The self-diffusion of water in Artemia cysts

ARCHIVES OF BIOCHEMISTRYAND BIOPHYSICS Vol. 210, No. 2, September, pp. 517-524, 1981

The Self-Diffusion of Water in Arfemia Cysts P. K. SEITZ,* D. C. CHANG,?$ C. F. HAZLEWOOD,t$ H. E. RORSCHACH,T$ AND J. S. CLEGGO *University of Texas Medical Branch, Department of Psychiatry, Galveston, Texas 77550; TBaylor College of Medicine Departments of Physiology and Pediatrics, Houston, Texas 77080; $R.ice University, Department of Physics, Houston, Texas 77001; and OUniversity of Miami, Laboratory for Quantitative Biology, Coral Gables, Flm’da $$I.%$ Received July 14, 1980 The self-diffusion coefficient of water molecules has been measured by nuclear magnetic resonance in cysts of Artemia over a wide range of hydration. Compared to the value for bulk water, the diffusion coefficient is reduced by a factor of 7 at the highest hydration and by approximately 100 at the lowest hydration. The results are used to evaluate various models that have been proposed to account for the reduction of water self-diffusion coefficients in complex systems.

Knowledge of the physical-chemical properties of cellular water is essential for a complete understanding of cell structure and function. One technique commonly used to study water in biological systems is nuclear magnetic resonance (NMR) spectroscopy. Many reports of studies have shown that the relaxation times (Z’i and T2) and the self-diffusion coefficient (D) of cellular water protons are reduced compared with corresponding values for bulk water, but the interpretations attached to these observations differ greatly according to the model chosen (l-8). One possible way to test these various models is to study the hydration dependence of the physical parameters predicted by the particular model; that is, how the water content of living cells influences Tl, Tz, and D. Unfortunately, most cells and tissues cannot tolerate wide variations in their water contents without significant effects on viability. There are, however, notable exceptions, one of which is the cyst of the brine shrimp, Artenzia, which can undergo repeated cycles of hydration-dehydration with negligible effects on viability (6). Therefore, we have chosen this system as a useful biological model for the study of cell water. In the present paper, we describe measurements of the self-diffusion 517

coefficient of water protons as a function of cyst water content, and we evaluate the results in terms of various models that have been advanced for the interpretations of NMR data. We have also measured the relaxation times Tl and Tz, and these results will be reported in a separate paper. METHODS

AND MATERIALS

(A) The biological model system. The cysts of Artemia, a primitive crustacean called the brine shrimp, consist of an inner mass of about 4000 cells surrounded by a complex noncellular shell. Their ultrastructure (g-11), biochemistry (12-14), and physical properties (6, 13, 15) have been described in some detail, and they have been used for the study of a wide variety of biological problems (16). The cysts used in these experiments were purchased from San Francisco Bay Brand, Inc., Menlo Park, California. Approximately 87% of this population, after processing, produced viable larvae when incubated at 25°C in seawater for 72 h. Large numbers of cysts were prepared by a thorough washing procedure carried out at 2-4°C in order to suppress metabolic activity. The cysts were then dried at room temperature, separated by size (average diameter approximately 200 pm), and stored in a desiccator over CaSO, until used (17). Two different procedures were utilized to prepare cysts at the desired water contents (17). For the lower 0603-9861/81/100517-08$02.06/O Copyright

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All rights

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1981 by Academic

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in any form reserved.

518

SEITZ ET AL.

