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Effects of temperature and field strength on the NMR relaxation times of 23Na in frog striated muscle
291
Biochimica et Biophysica Acta, 354 (1974) 291--304 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
BBA 27440
EFFECTS OF TEMPERATURE AND FIELD STRENGTH ON THE NMR RELAXATION TIMES OF 2 3 Na IN FROG STRIATED MUSCLE
MORDECHAI SHPORER and MORTIMER M. CIVAN
Department of Isotope Research, The Weizmann Institute of Science, R(hovot, Israel and the Departments of Physiology and Medicine, University of Pennsylvania School of Medicine Philadelphia, Pa. 191 74 (U.S.A.) (Received February 6th, 1974)
Summary Pulsed NMR techniques have been applied to the study of the relaxation parameters characterizing 23 Na within frog striated muscle. Experiments were performed at 3°C, 22--24°C and 39°C at a Larmor frequency of 15.7 MHz; at 22--24°C, measurements were obtained both at 15.7 MHz and at 7.85 MHz. As previously reported, only a single spin-lattice relaxation time (T1) was observed, but both slow (T~)i and fast (T2)xi components of the spin-spin relaxation time were measured. The effect of temperature (0) upon (1/TI) was qualitatively similar to that reported for 23 Na-in free solution; (0) did not significantly affect (l/T2) over the range of temperatures studied. (l/T2)i, and to a lesser degree, (1/Tt) exhibited a modest inverse dependence of doubtful significance on the Larmor frequency. The data are examined within the framework of a simple specific model; a conservative value is assumed for the quadrupolar coupling constant characterizing immobilized intracellular Na÷. Within this framework, the results suggest that the fraction of bound ions whose molecular tumbling is severely restricted does not exceed some few percent of the total sodium population.
Introduction The composition of the fluid within biological cells differs markedly from that of the fluid bathing the cell exterior. In most cells the intracellular concentration of Na ÷ is considerably lower, and the intracellular concentration of K÷ considerably greater than in the extracellular fluid. It seems clear that this phenomenon must arise, at least in part, from ion-selective transport properties of the plasma membrane [1--5]. However, the composition of the intmcellular fluid may also reflect differential binding properties of sites within the cell. Without attempting a rigorous definition of "binding", the term will be used in the present context to specifically denote restricted molecular motion.
292 A variety of techniques have been utilized in an effort to define the precise a m o u n t and significance of the putative binding of Na and K within the cell [6,7]. In particular the techniques of NMR have appeared to offer considerable promise. The NMR spectrum of 23 Na of living tissue may be measured, following which the tissue m a y be ashed, solvent added to restore the volume, and the NMR spectrum reexamined. Cope [8,9] was the first to observe that the relative intensity of the 23 Na signal before ashing each of several biological preparations was 30--40% of the intensity following ashing. Using pulsed NMR techniques [10], 30--40% of the anticipated signal was found to be characterized by a relatively slow transverse relaxation time (T2); a relatively rapid decay time was also observed and attributed to the remainder of the signal. The simplest interpretation was that the NMR data defined two populations of Na nuclei. One population, consisting of 60--70% of the Na nuclei, was considered bound; the second population, consisting of 30--40% of the Na nuclei, was thought to be free and solely responsible for the NMR-visible spectrum. Whatever exchange existed between the two populations was considered to be slow. A number of investigators have subsequently examined a wider spectrum of biological preparations, confirming Cope's observations, and drawing similar conclusions from the data [ 1 1 - - 1 6 ] . More recently, partly on the basis of studies of the 23 Na spectrum of unoriented liquid crystals of sodium lineolate in water, we have suggested [ 17] that the NMR data obtained from biological tissue need n o t necessarily reflect t w o distinct populations of Na nuclei. Rather, the data may arise from a nuclear quadrupolar interaction affecting a single population (defined in terms of NMR parameters) of Na. Similar data have since been obtained with unoriented liquid crystals of lecithin--Na--cholate in water [18]~ oriented liquid crystals of sodium decyl sulfate--decyl alcohol--Na2 SO4 in water [ 1 9 ] , and oriented DNA samples [ 2 0 ] . This alternative interpretation of the biological data has received strong support from the studies of striated muscle by Berendsen and Edzes [ 2 1 ] . Although t w o c o m p o n e n t s of the spin-spin relaxation time (T2) were observed, as noted previously, only a single spin-lattice relaxation time ( T , ) could be detected. Since these most recent investigations favor the alternative view, it has seemed desirable to estimate the fraction of Na b o u n d within the cell, under the more likely assumption that the NMR spectrum indeed arises from the entire population of Na nuclei. Until now no data have been presented permitting estimation of the fraction b o u n d within this frame of reference. As m a y be appreciated from Eqn 6A of the Appendix, the existence of a narrow central spectra line, per se, at a single temperature and magnetic field strength does n o t necessitate that the tissue Na be entirely free, and m a y even characterize b o u n d Na under certain conditions.* The following experiments were performed in order to examine the effect of temperature and strength of magnetic field u p o n the relaxation times characterizing 23 Na within frog striated muscle. Examination of these data b y means of the equations presented in the Appendix sug* F r o m E q n 6 A , a n a r r o w central c o m p o n e n t is p r e d i c t e d in the region o f s l o w t u m b l i n g (W~ ~ 1)~ the m i n i m u m v a l u e o f ( l / T 2 ) I = ( 2 / ~ ( D / W ) 2 (D) w h e n I" = ~ J ~ D . (W is the L a r m o r f r e q u e n c y , T is the correlation time, and D is 1 / 4 o f the q u a d r u p o l a r coupling c o n s t a n t . )
293 gests that only a modest fraction of the Na ÷ within frog striated muscle may be bound, i.e., subject to severe restriction of molecular tumbling. Materials and methods
Sartorius, semitendinosus and gastrocnemius muscles were exised intact from doubly-pithed native Israeli frogs, Rana esculenta, which had been mainrained fasting in water at room temperature. In 3 of the 11 experiments performed, the muscles were rinsed in an aerated Ringer's solution similar to that used previously [22,23] (NaC1 115.5 mM; KCI, 2.5 mM; CaC12 1.8 mM; Na2HPO4, 2.5 mM; NaH2PO4, 0.5 mM; and d-tubocurarine chloride, 9 mg/ liter). After several minutes these muscles were blotted dry on Whatman No. 542 filter paper, and gently packed in a glass test tube (outside diameter 10 mm, wall thickness 0.5 mm) to a height of 1--1.5 cm. Because of the low intracellular sodium concentration of fresh muscle, the signal to noise ratio was marginally adequate for the measurements performed, approaching the limit of resolution of the current apparatus. In order to enhance this precision in the remaining 8 studies, the intracellular Na concentration was enhanced in one of two ways. In 3 experiments the muscles were incubated at 4°C for 44.5--104 h in the standard Ringer's solution, before undergoing NMR analysis. In the remaining 5 experiments, the sodium concentration was enhanced by incubating the tissues in low K Ringer's solution, similar to the techniques used by Carey and Conway [24], Beaug~ and Sjodin [25], and Ling and Cope [13]. The muscles were immersed immediately in a K-free Ringer's solution, identical to the solution discussed above except for the absence of KC1; these preparations were subsequently incubated at 4°C for 23--58 h. The details of the tissue incubation are presented for each experiment in Tables I and II. Similar results were obtained for fresh and incubated tissues. All measurements were performed with a Bruker Pulsed NMR B-KR Spectrometer (Bruker Physik AG, Karlsruhe, Germany) at two frequencies (W), 15.7 MHz (9.9 • 107 tad • s-1 ) and 7.85 MHz (4.9 • 107 tad • s-1 ); the strength (Ho) of the steady magnetic field provided by a 12 inch model V 4012 A-HR electromagnet system of a Varian (Palo Alto, California) DP-60 NMR spectrometer was adjusted appropriately for each frequency. The temperature of the sample was controlled by flowing N2 gas, thermally regulated by a Bruker B-ST 100/700 Heating Unit, around the sample. The temperature of the muscles was measured by means of a thermocouple placed 1 cm below the test tube; previous experience had demonstrated that over the range of temperatures examined, the temperatures of the sample and thermocouple are identical to within 1 ° C. Because of the unfavorable signal-to-noise ratio of the measurements, the NMR signal was continuously averaged by means of a Hewlett-Packard No. 5480B Signal Analyzer System (Santa Clara, Calif.) operated in the average mode. T1 was measured by studying the free-induction decay of the signal following pairs of pulses of 180 ° and 90 ° . Specifically, the height of the decaying signal was measured at a fixed time, within 2 ms following the 90 ° pulse, as a
294 function of the time interval between the initial 180 ° and the subsequent 90 ° pulse. Measurements were performed by continuously displaying the timeaveraged trace of the free induction decay on the oscilloscope; after a satisfactory signal to noise ratio had been attained, the amplitude of the pulse was measured directly on the oscilloscope face. T2 was measured in t w o ways. First, the amplitude of the echo following 90 ° and 180 ° pulses was measured as a function of the separation between the initial 90 ° and subsequent 180 ° pulse. Once again, the time-averaged o u t p u t was continuously displayed on the oscilloscope until the signal to noise ratio permitted adequately precise measurement directly from the oscilloscope face. Second, the signal to noise ratio of the measurements performed at high magnetic field intensity was sufficiently favorable to permit use of the CarrPurcell-Meiboom-Gill Pulse Sequence, employing intervals of 1 and 2 ms between the 180 ° pulses. After a period of time-averaging, usually of 10--20 min duration, the o u t p u t was recorded on a paper chart recorder and the amplitude decay measured. No significant differences :were observed between results obtained by the two different techniques. Since the first technique is sensitive to the effects of ion diffusion and magnetic field gradients, these effects must have been of minor significance in comparison with the magnitude of the experimental error at the high magnetic field. The relaxation times T1 and T2 were finally calculated by plotting the data on semi-log paper and choosing b y eye the line with best fit. In general, the results presented in Tables I and II are averages obtained from ,qome four such measurements. Results In the current studies, measurements of T1 revealed b u t a single exponential decay. However, measurements of T~ indicated the presence of b o t h a rapid and slow component, as previously reported [21]. In those experiments where application of the Carr-Purcell-Meiboom-Gill Pulse Sequence technique was feasible, the fast c o m p o n e n t (1/T2)ii was found to be between 230 and 690 s -1, with a mean value of 350 s-'. The precision of measurement of ( l / T 2 ) i i was, however, inadequate to provide more than a rough estimate of this parameter; furthermore, the data were t o o imprecise to conclude whether or n o t ( l / T 2 ) i i was a function of magnetic field strength (Ho) or of temperature (0) over the range of experimental conditions examined. The effects of changes in temperature on the relaxation times (T1) and (T~)i (the slow c o m p o n e n t of transverse decay) are presented in Table I. In each of the four experiments of the series, (1/T1) and (1/T2)I were successively measured at the ambient temperature of the r o o m (22--24°C), at 3°C, at 39°C, and finally at room temperature once again; the range of temperatures studied was chosen to depart as little as possible from physiologically significant conditions. No systematic changes were noticed in the measurements over the periods of observation of as long as 3 h at each temperature. It should be noticed, however, that both (1/T~) and (1/T2)i did increase somewhat over the approximately 8--12 h period required for each experiment. These slow time-dependent changes in the relaxation times were one of the
295 TABLE I EFFECTS OF TEMPERATURE ON THE LONGITUDINAL R E L A X A T I O N TIME (T 1) AND THE SLOW COMPONENT (T2) I OF THE TRANSVERSE R E L A X A T I O N TIME The data are p r e s e n t e d in the same order as the s e q u e n c e of the e x p e r i m e n t a l p r o t o c o l (22--24°C, 3°C, 39°C and finally 22--24°C o n c e again). The final c o l u m n at the right describes t h e c o n d i t i o n s o f the i n c u b a t i o n p r o c e d u r e . Muscles w e r e b a t h e d either in the standard Ringer's s o l u t i o n or in K-free Ringer's s o l u t i o n and either studied straightaway ("fresh"), or after i n c u b a t i o n at 4°C for the p e r i o d of t i m e indicated. ( 1 / T I ) is s e e n t o be inversely d e p e n d e n t u p o n temperature, w h i l e ( 1 / T 2 ) I appears to be i n d e p e n d e n t o f t e m p e r a t u r e over the range studied; the difference b e t w e e n these t w o parameters seems to be directly d e p e n d e n t o n temperature.
