Bioelectrochemisfty and Bioenergefics, 13 (1984) 103-l 14

A section of J. Electroanal. Chem., and constituting Vol. 174 (1984)

Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

103

70!2-COMPLEX DIELECTRIC CONSTANTS OF HUMAN SERA

PROTEIN-BOUND WATER BEHAVIOUR IN BOWEL CANCER PATIENTS

ALDO CASALEGGIO, CLAUDIO MARTINI, MAURO MORANDO and SANDRO RIDELLA

Istituto per i Circuiti Elettronici, C. N. R., Genova (Itab)

GIUSEPPE S. MELA and LIVIO SPIGA

I.S. M.I., Catiedra di Clinica Medica R, Universitir di Genova, Genova (Ita@)

ETTORE INTRA

Ospedale Galliera, Geneva (Itab)

(Revised manuscript received October 11th 1984)

SUMMARY

The complex dielectric constants of human sera have been measured in the frequency range 50-1000

MHz using a Hewlett-Packard 4191A RF Impedance Analyzer. The properties of water bound to the

proteins are investigated and the implications to the pathological conditions of the subjects are studied.

The proteins from cancer patients are significantly more hydrated than normal ones. This is particularly

noticeable for gamma-globulins, thus suggesting an immunological defect in cancer patients.

SPECIAL SYMBOLS USED IN THIS PAPER

i,, L., N P09l PC” PW p(t) R

R,. R2

V

02

ii, 82 AC’, AE”

cost function

frequency (Hz)

relaxation frequency of the free water (Hz)

relaxation frequency of the bound water (Hz)

electrical lengths (m)

normality of the free water (eq dmm3)

protein chemical molar concentration (Mel mW3)

protein chemical volume concentration (protein volume/total volume)

protein chemical weight concentration (kg m-‘)

negative probability of r

ratio between the number of molecules of bound water for one protein molecule

characteristic impedances (62)

Student’s statistical test

volume fraction volume fraction of the suspended medium

form factor

parameters characterizing the protein surface

differences between the experimental and the model values

0302-4598/84/$03.00 0 1984 Elsevier Sequoia S.A.

104

c = C - j c " C r

C tt

Go

GO

El

C2

Coo c~ CA

P ff

if0 o$

X 2

Subscripts

complex permittivity real part of the complex permittivity (includes dipole effect) imaginary part of the complex permittivity (includes ion effect) dielectric constant of free space: 8.854 × 10 -12 F / m static permittivity of the free water permittivity of the suspending medium permittivity of the suspended medium high frequency permittivity of the free water high frequency permittivity of the bound water difference between the bound and free water permittivities complex reflection coefficient conductivity [(fi m)- 1 ] static conductivity of the free water [(fi m) -1 ] static conductivity of the bound water [(fi m) -1 ] chi-square statistical test

b w

fw iw

P X, y, Z

bound water free water immobilized water protein three different normalities

Abbreviations

CDC f.d. HP IgG r / ° ] n . r

s.d.

Control Data Corporation freedom degree HewletbPackard serum gamma-globulins nuclear magnetic resonance standard deviation

INTRODUCTION

The measurement of the complex dielectric constants of biological materials in the radio and microwave frequency range has been made either for the evaluation of power absorbed by tissues for therapeutic applications [1] or for the characterization of the properties of cells [2]. A few measurements have been performed in an attempt to correlate these properties with the pathological conditions of the individ- uals from whom the sample has been obtained [3-5].

In this paper we describe: (1) a procedure for obtaining the complex dielectric constant of a small amount

of human sera in the frequency range 50-1000 MHz; (2) a model which fits the obtained data and characterizes the surface properties

of the protein in the suspension and the water-ion behaviour near the macromole- cules; and

(3) the correlation between the properties of the water bound to proteins and the pathological conditions of the subjects.

105

COMPLEX DIELECTRIC CONSTANT MEASUREMENT

The measured electrical quantity is the complex dielectric constant E = E’ - jc”, where both E’ and c” are real positive numbers, and in general, frequency dependent, andj=m.

The materials under consideration have a finite d.c. conductivity (I and this is included in e” (a = 2rfc&‘, where f is the frequency, c, = 8.854 X lo-‘* F/m). Then in the complex dielectric constant both the ion and the dipole effects are included.

