Relationship between Nonlinear Pressure-Induced Chemical Shift

Article pubs.acs.org/JPCB

Relationship between Nonlinear Pressure-Induced Chemical Shift Changes and Thermodynamic Parameters Markus Beck Erlach,† Joerg Koehler,† Beate Moeser,‡ Dominik Horinek,‡ Werner Kremer,† and Hans Robert Kalbitzer*,† †

Institute of Biophysics and Physical Biochemistry and Centre of Magnetic Resonance in Chemistry and Biophysics, University of Regensburg, 93040 Regensburg, Germany ‡ Institute of Physical and Theoretical Chemistry, University of Regensburg, 93040 Regensburg, Germany ABSTRACT: NMR chemical shift analysis is a powerful method to investigate local changes in the environment of the observed nuclear spin of a polypeptide that are induced by application of high hydrostatic pressure. Usually, in the fast exchange regime, the pressure dependence of chemical shifts is analyzed by a second order Taylor expansion providing the first- and second-order pressure coefficient B1 and B2. The coefficients then are interpreted in a qualitative manner. We show here that in a two-state model, the ratio of B2/B1 is related to thermodynamic parameters, namely the ratio of the difference of compressibility factors Δβ′ and partial molar volumes ΔV. The analysis is applied to the random-coil model peptides Ac-Gly-Gly-Xxx-Ala-NH2, with Xxx being one of the 20 proteinogenic amino acids. The analysis gives an average Δβ′/ΔV ratio of 1.6 GPa−1 provided the condition |ΔG0| ≪ 2RT holds for the difference of the Gibbs free energies (ΔG0) of the two states at the temperature (T0) and the pressure (p0). The amide proton and nitrogen B2/B1 of a given amino acid Xxx are strongly correlated, indicating that their pressure-dependent chemical shift changes are due to the same thermodynamic process. As a possible physical mechanism providing a two-state model, the hydrogen bonding of water with the corresponding amide protein was simulated for isoleucine in position Xxx. The obtained free energy could satisfy the relation |ΔG0| ≪ 2RT. The derived relation was applied to the βamyloid peptide Aβ and the phosphocarrier protein HPr from S. carnosus. For the transition of state 1 to state 2′ of Aβ, the derived relation of B2/B1 to Δβ′/ΔV can be confirmed experimentally. The HPr protein is characterized by substantially higher negative B2/B1 values than those found in the tetrapeptides with an average value of approximately −5.1 GPa−1 (Δβ′/ΔV of 5.1 GPa−1 provided |ΔG0| ≪ 2RT holds). Qualitatively, the B2/B1 ratio can be used to predict regions of the HPr protein involved in the interaction with enzyme I or HPr-kinase/phosphatase.

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INTRODUCTION With the help of high-pressure NMR spectroscopy, one can obtain novel information about protein biochemistry and biophysics at atomic resolution (for recent reviews see, for example, Akasaka et al.1 and Kitahara et al.2). The analysis of the pressure response of a protein can give important information on the local and global mechanical properties of a protein ensemble. Pressure can be used to stabilize conformations of the protein that have a very low population at atmospheric pressure.2−7 As we could show for the human prion protein intermediate states with relative concentrations lower than 5 × 10−4 at ambient pressure can be identified at high pressure.5,6 In the field of protein NMR the use of high pressure cells that can be used in a standard probe head and are connected with an online pressure system have gained general acceptance. Initially quartz, borosilicate glass, and sapphire cells were used,8−11 but recently ceramic cells have shown superior properties.12,13 Since high pressure induces structural changes in proteins, it also influences all structure-dependent NMR parameters. The most important parameter for protein NMR is the chemical © 2014 American Chemical Society

shift perturbation since it can be observed with high accuracy and sensitivity. An early finding in high-pressure NMR spectroscopy of proteins was the observation that the pressure dependence of chemical shifts is often nonlinear and differs from atom-to-atom in the macromolecule.3,14 Usually, the pressure-dependent chemical shifts are fitted with a secondorder polynomial that is understood as a purely phenomenological description.4 The obtained pressure coefficients cannot be interpreted in quantitative terms. Qualitatively, large secondorder coefficients are associated with strong conformational changes. Only when the chemical shift changes with pressure show a clear saturation behavior, the data can be fitted stably with a thermodynamic model, including the differences of partial molar volumes (ΔV) and compressibility factors (Δβ′). In this paper, we will propose methods to derive meaningful thermodynamic parameters from the pressure coefficients and apply them to published data of random-coil model peptides,15,16 the Aβ peptide,7 and the HPr protein.14 Received: March 17, 2014 Revised: May 1, 2014 Published: May 5, 2014 5681

