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J. Phys. Chem. 1980, 84, 2320-2325
NMR Study of the Freezing/Thawing Mechanism of Water in Polyacrylamide Gel Seiji Katayama and Shlzuo Fujiwara” Shizuoka College of Pharmacy 2-2- 1, Oshika, Shlzuoka 422, Japan, and Department of Chemistry, Faculty of Science, The University of Tokyo, Hongo, Tokyo 113, Japan (Received: October 2, 1978; In Final Form: March 11, 1980)
NMR of water in polyacrylamide gels was investigated with respect to the spin-lattice relaxation time, T,, the line width, and the relative amount of unfrozen water, in the range from 23 to -80 “C. With respect to all of the properties investigated, characteristic temperature hysteresis loops were observed. Four thermal equilibrium states exist, each corresponding to a temperature or range: (A) bulk water-associated water (-4 “C), (B) bulk water-unfrozen water-ice (-8--3 “C), (C) unfrozen water-ice (-8--60 “C), and (D) ice (--60 “C for 30% gel), the ice temperature depends on the gel density. The freezing/thawing mechanism as characterized by the phase transformations among these thermal equilibrium states is discussed in detail, together with the characterizationof the unfrozen water. The results based on proton NMR studies were well supported by “ 0 NMR data.
Introduction The states of water in any biological media are wellknown to consist of a large amount of “free water” and a small amount of “associated water”. As the biological media are cooled below the freezing point of free water, an unfrozen portion of water can be easily observed via its broad signal by NMR.I Under these conditions, as free water freezes, associated water may be freed. Unfrozen water interacts intimately with the associated (or hydration) water in biological media. Investigations of the unfrozen water have been carried out simultaneously with those of the associated water and have contributed much to the elucidation of the function of the associated Kuntz has discussed the water of hydration in various protein solutions at -35 O C , along with the relative amounts of unfrozen water, which give the most reasonable values for the amount of associated water.l+ However, as the authors observed the cooling process of the gel sample, it was determined that the relative amount of unfrozen water has a pronounced temperature dependen~e.~ The stoichiometric relationship between the associated water and the unfrozen water is not always evident, although it is almost certain that the unfrozen water originates from the associated water. Furthermore, the structural state and the mobility of the unfrozen water depend considerably upon the species of biological media involved, their concentrations, and the observed temperature. Thus, the nature of unfrozen water has remained uncertain.lOJ1 Freezing/ thawing behavior of water molecules in any biological media is a subject of great interest and a matter of theoretical and practical c o n ~ e r n . ~ The - ~ *unfrozen ~~~~ water observed in the biological media seems to play a main part in the freezinglthawing mechanism, which can be correlated to the nature of the essential cryoprotection of biological media, such as cells. It is, in general, difficult to investigate the freezing/thawing mechanism of biomedia. The polyacrylamide gel used in the present experiment can be taken as a simplified model for the biosystems, which can facilitate the investigation of the freezinglthawing mechanism. The results obtained seem to provide a basis €or understanding of the freezing/ thawing mechanism of the various biomedia. In the present paper, the temperature dependences of ‘H and I7O NMR of water in polyacrylamide (PAA) gels are examined with respect to the relative amount of unfrozen water, the proton spin-lattice relaxation time (T,), *Department of Chemistry, University of Tokyo.
0022-3654/80/2084-2320$01 .OO/O
and the line width. Four thermal equilibrium states and a freezinglthawing mechanism arising from phase conversions among them are discussed in detail, together with characterization of the unfrozen water.
