Temperature Dependence of Logarithmic-like Relaxational Dynamics

Letter pubs.acs.org/JPCL

Temperature Dependence of Logarithmic-like Relaxational Dynamics of Hydrated tRNA Xiang-qiang Chu,*,†,‡ Eugene Mamontov,§ Hugh O’Neill,‡ and Qiu Zhang‡ †

Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, United States Biology and Soft Matter Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States § Chemical and Engineering Materials Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ‡

S Supporting Information *

ABSTRACT: The dynamics of RNA within the β-relaxation region of 10 ps to 1 ns is crucial to its biological function. Because of its simpler chemical building blocks and the lack of the side methyl groups, faster relaxational dynamics of RNA compared to proteins can be expected. However, the situation is actually opposite. In this work, the relaxational dynamics of tRNA is measured by quasielastic neutron scattering and analyzed using the mode coupling theory, originally developed for glass-forming liquids. Our results reveal that the dynamics of tRNA follows a log-decay within the βrelaxation region, which is an important trait demonstrated by the dynamics of proteins. The dynamics of hydrated tRNA and lysozyme compared in the time domain further demonstrate that the slower dynamics of tRNA relative to proteins originates from the difference in the folded states of tRNA and proteins, as well as the influence of their hydration water. SECTION: Biophysical Chemistry and Biomolecules

R

constituents (molecules or amino acid residues) assemble, and a complex energy landscape (EL). The EL concept was proposed by Frauenfelder and co-workers16−18 for proteins composed of a large number of alternative conformations at similar energies.10,19 Thus, the relaxation dynamics of globular proteins can also be described by the MCT,9,20 which predicts that the appearance of a logarithmic decay for a glass forming liquid is in the vicinity of a so-called A3 singularity.21−23 This phenomenon has been predicted by molecular dynamics (MD) simulation24 and observed in the time range of 10 ps to 1 ns by neutron scattering experiments3 in a globular protein lysozyme and an oligomeric protein IPPase.4 Before MCT was employed to describe the protein dynamics, this dynamics has been interpreted using various theoretical concepts, such as trapping models,25,26 fractional Brownian dynamics,27,28 and fractional Fokker−Planck (FFP) approaches.29,30 In addition, MD simulations were used to determine the applicability of all these theories to the logarithmic-like relaxation of proteins and proved that MCT allows us to rationalize findings at ambient temperatures.31 Our work will further show that MCT is also applicable over a wide temperature range.

NA (ribonucleic acid) is a biopolymer actively involved in several important steps during the translation of genetic information from DNA into protein products. From a molecular perspective, the chemical building blocks of RNA are simpler than those in proteins. Specifically, the lack of side methyl groups in RNA might preclude the enhanced dynamics due to methyl group rotation observed in proteins. Thus the relaxational dynamics of RNA is expected to be faster compared to proteins. However, it has been reported that the dynamics of tRNA is actually slower compared to protein dynamics.1,2 Additionally, recent neutron scattering studies of the relaxation dynamics of proteins3,4 have shown a logarithmic-like decay in the time range of several picoseconds to several nanoseconds through measurements using the new generation of backscattering spectrometers.5−7 These new advances now make it possible to directly compare the relaxational dynamics of RNA and globular proteins in the time domain that is most directly related to their biological functions. Furthermore, it is of great interest to know whether the relaxational dynamics of RNA also displays a logarithmic-like decay in the same time range as the dynamics of globular3 and oligomeric proteins.4 It has been popular in the literature to describe the slow dynamics of globular proteins by the mode coupling theory (MCT), which had been originally developed for glass forming molecular liquids.8,9 The dynamics of native globular proteins shares common properties with the dynamics of glass-forming liquids,8−15 such as noncrystalline packing, in which the © 2013 American Chemical Society

Received: January 19, 2013 Accepted: March 4, 2013 Published: March 4, 2013 936

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Figure 1. Left panel: QENS spectra of hydrated tRNA at temperatures from T = 240 K up to 340 K,10 K intervals. Right panel: ISF of the QENS spectra at each temperature, following the same color sign. Data shown in both panels are at Q = 0.7.