dx.doi.org/10.1021/jp502664a | J. Phys. Chem. B 2014, 118, 5681−5690

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MATERIALS AND METHODS Tetrapeptides. The samples contained 5 mM Ac-GGXANH 2 and 20 mM perdeuterated Tris-HCl (tris(hydroxymethyl)aminomethane hydrochlorid) in 90% H2O and 10% D2O. X corresponds to one of the 20 canonical amino acids. As an internal reference, 0.5 mM DSS (4,4-dimethyl-4silapentane-sulfonic acid) was added. In general, the pH value was adjusted to 6.7 with a Hamilton Spintrode attached to a Beckman Coulter pH meter. Ac-GGHA-NH2 was measured at pH 4.0 and pH 8.5. All data were measured at 283 K with an 800 MHz Bruker Avance spectrometer with a QXI probe. For more detailed experimental settings see Koehler et al.16 β-Amyloid Peptide Aβ(1−40). The sample contained 474 μM 15N-enriched human Aβ(1−40) in 50 mM Tris-d11, 90 mM NaCl, 50 μM DSS, 0.1 mM dioxane, 1 mM NaN3, 0.5 mM EDTA-d16, and 8% D2O, at pH 7.0 (for details see Munte et al.7). HPr Protein. 1.5 mM uniformly 15N-labeled HPr protein from S. carnosus was solved in 350 μL of buffer (10 mM TrisHCl, 0.5 mM NaN3, 0.5 mM p-APMSF, 0.5 mM EDTA, 0.05 mM 3-(trimethylsilyl)-2,2′,3,3′-tetradeuteropropionate (TSPd4), 2.2 mM dioxane in 87.5% H2O, and 12.5% D2O, at pH 7.14). NMR spectra were measured at pressures of 4, 50, 100, 150, and 200 MPa and at a temperature of 298 K on a Bruker DMX-750 spectrometer. The 1H chemical shifts are referred to the internal reference TSP, and 15N chemical shifts are referenced to TSP indirectly.17 For additional experimental details, see Kalbitzer et al.14 Molecular Dynamics Calculations. The tetrapeptide AcGly-Gly-Ile-Ala-NH2 was built with AmberTools18 using the ff03.r1 Amber force field19 and converted to Gromacs syntax with acpype.20 The structure is solvated in a 5 nm cubic box with TIP4P2005 water.21 The equilibrated system is simulated for 300 ns with a 2 fs time step at a temperature of 300 K (maintained with a stochastic velocity-rescaling thermostat22) and either 0.1 or 200 MPa isotropic pressure (maintained with a Parrinello−Rahman barostat).23 All simulations are performed with Gromacs 4.5.24 The Lennard-Jones interactions are included up to a cutoff-radius of 0.85 nm, and the truncation error is accounted for in the calculation of the energy and the pressure. Electrostatic interactions are included with the smooth particle-mesh Ewald summation method.25 The existence of an NH−water hydrogen bond is determined by the standard geometric criterion26 (donor−acceptor distance less than 3.5 Å and hydrogen-donor−acceptor angle less than 30 degrees). The probability pHB of a hydrogen bond is the fraction of time steps (n) in which one or very rarely 2 hydrogen bonds are present during the simulation period. The free-energy difference associated with hydrogen-bond breakage is obtained by ΔG = RT ln[pHB/(1-pHB)] with pHB, the probability to find a hydrogen-bonded water molecule. The partial molar volume difference follows simply from the data at 0.1 and 200 MPa as by ΔV = [ΔG(200 MPa) − ΔG(0.1 MPa)]/199.9 MPa. Software and Data Evaluation. The original data published by Koehler et al.16 were reevaluated and the ratio B2/B1 = −Δβ′(p0)/ΔV(p0) was recalculated from the pressure dependence of the amide proton shifts of the amino acid X. For the Aβ peptide, the ratio B2/B1 and additionally the ratio Δβ′/ ΔV has been recalculated from the published data. For an HPr protein, the ratio B2/B1 was calculated from the published values.14 Data were Fourier-transformed with the program

TOPSPIN (Bruker Bioscience Corporation). The coefficients B1 and B2 have been evaluated by fitting the obtained pressure dependence of the chemical shift with the model of eq 1. The statistical software R27 has been used for fitting, data manipulation, and plotting.

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RESULTS AND DISCUSSION Theory. In the absence of a suitable model, the pressure dependence of chemical shifts δ(p) at constant temperature can be represented as a Taylor series around the pressure p0 as δ(p) = B0 + B1(p − p0 ) +

1 B2 (p − p0 )2 + ... 2

(1)

with B0 = δ(p0 ) B1 =

∂δ (p ) ∂p 0

B2 =

∂ 2δ (p ) ∂p2 0

(2)

Generally, the observed chemical shift of a spin i in an ensemble with N members in fast exchange on the NMR timescale is the frequency-weighted average of the individual chemical shifts (δi). In thermal equilibrium of M states sj and M* ≤ M states with average chemical shifts [δi(sj)] in fast exchange on the NMR timescale, the observed chemical shift of spin i can be written as28 M*

⟨δi⟩ =

∑ p*(sj)δi(sj) = j=1

1 Z*

M*

∑ δi(sj)e−G(s )/RT j

j=1

(3)

with p(sj) the probability of the state sj, Gj = G(sj), the corresponding Gibbs free energy, and Z* the partition function of all M* states. The simplest physical model to describe the chemical shift changes with pressure would be a two-state model with the states 1 and 2 characterized by two chemical shifts δ1 and δ2 of a given nucleus i and the correspondent Gibbs free energies G1 and G2. When the exchange between the two states is fast on the NMR timescale (that is |Δωτe| ≪ 1; Δω, difference of the resonance frequencies ω1 and ω2; τe, exchange correlation time), eq 3 can be rewritten as δ= = =

δ1e−G1/ RT + δ2e−G2 / RT e−G1/ RT + e−G2 / RT δ1eΔG / RT + δ2 1 + eΔG / RT

δ eΔG / RT + δ2 1 1 − (δ1 + δ2) (δ1 + δ2) + 1 ΔG / RT 2 2 1+e

=

1 1 eΔG / RT − 1 (δ1 + δ2) − (δ2 − δ1) 2 2 1 + eΔG / RT

=

⎛ ΔG ⎞ 1 1 ⎟ (δ1 + δ2) − (δ2 − δ1) tanh⎜ ⎝ 2RT ⎠ 2 2

(4)

With ΔG0 = G2(p0, T0) − G1(p0, T0) = ΔG(p0, T0), the Taylor expansion of eq 4 gives 5682


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⎛ ΔG° ⎞ 1 1 (δ1 + δ2) − (δ2 − δ1) tanh⎜ ⎟ 2 2 ⎝ 2RT0 ⎠

B1 = −

ΔV (p0 ) Δβ′(p0 ) B2 − =− B1 ΔV (p0 ) RT0

⎛ ΔG° ⎞⎤ (δ2 − δ1) ∂ΔG(p0 ) ⎡ ⎢1 − tanh2⎜ ⎟⎥ ∂p ⎢⎣ 4RT0 ⎝ 2RT0 ⎠⎥⎦

⎛ ΔG° ⎞⎤ (δ2 − δ1) ⎡ ⎢1 − tanh2⎜ ⎟⎥ 4RT0 ⎢⎣ ⎝ 2RT0 ⎠⎥⎦ 2 ⎡ ∂ 2ΔG(p ) 1 ⎛ ∂ΔG(p0 ) ⎞ 0 ⎢ ⎜⎜ ⎟⎟ − ⎢ ∂p2 RT0 ⎝ ∂p ⎠ ⎣ ⎛ ΔG° ⎞⎤ tanh⎜ ⎟⎥ ⎝ 2RT0 ⎠⎥⎦

