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2009, 113, 9055–9058 Published on Web 06/17/2009
Dynamics and Hydration Behavior of a Short Collagen Model Polypeptide, (L-Prolyl-L-ProlylGlycyl)5, in Aqueous Media Toshiyuki Shikata,* Nao Yoshida, Ayako Minakawa, and Kenji Okuyama Department of Macromolecular Science, Osaka UniVersity, Toyonaka, Osaka 560-0043, Japan ReceiVed: May 15, 2009; ReVised Manuscript ReceiVed: May 31, 2009
A short collagen model polypeptide, (L-prolyl-L-prolylglycyl)5 (PPG5), behaves as a fully dissociated flexible zwitterionic polymer chain in pure water. Its first and third normal modes of chain conformational fluctuation were detected as distinct dielectric relaxation modes. Addition of acetic acid at 30 mM to an aqueous solution of PPG5 effectively suppressed the overall relaxation strength by protonation of the carboxy termini of the polypeptide. Furthermore, the hydration number per PPG5 molecule was determined to be 130 by dielectric relaxation (DR) spectroscopy over a frequency range from 1 MHz to 20 GHz; this value was not affected by the addition of acetic acid. Collagen is the most abundant structural protein in animals with an XYG (G, glycine; X and Y, any amino acid residue) repeating sequence and forms a triple helix in nature.1,2 The denaturation temperature of the collagen leads to deconstruction of the triple helix into flexible single coils of polypeptide chains and is governed by the amino acid sequence.1-3 In order to understand the overall thermal properties of collagen and its triple-helical structure, a series of model polypeptides mimicking the XYG sequence were synthesized and successfully studied.4,5 (PPG)n (P, L-proline; hereafter PPGn), the simplest collagen model polypeptide, displayed reversible conformational changes between the triple helix and single coils. Furthermore, X-ray diffraction of its single crystal revealed 7/2-helical symmetry of three strands, consistent with native collagen when n g 9.5-7 However, since PPG5 does not form triple helices in aqueous media,8 it is useful for study of the dynamics and hydration of collagen in the flexible coil state. Dielectric relaxation (DR) measurements, which yield the relaxation times of electric dipoles with high precision, are powerful probes of the dynamics of any system containing molecules and/or groups bearing electric dipoles. DR techniques are also useful for determining hydration numbers in aqueous solutions, since the simple water molecule possesses a large dipole moment.9 Figure 1 shows the DR spectra of a 23.0 mM aqueous solution of PPG5 (3.0% in weight) at 25 °C, highlighting the real and imaginary parts of electric permittivity (ε′ and ε′′) versus angular frequency (ω). The DR spectra for pure water, εW′ and εW′′ (black chains), are also plotted in the same figure. The PPG5 solution shows two characteristic major DR processes in the ranges ω ∼ 108 and ω ∼ 1011 s-1. According to linear theory,10 all of the obtained DR spectra were perfectly decomposed into Debye-type relaxation modes as provided by the relationship * To whom correspondence should be addressed. E-mail: shikata@ chem.sci.osaka-u.ac.jp.
10.1021/jp904568r CCC: $40.75
ε′ )
ε
∑ 1 + ωj 2τ 2 + ε∞ j
and
j
ε′′ )
ε ωτ
∑ 1 +j ω2jτ 2 j
j
(1) where τj and εj are the relaxation time and strength for each mode (j ) 1-4 from the fastest mode) and ε∞ is the ω-independent electric permittivity. Figure 1 also shows the constituent relaxation modes (dotted lines, j ) 1-4) and consequent fit curves (solid orange lines) for the ε′ and ε′′ data. Aqueous PPG5 solutions displayed a pronounced DR mode j ) 4 at ω ∼ 2.5 × 108 s-1 with a relaxation time of τ4 ∼ 4 ns, independent of concentration. The relaxation strength of mode ε4 increased directly with concentration, as is evident in Figure 4. A weak DR mode was identified at ω ∼ 2.0 × 109 s-1 (τ3 ∼ 0.5 ns) and was also independent of concentration. Since PPG5 does not form triple helices in aqueous media at 25 °C,8 the DR spectra shown in Figure 1 reflect the dynamics of PPG5 in the single coil state. In single coils of polypeptide chains, the motions of a pair of opposite electric charges play an essential role in the overall DR processes. These charges are located at
Figure 1. Frequency (ω) dependencies of the real and imaginary parts (ε′ and ε′′) of electric permittivity for the aqueous PPG5 solution at c ) 23.0 mM and εW′ and εW′′ (black chains) for pure water at 25 °C. This figure also contains constituent relaxation modes (j ) 1-4, dotted lines) and the total fit curves (solid orange lines) for ε′ and ε′′.
