nmr studies on perdeuterated c-phycocyanin
TRANSCRIPT
PHYSICAL REVIEW E 89, 032710 (2014)
Vanishing amplitude of backbone dynamics causes a true protein dynamical transition:2H NMR studies on perdeuterated C-phycocyanin
Kerstin Kampf, Beke Kremmling, and Michael Vogel*
Institut fur Festkorperphysik, Technische Universitat Darmstadt, 64289 Darmstadt, Germany(Received 2 October 2013; published 17 March 2014)
Using a combination of 2H nuclear magnetic resonance (NMR) methods, we study internal rotational dynamicsof the perdeuterated protein C-phycocyanin (CPC) in dry and hydrated states over broad temperature and dynamicranges with high angular resolution. Separating 2H NMR signals from methyl deuterons, we show that basicallyall backbone deuterons exhibit highly restricted motion occurring on time scales faster than microseconds. Theamplitude of this motion increases when a hydration shell exists, while it decreases upon cooling and vanishesnear 175 K. We conclude that the vanishing of the highly restricted motion marks a dynamical transition, whichis independent of the time window and of a fundamental importance. This conclusion is supported by resultsfrom experimental and computational studies of the proteins myoglobin and elastin. In particular, we argue basedon findings in molecular dynamics simulations that the behavior of the highly restricted motion of proteins atthe dynamical transition resembles that of a characteristic secondary relaxation of liquids at the glass transition,namely the nearly constant loss. Furthermore, 2H NMR studies on perdeuterated CPC reveal that, in additionto highly restricted motion, small fractions of backbone segments exhibit weakly restricted dynamics whentemperature and hydration are sufficiently high.
DOI: 10.1103/PhysRevE.89.032710 PACS number(s): 87.14.E−, 64.70.kj, 82.56.−b, 87.15.kr
I. INTRODUCTION
Protein dynamics are of utmost importance for proteinfunctions, but their understanding remains a great challengedue to their high complexity. Protein motions cover manytime scales, involve entities of various sizes, and couple tosolvent dynamics. It was argued that solvent fluctuations in thebulk and at the interface cause protein large-scale α relaxationand small-scale β relaxation, respectively, both being relevantfor biological function [1]. Valuable insights were availablefrom studies in broad temperature ranges. In this context,the dynamical transition (DT) of proteins arose considerableinterest [2]. It marks a sudden increase of atomic displacementsupon heating, which was observed for solvated, but not for dry,proteins at cryogenic temperatures by neutron scattering [2]and other methods [3,4] and which is possibly related to anonset of biochemical activity [5].
Despite vigorous research, the DT of proteins remainsa puzzle and various explanations exist. Two-state modelsexplain the temperature-dependent displacements in terms ofvariations in the populations of energetically diverse states[2,3,6]. Based on the argument that protein dynamics are slavedby solvent motions [1], the DT was attributed to an onset ofα [7] or β [8] relaxations of the solvent or to a liquid-liquidphase transition of water [9]. Other workers argued that therise of the atomic displacements does not indicate fundamentalchanges in dynamics, but it occurs when relaxation times enterexperimental time windows [1,10–12]. Recently, a two-stepscenario was reported [7,8]. A high-temperature (Thigh) stepof atomic displacements was related to α or β relaxationsentering the time window, while a low-temperature (Tlow) stepwas found to be independent of the spectrometer resolutionand attributed to a glass transition, where Tlow ≈ 175 K forhydrated proteins.
Neutron scattering, employed in most works on the DTof proteins, offers several benefits, but disadvantages are thelimitation to fast motions and interference of contributionsfrom backbone (B) and methyl (M) hydrogens, which ex-hibit different dynamics [13,14]. Recently, nuclear magneticresonance (NMR) studies on solid-state samples proved apowerful alternative to investigate internal protein motions[15–19]. They enable insights into both geometries and ratesof the dynamics. Like 15N NMR [17], 2H NMR spin-latticerelaxation (SLR) and line-shape anisotropy (LSA) studiesrevealed that proteins show restricted reorientations withangular amplitudes of 10◦–40◦ and correlation times in theps and ns regimes at ambient temperatures [20–25].