Here, the ratio B2/B1 is explicitly dependent on the temperature T, and a 1/T-dependence can be used as an indicator that eq 13 holds. Conversely, from the 1/T dependence of B2/B1, it is possible to estimate the partial molar volume difference ΔV and the compressibility factor difference Δβ′. The above equations can be transformed easily to quantities measured by non-NMR methods such as measurements of the ultrasound velocities by the relation

B2 = −

Δβ′ = V2β2 − V1β1 = β ΔV + Δβ V

B2 = B1

∂p2 ∂ΔG(p0 )

−

∂p

⎛ ΔG° ⎞ 1 ⎛ ∂ΔG(p0 ) ⎞ ⎜⎜ ⎟⎟ tanh⎜ ⎟ RT0 ⎝ ∂p ⎠ ⎝ 2RT0 ⎠

(6)

The first derivative of ΔG

⎛ ∂ΔG ⎞ ⎜ ⎟ = ΔV ⎝ ∂p ⎠T

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RESULTS The relations between the ratio of the Taylor coefficients B2 and B1 and the ratio of the compressibility factors β′ and the partial molar volumes ΔV derived above (eqs 11 and 13) are formally correct. However, their application requires that the simple two-state model with pressure-independent chemical shifts δ1 and δ2 describes the real situation sufficiently well. Independent of the thermodynamic interpretation, the description of pressure effects by B2/B1 values can have advantages in the analysis of data as we will show in the following. Relation between the B2/B1 Values and Thermodynamic Parameters in a Weakly Structured Polypeptide. To give proof that the obtained relationship between Taylor coefficients and the ratio of differences in compressibility factors and partial molar volume differences is correct, we have tested thermodynamic data of amyloid-β (Aβ) against the ratio of its Taylor coefficients. The amyloid-β peptide was used because it shows relatively small ΔG0 values, and therefore, many amino acids in Aβ fulfill the prerequisite of eq 11. We have recently published a high-pressure NMR study of Aβ(1− 40), the β-amyloid peptide involved in the development of Alzheimers disease.7 An analysis of the data identifies three different conformational states, including a transition between state 1 and state 2′ with a ΔG0 of 1.7 and 2.1 kJ mol−1 at 277 and 288 K, respectively. Before the data were analyzed, the pressure dependence of random-coil peptides was subtracted. Therefore, the obtained parameters correspond to a conformational transition of the partially folded peptide. The experimental B2/B1 ratios are plotted as a function of Δβ′/ ΔV at two temperatures for the 1−2′ transition (Figure 1). Due to the fact that eq 11 only holds true for |ΔG0| ≪ 2RT, we only considered amino acids with a free-energy change of |ΔG0| < RT. The correlation between Δβ′/ΔV and B2/B1 is almost perfect with correlation coefficients of r = 0.989 for 277 K and r = 0.999 for 288 K. In agreement with the derived

(7)

represents the partial molar volume difference and the second derivative of ΔG ⎛ ∂ 2ΔG ⎞ ∂ΔV ⎟ = ⎜ = : −Δβ′ 2 ∂p ⎝ ∂p ⎠ T

(8)

represents the difference of the compressibility factor β′ (note that the sign of this factor is not defined uniquely in literature) that is ⎛ ΔG° ⎞ ΔV (p0 ) Δβ′(p0 ) B2 − =− tanh⎜ ⎟ ΔV (p0 ) B1 RT0 ⎝ 2RT0 ⎠

(9)

with ΔG° ≪1 2RT

(10)

Equation 9 can be simplified to Δβ′(p0 ) B2 =− B1 ΔV (p0 )

(11)

The ratio of the first- and second-order pressure coefficients would thus correspond to the ratio of the partial molar volume difference and the compressibility change associated with the two states considered. For ΔG° ≫1 2RT

(14)

with ⟨β⟩ and Δβ the mean and the difference of the partial molar compressibilities β of the two states and ⟨V⟩ the mean of the partial molar volumes V. The first term of eq 14 often is neglected and set to zero (see e.g., Kitahara et al.2). In the above description, it is assumed that the chemical shifts δ1 and δ2 in the two states are independent of pressure. A factor that always should influence the chemical shifts is the pressure-dependent structure of the water shell surrounding a molecule under consideration. However, as long as this pressure dependence is small compared to the chemical shift difference Δδ, it can be ignored.

(5)

An expression that is independent of the chemical shifts can be derived as ∂ 2ΔG(p0 )

(13)

(12)

one obtains 5683



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Table 1. Ratio of Second- and First-Order Pressure Coefficients for the Model Peptides Ac-GGXA-NH2a and GGXAb amino acid X

B2/B1 (GPa−1) Ac-GGXA-NH2

Ala Arg Asn Asp Cys Gln Glu Gly His4.0 His8.5 His5.4 Ile Leu Lys Met Phe Protrans Procis Ser Thr Trp Tyr Val Mean

Figure 1. Correlation of B2/B1 with Δβ′/ΔV in the β-amyloid peptide Aβ(1−40).7 Δβ′/ΔV is plotted as a function of B2/B1 for the 1H (○,●) and 15N (Δ,▲) chemical shifts of Aβ(1−40) for the two data sets recorded at 277 K (unfilled symbols) and 288 K (filled symbols), respectively. Data were analyzed for the transition of state 1 to state 2′ with ΔG0 1.7 ± 0.9 kJ mol−1 (277 K) and 2.1 ± 0.8 kJ mol−1 (288 K), respectively. At 277 K, the correlation coefficient is r = 0.989, and at 288 K, it is r = 0.999.

