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Translational Diffusion Constants of Short Peptides: Measurement by NMR and Their Use in Structural Studies of Peptides Hongxia Pei, Markus W. Germann, and Stuart A. Allison* Department of Chemistry, Georgia State UniVersity, P.O. Box 4098, Atlanta, Georgia 30302-4098 ReceiVed: March 10, 2009; ReVised Manuscript ReceiVed: May 15, 2009
In this work, pulsed field gradient NMR is used to measure the translational self-diffusion constants (DT’s) of five simple peptides (GG, GR, GGR, GGNA, and GGRA) as well as glycine, G, at low concentration. The experiments were carried out in D2O at 298 K at pD ) 3.5 in 80 mM sodium phosphate buffer. Of the five peptides, four are being reported for the first time (all except GG) and the results of G and GG are compared with DT’s from the literature. When corrected for differences in solvent viscosity and temperature, the discrepancy between DT’s of G and GG measured in the present work are lower than previously published values by several percent. Given the range of values reported in the literature for specific values of the amino acids by different groups, this discrepancy is regarded as reasonable. Diffusion constants can provide useful information about molecular size and conformation. Modeling a peptide made up of N amino acids as 2N beads (2 for each amino acid present in the peptide), we examine the diffusion constants of the abovementioned peptides and conclude they are consistent with unfolded or random conformations in solution. Also, by comparing the diffusion constants of G and GG, an estimate of the change in solvation volume due to the loss of a water molecule can be estimated. 1. Introduction NMR has become a powerful method in the study of macromolecular structure. One application involves using pulsed field gradients (PFGs) to measure the translational diffusion constant, DT, of molecules of variable sizes.1-3 This approach can be applied at very low concentrations and has been used to measure diffusion of molecules in both free solution and micelle environments; see, e.g., refs 4 and 5. For macromolecules with molecular masses exceeding approximately 10 kDa, dynamic light scattering is perhaps the most effective method available to determine DT,6,7 but it cannot be used for smaller molecules. For small molecules, boundary spreading methods due to a concentration gradient have been used for many years8,9 and continue to be useful at the present time.10 However, an advantage of PFG NMR over concentration gradient methodologies is the substantially lower sample concentrations that can be used, permitting the study of compounds with low solubility. For the short peptides studied in the present work, concentrations in the 5-20 mM range were employed. In concentration gradient studies of amino acids, the range is typically 10-500 mM.8-10 Also, since diffusion constants vary with concentration, the extrapolation to zero concentration is expected to be more accurate due to the lower sample concentrations employed. Recently, PFG NMR was successfully used to measure DT for several amino acids and to estimate DT0, the translational diffusion constant in the limit of zero peptide concentration, by simple extrapolation.11 Diffusion constants in the limit of zero concentration, in turn, are sensitive to molecular size and conformation and consequently are of considerable value in elucidating molecular structure. The principal objective of this work is the determination of DT and DT0 for five short peptides: Gly-Gly (GG), Gly-Arg (GR), Gly-Gly-Arg (GGR), Gly-Gly-Asn-Ala (GGNA), and * Corresponding author. Telephone: (404) 413-5519. E-mail: sallison@ gsu.edu.