Here, 2H NMR SLR and LSA studies are combined with2H NMR stimulated-echo (STE) experiments to investigateprotein dynamics. This approach covers a dynamic range of10 orders of magnitude, as required in view of stretched-exponential or power-law correlation functions of proteinmotion found by other methods [10,26–31]. Moreover, itenables detection of restricted reorientation with amplitudesdown to 1◦–2◦ [32]. Previously, the broad time window andhigh angular resolution of 2H NMR provided us with insightsinto solvent dynamics at protein surfaces [33–36] and β
relaxations in organic glasses [37–39].Using these capabilities and the possibility to separate
B and M signals in 2H NMR, we show that disorderedC-phycocyanin (CPC) exhibits weakly and highly restrictedbackbone motions, which are solvent coupled. The correlationtime of the highly restricted motion does not cross the timewindow upon cooling, but its angular amplitude decreasesand vanishes near 175 K, indicating a true DT. In orderto determine whether the behavior is common to variousproteins, we contrast these results with 2H NMR data formyoglobin (MYO) and elastin (ELA) from our previous stud-ies [33,34]. In addition, we exploit that molecular dynamics(MD) simulations proved well suited for investigations of theDT of proteins [4,40–42]. Specifically, 2H NMR results are
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KERSTIN KAMPF, BEKE KREMMLING, AND MICHAEL VOGEL PHYSICAL REVIEW E 89, 032710 (2014)
calculated from simulation data for hydrated MYO and ELA[30,43] to ascertain temperature-dependent protein dynamics.
II. METHODS
A. Experimental methods
Disordered samples of perdeuterated CPC are studied in thedry state and in a hydrated state (h = 0.3 g/g). Occasionally,we consider mixtures with higher hydration levels, whichfeature freezable free water. Previous works described thesample preparation [44] and the experimental setup [35], whichoperates at a Larmor frequency of ωL = 2π × 46.1 MHz.
In the studied CPC samples, the deuterons are in C–2Hbonds of the protein. 2H NMR probes their quadrupolarfrequencies [45],
ωQ = ± δ
2(3 cos2 θ − 1), (1)
which depend on the angle θ between bond axis and magneticfield B0. The anisotropy parameter δ describes the strengthof the quadrupolar interaction and, thus, the width of thespectrum. For C–2H bonds, δ ≈ 2π × 125 kHz.
In our case of disordered samples, 2H LSA studies revealbroad and narrow spectra when C–2H bond reorientation isslow and fast on the time scale, τ ≈ 1/δ ≈ 1 μs, respectively.While the powder average results in a Pake shape of the broadline, the geometry of the motion determines the shape of thenarrow line. Unlike B deuterons, M deuterons of perdeuteratedCPC are subject to fast methyl group rotation. Such uniaxialrotations lead to a Pake spectrum characterized by a motionallyaveraged and, hence, smaller anisotropy parameter [45],
δ = ± δ
2(3 cos2 χ − 1). (2)
Here χ is the angle between the rotation axis and possible bondorientations. Thus, the B and M deuterons exhibit a broaderand narrower Pake spectrum, respectively, enabling spectraldiscrimination.
B. Computational methods
We consider two protein-water mixtures with the samehydration level of h = 0.3 g/g. To enable calculations of NMRobservables, we use all-atom models of both systems. Hy-drated MYO consists of 4 protein and 1200 water molecules.The MD simulations for this model were performed in previouswork [30]. Hydrated ELA, as simulated in this work, comprises1 polypeptide (VPGVG)50 and 342 water molecules. In priorstudies [30,43], we performed MD simulations for an united-atom model of this mixture. While the obtained data revealedthat mixtures with 1 and 8 (VPGVG)50 polypeptides exhibitcomparable structural and dynamical properties, they did notallow us to compute NMR observables, because the relevantbonds are not explicitly considered in the force field, makingthe new simulations of this work necessary.
The GROMACS simulation software package was used forall MD simulations [46]. The GROMOS96 43a2 force field wasutilized for the proteins and the SPC/E model was employedfor water. Atomic trajectories with lengths of up to 1.2 μswere calculated. Further simulation details can be found in ourprevious studies [30,43].