equations, the ordinate intercepts for the two temperatures are close to 0 GPa−1 (Figure 1). Pressure-Dependence in Random-Coil Model Peptides. As a first application, we calculated the ratio of the second- and first-order pressure coefficients B2 and B1 for the “random-coil” model peptides Ac-GGXA-NH2.16 The amide proton and nitrogen shifts of the central amino acid X were fitted to a second-order Taylor expansion (eq 1) leading to a set of parameters describing the pressure response of the tetrapeptides in a pressure range of 0.1 to 200 MPa (Table 1). In addition, the B2/B1 values of the unprotected tetrapeptides GGXA15 are listed in Table 1. The B2/B1 ratios are plotted in Figure 2 for the different amino acids and ordered according to the magnitude of the B2/B1 ratio. The obtained B2/B1 values for amide protons as well as nitrogens are in the range between −0.2 and −2.5 GPa−1. Within the limits of error, the mean values of B2/B1 for the two nuclei are identical (−1.5 ± 0.3 GPa−1 for the amide protons and −1.6 ± 0.2 GPa−1 for the amide nitrogens). In the thermodynamical interpretation, this would mean that on average the ratio of Δβ′(p0)/ΔV(p0) is similar for the amide nitrogens and protons and that the two nuclei sense essentially the same physical process. In agreement with this observation, the B2/B1 values of protons and nitrogens of a given amide group show a correlation of about r = 0.69, indicating that similar but not identical effects determine the pressure response of amide protons and nitrogens (Figure 3). The deviation from a perfect correlation may mainly be due to the relatively large errors in the determination of the B2/B1 ratio (Table 1). Although the ratio B2/B1 for most amino acids is close to its average value of approximately −1.5 GPa−1, significantly larger negative values for protons and nitrogens can be found for tyrosine and phenylalanine residues and smaller negative values for glycine and alanine. This observation suggests a possible

1

H

−0.7 −0.9 −1.7 −1.7 −1.8 −0.8 −0.2 −0.8 −1.8 − − −2.0 −1.9 −1.8 −1.3 −2.5 − − −2.0 −1.5 −1.4 −2.4 −0.7 −1.5

± ± ± ± ± ± ± ± ±

0.4 0.4 0.6 0.3 0.2 0.6 0.6 0.5 0.2

± ± ± ± ±

0.4 0.5 0.4 0.4 0.4

± ± ± ± ± ±

0.8 0.3 0.4 0.8 0.3 0.3

a

B2/B1 (GPa−1) GGXA 1

b

H

−1.4 −0.3 2.6 1.2 0.0 0.3 −1.8c 0.8 − − −1.7 −2.1 −1.8 −1.4 −1.5 0.4 − − −1.4 −1.2 −2.0 −1.1 −1.5 −0.7 ± 0.6

B2/B1 (GPa−1) Ac-GGXA-NH2a 15

−1.1 −1.6 −1.2 −1.8 −1.4 −1.5 −1.2 −1.1 −1.7 −2.2 − −1.6 −2.2 −1.5 −1.4 −2.4 −1.4 −0.6 −1.4 −1.4 −1.7 −2.5 −1.5 −1.6

N ± ± ± ± ± ± ± ± ± ±

0.1 0.1 0.6 0.2 0.3 0.2 0.6 0.2 0.2 0.3

± ± ± ± ± ± ± ± ± ± ± ± ±

0.1 0.4 0.1 0.2 0.1 0.1 0.1 0.4 0.1 0.1 0.2 0.1 0.2

B2/B1 = −Δβ′(p0)/ΔV(p0) was recalculated from the pressure dependence of the amide proton and nitrogen shifts of the amino acid X published by Koehler et al.16 The samples contained approximately 5 mM Ac-GGXA-NH2 in 20 mM Tris-d11-HCl, pH 6.7, and experiments were performed at 283 K. bThe samples for Arnold et al.15 contained approximately 5 mM GGXA, 50 mM phosphate buffer, 1 μM NaN3, 20% D2O, 0.1 mM DSS, pH 5.4, and experiments have been performed at 305 K. The error of the mean has been calculated with two-tailed student distribution and corresponds to 0.95 confidence interval. cData for GGEA-OMe29. a

correlation between B2/B1 and the molecular mass of the amino acid X. Indeed, for 15N a significant negative correlation with a correlation coefficient of r = −0.54 can be found; for protons, the correlation is clearly weaker with r = −0.32. The data of the nonprotected tetrapeptides GGXA from Arnold et al.15 were reanalyzed, and the obtained B2/B1 values were also listed in Table 1. Only proton values were reported here. The mean B2/B1 value of GGXA is with −0.8 GPa−1 larger than −1.5 GPa−1 obtained for the protected peptides. However, within the limits of error they do not differ significantly, although the absolute chemical shifts of the amide protons in the two data sets are quite different. This is mainly caused by differences in temperature and pH but also due to the presence of the partially charged N-terminal amino and C-terminal carboxyl groups. For individual amino acids X, significantly different B2/B1 values were observed; especially for some residues in GGXA, positive B2/B1 ratios could be found. It could be an indirect, pressure-independent effect of the charged groups on the equilibrium state of the peptide but is most likely due to changes of the partial charges of the Nterminal and C-terminal groups with pressure. A change of the 5684



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Figure 2. Ratio B2/B1 for the model peptides GGXA and Ac-GGXA-NH2. B2/B1 was recalculated from the pressure dependence of the amide proton shifts of the amino acid X published by Arnold et al.,15 Kremer and co-workers29,30 (for GGEA-OMe), and Koehler et al.16 The samples for Koehler et al.16 contained approximately 5 mM Ac-GGXA-NH2 in 20 mM Tris-d11-HCl, pH 6.7, and experiments were performed at 283 K. The samples for Arnold et al.15 and Kremer et al.30 contained approximately 5 mM GGXA (except for Glu where GGEA-OMe has been used),29 50 mM phosphate buffer, 1 μM NaN3, 20% D2O, 0.1 mM DSS, pH 5.4, and experiments were performed at 305 K. Black bars and gray bars represent amide nitrogen and proton shifts in Ac-GGXA-NH2, respectively. White bars represent amide proton shifts in GGXA.