Expt
Temp. (°C)
(1 IT 1) (s-l)
(1 IT2) I (s-1)
(1 IT2) I - (1 IT1) (s-l)
Conditions of incubation
A
24 3 39 23
41 58 35 46
76 80 64 78
35 22 29 31
Standard Ringer's solution 104 h, 4°C
B
24 3 39 22
45 77 38 48
72 88 83 86
28 11 45 39
Fresh Ringer's solution
C
24 3 39 23
46 78 43 50
83 94 88 94
37 16 46 44
Fresh Ringer's solution
D
23 3 39 23
38 53 38 47
70 86 76 91
32 34 38 44
Ringer's solution K-free, 23 h, 4°C
~
limiting factors in determing the precision of the current measurements. Although averaging the signal amplitudes over sufficiently long periods enhanced the precision of the measurements, the longer the periods of measurement, the more likely was it to observe a significant spontaneous change within the tissue. The spontaneous changes in (1/Tl) were smaller than the changes induced by altering the temperature. It is clear, then, that (1/T1) was inversely dependent upon temperature. However, no significant changes in (1/T2)i were noted. It should also be observed that, in general, the magnitude of the difference, (1/7'2)I--(1/T1 ), was inversely dependent upon temperatures. The behavior of (1/T2)i and (1/T1) as functions of temperature may be more easily appreciated from Figs 1A and 1B respectively. The normalized data from Table I have been plotted as functions of (1/0) (°K -1 ); normalization was performed by dividing (1/T2)i or (1/Tl) by the corresponding values obtained at 39 ° C. The solid lines have been taken from Fig. 8 of Eisenstadt and Friedman [26], describing the relationship of ( l / T 1 ) for 23 NaC1 in dilute aqueous solutions as a function of (1/0). Eisenstadt and Friedman determined this relationship for (1/T~), using pulsed NMR techniques. Hall et al. [27] have examined the line width of 1 molal 23 NaBr in aqueous solution; their estimations of (1/T2) as a function of (1/0) agree to within 10% of the values reported by Eisenstadt and Friedman. The solid lines may therefore be taken as
296 8°C 59
i ~20
I Exp A o " B o
"
~
24 I
3 F--
A
G •
~2
~
o
,o
./" I
"o 1
2.0
I
! --I
I
B
o
~-
o
,4
•
e ,0
I
I
I
I
I
32
33
34
35
36
t
I/8°K x I 0 ~'
Fig. 1. T e m p e r a t u r e d e p e n d e n c e o f ( l / T 2 ) a n d ( l / T 1 ) o f 2 3 N a in m u s c l e . T h e d a t a p o i n t s h a v e b e e n d e r i v e d f r o m t h e r e s u l t s o f t h e f o u r e x p e r i m e n t s p r e s e n t e d in T a b l e I. N o r m a l i z a t i o n o f t h e d a t a o f Figs 2 A a n d 2 B h a s b e e n p e r f o r m e d b y d i v i d i n g t h e m e a s u r e d v a l u e s a t a g i v e n t e m p e r a t u r e b y t h e c o r r e s p o n d i n g v a l u e s a t 3 9 ° C . T h e s o l i d l i n e s d e s c r i b i n g t h e r e l a t i o n s h i p f o r 2 3 N a in d i l u t e a q u e o u s s o l u t i o n w e r e o b t a i n e d f r o m Fig. 8 o f r e f . 2 6 .
a satisfactory reflection of the behavior both of (1/T2)x and (1/T1) as functions of ( l / P ) for Na in dilute aqueous solution. It will be appreciated from Fig. 1B that the behavior of (l/T1) of 23 Na in muscle as a function of ( l / P ) is qualitatively similar to, albeit quantitatively less striking than, that of 23 Na in aqueous solution. However, as demonstrated b y Fig. 1A, it is d o u b t f u l that any change whatsoever was induced in the (l/T2)i of 23 Na in muscle, over the range o f temperatures examined.. In aqueous solution, as noted in the Discussion, under conditions of rapid molecular tumbling, TI = T2. Furthermore, (1/T1) and (1/T2) should increase similarly, as (1/0) is increased. We might suspect, therefore, that the relaxation times (T2)i, and to some extent, T~, might contain contributions reflecting slow molecular tumbling. If so, the relaxation times would be expected to depend on Ho. On the basis of these considerations, the following experiments were performed. In Experiments E, H and J (Table II), the preparations were studied at Larmor frequency (W) of 15.7 MHz. The frequency wa~ then reduced to 7.8 MHz, and the samples were left for 2--10 h, while the magnetic field restabilized. In Experiments F, I and K, the sequence was reversed; the muscles were first studied at the lower, and subsequently at the higher field. As may be appreciated from Table II, (1/T2)i was consistently higher, b y some 21 s-' on the average at a Larmor frequency of 15.7 MHz, irrespective of the sequence of measurements. The effect of field on (1/T,) was far more subtle; although an average increase o f some 4 s-1 was observed after the field intensity was halved, the magnitude of the effect was less than that of experimental error and therefore of equivocal significance.
297 T A B L E II EFFECT OF MAGNETIC FIELD STRENGTH ON THE LONGITUDINAL RELAXATION AND THE SLOW COMPONENT (T2) I OF THE TRANSVERSE RELAXATION TIME
TIME (T l)
T h e samples o f E x p t s E, H a n d J were first studied at a L a r m o r f r e q u e n c y o f 1 5 . 7 M H z ( " h i g h " ) a n d s u b s e q u e n t l y at a f r e q u e n c y o f 7 . 8 5 M H z C ' l o w " ) ; the samples o f E x p t s F, I a n d K were studied in reverse order. T h e results d e m o n s t r a t e that ( 1 / T 2 ) I w a s c o n s i s t e n t l y b u t m o d e s t l y increased b y l o w e r i n g the magnetic field; qualitatively similar, b u t m o r e e q u i v o c a l changes w e r e n o t e d in ( 1 / T 1 ).
Expt.
( 1 / T 1) (s- 1 )
( l / T 2 ) I (s -1)
Conditions of incubation
Low
High
A
Low
E
49
42
7
92
76
16
F
44
48
- 4
103
70
33
G
--
42
--
--
66
--
H
46
42
4
88
68
21
I
43
37
6
86
66
20
J
44
38
6
86
70
16
K
--
36
--
99
81
18
Average -+S.E.