The main difficulties of the measurements of the complex dielectric constants of human biological materials at radio and microwave frequencies are:

(1) in general the material is highly sensitive to thermal variations;

(2) the measurements must be taken very quickly in order to characterize a large number of samples to make significant statistical analyses of the results;

(3) moreover, denaturation problems due to heating can be avoided by fast measurements.

A schematic lateral view of the sample holder used is shown in Fig. 1. The holder is essentially a cylinder with circular cross-section, 7 X low3 m in inner diameter, divided into two parts. The material to be measured is placed in the upper part, which is actually a coaxial line (length 4 x lop3 m) terminated in a circular waveguide. A Teflon disk prevents leakage ‘of the sample into the lower part, which is a coaxial line with a characteristic impedance. of 50 a, terminated at section A-A’ by a standard APC 7 connector. At section A-A’ the structure is connected to a Hewlett-Packard 4191A RF Impedance Analyzer controlled by an HP85 Computer using IEEE 488 Bus. Logarithmic swept measurements were taken at 39 points between 50 and 1000 MHz. Repeated testing showed that this was sufficient to fill

Fig. 1. A schematic longitudinal view of the sample holder.

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the holder with a liquid column a few millimeters higher than the top of the inner conductor. The addition of more sample did not show any effect on the complex reflection coefficient at section A-A’. This result was expected based on previous measurements [5] and from theory [6]. Then the quantity of material needed to fill the holder is less than 5 X lo-’ m3.

Following Bussey [6], the holder of Fig. 1 can be modelled with a chain of two lines terminated in an open circuit. The first line (characteristic impedance R,, electrical length L,, both in vacuum) represents the segment from A-A’ to B-B’. The second line represents the structure from B-B’ (characteristic impedance R,, electrical length L,, both in vacuum): it is filled with the material to be tested. The length L, takes into account the length of the inner conductor and that of the terminating circular waveguide. Repeated measurements of NaCl solution (normal-

ity 0.0, 0.077, 0.098, 0.154, 0.196 eq/dm3) were made: these values were stored in a CDC cyber 170/720 computer. Using expressions of the complex dielectric con- stants of NaCl solutions due to Stogryn [7], which are functions of NaCl normality, frequency, and temperature (measured, for every sample, with a thermistor using a digital ohmmeter), and using [8] the optimization procedure due to Hook-Jeeves, the unknown parameters R,, R,, L, and L, were found to be: R, = 47.93 Q, R, = 102.9

Q, L, = 9.063 X 10m3 m, L, = 5.266 X 10e3 m. These values compare favourably with the geometrical dimensions of the holder. The procedure was the following:

(1) four values for R,, R,, L,, L, were considered; (2) the values of the complex dielectric constant of the measured NaCl solutions

were obtained from the complex reflection coefficients, solving the complex tran- scendental equations obtained from the two-line chain model previously mentioned;

(3) these values were compared with those obtained from the Stogryn expressions and the magnitude of the differences was summed;

(4) the differences were minimized by readjusting the values of R,, R,, L,, L,. The difference between the complex dielectric constant, obtained from the

measured complex reflection coefficients using the two-line chain model with the

optimized values of R,, R,, L,, L,, and the Stogryn values was l%, which was within the range of accuracy of the HP4191A.

The procedure actually used is different from that described above, since to obtain the complex permittivity solving the complex transcendental equations of the measured complex reflection coefficient involves a long computation and is beyond the capability of a personal computer if the result has to be obtained in real time (less than 1 mm).

We used the procedure described previously [5]: (1) during the calibration task three known NaCl solutions (0.0, 0.077, 0.154

eq/dm3) were measured and the complex reflection coefficients were stored in the

HP85 computer (P,, pr, P,); (2) the complex dielectric constants of the three NaCl solutions were computed

from the Stogryn equation [7] (cX, E,,, E,); (3) the complex reflection coefficient of the unknown material was measured and

stored in the HP85 computer (p);

107

(4) the value of the complex dielectric constant of the material under test was computed from the cross ratio expression:

This procedure is very quick: the time required for step (3) is about 40 s and that for step (4) is about 30 s.

