Transverse and Rotating Frame NMR Relaxation in Muscle Tissue

42 Bounds on Bound Water: Transverse and Rotating Frame NMR Relaxation in Muscle Tissue H. A. RESING and A. N. GARROWAY Naval Research Laboratory, Washington, D. C. 20375

Downloaded by CORNELL UNIV on October 2, 2016 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0034.ch042

K. R. FOSTER The University of Pennsylvania, Philadelphia, Pa. 19104

Most of the water in muscle tissue has an NMR transverse relaxation time (T2) about one-fiftieth that of the pure liquid, an effect known for twenty years (1) without an interpretation of concensus (2,3), despite proposed use of NMR relaxation measurements for cancer diagnosis (4,5). NMR data in rat (3) and frog (6) skeletal muscle suggest that a small observed proton fraction with a T2 of about one msec exchanges at an "intermediate" rate (7,8) with the major portion of cell water, and thus lowers the relaxation time of this major fraction below that of pure water. We reported earlier (9) that single muscle cells from the giant barnacle, Balanus nubilus, also exhibit a small proton fraction with a millisecond T 2 . However, within experimental limits, these protons do not exchange withD2Oin times as long as 24 hours, and cannot be the cause of the proton relaxation in the major portion of tissue water. In contrast the non-freezing water protons which we observed (9) at -34°C (attributed to "bound water" in studies (10) of protein solutions and tissues) do exchange with D2O and are clearly different from the non-exchangingprotons which we observe in these cells. Finally, we showed (9) that in the barnacle proton and deuteron transverse relaxation times for the major portion of the muscle water do fit an "intermediate exchange rate" model which requires only 0.1% of the water molecules to be in an "irrotationally bound" state at room temperature. The reader is referred to the earlier work (9) for experimental details and the more global picture. The purpose of this paper is to describe more fully the "intermediate exchange rate" model proposed earlier (9) and to examine its consequences for rotating frame relaxation time (T1p) measurements in muscle systems. The model predicts a T1p dispersion in "H1 space" centered about a value of H1 equal to the r.m.s. local field of the irrotationally bound water molecule, ca. 3 gauss. Available data for frog (11) and mouse (12) muscle systems are in semiquantitative agreement with the model 516 Resing and Wade; Magnetic Resonance in Colloid and Interface Science ACS Symposium Series; American Chemical Society: Washington, DC, 1976.

42.

Bound Water

RESiNG ET AL.

517

In muscle t i s s u e , proton transverse r e l a x a t i o n can g e n e r a l l y be d e s c r i b e d as the sum of f o u r e x p o n e n t i a l decays; the proton f r a c t i o n s ( i . e . f r a c t i o n a l amplitudes corresponding to each o f the e x p o n e n t i a l terms) are l a b e l e d (3,9) by the mnemonics " p r o t e i n " , "msec", "major" and " e x t r a c e l l u l a r " i n order o f i n c r e a s i n g r e s p e c t i v e T v a l u e s . F r a c t i o n s and values f o r the r a t (3) and barnacle systems are assembled i n Table I . I n t h i s paper we concentrate on the "major" proton f r a c t i o n , which accounts f o r over 90% of the water i n the barnacle f i b e r and has a T about 1% t h a t of bulk water. Other important f e a t u r e s found f o r the barnacle f i b e r (9) are these: a) the r a t i o o f the deuterium transverse r e l a x a t i o n time ( i n a deuterated barnacle) to that of protons ( i n undeuterated barnacle) i s much s m a l l e r than f o r the b u l k l i q u i d s ; b) on d e u t e r a t i o n the proton r e l a x a t i o n time i n the barnacle does not r i s e as much as would be expected f o r a s i m i l a r d e u t e r a t i o n l e v e l i n the b u l k l i q u i d ; and c) on lowering the temperature t o 5°C there i s a s m a l l but s i g n i f i c a n t r i s e i n T^. A l l o f these f a c t s are c o n s i s t e n t w i t h an exchange model i n which exchange r a t e s are j u s t a t the b o r d e r l i n e between " i n t e r m e d i a t e " and f a s t " , as we d i s c u s s below. The s i m p l i s t i c i n t e r p r e t a t i o n f o r the s m a l l T^, t h a t the i n t r a c e l l u l a r water i s one hundred times more v i s c o u s , i s , o f course, r e j e c t e d , mainly because d i f f u s i o n i n i n t r a c e l l u l a r water i s not much l e s s than i n b u l k water (13). 2


