Unfolding Dynamics of Poly

Article pubs.acs.org/JPCB

Comparative Study of the Folding/Unfolding Dynamics of Poly(glutamic acid) in Light and Heavy Water Lucille Mendonça, Andreas Steinbacher,† Raphael̈ Bouganne, and François Hache* Laboratoire d’Optique et Biosciences, École Polytechnique, CNRS, INSERM 91128 Palaiseau cedex, France ABSTRACT: The folding/unfolding equilibrium is investigated in poly(glutamic acid) (PGA) by two complementary sets of experiments: temperature-dependent steady-state circular dichroism spectra on the one hand and time-resolved circular dichroism measurements coupled with a T-jump experiment on the other hand. The experiments are performed for PGA dissolved in water for various pH values, as well as in heavy water. The kinetic and thermodynamic parameters extracted from these measurements are shown to be markedly different between light and heavy water, which is assigned to the difference in hydrogen bond energies in both solvents.

Gooding et al.,9 providing a wealth of information on the dynamics in these systems. In both cases, the monitoring of the unfolding was performed by detecting absorption changes within the amide I′ bands in the infrared (IR) spectral range. This technique is very efficient and yields very precise measurements of the corresponding relaxation time scales, allowing, for example, nonexponential behavior to be detected.9 However, it suffers from two main drawbacks. First, it brings clear but only qualitative indication of the unfolding of αhelices. Due to the width of the amide I′ bands in the IR range and due to the partial overlap of the bands corresponding to a random coil and α-helix, it is difficult to extract quantitative information on the helical fraction. Second, but more important, heavy water must be used as solvent for these experiments because of the strong absorption of water in the same spectral domain. Even though it is not supposed to alter the measured dynamics, it is regrettable not to be able to work in the physiological solvent, which is made up mainly of natural water. In this sense, techniques that detect circular dichroism (CD) changes appear quite complementary to IR absorption techniques as they allow deducing quantitative information on the helical content in peptides and proteins. Furthermore, because they are usually carried out in the visible or ultraviolet (UV) spectrum, they can be used with light or heavy water as solvent. However, because CD signals are usually very weak, such experiments often yield noisy signals and less precise determination of the relaxation rates. In this work, we present T-jump experiments in a partially folded PGA sample and show how to monitor the peptide unfolding through the measurement of CD in the far UV. CD,

1. INTRODUCTION Secondary structure formation dynamics remains an important issue with respect to the much broader protein folding understanding. Indeed, experimental1 and computational2 evidence reveals that complex protein folding often starts with the formation of secondary structures which then arrange to shape the tertiary structure of the protein.3 Especially αhelices are very common in proteins, and they are known to be the most rapidly forming secondary structures.4 As such, they have triggered several remarkable experiments aimed at measuring the time scales involved in the first steps of this structural shaping.5 Poly(L-glutamic acid) (PGA) is a reference system for the investigation of the first stages in α-helix dynamics because it folds into an α-helix in a very pHdependent manner.6 At high pH (pH > 6.5), all the pending acidic chains are deprotonated and become negatively charged. Hence, the strong electric repulsion which then exists tends to separate the side chains and prevents the formation of the αhelix. On the other hand, at low pH (pH < 4.5), when all side chains are protonated, the subsequent charge neutrality allows the formation of the secondary structure. In the middle range, the side chains are partially protonated, resulting in a partial folding of PGA into α-helices. In such an intermediate pH range, the helical fraction of the peptide becomes strongly temperature-dependent, and one observes increased denaturation with increasing temperature. A detailed thermodynamic study of this feature can be found in ref 8. This system is therefore very well adapted to a temperature-jump (T-jump) experiment, in which one can monitor the unfolding process and therefore find its relaxation time. Many experimental techniques have been implemented to study the dynamics in protein folding, yielding complementary insights into the elementary mechanisms.7 PGA unfolding has already been carried out by Krejtschi and Hauser8 and by © 2014 American Chemical Society

