependent on the choice of mixture formula and is very sensitive to the value assumed for the partial specific volume of the solute. The shape of the solute molecule also figures in the calculation, and this may not be known accurately. For these reasons it has been considered preferable to calculate the hydration from the amplitude of the b - d i ~ p e r s i o n , ~rather . ~ ~ than from the dielectric decrement. I n the present work, however, we are concerned with comparing the values of hydration for various types of lipoprotein of similar molecular shape and partial specific volume; therefore the disadvantages normally associated with the method disappear and the advantages of a measurement at one frequency only become immediately apparent. The relative permittivity at 800 MHz was measured for aqueous solutions of lipoproteins isolated from the sera of sixteen normal subjects and fifteen patients with type I 1 familial hyperbetalipoproteinaemia (FH), a condition characterized by high concentrations of LDL and associated with an increased risk of ischaemic heart disease.38 Of the fifteen patients considered in this particular study, seven were homozygotes and eight heterozygotes, although in general the proportion of
Essex ef al.: Lipoproteins in Aqueous Solution
151
homoLygotes is very much smaller than that of the heterozygotes. Patients in the latter group are prone to develop ischaemic heart disease at an early age, the expectation ofcoronary death for heterozygous men being about 50",, before the age of 55.39The much rarer homozygotes are likely to die in their late teens or early twenties. The results obtained for the controls are shown in F I G U R7,~ where the expected linearity between relative permittivity and solute concentration is seen. The dielectric decrements for the normals and for both categories of patient are 8. shown i n FIGUKF A statistical analysis of the decrements was carried out in two stages. First, an analysis of variance was performed on the data and the value of the F ratio (variance between the samples/variance within the samples) gave F = 8.82. Tabulated
79-
ITypical error 6'
707776-
7574 *
7372
-
71-
70 I 0
20
40 60 LDL concentration(mg/ml)
a0
FIGURI.7. Variation with concentration of permittivity of norniiil h u m a n LDL. solution a t 800 M H L .
Annals New York Academy of Sciences
152
values4' of F with (2.28) degrees of freedom at the 997, level give F = 5.45. 95:" confidence intervals then evaluated, using a l-distribution, showed the following mean values and upper and lower 95';" confidence limits for GSoO: Normal, 105.9 < 107.4 < 109.0; heterozygote, 109.8 < 112.2 < 114.7; homozygote, 110.8 < 115.6 < 120.4. Hence there is strong evidence that GSoO depends upon the clinical condition of the patient and, in particular, that abnormals can be distinguished from nor-
t
A
161 A
A
m
A A A
.
0
.
. . . .... 8 .
0
.
0
,105 *
,100
. ..
-
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Sample Number
8. Values of 6800 for aqueous solutions of LDL. homozygotes.
FIGURE A =
0
0 =
normals;
=
heterozygotes;
mals. Following the analysis of variance, a subsequent t-test carried out between the means of the normals and heterozygotes gave a value of t = 4.03, as compared with a value of 2.84 for 22 degrees at the 997; confidence level obtained from statistical tables. The statistically significant differences in dsoO may be interpreted at a molecular level as follows. For a suspension of macroscopic spheroids of relative permittivity tp in a con-
Essex et al.: Lipoproteins in Aqueous Solution
153
tinuum of relative permittivity c, the relative permittivity of the mixture is given4' by t , where t
-= t
-
t,
+ Xt,
P-.