Experimental Section Acrylamide (AA) and N,N’-methylenebis(acry1amide) (MBA) were obtained from Tokyo Kasei Co., Ltd. and were used for preparation of polyacrylamide gel samples. Acrylamide was recrystallized and was further purified by repeated sublimation under high vacuum before preparation of the samples. Water used in the present experiment was deionized H20 and D20 (E. Merck, 99.75%),distilled several times to remove paramagnetic impurities. H2I7O (10% enriched, The British Oxygen Co., Ltd.) was used for preparation of the labeled gel samples. Polyacrylamide gel samples were produced from the aqueous solutions with AA and MBA disolved in a D20-H20 mixture (50%),the molar ratio of AA and MBA being 80 to 1. Gelations of these solutions were all done by photopolymerization after addition of a small amount of ammonium persulfate as an accelerator for polymerization. In this way, gel samples of 5, 10, 15, 20, and 30% by weight were prepared for measurements by ‘H NMR, and the 30% gel sample labeled by HJ70 was prepared for measurement by 170 NMR. NMR temperature dependences of water in the gel samples were measured with respect to three physical properties of water, a spin-lattice relaxation time, T1,a line width, and the relative amount of unfrozen water. The lH NMR measurements were performed on a JEOL FX100 high-resolution NMR spectrometer, and the 170 measurements on a Varian FT-80 spectrometer. Thermal regulation of the samples was accomplished by means of the variable temperature units attached to the instruments. Temperatures were monitored by a standard thermometer inserted directly into the NMR probe and were controlled to within f 1 . 5 “C. The T1 measurements for sharp resonance signals of water in the gels were performed by using the built-in DQD Auto-T, (180-i-90) routine of the JEOL instrument, where initially FID signals following the 90” pulse in the repeated 180-7-90 pulse sequences were stored in the data cassette tape, and latter T , was calculated by the least-squares method, after the Fourier transformation of the stored FID’s. These procedures were automatically performed by the accompanying minicomputer. On the other hand, T, values for broad signals such as for an unfrozen water 0 1980 American Chemical Soclety
Freezing/Thawing of Water in Polyacrylamide Gel
TABLE I : Sweep-Width Dependences on Signal Area of Unfrozen Water sweep width, Hz normalized signal area 5 000 100 7 000 115 10000 136 13 000 130
The Journal of Physical Chemjstry, Vol. 84,
No. 18, 1980 2321
L
+J W m 3
5
10.
N
L 0 ie E
=
7.5
ie
0
were estimated by the relationship 7,dl = T1/1.44, where T~~~~refers to the time required for the magnetization, inverted by ai 180" pulse, to be restored to zero. All of the T , values were estimated on the basis of the assumption of a single mode of relaxation. These were confirmed by examination of the linear relationships between magnetization inversion recovery and time. The sweep width for measurements of the broad signals were 6000 Hz, and those for the sharp signals were 1000 Hz. The relative amounts of unfrozen water were estimated from the signal area, by comparison to that of the standard reference sample which was prepared by adding LiCl and MnClz to water (90% DzO). The IH NMR measurements were done by using glass tubes of 5 mm 0.d. and coaxial polypropylene tubes of 4.0 mm 0.d. filled with the gel samples, and those for l7O NMR were carried out by using glass tubes of 10 mm 0.d. and coaxial Teflon tubes of 9 mm 0.d. filled with the labeled gel samples. The use of coaxial tubes was effective in preventing the cracking of the sample tubes at temperatures below the freezing point of water. The measured properties were all affected only slightly by the length of time that the sample was held at any given temperature. The samples which reached a constant temperature in a period of ca. 10 min were maintained at this temperature for a further period of 1 h. This treatment resulted in good reproducibility of the NMR measurements, Le., within ca. &4%. The temperature change (direction indicated by figures) was performed in a cyclic manner, with temperature first decreasing and then increasing. The signal ,area of a broad resonance line is well-known to be sensitive to sweep width, because a finite sweep width removes the wings of the Lorenztian line. In other words, it is difficult to observe the signal area by using the real base line of the signal. Even a small difference in the base line results in a large error in the signal area. Therefore, sweep-width dependence on the signal area was examined by using a P,4A gel sample (10%) under the following experimental conditions: sweep width, 5,7,9, and 13 kHz, and filter range, 10 kHz, where the filter range of the instrument was made as large as possible; and in order to obtain the real base line, the signal gain of the instrument was made as high as possible without increasing the S / N ratio. Consequently, it was found that the sweep width was nearly independent of the signal area with the experimental error within ca. 36% (Table I). Although the error was somewhat large, this finding enabled the present discussions on the amount of unfrozen water and the line width, so far as these were all dealt with as relative comparisons.