4 -+2
High Fresh Ringer's solution K-free Ringer's s o l u t i o n 2 3 h, 4°C Ringers s o l u t i o n 4 6 h, 4 ° C K-free Ringer's s o l u t i o n 4 0 h, 4°C K-free R i n g e r ' s s o l u t i o n 3 1 . 5 h, 4°C Ringers s o l u t i o n 4 4 . 5 h~ 4 ° C K-free Ringer's s o l u t i o n 58 h, 4°C
21 +- 3
Discussion The results of the present studies have confirmed that the transverse relaxation time (T2) of 2 s Na within frog striated muscle consists o f at least two exponential components, (T2)i and (T2)II. The average value of (1/T2)i for all experiments at 22--24°C at a Larmor frequency (W) of 15.7 MHz (9.9 • 107 tad • sec-' ) was 73 s-' (Tables I and II). Measurements of the rapid component were considerably less precise, but (1/T2)II was found to be of the order of magnitude of 350 s-~ under the same conditions. As described previously, the longitudinal relaxation time (T~) was found to consist only of a single exponential component; the mean value of (1/T1) under the above conditions was 41 s-i . From Table I and Fig. 1, it is clear that (1/T~) was directly dependent upon (1/0), while (1/T2)i was not strongly influenced, if at all, by (0) over the range of temperatures studied. The difference (1/T2)I--(1/T~ ) was inversely dependent upon (1/8). (1/T2)I was, to some extent, inversely dependent upon the strength (Ho) of the steady magnetic field, while the effect of (Ho) on (1/TI) was even less marked (Table II). The results at high field (T, ¢ T2, dependence of (T2)i on 8) might be interpreted in terms of distribution of populations of Na within muscle, char-
298
acterized by different chemical shifts, with a chemical exchange between these various populations. However, chemical shifts of the 23 Na nucleus are characteristically small [ 2 8 ] . Furthermore, if the deviation in the behaviour of muscle from that in free solution were primarily determined by a distribution of chemical shifts, (l/T2)i should be directly dependent upon (Ho), whereas a modest inverse dependence was, in fact, observed. Therefore, quadrupole interactions seem to be primarily responsible for the effects noted in muscle. In order to develop a semiquantitative analysis, the current results will be examined within the framework of the following simplest possible model accommodating the data. A rapid exchange is envisaged between b o u n d and free species within a homogenous phase of Na ÷, resulting in a single population of 23 Na nuclei, with respect to NMR parameters. On the basis of the equations presented in Appendix A, and assuming a conservative estimate of the quadrupolar coupling constant (on the basis of the considerations of Appendix B), the approximate fractional binding of Na within the cell may then be calculated. Specifically, one species (f) of Na ÷ is considered free in solution within the cell, and is characterized by the correlation time Tf, the relaxation times (T1 f), (T2~)I and (T2~)ix, and by the mole fraction Pf; WT~ < 1. The second species (s), considered b o u n d to macromolecules within the cell is characterized b y a longer correlation time %, the relaxation times (T1 s), (T2 s), and (T2~)II, and by Ps, the mole fraction of Na ÷ bound; W%/> 1. Development of this model as in Appendix A leads to Eqns 18A and 24A: 2
2
(18A) X = 1/(1 + W2or~)-- 1/(1 + 16 W2oT~)
p~D2 =[ (5/4)(1/T~)H'2W° (W°/v~°°2--~) ]
(24A)
1 + 1/(:! + 4Wo2r~) where D is 1/4 of the quadrupolar coupling constant (e 2 qQ), (1/T2)II,2 wo is (1/T2)ix measured at a Larmor frequency of 2Wo, and X is defined by Eqn 17A of Appendix A: X =
(1/T2),I (1/T2)I, Wo -- (1/T~)b 2wo
Using Eqn 16A and the average values (Table lI) for [(1/T2s)i. Wo-(1/T2 s)i. 2 w o ] and (1/T2)ii, 2 , o of 21 s-' and 350 s-~ , respectively, the value for X m a y be calculated and introduced into Eqn 18A, which m a y then be solved for (W2oT~). Eqn 18A is satisfied when (WCor~) equals either 14.3 or 0.009. However, the following consideration indicates that only the solution (WCor~) = 14.3 is physically meaningful. From Eqns 9A, 12 A and 14A of Appendix A,
(1/T2~)II, >~ (1/T2s)I
(1)
From Eqns 1A and 2A of Appendix A, and from Eqn 1 above, 1 + 4Wo:r~ >> 1
(2)
299 Both E q n s l 8 A and 2 are satisfied when (W2or~)= 14.3, but n o t when (W2or~i) = 0.009; therefore, the former value constitutes an unique solution. introducing 1 4 . 3 for (Wo1"s) 2 2 into Eqn 24A, we find t h a t (PsD 2) = 5.61 • I ~ 9 tad 2 • S-2 . From the considerations of Appendix B, the value used by Chen and Reeves [19] of 0.8 MHz (5.0 • 106 tad • s-1 ) is a conservative lower bound for the quadrupolar coupling constant, so t h a t 0.2 MHz ( 1 . 3 - 1 0 6 tad • s-1 ) is a reasonable estimate of D. From these values, Ps is f o u n d to be 0 . 3 6 . 1 0 -2 . Even in the unlikely and extreme case t h a t e 2 qQ is as low as 0.5 MHz (3.1 • 106 tad • s-' ), Ps can be calculated to be 0.91 • 10 -2 . Therefore, within the framework of the simplest possible interpretations of the data, and subject to the realistic estimate of D, less than 1% of the total intracellular Na t appears to be bound. More complex models m a y , of course, be considered in evaluating the data presented. For example, muscle m a y be characterized by a certain long-range ordering similar to t h a t found in liquid crystals [17,21]. This ordering might arise from long-range polarization of the aqueous medium, or from a rapid exchange between immobilized and free fractions of Na t within domains. In this model, diffusion from domain to domain could modulate the average quadrupolar interaction; since the extent of the ordering could be large, this modulation might introduce a relatively long correlation time and provide contributions to the measured relaxation parameters [21]. However, in this and in other more complex interpretations of the data, the following considerations strongly suggest that only some few percent of the total Na* can be immobilized within striated muscle. The mean value for (1/T1) was found to be 41 s-~ ; as m a y be appreciated from Eqns 1A and 5A, 41 s-~ is then an upper b o u n d to (l/T2)I within each domain. This value is only 2--3 times greater than t h a t characterizing Na* in free solution [26]. Furthermore, (1/T2) was f o u n d to depend only weakly, and (1/T1) to depend n o t at all upon (Ho). If by "binding", we refer to severely restricted molecular m o v e m e n t of Na t with respect to its environment (two or more orders of magnitude more restricted than t h a t in water), it m a y be calculated t h a t no appreciable fraction of the intracellular Na* can be considered immobilized. Our calculations are very much based on the experimentally derived value for X (= (l/T2)II/A(1/T2 )i, In particular, the value for A(1/T2 )i in the denominator represents the small difference between two numbers measured with limited accuracy. A number of factors may have influenced the magnitude of (1/T2)i at the two frequencies, and thus modified the magnitude of the difference between them. As m a y be appreciated from Eqn 7A of the Appendix, when Wr ~ 1, the position of the resonance line depends on r. In a system as heterogeneous as muscle, a distribution o f correlation times, rather than a single correlation time, would be expected to characterize the bound states of Na in the tissue. Depending on the strength of the magnetic field, a contribution to ( l / T 2 ) i might thereby arise. Experimental factors m a y also have contributed to a systematic increase in (1/T~)i. Because of the unfavorable signal to noise ratio of 23 Na in muscle, it was necessary to entirely fill the space within the radio frequency (RF) coil
300 with the sample; such a procedure enhances the inhomogeneity of the R F magnetic field. In addition, diffusion within magnetic field gradients may cause experimental error. These sources of experimental error should be of particular significance at low magnetic field strength, where the precision of measurement was more limited, and where measurements of (T2) were necessarily performed with pairs of pulses of 90 ° and 180 ° , rather than with the pulse sequence used at higher field. Therefore, the data obtained are likely to provide an upper b o u n d to the true value of A(1/T2 )i; lower values would indicate an even smaller fraction of b o u n d sodium. Eqns 1A, 4A and 5A indicate that whenever (1/T2)i is field-dependent, a similar dependence of (1/T1) is expected. No such field-dependence o f (1/T1) was observed. Therefore it seems reasonably clear that the measured value for A(1/T2 )i reflects some or all of the experimental limitations noted above. We m a y conclude that several data are of particular interest. The (1/T2)i characterizing 23 Na in muscle is approximately 4--5 times larger than that in dilute aqueous solution, and is only weakly dependent u p o n the magnetic field intensity, while (1/T2)iI is within an order of magnitude larger than (1/T:)i. These observations, taken together with the estimations of the quadrupolar coupling constant, suggest that the fraction of b o u n d ions whose tumbling is severely restricted does not exceed some few percent of the total Na population contributing to the observed NMR signal. Appendix A
Development of equations used for data analysis On the basis of Redfield's General Relaxation Theory [ 2 9 ] , Hubbard [30] and Rubinstein et al. [31] have derived a formalism for the relaxation of transverse and longitudinal nuclear magnetization due to quadrupolar interaction. For nuclides such as 23 Na possessing a spin quantum n u m b e r (I) of 3/2, both relaxation processes can be analytically expressed as a superposition of two exponential decays. The t w o time constants characterizing transverse relaxation are: 4 (1/T2)I = - - D 2 r[1/(1 + W2r 2) + 1/(1 + 4W2T2)] (1A) 5 4 (1/T:)II =--D2T[1 + 1/(1 + 5
W2r2)]
(2A)
where T is the correlation time, and W is the Larmor frequency, for I = 3/2, and axial symmetry. D -
e2qQ 4
(3A)
where e 2 qQ is the quadrupole coupling constant. (l/T2)i characterizes the decay of 40% of the signal and can be attributed to the transition b e t w e e n the +(1/2) and --(1/2) Zeeman energy levels. (1/T2)ii characterizes the decay of the remaining 60% of the signal, and is attributable to the transitions between the +(3/2) and +(1/2), and --(1/2) and --(3/2) energy levels.