In order to show that this simplified procedure yields the same results as those obtained from the two-line model, a simulation was made (on the HP85 computer) using the following procedure:

(1) a typical sample with known complex dielectric constant (2) is considered; (2) using the two-line model the complex reflection coefficient (p) at section

A-A’ was calculated when the testing material was the same as at the previous point;

(3) in the same way, the complex reflection coefficients were obtained (p,, pY, p,) when the holder was filled with the three NaCl solutions (0.0, 0.077, 0.154 es/d&), whose complex dielectric constants were known from Stogryn [7] (c,, cy, E,);

(4) using equation (l), E was computed and compared with < for each frequency: the magnitude of the difference (z - Z) was always less than 0.001.

The agreement depends on the choice of calibration solutions, for each unknown sample. In fact the simulation just described was utilized for the optimization procedure to find the best concentrations of the three NaCl solutions for a typical human serum.

THE PROTEIN SURFACE MODEL

The problem of obtaining information of biological interest from the complex dielectric constant measurements of protein suspensions has been discussed by many authors [9,10]. A well-accepted model is the following (Fig. 2) [ll]:

(1) The protein is modelled as a sphere with cp = 2 - j0; the volume fraction of the proteins in the whole suspension is up [9,10].

Fig. 2. The protein surface model.

108

(2) A shell of immobilized water (tiw = 5 - j0) surrounds the protein, and its volume fraction in the whole suspension is uiw [12].

(3) The complex dielectric constant of bound water (whose volume fraction in the suspension is us__) is given by:

(2)

where:

c;=e..&+e* (3)

fs = BlfO (4 08 = P*% (5) where-the values of E, (high frequency dielectric constant), c,, (static dielectric con&ant), f0 (relaxation frequency) and a,, (d.c conductivity) are obtained from Stogryn, as a function of temperature and equivalent NaCl normality; fl, and & are the parameters characterizing the protein surface, and they will be obtained from the measurement of the complex dielectric constant of the protein suspension.

(4) The expression of Ed, for free water is the same as Stogryn’s equation; its volume fraction in the suspension is u,,,,.

Some comments might be appropriate with regard to previous definitions:

(1) Obviously,

UP + uiw + U& + urw = 1 (6)

(2) The NaCl equivalent normality means the NaCl concentration which behaves, as far as the complex dielectric constant is concerned, like the solution under test (which may contain many different types of ions). The reason why Stogryn’s expressions are originally used is that they are the only avaiiable analytical expres-

sions which give E as a function of frequency, temperature and normality. (3) The expressions of the complex dielectric constant of the bound water,

equations (2)-(5), fit the experimental results very well. In order to justify these expressions, the following considerations, deduced from the literature [9,10], may be given: (a) the relaxation frequency of the bound water is smaller than that of free water due to the increased rotational viscosity near the protein surface [13]; (b) fitting our experimental data, we found that the best approach was to assume the bound water conductivity to be equal to the free water conductivity (& = 1); (c) the high frequency dielectric constant of bound water is greater than that of the free water, and the difference has been estimated, eA = c0 - E, = 75, by fitting our data as well as that from the literature [9,10].

We used [14] the mixture expression proposed by Maxwell-Wagner-Fricke in order to obtain the complex dielectric constant of the suspension:

Q - e1 c2 -cl -=u -

E + XC, *E* + XC, (7)

where E, E, and c2 are the complex dielectric constants of the suspension, suspend-

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ing medium and suspended particle, respectively; u2 is the volume fraction of the suspended particle and x is a form factor which is equal to 2 for the sphere.

Thus starting from the protein and the immobilized water, using equation (7) one can obtain the equivalent complex dielectric constant of the mixture. This is the value of E at the first step. Now, considering this mixture as a new suspended particle, of calculated permittivity c2 = E, it is possible to compute, using equation (7) again, the permittivity of the mixture of this particle with the next shell. The complex permittivity of the whole suspension is obtained iterating this procedure for all the shells shown in Fig. 2 and it can be compared with the measured value.

The parameters of biological interest can be fitted by this model but the optimization is time consuming and the results cannot be obtained in real time using a small computer such as the HP85.

It is easy to show [15] that equation (7) is equivalent to

c = c, x(1 -02) +E (1 +xJ2u2

x + u2 2( u2+x)2 (8)

if 1 cl I(u2 + x) IS=- Jc2 I(1 - u2). This condition is always satisfied for the three mixtures studied in this work. Then the complex dielectric constant of the suspen- sion is a linear combination of E,,, eiw, et,,,, and e,,,,.