The sample was then hydrated using isopiestic conditions by incubation in a sealed container containing 99.9% D2O. The level of hydration was controlled by varying the incubation time. The final hydration level of the tRNA was 0.51 g of D2O per gram of tRNA (h = 0.51). QENS experiments were performed on a nearbackscattering spectrometer BASIS,6,7 at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL). For the chosen experimental setup, the BASIS had an energy resolution of 3.4 μeV (full-width at half-maximum, for the Qaveraged resolution value) and an extended dynamic range of ±200 μeV compared to the previously used ±100 μeV. The QENS data were collected at 11 different temperatures from T = 240 K up to 340 K, 10 K intervals. In addition, we collected data set at 20 K to characterize the energy resolution of the instruments. The QENS measurement gives a convolution of the selfdynamic structure factor SH(Q,ω) of the hydrogen atom in a typical biopolymer molecule (tRNA in this study) with the energy resolution function R(Q,ω) of the instrument (in this case, measurement of the sample at 20 K), i.e., Sm(Q,ω) = SH(Q,ω) ⊗ R(Q,ω), where Sm(Q,ω) is the measured QENS intensity. By taking a Fourier transform of the above equation, the convolution is reduced to a multiplication:

One of the distinctive features of complex systems is a slow nonexponential relaxation of the intermediate scattering function (ISF) FH(Q,t), observed in a wide range of time scales. The ISF is referred to as the density−density time correlation function of a single hydrogen particle in the biomolecule measured by neutron scattering experiments. It is used to describe the relaxational processes in the dynamics of the biomolecule and is the primary quantity of theoretical interest related to the experiment. The time dependence of the ISF of a complex system usually follows three steps: a short-time Gaussian-like ballistic region is at first followed by the β-relaxation region, which is governed by either two power-law decays, or a logarithmic decay. In turn, the βrelaxation region finally evolves into the α-relaxation region that is governed by a stretched exponential decay, or Kohlrausch− Williams−Watts (KWW) law. This type of relaxation is observed in complex systems,32 such as biomolecules and glasses, while the simple exponential relaxation (or Debye law) is typical for simple systems such as high-temperature liquids. However, although both biomolecules and glasses are aperiodic, the organization of biomolecules’ EL is far more sophisticated compared to glass. Since protein and RNA structures are exceptionally sensitive to the interactions of their hydrogen bonds with water, the diffusive dynamics of hydration water in proteins and RNA measured by quasielastic neutron scattering (QENS) reveals important information on the biopolymer’s global and local conformational flexibility, and, in turn, its functionality.19 In this study, the relaxational dynamics of tRNA is explored in a faster time range compared to the previous experiments on protein molecules3 by using QENS measurements with an extended dynamical range. A logarithmic-like decay is observed in the ISF in the time domain obtained from Fourier transformation of the background-corrected QENS spectra. The ISF of tRNA molecules is then analyzed by an asymptotic formula developed from the MCT and is compared directly in the time domain with that of lysozyme molecules obtained in the previous experiments. We clearly see that the relaxational dynamics of tRNA is much slower than that of the lysozyme. Additionally, the characteristic β-relaxation time τβ(T) is extracted from the fitting parameters of the log-decay and is demonstrated to undergo a transition at a temperature of about 240 K, which is similar to the so-called “dynamic transition” of hydrated tRNA molecule.33 The data was collected from yeast tRNA (Sigma Aldrich R8759, 21 A260 Units/mg). The nucleic acid sample was dissolved in D2O and lyophilized to exchange labile hydrogen atoms for deuterium atoms. This process was repeated twice.

Fm(Q , t ) = FH(Q , t ) × R(Q , t )

(1)

where FH(Q,t) is defined as the ISF of the hydrogen atoms of tRNA molecule, which is the Fourier transform of the selfdynamic structure factor SH(Q,ω). From eq 1, FH(Q,t) can be calculated as FH(Q , t ) = Fm(Q , t )/R(Q , t )

(2)

where Fm(Q,t) is the Fourier transform of the measured data (after subtracting the background) Fm(Q,t) = FT[Sm(Q,ω)], and R(Q,t) is the Fourier transform of the resolution function. Here, the following asymptotic expression derived from MCT is used to fit the ISF FH(Q,t):21−24 FH(Q , t ) ∼ [f (Q , T ) − H1(Q , T ) ln(t /τβ(T )) + H2(Q , T ) ln 2(t /τβ(T ))] exp(t /τα(Q , T ))

(3)

where τβ(T) and τα(Q,T) are the characteristic β- and αrelaxation times, respectively, and f(Q,T) is the T-dependent prefactor proportional to the Debye−Waller factor for small Q values, f(Q,T) = exp[−A(T)Q2]. The Q-dependent parameters H1(Q,T) and H2(Q,T) can be written as H1(Q,T) = h1(Q)B1(T) 937

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Figure 2. Analysis of the ISF of tRNA in the β-relaxation range according to eq 4. The upper three panels show the fitting at three lower temperatures T = 260, 270, and 280 K; The lower three panels show the fitting at three higher temperatures T = 320, 330, and 340 K. ISFs are calculated from the analysis of QENS spectra at seven Q values. Black solid lines represent the fitted curves of the ISFs at all seven Q values at each temperature.