301 The following expressions have been obtained for the two longitudinal relaxation times: 8
(1/T1)I = ~ D2T/( 1 + 4W2r2 )
(4A)
(1/Ti)H =8D2 r/(1 + W2r2) 5
(SA)
(l/T1)i characterizes the decay of 20% of the signal intensity and (l/T1)ii characterizes the remaining 80%. Since (1/TI)i can differ from (1/T~)H at most by a factor of 4, and reflects only 20% of the signal intensity, (1/Tx)i could not have been detectable within the limits of resolution of the present study. Therefore, in the current context, the term (1/T~) shall refer specifically to (1/T1)H. The validity ol the expressions above is limited to correlation times small enough such that 1 >>Dr. On the basis of more general considerations the expression in Eqn.lA has recently been extended by Baram et al. [32] to larger values of the correlation time r, such that 1 ~ (D/W)Dr. 4 298 (D) 2 (1/T2)I =--D2r5 [1/(1 + W2r2) + 1/(1 + 4W2r2)] + ~ - ~ ~ D~r
(6A)
On the basis of the same theory, a frequency shift (SW), dependent upon D, T and W is expected. 4 D2 5W =-- m [W2r2/(1 + W2r2)_ 2W2~2/(1 + 4W2r2)] (7A) 5 W In order to apply these equations to the data presented, the simple model of a homogenous phase of two species of Na ÷ is considered. One species (f) is considered free in solution within the cell, and is characterized by the correlation time rt, the relaxation times (Tit), (T2f)I and (T2fhi, and by the mole fraction Pf; Wrf ~ 1. The second species (s), considered bound by macromolecules within the cell, is characterized by a longer correlation time rs, the relaxation times (Tls), (T2s)i and (TI,)II, and by Ps, the mole fraction of Na ÷ bound; WTs ~ 1. The measured relaxation times will therefore consist of contributions from both species of Na ÷ [33] : (l/T1) = (Ps/Tss)
+
(Pf/Tlf)
(1/T2)I = (Ps/T2s)I + (P~/T2f)I (1/T:)ix = (P./T2.)II +
(P~/T2f)H
(8A) (9A) (10A)
Since Species f is considered to be free in solution, Wrf ~ I, so that Eqns 1A, 2 A and 5 A require that:
(Pt/Tlf) = (Pf/T2f)! = (Pf/T2f )xl
(llA)
Furthermore, from the same equations all of the terms of Eqn 11A are independent of (H o). From the data presented, ( 1 / T l ) i i = 350 S-1 and (1/T2)I = 73 s-1 , so that to a first approximation:
302
(1/T2)n >>(1/T2)I
(12A)
From Eqns 9A--12A: ( P f / T 2 f ) i I + ( P s / T 2 s ) i i = (1/T2)II >~ (1/T2)I > ( P f / T 2 f ) i i
(13A)
From 10A and 13A, (1/T2)II ~ (P./T2,)II
(14A)
Since (Pf/T2 f)x and (P~/T2 f)i x are independent of Ho, A (1/T2)I -= (1/T2h, Wo -- (1/T2)I, 2Wo
(15A)
From 9A and 15A, A(1/T2), = (P,) [(1/T2,)I, w° -- (1/T2.)I, ~w° ]
(16A)
where the indices (Wo) and (2Wo) refer to measurements performed at Larmor frequencies of 7.85 MHz (4.93 rad • s-') and 15.7 MHz (9.87 tad • sec-'), respectively. X = (1/T2)II / A(1/T2)I
(17A)
From Eqns 14A, 16A, and 17A,
X=
(1/T2s)n (I/T2,),, wo - - ( I / T 2 , ) , , 2w°
(18A)
From Eqns 2A and 14A, (1/T2)n,2w ° = (4/5) P, D2r,[l + l / { l + 4 W~,T.)] 2 2
(19A)
From Eqns 1A and 16A, 2 2 A(1/T2)I = (4/5)P, D2r, [1/(1 + Wor.)
_
1/(1 + 16W2or~)]
(20A)
(PsD 2 ) and (rs) appear as two unknowns. Dividing Eqn 19A by Eqn 20A, 1 + 1/(1 + 4Wo2r~) X =
1/(1 + W:or~) -- 1/(1 + 16W2or~)
"1
J
(21A)
From 19A, [ (514)(llT2)n, 2w¢ ( l / r . ) ] (~sD2) = k 1 + 1/(1 + 4~V2oT~) J
(22A)
(1/r.) = (Wo)lx/W2o r.2
(23A)
From 22A and 23A,
(PsD2) =
(5/4)(1/T2)H, 2Wo (Wo/V~oor~) 1 + 1/(1 + 4W2or~)
(24A)
Eqns 17A, 18A and 24A are the basic equations used in the text for data analysis.
303 Appendix B
Estimation of the quadrupolar coupling constant The quadrupolar coupling constant (e 2 qQ) cannot be directly calculated from the results of the present study. However, from the following considerations, the value of 0.8 MHz (5.0 • 106 tad • s-' ) used by Chen and Reeves [19] seems to be a conservative lower bound for e 2 qQ. It has been well established that the correlation times determining the quadrupolar relaxation rat~s of the alkali metal ions in aqueous solutions reflect the reorientation rates of the water molecules in the hydration sphere of the cations [28,34] *. The reorientation rate of water molecules in bulk water is characterized by a correlation time r = 3 • 10 -12 s [28 34]. In general, the correlation times characterizing the molecular tumbling of water within the hydration spheres of the alkali metal ions is n o t greatly different from this value [28,34]. Reorientation of the water molecules in the vicinity of Li ÷ has been reported to be characterized by a (r) of 7 • 10-' 2 s [35], while the correlation times for water in the vicinity of the other alkali ions monotonically falls with increasing size of the non-hydrated nucleus [36]. The reorientation rate of water molecules within the sphere of hydration of Na ÷ is therefore within the range of 3--7 • 10-12 s. From Eqn 5A and the value of (1/T1) = 18 s-' for Na ÷ in dilute aqueous solution [26], the quadrupolar coupling constant characterizing Na ÷ in water is 0.8--1.2 MHz (5.0--7.5 • 106 rad • sec-' ). In a bound state, a less symmetric arrangement of ligands would be expected than in dilute aqueous solution, and therefore a larger value for e 2 qQ should prevail. Even in the unlikely event that bound Na is surrounded by a symmetric cage of dipoles similar to that surrounding Na complexed to a variety of ionophores, e2qQ would n o t be very different from 0.8 MHz ( 5 . 0 . 1 0 4 t a d " sec-') [37]. The m i n i m u m value for such complexed Na has been estimated to be 0.5 MHz, characterizing the Na within monactin, where Na is t h o u g h t to exist in a very regular cubic cage of oxygens. As noted in the text, the precise value for the quadrupolar coupling constant is not critical; setting e 2 qQ = 0.8 or 0.5 MHz leads to qualitatively similar conclusions. The value of 0.8 MHz is used in the text as the most realistic conservative estimate of e 2 qQ. Acknowledgements This study was supported, in part, by a Grant-in-Aid (71 847) from the American Heart Association and a Research Grant (GB-40040X) from the National Science Foundation. Dr Civan is an Established Investigator (70 148) of the American Heart Association. References 1 Baker, P.F., H o d g k i n , A.L. a n d Shaw, T.I. ( 1 9 6 1 ) N a t u r e 1 9 0 , 8 8 5 - - 8 8 7 2 0 i k a w a , T., S p y r o p o u l o s , C.S., Tasaki, L a n d Teorell, T. ( 1 9 6 1 ) A c t a Physiol. Scand. 52, 1 9 5 - - 1 9 6 * Elsewhere in t h e t e x t , for p u r p o s e s o f b r e v i t y , we l o o s e l y r e f e r t o t h e rate o f t u m b U n g o f N a + w i t h r e s p e c t t o its e n v i r o n m e n t . We s h o u l d e m p h a s i z e t h a t w e are s p e c i f i c a l l y referring t o t h e rate o f f l u c t u a U o n o f t h e e l e c t r i c field gradient a p p l i e d t o t h e N a + nucleus.
304
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
Tasaki, I., Singer, I. and Takenaka, T. (1965) J. Gen. Physiol. 48, 1095--1123 Huneeus-Cox, F., Fernandez. H.L. and Smith, B.H. (1966) Biophys. J. 6, 675--689 Hoffman, J.F. (1962) J. Gen. Physiol. 45, 837---859 Fenichel, I.R. and Horowitz, S.B. (1969) in Biological Membranes (Dowben, R.M., ed.), pp. 177--221 J. & A. Churchill Ltd., London Hazlewood, C.F., ed. (1973) Ann. N.Y. Acad. Sci. 204, 1--631 Cope, F.W. (1965) Proc. Natl. Acad. Sci. U.S. 54, 225---227 Cope, F.W. (1967) J. Gen. Physiol. 50, 1353--1375 Cope, F.W. (1970) Biophys. J. 10, 843--858 Cope, F.W. (1970) Physiol. Chem. Phys. 2,545--550 Czeisler, J.L., Fritz, Jr, O.G. and Swift, T.J. (1970) Biophys. J. 10, 260--268 Ling, G.N. and Cope, F.W. (1969) Science 163, 1335--1336 Martinez, D., Silvidi, A.A. and Stokes, R.M. (1969) Biophys. J. 9, 1256--1260 Reisin, I.L., Rotunno, C.A., Corehs, L., Kowalewski, V. and Cereijido, M. (1970) Physiol. Chem. Phys. 2, 171--179 R o t u n n o , C.A., Kowalewski, V. and Cereijido, M. (1967) Biochim. Biophys. Acta 135, 170--173 Shporer, M. and Civan, M.M. (1972) Biophys, J. 12, 114--122 Lindblom, G. (1971) Aeta Chem. Scand. 25, 2767--2768 Chen, D.M. and Reeves, L.W. (1972) J. Am. Chem. Soc. 94, 4384--4386 Edzes, H.T., Rupprccht, A. and Berendsen, H.J.C. (1972) Bioehem. Biophys. Res. Commun, 46. 790--794 Berendsen, H.J.C. and Edzes, H.T. (1973) Ann. N.Y. Acad. Sci. 204, 459--480 Civan, M.M. and Podolsky, R.J. (1966) J. Physiol. 184, 511--534 Civan, M.M. and Shporer, M. (1972) Biophys. J. 12,404--413 Carey, M.J. and Conway, E.J. (1954) J. Physiol. 125, 232--250 Beaugd, L.A. and Sjodin, R.A. (1968) J. Physiol. 194, 105--123 Eisenstadt, M. and Friedman, H.L. (1967) J. Chem. Phys. 46, 2182--2193 Hall, C., Richards, R.E., Schulz, G.N. and Sharp, R.R. (1969) Mol. Phys. 16,529--544 Hertz, H.G. (1967) Prog. Nucl. Magn. Resonance Spectrom. 3 , 1 5 9 - - 2 3 0 Redfield, A.G. (1965) in Advances in Magnetic Resonance (Waugh, J.S., ed.), pp, 1--32, Academic Press, New York Hubbard, P.S. (1970) J. Chem. Phys. 53,985--987 Rubinstein, M., Be.ram, A. and Luz, Z. (1971) Mol. Phys. 20, 67--80 Baram, A., Luz, Z. and Alexander, S. (1973) J. Chem. Phys. 58, 4558~-4564 Bull, T.E. (1972) J. Magn. Resonance 8,344--353 Deverell, C. (1969) Progr. Nucl. Magn. Resonance Spetrom. 4, 235--334 O'Reilly, D.E. and Peterson, E.M. (1969) J. Chem. Phys. 51, 4906--4908 Samoilov, O. Ya. (1972:)AnWater and aqueous solutions: Structure, Thermodynamics, and Transport Processes (Home, R.A., ed.), pp. 597---612, Wiley-lnterseienee, New York Haynes, D.H., Pressman, B.C. and Kowalsky, A. (1971) Biochemistry 10, 8 5 2 4 8 6 0
Biochimica et Biophysica Acta, 354 (1974) 291--304 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
BBA 27440
EFFECTS OF TEMPERATURE AND FIELD STRENGTH ON THE NMR RELAXATION TIMES OF 2 3 Na IN FROG STRIATED MUSCLE
MORDECHAI SHPORER and MORTIMER M. CIVAN
Department of Isotope Research, The Weizmann Institute of Science, R(hovot, Israel and the Departments of Physiology and Medicine, University of Pennsylvania School of Medicine Philadelphia, Pa. 191 74 (U.S.A.) (Received February 6th, 1974)
Summary Pulsed NMR techniques have been applied to the study of the relaxation parameters characterizing 23 Na within frog striated muscle. Experiments were performed at 3°C, 22--24°C and 39°C at a Larmor frequency of 15.7 MHz; at 22--24°C, measurements were obtained both at 15.7 MHz and at 7.85 MHz. As previously reported, only a single spin-lattice relaxation time (T1) was observed, but both slow (T~)i and fast (T2)xi components of the spin-spin relaxation time were measured. The effect of temperature (0) upon (1/TI) was qualitatively similar to that reported for 23 Na-in free solution; (0) did not significantly affect (l/T2) over the range of temperatures studied. (l/T2)i, and to a lesser degree, (1/Tt) exhibited a modest inverse dependence of doubtful significance on the Larmor frequency. The data are examined within the framework of a simple specific model; a conservative value is assumed for the quadrupolar coupling constant characterizing immobilized intracellular Na÷. Within this framework, the results suggest that the fraction of bound ions whose molecular tumbling is severely restricted does not exceed some few percent of the total sodium population.