2

Model f o r Transverse

Relaxation

The low value o f T i s b e l i e v e d to a r i s e as an "averaging" e f f e c t by exchange of water of normal v i s c o s i t y w i t h bound water molecules o r other proton species which are r e l a t i v e l y l e s s f r e e to move and hence have s m a l l e r T^ v a l u e s . I f the f r a c t i o n P^ of bound protons i s r e l a t i v e l y s m a l l then equation (1) i s a p p l i c a b l e f o r the observed transverse r e l a x a t i o n time T„ ' o f the major f r a c t i o n ( 8 ) : 2

a

( T

2a'

) _ 1

T

» 2a

_ 1

+

P

b

[ (

1

"V

b

T

+

V * '

(

1

)

where T« i s the i n t r i n s i c r e l a x a t i o n time o f the " f r e e " water (about têat of b u l k w a t e r ) , τ, (τ ) i s the l i f e t i m e o f a proton i n the bound ( f r e e ) s t a t e , ana T^, i s the i n t r i n s i c r e l a x a t i o n time i n the bound s t a t e . By d e t a i l e d balance T

a

/ ( 1

-V " V b P

( 2 )

Each "term" o f equation (1) dominates i n a given temperature ( i . e . exchange r a t e ) range, as i s shown s c h e m a t i c a l l y i n F i g u r e 1 f o r a h y p o t h e t i c a l system i n which P^ = 0.01. These ranges are l a b e l e d "slow", " i n t e r m e d i a t e " , and " f a s t " a c c o r d i n g l y as the f i r s t ( i n t r i n s i c r e l a x a t i o n of the " f r e e " s t a t e ) , second ( r a t e o f exchange i n t o the bound s t a t e ) o r t h i r d (weighted average

Resing and Wade; Magnetic Resonance in Colloid and Interface Science ACS Symposium Series; American Chemical Society: Washington, DC, 1976.

518

MAGNETIC RESONANCE


r e l a x a t i o n i n the bound s t a t e ) "term" o f equation (1) predominates r e s p e c t i v e l y . I n t h i s paper the i n t r i n s i c r e l a x a t i o n r a t e i n the f r e e s t a t e i s n e g l e c t e d because the observed v a l u e o f " is so s m a l l . The complete range o f behavior i l l u s t r a t e d i n F i g u r e 1 has been observed, f o r example, i n a recent study (8) o f a hydrolyzed z e o l i t e system. Â s e t o f experiments i n v o l v i n g d e u t e r a t i o n was c a r r i e d out by Woessner, e t a l . (14) and T^ minima were observed f o r aqueous agarose g e l s ; i n t e r p r e t a t i o n , along the l i n e s g i v e n i n t h i s paper, r e q u i r e d strange temperature dependence f o r P, however; t h a t v e r y complete s e t o f data a r e not s u b j e c t t o tne simple i n t e r p r e t a t i o n we g i v e here f o r the barnacle f i b e r . The working hypothesis i s t h a t the bound s t a t e c o n s i s t s o f water molecules i r r o t a t i o n a l l y bound t o a r i g i d s u b s t r a t e (15). The o n l y motion such a molecule executes i s i t s jump out o f the bound s t a t e ; t h i s means t h a t t h e r e i s no d i p o l a r (or quadrupolar, i n the case o f deuterons) m o t i o n a l averaging i n the bound s t a t e , and t h a t the c o r r e l a t i o n time f o r the bound molecule i s i t s l i f e time i n the bound s t a t e , τ^. Thus, i n the m o t i o n a l narrowing r e g i o n the i n t r i n s i c r e l a x a t i o n time f o r the bound s t a t e i s g i v e n as (16)