tp
tp
-
tw
+ Xt,
I n this equation p is the volume concentration of the spheroids and equals two if the particle is a sphere, but is greater than two for either a prolate or an oblate spheroid. In the present context to refers to a hydrated particle and the numerator of the left-hand side of Equation 2 is the product of the decrement and the solute concentration expressed as a fraction by weight. In general, cp is some assumed function of the relative permittivity ( c h ) of the bound water (water of hydration) and the relative permittivity ( t L ) of the solute core, the precise nature of the function depending upon the assumed model for the hydrated particle. In the present work, however, we are concerned with measuring differences in hydration (absolute values being relatively unimportant). and so the approximation t p N t h N tL E 5 at a frequency of 800 MHz can be made. Using the fact that all solutions are dilute ( p < 0.08). Equation 2 can be reduced'0337to the following convenient approximation ii+
w =
k K
(31
-66800
where wis the water of hydration expressed as a weight fraction. K = ( I + x ) / x and k is a constant of value 13.5 for the concentrations being considered in the present work. The partial specific volume (psv) of the solute particle is represented by Eand takes a value of 0.97 for LDL. Using Equation 3 . the values of hydration can be calculated for the three categories of LDL investigated. The shape of the LDL molecules as judged from electron micrographs appeared to deviate from spherical to a negligible extent, in which case K = 1.5 and the values of hydration are 0.04 0.02 (Normal), 0.09 j= 0.02 (heterozygote) and 0.12 + 0.04 (homozygote). The errors are the 95% confidence intervals, which, as seen from Equation 3, are directly proportional to the 95",, confidence intervals obtained for the values of dS00. Since Gsoo is dependent on iiand K as well as w , the question arises whether the dielectric results could be explained by a change either in shape or in partial specific volume, between the three forms of LDL. The first proposition can be rejected by noting that ultracentrifuge experiments show3xthat the abnormal lipoprotein has an increased S, (flotation rate) over that of the normal. which would require a change of shape in the opposite direction to that needed to explain the dielectric data. Therefore the observed differences in GSoo must mean that the quantity (ij + w ) varies between the three categories of LDL studied, and since appreciable variations in fi appear unthe best interpretation of the dielectric measurements is that the lipoprotein hydration depends on whether the LDL originates from normal serum or whether it is produced by the gene responsible for hyperbetalipoproteinaemia. This further supports the hypothesis proposed previously in a pilot study" carried out on the dielectric properties of normal and abnormal LDL.
*
154
Annals New York Academy of Sciences A c K N Ow L E L)CME NTS
Thanks are due to the Wellcome Trust for supporting CGE, GPS and MSS during the investigations and for financing the purchase of apparatus. Acknowledgment is also due to the Central Research Fund of London University for an equipment grant. We are indebted to Dr. A. Suggett, Unilever Ltd, Colworth House, Sharnbrook, U.K.. and to M r . R. Lamote, of the Simon Stevin Instituut, Brugge, Belgium, for making the TDS measurements and low-frequency bridge determinations, respectively. REFF R E NC E s I.
ONCI-FY. J . L . 1943. In Proteins. Amino-Acids and Peptides. E. J . Cohn and J . T.
2. 3.
PI:NNOCK. B. t.& H . P. SCHWAN. 1969. J . Phys. Cheni. (Ithaca) 73: 2600 2610. MOSFR. P., P. Q. SOUIRI~& C . T. O'KONSKI.1966. J . Phys. Chem. (Ithaca) 7k7.14 755. GRANT, E. H.. BARBARA G. R. MITTON, G . P. SOUTH & R. J . SHEPPARD. 1974. Biocheni. J. 139: 375 380. AARON.MARGARET W . & E. H. GRANT. 1967.Trans. Faraday Soc.63:2177 2180. S t i w k i t : m . J . C. W . & E. H . GRANT. 1968. Proc. R . Soc. Lond. A307: 3 3 5 ~357. MANI)PI.M. This volume. S T O C K M A YWL.RH, . This volume. M A R C H A I . . E. This volume. GRANT-. E. H . , R. J . SIiFPPAm, G . L . MII.I.S & J O A N S I A C K . 1972. Lancet i : l 159 1161. SCIIWAN,H . P., S. TAKASIIIMA. V . K . MIYAMOTO & W . STOKh1:NIC.S. 1970. Biophys. J. 10: I102 I 119. R t u w o o u , W . R., S. TAKASIIIMA, H. P. SCHWAN & T. E. T l i o M w ) N . 1972. Biochim. Biophys. Acta 255: 557 566. SOUTH. G . P. 1970. Ph.D. Thesis. University o f London. London. England. G R A N TE.. H.. G . P. SOUTII, s. T A K A S H I M A & H. I C H I M U K A . 1971. Biochenl. J . 122: 691 699. E S S E X , G., ~ . G. P. SOUTH.K. J. SHEPPARD & E. H. GRANT.1975. J . Phys. E. 8:
Edsall. Eds.: Chapt. 22. Reinhold Publishing Corporation. N e w York. N.Y.