Gly-Gly-Arg-Ala (GGRA), by field gradient NMR. The diffusion constant of the amino acid glycine, G, is also reported. For G and GG, we are able to compare our DT values with earlier results measured by the concentration gradient methods.8-10,12 The results for G and GG are also used to adjust one parameter, the “side bead” radius of glycine, in a “bead model” that we have found particularly useful in studies of the free solution electrophoretic mobility of peptides.13 Also, when two G’s condense to form GG, a single water molecule is lost and we are able to estimate the change in solvation volume due to the loss of a water molecule. We then use the peptide bead model along with the DT’s determined in this work to examine the solution conformation of the remaining peptides. Two of these, GGNA and GGRA, have been the subject of detailed study by free solution electrophoresis.14,15 2. Materials and Methods 2.1. Peptide Samples. Peptide samples (GenScript) were prepared in D2O in a buffer consisting of 80 mM sodium phosphate. Unless otherwise noted, the peptide concentration was 5 mM. For peptides GG and GGRA the concentration was varied from 5 to 20 mM and the diffusion constants at zero concentration were estimated by extrapolation. The pH* (uncorrected meter reading) was adjusted to 3.05-3.09 with DCl. This corresponds to a pD of approximately 3.5.16 2.2. NMR Spectroscopy. NMR spectra were acquired on a Bruker Avance 500 MHz spectrometer equipped with a 10 A gradient amplifier using a 5 mm TBI probe head 1H{13C, X} with a shielded Z-gradient coil. The gradient coil of the probe head was calibrated to 5.72 G/(cm A) using a 5 mm NMR tube (Shigemi) with a 14 mm sample window using 99.96% D2O. All DT measurements were recorded at 298 K using a pseudotwo-dimensional stimulated echo pulse program with one spoil gradient(“stegp1s”)(Brukerpulsesequence“stegp1s,v.1.1.2.2”).17,18 The NMR pulse sequence and parameters are shown in Figure 1. Prior to determining the diffusion constant, the diffusion
10.1021/jp902143q CCC: $40.75 2009 American Chemical Society Published on Web 06/17/2009
Short Peptide Translational Diffusion Constants
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DT0(H2O, 298 K) ) 1.226DT0(D2O, 298 K)
Figure 1. NMR pulse scheme for the diffusion measurement. All gradients were applied as sine shapes. The spoil gradient (-9.8 G/cm) was 1.1 ms, the diffusion time (∆) was set to 200 ms, and the diffusion gradient length (δ) was varied from 1.16 to 1.9 ms depending on the molecular size (e.g., 1.16 ms for GG and 1.9 ms for the GGRA peptide). For the diffusion measurements the gradient strength was varied from 2.86 to 54.6 G/cm.
gradient length (δ) was optimized to ensure complete data sampling. In the subsequent measurements the gradient strength was varied in 16 increments while all other parameters were kept constant. Typically, 16-32 scans were collected for each experiment, using a relaxation delay of 8 s and 1-2 Hz line broadening. The data were processed and analyzed using the T1/T2 package of XwinNMR 3.5. With the gradient calibration, a DT of HDO (99.96% D2O) of 2.24 × 10-9 m2/s at 298 K is obtained. This is in agreement with previously reported DT’s of HDO, which range from 1.90 × 10-9 to 2.51 × 10-9 m2/s.19,20 2.3. Modeling of Peptides. In this work, a peptide made up of N amino acids is modeled as a string of 2N beads and has been described in detail previously.13 For each amino acid, one bead represents a “backbone” bead and the other represents the side group of the particular amino acid. For peptides ranging from two or more amino acids, a peptide conformation can be defined by a succession of dihedral angles. In the present work as in ref 13, several hundred conformations are generated at random and the translational diffusion constant of each conformation is computed. These are then averaged to determine DT0 for a particular peptide. This modeling procedure is described in more detail in section 4. 3. Results All NMR experiments on amino acid and peptide samples were carried out in D2O at 298 K in a buffer solution containing 80 mM sodium phosphate at pD = 3.5. The translational diffusion constant in the limit of zero amino acid or peptide concentration, DT0, is related to the hydrodynamic radius, Rh, by the relation
DT0 )
kBT 6πηRh
(1)