Results and Discussion Figure 1 shows the temperature dependence of the relative amount of unfrozen water in the PAA gel (15%). As the gel sample is gradually cooled from room temperature (23 "C) to ca. -80 "C, a sharp resonance signal is observed until ca. -8 "C. However, a broad resonance signal suddenly appears at -8 "C, concurrent with disappearance of thle sharp signal. The broad signal is wellknown to arise from an unfrozen portion of water.l The relative amount of unfrozen water decreases linearly with
%
5.0
u E LJ W
L 0
a
2.5
0
-20
-40
Temp. ("C)
Flgure 1. Temperature dependence of the percentage of unfrozen water in the 15% PAA gel. The arrows denote the direction of temperature change.
k
1-300
Hz
Figure 2. NMR spectrum which is observed only on the pathway of temperature increase in the range from ca. 3 to ca. -8 "C. The broad signal results from an apparent unfrozen water which arises from the intrinsic unfrozen water and the exchangeable bulk water melted, and the sharp signal inverted results from a nonexchangeable portion of bulk water melted. The spectrum is observed only when the magnetization inverted by 180" pulse returns to near zero.
a decrease in temperature in the range from -8 to -46 "C, and its signal finally disappears at ca. -46 "C. As the temperature is raised from the lower values, the broad signal is not observed until -46 "C, at which point it becomes detectable. The amount of unfrozen water increases linearly with an increase in temperature in the range from -46 to -8 OC. The pathway during the temperature increase in this range is the same as that in the case of the decreasing temperature. However, during the temperature increase, a further steep increase in the amount of unfrozen water is found above -8 "C, which was not observed in the pathway in the case of decreasing temperature. The steep increase observed can be accounted for by the fact that the broad signal arises from an "apparent" unfrozen water, which comprises the intrinsic unfrozen water and the bulk water melted with an increase in temperature, with the apparent unfrozen water observed as a single component because of rapid exchange between the latter two forms. When the magnetization of water inverted by the 180" pulse returns to near zero, the presence of a small amount of an unexchangeable portion of the bulk water can be observed in the spectrum as a sharp inverted resonance signal (Figure 2), together with the broad signal of the "apparent" unfrozen water. In the figure, they can be easily identified by means of their differing relaxation times. The above observation can be made only along the increasing temperature pathway, in the range from 3 to -8 "C, and never during the temperature decrease. In other words, there are different pathways determined by increasing or decreasing of temperature. Similar temperature hysteresis loops were also observed in the other
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The Journal of Physical Chemistry, Vol. 84, No. 18, 1980
Katayama and Fujiwara
a
$\
\
-40
-20
0
-60
Temp. ( " C )
Flgure 3. Temperature dependencies of the percentage of unfrozen water in the PAA gels (5, 10, 20, and 30%): (0) process of temperature decrease; ( 0 )process of temperature increase. 20
0
-40
-20
Temp. ("C)
Flgure 5. Temperature dependencies of the T , of water in the PAA gels (5, 10,20, and 30%): (0) 5 % PAA gel; (A)10% PAA gel; (0) 20% PAA gel; (V)30% PAA gel.
I
I. 20
A I .( 0
-
700
N
I
-20
1
-40
.c
500
+J
U
Temp. ("C)
.r
3
Figure 4. Temperature dependence of the T I of water in the 15% PAA gel. The arrows denote the direction of temperature change.
300 .r
2
gel samples of 5, 10, 20, and 30% by weight (Figure 3). Figure 3 shows that the temperature hysteresis curves are shifted in parallel fashion toward higher values of the relative amount of unfrozen water with an increase in concentration of the gel. These shifts parallel the fact that the percentage of unfrozen water increases linearly with an increase in concentration of the PAA gel as mentioned It is found that the gel concentration does not previo~sly.~ influence the critical temperature of -8 "C corresponding to the phase transformation from the bulk water to ice; however, it noticeably lowers the freezing point of unfrozen water. Figure 4 shows the plots of T1of water in the PAA gel (15%) against temperature. As the sample is cooled from room temperature, Tldecreases linearly. At ca. -8 "C, Tl drops abruptly from ca. 0.4 s to ca. 30 ms. In the range from -8 to -46 "C, T1decreases slightly with decreasing temperature. When the temperature is raised from the lower values, TIincreases slightly, following the same pathway as followed during the temperature decrease, in the range from -46 to -8 "C. In the range from -8 to 3 "C, as the temperature is increased, T1shows a gradual increase along a pathway different from that followed during a temperature decrease. At ca. 3 "C, the values of T1on the two pathways coincide, and, with further increasing temperature, Tlincreases linearly, taking the same pathway as it did during the temperature decrease. Therefore a characteristic temperature hysteresis loop is observed in the T1 behavior. Similar temperature hysteresis loops were obtained in the case of the other gel samples (5,10,20, and 30%) as shown in Figure 5. The TI curves in the range above -8 "C are considerably influenced by the gel concentration and in this region are shifted in parallel fashion toward lower T1values with an
100
0
10
-10 Temp. ( " C )
Figure 6, Temperature dependence of the line width of water in the 15% PAA gel. The arrows denote the direction of temperature change.