Received: February 5, 2014 Revised: April 29, 2014 Published: April 30, 2014 5350

dx.doi.org/10.1021/jp501282z | J. Phys. Chem. B 2014, 118, 5350−5356

The Journal of Physical Chemistry B

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the ν2 + ν3 overtone in heavy water). The achievable pump pulse energies lie between 2 and 6 mJ, depending on the excitation wavelength. The pump beam is focused onto a 500 × 300 μm2 spot in a 100 μm optical path silica cell (Hellma QS165). This cell is continuously rotated (3 Hz) to avoid any cumulative effect, and thus, each pump pulse excites a fresh part of the sample. External water circulation allows the cell temperature to be fixed by an external thermalizer. We calibrate the temperature rise in the sample with a bromothymol blue solution,12 which enables us to monitor the temperature jump and its dynamics. This calibration experiment is carried out in the same cell. As explained later, the measured T-jumps are in full agreement with the CD variation that we measure in our experiments. In these conditions, T-jumps between 2 and 8 K are obtained. The cell temperature remains constant for about 800 μs and relaxes back to the temperature set by the external thermalizer within a few milliseconds.12 These temperature jumps were smaller in D2O because absorption of D2O at 1.9 μm (14 cm−1) is weaker than that of H2O at 1.5 μm (32 cm−1) and because the pulse energy was smaller at 1.9 μm compared to the pulse energy at 1.5 μm. Circular dichroism is probed at 220 nm, which corresponds to a characteristic band of α-helices.9 The probe is generated from an 82 MHz titanium−sapphire femtosecond laser by frequency-quadrupling within a two-stage BBO frequency converter.11 The probe beam is focused onto a 30 × 100 μm2 spot at the sample position; this is smaller than the pump beam to ensure that we probe a uniformly heated sample, even though the cell is continuously rotated. The transmitted beam is then monitored by a photomultiplier tube (PMT) whose output signal is recorded via a 500 MHz digital oscilloscope that also processes the data. To obtain the CD, we alternately polarize the probe beam left or right circularly with a longitudinal Pockels cell by applying ±600 V. Left and right circularly polarized probes are processed separately in two distinct channels of the oscilloscope, and the CD is obtained by subtracting these two sets of data. Because we look for very tiny signals and even smaller CD changes, we increase the signal-tonoise ratio by inserting a 4.7 kΩ load at the input of the oscilloscope. With this approach, the pulsed probe beam can be detected like a continuous beam with the PMT and the oscilloscope. This extra load introduces a 0.37 μs RC time constant which we deconvolve from the observed dynamics. For all time scales presented in the following, this correction is taken into account. Typically, oscilloscope traces are averaged over 512 pump shots for one circular polarization, and these curves are averaged for another 10 times to deliver reliable results. The fact that the measurements for left and right polarization are sequential deserves some comments. Indeed, due to slow fluctuations of the laser source, such a procedure prevents a good measure of the steady-state CD. However, we have checked that our laser is very stable on short time scales (submillisecond) and that the relative variation of the CD is accurately measured in our experiments resulting in changes in CD that are insensitive to the slow fluctuations. The CD we measure in the following is CD = (2(IL − IR)/(IL + IR)) = (αL − αR)L, where IL,R (αL,R) is the measured intensity (absorption coefficient) for left and right circularly polarized light, respectively, and L the cell thickness, in our case 100 μm. It is connected to the molar ellipticity [θ] (in deg cm2 dmol−1 per residue) through

namely the difference in absorption between left and right circularly polarized light, is indeed a sensitive probe for molecule conformation. More specifically, measuring the CD in the far UV yields very precise information on the secondary structure of proteins.10 This kind of measurement may even be made quantitative for simple peptides if carried out at 222 nm. Using the formula derived by Baldwin,11 we directly obtain the helical fraction h in the peptide. By monitoring the far-UV CD as a function of time after the T-jump excitation, we will therefore be able to quantitatively follow the decrease of helical fraction during the peptide denaturation. In addition, CD provides another exciting feature. Because the probing of CD is performed in the far-UV regime, where neither light nor heavy water absorbs, it is possible to investigate the same sample in these two solvents with the same apparatus to directly compare the influence of the solvent deuteration on the peptide dynamics. In order to gain information about the energetics of the folding/unfolding equilibrium, we need to also investigate some steady-state thermodynamic properties. Hence, in the following, we present two types of measurements: temperaturedependent steady-state CD spectra and time-resolved CD measurements in a T-jump experiment. The latter are done for a large range of starting temperatures, leading to several interesting results. First, we measure quantitatively the helical fraction in both solvents and their time evolution after a typical 2−8 K T-jump. Second, by exploiting the two sets of data, we determine the folding and unfolding rates for each temperature and furthermore extract the relevant activation energies from an Arrhenius plot for the various processes. We investigated PGA in H2O at various pH values, as well as PGA in D2O at pD = 4.7, allowing us to study the influence of the solvent. Surprisingly, we find strong differences between the two solvents, which will be discussed in more detail in the final section.