This modelling procedure gives the following expression of the complex permittiv- ity of the whole suspension:

x(1 - up - uiw - UbW E = Efw

> + (l + x)2(ur + uiw + ubw) X

x + up + Ubw + uiw (up + uiw + u&, + x)’

I ( x l-

’ ‘bw

x+

\

+X)Z ‘iw+%

uiw+“p+ubw

uiw + up zx

+x

uiw + Up + ubw

X x(1 -&)

‘iw UP

x+-- up + uiw

(9)

A detailed analysis showed that the complex dielectric constant of the suspension is the ratio between two polynomials of third degree of complex frequency, whose coefficients are functions of four parameters of biological interest:

(1) the quantity of immobilized water ( ui,); (2) the quantity of bound water (u,,);

(3) the relaxation frequency of bound water (fS); and (4) the NaCl equivalent normality in the suspension [12]. The volume fraction of protein in the suspension was obtained from biochemical

measurements and the volume fraction of free water may be obtained from equation (6). Then the coefficients of the polynomials may be fitted easily from the experi- mental data [16] and from these one may obtain the four unknown parameters.

On an HP85 this procedure takes 35 s and enables the operator to obtain, immediately after measurements, the values of the parameters which characterize a

serum. In Figs. 3 and 4 a typical result for E’ and 6” of the human serum from a normal

subject is presented. A parameter for evaluating the best fit has been defined as l/2

C = [

c ( A<12 + A~“‘)/39 freq. 1

where Ar’ and h” are the differences between the experimental and the model values. The range of the values of parameter C is 0.1-0.2 for all the measured human sera: this is also the range of the differences ]A&] and ]h”] for a serum as a function of frequency. For the data of Figs. 3 and 4, the measured temperature is 23.04”C and the biochemical protein volume is ur, = 0.054; the optimized values (C = 0.16) are uiW = 0.006, u,,,,. = 0.029, fa = 244 MHz, and N = 0.130 eq/dm3.

BIOLOGICAL METHODS AND RESULTS

Subjects

About 1200 normal young blood donors voluntarily agreed to participate in this

clinical trial. For each subject, blood was sampled before breakfast, after at least 20 min rest. Excluded from this normal group were the cases who showed any illness 6

73- 0. l *.

l . l *. .

72- ‘. l .

-W l *. .

71- l *. l . l . l . l .

70 - 0. l .

0.

f (MHz) -0.

I I 8 I I 50 101 206 420 1000

Fig. 3. The red part of the complex dielectric constant of a normal serum.

111

months before and/or after the blood was drawn, as well as any abnormalities in routine clinical and laboratory examinations. After screening, we selected 697 normal subjects.

61 patients with untreated, histologically confirmed cancer of the bowel without any sign of methastases, volunteered to participate in this project. Also in these cases, blood was obtained before breakfast, at rest.

Biological methods

For each subject, the amount (by weight) of various types of blood serum proteins was obtained from the total protein weight concentration (p,,) and standard electrophoresis of serum proteins. Thereafter, from the average molecular weight and the average partial specific volume of each type of serum protein, their mean molar concentration and volume concentration were evaluated. Summing these values for the different protein types, the total protein molar concentration, p,, (in mol/dm3), and the total protein volume concentration, p,, = up (adim.) were obtained.

Moreover, the total ion concentration, N (in eq/dm3), was evaluated using an atomic absorption spectrophotometer.

Dielectric measurements

Calibration of the automatic network analyzer was always tested using the commercially available E.magel@ (Behringer) as a standard, a very stable 10m3 M solution of 35 000 molecular weight gelatine in saline. Calibration was accepted only when the dielectric measurements of Emagel@ did not significantly differ from a set of values which had previously been measured with high precision under best conditions [17].

Results

From the dielectric and biochemical determinations, we can define some parame- ters to study human normal and pathological subjects; the most important one is the

50 101 206 420 1000

Fig. 4. The imaginary part of the complex dielectric constant of a normal serum.

112

ratio between the number of molecules of bound water for one protein molecule, R:

R=Lvb” 18 pan

(10)

This normalization is necessary because the total amount of proteins in sera varies, though within narrow limits, from one subject to another. In normal subjects the parameter R is distributed normally (x2 = 11.8, f.d. = 12) and shows an average

value of 2206 k 165 s.d.: on the contrary, cancer subjects demonstrate average R

equal to 2564 * 342. The difference between these two mean values is clearly beyond experimental error [t = 14.441, p(t) -e lo-‘]. Therefore one can conclude that cancer serum proteins are more hydrated than normal ones.