N
5
1500
c
+ -0
'2
1000
W I8 C
500
-10
-20
-30
-40 -50 Temp. ( " C )
Flgure 7. Temperature dependence of the line width of water in the 15% PAA gel. The arrows denote the direction of temperature change.
increase in concentration of the gel, whereas in the range below -8 "C they are not influenced by the gel concentration. On the other hand, it was found that the gel concentration does not affect the critical temperature of -8 and 3 "C, which correspond to the phase transformations from bulk water to ice and from ice to bulk water, respectively. The temperature dependences of the line width of water in the PAA gel (15%)are shown in Figures 6 and 7. As the gel sample is cooled from room temperature, the line
The Journal of Physical Chemistry, Vol. 84, No. 18, 1980 2323
FreezingIThawing of Water in Polyacrylamide Gel
0
-20
-40
-60 Temp ('C )
Flgure 8. Temperature dependences of the line width of water in the PAA gels (5, 10, 20, and 30%): ( 0 )5 % PAA gel; (A)10% PAA gel; (0)20% PAA gel; (V)30% PAA gel.
width remains nearly unaltered until -8 "C, where it abruptly jumps to ca. 300 Hz (Figure 6). The sudden increase corresponds to the fact that the unfrozen water suddenly appears, with concurrent disappearance of the bulk water. The broad siginal is linearly broadened with further temperature decrease. It increases to over ca. 1500 Hz at -46 "C and finally becomes undetectable below -46 " C (Figure 7). As the temperature is raised from the lower values, the broad signal begins to appear at -46 "C. The line width decreases linearly in the range from -46 to -8 "C, taking the same pathiway as does the line width during a temperature decrease. The line width in the range from -8 to 3 " C gradually decreases in a fashion different from that in the case of decreasing temperature. With a further increase of temperature above 3 "C, the line width follows the same pathway as it does during a temperature decrease. Thus, a specific temperature hysteresis loop is also found in the line-width behavior. Similar phenomena were observed in the case of the other gel samples (5,10,20, and 30%),as shown in Figure 8. Consequently, it was found that the critical temperatures of -8 and 3 "C, which refer to the phase transformations from bulk water to ice and from ice to bulk water, respectively, are little affected by the gel concentration. Further, it was found that the curve of the line width in the region below -8 "C is considerably affected by thle gel concentration; that is, it varies from a steep slope tlo a more gradual slope with an increase in concentration. From the observed temperature dependences, it may be concluded that there are four thermal equilibrium states, each corresponding to a temperature or range: (A)bulk water-associated water (-4 "C), (B) bulk water-unfrozen water-ice ( - 3 - 4 "C), (C) unfrozen water-ice (-8--60 "C), (D) ice (--60 "C), where -60 "C is for the case of 30% P A A gel and is variable with concentration of the gel. State A,which consists of a large amount of bulk water and a small amount of associated water, appears both in the range above -8 "C during a temperature decrease and in the range above 3 "C during a temperature increase. State A is a liquid phase which can ble accounted for by the two-phase because of the rapid exchange between the associated water and the bulk water, although state A in the range from 3 to -8 "C which appears only during a temperature decrease is a complicated intermediate.3M1 State B, which consists of the three components unfrozen water, bulk water, and ice, appears in the range from 3 to -8 "C1 only during a temperature increase, and it is responsible for the temperature hysteresis loops in this system. State C:, which consists of unfrozen water and ice, appears in the range from -8 to -60 "C. State D, which consists of ice, appears below -60 "C.
Figure 9. Schematic representation of the freezinghawing mechanism among the four thermal equilibrium states (A, 8 , C, and D). The solid arrows denote the process of temperature decrease, and the dotted arrows denote the process of temperature increase.
10
20
30 PAA c o n c . ( S )
Figure 10. Temperature ranges in which the unfrozen water can exist in the PAA gels: (0)the upper limits of the presence of the unfrozen water; (0)the lower limits of the presence of the unfrozen water.