hydrations (up to 0.3 g HeO/g dry cysts), sorption of water from the vapor phase of saturated solutions of various salts was used. In order to achieve higher hydrations (-0.3 to 1.4g HaO/g dry wt), cysts were immersed overnight at 0°C in NaCl solutions of different concentrations, then rinsed free of NaCl, and the surface water was removed quickly. Since the shell of the cyst is impermeable to NaCl, the amount of water taken up is determined strictly by water activity of the NaCl solution. The two hydration methods are essentially equivalent (17), and no detectable differences in the NMR measurements on samples of equal hydration prepared by the two methods were observed. Water contents were determined gravimetrically after the NMR measurements were made, dry weight being determined after heating at 103-105°C for 24 h. (B) The physzcal measurements. NMR measurements were made using a Bruker SXP spectrometer equipped with a Varian 12-in electromagnet. The magnetic field strength, HO,was approximately 7 kG and the frequency was 30 MHz. Data were recorded in digital form on a Nicolet 1074 signal averager. The diffusion coefficient was measured by the spin-echo technique in which a static field gradient was applied to the sample. The spacing between the 90” pulse and the echo (the “measuring time” 27) was 40 ms in all measurements. The details of this method are given in earlier publications (1). Usually, we measured the echo decay (A/b) at several settings of the magnetic field gradient (G). The diffusion coefficient was obtained from the slope of an (h/ho) vs @ plot. Figure 1 is a sample graph showing a typical result of the measurement of D using the spin-echo method (1, 18).

10 IF

cysts (L 4 g/g1

gas AZ

.,IL?!--

10

20

27 = 4 msec

30

40

50

G2[IgausslcmP] FIG. 1. The log of the echo decay (A&Q) is plotted as a function of the square of the magnetic field gradient (G). The solid circles are data obtained on bulk water whereas the open circles are data collected on Artemta cysts. All data were obtained with a 27 spacing of 40 ms.

RESULTS

AND DISCUSSIONS

Diffusion coefficients were measured on cysts with hydrations ranging from 0.02 to 1.49 g H,O/g dry cysts and are displayed in Fig. 2. The two error bars indicate the standard deviation of five measurements on a single sample. The value of D for pure (bulk) water, measured under identical conditions, was found to be 2.4 X 10e5 cm2/s. In most biological systems, D is usually reduced relative to bulk water by a factor of about 2. (Red blood cells, liver tissue, and amphibian oocytes are exceptions where D is reduced by as much as a factor of 6-7.) The reduction of D in Artemia cysts, however, is more profound. At the maximal hydration of cysts (1.4 g of H20/ g of dry solids), the self-diffusion coefficient for water protons is less than 4 X lop6 cm2/s (a factor of ‘7lower than that of bulk water). As the hydration of the cysts is reduced from the maximal value to 0.2 g H20/g dry solids, D is reduced further in a monotonic manner (see Fig. 2). (At lower hydrations, D appears to increase slightly, but the experimental error at the lowest hydrations is large.) The minimum value for D is approximately 2 X lo-? cm2/s which is almost a factor of 100 lower than that for bulk water and is much lower than any observed diffusion coefficient of water reported for viable tissues (19-25). Measurements of the diffusion coefficient (D), by NMR techniques give an averaged measurement of a major bulk property of water. The time over which our measurements were made (27 2: 40 ms) was sufficiently long to allow significant interaction of the water molecules with cellular constituents. Consequently, one needs to consider what effects cellular compartment walls (membranes) and other obstructive barriers (macromolecules) might have on the diffusion of water when studying the changes in D in complex interfacial systems. There are currently three general physical models which have been proposed to explain the reduction of the diffusion coefficient in interfacial systems. (A) Com-

SELF-DIFFUSION

I

0.2

FIG. 2. Water

self-diffusion

coefficient

OF WATER

I

1

I

1

0.4 0.6 0.8 10 Cyst Hydration-w ( g H$/g dried cysts1

(D) of

partmentalization models contain the assumption that the measured D is smaller than the actual value of the diffusion coefficient (Do) because water molecules encounter barriers during the spin-echo measurements and, therefore, their diffusion is restricted. These barriers are proposed to be either permeable (26) or impermeable (27,28). (B) Obstruction models contain the assumption that the bulk diffusive properties of tissue water are unchanged from bulk water, but the diffusion path length is increased because of obstructions by macromolecules, subcellular organelles, and by direct hydration effects (i.e., a small portion of the water is considered to be macromolecular hydration water and not freely diffusive) (1, 20,29,30). (C) Surface adsorption1 models 1 The term su$bce-adsorption model is used here to represent the general notion that cellular macromolecules influence the physical properties of hulk

Artemia

519

IN Artemia

1

1.2

cysts as a function

of cyst hydration.

propose that the presence of the numerous subcellular surfaces affect the physical properties of a substantial fraction of the water which may exhibit transport properties different than those of bulk water. Extensive discussions of these various “adsorption” hypotheses may be found in other publications (31-43). The remainder of this section will be concerned with our evaluation of each of these models. (A) Compartmentalization Models (1) Impermeable walls. We will first analyze the data according to the compartmentalization theory. In a one-dimensional model, Robertson (27) and Wayne and Cotts (28) assumed that the motion of the spins is restricted by impermeable water over distances ular layer.

much greater

than one molec-

SEITZ ET AL.