Assuming that the amount of bound water in the sample shows a linear relation- ship with the protein concentration, at least within a narrow range, from the bound water molar concentration, ubW - l/18, and the molar amount of each protein type, one can calculate using multiple regression analysis the number of bound water molecules for each blood protein type. In normal subjects, blood serum albumin binds 1409 f 38 water molecules, with a weight/weight hydration ratio of about 0.37, and serum gamma-globulins bind 3111 f 200 molecules of water, with a weight/weight ratio of about 0.36. These findings agree very well with those obtained with different methods using purified proteins [18].

Moreover, calculating, with the method mentioned above, the number of water molecules bound to cancer gamma-globulins, one finds a value of 3283 _t 695, which is significantly higher [t = 4.7, p(t) -c lop61 than that of normal gamma-globulins.

DISCUSSION

The necessity to have available a quick and precise method to measure water and ions bound to protein is obvious in view of the physiological role of protein-bound water.

The folding of protein chains depends not only on its primary structure but also on the relation between water molecules and hydrophobic and/or charged side groups, which force water molecules into an abnormal pattern in relation to hydrophobic groups, thus exerting a strong influence on the chain spatial conforma- tion [18]. Moreover, water dipole molecules may form a chain, linking electrochem- ically two or more distant charged points of the protein molecule, thus allowing the Grotthus mechanism on the surface of the macromolecule [19]. Protein-bound water clusters around charged groups on the protein surface may cause some protein reactive groups to be masked for even specific ligands [20].

Recent studies suggest that it is the protein-bound water which imposes its dynamics on the protein molecule [21]. At physiological temperature, water mole- cules can reorient at a fast rate and therefore exert a frictional force on the internal motion of the protein, which can thereby fluctuate between conformational substates at a fast rate. Usually, the potential barrier between conformational substates is higher in comparison with thermal energy, nevertheless, the reorientation of the

113

dipole moment of water molecules leads to local fluctuations of the electric field: occasionally, these potential modulations may reach an amplitude so large that the barrier height can be lowered to such an extent that the system undergoes a transition from one substate to another, because the local fluctuations of the electric field interact with the polar groups located on the surface of the macromolecule, causing them to move.

From the foregoing, it follows that the amount of bound-water of proteins and its physical state are strongly related to the secondary and tertiary structures, to subconformational fluctuations, to the activity of reactive groups on the surface, and thus to the biological activity of the protein itself.

In the past years, some indirect experimental evidence has been found suggesting that the protein-water interaction may be involved in living matter during malig-

nancies [22]. Blood serum proteins from individuals with malignancies might be abnormally

structured or might fluctuate abnormally between their conformational substates, thus showing an increased affinity for some ligands, and a decreased affinity for other ligands, thereby behaving like crazy proteins. It is indeed a well-known fact that allosteric substates of human serum albumin show quite different affinities for several ligands [23], and that there is an intra-isotypic binding heterogeneity between IgG iso-types and some proteins [24]. These considerations might be of interest, remembering that the present data suggest that, among cancer serum proteins, mainly gamma-globulins are more hydrated than normal proteins, thus giving further evidence of an immunological disorder during malignancies.

These abnormalities might be characteristic features of some diagnostic value. Blood serum protein from patients with untreated solid cancer [25] and plasma

cell myeloma [26] were shown to be more hydrated than normal ones. At the present state-of-the-art, such a higher-than-normal hydration was found

exclusively in the serum protein of patients with malignancies, whereas the serum protein hydration was found to be normal in the individuals without malignancies, and it does not depend on the total protein composition of sera [27,28]. Moreover, the relaxation frequency of the bound water of serum proteins from cancer and plasma cell myeloma is found to be lower than normal, thus suggesting that these molecules may rotate at a rate lower than normal serum proteins [12,27,28].

CONCLUSION

The properties of water bound to proteins are becoming an important tool for biochemical research and for clinical purposes.

Biochemical measurements of protein-bound water are very cumbersome. Many biophysical methods are suitable for the study of protein-bound water, e.g. calorim- etry, viscosimetry and, above all, n.m.r. Dielectric techniques compare favourably with these methods, in many cases being quicker, cheaper and more reliable.

114

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