2

Here O i s the Van V l e c k (17) second moment o f a proton i n a bound molecule due both t o i t s i n t r a m o l e c u l a r p a r t n e r and t o protons i n the s u b s t r a t e t o which i t i s bound. The s u b s c r i p t zero on T ^ i n d i c a t e s a muscle o f n a t u r a l i s o t o p i c composition. A consequence o f the e q u a l i t y o f exchange and c o r r e l a t i o n times i s t h a t the P,/T and the P,/[(1-P ) τ^] c o n t r i b u t i o n s a r e governed^by tne same a c t i v a t i o n energy, g i v i n g r i s e t o slopes o f T vs Τ equal i n magnitude but o p p o s i t e i n s i g n f o r the f a s t and i n t e r m e d i a t e exchange regimes. I t i s the s m a l l p o s i t i v e slope observed (9) f o r T^, r e f e r r e d t o e a r l i e r , which leads us to suppose t h a t the i n t e r m e d i a t e exchange r a t e regime may represent the r e l a x a t i o n f o r the major p r o t o n f r a c t i o n i n the barnacle muscle. Q

2b

b

2

Isotopic Effects Of the parameters necessary f o r f u r t h e r development P^, the f r a c t i o n o f protons (and/or deuterons) i n the bound s t a t e , and the bound s t a t e l i f e t i m e do not depend s i g n i f i c a n t l y on the d e u t e r a t i o n l e v e l . There may indeed be a mass e f f e c t on τ^, b u t i f whole water molecules t r a v e r s e the exchange r e a c t i o n c o o r d i n a t e , t h i s e f f e c t should be minimal. Only T^^, through the second moment, i s s i g n i f i c a n t l y a f f e c t e d by i s o t o p i c composition. The second moment, a mean square i n t e r a c t i o n s t r e n g t h , i s o f d i p o l a r o r i g i n f o r protons and o f quadrupolar o r i g i n f o r deuterons. F o r


42.

RESiNG ET A L .

Bound Water


Fast

519

-^-Intermediate^

(J*v

τ)

α

-

Τ"*

Slow

1

Figure 1. Theoretical transverse relaxation times vs, inverse temperature for the model of irrotationally bound water molecules (P = 0.01) in exchange with free water, according to Equation 1 of text. The inverse temperature scale is uncalibrated, but the section B-B corresponds roughly to room temperature for barnacle fibers. The three exchange rate regimes are indicated above. The curves correspond (from top to bottom) to proton relaxation in a partially deuterated system, proton re laxation in a system of normal isotopic composition (T '), and deuteron relaxation (Ό). The intrinsic relaxation time T is also indicated. h

tno

xt)0


MAGNETIC RESONANCE

520

• DEUTERON T Ο PROTON Τ2 X PROTON T, (2.4G)


2

Ο PROTON T

lp

IN DEUTERATED FIBERS

FAST EXCHANGE

/

'

β

- BEST FIT GIVES T / P = 5.3 ± 2 msec τ « 35 ± 10 msec 2 b

T

b

2b X 2

* I for

for

Q,X

* fL for Ο 1

INTERMEDIATE EXCHANGE ( T 2 i , / P ~ 0) b

8

9

10 II

12 13

X Science

Figure 2. Plot of T ' vs. χ for the "major" water fraction in barnacle muscle fiber. Line hbeled "fast exchange" corresponds to section F - F of Figure 1; likewise "interme diate" to section I-I, and "bestfit"to B-B. Note: T = T V of text (9). fa

Èob$


42.

Bound Water

RESiNG ET AL.

521

the deuterons i t i s predominantly i n t r a m o l e c u l a r i n o r i g i n . For the protons, i f the i n t r a m o l e c u l a r p a r t were dominant, o r t o the extent t h a t the surroundings a r e a l s o deuterated, the second moment i n t|e p a r t i a l l y deuterated system may be w r i t t e n as °d ^ * f a c t i o n o f pjotons remaining a f t e r d e u t e r a t i o n . ^Ag a p r e l i m i n a r y estimate o i s taken t o be 1.6 χ 10 r a d s , a p p r o p r i a t e t o a s i n g l e water molecule.) Thus the i n t r i n s i c r e l a x a t i o n time f o r bound protons i n a p a r t i a l l y deuterated system T^^, becomes (18) =