Figure 3. (A) fitting parameter H1(Q,T) as a function of Q at different temperatures. It is fitted to a power law of Q, i.e., H1(Q,T) = B1(T)Qβ, where β spans from 1.0 to 2.0. (B) The fitted B1(T) values plotted as a function of temperature. (C,D) The characteristic β-relaxation time τβ(T) extracted as a Qindependent fitting parameter. Left: over plot of τβ(T) and MSD of hydrogen atoms in RNA molecules33 as functions of temperature. Right: Arrhenius plot of τβ(T) in a log scale against 1000/T.

and H2(Q,T) = h1(Q)B2(Q,T), where h1(Q) is a power law of Q

FH(Q , t ) ∼ [f (Q , T ) − H1(Q , T ) ln(t /τβ(T ))

β

for small Q values, i.e., H1(Q,T) = B1(T)Q . H1(Q,T) and

+ H2(Q , T ) ln 2(t /τβ(T ))]

H2(Q,T) represent the first- and second-order logarithmic decay

(4)

Figure 1 shows the normalized QENS spectra (left panel) and the calculated ISF FH(Q,t) (right panel) of the QENS spectra after Fourier transformation. Before Fourier transformation, the background has been carefully evaluated and subtracted, following the procedure described in ref 3. The broadening of the central peaks from the resolution function indicates the quasi-elastic scattering of neutrons by the hydrogen atoms in the

parameters, respectively.23−34 In our measurement, the time range (10 ps to 1 ns) is much shorter than the α-relaxation time range, i.e., t is much smaller than τα; thus, the last exponential factor is very close to unity. Now eq 3 can be written as a simpler expression: 938

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Figure 4. Comparison of the dynamics of hydrated tRNA and lysozyme at physiological temperature T = 300K. Upper panel: ISFs of tRNA and lysozyme compared at seven Q values. The open symbols represent data belonging to lysozyme (LYZ), while the solid symbols are those of tRNA. The solid lines are the fitted curves of the ISFs of tRNA and lysozyme, respectively. Lower panel: fitting parameter H1(Q,T) of tRNA and lysozyme plotted as a function of Q at T = 300 K.

temperatures, which has already been shown in Figure 1. The black curves fit the data well at each Q value within the experimental measured time range ∼10 ps to less than 1 ns, enforced by the limit of the instrumental resolution. The fitting results show that A(T) has a value close to 0, and all the FH(Q,t) at all seven Q values merge to a value f(Q,T) very close to 1 at a specific short time τβ(T) around 10 ps. The Qdependent parameters H1(Q,T) and H2(Q,T) are obtained by fitting the curves in the measured time range. Figure 3 (A) shows the Q dependence of the parameter H1(Q,T), which is found to obey a power law in Q at small Q values, i.e., H1(Q,T) = B1(T)Qβ, where the power β is within the range of 1.0−2.0. The fitted parameter B1(T) is plotted in Figure 3B as a function of temperature. The characteristic β-relaxation time τβ(T) is plotted as a function of temperature in Figure 3C,D. It is interesting to note that there is some kind of transition at about 240 K, by fitting the τβ(T) versus 1000/T plot (the so-called Arrhenius plot) using the Vogel−Fulcher−Tammann (VFT) law, τ0 = τ1 exp[DT0/(T − T0)]. Here D is a dimensionless parameter providing the measure of fragility, and T0 is the ideal glass transition temperature. The VFT behavior is typical of the αprocess. We use it here to fit τβ(T), which shows apparent nonArrhenius behavior, although it is actually in the β-relaxation