2. EXPERIMENTAL SECTION 2.1. Sample Preparation. The PGA sample was purchased from Sigma-Aldrich (Product No. P4886, CAS No. 26247-790) and dissolved in light or heavy water without further purification. The molar weight of this sample is 64 000, corresponding to about 500 residues per peptide. As stated above, the pH value of the sample is an important parameter for our experiments and we chose to work at various pH values ranging from 4.2 to 5.4. In this pH range, the polypeptide is partially folded, without aggregation problems.6 The sample concentration is fixed at about 20 mg/mL throughout the experiments, which corresponds to a concentration of 0.155 M in terms of glutamic acid residues. In the case of light water, precise pH adjustment is performed by adding small amounts of 0.3 M HCl and NaOH solutions. The pH was measured with a Hanna HI1083B pH meter. To compare the two solvents, we also prepared PGA in heavy water. In that case, pD adjustment is done with DCl and NaOD. We chose to work at pD = 4.7 using the relation pD = pH + 0.4. 2.2. Experimental Setup of the T-Jump Experiments. Excitation of the sample is based on our recently introduced Tjump method, in which a laser pulse is used to instantaneously heat the solvent (light or heavy water).12 To achieve this rapid heating, we start from a nanosecond 20 Hz Nd:YAG laser, which pumps an optical parametric oscillator (OPO). We tune the output of the OPO to either 1.5 μm (corresponding to the ν2 + ν3 overtone in light water) or 1.9 μm (corresponding to 5351


The Journal of Physical Chemistry B [θ ] =

3298 CD ln 10 cL

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helix, h(0), which is unknown. Denoting η = Keq/(1 + Keq) the proportion of partially folded PGA, the helical fraction of the sample as a function of temperature reads,

(1)

Our experimental conditions yield CD = β[θ] with β = 8.3 × 10−7 (deg cm2 dmol−1)−1.

h(T ) = h(0)η(T )

(2)

Keq is a function of the Gibbs free energy ΔG0:

3. EXPERIMENTS 3.1. Steady-State CD Spectra. We have measured the CD spectra in the 200−250 nm range for our PGA samples in H2O and D2O for a set of temperatures ranging from 279 to 358 K with a home-built spectropolarimeter. The outcome of this measurement is displayed in the inset of Figure 1. With eq 1,

⎛ −ΔG 0(T ) ⎞ Keq(T ) = exp⎜ ⎟ RT ⎠ ⎝

(3)

where R refers to the universal gas constant. The free energy is in turn a function of the enthalpy change ΔHm, of the heat capacity ΔCm and of the melting temperature Tm:8 ΔG 0(T ) = ΔHm + ΔCm(T − Tm) ⎛ ΔHm T ⎞ − T⎜ + ΔCm ln ⎟ Tm ⎠ ⎝ Tm

(4)

However, the very smooth shape of our melting curves prevents us from extracting thermodynamic parameters with a good accuracy, especially for the heat capacity. We checked that feature by varying the magnitude and even the sign of ΔCm, which always yielded a satisfactory fit. The difficulty of extracting ΔCm from such curves has already been acknowledged in the literature.8,15 We have therefore abandoned the idea of extracting ΔHm and ΔCm simultaneously and have expressed ΔG0(T) as

Figure 1. Helical fraction for PGA dissolved in light water for pH = 4.7 (blue dots) and in heavy water for pD = 4.7 (black squares) as a function of temperature. The red lines are fits using eqs 3−6 (see text). The inset shows steady-state CD spectra in H2O for temperatures ranging between 279 and 358 K.