Introduction The composition of the fluid within biological cells differs markedly from that of the fluid bathing the cell exterior. In most cells the intracellular concentration of Na ÷ is considerably lower, and the intracellular concentration of K÷ considerably greater than in the extracellular fluid. It seems clear that this phenomenon must arise, at least in part, from ion-selective transport properties of the plasma membrane [1--5]. However, the composition of the intmcellular fluid may also reflect differential binding properties of sites within the cell. Without attempting a rigorous definition of "binding", the term will be used in the present context to specifically denote restricted molecular motion.
292 A variety of techniques have been utilized in an effort to define the precise a m o u n t and significance of the putative binding of Na and K within the cell [6,7]. In particular the techniques of NMR have appeared to offer considerable promise. The NMR spectrum of 23 Na of living tissue may be measured, following which the tissue m a y be ashed, solvent added to restore the volume, and the NMR spectrum reexamined. Cope [8,9] was the first to observe that the relative intensity of the 23 Na signal before ashing each of several biological preparations was 30--40% of the intensity following ashing. Using pulsed NMR techniques [10], 30--40% of the anticipated signal was found to be characterized by a relatively slow transverse relaxation time (T2); a relatively rapid decay time was also observed and attributed to the remainder of the signal. The simplest interpretation was that the NMR data defined two populations of Na nuclei. One population, consisting of 60--70% of the Na nuclei, was considered bound; the second population, consisting of 30--40% of the Na nuclei, was thought to be free and solely responsible for the NMR-visible spectrum. Whatever exchange existed between the two populations was considered to be slow. A number of investigators have subsequently examined a wider spectrum of biological preparations, confirming Cope's observations, and drawing similar conclusions from the data [ 1 1 - - 1 6 ] . More recently, partly on the basis of studies of the 23 Na spectrum of unoriented liquid crystals of sodium lineolate in water, we have suggested [ 17] that the NMR data obtained from biological tissue need n o t necessarily reflect t w o distinct populations of Na nuclei. Rather, the data may arise from a nuclear quadrupolar interaction affecting a single population (defined in terms of NMR parameters) of Na. Similar data have since been obtained with unoriented liquid crystals of lecithin--Na--cholate in water [18]~ oriented liquid crystals of sodium decyl sulfate--decyl alcohol--Na2 SO4 in water [ 1 9 ] , and oriented DNA samples [ 2 0 ] . This alternative interpretation of the biological data has received strong support from the studies of striated muscle by Berendsen and Edzes [ 2 1 ] . Although t w o c o m p o n e n t s of the spin-spin relaxation time (T2) were observed, as noted previously, only a single spin-lattice relaxation time ( T , ) could be detected. Since these most recent investigations favor the alternative view, it has seemed desirable to estimate the fraction of Na b o u n d within the cell, under the more likely assumption that the NMR spectrum indeed arises from the entire population of Na nuclei. Until now no data have been presented permitting estimation of the fraction b o u n d within this frame of reference. As m a y be appreciated from Eqn 6A of the Appendix, the existence of a narrow central spectra line, per se, at a single temperature and magnetic field strength does n o t necessitate that the tissue Na be entirely free, and m a y even characterize b o u n d Na under certain conditions.* The following experiments were performed in order to examine the effect of temperature and strength of magnetic field u p o n the relaxation times characterizing 23 Na within frog striated muscle. Examination of these data b y means of the equations presented in the Appendix sug* F r o m E q n 6 A , a n a r r o w central c o m p o n e n t is p r e d i c t e d in the region o f s l o w t u m b l i n g (W~ ~ 1)~ the m i n i m u m v a l u e o f ( l / T 2 ) I = ( 2 / ~ ( D / W ) 2 (D) w h e n I" = ~ J ~ D . (W is the L a r m o r f r e q u e n c y , T is the correlation time, and D is 1 / 4 o f the q u a d r u p o l a r coupling c o n s t a n t . )
293 gests that only a modest fraction of the Na ÷ within frog striated muscle may be bound, i.e., subject to severe restriction of molecular tumbling. Materials and methods
Sartorius, semitendinosus and gastrocnemius muscles were exised intact from doubly-pithed native Israeli frogs, Rana esculenta, which had been mainrained fasting in water at room temperature. In 3 of the 11 experiments performed, the muscles were rinsed in an aerated Ringer's solution similar to that used previously [22,23] (NaC1 115.5 mM; KCI, 2.5 mM; CaC12 1.8 mM; Na2HPO4, 2.5 mM; NaH2PO4, 0.5 mM; and d-tubocurarine chloride, 9 mg/ liter). After several minutes these muscles were blotted dry on Whatman No. 542 filter paper, and gently packed in a glass test tube (outside diameter 10 mm, wall thickness 0.5 mm) to a height of 1--1.5 cm. Because of the low intracellular sodium concentration of fresh muscle, the signal to noise ratio was marginally adequate for the measurements performed, approaching the limit of resolution of the current apparatus. In order to enhance this precision in the remaining 8 studies, the intracellular Na concentration was enhanced in one of two ways. In 3 experiments the muscles were incubated at 4°C for 44.5--104 h in the standard Ringer's solution, before undergoing NMR analysis. In the remaining 5 experiments, the sodium concentration was enhanced by incubating the tissues in low K Ringer's solution, similar to the techniques used by Carey and Conway [24], Beaug~ and Sjodin [25], and Ling and Cope [13]. The muscles were immersed immediately in a K-free Ringer's solution, identical to the solution discussed above except for the absence of KC1; these preparations were subsequently incubated at 4°C for 23--58 h. The details of the tissue incubation are presented for each experiment in Tables I and II. Similar results were obtained for fresh and incubated tissues. All measurements were performed with a Bruker Pulsed NMR B-KR Spectrometer (Bruker Physik AG, Karlsruhe, Germany) at two frequencies (W), 15.7 MHz (9.9 • 107 tad • s-1 ) and 7.85 MHz (4.9 • 107 tad • s-1 ); the strength (Ho) of the steady magnetic field provided by a 12 inch model V 4012 A-HR electromagnet system of a Varian (Palo Alto, California) DP-60 NMR spectrometer was adjusted appropriately for each frequency. The temperature of the sample was controlled by flowing N2 gas, thermally regulated by a Bruker B-ST 100/700 Heating Unit, around the sample. The temperature of the muscles was measured by means of a thermocouple placed 1 cm below the test tube; previous experience had demonstrated that over the range of temperatures examined, the temperatures of the sample and thermocouple are identical to within 1 ° C. Because of the unfavorable signal-to-noise ratio of the measurements, the NMR signal was continuously averaged by means of a Hewlett-Packard No. 5480B Signal Analyzer System (Santa Clara, Calif.) operated in the average mode. T1 was measured by studying the free-induction decay of the signal following pairs of pulses of 180 ° and 90 ° . Specifically, the height of the decaying signal was measured at a fixed time, within 2 ms following the 90 ° pulse, as a
294 function of the time interval between the initial 180 ° and the subsequent 90 ° pulse. Measurements were performed by continuously displaying the timeaveraged trace of the free induction decay on the oscilloscope; after a satisfactory signal to noise ratio had been attained, the amplitude of the pulse was measured directly on the oscilloscope face. T2 was measured in t w o ways. First, the amplitude of the echo following 90 ° and 180 ° pulses was measured as a function of the separation between the initial 90 ° and subsequent 180 ° pulse. Once again, the time-averaged o u t p u t was continuously displayed on the oscilloscope until the signal to noise ratio permitted adequately precise measurement directly from the oscilloscope face. Second, the signal to noise ratio of the measurements performed at high magnetic field intensity was sufficiently favorable to permit use of the CarrPurcell-Meiboom-Gill Pulse Sequence, employing intervals of 1 and 2 ms between the 180 ° pulses. After a period of time-averaging, usually of 10--20 min duration, the o u t p u t was recorded on a paper chart recorder and the amplitude decay measured. No significant differences :were observed between results obtained by the two different techniques. Since the first technique is sensitive to the effects of ion diffusion and magnetic field gradients, these effects must have been of minor significance in comparison with the magnitude of the experimental error at the high magnetic field. The relaxation times T1 and T2 were finally calculated by plotting the data on semi-log paper and choosing b y eye the line with best fit. In general, the results presented in Tables I and II are averages obtained from ,qome four such measurements. Results In the current studies, measurements of T1 revealed b u t a single exponential decay. However, measurements of T~ indicated the presence of b o t h a rapid and slow component, as previously reported [21]. In those experiments where application of the Carr-Purcell-Meiboom-Gill Pulse Sequence technique was feasible, the fast c o m p o n e n t (1/T2)ii was found to be between 230 and 690 s -1, with a mean value of 350 s-'. The precision of measurement of ( l / T 2 ) i i was, however, inadequate to provide more than a rough estimate of this parameter; furthermore, the data were t o o imprecise to conclude whether or n o t ( l / T 2 ) i i was a function of magnetic field strength (Ho) or of temperature (0) over the range of experimental conditions examined. The effects of changes in temperature on the relaxation times (T1) and (T~)i (the slow c o m p o n e n t of transverse decay) are presented in Table I. In each of the four experiments of the series, (1/T1) and (1/T2)I were successively measured at the ambient temperature of the r o o m (22--24°C), at 3°C, at 39°C, and finally at room temperature once again; the range of temperatures studied was chosen to depart as little as possible from physiologically significant conditions. No systematic changes were noticed in the measurements over the periods of observation of as long as 3 h at each temperature. It should be noticed, however, that both (1/T~) and (1/T2)i did increase somewhat over the approximately 8--12 h period required for each experiment. These slow time-dependent changes in the relaxation times were one of the
295 TABLE I EFFECTS OF TEMPERATURE ON THE LONGITUDINAL R E L A X A T I O N TIME (T 1) AND THE SLOW COMPONENT (T2) I OF THE TRANSVERSE R E L A X A T I O N TIME The data are p r e s e n t e d in the same order as the s e q u e n c e of the e x p e r i m e n t a l p r o t o c o l (22--24°C, 3°C, 39°C and finally 22--24°C o n c e again). The final c o l u m n at the right describes t h e c o n d i t i o n s o f the i n c u b a t i o n p r o c e d u r e . Muscles w e r e b a t h e d either in the standard Ringer's s o l u t i o n or in K-free Ringer's s o l u t i o n and either studied straightaway ("fresh"), or after i n c u b a t i o n at 4°C for the p e r i o d of t i m e indicated. ( 1 / T I ) is s e e n t o be inversely d e p e n d e n t u p o n temperature, w h i l e ( 1 / T 2 ) I appears to be i n d e p e n d e n t o f t e m p e r a t u r e over the range studied; the difference b e t w e e n these t w o parameters seems to be directly d e p e n d e n t o n temperature.