sample. As the temperature is increased, the central peak becomes broader, which implies the faster dynamics of hydrogen atoms in the tRNA molecules. The ISFs for each temperature ranging from 240 K to 340 K are shown in the time range of 10 ps to 1 ns, at Q = 0.7 Å−1. In this time range, we observe an apparent logarithmic-like relaxation process, which has been recently reported for lysozyme molecules using both computer simulations24 and neutron scattering experiments.3 This βrelaxation of hydrogen atoms in the tRNA molecules becomes faster as the temperature is increased. This result is intuitive and straightforward, and can be easily observed from the right panel of Figure 1. The ISF FH(Q,t) is analyzed quantitatively according to eq 4, the asymptotic expression derived from MCT. Four parameters, A(T), τβ(T), H1(Q,T), and H2(Q,T), are used in the fitting, where A(T) and τβ(T) are Q-independent parameters, and A(T) represents the prefactor f(Q,T) related to the Debye−Waller factor. The ISFs are analyzed at seven Q values using global fitting to fit the Q-independent and the Q-dependent parameters simultaneously. Figure 2 shows the fitting results at six different temperatures among all 11 temperatures we analyzed. Note that different scales are used in plotting the panels for lower and higher temperatures since the relaxation is much faster at higher 939

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physiological temperature T = 300 K. It is evident that the relaxational dynamics of tRNA is actually slower than that of the lysozyme, at every Q value ranging from 0.5 to 1.7 Å−1. To make the observation more quantitative, the slope of the logarithmic decay H1(Q,T) of both tRNA and lysozyme3 are plotted as functions of Q in the lower panel of Figure 4. The fact that H1(Q,T) of tRNA is smaller than that of lysozyme at each Q provides further evidence that the relaxational dynamics of tRNA decays slower than that of lysozyme. This observation is consistent with the earlier literature reports,1,2,39 despite the intuitive expectation of the faster relaxation dynamics in tRNA compared to proteins due to its simpler chemical building blocks and the lack of side methyl groups. This nonintuitive, at a first glance, result can be understood from two aspects: (1) the difference in the structures of the tRNA and protein and (2) the contribution of the dynamics of the hydration water surrounding them. In proteins, ∼25% of non-exchangeable H-atoms are on methyl groups, but in tRNA it is only ∼3%.1,39,48 That is, tRNA has a much smaller number of methyl groups compared to lysozyme and other protein molecules. Recent MD simulation results reveal that methyl group rotations in hydrated proteins contribute significantly to neutron scattering spectra on the pisosecond to nanosecond time scale.49 This is one of the reasons why the relaxational dynamics in the protein is actually faster than the dynamics in tRNA in the observation time range of picoseconds to nanoseconds. Additionally, a number of the internal methyl groups in proteins and the less exposure of protein residues to the solvent lead to weaker temperature variation in the protein dynamics3 compared to the tRNA dynamics. In a more recent study,50 it has been proposed that tRNA dynamics is strongly influenced by the electrostatic environment, in addition to the motions of local water molecules.1 The fitting results in Figure 3 show that the measured log-decay is both Qand T-dependent, indicating that this decay can include both the β-relaxation process and other solvent dependent processes. Thus, the dynamics of both protein and tRNA are strongly related to the solvent dynamics, as has been indicated in earlier literature.1,37 Additionally, the more hydrophilic and more open structure of tRNA compared to protein induces larger amplitude of hydration-induced structural relaxation, resulting in almost twice the relaxation motion on the length scale of tRNA.1 This suggests longer average relaxation time of tRNA compared to lysozyme, and further explains why the measured relaxational dynamics of tRNA is slower, as evident in Figure 4. This slower relaxational dynamics of tRNA compared to protein also reflects the difference in their MSD profiles as a function of temperature39 and, as a consequence, their different dynamical transition temperature. The prevailing opinion on the origin of this dynamical transition in the MSD is that it originates when the relaxation time crosses the resolution window of the measurement,36,41,51 although some recent work42,43 argues that the temperature evolution of the MSD exhibits two kinks that do and do not depend on the time window of the experiment. On the basis of this opinion, the longer relaxation time and smaller MSD of tRNA results in crossing the resolution window at a higher temperature (240 K33 compared to 220 K in proteins). In summary, the relaxational dynamics of tRNA has been studied in the extended time range of 10 ps to 1 ns. It clearly shows a logarithmic-like decay in this β-relaxation time range. This observation suggests log-decay to be the dynamical behavior common to proteins and tRNA, and probably other biopolymers. The dynamics of hydrated tRNA and lysozyme are compared at a