ΔG 0(T ) = A[T − Tm]

(5)

which allows to neglect the ln term in eq 4, which has a weaker dependence with T. Within a good approximation, the parameter A is equal to −ΔHm/Tm, with ΔCm close to zero. Finally, the adjustment of the melting curves relies on three parameters: A, which yields the folding/unfolding reaction enthalpy; Tm, the transition temperature; and h(0), the low temperature helical fraction, which is a function of the pH value. Actually, the three parameters have very different and independent influences: A gives the steepness of the melting curve, Tm gives its position, and h(0) gives its amplitude. The parameters obtained with this procedure are displayed in Table 1 for H2O and D2O. Noticeably, we obtain quite different values for A with the two solvents, even if the transition temperatures are in the same range. 3.2. T-Jump Experiments. Besides the steady-state measurements, we carried out T-jump experiments for the two solvents for various starting temperatures. For all experiments, we measured the change in absorption and CD at a probe wavelength of 220 nm. An example is given in Figure 2 for PGA dissolved in H2O (pH = 4.7) for a final temperature of 299 K. For each experiment, we could measure the starting helical fraction and verify that it was consistent with the steadystate measurements. The drop in helical fraction gave us the final temperature of the sample. Temperature jumps between 4 and 8 K were obtained in H2O, and temperature jumps between 2 and 4 K were obtained in D2O; these values are in agreement with the independent temperature calibration performed previously with bromothymol blue. The temperature jump is lower in D2O because of experimental constraints, as our laser system could not obtain more energy at 1.9 μm. This results in much noisier measurements in D2O compared to H2O. We have nevertheless verified in H2O that the measured relaxation times were independent of the size of the

we can convert the measured CD into the peptide helical fraction. The resulting helical fractions are plotted in Figure 1 for H2O and D2O as a function of temperature for pH and pD equal to 4.7. We have emphasized this particular value of pH as it corresponds to a helical fraction close to 0.5 while avoiding any aggregation problems. As expected, helical fraction decreases with increased temperature. Comparison of the curves for H2O and D2O is very instructive. First of all, one can see that despite the fact that pH = pD = 4.7 are fixed to the same value, the helical fraction at low temperature is slightly higher in D2O than in H2O. This difference can be traced back to the protonation of PGA in both solvents. Indeed, the dissociation constant of weak acids (Ka) is known to be weaker in D2O compared to H2O,13 which means that, for a fixed concentration of H+ or D+ ions, PGA is more protonated in heavy water and therefore more folded. Second, the shapes of the two curves are remarkably different. Whereas one observes clearly a sigmoid shape in D2O, the curve is almost linear in H2O. This difference is an immediate indication that the enthalpy change in the folding reaction is weaker in light water than in heavy water.14 This feature will be confirmed by the kinetic curves discussed below. The melting curves (confer Figure 1) allow us to extract thermodynamic parameters. In particular, it is possible to obtain the equilibrium constant Keq of the unfolding ⇌ folding reaction. Note, however, that at a given pH, the PGA is supposed to come up in a partially folded state at low temperature and as a complete random coil configuration at high temperature. The unfolding state therefore corresponds to h = 0, whereas the folded state corresponds to a partially folded 5352



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This assumption has been somewhat challenged by Volk’s work9 in which stretched exponential curves were obtained. Note, however, that in ref 9, the stretching coefficient gets closer to 1 when the pD value decreases and that for acidic samples, the correction becomes rather small. In our work, relaxation curves that we obtain are monoexponential within our accuracy (Figure 2), so we will adhere to this approximation, allowing us to obtain quantitative results. In the two-state model, PGA is supposed to undertake only two forms: folded and unfolded. At each temperature, there is equilibrium between the two forms: kf

PGA unfolded ⇄ PGA folded ku

Here, kf and ku refer to the folded and unfolded rates, respectively, that we would like to determine. The procedure to determine both rates has been thoroughly described in ref 8, and we followed it closely. The two sets of experiments that we performed allow us to extract these two rates. Indeed, measurement of the denaturation time in a T-jump experiment only yields an effective rate, kobs, which is the sum of the two rates:

Figure 2. Absorption change (top) and CD change (bottom) in PGA in H2O (pH = 4.7) for a final temperature of 299 K as a function of time. The solid lines correspond to monoexponential fits with a time constant of 1.3 μs.