-100 0 100ν (kHz)
-100 0 100ν (kHz)
-100 0 100ν (kHz)
(a)
hydrateddry
(b)
160 K210 K260 K300 K
(c)
Δ100 μs20 μs
Δ
FIG. 1. (Color online) 2H NMR spectra obtained from the solid-echo pulse sequence, 90◦
x--90◦y-t , at the indicated temperatures:
(a) dry CPC ( = 20 μs), (b) hydrated CPC ( = 20 μs), and(c) hydrated CPC ( = 100 μs). The dashed lines are spectrafrom simulations for a cone model with χ = 4◦ and τ =10 μs for(b) = 20 μs and (c) = 100 μs using δ = 2π × 125 kHz.
For a calculation of 2H NMR results from the MDsimulation data, we follow the methodology used in prior workon polymer melts [47]. Briefly, we exploit that the quadrupolarfrequencies ωQ are determined by the bond orientations. Thus,the time dependence of the resonance frequency is obtainedfrom the rotational motion of the bond vector. To calculate2H NMR correlation functions, we do not distinguish betweenprotons and deuterons and assume that the reorientation ofthe C–1H bonds in the simulations determines the results inthe same way as the reorientation of the C–2H bonds in themeasurements, i.e., we use Eq. (1). The calculated quantitiesresult from averages over several time origins and all backboneC–1H bonds; see below.
III. RESULTS
A. NMR experiments
As outlined in Sec. II A, the presence and absence of methylreorientation and, hence, of motional averaging leads to narrowand broad Pake spectra for M and B deuterons, respectively.This possibility of spectral discrimination of M and B signalsis evident from 2H NMR spectra of dry and hydrated CPC inFig. 1.
To selectively ascertain backbone dynamics, we focus onthe broad B component in the following. An increase oftemperature does not lead to major changes but to minorreduction of the spectral width, which can be quantifiedwhen we determine the anisotropy parameter δexp(T ) of theB component. In Fig. 2(a), we observe δexp = δ at T <
3 4 5 61000 / T (K)
0.96
0.98
1.00
δ exp(T
) / δ
3 4 5 61000 / T (K)
02
46
8
10
χ/ °
hyd
dry
(a) (b)
χ
2H
C
FIG. 2. (a) Normalized anisotropy parameter δexp(T )/δ for Bdeuterons in dry and hydrated CPC together with the cone model.(b) Semiopening angles χ obtained from δexp(T )/δ within the conemodel using Eq. (2).
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175 K, indicating an absence of backbone dynamics withτ � 1 μs. At T > 175 K, the LSA continuously decreaseswhen the temperature is increased. This motional narrowingis weak but more pronounced for hydrated CPC than for dryCPC, indicating that the backbone motion is highly restrictedand water coupled.
When an increase of temperature affects the rate but not thegeometry of a motion, a transition from the static value δ to theaveraged value δ occurs upon crossing the time scale τ = 1/δ.We do not observe such transition between plateau values δ
and δ in a narrow temperature range. Rather, the temperaturedependence of δexp can be rationalized when the motion isfast (τ � 1/δ) at all temperatures, but becomes less restrictedupon heating. In such case, the ratio δexp/δ can be identifiedwith the motional order parameter S = δ/δ, used to analyze2H LSA of lysozyme [22]. Then room-temperatue values ofS ≈ 0.98 for dry CPC and S ≈ 0.96 for hydrated CPC indicatethat existence of a hydration shell enlarges the amplitude of thehighly restricted motion. The order parameters can be mappedonto angular amplitudes within motional models. For jumps onthe surface of a cone, the semi-opening angle of the cone, χ , isobtained from Eq. (2), yielding χ = 7◦ for dry CPC and χ =10◦ for hydrated CPC at room temperature. In Fig. 2(b), wesee that, upon cooling, χ decreases with 1/T until it vanishesat Tx ≈ 175 K, which interestingly coincides with Tlow fromneutron scattering [7,8].
