Structure, Dynamics, and Hydration of a Collagen Model Polypeptide

Sep 17, 2009 - Ken Terao , Kazunori Mizuno , and Hans Peter Bächinger. The Journal of ... Toshiyuki Shikata , Nao Yoshida and Kenji Okuyama. The Jour...
0 downloads 0 Views 1023KB Size
Download PDF
14504

J. Phys. Chem. B 2009, 113, 14504–14512

Structure, Dynamics, and Hydration of a Collagen Model Polypeptide, (L-Prolyl-L-ProlylGlycyl)10, in Aqueous Media: a Chemical Equilibrium Analysis of Triple Helix-to-Single Coil Transition Toshiyuki Shikata,* Ayako Minakawa, and Kenji Okuyama Department of Macromolecular Science, Osaka UniVersity, Toyonaka, Osaka 560-0043, Japan ReceiVed: July 16, 2009; ReVised Manuscript ReceiVed: August 26, 2009

The structure, dynamics, and hydration behavior of a collagen model polypeptide, (L-prolyl-L-prolylglycyl)10 (PPG10), were investigated in pure water and dilute acetic acid over a wide temperature range using broadband dielectric relaxation (DR) techniques that spanned frequencies from 1 kHz to 20 GHz. All samples showed pronounced dielectric dispersion with two major relaxation processes around 3 MHz and 20 GHz. Because DR measurements sensitively probe dipoles and their dynamics, the structures and ionization states of the carboxy and amino termini of aqueous PPG10 were precisely determined from the relaxation times and strengths in the 3 MHz frequency range. In solution, PPG10 formed mixtures of monodisperse rods as triple helices with lengths and diameters of 8.6 and 1.5 nm, respectively, and monomeric random coils with radii of ∼1.4 nm. Ionization of the C-terminus was suppressed by the addition of acetic acid in both states. The fraction of random coils (fcoil) was found to be a function of temperature (T) and the concentration of PPG10 (c). At low temperatures, small fcoil values were found, which increased with temperature to reach fcoil ) 1 at ∼60 °C, irrespective of c. This phenomenon, well-known as a triple helix-to-single coil transition, is discussed on the basis of the chemical reaction, (PPG10)3 a 3PPG10, with an equilibrium constant of K ) 3(c/55.6)2fcoil3(1 - fcoil)-1. The standard enthalpy change evaluated from Arrhenius plots (ln K versus T-1) was found to change dramatically at the same transition temperature that was previously determined by using optical rotation experiments. The other major DR process, observed at ∼20 GHz, was assigned to free and hydrated water molecules and used to determine the average hydration number (m) per PPG10. The m values for the triple helix and random coil state at 25 °C were evaluated to be mth ) 60-70 and mcoil ) 250-270. The mth value was in reasonable agreement with the number of hydrated water molecules in crystals of (PPG10)3 residing in the first and second hydration shells around the amino acid residues. This agreement suggests that the structure of the triple helix in crystals is very similar to that in aqueous solution, including the location of hydrated water molecules. Introduction Type I collagen is the most abundant structural protein in multicellular organisms. It has a repeating Gly-X-Y (Gly: glycine and X/Y denote any amino acids) sequence that forms triple helices in many types of tissue. Collagen has characteristic thermal properties, depending on the organism and tissue.1-3 At the denaturation temperature of collagen, which is strongly correlated with the body temperature of the species, the triple helices dissociate into flexible coils of individual polypeptide chains. This triple helix-to-single coil transition is considerably affected by the amino acid sequence of the collagen. However, quantitative studies of the triple helix-to-single coil transitions of native collagens have not been practical due to their unusual amino acid sequences and incomplete renaturation in vitro. A few decades ago, optical rotation experiments revealed that synthetic collagen model peptides (Pro-Pro-Gly)n (n ) 10 and 20; Pro: L-proline; hereafter PPGn) undergo reversible conformational changes between triple-helix and single-coil states in a fashion similar to that of native collagens.4-6 X-ray diffraction experiments on single crystals of PPGn (n g 9) revealed a 7/2helical symmetry with three polypeptide chains.6-8 Many collagen model polypeptides were reported to have average helical pitches resembling that of the 7/2-helical model for * Corresponding author. E-mail: [email protected].