kobs = k f + k u

temperature jump. For the sample in H2O at pH = 4.7, we performed 24 measurements in total for final temperatures ranging between 291 and 321 K; in D2O at pD = 4.7, a total of 34 measurements were taken because of the smaller temperature jump for final temperatures between 288 and 310 K. The measured relaxation times are plotted in Figure 3. When possible, both absorption and CD curves were fitted and

(6)

as expected from the equilibrium relation. One therefore needs another relation between these two rates, which is given by the melting curves of PGA, such as the measure of the steady-state CD at 222 nm as a function of temperature in our case. These curves provide an equilibrium constant, Keq, which is related to the two rates through the following relation:16 Keq =

kf ku

(7)

Knowledge of kobs and Keq therefore allows a unique set of kf and ku to be determined for various temperatures. With these values, one can obtain an estimate of the activation energies following the Arrhenius formula: ⎛ −Ea f,u ⎞ ⎟ k f,u ∝ exp⎜ ⎝ RT ⎠

(8)

Arrhenius plots for the folding and unfolding processes in H2O (pH = 4.7) and D2O (pD = 4.7) are shown in Figure 4. Within the uncertainty of our measurements, we obtain a nice linear fit in agreement with our two-state assumption. Qualitatively, such behavior was also observed by Hauser.8

Figure 3. Relaxation times measured for various final temperatures for PGA in H2O, pH = 4.7 (blue dots), and in D2O, pD = 4.7 (black squares). The solid lines are not fits but provide a guide to the eye.

4. RESULTS AND DISCUSSION We carried out two sets of experiments for PGA samples in H2O with five different pH values equal to 4.2, 4.4, 4.7, 5.0, and 5.4. It was not possible to use more acidic pH values (pH ≤ 4) because, thereupon, an irreversible aggregation occurred.6,17,18 The helical fractions inferred from the melting curves are displayed in Table 1. When the pH value increases from 4.2 to 5.0, we observe a slight decrease of the helical fraction, followed by a strong drop at pH = 5.4 (Figure 5a). This feature is in very good agreement with the results presented in ref 19, where the helical fraction is shown to decrease strongly when the pH value changes from 5 to 5.5. As expected, when the pH value decreases, the side chain of the glutamate residues becomes protonated and uncharged, favoring the folding of the peptide. When pH increases, the side

yielded similar decay time scales. When the CD change was too small or too noisy, we extracted the times from the absorption curves and checked that they were compatible with the CD curves. It is noteworthy that the relaxation times in H2O are noticeably larger than those in D2O, especially at high temperatures (refer to section 4 for more details). For other pH values in H2O, we carried out about 10 measurements for final temperatures between 281 and 318 K. 3.3. Activation Energies. In order to extract reliable information about the thermodynamics and kinetics of PGA in both solvents, we suppose that PGA obeys a two-state model. Such a hypothesis has been supported by Hauser’s work8 for a time interval from 500 ns to 200 μs, which corresponds to ours. 5353



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Figure 4. Arrhenius plots for the folding/unfolding reaction rates in H2O (pH = 4.7) and in D2O (pD = 4.7). The solid red lines are linear fits yielding the activation energies (eq 8).

chains are more charged, and electrostatic repulsion prevents the folding. From the melting curves, the equilibrium energy parameter A and the transition temperatures Tm are obtained (Table 1). The nature of the sample at pH = 5.4 is quite different from the other samples, as can be seen from Table 1. Whereas the other samples have similar thermodynamic parameters, the one at pH = 5.4 has much lower values for A and Tm. This feature is probably connected to its very weak helical fraction, which is confirmed by the fact that no dynamics could be observed for this sample in the T-jump experiments. In the remaining discussion, we will therefore concentrate on the other four samples. We obtained similar transition temperatures for the three most acidic pH values but a slightly lower one at pH = 5.0. We can see that when pH varies between 4.2 and 5.0, the equilibrium enthalpy difference slightly increases from 42 to 45 kJ/mol. We measured the relaxation times for several temperatures with the T-jump experiments. The relaxation times range between 1.5 and 2.0 μs at low temperature and decrease to 0.6−1.0 μs for higher temperatures. These times are in good agreement with previous measurements.7,8,11 Interestingly, we obtained a nonmonotonic variation of the relaxation times with respect to the pH value. For pH values of 4.2, 4.4, 4.7, and 5.0 and a final temperature of 293 K, we obtained relaxation times equal to 0.6, 0.5, 1.5, and 1.2 μs, respectively. We determined the uncertainty of the time scales to ±0.2 μs. This feature is in agreement with refs 9 and 20, in which longer relaxation times were measured when the helical fraction is close to 0.5, again in agreement with simple kinetic processes.9 The T-jump experiments yielded the activation energies for the folding and unfolding processes, as displayed in Table 1 and plotted in