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Letters
τbs p )
b2ζ 12kBT sin2
πp 2N
( )
(2)
Furthermore, the relaxation strength (εpbs) for each odd normal mode is described with a constant (F) that depends on the expression of a local electric field and the mean square of the dipole moment, (〈(µpbs)2〉). This is provided by Figure 2. Relationship between dielectric relaxation time (τj) and PPG5 concentration (c) in pure water and a 30 mM acetic acid solution. The small, closed symbols represent data for the PPG5 pure water solution.
bs 2 εbs p ) cF〈(µp ) 〉
(3)
and
〈(µbsp )2〉 )
Figure 3. Schematic depiction of the approximate rescale of a dipolar, zwitterionic polymer chain into a bead-and-spring model chain consisting of four beads and three springs and the first and third normal modes in the conformation of the model chain.
2(N - 1)b2e2(qi + qf)2 π2p2
When polymer chains possess electric dipole vectors parallel to their backbones (in the same direction), the sum of the vectors leads to finite electric charges located at each end, and the DR process is expressed in the same manner as the zwitterionic polymer.11 Such polymers, termed type-A polymers, have been well studied and are useful tools to probe polymer chain dynamics in both bulk and solution.12 On the other hand, Stokes-Einstein-Debye theory11,13 predicts a DR time (τSED) for a coil with a mean square radius of rotation (〈S2〉) as follows.
τSED ) Figure 4. Relationship between concentration-reduced dielectric relaxation strength (εjc-1, j g 2) for each relaxation mode j and c in pure water and a 30 mM acetic acid solution. The small, closed symbols represent data for the PPG5 pure water solution.
the polypeptide termini due to the dissociation of the carboxy (C-) and amino (N-) ends of the chain (eqi and -eqf; e represents an elementary electric charge, and qi and qf represent the degrees of dissociation of the initial and final termini). According to theoretical considerations of the dynamics of polymer chains bearing opposite electric charges at each terminus (i.e., zwitterionic, dipolar polymers) based on the standard bead-and-spring model,11 DR parameters due to the time-dependent fluctuation of polymer conformations have been calculated. In the bead-and-spring model, a polymer molecule is approximated to be a sequential chain of N beads with a coefficient of friction (ζ) connected by N - 1 springs (e.g., segments or subchains) with a mean square extension (b2) and a spring constant of κ ) 3kBTb-2 as depicted schematically in Figure 3.11 In this equation, kBT is the product of Boltzmann’s constant and the absolute temperature. The time-dependent conformational fluctuation of this model chain is described as the superposition of each fundamental normal mode (p). In the case of zwitterionic polymers, dielectrically detectable normal modes are of only odd number with the chain conformation, in which the terminus beads move in opposite directions, as shown in Figure 3. This is because even normal modes do not generate detectable electric dipoles. Assuming a freely draining condition, the DR time of the bead-and-spring model (τpbs) for each odd normal mode p is provided by
(4)
4πη〈S2〉3/2 kBT
(5)
where η represents the viscosity of a solvent. 〈S2〉1/2 was previously determined to be ∼1 nm14 for single coil polypeptides similar to PPG5 in aqueous media and leads to τSED ∼ 3 ns at 25 °C. This result is in accordance with τ4, as shown in Figure 2. Since τSED has the same physical meaning as τ1bs in the zwitterionic polymer,11 the observed DR mode j ) 4 was assigned to the slowest normal mode p ) 1. Since the ratio of τ4/τ3 (∼6) for PPG5 solutions (Figure 2) agreed with the ratio of τ1bs/τ3bs, assuming N ) 4 is independent of the addition of acetic acid, the modes j ) 4 and j ) 3 were assigned to the normal modes p ) 1 and p ) 3 for the single coil of PPG5. In this case, the segment consisted of five amino acid residues. Other higher modes possessing p g 5 were undetectable due to a lack of normal modes resulting from the low value of N. According to the previous studies on the solution properties of a series of collagen model polypeptides,14 it is likely that in aqueous media PPGn is described with an unperturbed wormlike chain bearing a contour length per amino residue and a Kuhn segment length of 0.33 and ∼2 nm, respectively, but without thickness. Then, PPGn-type collagen model polypeptides in the single coil state longer than PPG10 would behave as Gaussian chains in solution. Although PPG5 is not a perfect Gaussian chain, here we discuss the chain dynamics of PPG5 based on the behavior of a bead-and-spring model chain with N ) 4 for simplicity. Although the ratio ε4c-1/ε3c-1 ()ε1bs/ε3bs) was predicted to be 9 according to the above bead-and-spring model, the experimental value was determined to be ∼7 in aqueous solutions and was slightly lower than the value as shown in Figure 4. The discrepancy suggests the presence of other DR processes that should be taken into account. This trend becomes more
Letters
Figure 5. Dependence of the ratio of the dielectric relaxation strength for mode j ) 1 to that of pure water (ε1εW-1) on c for PPG5 solutions in pure water and 30 mM acetic acid.