2H NMR spectra recorded with the solid-echo method aremore sensitive to restricted motion for long solid-echo delays. Specifically, a strongly reduced intensity in the center ofsuch spectra results from small-angle fluctuations with 1 �χ � 10◦ when τ ≈ 1/δ [37–39]. In Fig. 1, this characteristicchange of the line shape is evident from comparison of spectrafor = 20 μs and = 100 μs obtained from simulations ofthe cone model with χ = 4◦ (dashed lines) [32]. This effectis not observed in the spectra of hydrated CPC measured for = 100 μs in the range 160–310 K. Despite interference ofM signals, we see in Fig. 1(c) that the intensity in the centerof the B spectrum does not vanish but is basically independentof temperature. Hence, at none of these temperatures, asignificant fraction of C–2H bonds exhibits highly restrictedmotion with τ ≈ 1/δ, further ruling out that the line narrowingδexp(T ) is due to a crossover between the limits τ � 1/δ andτ � 1/δ, i.e., from a speedup of dynamics. Rather, it resultsfrom fast small-angle fluctuations, which are less restrictedat higher temperatures. Hence, the onset of this backbonemotion at Tx ≈ 175 K marks a fundamental change of proteindynamics.
For hydrated CPC above 240 K, a narrow central line isanother characteristic spectral feature. In Fig. 1, it is evidentthat its spectral intensity grows with increasing temperatureand amounts to ca. 1% of the total intensity at 300 K. For dryCPC, the narrow line is absent. Additional 2H NMR spectrafor various hydration levels h = 0.0–1.0 g/g are displayed inFig. 3. It can be seen that the narrow line grows with increasinghydration at 300 K, while it is very weak and independent of thewater content for h � 0.3 g/g and T < 270 K when free water,which is not in contact with the protein, is frozen. The obser-vation of such a narrow line means that, above 240 K, a smallfraction of backbone segments show weakly restricted motionwith τ � 1/δ, which relies on an existence of bulk water.
-50 0 50ν (kHz)
-50 0 50ν (kHz)
240-250 K
(a) (b)
1.0 g/g
300 K
0.5 g/g
0.3 g/g
0.0 g/g
FIG. 3. (Color online) 2H NMR spectra for the indicated hydra-tion levels: (a) T = 300 K and (b) T = 250 K for h = 1.0 g/g andT = 240 K for the other hydration levels. The data were recordedwith the solid-echo pulse sequence for an echo delay of = 20 μs.
Next, we compare 2H SLR for dry and hydrated CPC. Aftersaturation, the magnetization builds up in two nonexponentialsteps, see Fig. 4(a), which can be assigned to M and Bdeuterons by spectral analysis. Hence, we fit the buildup ofnormalized magnetization m(t)/m∞ to a superposition of twostretched-exponential SLR functions,
m(t)/m∞ = 1−�(t) = 1−[aM�M (t)+aB�B(t)]. (3)
Here aM + aB = 1 and the SLR functions of the deuteronspecies are �S(t) = exp[−(t/T1S)βS ] (S ∈{M,B}). The SLRtimes T1S and stretching parameters βS of dry and hydratedCPC are shown in Fig. 4(b). SLR times show a minimumfor τ ≈ 1/ωL ≈ 1 ns. While T1M exhibits such minimum fordry and hydrated CPC, indicating that methyl group jumpscross the 1-ns time scale, T1B continuously decreases whenraising the temperature near room temperature, in particular.Specifically, T1B does not exhibit substantial dependencies ontemperature and hydration below Tx ≈ 175 K but only aboveTx , where it is shorter for hydrated CPC than for dry CPC. Thismeans that a hydration shell facilitates backbone dynamics thatare effective for SLR. When we compare the present data withprevious results for B deuterons of hydrated ELA and hydrated
10-4
10-2
100
102
t (s)
0.0
0.5
1.0
m(t
) / m
∞
240 K157 K
4 5 6 71000 / T (K)
10-2
10-1
100
T1M
, T1B
(s)
4 5 6 70.5
1
β M, β
B
(a) (b)
FIG. 4. (Color online) (a) Buildup of normalized magnetizationm(t)/m∞ for dry CPC (open symbols) and hydrated CPC (solidsymbols) at 157 and 240 K. The lines are fits with Eq. (3).(b) Resulting fit parameters. Main panel: SLR times T1M and T1B .Inset: Stretching parameters βM and βB . 2H SLR times T1 of amidedeuterons in hydrated MYO (∗, h = 0.30 g/g) and hydrated ELA (×,h = 0.43 g/g) are shown for comparison [33,34].