indicating that part of the pressure dependence of chemical shifts of the glutamate amide group originates from the interaction of the side chain carboxyl group with the partly protonated C-terminal carboxyl group and is not an intrinsic property of the glutamate side chain. Also, the B2/B1 ratio is clearly dependent on the state of the C-terminal carboxyl group. Analyzing data obtained by high-pressure NMR spectroscopy by a Taylor series is a convenient way to quantify the localized pressure response of a protein because in most cases the pressure dependence of chemical shifts can be determined with sufficient accuracy by a second-order polynomial. The disadvantage of this type of analysis of the experimental data is the fact that the parameters obtained primarily do not have an obvious physical meaning. However, we have shown above that the ratio of the first- and second-order pressure coefficients has a well-defined thermodynamic meaning, provided that the process causing the nonlinear behavior of the chemical shifts is caused by a two-state process and that |ΔG0| ≪ 2RT holds true. If we make the assumption that these conditions are fulfilled for our model peptides then the ratio of B2/B1 given in Table 1 would describe the ratio of the difference of the compressibility factors β′ and the partial molar volumes V of the two states. Within the limits of errors, the mean values of Δβ′/ΔV are equal for the amide protons and amide nitrogens indicating that the same pressure-dependent process influences the two nuclei. This is also confirmed by the correlation analysis (Figure 3). For all residues, the B2/B1 ratio for 15N and 1H is negative, a fact that supports the validity of the thermodynamical interpretation where the ratio of the compressibility difference to the partial volume difference usually is positive. The chemical shifts of the amide protons and nitrogens are strongly influenced by hydrogen bonding with water, water exposure, and electric field effects (e.g., see Avbelj et al.32). Therefore, these factors also probably determine the observed amino acid specific pressure response. Especially, the mean hydrogen bond length decreases substantially with pressure. Thus, the observed pressure-dependent chemical shift changes

Figure 3. Correlation between the amide proton and nitrogen B2/B1 ratios in Ac-GGXA-NH2. B2/B1 was calculated from the pressure dependence of the amide proton and nitrogen shifts of the amino acid X published by Koehler et al.16 The samples contained approximately 5 mM Ac-GGXA-NH2 in 20 mM Tris-d11-HCl, pH 6.7, and experiments were performed at 283 K. The linear correlation coefficient is r = 0.69.

protonation state of nearby charged groups by a pH-change usually leads to pH-dependent chemical shift changes in neighboring amino acids. In general, one would expect an increased protonation of amino groups and a deprotonation of the carboxyl groups with pressure.31 An example is the glutamate containing peptide,15,29 where we have shown earlier that the pressure response of the glutamate protons is clearly dependent on the charge of the C-terminal carboxyl group in the nonprotected tetrapeptide: the methyl ester of the Cterminal carboxyl group significantly decreases the nonlinearity, 5685



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can assume that |ΔG0| is smaller than 2RT. Similarly, for the Aβ-amyloid we showed that the B2/B1 ratio is clearly temperature independent as to be expected for |ΔG0| ≪ 2RT. From these data we can conclude that for the process causing the pressure dependence of the amide proton chemical shifts the values of |ΔG0| for isoleucine 3 and alanine 4 are smaller than approximately 2.6 kJ mol−1. A different behavior can be found for the two glycines, where for glycine 1, the ratio of B2/B1 is temperature independent in the range from 308 to 293 K but at lower temperatures shows a strong 1/T dependence. For glycine 2, the data is not complete due to strong overlapping of the NMR signal with the alanine 4 signal. It shows a relatively large linear 1/T-dependence with a slope that is quite similar to that of glycine 1 at low temperatures. If eq 13 holds true, we can calculate the volume difference ΔV from the slope, leading to a value of −63 mL mol−1, which is a rather big value for a volume change of a small peptide. However, one has to take into consideration that the amide groups are only reporter groups for possibly nonlocalized processes that may encompass, for example, changes of the surrounding water shell. As both glycines show a temperature dependence of the B2/B1 ratio, a |ΔG0| value much bigger than 4.6 kJ mol−1 would be the consequence. A feature distinguishing the two glycine residues from the other two residues is the missing side chain and thus the much higher flexibility in the Nterminus of the tetrapeptide and very different allowed backbone angles in the Ramachandran plot. One can speculate that these features determine the observed transition to a state that is rarely occurring at ambient pressure (e.g., an ordered state in this region). Amide Hydrogen Bonds with Water in Ac-Gly-Gly-IleAla-NH2 at Various Pressures. The equations derived above assume that the chemical shift change with pressure can be represented by a two-state system. Since hydrogen bonding is known to influence the amide chemical shifts, a two-state system possibly responsible for the observed pressure dependence would be defined by the existence or absence of a water molecule that is hydrogen bonded to the correspondent amide group. In a molecular dynamics (MD) simulation, the simplest way to distinguish whether an NH group is involved in a hydrogen bond to a solvent molecule or not is by the standard geometric criterion. In Table 2, we summarize simulation results for the four peptide NH groups in Ac-Gly-Gly-Ile-AlaNH2. For all four peptide groups, we observe a free energy of hydrogen bond formation in the range between 1 and 2 kJ/mol, less than the thermal energy RT = 2.4 kJ/mol at 283 K, which justifies the application of the limiting expression (eq 10) for this peptide. If this applies to the process determining the observed pressure response of the chemical shifts, the ratio of B2/B1 should be independent of temperature as it is found experimentally for Ile3 and Ala4 (Figure 4). The pressure

of the amide nuclei could mainly be due to the latter effect that could be presented in first approximation in a two-state model by the amide group of amino acid X either involved in a hydrogen bond or not. However, also the limitation of such a model is obvious since the pressure-dependent shortening of the hydrogen bond length will also lead to a downfield shift of the resonances independent of the population of the hydrogen bound state. This means that for the interpretation of peptide B2/B1 values, one has to be aware that they may have a contribution of Δβ′/ΔV, but that this is not the only factor determining the pressure response. Another possibility for analysis is to investigate the temperature dependence of the B2/B1 ratio. For |ΔG0| ≪ 2RT we would not expect any temperature dependence (eq 11), whereas for |ΔG 0| ≫ 2RT a linear temperature dependence with a slope of ΔV/R is expected (eq 13). To investigate the temperature dependence of B2/B1 we performed a temperature/pressure series for the model peptide Ac-GGIANH2 (Figure 4).