Phase transformations among the thermal equilibrium states described above are closely related to the freezing/thawing mechanism in the following sense. A schematic representation is shown in Figure 9. States D and C are obtained by abrupt and gradual cooling of state A, respectively. Upon gradual cooling, state A is transformed into state C, and state C is transformed into state D. On the contrary, state D is transformed successively into states C, B, and A during an increase of temperature. Furthermore, it is possible to discuss the phase transformations of each component of water in the thermal equilibrium states. During a cooling process, phase transformations from bulk water to ice and from associated water to unfrozen water take place discretely at -8 "C, and the subsequent freezing step below -8 "C is the gradual phase transformation from unfrozen water to ice. On the contrary, during a warming process, the gradual melting of ice which arises from unfrozen water proceeds until -8 "C, after which the melting of ice which arises from bulk water follows in the range from -8 to 3 "C. Figure 10 shows the concentration dependence of the P A A gel on the temperature range such that unfrozen water can be present. The temperature range is broadened with an increase in concentration of the gel. The critical temperature of -8 "C,the upper limit of the temperature range in which unfrozen water can be present, is nearly independent of the gel concentration. However, the lower limit of the temperature range is linearly lowered with an
2324
The Journal of Physical Chemistry, Vol. 84, No. 18, 1980 0,
I
L
I
20
10
0
-10
Temp. ( " C ) Figure 11. Temperature dependence of the relative intensity of I7O NMR of the labeled water in the 30% PAA gel. The arrows denote the direction of temperature change.
$ 1 5
I
300
20
10
0
-10 Temp. ( " C )
Figure 12. Temperature dependence of the line width of I7O NMR of the hbeled water in the 30% PAA gel. The arrows denote the direction of temperature change.
increase in concentration of the gel and in the case of the 30% PAA gel goes below -60 "C. The above result is of interest in connection with frozen biosubstances in the following sense. Watery biosubstances which have an abundance of bulk water in comparison to associated water are known to be easily damaged by freezing. In this case, the temperature range in which unfrozen water is observed is markedly narrow. In marked contrast, the waterless biosubstances which have an abundance of associated water in comparison to bulk water have the property of cryoprotection. In this case, the temperature range in which unfrozen water is observed is broadened, and the lower limit goes down to ea. -70 Figures 11 and 12 show the NMR temperature dependencies of 170in labeled water in the 30% PAA gel. The abrupt reduction of relative intensity of the 170resonance signal is observed at ca. -8 "C during the cooling process. To the contrary, the marked recovery of the relative intensity is observed at ca. 3 "C during a temperature increase (Figure 11). Figure 1 2 shows the temperature dependence of the line width of the 170resonance signal. The line width linearly increases with a decrease in temperature, changing from ca. 80 to ea. 200 Hz. Finally the line width disappears at ca. -8 "C. On the other hand, the line begins to appear, with a width of ea. 400 Hz, at ea. 0 "C during a temperature increase. Then the line width reduces abruptly with an increase in temperature, and the temperature dependency becomes identical with that observed in the case of cooling, at temperatures above ca. 4
Katayama and Fujiwara
"C. The 170resonance signal of unfrozen water cannot be observed because of quadrupole relaxation of 170. In summary, the above results obtained by use of 170NMR well support the freezing/thawing mechanism discussed on the basis of lH NMR results. The mobility of unfrozen water is of importance in connection wth characterization of unfrozen water. O ~ t h r e and d ~ ~other researcher^^^-^^ have referred to the fact that the associated water in gels and biopolymer solutions has distributed correlation times (7,). However, the problems of the correlation time of unfrozen water and its distribution have not yet been completely elucidated. The results of the present experiment suggest that the unfrozen water may have distributed correlation times and an inhomogeneous structural ordering. If the unfrozen water were formed of a single component of correlation time 7,,a monochromatic freezing point for unfrozen water should be obtained. In fact, the freezing of the unfrozen water proceeds continuously beginning with the fraction of smaller T,, that is, the less restricted part of unfrozen water, situated far from the polymer chains of the gel. To the contrary, the melting of unfrozen water begins with the fraction of larger 7,,that