Expt
Temp. (°C)
(1 IT 1) (s-l)
(1 IT2) I (s-1)
(1 IT2) I - (1 IT1) (s-l)
Conditions of incubation
A
24 3 39 23
41 58 35 46
76 80 64 78
35 22 29 31
Standard Ringer's solution 104 h, 4°C
B
24 3 39 22
45 77 38 48
72 88 83 86
28 11 45 39
Fresh Ringer's solution
C
24 3 39 23
46 78 43 50
83 94 88 94
37 16 46 44
Fresh Ringer's solution
D
23 3 39 23
38 53 38 47
70 86 76 91
32 34 38 44
Ringer's solution K-free, 23 h, 4°C
~
limiting factors in determing the precision of the current measurements. Although averaging the signal amplitudes over sufficiently long periods enhanced the precision of the measurements, the longer the periods of measurement, the more likely was it to observe a significant spontaneous change within the tissue. The spontaneous changes in (1/Tl) were smaller than the changes induced by altering the temperature. It is clear, then, that (1/T1) was inversely dependent upon temperature. However, no significant changes in (1/T2)i were noted. It should also be observed that, in general, the magnitude of the difference, (1/7'2)I--(1/T1 ), was inversely dependent upon temperatures. The behavior of (1/T2)i and (1/T1) as functions of temperature may be more easily appreciated from Figs 1A and 1B respectively. The normalized data from Table I have been plotted as functions of (1/0) (°K -1 ); normalization was performed by dividing (1/T2)i or (1/Tl) by the corresponding values obtained at 39 ° C. The solid lines have been taken from Fig. 8 of Eisenstadt and Friedman [26], describing the relationship of ( l / T 1 ) for 23 NaC1 in dilute aqueous solutions as a function of (1/0). Eisenstadt and Friedman determined this relationship for (1/T~), using pulsed NMR techniques. Hall et al. [27] have examined the line width of 1 molal 23 NaBr in aqueous solution; their estimations of (1/T2) as a function of (1/0) agree to within 10% of the values reported by Eisenstadt and Friedman. The solid lines may therefore be taken as
296 8°C 59
i ~20
I Exp A o " B o
"
~
24 I
3 F--
A
G •
~2
~
o
,o
./" I
"o 1
2.0
I
! --I
I
B
o
~-
o
,4
•
e ,0
I
I
I
I
I
32
33
34
35
36
t
I/8°K x I 0 ~'
Fig. 1. T e m p e r a t u r e d e p e n d e n c e o f ( l / T 2 ) a n d ( l / T 1 ) o f 2 3 N a in m u s c l e . T h e d a t a p o i n t s h a v e b e e n d e r i v e d f r o m t h e r e s u l t s o f t h e f o u r e x p e r i m e n t s p r e s e n t e d in T a b l e I. N o r m a l i z a t i o n o f t h e d a t a o f Figs 2 A a n d 2 B h a s b e e n p e r f o r m e d b y d i v i d i n g t h e m e a s u r e d v a l u e s a t a g i v e n t e m p e r a t u r e b y t h e c o r r e s p o n d i n g v a l u e s a t 3 9 ° C . T h e s o l i d l i n e s d e s c r i b i n g t h e r e l a t i o n s h i p f o r 2 3 N a in d i l u t e a q u e o u s s o l u t i o n w e r e o b t a i n e d f r o m Fig. 8 o f r e f . 2 6 .
a satisfactory reflection of the behavior both of (1/T2)x and (1/T1) as functions of ( l / P ) for Na in dilute aqueous solution. It will be appreciated from Fig. 1B that the behavior of (l/T1) of 23 Na in muscle as a function of ( l / P ) is qualitatively similar to, albeit quantitatively less striking than, that of 23 Na in aqueous solution. However, as demonstrated b y Fig. 1A, it is d o u b t f u l that any change whatsoever was induced in the (l/T2)i of 23 Na in muscle, over the range o f temperatures examined.. In aqueous solution, as noted in the Discussion, under conditions of rapid molecular tumbling, TI = T2. Furthermore, (1/T1) and (1/T2) should increase similarly, as (1/0) is increased. We might suspect, therefore, that the relaxation times (T2)i, and to some extent, T~, might contain contributions reflecting slow molecular tumbling. If so, the relaxation times would be expected to depend on Ho. On the basis of these considerations, the following experiments were performed. In Experiments E, H and J (Table II), the preparations were studied at Larmor frequency (W) of 15.7 MHz. The frequency wa~ then reduced to 7.8 MHz, and the samples were left for 2--10 h, while the magnetic field restabilized. In Experiments F, I and K, the sequence was reversed; the muscles were first studied at the lower, and subsequently at the higher field. As may be appreciated from Table II, (1/T2)i was consistently higher, b y some 21 s-' on the average at a Larmor frequency of 15.7 MHz, irrespective of the sequence of measurements. The effect of field on (1/T,) was far more subtle; although an average increase o f some 4 s-1 was observed after the field intensity was halved, the magnitude of the effect was less than that of experimental error and therefore of equivocal significance.
297 T A B L E II EFFECT OF MAGNETIC FIELD STRENGTH ON THE LONGITUDINAL RELAXATION AND THE SLOW COMPONENT (T2) I OF THE TRANSVERSE RELAXATION TIME
TIME (T l)
T h e samples o f E x p t s E, H a n d J were first studied at a L a r m o r f r e q u e n c y o f 1 5 . 7 M H z ( " h i g h " ) a n d s u b s e q u e n t l y at a f r e q u e n c y o f 7 . 8 5 M H z C ' l o w " ) ; the samples o f E x p t s F, I a n d K were studied in reverse order. T h e results d e m o n s t r a t e that ( 1 / T 2 ) I w a s c o n s i s t e n t l y b u t m o d e s t l y increased b y l o w e r i n g the magnetic field; qualitatively similar, b u t m o r e e q u i v o c a l changes w e r e n o t e d in ( 1 / T 1 ).
Expt.
( 1 / T 1) (s- 1 )
( l / T 2 ) I (s -1)
Conditions of incubation
Low
High
A
Low
E
49
42
7
92
76
16
F
44
48
- 4
103
70
33
G
--
42
--
--
66
--
H
46
42
4
88
68
21
I
43
37
6
86
66
20
J
44
38
6
86
70
16
K
--
36
--
99
81
18
Average -+S.E.