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MYO in Fig. 4(b) [33,34], we observe similar SLR behavior,implying that various proteins exhibit comparable backbonedynamics.
Two limiting scenarios can, in principle, rationalize theobserved decrease of T1B upon heating at T > Tx . First, back-bone dynamics speeds up for a fixed geometry and, second,it becomes less restricted for a fixed rate. The first scenarioassumes correlation times τ � 1/ωL, while the second onesupposes restricted motion, for which T1 ∝ 1/(1 − S2) [22,48].In both limits, T1B is determined by another mechanism below175 K, when backbone motion is too slow or too restricted tobe effective for SLR. The first scenario may explain the SLRtimes but not the LSA data, as discussed above. The secondscenario is consistent with both SLR and LSA effects, i.e.,changes in the temperature dependence at Tx can be tracedback to a vanishing amplitude of highly restricted motion.
The stretching parameters βS are largely independent oftemperature and hydration; see the inset of Fig. 4(b). Values ofβM ≈ 0.93 and βB ≈ 0.55 show that deviations from exponen-tial relaxation (βS = 1) are weak for M deuterons but strong forB deuterons. The latter finding indicates a broad distribution ofT1B times and, thus, of motional geometries and/or correlationtimes. A high complexity of protein dynamics was alsoreported in previous studies [10,27–31]. Therefore, extendedmodel-free approaches [48], which were often used in NMRapproaches to characterize dynamics in terms of two orderparameters and correlation times [15,22,23], are too simplisticso we refrain from such analysis.
Finally, we perform 2H STE experiments, which correlatethe frequencies ωQ of a deuteron during two short evolutiontimes, tp � τ , separated by a longer mixing time, tm τ , inthe μs-to-ms range. Variation of tm for fixed tp allows us tomeasure the correlation function [45,49],
F cos2 (tm; tp) ∝ 〈cos[ωQ(0)tp] cos[ωQ(tm)tp]〉. (4)
Here 〈. . . 〉 denotes the ensemble average. F cos2 (tm) decays
when molecular reorientation alters the value of ωQ duringtm. However, it can also decrease due to SLR. The angularresolution of the experiment is high for large tp [49]. Inparticular, previous STE works [37–39] demonstrated thathighly restricted motion can be probed for tp = 30 μs, asis also evident from simulated data for the cone model in theinset of Fig. 5.
Dynamics slowing down across τ ≈ 1 μs exits the timewindow of LSA studies and enters that of STE methods.Therefore, if the 2H NMR spectra of CPC ceased to changebecause of a slowdown of the weakly and highly restrictedmotions, these dynamics would occur in the dynamic range ofSTE experiments at 240 K and 175 K, respectively. Figure 5shows F cos
2 (tm; tp = 30 μs) of dry and hydrated CPC at thesetemperatures. For both samples and temperatures, we seetwo-step decays of F cos
2 (tm), which resemble that of �(tm).Specifically, the steps of both functions have similar timeconstants but somewhat different relative heights. The lattereffect is a consequence of the fact that the height of theSTE signal depends on not only the number of M and Bdeuterons but also the value of δtp [49,50], which differs forboth deuteron species. Thus, F cos
2 (tm) decreases due to spinrelaxation, preventing interpretation in terms of a rotationalcorrelation function of protein dynamics.
10-4
10-3
10-2
10-1
100
101
tm
(s)
0
0.2
0.4
0.6
0.8
1
F2co
s , FB
F2
cos dry
F2
cos hyd
FB dry
FB hyd
10-4
10-3
10-2
10-1
100
101
tm
(s)
log(t)0
0.5
1
(a) (b)
175 K 240 K
1°
4°
2°3°
10°
FIG. 5. (Color online) F cos2 (tm) and FB (tm) of dry CPC (open
symbols) and hydrated CPC (solid symbols) from STE experimentsfor tp = 30 μs at (a) 175 K and (b) 240 K. FB (tm) is the spectralintensity of STE spectra in the range |ωQ| �2π × 40 kHz. It exclu-sively results from B deuterons. The corresponding SLR functions�(tm) and �B (tm) are shown as dashed and solid lines, respectively.Inset: F cos
2 (tm) for tp = 30 μs, as obtained from simulations forrandom jumps (τ = 10 ms) on surfaces of cones with the indicatedsemiopening angles χ .
