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Characterization of polyproline-water system by NMR spin grouping and exchange analysis
J. Stanley, H. Peemoeller
To cite this version:
J. Stanley, H. Peemoeller. Characterization of polyproline-water system by NMR spin group- ing and exchange analysis. Journal de Physique II, EDP Sciences, 1991, 1 (12), pp.1491-1503.
�10.1051/jp2:1991165�. �jpa-00247606�
J. Phys. II France1 (1991) 1491-1503 DtCEMBRE 1991, PAGE 1491
Classification Physics Abstracts
61.16N 76.60E 87.15H
Characterization of polyproline-water system by NMR spin grouping and exchange analysis
J. A. Stanley and H. Peemoeller
Guelph-Waterloo Program for Graduate Work in Physics, Department of Physics, University of Waterloo, Waterloo, Ontario, Canada N2L 3Gl
(Received 26 June 1991, accepted 2 September 1991)
Abstract. Proton NMR spin grouping experiments (Ti, Tip, Tj ~) and T2 measurements were
performed in dry and hydrated polyproline powders. The results in the hydrated samples were
analyzed for magnetization exchange using a linear three site ~proline -H2O- proline) exchange scenario. The intrinsic proline and water proton relaxation parameters as well as the
exchange rates were obtained. All proline protons are effectively coupled to the water protons.
Perhaps the most significant result is the observation, for the first time, of a very large spin-spin coupling rate ((3.0 ± 1.5 x 10~ s~ ) between water protons and a small fraction of the polymer
proton population.
l~ Introducfion~
To characterize the molecular dynamics of systems of biophysical interest such as hydrated protein molecules or tissues using nuclear spin relaxation data, one requires relaxation
information about the individual spin groups making up the system. However, interpreting
the NMR signals from these heterogeneous systems is often difficult because of I) overlap-
ping resonance lines originating from structurally and dynamically different spin groups, and
2) the presence of magnetization exchange between the macromolecule spins and the more mobile water spins. As a consequence, the observed relaxation parameters (magnetization
fractions and relaxation rates) are only apparent parameters. The inherent or intrinsic relaxation parameters, as well as the exchange rates, must be extracted from the nuclear spin
relaxation data in order to obtain meaningful information about the coordination and
dynamics of molecules in such systems.
In the presence of magnetization exchange between spin groups it is possible to obtain information about the intrinsic relaxation parameters by analyzing the apparent relaxation parameters for exchange [1, 2]. For such analysis to be meaningful, however, it is essential that the apparent or observed spin relaxation behaviour is characterized as precisely as possible. The NMR spin grouping technique [3] makes it possible, in these heterogeneous
systems, to resolve the spin group distribution needed for such characterization. NMR spin grouping involves the reconstruction of free induction decays (FlD's) of each spin group from
1492 JOURNAL DE PHYSIQUE II M 12
spin-lattice relaxation measurements at high field (Ti) and/or at low field (Ti~). In this
procedure the spin-lattice relaxation and spin-spin relaxation (T2) behaviour of the
magnetization are correlated.
Magnetization exchange between spin groups in these systems often is in or near the fast exchange limit. In this limit only a single apparent relaxation component is observed. Then, information about the exchange process is not readily available from standard relaxation
measurements using for example the inversion recovery sequence in which a hard (H) 180°
preparation pulse is followed by a hard 90° monitor pulse a time T later. Edzes and Samulski [4] have shown that in solid-liquid systems this difficulty can be circumvented by using the
selective inversion recovery pulse sequence, soft (S) 180° preparation pulse T hard 90°
monitor pulse, as long as t~, the length of the soft inverting pulse, can be adjusted to satisfy MI ~'~ < t~ < T~ (liquid), where M~ is the second moment of the resonance line of the solid- like spin group and T~ (liquid) is the spin-spin relaxation time of the liquid-like spin group.
This approach -has found a number of applications [4-6] and has been very effectively combined with NMR spin grouping [7-9].
With the aim of elucidating the details of molecular interaction and dynamics at the
polymer-water interface, we have applied the methods mentioned above to hydrated poly- proline, a well defined polymer. It is expected that the water binding sites on this polymer should be well defined and that a more straightforward interpretation of relaxation results follows. In addition, the macromolecule was hydrated to a level much below that required to form a solution sq that the complications introduced by the tumbling motion of the
macromolecule in solution are absent.
2. Experimental procedure.
2.I SAMPLE PREPARATION. The polyproline (Sigma Chemical Company) was purified [10]
to remove paramagnetic impurities by dissolving lgm of the material in 80ml of
distilled/deionized water and dialyzing the solution for 32 h ; the last 16 h in distilled/deioni-
zed water. During this procedure the dialysate was changed every four hours. The
polypeptide solution was then freeze-dried and the resulting powder stored at -5 °C in an air
tight vessel.