4 -+2
High Fresh Ringer's solution K-free Ringer's s o l u t i o n 2 3 h, 4°C Ringers s o l u t i o n 4 6 h, 4 ° C K-free Ringer's s o l u t i o n 4 0 h, 4°C K-free R i n g e r ' s s o l u t i o n 3 1 . 5 h, 4°C Ringers s o l u t i o n 4 4 . 5 h~ 4 ° C K-free Ringer's s o l u t i o n 58 h, 4°C
21 +- 3
Discussion The results of the present studies have confirmed that the transverse relaxation time (T2) of 2 s Na within frog striated muscle consists o f at least two exponential components, (T2)i and (T2)II. The average value of (1/T2)i for all experiments at 22--24°C at a Larmor frequency (W) of 15.7 MHz (9.9 • 107 tad • sec-' ) was 73 s-' (Tables I and II). Measurements of the rapid component were considerably less precise, but (1/T2)II was found to be of the order of magnitude of 350 s-~ under the same conditions. As described previously, the longitudinal relaxation time (T~) was found to consist only of a single exponential component; the mean value of (1/T1) under the above conditions was 41 s-i . From Table I and Fig. 1, it is clear that (1/T~) was directly dependent upon (1/0), while (1/T2)i was not strongly influenced, if at all, by (0) over the range of temperatures studied. The difference (1/T2)I--(1/T~ ) was inversely dependent upon (1/8). (1/T2)I was, to some extent, inversely dependent upon the strength (Ho) of the steady magnetic field, while the effect of (Ho) on (1/TI) was even less marked (Table II). The results at high field (T, ¢ T2, dependence of (T2)i on 8) might be interpreted in terms of distribution of populations of Na within muscle, char-
298
acterized by different chemical shifts, with a chemical exchange between these various populations. However, chemical shifts of the 23 Na nucleus are characteristically small [ 2 8 ] . Furthermore, if the deviation in the behaviour of muscle from that in free solution were primarily determined by a distribution of chemical shifts, (l/T2)i should be directly dependent upon (Ho), whereas a modest inverse dependence was, in fact, observed. Therefore, quadrupole interactions seem to be primarily responsible for the effects noted in muscle. In order to develop a semiquantitative analysis, the current results will be examined within the framework of the following simplest possible model accommodating the data. A rapid exchange is envisaged between b o u n d and free species within a homogenous phase of Na ÷, resulting in a single population of 23 Na nuclei, with respect to NMR parameters. On the basis of the equations presented in Appendix A, and assuming a conservative estimate of the quadrupolar coupling constant (on the basis of the considerations of Appendix B), the approximate fractional binding of Na within the cell may then be calculated. Specifically, one species (f) of Na ÷ is considered free in solution within the cell, and is characterized by the correlation time Tf, the relaxation times (T1 f), (T2~)I and (T2~)ix, and by the mole fraction Pf; WT~ < 1. The second species (s), considered b o u n d to macromolecules within the cell is characterized b y a longer correlation time %, the relaxation times (T1 s), (T2 s), and (T2~)II, and by Ps, the mole fraction of Na ÷ bound; W%/> 1. Development of this model as in Appendix A leads to Eqns 18A and 24A: 2
2
(18A) X = 1/(1 + W2or~)-- 1/(1 + 16 W2oT~)
p~D2 =[ (5/4)(1/T~)H'2W° (W°/v~°°2--~) ]
(24A)
1 + 1/(:! + 4Wo2r~) where D is 1/4 of the quadrupolar coupling constant (e 2 qQ), (1/T2)II,2 wo is (1/T2)ix measured at a Larmor frequency of 2Wo, and X is defined by Eqn 17A of Appendix A: X =
(1/T2),I (1/T2)I, Wo -- (1/T~)b 2wo
Using Eqn 16A and the average values (Table lI) for [(1/T2s)i. Wo-(1/T2 s)i. 2 w o ] and (1/T2)ii, 2 , o of 21 s-' and 350 s-~ , respectively, the value for X m a y be calculated and introduced into Eqn 18A, which m a y then be solved for (W2oT~). Eqn 18A is satisfied when (WCor~) equals either 14.3 or 0.009. However, the following consideration indicates that only the solution (WCor~) = 14.3 is physically meaningful. From Eqns 9A, 12 A and 14A of Appendix A,
(1/T2~)II, >~ (1/T2s)I
(1)
From Eqns 1A and 2A of Appendix A, and from Eqn 1 above, 1 + 4Wo:r~ >> 1
(2)
299 Both E q n s l 8 A and 2 are satisfied when (W2or~)= 14.3, but n o t when (W2or~i) = 0.009; therefore, the former value constitutes an unique solution. introducing 1 4 . 3 for (Wo1"s) 2 2 into Eqn 24A, we find t h a t (PsD 2) = 5.61 • I ~ 9 tad 2 • S-2 . From the considerations of Appendix B, the value used by Chen and Reeves [19] of 0.8 MHz (5.0 • 106 tad • s-1 ) is a conservative lower bound for the quadrupolar coupling constant, so t h a t 0.2 MHz ( 1 . 3 - 1 0 6 tad • s-1 ) is a reasonable estimate of D. From these values, Ps is f o u n d to be 0 . 3 6 . 1 0 -2 . Even in the unlikely and extreme case t h a t e 2 qQ is as low as 0.5 MHz (3.1 • 106 tad • s-' ), Ps can be calculated to be 0.91 • 10 -2 . Therefore, within the framework of the simplest possible interpretations of the data, and subject to the realistic estimate of D, less than 1% of the total intracellular Na t appears to be bound. More complex models m a y , of course, be considered in evaluating the data presented. For example, muscle m a y be characterized by a certain long-range ordering similar to t h a t found in liquid crystals [17,21]. This ordering might arise from long-range polarization of the aqueous medium, or from a rapid exchange between immobilized and free fractions of Na t within domains. In this model, diffusion from domain to domain could modulate the average quadrupolar interaction; since the extent of the ordering could be large, this modulation might introduce a relatively long correlation time and provide contributions to the measured relaxation parameters [21]. However, in this and in other more complex interpretations of the data, the following considerations strongly suggest that only some few percent of the total Na* can be immobilized within striated muscle. The mean value for (1/T1) was found to be 41 s-~ ; as m a y be appreciated from Eqns 1A and 5A, 41 s-~ is then an upper b o u n d to (l/T2)I within each domain. This value is only 2--3 times greater than t h a t characterizing Na* in free solution [26]. Furthermore, (1/T2) was f o u n d to depend only weakly, and (1/T1) to depend n o t at all upon (Ho). If by "binding", we refer to severely restricted molecular m o v e m e n t of Na t with respect to its environment (two or more orders of magnitude more restricted than t h a t in water), it m a y be calculated t h a t no appreciable fraction of the intracellular Na* can be considered immobilized. Our calculations are very much based on the experimentally derived value for X (= (l/T2)II/A(1/T2 )i, In particular, the value for A(1/T2 )i in the denominator represents the small difference between two numbers measured with limited accuracy. A number of factors may have influenced the magnitude of (1/T2)i at the two frequencies, and thus modified the magnitude of the difference between them. As m a y be appreciated from Eqn 7A of the Appendix, when Wr ~ 1, the position of the resonance line depends on r. In a system as heterogeneous as muscle, a distribution o f correlation times, rather than a single correlation time, would be expected to characterize the bound states of Na in the tissue. Depending on the strength of the magnetic field, a contribution to ( l / T 2 ) i might thereby arise. Experimental factors m a y also have contributed to a systematic increase in (1/T~)i. Because of the unfavorable signal to noise ratio of 23 Na in muscle, it was necessary to entirely fill the space within the radio frequency (RF) coil
300 with the sample; such a procedure enhances the inhomogeneity of the R F magnetic field. In addition, diffusion within magnetic field gradients may cause experimental error. These sources of experimental error should be of particular significance at low magnetic field strength, where the precision of measurement was more limited, and where measurements of (T2) were necessarily performed with pairs of pulses of 90 ° and 180 ° , rather than with the pulse sequence used at higher field. Therefore, the data obtained are likely to provide an upper b o u n d to the true value of A(1/T2 )i; lower values would indicate an even smaller fraction of b o u n d sodium. Eqns 1A, 4A and 5A indicate that whenever (1/T2)i is field-dependent, a similar dependence of (1/T1) is expected. No such field-dependence o f (1/T1) was observed. Therefore it seems reasonably clear that the measured value for A(1/T2 )i reflects some or all of the experimental limitations noted above. We m a y conclude that several data are of particular interest. The (1/T2)i characterizing 23 Na in muscle is approximately 4--5 times larger than that in dilute aqueous solution, and is only weakly dependent u p o n the magnetic field intensity, while (1/T2)iI is within an order of magnitude larger than (1/T:)i. These observations, taken together with the estimations of the quadrupolar coupling constant, suggest that the fraction of b o u n d ions whose tumbling is severely restricted does not exceed some few percent of the total Na population contributing to the observed NMR signal. Appendix A
Development of equations used for data analysis On the basis of Redfield's General Relaxation Theory [ 2 9 ] , Hubbard [30] and Rubinstein et al. [31] have derived a formalism for the relaxation of transverse and longitudinal nuclear magnetization due to quadrupolar interaction. For nuclides such as 23 Na possessing a spin quantum n u m b e r (I) of 3/2, both relaxation processes can be analytically expressed as a superposition of two exponential decays. The t w o time constants characterizing transverse relaxation are: 4 (1/T2)I = - - D 2 r[1/(1 + W2r 2) + 1/(1 + 4W2T2)] (1A) 5 4 (1/T:)II =--D2T[1 + 1/(1 + 5
W2r2)]
(2A)
where T is the correlation time, and W is the Larmor frequency, for I = 3/2, and axial symmetry. D -
e2qQ 4
(3A)
where e 2 qQ is the quadrupole coupling constant. (l/T2)i characterizes the decay of 40% of the signal and can be attributed to the transition b e t w e e n the +(1/2) and --(1/2) Zeeman energy levels. (1/T2)ii characterizes the decay of the remaining 60% of the signal, and is attributable to the transitions between the +(3/2) and +(1/2), and --(1/2) and --(3/2) energy levels.