Figure 4. Temperature dependence of Ac-GGIA-NH2. Plot of the B2/ B1 ratio against 1/T for G1(●), G2 (▲), I3 (■), and A4 (⧫). The experiments have been performed at 278, 283, 288, 293, 298, 303, and 308 K. For each temperature, a pressure series has been performed at 3, 20, 40, 60, 80, 100, 120, 140, 160, 180, and 200 MPa. Overall, the error was negligible (approximately symbol size).

In Figure 4, we can see three different behaviors for the four amino acids in Ac-GGIA-NH2. The isoleucine 3 and the alanine 4 show nearly no temperature dependence, and therefore we

Table 2. Molecular Dynamics Predictions of the Average Peptide NH-Water Hydrogen Bonds of the Four Peptide Groups at 0.1 and 200 MPa and the Resulting Thermodynamic Parameters Gly1 pHB at 0.1 MPa pHB at 200 MPa ΔG at 0.1 MPa (kJ/mol) ΔG at 200 MPa (kJ/mol) ΔG pressure shift (kJ/mol) ΔV (mL mol−1)

0.633 0.643 1.36 1.47 0.11 0.55

± ± ± ± ± ±

0.002 0.002 0.02 0.02 0.03 0.25

Gly2 0.600 0.611 1.02 1.13 0.11 0.55 5686

± ± ± ± ± ±

0.003 0.003 0.03 0.03 0.04 0.20

Ile3 0.681 0.687 1.90 1.96 0.06 0.30

± ± ± ± ± ±

0.009 0.011 0.10 0.13 0.16 0.80

Ala4 0.674 0.660 1.82 1.66 −0.16 −0.78

± ± ± ± ± ±

0.024 0.019 0.27 0.22 0.35 1.8



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Table 3. Ratio of Second- And First-Order Pressure Coefficients for the Amide 1H and 15N Resonances of HPr from S. carnosusa Ala Arg Asn Asp Gln Glu Gly His Ile Leu Lys Met Phe Ser Thr Tyr Val Mean

B2/B1 1H (GPa−1)

σ 1H (GPa−1)

B2/B1 15N (GPa−1)

σ 15N (GPa−1)

0.3 2.5 19.0 4.7 −14.1 −18.9 −10.6 −17.1 5.3 5.9 −2.2 −16.7 −0.4 −18.9 −7.3 −0.9 −14.3 −4.9

9.0 − 33.2 12.9 16.9 28.2 21.7 − 39.2 12.4 3.8 13.9 − 42.6 18.1 0.9 21.6 10.9

−8.0 −0.7 −1.6 −1.6 0.3 −2.1 −1.7 −11.1 −13.1 −0.7 −2.7 −4.5 −5.3 −3.1 −27.3 −3.5 −2.1 −5.2

15.0 − 0.2 3.1 2.5 2.3 6.0 − 29.2 4.0 2.8 8.8 − 4.2 65.8 1.4 1.5 6.8

a B2/B1 was recalculated from the pressure dependence of the amide 1H and 15N shifts of HPr from S. carnosus published by Kalbitzer et al.14 Before calculating the B2/B1 ratio, the random-coil shifts from Koehler et al.16 were subtracted. The samples contained approximately 1.4 mM uniformly 15N labeled HPr protein in 10 mM Tris-HCl, 0.5 mM NaN3, 0.5 mM p-APMSF, 0.5 mM EDTA, 0.05 mM 3-(trimethylsilyl)-2,2′,3,3′tetradeuteropropionate (TSP-d4), 2.2 mM dioxane in 87.5% H2O/12.5% D2O, 298 K, pH 7.15. Errors were calculated as described in Materials and Methods.

Figure 5. Ratio of B2/B1 for HPr from S. carnosus for 1H and 15N. B2/B1 was recalculated from the pressure dependence of the amide 1H and 15N shifts of HPr from S. carnosus published by Kalbitzer et al.14 For details see Table 3. Black bars represent 15N shifts and gray bars represent 1H shifts.

reasons: first, it is only related to properties of the first solvation shell of the NH group and ignores that the electric field is a superposition to which all solvent molecules contribute. Second, the hydrogen bond definition itself is also subject to some arbitrariness, because a hydrogen bond cannot be unequivocally defined based on classical MD simulation data (which leads to geometric, energetic, or topological criteria that deviate in their hydrogen bond predictions).33 Pressure Dependence in a Model Protein. Well-folded proteins usually show much larger pressure responses of the chemical shifts than unfolded peptides. In addition to the small effects observed in random coil peptides often rather large nonlinear effects can be observed. They usually are interpreted as local or global conformational changes. As an example, we studied the histidine containing phosphocarrier protein (HPr) from S. carnosus, where the pressure dependence of the amide nitrogen and proton resonances were published earlier.14 We

response of the two glycines are positive and of comparable size in the MD data. However, at low temperatures a clear temperature dependence of the ratio of B2/B1 for the two glycine residues is observed in the experiments (Figure 4), indicating that other (additional) processes such as conformational equilibria must determine the pressure reponse. The Ile and Ala pressure responses predicted by MD have a larger error and are insignificant within the estimated error. The partial molar volume differences obtained from the first linear pressure shifts are about ΔV ≈ 1 Å3 for the two glycine groups. It is evident that very long simulation times are required for the convergence of the pressure shifts related to hydrogen-bonding properties. At the simulation time of 300 ns in this work, not all of the desired thermodynamic properties are obtainable with sufficient statistical accuracy. The classification of the solvent influence based on the existence of a hydrogen bond or not is very simplistic for two 5687