520

walls in the direction parallel to the static magnetic field gradient. This work has been extended by Neumann (44) to include regions bounded by spherical and cylindrical surfaces. In the case of spherical boundaries, when the observation time (27) is sufficiently long with respect to the diffusion time (I$, that is, when

and substituting

into Eq. [2] yields D a W”‘3.

[31

In Fig. 3, log D is plotted against log W. Some of the data of Fig. 1 at the lowest hydrations have been omitted. For these low hydrations, the water is probably adsorbed on the cellular surfaces and would not be describable by a compartment 27 % g td, model. The solid line is the prediction of Eq. [3], when the curve is fit to the data then the simplified equation point at W = 1 g H20/g dry solid. The experimental data agree well with Eq. [3]. D=6L Thus, the hydration data appear to supPI 175 Dlj( 2T)2 port the impermeable-wall-compartment applies. (The numerical factors appearing model. To further test this model, the temin Eqs. [l] and [2] were obtained from Eqs. perature dependence of the diffusion coef[22] and [27] of Ref. (44).) The terms in ficient should be studied. According to Eq. [2], the temperature dependence of D Eqs. [l] and [2] are defined by: should be opposite to that of Do, since D a l/D,. That is, although the actual diftd = a2/D(,, fusion coefficient Do increases with tema = the diameter of the spherical perature, the increased motions of spins compartments within a confined compartment give a motional averaging that would reduce the D,, = the diffusion coefficient of bulk apparent value of D. We are in the process of conducting a study to determine the water temperature dependence of the D in cysts Since D/D0 for the most hydrated cysts and, therefore, to further evaluate the adis 0.17, the value of %/td from Robertson’s equacy of the compartment model. universal curve of D/D0 versus %/td is Another test of this compartmentalizaabout 0.55, which is almost three times the tion model is to examine the 27 dependence value of 83/480. (We have used Robert- of the observed D. In our experiment, D son’s universal curve for plane boundaries for this estimate, since Neumann’s paper (44) does not contain such curves.) For cysts of lower hydrations, D/D0 is much / OOCWO smaller and, hence, %/td is even larger. Therefore, Eq. [l] is satisfied and the efl fective diffusion should be approximated by Eq. [2], if the compartmentalization effect is important. If the cellular water is considered to be contained in a fixed number of spherical “pockets” of diameter a, the volume of these “pockets” must decrease in proportion to the hydration. Then cl

/:

v

OlL

a3 a w where W is the hydration, measured in grams Hz0 per gram dry solids. Therefore, a a W’3

01

c n k 11’1”

10 W

10 0

FIG. 3. The NMR-measured diffusion coefficient D is plotted as a function of hydration on a log-log scale. The solid line D cc JV” is obtained from a compartment model (see Eq. [3]).

SELF-DIFFUSION

OF WATER IN Artemia

was measured with 27 = 40 ms. In a preliminary study reported by Tanner ((45) and personal communication) the D of water was measured in brine shrimp using a pulsed field gradient method. He found the observed D (measured with 27 varying from hundreds of milliseconds to less than 1 ms) to vary from l-3 X 10e6cm2/s. These values are similar to ours. Therefore, the observed D apparently is not sensitive to 27, a finding which does not agree with the relation predicted by the impermeablewall-compartment model (i.e., Eq. [2]). (2) Permeable walls. To analyze the case in which the walls are permeable, we again utilize the results of Tanner (26). Tanner has presented results for D/D0 as a function of measuring time 27 for a one-dimensional chain of equally spaced barriers of permeability p separating compartments of width a in which the diffusion coefficient is Do. D (27) is the apparent diffusion coefficient as determined in a spir .echo experiment with measuring time 27. We assume that the water in a brine shrimp cyst is contained in spherical pockets, of diameter a, that are connected by paths that can be described by a permeability p. These paths might be regarded as channels through cell membranes or, more generally, as surfaces within the cell on which there is a layer of hydration water. Since the measuring time of our experiments is 27 = 40 ms, the reduced time would be: t’ = (D(0))/a2 27 = 25 if we take, a = 2 X lop4 cm and D(0) = 2.5 X 10m5 cm2/s. In the limit t’ % 1, Eq. [ll] in Tanner’s paper (26) gives WC Do