σ

9

w

i e r e

s t n e

q

2

2bd " H % V 2 Here the e f f e c t s on σ o f a l l non-proton magnetic f i e l d s a r e excluded. For the deuterons, the mean square i n t e r a c t i o n s t r e n g t h of the quadrupole moment w i t h i t s l o c a l e l e c t r i c f i e l d gradient i n a d e u t e r o x y l group i s about t e n times stronger than the protonproton n u c l e a r magnetic d i p o l a r second moment i n a water mole c u l e (8, 19); f o r a deuteron the i n t r i n s i c r e l a x a t i o n time i n the bound s t a t e may then be w r i t t e n as


T

_ 1

f

2

( 4 )

In (5) a l l r e l a x a t i o n mechanisms other than quadrupolar are n e g l e c t e d . The consequences o f equations (4) and (5) on equation (1) are a l s o i l l u s t r a t e d i n F i g u r e 1, under the assump t i o n that T and T ^ a r e s i m i l a r l y a f f e c t e d by d e u t e r a t i o n o r n u c l e a r specfes. 2

Transverse R e l a x a t i o n i n Barnacle Muscle F i b e r Our experiment c o n s i s t s i n making an i s o t h e r m a l s e c t i o n through F i g u r e 1. We d e s i r e t o f i n d out i n what exchange r a t e regime the barnacle muscle system i s by comparison o f the observed T^ ^ those i l l u s t r a t e d i n F i g u r e 1, namely: a) I - I , i n t e r m e d i a t e , no dependence o f 2 a ' on d e u t e r a t i o n l e v e l or i s o t o p i c s p e c i e s ; b) F-F, f a s t exchange, f u l l dependence; c) B-B, b o r d e r l i n e , moderated dependence. s

e

c

t

i

o

n

t o

a

T

A simple summary o f the above, very r e s t r i c t i v e , model i s given by the e x p r e s s i o n :

V

T

= a

+

X

W V

( 6 )

This c o n v e n i e n t l y l i n e a r equation a l l o w s the s e c t i o n s through F i g u r e 1 t o be p l o t t e d v s the parameter x, wtjich i s f for protons i n the deuterated muscle, o r σ / O ^ 0.1 f o r the deuterons. The data f o r the barnacle muscle a r e p l o t t e d vs χ i n F i g u r e 2, along w i t h the l i m i t i n g s e c t i o n s f o r f a s t and i n t e r mediate exchange according t o equation ( 6 ) . F i g u r e 2 suggests that a b o r d e r l i n e s e c i o n such as B-B i s most n e a r l y a p p l i c a b l e ; f l

q


522

MAGNETIC RESONANCE

the best f i t t i n g parameters are i n d i c a t e d . From the slope (T /P^)and i n t e r c e p t (τ ) and equations (2) and (3) above,the freeîy a d j u s t a b l e parameters are deduced as P, = (0.08 + 0.02)%, and T « 3 . 5 + 1 . 5 ys (or e q u i v a l e n t l y « 20 + 10 y s e c ) . Thus about one molecule per thousand, i r r o t a t i o n a l l y bound f o r o n l y tens o f microseconds,can account f o r the transverse r e l a x a t i o n times o f the great m a j o r i t y o f the water i n b a r n a c l e muscle c e l l s . Such a s m a l l f r a c t i o n i s u n l i k e l y to be found by searching f o r i t s c o n t r i b u t i o n t o the f r e e i n d u c t i o n decay, even though i t i s i n p r i n c i p l e observable. We make no attempt here t o e x p l a i n the v a l u e o f P i n terms o f b i o c h e m i c a l s t r u c t u r e ; the o n l y i m p l i c a t i o n o f t h i s model i s that there i s some s u b s t r a t e which can b i n d a water molecule f o r 20 microseconds and not move i t s e l f during t h i s time. 2b