range. This apparent non-Arrhenius behavior of the relaxation time is well-known in protein dynamics, and has been observed in many previous experiments.4,34−36 It is revealing to show that, despite major differences in the structure of proteins and tRNA, the characteristic β-relaxation time τβ(T) of tRNA is also nonArrhenius. This suggests that the non-Arrhenius behavior in the relaxation time is a common feature in the dynamics of biopolymers. In fact, even though β-relaxations in biomolecules can be described by the MCT, its physical origin is by no means the same as for the β-relaxation in the MCT of simple glassforming systems. The dynamic coupling between β-fluctuations in biomolecules and α-fluctuations of the solvent (or, more specifically, the solvation shell)37,38 naturally and intuitively leads to super-Arrhenius temperature dependence of β-relaxations in biomolecules. Here we show that β-relaxations in hydrated powders of biomolecules are characterized by super-Arrhenius behavior, just as the α-fluctuations of the hydration water. It is also very interesting to observe the same low-temperature dynamical transition at about a relatively high (compared to proteins) temperature of 240 K, consistent with the result obtained by analysis of the mean squared displacement (MSD) of hydrogen atoms in the RNA molecules measured in earlier studies.33,39 The temperature and Q-dependence of H2(Q,T) are shown in Figure S1, Supporting Information (SI). From MCT predictions, the change of sign of H2 or the so-called concave− convex crossover is the indication of higher order singularities. However, from previous MD simulation results,24,31 this concave−convex crossover only happens at Q values larger than ∼4 Å−1, corresponding to a length scale of roughly 1 Å. The QENS experiments at BASIS can only measure at Q values up to 2 Å−1. Thus our experimental results show only negative values in H2(Q,T). In Figure 3C, the previous MSD result33,40 is overplotted with τβ(T) of tRNA as a function of temperature to demonstrate this consistency in the dynamic transition of tRNA determined by different methods. Indeed, the dynamic transition in tRNA is supposed to have the same origin as the protein dynamic transition, as had been discussed extensively in the recent literature.35,37−43 The general idea is that this low-temperature dynamic transition in a biomolecule is intimately related to the dynamics and glass transition of its solvent, which is a common dynamic property of glass formers. Recent studies combining neutron scattering with MD simulations also demonstrate that this protein dynamical transition correlates with the relaxation in the hydrogen bond network formed between protein and hydration water.44,45 From Figure 3C,D, one can observe that above T ∼ 320 K, the temperature dependence of τβ(T) does not follow the VFT law anymore and apparently switches to another dynamic behavior. Here we fit the data points with a straight line to show this Arrhenius-like behavior in Figure 3D, since it is hard to determine whether it is an Arrhenius behavior due to the limited data points here. This high-temperature dynamic transition of τβ(T) is possibly related to the high-temperature denaturation of tRNA, which is similar to the high-temperature denaturation of proteins and its hydration water,4,46 and is suggested to correlate with the relaxation in the hydrogen bond network formed between protein and hydration water.44−46 Another realistic possibility is a partial dehydration of the sample above 320 K, as we have observed in the past for hydration water on oxide surfaces.47 In Figure 4, the relaxational dynamics of tRNA is directly compared in the time domain to that of the lysozyme at a 940

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physiological temperature T = 300 K in the time domain within the same β-relaxation time range. Our results directly show that the β-relaxation of tRNA is slower than that of the protein lysozyme. This result is consistent with previous literature1,2,39 and can be explained on the basis of the difference in the folded states of tRNA and proteins and the influence of the solvent (in this case, water). The lack of methyl group rotational motions in tRNA is another reason why the total dynamics of RNA is slower than that of proteins. The temperature dependence of the characteristic β-relaxation time τβ(T) fitted by the asymptotic formula derived from the MCT is plotted as a function of temperature (Figure 3) and shows a stronger temperature dependence in tRNA dynamics compared to protein dynamics.3 It implies a dynamic transition at about 240 K for tRNA, which is a higher temperature compared to the dynamic transition temperature in proteins, and is consistent with the previous observation of dynamic transition in the MSDs of hydrated RNA molecules.33,39

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ASSOCIATED CONTENT

* Supporting Information S

Supporting Information includes the temperature and Qdependence of fitting parameter H2(Q,T). This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The neutron scattering experiment at Oak Ridge National Laboratory’s (ORNL) Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. The authors also acknowledge ORNL’s Center for Structural Molecular Biology (Project ERKP291) supported by the Office of Biological and Environmental Research, US DOE. ORNL is managed by UTBattelle, LLC, for the US Department of Energy (DOE) under contract no. DE-AC05- 00OR22725.

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REFERENCES

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The Journal of Physical Chemistry Letters

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dx.doi.org/10.1021/jz400128u | J. Phys. Chem. Lett. 2013, 4, 936−942