301 The following expressions have been obtained for the two longitudinal relaxation times: 8
(1/T1)I = ~ D2T/( 1 + 4W2r2 )
(4A)
(1/Ti)H =8D2 r/(1 + W2r2) 5
(SA)
(l/T1)i characterizes the decay of 20% of the signal intensity and (l/T1)ii characterizes the remaining 80%. Since (1/TI)i can differ from (1/T~)H at most by a factor of 4, and reflects only 20% of the signal intensity, (1/Tx)i could not have been detectable within the limits of resolution of the present study. Therefore, in the current context, the term (1/T~) shall refer specifically to (1/T1)H. The validity ol the expressions above is limited to correlation times small enough such that 1 >>Dr. On the basis of more general considerations the expression in Eqn.lA has recently been extended by Baram et al. [32] to larger values of the correlation time r, such that 1 ~ (D/W)Dr. 4 298 (D) 2 (1/T2)I =--D2r5 [1/(1 + W2r2) + 1/(1 + 4W2r2)] + ~ - ~ ~ D~r
(6A)
On the basis of the same theory, a frequency shift (SW), dependent upon D, T and W is expected. 4 D2 5W =-- m [W2r2/(1 + W2r2)_ 2W2~2/(1 + 4W2r2)] (7A) 5 W In order to apply these equations to the data presented, the simple model of a homogenous phase of two species of Na ÷ is considered. One species (f) is considered free in solution within the cell, and is characterized by the correlation time rt, the relaxation times (Tit), (T2f)I and (T2fhi, and by the mole fraction Pf; Wrf ~ 1. The second species (s), considered bound by macromolecules within the cell, is characterized by a longer correlation time rs, the relaxation times (Tls), (T2s)i and (TI,)II, and by Ps, the mole fraction of Na ÷ bound; WTs ~ 1. The measured relaxation times will therefore consist of contributions from both species of Na ÷ [33] : (l/T1) = (Ps/Tss)
+
(Pf/Tlf)
(1/T2)I = (Ps/T2s)I + (P~/T2f)I (1/T:)ix = (P./T2.)II +
(P~/T2f)H
(8A) (9A) (10A)
Since Species f is considered to be free in solution, Wrf ~ I, so that Eqns 1A, 2 A and 5 A require that:
(Pt/Tlf) = (Pf/T2f)! = (Pf/T2f )xl
(llA)
Furthermore, from the same equations all of the terms of Eqn 11A are independent of (H o). From the data presented, ( 1 / T l ) i i = 350 S-1 and (1/T2)I = 73 s-1 , so that to a first approximation:
302
(1/T2)n >>(1/T2)I
(12A)
From Eqns 9A--12A: ( P f / T 2 f ) i I + ( P s / T 2 s ) i i = (1/T2)II >~ (1/T2)I > ( P f / T 2 f ) i i
(13A)
From 10A and 13A, (1/T2)II ~ (P./T2,)II
(14A)
Since (Pf/T2 f)x and (P~/T2 f)i x are independent of Ho, A (1/T2)I -= (1/T2h, Wo -- (1/T2)I, 2Wo
(15A)
From 9A and 15A, A(1/T2), = (P,) [(1/T2,)I, w° -- (1/T2.)I, ~w° ]
(16A)
where the indices (Wo) and (2Wo) refer to measurements performed at Larmor frequencies of 7.85 MHz (4.93 rad • s-') and 15.7 MHz (9.87 tad • sec-'), respectively. X = (1/T2)II / A(1/T2)I
(17A)
From Eqns 14A, 16A, and 17A,
X=
(1/T2s)n (I/T2,),, wo - - ( I / T 2 , ) , , 2w°
(18A)
From Eqns 2A and 14A, (1/T2)n,2w ° = (4/5) P, D2r,[l + l / { l + 4 W~,T.)] 2 2
(19A)
From Eqns 1A and 16A, 2 2 A(1/T2)I = (4/5)P, D2r, [1/(1 + Wor.)
_
1/(1 + 16W2or~)]
(20A)
(PsD 2 ) and (rs) appear as two unknowns. Dividing Eqn 19A by Eqn 20A, 1 + 1/(1 + 4Wo2r~) X =
1/(1 + W:or~) -- 1/(1 + 16W2or~)
"1
J
(21A)
From 19A, [ (514)(llT2)n, 2w¢ ( l / r . ) ] (~sD2) = k 1 + 1/(1 + 4~V2oT~) J
(22A)
(1/r.) = (Wo)lx/W2o r.2
(23A)
From 22A and 23A,
(PsD2) =
(5/4)(1/T2)H, 2Wo (Wo/V~oor~) 1 + 1/(1 + 4W2or~)
(24A)
Eqns 17A, 18A and 24A are the basic equations used in the text for data analysis.
303 Appendix B
Estimation of the quadrupolar coupling constant The quadrupolar coupling constant (e 2 qQ) cannot be directly calculated from the results of the present study. However, from the following considerations, the value of 0.8 MHz (5.0 • 106 tad • s-' ) used by Chen and Reeves [19] seems to be a conservative lower bound for e 2 qQ. It has been well established that the correlation times determining the quadrupolar relaxation rat~s of the alkali metal ions in aqueous solutions reflect the reorientation rates of the water molecules in the hydration sphere of the cations [28,34] *. The reorientation rate of water molecules in bulk water is characterized by a correlation time r = 3 • 10 -12 s [28 34]. In general, the correlation times characterizing the molecular tumbling of water within the hydration spheres of the alkali metal ions is n o t greatly different from this value [28,34]. Reorientation of the water molecules in the vicinity of Li ÷ has been reported to be characterized by a (r) of 7 • 10-' 2 s [35], while the correlation times for water in the vicinity of the other alkali ions monotonically falls with increasing size of the non-hydrated nucleus [36]. The reorientation rate of water molecules within the sphere of hydration of Na ÷ is therefore within the range of 3--7 • 10-12 s. From Eqn 5A and the value of (1/T1) = 18 s-' for Na ÷ in dilute aqueous solution [26], the quadrupolar coupling constant characterizing Na ÷ in water is 0.8--1.2 MHz (5.0--7.5 • 106 rad • sec-' ). In a bound state, a less symmetric arrangement of ligands would be expected than in dilute aqueous solution, and therefore a larger value for e 2 qQ should prevail. Even in the unlikely event that bound Na is surrounded by a symmetric cage of dipoles similar to that surrounding Na complexed to a variety of ionophores, e2qQ would n o t be very different from 0.8 MHz ( 5 . 0 . 1 0 4 t a d " sec-') [37]. The m i n i m u m value for such complexed Na has been estimated to be 0.5 MHz, characterizing the Na within monactin, where Na is t h o u g h t to exist in a very regular cubic cage of oxygens. As noted in the text, the precise value for the quadrupolar coupling constant is not critical; setting e 2 qQ = 0.8 or 0.5 MHz leads to qualitatively similar conclusions. The value of 0.8 MHz is used in the text as the most realistic conservative estimate of e 2 qQ. Acknowledgements This study was supported, in part, by a Grant-in-Aid (71 847) from the American Heart Association and a Research Grant (GB-40040X) from the National Science Foundation. Dr Civan is an Established Investigator (70 148) of the American Heart Association. References 1 Baker, P.F., H o d g k i n , A.L. a n d Shaw, T.I. ( 1 9 6 1 ) N a t u r e 1 9 0 , 8 8 5 - - 8 8 7 2 0 i k a w a , T., S p y r o p o u l o s , C.S., Tasaki, L a n d Teorell, T. ( 1 9 6 1 ) A c t a Physiol. Scand. 52, 1 9 5 - - 1 9 6 * Elsewhere in t h e t e x t , for p u r p o s e s o f b r e v i t y , we l o o s e l y r e f e r t o t h e rate o f t u m b U n g o f N a + w i t h r e s p e c t t o its e n v i r o n m e n t . We s h o u l d e m p h a s i z e t h a t w e are s p e c i f i c a l l y referring t o t h e rate o f f l u c t u a U o n o f t h e e l e c t r i c field gradient a p p l i e d t o t h e N a + nucleus.
304
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
Tasaki, I., Singer, I. and Takenaka, T. (1965) J. Gen. Physiol. 48, 1095--1123 Huneeus-Cox, F., Fernandez. H.L. and Smith, B.H. (1966) Biophys. J. 6, 675--689 Hoffman, J.F. (1962) J. Gen. Physiol. 45, 837---859 Fenichel, I.R. and Horowitz, S.B. (1969) in Biological Membranes (Dowben, R.M., ed.), pp. 177--221 J. & A. Churchill Ltd., London Hazlewood, C.F., ed. (1973) Ann. N.Y. Acad. Sci. 204, 1--631 Cope, F.W. (1965) Proc. Natl. Acad. Sci. U.S. 54, 225---227 Cope, F.W. (1967) J. Gen. Physiol. 50, 1353--1375 Cope, F.W. (1970) Biophys. J. 10, 843--858 Cope, F.W. (1970) Physiol. Chem. Phys. 2,545--550 Czeisler, J.L., Fritz, Jr, O.G. and Swift, T.J. (1970) Biophys. J. 10, 260--268 Ling, G.N. and Cope, F.W. (1969) Science 163, 1335--1336 Martinez, D., Silvidi, A.A. and Stokes, R.M. (1969) Biophys. J. 9, 1256--1260 Reisin, I.L., Rotunno, C.A., Corehs, L., Kowalewski, V. and Cereijido, M. (1970) Physiol. Chem. Phys. 2, 171--179 R o t u n n o , C.A., Kowalewski, V. and Cereijido, M. (1967) Biochim. Biophys. Acta 135, 170--173 Shporer, M. and Civan, M.M. (1972) Biophys, J. 12, 114--122 Lindblom, G. (1971) Aeta Chem. Scand. 25, 2767--2768 Chen, D.M. and Reeves, L.W. (1972) J. Am. Chem. Soc. 94, 4384--4386 Edzes, H.T., Rupprccht, A. and Berendsen, H.J.C. (1972) Bioehem. Biophys. Res. Commun, 46. 790--794 Berendsen, H.J.C. and Edzes, H.T. (1973) Ann. N.Y. Acad. Sci. 204, 459--480 Civan, M.M. and Podolsky, R.J. (1966) J. Physiol. 184, 511--534 Civan, M.M. and Shporer, M. (1972) Biophys. J. 12,404--413 Carey, M.J. and Conway, E.J. (1954) J. Physiol. 125, 232--250 Beaugd, L.A. and Sjodin, R.A. (1968) J. Physiol. 194, 105--123 Eisenstadt, M. and Friedman, H.L. (1967) J. Chem. Phys. 46, 2182--2193 Hall, C., Richards, R.E., Schulz, G.N. and Sharp, R.R. (1969) Mol. Phys. 16,529--544 Hertz, H.G. (1967) Prog. Nucl. Magn. Resonance Spectrom. 3 , 1 5 9 - - 2 3 0 Redfield, A.G. (1965) in Advances in Magnetic Resonance (Waugh, J.S., ed.), pp, 1--32, Academic Press, New York Hubbard, P.S. (1970) J. Chem. Phys. 53,985--987 Rubinstein, M., Be.ram, A. and Luz, Z. (1971) Mol. Phys. 20, 67--80 Baram, A., Luz, Z. and Alexander, S. (1973) J. Chem. Phys. 58, 4558~-4564 Bull, T.E. (1972) J. Magn. Resonance 8,344--353 Deverell, C. (1969) Progr. Nucl. Magn. Resonance Spetrom. 4, 235--334 O'Reilly, D.E. and Peterson, E.M. (1969) J. Chem. Phys. 51, 4906--4908 Samoilov, O. Ya. (1972:)AnWater and aqueous solutions: Structure, Thermodynamics, and Transport Processes (Home, R.A., ed.), pp. 597---612, Wiley-lnterseienee, New York Haynes, D.H., Pressman, B.C. and Kowalsky, A. (1971) Biochemistry 10, 8 5 2 4 8 6 0