significant in 30 mM acetic acid PPG5 solutions, where ε4c-1/ε3c-1 ∼ 5, as shown in Figure 4. The first conceivable reason for these discrepancies is non-Gaussian behavior of PPG5, and the second reason, the presence of dipoles of amide groups in monomers. Amino acid residues in polypeptides possess amide groups bearing relatively large dipole moments, which are possibly the origin for the behavior of type-B polymers; the type-B polymers are classified as polymers bearing dipoles perpendicular to their backbones.11 In principle, the chain segment behaves as the smallest repeat unit to the chain conformation providing Gaussian statistics and also the elementary dynamic process for global chain dynamics. The segment in the single coil of PPG5 likely bears additional dipoles due to the amide groups of amino acid residues, of which a DR process is only observed at τ3, because molecular motions at the monomeric amino acid residue level are highly correlated in segments and are random in direction. Furthermore, no DR process was found in a frequency range corresponding to relaxation times between τ3 and τ2. In our previous studies,15 excessive DR strength due to the presence of solutes observed in aqueous media correlated well with the solute dipole moments by the relationship proposed by Oncley.16 This relationship determined a constant in eq 3 as F ) NA(2εvkBT)-1, where NA and εv are Avogadro’s number and the electric permittivity of a vacuum, respectively. Applying this expression of F to the ε4c-1 data in Figure 4, the dipole moment of mode j ) 4 (p ) 1 for the bead-and-spring model) was determined to be |µ4| ) 3.2 × 10-26 Ccm, resulting in an end-to-end distance of 〈R2〉1/2 ()(N - 1)1/2b) ) 2.2 nm, assuming full dissociation of both the C- and N-termini, qi ) qf ) 1, independent of the concentration. Since the ratio 〈R2〉1/2/〈S2〉1/2 ∼ 2.2 is slightly smaller than 6 ∼ 2.4 for Gaussian chains but close in value, PPG5 approximately behaves as a fully dissociated Gaussian chain.11 Similar considerations were also possible based on the value of the relaxation time, τ4. The coefficient of friction of the segment is given as ζ ) 6πηr, with its radius (r) determined by Stokes-Einstein law. Assuming r ) b, τ4 ) 4 ns, and N ) 4, the relationship b ) 1.2 nm and 〈R2〉1/2 ) 2.1 nm was obtained, of which the value for 〈R2〉1/2 was in accordance with the results for ε4 discussed above. The reason for these slight systematic deviations of the ratio 〈R2〉1/2/〈S2〉1/2 from the value for Gaussian chains resulted from the non-Gaussian behavior of PPG5. Moreover, in acetic acid, the value of 〈R2〉1/2/〈S2〉1/2 was reduced to ∼1.7 if one assumes qi ) qf ) 1. The protonation of a portion of the C-termini by the addition of acetic acid effectively suppressed the number of dipolar, zwitterionic forms of PPG5. A polymer chain bearing an electric charge at one terminus, monopolar chain (e.g., qi ) 1 and qf ) 0) also displays a DR normal mode p, whose strength (εpbs) is only 1/4 of the zwitterionic polymer, but with identical properties to the monopolar chain apart from the electric charge condition.11
J. Phys. Chem. B, Vol. 113, No. 27, 2009 9057 The relaxation process identified ω ∼ 1011 s-1, which was assigned to the contribution of free water molecules belonging to bulk water, since εW′ and εW′′ for pure water display a similar DR process in the same ω range as observed in Figure 1. This major DR process includes the contribution of both free and hydrated water molecules. The fastest relaxation mode, identified at τ1 ∼ 8.3 ps, was assigned to the relaxation mode of free water molecules as described above. It has been well documented that depression in relaxation strength for mode j ) 1 in solution relative to that of pure water is described by the relationship
j Pc ε1 1 - 10-3V j Wcm - 10-3V ) εW j Pc/2 1 + 10-3V
(6)