Figure 5. (a) Helical fraction and (b) folding/unfolding activation energies for PGA dissolved in H2O for various pH values.

Figure 5b. We observe a slight decrease of the activation energy with increased pH, for both the folding and unfolding reactions. We also carried out experiments for D2O as solvent with pD = 4.7. This pD value was chosen because it falls within the range studied for H2O in terms of H+/D+ concentration, as well as in terms of low temperature helical fraction yielding meaningful comparisons. Two different samples were prepared and investigated. They yielded reproducible results that markedly differ from the ones obtained in H2O. From the melting curves (Figure 1b), we could infer a helical fraction at low temperature equal to 0.55, higher than in H2O at pH = 4.7. This feature is a first sign of the clear difference that exists between light and heavy water despite their very strong resemblance. Actually, in terms of folding, a solution at pD = 4.7 is close to a solution at a pH value around 4.2. As already stated, T-jump experiments were somewhat difficult, and the measured times are more dispersed (see error bars in Figure 3), but one can clearly see that variation of the relaxation times with temperature is more pronounced for D2O than for H2O (confer Figure 3). However, the final estimate for the activation energies is much more precise due to the logarithmic variation of the relaxation rate with the activation energy. The striking point is that all the energetic parameters are much stronger in D2O than in H2O at pH = 4.2 or 4.7 (Table 1). This is true for the equilibrium enthalpy difference, which is about twice as strong in D2O as it is in H2O (− 102 vs −45 kJ/mol), as well as for the activation energies. To emphasize these surprising

Table 1. Parameters Extracted from the Experiments pH/pD H2O

D2O

4.2 4.4 4.7 5.0 5.4 4.7

h(0)a 0.54 0.51 0.47 0.42 0.17 0.55

± ± ± ± ± ±

0.03 0.03 0.02 0.02 0.03 0.02

A (J/(K/mol))a 134 139 128 133 72 313

± ± ± ± ± ±

4 3 3 5 6 22

Tm (K)a 337 323 337 312 282 329

± ± ± ± ± ±

2 2 2 2 11 2

Ea,f (kJ/mol)b 21 11 7 6

± ± ± ±

4 2 3 5

21 ± 6

Ea,u (kJ/mol)b 5 3 4 6

−45 −45 −43 −42

128 ± 6

−102

66 56 50 48

± ± ± ±

ΔHm (kJ/mol)c

Low-temperature helical fraction, h(0); equilibrium energy parameter, A (≈ − ΔHm/Tm); and transition temperature, Tm, are obtained from the melting curves (Figure 1). bActivation energy for the folding (Ea,f) and unfolding (Ea,u) reactions are extracted from the previous parameters and the T-jump experiments. cThe equilibrium enthalpy difference (ΔHm = Hf − Hu) can be calculated either as ΔHm = ATm or as ΔHm = Ea,f − Ea,u.

a

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times are similar in both solvents. The importance of the interaction of PGA with the surrounding water molecules has already been observed by changing the osmotic pressure;22 furthermore, such a stabilization effect of heavy water was recently observed in β-turns.23 A strong isotope effect was also measured in the thermodynamics of biotin repressor dimers.24 However, another possibility could be connected to the aforementioned difference in the pKa values in the two solvents. Indeed, when temperature varies, the pKa value also varies, which modifies the protonation state of PGA and thus its folding properties. In ref 9, it was concluded that the dynamics of PGA rely on a complicated interplay between thermodynamic process and protonating/deprotonating processes which take place in such a weak acid as PGA. It is likely, although not documented in literature, that the pKa variation with temperature could be somewhat different between light and heavy water. Thus, an interesting further study would be to investigate the dynamics of a nonacidic peptide such as alanine-rich peptides in light and heavy water, such as (AAAK)n, which has already studied by several groups.25,26 This would help to clarify the origin of this light and heavy water difference further.

results, we have schematically drawn the energetic profile for both solvents for pH = 4.2 and pD = 4.7 in Figure 6, where it clearly appears that as long as thermodynamic equilibrium is concerned, light and heavy water are two quite different solvents for a peptide like PGA.