To test this conclusion, we calculate STE spectra fromthe STE signals and integrate the spectral intensities from Bdeuterons at |ωQ| � 2π × 40 kHz. Observing this integratedintensity as a function of tm approximates the correlationfunction of B deuterons, FB(tm). We find FB(tm)∝�B(tm), seeFig. 5, i.e., the decay exclusively results from SLR. Hence, STEexperiments do not probe dynamics in the μs-to-ms range fordry and hydrated CPC. Consequently, the fraction of segmentsshowing weakly restricted motion is too small to be detected at240 K and the amplitude of the highly restricted motion is toosmall to be probed at 175 K. At the same time, the motions canoccur outside the STE time window. In particular, the highlyrestricted motion is, despite sufficient amplitude, not observedat 240 K due to τ < 1 μs.
B. MD simulations
Having used 2H NMR methods to characterize the internaldynamics of CPC and to ascertain comparable behavior forELA and MYO, it is interesting to determine whether ourexperimental findings are consistent with simulation results.Striving for a straightforward comparison, we recall thatmolecular reorientation dynamics is probed in 2H NMR andcalculate rotational correlation functions from present andprevious MD data for hydrated ELA and MYO [30,43].Specifically, we study the reorientation of C–1H bonds inthe backbones of the ELA and MYO models based on thecorrelation function
F2(t) ∝ 〈P2[cos (θ (0))]P2[cos (θ (t))]〉. (5)
As the Legendre polynomial P2[cos θ ] is proportional to the2H NMR frequency ωQ, see Eq. (1), F2(t) is closely relatedto STE decays. In order to determine to what extent theoverall tumbling motion of the protein molecules affects F2(t),we compare correlation functions resulting with and withoutcorrection of the atomic trajectories for the global molecularreorientation.
In Fig. 6(a), we show F2(t) calculated from MD sim-ulations for hydrated ELA at various temperatures. Apart
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100
101
102
103
t (ps)
0.80
0.85
0.90
0.95
F2 200 K
220 K240 K260 K280 K310 K
3 3.5 4 4.5 5 5.51000 / T (K)
0.00
0.02
0.04
0.06
Δ F
2
MYOELA
(a) (b)
FIG. 6. (Color online) Results from MD simulations for hydratedELA and hydrated MYO: (a) F2(t) characterizing ELA backbonereorientation at the indicated temperatures. Correlation functionsobtained with (solid lines) and without (dashed lines) correction forthe overall tumbling motion are compared. At 200 K, the curvesnearly coincide. (b) Temperature-dependent loss of correlation in thetime window 1 ps–1 ns, i.e., F2 = F2(t = 1 ps) − F2(t = 1 ns).The data result from trajectories corrected for overall tumbling. Thesolid line is a guide to the eye.
from vibrational motion outside the studied time window,two dynamic regimes can be distinguished. A weak decayat short times gives way to a steeper decrease at long times.When we compare correlation functions obtained with andwithout correction for the overall tumbling motion, we observethat both dynamical regimes exist within the molecular frameand, hence, they are of intramolecular origin. However, globalmolecular reorientation leads to an additional damping, inparticular, for long times and ambient temperature. Therefore,the further analysis uses correlation functions corrected foroverall tumbling.
The short-time decay is less prominent at lower tempera-tures and nearly linear in a semilogarithmic representation.In previous simulations [30], we showed that it can bedescribed by power-law or logarithmic-like decays, indicatinganomalous dynamics without a characteristic time scale. Forexample, we showed that the simulation data are consistentwith the model of fractional diffusion in a harmonic potential.Then the decrease of the atomic displacements upon coolingis not due to a longer time scale but rather to reduced positionfluctuations at lower temperatures, according to the Boltzmanndistribution in the harmonic potential. Similarly, we observedfor the highly restricted motion in the present experimentalstudy that the temperature dependence does not result froma variation of the time scale but of the angular amplitude.Furthermore, in both measurements and computations, the lossof correlation is very small. In view of these similarities, wepropose that the strongly anomalous dynamics observed in thesimulation studies is probed by our experimental approach ashighly restricted motion.