j P and V j W are the partial molar volumes of solute and where V water molecules, respectively, and m is the number of hydrated water molecules per solute molecule.9,15 The concentration dependence of ε1εW-1 is perfectly described with m ∼ 130 irrespective of the addition of acetic acid, as shown in Figure 5. DR mode j ) 2 was assigned to an exchange process of hydrated water molecules for bulk free water molecules, since the normalized relaxation strength (ε2(cm)-1 ∼ 1.4 M-1) is j WεW ) 1.3 M-1. Further, slightly greater than the value of 10-3V τ2 is approximately 3 times as long as τ1 ()τw), which is typically observed in aqueous systems including the exchange process of hydrated water molecules.9,15 Consequently, PPG5 behaves as a fully dissociated flexible zwitterionic polymer chain in pure water, and a portion of the C-termini are protonated by the addition of acetic acid. The first and third normal modes in the chain conformational fluctuation are detectable as distinct DR modes. The hydration number per PPG5 molecule in aqueous media was determined to be 130 and was independent of the addition of acetic acid. Highly purified (monodisperse) PPG5 was purchased from Peptide Institute Inc. (Osaka) and used without further purification. Highly deionized water was obtained by an Elix-UV3 system (Millipore-Japan, Tokyo) with a specific residence higher than 15 MΩcm and was used as a solvent. The concentration of PPG5 in aqueous solutions and 30 mM acetic acid ranged from 7.78 to 23.0 mM (1.0 to 3.0% in weight). DR measurements were conducted over ω ranges from 6.28 × 106 to 1.26 × 1011 s-1 (1 MHz to 20 GHz) using two systems at 25 °C. The low ω range up to 1.88 × 1010 s-1 was covered by an RF LCR meter (Agilent Technologies, 4287A) equipped with a homemade electrode cell and a vacant capacitance of C0 ) 0.23 pF. In this system, ε′ and ε′′ were evaluated by the formulas ε′ ) CC0-1 and ε′′ ) (G - Gdc)C0-1ω-1, where C, G, and Gdc are the capacitance of the electrode cell filled with samples, the conductivity of the samples, and the direct current conductivity due to ionic components, respectively. A dielectric material probe system consisting of a network analyzer (HewlettPackard, 8720ES) was used in the ω range from 3.14 × 108 to 1.26 × 1011 s-1. In this system, ε′ and ε′′ were calculated by internal software. The temperatures of sample solutions were controlled by circulating thermostatted water. Details of the measurement procedures are described elsewhere.9,15 The value j p for PPG5 in both aqueous and acetic acid solutions at T of V ) 25 °C was determined to be 903 cm3 mol-1 by density measurements of the solutions using a DMA5000 densitometer (Anton Paar, Graz, Austria). Acknowledgment. This work was supported by KAKENHI (Grant-in-Aid for Scientific Research on Priority Area “Soft
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Matter Physics”) from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and also another KAKENHI (Grant-in-Aid for Scientific Research (B) 21350064) from Japan Society for the Promotion of Science. References and Notes (1) Privalov, P. L. AdV. Protein Chem. 1982, 35, 1–104. (2) Gustavson, K. H. The Chemistry and ReactiVity of Collagen; Academic Press: New York, 1956. (3) Ramachandran, G. N.; Ramakrishnan, C. In Biochemistry of Collagen; Ranmchandran, G. N., Reddi, A. H., Eds.; Plenum: New York, 1976; pp 45-84. (4) Kobayashi, Y.; Sakai, R.; Kakiuchi, K.; Isemura, T. Biopolymers 1970, 9, 415–425. (5) Okuyama, K.; Tanaka, N.; Ashida, T.; Kakudo, M.; Sakakibara, S. J. Mol. Biol. 1972, 72, 571–576.
Letters (6) Okuyama, K.; Okuyama, K.; Arnot, S.; Takayanagi, M.; Kakudo, M. J. Mol. Biol. 1981, 152, 427–443. (7) Okuyama, K. Connect. Tissue Res. 2008, 49, 299–310. (8) Berg, R. A.; Olsen, B. R.; Prockop, D. J. J. Biol. Chem. 1970, 21, 5759–5763. (9) Ono, Y.; Shikata, T. J. Am. Chem. Soc. 2006, 128, 10030–10031. (10) Daniel, V. V. Dielectric Relaxation; Academic Press: New York, 1967; pp 72-73. (11) (a) Stockmayer, W. H.; Baur, M. E. J. Am. Chem. Soc. 1964, 86, 3485–3489. (b) Stockmayer, W. H. Pure Appl. Chem. 1967, 15, 539–554. (12) Watanabe, H. Prog. Polym. Sci. 1999, 24, 1253–1403. (13) Debye, P. Polar Molecules; Dover: New York, 1945; pp 77-89. (14) Terao, K.; Mizuno, K.; Murashima, M.; Kita, Y.; Hongo, C.; Okuyana, K.; Norisuye, T.; Ba¨chinger, H. P. Macromolecules 2008, 41, 7203–7210. (15) Ono, Y.; Shikata, T. J. Phys. Chem. B 2006, 110, 9426–9433. (16) Oncley, J. L. Chem. ReV. 1942, 30, 433–450.
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