All thin walled 7.5 mm O.D. NMR sample tubes and associated glassware used in the
experiments were immersed in a 50 9b sulphuric/50 9b nitric acid solution for 24 h followed by
a thorough rinsing with distilled/deionized water. The glassware was then immersed in a 0.01M EDTA solution for 24 h and then thoroughly rinsed using distilled/deionized water.
In this study, a dry polyproline sample and a polyproline sample hydrated at a moisture
content (MC) of 9.8 9b H~O were used. Here we define MC
= [wt. H20/(wt. H~O + poly- peptide)] x 100. To prepare the dry sample, roughly 60 mg of polyproline was placed in a pre-
weighed NMR sample tube. The sample was dried under vacuum (10.4 Torr) for 24 h. With the sample still under vacuum, the sample tube was flame sealed. The dry weight of the polyproline was determined from the weight of the empty NMR tube and the final, combined
weight of tube and sample.
To prepare the hydrated sample, the polyproline was placed in a vessel in which 100 9b relative humidity was maintained. Once the appropriate hydration level was obtained, the
sample tube was flamed sealed. The level of hydration was calculated from the dry sample weight and the weight of the final sample.
2.2 NMR MEASUREMENTS. Proton T~, Tj, Tj
~
and Tio measurements were performed
using a home built, broad band, pulsed NMR spectrometer operating at 30 MHz and a Varian
HA-60 electromagnet. A Datalab912 transient waveform recorder in conjunction with a
M 12 CHARACTERIZATION OF HYDRATED POLYPROLINE BY NMR 1493
Hewlett-Packard (Palo-Alto, CA) model 9816 computer were used for data acquisition and
analysis. The Gill-Meiboom modified Carr-Purcell pulse sequence ill] was used to measure T~. Ti was measured using I) a selective inversion recovery pulse sequence involving a
selective or soft preparation pulse in which the 180° pulse had a duration of 100 ~cs followed by
a non-selective or hard monitor pulse and it) a non-selective inversion recovery pulse sequence involving non-selective or hard preparation and monitor pulses. Experiments (I) and (it) are also referred to as SH Ti and HH Tj experiments, respectively. Tj
~
measurements were performed using the spin-locking sequence with Bi fields of10 and 2 Gauss. The Jeener-
Broekaert pulse sequence [12] was used for the TiD measurements.
In cases where the recovery or decay curve was non-exponential it was decomposed into
components using an interactive combination of statistical and graphical approaches [3]. In the present study the relaxation times of component magnetizations in any particular analysis differed sufficiently to make the decompositions unambiguous. In all cases spin grouping was
used in the analysis of the data. All experiments were performed at 293 K.
2.3 EXCHANGE ANALYSiS. Consider three spin reservoirs, coupled to each other through
magnetization transfer processes as depicted in figure la for the case involving spin-lattice
relaxation. The time evolution of the magnetization is given by the Bloch equations modified to include such transfer or exchange ill. We label the three reservoirs or sites a, b and c. Let
the reduced magnetization of site I (=a, b, c) be defined through m;(T)=
(M~; -Mz,(T))/2 M~, for the inversion recovery experiment, m~(T)
= M~;(T)/Adj; for the
Ti~ experiment where the spin locking field is applied along the y-axis, and m;(T)
=
M~;(T)/fifj~ for the T2 experiment. Then, the evolution of the magnetization is governed by
the coupled differential equations
~fj(~~ = (1~ + k~~ + k~b) m~(T + k~bmb(T + k~ m~(T (la)
~flj(~~ = (Rb + kb~ + kb~) mb(T) + kb~ m~(T) + kb~m~(T) (16)
~l~(~ " (Rc + kcb + kcal'llc(T) + kca"~a(T ) + kcb"~b(T ) ('C)
where k~~ is the rate of magnetization exchange from a to b,k~~ is the rate for exchange from b to a, and similarly for the other exchange rates (see Fig. la). R; is the intrinsic relaxation rate of the I-th site.
The solution to equations (I) gives for each site
@(T)
= Cl e~~ ~ + Cle~~°~ + Cl e~~~ ~ (2) where the C;'s and A's are the apparent magnetization fractions and apparent relaxation rates, respectively. The +, 0 and indicate the parameters for the apparent magnetization
components with the fastest, intermediate and slowest observed relaxation times, respectively.