is, the more restricted part of unfrozen water, positioned near the polymer chains of the gel. The value of Tl of the unfrozen water at -8 "C is reduced slightly with an increase in concentration of the gel, varying from ca. 80 to ca. 26 ms for concentration changes from 5 to 30%. The value of T1 of the unfrozen water at the lowest temperature that the unfrozen water can be present is of the order of ca. 10" s, and in this case a concentration dependence on the value of T1 cannot be discerned. Accordingly, it may be concluded that the correlation times of the unfrozen water estimated are continuously distribto ca. lowss. uted over the range from ca. Assuming a single mode of correlation time for the unfrozen water in this system, the activation energy (E,) of restriction of motion of the unfrozen water can be easily estimated, when the Arrhenius plots of In 7, vs. 1 / T are nearly linear. The activation energy (E,) estimated is ca. 9-15 kcal/mol. The value is about two or three times those of the activation energy (ca. 5 kcal/mol) for the unfrozen water in m i t o ~ h o n d r i aor~ the ~ energy (ca. 4.5 kcal/mol) required for the cleavage of a hydrogen bond of water and is in accord with the value of activation energy (ca. 13.5-15 kcal/mol) of restriction of motion in water in i ~ e . ~ ~ ~ The fact that the freezing point of bulk water in the PAA gel is lowered to -8 "C can be interpreted in terms of either solubility of PAA or internal pressure. The former is not appropriate to the present system, because it is not clear whether the PAA molecule is soluble in water. The latter seems to be reasonable, in the following sense. The expansion coefficient of the network polymer of PAA gel is much smaller than that of water. The water molecules inside the microspace constructed of the rigid network may be markedly prevented from thermal expansion. The prevention of the thermal expansion causes a high pressure which is characterized by the internal pressure (dU/dv),. The phase transformation between water and ice brings about the pronounced volume expansion which is responsible for the high pressure. The high pressure occurring contributes to the depression of the freezing point of water. The internal pressure (dU/dv)T is thermodynamically written as follows: ( d U / d v ) ~= -P -k (dP/dT)"T where the pressure which is responsible for the depression of the freezing point can be expressed by the ClapeyronClausius equation as
FreezinglThawing of Water in Polyacrylamide Gel
(ap/an,T = A E J V for the phase transformation from liquid to solid. It is, therefore, possible to estimate easily the internal pressure. The internal pressure which causes the freezing point depression of 8 “C is ea. 1.1X lo3 atm (AE, = 1.4 kcal/ mol, &e) = 0.9168 g/cm3, p(water) = 0.9999 g/mol, accordingly AV = 1.6 cm3/mol). The internal pressure is essentially of a transient character; therefore, the increment of the internal pressure occur.ringdisappears after the phase transformation. This interpretation seems to be closely related to the mechanism of cryoprotection of biosystems, which will be mentioned in a forthcoming paper. The most interesting result of the present study is the relatively detailed characterization of the unfrozen water which is possible. Further, the present measurements lead to the breaking of new conceptual ground, physicochemically related to the freezing/thawing mechanism at the molecular level.
Achnowled,grnent. We thank Professor H. Iwamura of The Institute for Molecular Science for the use of the NMR spectrometers. References and Notes (1) I. D. Kuntz, Jr., T. S. Brassfield, G. D. Law, and G. V. Purcell, Science, 163, 1329 (1969). (2) I. D. Kuntz, Jr. and T. S. Brassfield, Arch Biochem. Biophys., 142, 660 (1971) (3) I. D. Kuntz, Jr., J. Am. Chem. Soc., 93, 514, 516 (1971). (4) J. P. White, D. Kuntz, andC. R. Cantor, J. Mol. Biol., 64, 511 (1971). (5) I. D. Kuntz, Jr., Adv. Protein Chem., 281, 239 (1974). (6) I. D. Kuntz, Jr., Water Relat. Foods, toroc. Int. Symp., 1974. (7) I. D. Kuntz, Jr., A. Zipp, and T. L. James, ACS Symp. Ser., 34, 499 (1976). (8) I. D. Kuntz, Jr. and W. Kauzmann, Adv. Protein Chem., 28, 239 (1974). (9) S. Katayama and S. Fujiwara, J. Am. Chem. Soc., 101,4485 (1979). (10) D. C. Cang and D. E Woessner, Science, 198, 1180 (1977). (11) H. A. Resing, K. R. Foster, and A. N. Garroway, Science, 198, 1181 (1977). (12) D. E. Woesrmer and U. S. Snowden, Jr., J. Colloid Interface Sci., 34, 290 (1970). (13) B. Lwbas and T. Wilezok, Biopolymers, ‘IO, 1267 (1971). (14) S. Harvey and P. Hoekstra, J . Phys. Chem., 76, 2987 (1972). (15) H.A. Resing and R. A. Neihof, J. Col/oUInt&ace Sci.,34, 480 (1970). (16) G. S. Byostrov, N. I. Nikolaev, and G. I. Romanenko, Blofizika, 18, 484 (1973). (17) T. 0. Perry, Science, 171, 29 (1971). /[.
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