For a test of this hypothesis, we use the MD data todetermine the loss of correlation F2 in the time window1 ps–1 ns as a function of temperature. This range ischosen to minimize contributions from vibrational motion andadditional relaxation at shorter and longer times, respectively.Nonetheless, the latter relaxation affects the results nearambient temperatures. In Fig. 6(b), we see that, upon cooling,F2 continuously decreases until it vanishes at 150–200 K,resembling the results for the experimentally determined cone
angle χ ; see Fig. 2. These similarities further support ourconclusion that NMR experiments and MD simulations probethe same highly restricted anomalous protein dynamics. Asfor the long-time decay in the simulation, the molecular originand a possible relation to the weakly restricted motion foundin the experiment needs to be ascertained in future work.
IV. CONCLUSIONS
2H NMR provided straightforward access to backbonereorientation of dry and hydrated CPC. We observed twowater-coupled dynamical processes. A combination of SLR,LSA, and STE methods clearly showed that most backbonesegments exhibit highly restricted motion, which is fast (τ <
1 μs) at all temperatures. It loses amplitude upon coolingand vanishes at Tx ≈ 175 K, while it gains amplitude wheninterfacial water exists. For hydrated CPC, cone modelsyielded an angle of χ = 10◦ at room temperature. However,nonexponential SLR indicated broad distributions of motionalgeometries and/or correlation times. Comparison with 2HNMR data for hydrated ELA and MYO implied that variousproteins share this highly restricted motion. In addition, the 2HNMR results revealed that a small fraction of CPC backboneunits exhibit weakly restricted motion above 240 K. Thisfraction is sensitive to the existence of bulk water and increaseswith increasing temperature.
Our results can be related to the two-step scenario of theDT [7,8]. Based on the finding Tlow ≈ Tx , we conclude thata fundamental change of protein dynamics, i.e., a true DT,occurs at this temperature. While neutron scattering analysesof the low-temperature step suffer from methyl contributions,2H NMR clearly shows that the effect originates from thevanishing amplitude of the highly restricted motion and, hence,from modifications in geometries rather than rates of backbonedynamics. For hydrated CPC, the high-temperature step wasobserved at Thigh ≈ 225–240 K [51]. In this range, the weaklyrestricted motion sets in, but whether the effect is related to theincrease of atomic displacements probed by neutron scatteringdeserves further clarification. Recent studies argued that thelatter observation does not mark a true transition in proteinmobility, but it occurs when a relaxation process enters thetime window of the respective experiment [1,10–12].
The low-temperature step was recently attributed to a glasstransition [7,8]. For example, it was ascribed to a rattling mo-tion of atoms caged by anharmonic intermolecular potentials,which gains amplitude upon crossing a glass transition but hasno characteristic time and results in a nearly constant loss [8].Such relation between protein motion and glassy dynamicsis consistent with present and previous simulation results forhydrated ELA and MYO [30,43]. In particular, power-law orlogarithmic-like decays of computational correlation functionsindicate anomalous dynamics, which lacks a characteristictime. The amplitude of this dynamics is small and decreasesupon cooling until it vanishes not too far below 200 K. Hence,the small amplitude anomalous dynamics found in MD simu-lations and the highly restricted backbone motion observed inNMR experiments share a common phenomenology. In viewof these similarities, we conclude that the experimental andcomputational studies probe the same motion and propose thatthe vanishing amplitude of this anomalous dynamics is at the
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origin of the low-temperature step, akin to conclusions drawnfrom comparison of protein and glass transition features [8].
In future work, it may be worthwhile to study whetherthe observed protein motions are related to the α and β
relaxations of Frauenfelder’s slaving concept [1]. Specifically,it should be clarified whether the highly restricted motionwith a temperature-dependent amplitude, which involves mostbackbone segments, is related in some way to the β relaxationand whether the weakly restricted motion, shown by fewbackbone segments, is, in view of a strong coupling to bulkwater, associated with the α relaxation. In any case, the former
protein motion resembles caged dynamics of glass formers, butthe latter should be distinguished from the structural relaxationof supercooled liquids, which involves all rather than a fewentities.
ACKNOWLEDGMENTS
We thank W. Doster for providing us with the CPC aswell as the Verband Chemischer Industrie and the DeutscheForschungsgemeinschaft (Vo-905/8-1) for funding.
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