p l+P’

where P = a13is the reduced permeability. Do If we are to fit this expression to the experimental values of D/Do, then P must be 4 1, since D/Do 4 1. Thus, D/Do N P or D N ap. With the same assumptions that lead to Eq. [3], we have a cc Un’3. It is more difficult to make a reliable estimate of how

521

p would depend on IV. It appears from Fig. 3 that if one assumes p CC IV, Tanner’s Model would give good agreement with our data. The temperature dependence of this model differs from that predicted by the impermeable wall model. The temperature dependence of D is the same as that of the permeability p, so that if we regard p as determined by the transport through channels or surface layers of hydration water, we would expect a temperature dependence for p that would be the same as that of the diffusion coefficient for the hydration water, which would probably not differ greatly from that for bulk water. Therefore, Tanner’s model could explain the hydration dependence of the observed diffusion coefficient, provided that the relationship p cc W is satisfied. We are not aware of any experimental data which provide justification for this relation. Thus, further evaluation of this model requires the temperature studies previously mentioned and studies on the dependence of p on IV. (B) Obstruction Models (1) Wang’s model. In our analysis of the reduction of D for the nonspecific obstruction effect, we first consider the customary treatment of Wang (29) which was developed for capillary flow measurements of D in dilute protein solutions. It is not strictly applicable to spin-echo measurements and is not accurate at high molecular concentrations. Nevertheless, its frequent use justifies its consideration here. Wang assumed the protein molecules to be stationary and impenetrable and concluded that D/Do = 1 - a+,

[41

where D and Do are as defined earlier and a! is a dimensionless numerical coefficient dependent on the geometrical shape of the protein (CY= 1.5 for spheres), @is the volume fraction occupied by the protein and is given by (l/d)/((l/d) + IV), where d is the average density of the protein. (If d

522

SEITZ ET AL.

= 1.3 (46), @Jfor a fully hydrated Artemia cyst would be about 0.35.) Wang also considered the direct hydration effect in which a certain fraction of the water molecules is considered to be bound tightly to the proteins and not freely diffusible. This fraction is f = Cd Co, where

36 32 28 24 -

Ch = grams of bound water per milliliter of solution Co = grams of total water per milliliter of solution

I 0

02

0.4 06

Thus, Eq. [4] becomes ;

= (1 - a@)(1 - C,/C,). 0

[51

If one makes the assumption that above a certain minimum water concentration (below which all the water molecules are “bound”), Ch is proportional to the concentration of dry solids, then b ch

= b@d

= cl,dj

+

w,

co = 1 - a. Figure 4 plots D/Do as a function of W for several values of b for a! = 1.5 and d = 1.3. This model gives a much more rapid variation of D/Do with W than the experimental curve. (2) Rorschach’s model. A more recently developed model of obstruction, and one that is directly applicable to spin-echo measurements, is that of Rorschach ((1) and unpublished), who analyzed the influence of obstructions on the Bloch-Torrey equation (47). For a cubical array of spheres these calculations yield D/Do =

’ 1 + 0.63+ ’

P-7

Other arrangements of obstructions have equations of the same form with the geometrical factor (i.e., the numerical coefficient preceding ‘P) dependent on the spa-

I

, 16

FIG. 4. The experimentally measured ratio D/D, is plotted as a function of hydration IV. The solid lines give the prediction of the obstruction model of Wang (see Eq. [5]).

tial arrangement of the macromolecules. If the direct hydration effect is included, Eq. [6] is D/D, =

where b is the grams bound water per gram protein, and

1

0.8 1.0 1.2 14 W

1-f 1 + 0.63@’