&

2 b


fe

On the other hand the v a l u e s o f T o r τ, which emerge are eminently reasonable i n terms o f the n.m.r. model proposed. The model o f an exchanging, i r r o t a t i o n a l l y bound water molecule, as sketched above, r e q u i r e s that the T " minimum be a t the same temperature as the m o t i o n a l narrowing onset (knee) f o r of the bound molecule (see F i g u r e 1 ) . This knee i s marked by the c o n d i t i o n that 2 b Q

2 &

T

2

\

T

T

b

o

( 7 )

* 2 b o * 2RL

where T i s the i n t r i n s i c , r i g i d - l a t t i c e r e l a x a t i o n time i n the bound s t a t e , about 10 ysec. C l e a r l y T - cannot become s m a l l e r than T„ . The p l o t o f experimental v a l u e s o f 2 ' vs χ (Figure 2) i m p l i e s a temperature s l i g h t l y lower than that of the T " minimum (Figures 1 and 2 ) . The v a l u e s o f ^2ho d e r i v e ! from the data by a p p l i c a t i o n o f the model are o f the order o f 10 ysec demanded by ( 7 ) ; t h i s i s a c r u c i a l t e s t ; the hypothesis l i v e s ! Note however that equations ( 3 ) , (4) and (5) apply only i n the m o t i o n a l narrowing r e g i o n , and b e g i n to break down (not c a t a s t r o p h i c a l l y though) as the r i g i d l a t t i c e r e g i o n , i . e . i n t e r m e d i a t e exchange r e g i o n i s approached. 2

2

T

a

a

n

d

2

R e l a x a t i o n i n the R o t a t i n g Frame The " i r r o t a t i o n a l l y bound water molecule" model may be t e s t e d f u r t h e r , f o r i t has c e r t a i n , not s u p e r f i c i a l l y obvious, i m p l i c a t i o n s f o r the r o t a t i n g frame r e l a x a t i o n experiment. And though such T- data do e x i s t i n the l i t e r a t u r e f o r other muscle systems (IYJ 12), the i n t e r p r e t a t i o n s g i v e n assume the f a s t exchange c o n d i t i o n , under which T- observed f o r the major f r a c t i o n (Τ- 0 i s simply Ρ /T^ ^, and any T^ d i s p e r s i o n which occurs i n t n i ^ o u n d s t a t e r e f l e c t s i t s w e i g h t e l c o n t r i b u t i o n i n the major f r a c t i o n (look ahead to equation (9 ') f o r T^ , ). The c o r r e l a t i o n time deduced from the T- ' d i s p e r s i o n i s then c h a r a c t e r i s t i c o f some motion i n the bound s t a t e which may o r may not be the exchange r e a c t i o n . (Equation (1) f o r Τ " i s assumed p


42.

Bound Water

RESiNG ET AL.

T

to h o l d as w e l l f o r i

p a

'>

523

m u t a t i s mutandis.)

In the intermediate exchange regime the s i t u a t i o n i s not so simple, as the f o l l o w i n g example w i l l make c l e a r . R e c a l l , from equations (1) and ( 2 ) , t h a t intermediate exchange i s c h a r a c t e r i z e d f o r 2 a ' ^ the i n e q u a l i t i e s T

ν


T

2a

>

T

>T

a b > 2b T

( 8 )

where the center i n e q u a l i t y holds because we are i n t e r e s t e d i n a system where Ρ > Ρ, . Retreat f o r a moment from the s p e c i f i c model o f i r r o t a t f o n a l l y bound water molecules and a l l o w the bound s t a t e to have a c o r r e l a t i o n time τ , which i s much l e s s than the bound s t a t e l i f e t i m e τ^. Suppose f n a t the bound s t a t e i s i n the m o t i o n a l narrowing (16), i . e . weak c o l l i s i o n (20), r e g i o n o f cb* l t i o n l i k e (3) a p p l i e s f o r T ^ . Under these c o n d i t i o n s the i n t r i n s i c r o t a t i n g frame r e l a x a t i o n time f o r the bound s t a t e i s given (21) as T

8

0

t t i a t

a

n

e c

u a

T

lpb -

= T

( 1+

4

Λ

2 τ

Transverse and Rotating Frame NMR Relaxation in Muscle Tissue

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