Transverse decay along the t-axis can be included in (2) by multiplying the right hand side by exp[- f;(t)] where the function f;(t)
= t/7~, for a liquid-like spin group with spin-spin
relaxation time T~; and f~(t)
= M~, t~/2 for a solid-like spin group with proton second
moment M~,. The observed (apparent) relaxation scenario is depicted in figure16. The
C,'s are functions of the intrinsic relaxation rates, the exchange rates and the fractions m,(o) of spins affected by the preparation pulse. The A's are functions of the intrinsic relaxation rates and the exchange rates. Details about the relations between intrinsic and apparent relaxation parameters can be found elsewhere [13].
1494 JOURNAL DE PHYSIQUE II bt 12 koc
p p c
~ ~
k~~ T2b ~2b
~cb
~aa
P~
i~ i-
R~
a)
b)
Fig. I.- Three site exchange scenario indicating a) the inherent relaxation parameters and b) the apparent relaxation parameters.
As detailed later, it was possible to characteRze the exchange by utilizing a simpler, linear three site exchange scenario in which k~~ and k~ in figure la are set to zero. The exchange modelling scheme [8, 13, 14] involves calculating the apparent relaxation parameters using
known inherent relaxation rates, known stoichiometric information ~p~, p~ and p~, the fractional spin group sizes), the expeRmental initial conditions (m~(o), m~(o) and
m~(o)), the conditions of detailed balance and parameterizing the inherent unknown parameters. The expressions relating inherent to apparent relaxation parameters are available elsewhere [13]. The apparent parameters are plotted as a function of one of the exchange
rates (say k~~) while holding the other exchange rate, k~, constant. The k~~ at wllich a best match, between modelled and apparent parameters exists is determined using a comparison
routine described elsewhere [15]. This routine simultaneously presents, as a function of k~~, the deviations between modelled and apparent parameters and relates these to the
standard deviations in the observed apparent parameters. A rapid determination of the
optimum value of k~~ for a particular set of the parameterized quantities follows. This is
repeated with k~ variable and k~~ fixed at the initial optimum value. The procedure is
repeated while methodically adjusting the unknown inherent parameters until the deviations between modelled and apparent parameters in each case are within acceptable limits.
Each polyproline molecule contains approximately 100 residues each containing 7 protons.
Thus, except for a possible small contribution (assumed negligible) to water proton-peptide proton magnetization exchange from chemical exchange of amino end group protons with
water protons, such magnetization exchange must result from mutual spin flips between the water and peptide protons. As a consequence of such intermolecular dipolar interactions the Zeeman spin energies of the solid-like and liquid-like spin reservoirs are mixed.
3. Results and discussion.
Several relaxation measurements were performed in the wet polyproline sample in order to affect as complete a characterization of the nuclear spin relaxation behaviour as possible. To this end T~ FID, T~ CPMG, Ti HH, Ti SH, and Ti
~
(lo G and 2 G) were measured in the wet
sample. In addition, the same measurements (excluding T~ CPMG and Tj SH and including TjD) were performed in a dry polyproline sample in order to obtain information about the
intrinsic spin relaxation parameters of the peptide.
bt 12 CHARACTERIZATION OF HYDRATED POLYPROLINE BY NMR 1495
3.I DRY POLYPROLINE. The main part of the proton FID in dry polyproline is a simple
Gaussian with T~ = 11 ~cs. Here T~ is taken as the time required for the magnetization to
decay to one-half its initial value. In addition, a single magnetization recovery curve (Tj
= 3.2 s) was observed. However, the magnetization decay curve in the rotating frame at 10 G and at 2 G exhibited bi-exponential behaviour and was decomposed into components using a procedure described elsewhere [3]. Figure 2 gives the results of spin grouping for the
above Tj
~
experiment at 10 G. The magnetization M~ plotted as a function of time (Fig. 2b) for each Tj~ component yields a separate FID. One FID of Gaussian shape and T~ =
(I1 ± 2) ~cs makes up (87 ± 6) 9b of the reconstructed signal. This magnetization has a
Tj~, averaged over time windows, of (62 ± 6) ms (Fig. 2a). A second reconstructed FID
((13 ± 2) 9b of the signal) of Gaussian shape has T~ = (24 ± 3) ~cs. This magnetization has
Ti~ = (18 ±3)ms. The parameters characterizing the reconstructed FID'S are given in table I. The results from spin grouping analysis of the data from the Ti experiment are also
summarized in table1.
Bo
~° ~ ° o o o ~ o o ° o o
~
40 w E
Q-
/
20
. *
e e e .
* *
* e
e
lo
5 lo 15 20
Time (~s)
O.8
o ~
o
w O-G o (f~)
w o
i ~ o
~ O.4 o
~ o
~ o
~
~ o
w
O.2 o
f
~ e .
e e *
* e
~ * e
K ~ j
* 0
0
O.08
5 IO 15 20
T ime (~s)
Fig. 2. NMR spin grouping results for Tj
~
experiment at 10 G for the dry polyproline sample. The open circles and filled circles represent parameters for the component magnetizations with the long and medium relaxation times, respectively. (a) Jj versus time. Relaxation times averaged over time windows are (A )~'
= (62 ± 6) ms and (1°)~
= (18 ± 3 ms. (b) The reconstructed FID'S.