4.
5. 6.
7. X.
9. 10.
I I. 12. 13. 14.
15.
3x5 389. R. J . 1972. J . Phys. D. 5: 1576 87. 16. SHEPPARI). . J . Phys. E. 5 : 1208 12. 17. S H t P P A K I ) . R. J. & E. H . G R A N T1972. R . Private communication. (See A('KNoWl.eDc;MliNTS.) I X . LAMOTE. A . Private communication. (See ACKNOWIE D G M E N T S . ) 19. SUGGFTT, Esstx, C. G . 1976. Ph.D. Thesis. University of London. London. England. SHFPPARI). R. J. 1973. J . Phys. D. 6: 790-794. S C H W A N . H . P., R. J. S t I E P P A K I ) & E. H. G R A N T1976. . J . Cheni. Phys. 64:2257 2258. SUGGETT, A . & A . H. CLARK.1976. J . Solution Chem. 5 : I 15. SctiwAN, H. P. 1957. Advances in Medical and Biological Physics 5 : 147 209. 25. S c k i W A N . H. P. 1974. In Biological EKects and Health Haiards o f Microwave Radiation. P. Czerski, Ed.: 152-59. Polish Medical Publishers. Warsaw. Poland. 26. SCHWARZ, G. 1962. J . Phys. Chem. (Ithaca) 66: 2634-42. G. L. MIILS, R. J . S H ~ P P A RJ I. )SLACK . & G . P. SOL~TII. 27. E s s t x , C . G., E. H. GRANT, To be published. G . P. & E. H . G R A N T1972. . Proc. R. Soc. Lond. A328: 371-87. 28. SOUTH. & S. TAKASIIIMA. 1974. J . Colloid. Interface Science 29. B E A R DR, . B.. T. F. MCMASTFK 48:92 99.
20. 21, 22. 23. 24.
Essex e! a / . : Lipoproteins in Aqueous Solution
155
30.
M ~ X M ~JL . CL. ,1892. A Treatise on Electricity and Magnetism. Oxford Univ. Press.
31. 32,
WAGNtK.
Oxl'ord, tngland.
33. 34.
35. 36. 37. 38. 39. 40. 41. 42. 43.
M4TI.C.
K . 1913. Ann. Phys.40:817 29. L. A . TARIXI.L. V . LLZ/.A.II, L . AGGERRECK & A . M . SCANL. 1972. J . Mol.
Biol. 70: 105-1 16. PA01 1 , H . & H . P. S C H w A N . 1959. Z . Nuturforsch. 146: 125 38: 6:621 633. C o l I . K . S . 1968. Membranes. Ions and Impulses. University o f California Press. Berkeley. Calif. BL'CHANAS.T. J . . C. H. HAGGIS. J . B . HASTED & B. G . R O ~ I N S O S 1952. . Proc. R . Soc. Lond. A213:379 91. GXANT,E. H . 1957. Phys. Med. Hiol. 2: 17 28. GRAhr. E. H.. S. E. K ~ 1 : l . i .& S. TAKASHIMA. 1968. J . Phys. Chem. (Ithaca) 72:4373 XO. Si.Ach, J . & G . 1.MII-IS. 1970. Clinica Chim. Acla 29: 15 2.5. SLACK. J . 1969. Lancet ii: 1380-82. L I N D I F \ . 0. W . & J . C. P. M I [ I.I:R. 1964. Cambridge Elementary Statistical tableb. Cambridge Univ. f'ress. Cambridge, England. F R l ( . h b . H . 1924. Phks. Rev. 24: 575 88. T o R o - < i o Y c , o , t. l95X. Ph.D. Thesis. Harvard University. Cambridge. Mass. FISIII-K. W . K..M . G . HAMMOND & C. L. WARMKE.1972. Biochemistry ll:51Y 2 5 .