where T is the temperature (in kelvin), kB is Boltzmann’s constant, and η is the solvent viscosity. For a low ionic strength D2O buffer at 298 K, η ) 1.091 cP (1.091 × 10-3 kg/(m s)).21 This compares to a viscosity of a low ionic strength H2O buffer at 298 K of 0.89 cP (8.9 × 10-4 kg/(m s)). Assuming Rh is unaffected by the substitution of H2O with D2O, we can correct “raw” diffusion constants measured in D2O to the corresponding diffusion constants in water at 298 K with
(2)
In this work, all diffusion constants reported have been corrected to water at 298 K. NMR experiments for GG and GGRA were carried out at 5, 10, and 20 mM peptide concentration, in order to examine the concentration dependence of DT. In the limit of zero concentration, DT0 values equal to 7.58 × 10-10 and 4.71 × 10-10 m2/s for GG and GGRA, respectively, are obtained by simple extrapolation. The ratio DT/DT0 is plotted in Figure 2 versus the peptide concentration for both GG and GGRA. The error bars reflect the estimated 1% relative uncertainty in the measured diffusion constants. The ratio DT(0 mM)/DT(20 mM) is 1.015 and 1.047 for GG and GGRA, respectively. For the remaining samples, DT was only measured at 5 mM. A 4% correction for a 20 mM sample would correspond to a 1% correction for a 5 mM sample, which is comparable to the relative error in the NMR measurements themselves. The DT0 values are summarized in Table 1. For the samples besides GG and GGRA, we simply approximate DT0 to the measured value at 5 mM peptide concentration. Also listed in Table 1 are effective hydrodynamic radii using eq 1 and DT0’s obtained from modeling. The modeling values shall be discussed in section 4. In comparing the present results with past work, there have been a number of previous experimental studies on both G and GG. For G, a detailed comparison of literature values for G were reported by Polson8 and the range appearing in Table 1 comes from that reference corrected to 298 K. Ma and co-workers recently reported values for G (concentration range from 100 to 500 mM) and other amino acids, and from their data, we estimate DT0 = 10.56 × 10-10 m2/s,10 which lies near the high end of the range reported in Table 1. The present NMR value (5 mM glycine) of 9.88 × 10-10 m2/s lies closer to the low end and is 6.7% lower than the recent concentration gradient measurement of ref 10. In a previous analysis of DT0’s of amino acids reported by different groups, discrepancies of up to 8% are reported, and the discrepancy observed for glycine in the present work falls within this range. For GG, the present NMR DT0 lies below previously reported values9,12 by about 4%, which is well within the 8% range mentioned above for the amino acids. 4. Discussion 4.1. Analysis of G and GG. In past work that has dealt primarily with the free solution electrophoretic mobility, µ, of peptides, we have developed and used a model in which each amino acid of a peptide chain is represented by two beads.13,22 One of these beads, the “backbone bead”, has a fixed radius of 0.19 nm and is chosen to reproduce the known average distance of 0.38 nm between near-neighbor R-carbons.23 The remaining “side bead” is of variable radius, as, depending on the amino acid. Its value is determined on the basis of the translational diffusion constant of the particular amino acid.11,13 Using wellestablished methods of bead hydrodynamics24 and modeling intersubunit hydrodynamic interaction at the level of the Rotne-Prager tensor,25 it is straightforward to estimate the side bead radius of an amino acid, modeled as a dimer of two touching beads of unequal radius, provided Rh is known (eq 1). For the Rh of G reported in Table 1, we obtain an as of 0.182 nm. However, when amino acids condense to form peptides, a single water molecule is lost for each amino acid added to a growing peptide chain. This is illustrated in Figure 3 for the condensation of two G’s to form GG. Due to the loss of water,
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Figure 2. DT/DT0 versus peptide concentration for GG and GGRA. The squares and diamonds correspond to experimental ratios for GG and GGRA, respectively. Measurements were carried out in D2O at 298 K in 80 mM sodium phosphate buffer at pD = 3.5. The lines correspond to linear fits of the data, and the vertical bars represent the estimated error.