PI

where f has the same meaning as in Wang’s model. Substituting the relations giving the hydration dependence of a, Eq. [7] becomes D/D, =

1-f 1+

0.63 * 1+ Wd

PI

The predictions made by the models of Wang and Rorschach are similar when 9 is small, but they begin to deviate for + 9 0.3. Equation [8] gives an even more rapid variation of D/Do with W than the Wang model, and it agrees poorly with the experimental results. (C) Surface Adsorption Models There are several hypotheses which propose that the physical properties of an appreciable fraction, or even all of the water in cells are different from those of ordinary bulk water (4, 31-43, 48, 49).

SELF-DIFFUSION

OF WATER

These views differ considerably with regard to the proportion of the total intracellular water that exhibits nonbulk properties; however, they all stress the importance of intracellular surfaces in determining the properties of cellular water. The most well developed of these is the association-induction (A-I) hypothesis (37, 38), in which it is proposed that cellular water “. . . exists as partially immobilized polarized multilayers” (p. 688 of Ref. (37)). The A-I hypothesis, as well as the other hypotheses expect that the diffusion coefficient of water should be reduced and would be a complicated function of position within the cell. The reduction of the diffusion would result from changes in the parameters of the conventional diffusion equations (e.g., activation energy, jump frequency, etc.). In order to evaluate these hypotheses, as a first approximation, and in the context of a phenomenological model, we will utilize an extension of the obstruction models. In our use of the obstruction-hydration models of Wang and Rorschach, we will drop the assumption that C,, is proportional to the concentration of the dry solids. We will instead allow the hydration fraction f = C&‘~ to be a free parameter that is adjusted so that Eq. [7] agrees with the experimental values of D/Do. Since the internal structure of Artemia is not known, we set the geometrical factor of Eq. [6] equal to 1.0 (instead of O&3), which represents the upper limit for a large obstruction effect. Equation [7] is then D/Do = $f$ from which f can be determined. Table I lists the values off for 0.2 < W < 1.4. Even allowing the maximum reduction due to obstructions, the fraction of the total water which comprises the macromolecular “hydration shell” would have to be very large and not strongly dependent on + (for example, f is 0.77 at the highest hydration, W = 1.4. At W = 0.2, f = 0.97; that is, practically all cyst water has to be hydration water in order to account for the reduction of D).

523

IN Artemiu TABLE

1

THE HYDRATION FRACTION~OF “NONDIFFUSING WATER” AS A FUNCTION OF HYDRATION W, THAT Is REQUIRED TO GIVE THE OBSERVED DEPENDENCE OF D ON W ACCORDING TO EQ [9]

W

f=l-g(l++) 0

1.4 1.0 0.6 0.2

0.77 0.83 0.91 0.97

SUMMARY

We have measured the hydration dependence of the self-diffusion coefficient (D) of water in Artemia cysts over their complete hydration (IV) range. The above analysis of the dependence of D on W permits four conclusions. First, the ratio D/ Do varies too slowly as a function of W to be satisfactorily explained by the obstruction models. Second, the hydration dependence of D is consistent with the impermeable compartment model (see Fig. 3) except that the 27 dependence predicted by this model does not agree with the experimental observations. Third, the dependence of D on hydration can be explained by Tanner’s compartmentalization model in which the compartment wall is partially permeable, provided that the relationship p a W is satisfied. Fourth, the large reduction of D in cyst water is consistent with the notion of the surface adsorption models, in which a substantial fraction (>77% ) of the water has a greatly reduced diffusion coefficient. But due to a lack of quantitative prediction in these models, the data can be used only in a qualitative way to test these models. ACKNOWLEDGMENTS This work was supported in part by ONR Contract NO994-‘76-C-0109, USPHS Grant GM20154, Robert A. Welch Foundation Grant Q-399, NSF Grants PCM7624037 and PCM79-26609 (J.S.C.), and USDA/SEA Grant to the Children’s Nutrition Research Center, Houston. C.F.H. is grateful for a private donation given in the memory of Stanley T. Weiner.

524

SEITZ ET AL.

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