1496 JOURNAL DE PHYSIQUE II M 12 Table I. Observed relaxation parameters of dry polyproline. The magnetization fractions given for the Ti
D experiment have not been a#usted to take into account the fact that the first 45° pulse of the Jeener-Broekaert sequence cannot be positioned so as to create maximum
dipolar order simultaneously for the two spin groups.
T~:
ioox
T~- (11+2) us
T~:
ioox
t iiz+z) us
T~- (3.2+.5) sec
T~ ( lo Gauss ):
P
13X+2X 87X+6X
T -iz4+3> us T -iii+z)
us
T~ (18+3) ms T~ (62+6) ms
~lp ~ ~~~~~ ~'
llX+3X 89X+6X
T -iz4+3)
us T -iii+zi
us
T~ (.6+.3) ms T~ (25+4) ms
~1©
13X+3X 87X+5X
T -123+3) us T -l12+2)
us
T~~- (.4+.3) ms T~~- (21+4) ms
Qualitatively similar results were obtained from Ti~ measurements at 2G and from TjD measurements. The corresponding spin grouping results are summaRzed in table I. The
magnetization fractions found in the Tj
~
expeRments have been adjusted to take into account transfer of order from Zeeman to dipolar reservoir. These spin-lattice relaxation times
measured are considerably shorter than those found for Tj~ at 10G. However, the
magnetization fraction and T~ of each component magnetization resolved is essentially the
same in both Tj~ experiments as well as in the Tj D experiment (Tab. I).
The fact that two component magnetizations were resolved in the Tj~ and TjD
experiments, and only one in the Ti experiment would, at first glance, suggest that two spin
groups on the polymer relax differently to the lattice, but that the magnetizations are mixed via spin diffusion on the Ti time scale. Because the spin diffusion constant is related to the
second moment M~[16] it should be instructive to calculate M~ for the various protons on the
polyproline molecule.
M 12 CHARACTERIZATION OF HYDRATED POLYPROLINE BY NMR 1497
Polyproline, by definition, is a chain of repeated proline residues (Fig. 3). These residues have one carbonyl group, no amide proton and a pyrolidine ring. Proline has a single hydrogen at the a-carbon and two hydrogens at the p, y, and 6-carbons (Fig. 3). The chain itself has a molecular weight of 7,100 which means that there are approximately 100 residues per chain. The hydrogens at the amino end of the chain are considered to make a negligible
contribution to relaxation rates.
N2 C82
~~i '.~
~
($o
&( ',
~ ~j ' Hj
~", ~WATER
'v o,
/~
~ '. H2
o
Fig.3. A possible water molecule binding site on the polyproline molecule in its helical conformation.
Utilizing the coordinate system indicated in an X-ray study of polyproline II [17], the inter- proton distances of protons on a residue were calculated and are listed in table II. With these distances, the second moment, the local field B[ in the rotating frame [18] and the spin-spin
relaxation times [16] were calculated. for each proton on a residue in the rigid-lattice regime (Tab. II). From table II, it is seen that the calculated T~'s for the protons on the p, y, and 6- carbons are similar with T~ 9 ~cs. The single proton on the a-carbon has its own distinct T~ =
21 ~cs. The protons on the a-carbons constitute 14 9b of the total number of protons on
the proline while the remainder of the protons constitute 86 9b.
Due to short T~ (s 21 ~Ls), resulting from interactions between protons on a residue and the small number (seven) of protons per residue, it is reasonable to expect that spin diffusion is strongly coupling the magnetizations of the intra-residue protonscJop the Ti
D, Ti~ and
Tj time scales. However, because of the much greater inter-proton distances involved, this
can not be the case for inter residue exchange. Protons belonging on different residues on a
polymer chain or protons belonging on different chains are not coupled strongly. Two values of Ti
~
and Ti
D, but one Tj value, are observed because some of the polyproline molecules, or segments, uncoupled due to large spatial separation, experience (slower) motions that contribute to the proton spin-lattice relaxation rates at low fields, but not to rates at high
fields. We designate the component " a" as the magnetization with short Tj~ and the component " b " as the magnetization with long Tj
~.
The Tj~ spin grouping results indicate that the protons of spin group a (shorter Ti ~) have somewhat longer T~ than those of spin group b. This may be understood as follows
Using electron microscopy the polyproline sample used was shown to be amorphous [19].
JOURNAL DE PHYS~OUE H T I,M 12, DkCEMBRE 1991 63