TABLE 1: DT0 (in 10-10 m2/s) and Rh for G and Peptidesa species
DT0 (present work)
Rhb (nm)
DT0 (past work)
DT0 (model)
errorc
G GG GR GGR GGRA GGNA
9.88 7.58 5.62 5.56 4.71 5.19
0.248 0.324 0.437 0.441 0.521 0.473
9.6-10.7 7.9-8.0 -
7.58 5.93 5.31 4.77 5.13
+0.055 -0.045 +0.013 -0.012
a In dilute aqueous buffer at 298 K. DT0(model)/DT0(experiment) - 1.
b
From eq 1.
c
Defined as
Figure 3. Illustration of the condensation of two G’s to form GG.
the side bead radius of glycine in GG will be different from the side bead radius in “free” glycine. Using the procedure described previously,13,22,26 several hundred peptide conformations are generated using random numbers to select the phi-psi angles between adjacent amino acids. Rotation matrices27 are used to properly position successive bead pairs in relation to other beads lower down the chain. For each conformation, we compute DT0 and also other transport properties such as the electrophoretic mobility.13,22,26 Secondary structure can also be incorporated into this methodology.26 Final transport properties are obtained by simply averaging the single conformation transport properties over all the different conformations generated. When this procedure is applied to GG (random secondary structure) and the side bead radius of each G is left as a variable parameter, as equal to 0.164 nm is necessary to match model and experimental DT0’s. We can view each G of GG as having lost half a water molecule each. The hydrodynamic radius, Rs, of a touching dimer of radii 0.190 and 0.164 nm is estimated to be 0.237 nm. This can be compared to Rh ) 0.248 nm for “free” glycine. If a small molecule with hydrodynamic radius Rh loses volume δV, the resultant hydrodynamic radius, Rs, can be estimated to be28
(
Rs ) Rh 1 -
3(δV) 4πRh3
)
1/3
(3)
Solving eq 3 for δV, we obtain 0.008 13 nm3 for the loss of half a water molecule or 0.0163 nm3 for the loss of one full water molecule. This is slightly smaller than the value of 0.0186 nm3 estimated previously.13 For a G entirely within a peptide chain, it will have lost one full water molecule. From eq 3, we estimate Rs ) 0.225 nm (using Rh ) 0.248 nm and δV ) 0.0163 nm3) and a side bead radius, as, equal to 0.143 nm. In what follows, we shall use these adjusted side bead radii of G in modeling the other peptides. The as values for the remaining amino acids are the same as before and are reported elsewhere.11 4.2. Comparison of DT0 between Experiment and Modeling for the Remaining Peptides. By employing the bead model described in the previous section, we obtain model translational diffusion constants summarized in Table 1 along with the corresponding experimental diffusion constants and hydrodynamic radii. In modeling, the temperature was taken to be 298 K and the “random” secondary structure was assumed.26 The model diffusion constants represent the average over several hundred independently generated conformations, and agreement between modeling and experiment lies within (5%. In an earlier modeling study of the electrophoretic mobility, µ, of GGRA and GGNA26 based on experiments by Messana and co-workers,14,15 it was concluded that the mobility data of GGNA were well explained by a random model of the peptide, but this was not the case for GGRA. For GGRA, a more compact model, possibly containing an I-turn, was necessary to explain the large absolute mobility observed experimentally.26 However, such a compact model structure yields DT0 ) 5.50 × 10-10 m2/s, which is higher than the experimental value by 17%. On the basis of the present NMR measurement of DT0, we conclude that the solution conformation of GGRA, or more precisely, the sample examined in our NMR experiment, is a more open “random” structure rather than a compact structure. 5. Summary In this work, field gradient NMR has been used to measure the translational diffusion constants of glycine and several short peptides. Where independent experimental data are available, the current NMR diffusion constants agree with previous values to within several percent. An advantage of NMR over concentration gradient methods is the much lower sample concentrations required. Furthermore, NMR can be used to determine translational diffusion constants of small molecules that are inaccessible to dynamic light scattering. Diffusion constants can provide valuable information about the solution conformation of peptides. When applied to short peptides such as GGNA and GGRA around a pH 3.5 in a low salt buffer, it is concluded unequivocally that the solution conformation is random and open and not compact. Acknowledgment. This work was supported by the Georgia Cancer Coalition (M.W.G.) and the Georgia Research Alliance. References and Notes (1) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288–292. (2) Stilbs, P. Prog. NMR Spectrosc. 1987, 19, 1–45. (3) Johnson, C. S. Prog. Nucl. Magn. Reson. Spectrosc. 1999, 34, 203– 256. (4) Syvitski, R. T.; Burton, I.; Mattatall, N. R.; Douglas, S. E.; Jakeman, D. L. Biochemistry 2005, 44, 7282–7293. (5) Inglis, S. R.; McGann, M. J.; Price, W. S.; Harding, M. M. FEBS Lett. 2006, 580, 3911–3915. (6) Berne, B. J.; Pecora, R. Dynamic Light Scattering; Wiley: New York, 1976.