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calculated the ratio of the second- to the first-order coefficient for all amino acid types using the 1H and the 15N chemical shifts, respectively (Table 3 and Figure 5). The obtained mean values of B2/B1 for the different amino acid types generally also have a negative sign in HPr as in the peptide, but their absolute values are significantly larger. The mean values for the HPr protein are −4.9 GPa−1 for 1H and −5.2 GPa−1 for 15N. This is in agreement with an analysis of Kitahara et al.2 of 21 different proteins where a weak negative correlation between the first- and second-order pressure coefficients were reported for the amide protons and nitrogens. In the protein not only the magnitude of the mean B2/B1 values is significantly larger than in the model peptides but also the standard deviation for a given amino acid type is in most cases larger than the correspondent mean value. This indicates that local structural effects dominate over the intrinsic effect of the amino acid type. The mean B2/B1 ratios of individual amino acid types in HPr vary between the largest positive mean value for 1H of 19.0 GPa−1 of asparagine residues and the smallest negative mean value for 1H of −18.9 GPa−1 of glutamate residues (Table 3). A significant correlation between the B2/B1 values of individual residues of the tetrapeptides and the protein also cannot be found (1H, r = −0.37; 15N, r = −0.07). Unlike the relatively good correlation between the ratios of B2/B1 for 1H and 15N backbone resonances found for the tetrapeptides, the B2/B1 ratios in the HPr protein for the two nuclei do not show a significant correlation with a correlation factor of r = −0.07. This is in line with the correlation analysis of B1 and B2 of a protein database,2 where a vanishing correlation between B1 and B2 for backbone protons or nitrogen was found. The only significant correlation observed was that between proton B2 and nitrogen B2 values of an amino acid in a given position. To investigate the pressure response of a protein, often the pressure coefficients B1 and B2 are used, whose magnitudes are assumed to be related in some way to the pressure-induced local structural changes. Alternatively, we introduce here the ratio of B2/B1 for pinpointing possible regions involved in conformational transition. As we have shown, the ratio of the second- to the first-order pressure coefficient is related qualitatively to the differences of the compressibility factors and the partial molar volume changes Δβ′ and ΔV, respectively. Large values indicate regions of the structure with a high relative compressibility difference. The B2/B1 values calculated for HPr from S. carnosus from different 15N,1H-HSQC spectra are plotted on the 3D-structure of the protein (Figure 6). In our test spectra of the model peptide, only negative values for the of B2/B1 ratio are observed. In our thermodynamical interpretation, it means that for the state with the smaller volume (ΔV < 0) also the change of the partial molar volume with pressure is smaller (Δβ′ < 0). When the B2/B1 ratio is positive, ΔV and Δβ′ have different signs, indicating that the state with the smaller partial volume would have a higher compressibility. In case of HPr, significant changes for the 1H data can be found near the helix b where the regulation by the kinase takes place at the important amino acid Ser46. Another prominent region, where significant changes can be found is loop 1, where at the end the active center can be found with the important His15. Also the general distribution of positive and negative values for B2/B1 can yield some information. Most of the amino acids show a negative B2/B1 ratio (blue colors), whereas positive values can be found more seldom. Interestingly, the regions with “atypical” positive values (L2,

Figure 6. Plot of B2/B1 ratios on the structure of HPr from S. carnosus. (a) Values calculated from the 1H chemical shifts, (b) from the 15N chemical shifts of the amide groups. Deviation from the mean Δ(B2/ B1) ≥ +σ (orange), 0 ≤ Δ(B2/B1) < +σ (red), −σ > Δ(B2/B1) < 0 (blue), and Δ(B2/B1) ≤ −σ (light blue). No values available (gray). Residues involved in the interaction with (c) enyme I34 and (d) HPrkinase/phosphatase (violet).35 The interaction surface was determined according to Schumann et al.36

L6, and helix b) are detected by 1H as well as 15N ratios of pressure coefficients. Here, the 1H nuclei seem to be more sensitive toward the change in pressure, whereas less sensitivity can be found for the 15N nuclei. This can be explained with the proton being more involved in the water interaction as the nitrogen. Interaction sites of proteins have to adapt in some way to the mutual surface features. In a conformational selection model they present an example for a two-state model. The interacting residues of HPr with enzyme I and HPr-kinase/phosphatase were depicted in Figure 6. It seems to suggest itself that the general pressure response is correlated to these specific dynamical features of the interacting sites. However, plotting the amide or nitrogen first- and second-order coefficients separately on the structure does not show a correlation of these values with the binding sites, large values of these parameters appear to be randomly distributed relative to these binding sites (data not shown). This is different when plotting the amide proton and nitrogen B2/B1 ratios on the HPr structure: here positive values of B2/B1 or highly negative values are predominantly found in these regions, indicating relatively high compressibility differences or unusual positive compressibility differences. However, in the complex conformational equilibria usually found in proteins, the two-state thermodynamic interpretation of the B2/B1 ratios may be too simple. The correlation of the B2/B1 with protein−protein interaction sites observed in HPr represents an interesting observation worth 5688