Figure 6. Schematic representation of the energy profiles for the unfolding ⇌ folding reaction in PGA for H2O, pH = 4.2 (red dotted line) and D2O, pD = 4.7 (black solid line), emphasizing the strong difference in equilibrium enthalpies despite the similar helix fraction in both samples. Also shown are the folding and unfolding activation energies for D2O.

5. CONCLUSION Helicity of PGA as a function of temperature and the pH or pD value has been studied in light and heavy water with the help of two complementary experiments. First, steady-state CD spectra have been recorded, and second, time-resolved CD measurements following a T-jump induced via a nanosecond laser pulse have been carried out. These two sets of experiments allowed us to obtain thermodynamic and kinetic parameters of the folding/unfolding equilibrium and to extract activation energies for these processes. We have carried out these experiments for light and heavy water and observed that for equivalent helical fraction, the enthalpies as well as the activation energies are sensibly higher in the latter case. This strong difference could have its origin either in the slightly stronger hydrogen bond energy in heavy water compared to light water or in the acidic pending group of PGA whose interaction with water plays a prominent role in the folding equilibrium of the polypeptide.

The difference in the activation energies can be traced back to two effects. On the one hand, the equilibrium enthalpy is very different for both solvents; on the other hand, the variation of the relaxation times with temperature is larger for D2O. It is possible to separate these two effects by mixing the equilibrium and dynamical data. For example, if we calculate the activation energies with the equilibrium data for D2O and the relaxation rates measured in H2O, we obtain Ea,f = 15 kJ/mol and Ea,u = 117 kJ/mol, as compared to Ea,f = 26 kJ/mol and Ea,u = 128 kJ/ mol when using the full data measured for D2O. This shows that even though most of the difference in the activation energies comes from the large difference in the equilibrium properties, the dynamic effects have a non-negligible contribution in the activation processes. This significant difference raises the question of how one can understand the origin of this feature. It might lie in the slight difference that exists between hydrogen bonds in the two solvents. It is indeed known that hydrogen bonds are slightly stronger in D2O compared to those in H2O with an energy difference about 1 kJ/mol.21 This difference can play a major role in the folding/unfolding reaction of a peptide. Actually, when a polypeptide such as PGA unfolds, it replaces intramolecular hydrogen bonds (between the CO group on residue i with the NH group of residue i + 4) by intermolecular bonds between the CO/NH groups and the surrounding water molecules. Concomitantly, hydrogen bonds between water molecules must be broken. The variation of enthalpy between the partially folded and the unfolded states reflects the energetic change between the intra- and inter-hydrogen bonds. This feature is consistent with the fact that the enthalpy difference is larger when the helical fraction is higher. This is also in agreement with the higher activation energies when the pH value decreases as the peptide is more folded and more hydrogen bonds are involved in the folding/unfolding processes. Note, however, that the higher viscosity of heavy water does not seem to play an important role, as the relaxation

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.S. thanks the German National Academic Foundation (Studienstiftung des deutschen Volkes) for a scholarship. REFERENCES

(1) Maity, H.; Maity, M.; Krishna, M. M. G.; Mayne, L.; Englander, S. W. Protein Folding: The Stepwise Assembly of Foldon Units. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 4741−4746. (2) Lindorff-Larsen, K.; Piana, S.; Dror, R. O.; Shaw, D. E. How FastFolding Proteins Fold. Science 2011, 334, 517−520. (3) Hockenmaier, J.; Joshi, A. K.; Dill, K. A. Routes are Trees: The Parsing Perspective on Protein Folding. Proteins 2007, 66, 1−15. (4) Finkelstein, A. V.; Galzitskaya, O. V. Physics of Protein Folding. Phys. Life Rev. 2004, 1, 23−56.

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Unfolding Dynamics of Poly

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