Short Peptide Translational Diffusion Constants (7) Schmitz, K. S. An Introduction to Dynamic Light Scattering by Macromolecules; Academic Press: New York, 1990. (8) Polson, A. Biochem. J. 1937, 31, 1903–1912. (9) Longsworth, L. G. Diffusion in Liquids and the Stokes-Einstein Relation. In Electrochemistry in Biology and Medicine; Shedlovsky, T., Ed.; Wiley: New York, 1955; pp 225-247. (10) Ma, Y.; Zhu, C.; Ma, P.; Yu, K. T. J. Chem. Eng. Data 2005, 50, 1192–1196. (11) Germann, M. W.; Turner, T.; Allison, S. A. J. Phys. Chem. B 2007, 111, 1452–1455. (12) Ellerton, H. D.; Reinfelds, G.; Mulcahy, D. E.; Dunlop, P. J. J. Phys. Chem. 1964, 68, 403–408. (13) Xin, Y; Mitchell, H.; Cameron, H.; Allison, S. A. J. Phys. Chem. B 2006, 110, 1038–1045. (14) Castagnola, M.; Rossetti, D. V.; Cassiano, L.; Misiti, F.; Pennacchietti, L.; Giardina, B.; Messana, I. Electrophoresis 1996, 17, 1925–1930. (15) Messana, I.; Rossetti, V.; Cassiano, L.; Misiti, F.; Giardina, B.; Castagnola, M. J. Chromatogr., B 1997, 699, 149–171. (16) Popov, K.; Ronkkomaki, H.; Lajunen, L. H. Pure Appl. Chem. 2006, 78, 663–675.
J. Phys. Chem. B, Vol. 113, No. 27, 2009 9329 (17) Kotch, F. W.; Sidorov, V.; Lam, Y. F.; Kayser, K. J.; Li, H.; Kaucher, M. S.; Davis, J. T. J. Am. Chem. Soc. 2003, 125, 15140–15150. (18) Tanner, J. E. J. Chem. Phys. 1970, 52, 2523–2526. (19) Mills, R. Bunsen-Ges. Ber. Phys. Chem. 1971, 75, 195–199. (20) Mills, R. J. Phys. Chem. 1973, 77, 685–688. (21) Hardy, R. C.; Cottingen, R. L. J. Chem. Phys. 1949, 17, 509–510. (22) Xin, Y.; Hess, R.; Ho, N.; Allison, S. A. J. Phys. Chem. B 2006, 110, 25033–25044. (23) Sasisekharan, V. In Collagen; Ramanathan, N., Ed.; Interscience: New York, 1962; p 39. (24) Garcia de la Torre, J.; Bloomfield, V. A. Q. ReV. Biophys. 1981, 14, 81–139. (25) Rotne, J.; Prager, S. J. Chem. Phys. 1969, 50, 4831–4837. (26) Pei, H.; Xin, Y.; Allison, S. A. J. Sep. Sci. 2008, 31, 555–564. (27) Flory, P. In Statistical Mechanics of Chain Molecules; Wiley: New York, 1969; Chapter 7. (28) Edward, J. T. J. Chem. Educ. 1970, 47, 261–270.
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