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(4) Akasaka, K.; Li, H. Low-lying Excited States of Proteins Revealed From Nonlinear Pressure Shifts in 1H and 15N NMR. Biochemistry 2001, 40, 8665−8671. (5) Kachel, N.; Kremer, W.; Zahn, R.; Kalbitzer, H. R. Observation of Intermediate States of the Human Prion Protein by High Pressure NMR Spectroscopy. BMC Struct. Biol. 2006, 16, 6. (6) Kremer, W.; Kachel, N.; Kuwata, K.; Akasaka, K.; Kalbitzer, H. R. Species Specific Differences in the Intermediate States of Human and Syrian Hamster Prion Protein Detected by High Pressure NMR Spectroscopy. J. Biol. Chem. 2007, 282, 22689−22698. (7) Munte, C. E.; Beck Erlach, M.; Kremer, W.; Koehler, J.; Kalbitzer, H. R. Distinct Conformational States of the Alzheimer β-Amyloid Peptide can be Detected by High Pressure NMR Spectroscopy. Angew. Chem. 2013, 125, 9111−9116; Angew. Chem., Int. Ed. 2013, 52, 8943− 8947. (8) Roe, D. R. Sapphire NMR Tube for High-resolution Studies at Elevated Pressure. J. Magn. Reson. 1985, 63, 388−391. (9) Urbauer, J. L.; Ehrhardt, M. R.; Bieber, R. J.; Flynn, P. F.; Wand, A. J. High Resolution Triple-resonance NMR Spectroscopy of a Novel Calmodulin Peptide Complex at Kilobar Pressures. J. Am. Chem. Soc. 1996, 118, 11329−11330. (10) Yamada, H.; Nishikawa, K.; Honda, M.; Shimura, T.; Akasaka, K.; Tabayashi, K. Pressure-resisting Cell for High-pressure, Highresolution Nuclear Magnetic Resonance Measurements at Very High Magnetic Fields. Rev. Sci. Instrum. 2001, 72, 1463−1471. (11) Arnold, M. R.; Kalbitzer, H. R.; Kremer, W. High-sensitivity Sapphire Cells for High Pressure NMR Spectroscopy on Proteins. J. Magn. Reson. 2003, 61, 127−131. (12) Beck Erlach, M.; Munte, C. E.; Kremer, W.; Hartl, R.; Rochelt, D.; Niesner, D.; Kalbitzer, H. R. Ceramic Cells for High Pressure NMR Spectroscopy on Proteins. J. Magn. Reson. 2010, 204, 196−199. (13) Peterson, R. W.; Wand, A. J. Self-contained High-pressure Cell, Apparatus, and Procedure for the Preparation of Encapsulated Proteins Dissolved in Low Viscosity Fluids for Nuclear Magnetic Resonance Spectroscopy. Rev. Sci. Instrum. 2005, 76, 094101-1− 094101-7. (14) Kalbitzer, H. R.; Görler, A.; Li, H.; Dubovskii, P.; Hengstenberg, W.; Kowolik, C.; Yamada, H.; Akasaka, K. 15N and 1H NMR Study of Histidine Containing Protein (HPr) from Staphylococcus carnosus at High Pressure. Protein Sci. 2000, 9, 693−703. (15) Arnold, M. R.; Kremer, W.; Lüdemann, H.-D.; Kalbitzer, H. R. 1 H-NMR Parameters of Common Amino Acid Residues Measured in Aqueous Solutions of the Linear Tetrapeptides Gly-Gly-X-Ala at Pressures Between 0.1 and 200 MPa. Biophys. Chem. 2002, 96, 129− 140. (16) Koehler, J.; Beck Erlach, M.; Crusca, E., Jr.; Kremer, W.; Munte, C. E.; Kalbitzer, H. R. Pressure Dependence of 15N Chemical Shifts in the Model Peptides Ac-Gly-Gly-X-Ala-NH2. Materials 2012, 5, 1774− 1786. (17) Wishart, D. S.; Bigam, C. G.; Yao, J.; Abildgaard, F.; Dyson, H. J.; Oldfield, E.; Markley, J. L.; Sykes, B. D. 1H, 13C and 15N Chemicalshift Referencing in Biomolecular NMR. J. Biomol. NMR 1995, 6, 135−140. (18) Case, D. A.; Darden, T. A.; Cheatham, T. E.; Simmerling, C. L.; Wang, J.; Duke, R. E.; Luo, R.; Walker, R. C.; Zhang, W.; Merz, K. M. et al. AMBER 12; University of California: San Francisco, 2012. (19) Duan, Y.; Wu, C.; Chowdhury, S.; Lee, M. C.; Xiong, G.; Zhang, W.; Yang, R.; Cieplak, P.; Luo, R.; Lee, T.; et al. A Point-Charge Force Field for Molecular Mechanics Simulations of Proteins Based on Condensed-phase Quantum Mechanical Calculations. J. Comput. Chem. 2003, 24, 1999−2012. (20) da Silva, A. W. S.; Vranken, W. F. ACPYPE: AnteChamber PYthon Parser Interface. BMC Res. Notes 2012, 5, 367. (21) Abascal, J. L.; Vega, C. A General Purpose Model for the Condensed Phases of Water: TIP4P/2005. J. Chem. Phys. 2005, 123, 234505. (22) E Bussi, G.; Donadio, D.; Parrinello, M. Canonical Sampling Through Velocity Rescaling. J. Chem. Phys. 2007, 126, 014101.

reporting but remains to be verified for other proteins in the future.

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CONCLUSIONS In this paper, we have shown that the ratio of the second-order polynomial coefficients B2/B1 has a thermodynamical meaning and can be expressed as the ratio of the compressibility factor change and the volume change Δβ′/ΔV between two states. However, the validity of this relation requires that the data can be described by a two-state model. We verified the validity of the equation by comparing the published Δβ′ and ΔV values7 from the amyloid-β peptide with recalculated values for B2/B1 for data points where the condition |ΔG0| ≪ 2RT holds. A good correlation between the values of Δβ′/ΔV derived from the Taylor approximation and those obtained by a complete thermodynamic analysis exists. If the pressure response of the amide group can be described by a two-state process with |ΔG0| ≪ 2RT, we would obtain a Δβ′/ΔV ratio of 1.5 GPa−1 for the model peptide Ac-Gly-Gly-Xxx-Ala-NH2. The physical nature of this process cannot be concluded from the data, but since amide proton shifts strongly depend on hydrogen bond formation, it could represent the on/off state of the water protons forming hydrogen bonds with the peptide group (including also the carbonyl group and possibly also the whole hydrogen bondage network around the peptide). The simulations of the hydrogen bonding in Ac-GGIA-NH2 show that at least in this example the correspondent ΔG values are in the range needed for our approximation. The pressuredependent chemical shift changes would be caused by their electric field effects on the shielding tensor.32,37 A protein usually exists in many different conformational substates. After correcting for the simple “random-coil like” pressure effects, the B2/B1 was calculated for the HPr protein. A first analysis suggests that it can give information about protein−protein interaction sites. However, from the limited database available, it cannot be decided if the predominantly positive B2/B1 values (corresponding to an unusual negative ratio of Δβ′/ΔV) observed for the binding sites of HPr reflects characteristic features of the compressibility of binding sites in general.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the DFG, the Fonds der Chemischen Industrie, and the Human Frontiers Science Foundation (HFSPO).

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REFERENCES

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Relationship between Nonlinear Pressure-Induced Chemical Shift

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