collagen. Furthermore, X-ray diffraction profiles of native collagens were also well-explained by the 7/2-helical symmetry.8 These results strongly suggested that native collagens and collagen model polypeptides adopt nearly identical triple-helical structures.8 Consequently, collagen model polypeptides, such as PPG10, have been used as effective model substances to investigate other basic properties of collagen, such as its hydration behavior in moisture and aqueous solution.9-12 In our previous study,13 we investigated the dielectric relaxation (DR) behavior of the aqueous model collagen peptide PPG5, which does not form triple helices,14 to determine the dynamics and hydration number of the single random coils. Because DR techniques are quite sensitive to the presence and dynamics of dipoles, the zwitterionic coils of PPG5 were accurately characterized. The first and third normal modes of chain conformational fluctuations of PPG5 were clearly detected as distinct dielectric relaxation modes.13 Addition of 30 mM acetic acid to an aqueous solution of PPG5 suppressed the overall relaxation strength by protonating the carboxy terminus. Furthermore, the hydration number was determined to be ∼130 per PPG5 molecule, since water molecules are also dipolar and their dynamics are precisely detectable.13-16 In this study, the DR behavior of an aqueous collagen model polypeptide, PPG10, was investigated in detail. PPG10 is long enough to form triple helices and was found to undergo a triple

10.1021/jp906719f CCC: $40.75  2009 American Chemical Society Published on Web 09/17/2009

PPG10 in Aqueous Media

J. Phys. Chem. B, Vol. 113, No. 43, 2009 14505

helix-to-single coil transition at ca. 30 °C.17 The DR data quantified the temperature-dependent populations to reveal the coexistence of both the single coils and triple helices from 10 to 60 °C and the associated equilibrium constant. The transition was interpreted on the basis of a cooperative change in the equilibrium constant at the transition temperature. Thermodynamic parameters such as the standard enthalpy and entropy changes were determined and compared with values reported in the literature determined by using a calorimetric method.19-22 A triggering event for the triple helix-to-single coil transition of aqueous PPG10 is also discussed. Experimental Section Materials. Highly purified, monodisperse PPG10 was purchased from Peptide Institute Inc. (Osaka) as a dry powder and used without any further purification. Highly pure acetic acid (>99.9%) was purchased from Wako Pure Chemicals Inc. Ltd. (Osaka). Deionized water with a specific resistance higher than 15 MΩ cm was obtained by using an Elix-UV3 system (Millipore-Japan, Tokyo) and used as a solvent for PPG10 at concentrations (c) lower than 1.2 mM (0.3% in weight). Because PPG10 was not soluble in pure water at c > 3.0 mM and room temperature, 20 mM of aqueous acetic acid was used as the solvent for PPG10 at concentrations of 3.9, 7.6, and 11 mM (0.98, 1.9, and 2.75% in weight, respectively). Methods. DR measurements were conducted at angular frequencies (ω) ranging from 6.28 × 103 to 1.26 × 1011 s-1 (1.0 kHz to 20 GHz) using three types of systems in the temperature range from 10 to 60 °C. Data in the lowest ω range, from 6.28 × 103 to 6.28 × 106 s-1, were acquired with a Precision LCR meter (Hewlett-Packard, 4282A) that was equipped with a homemade electrode cell with a vacant capacitance (C0) of ∼0.195 pF. For the middle ω range from 6.28 × 106 to 1.88 × 1010 s-1, an RF LCR meter (Agilent Technologies, 4287A) equipped with another homemade electrode cell with C0 ) 0.23 pF was used. For these systems, the real and imaginary parts of the complex permittivity (ε′ and ε′′) were evaluated using the conventional formulas of 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 impurities, respectively. A dielectric material probe system (Hewlett-Packard, 85070C) consisting of a network analyzer (Hewlett-Packard, 8720ES) was used in the ω range of 3.14 × 108 to 1.26 × 1011 s-1. In this case, ε′ and ε′′ were calculated from the reflection coefficient data using included software. The sample temperatures were controlled by circulating thermostatted water. Details of the measurement procedures are described elsewhere.14-16 We employed a nonlinear least-mean-square curve-fitting procedure using commercially available software, KaleidaGraph 3.5J (Synergy Software, Reading), and obtained fit curves (ε′fit and ε′′fit) for ε′ and ε′′ data. Assuming 4 Debype-type relaxation modes (j ) 1-4) as described later, the decomposition of ε′ and ε′′ data was performed at high-resolution as well as 1% of the magnitude of the largest relaxation strength in the examined spectra that quantitatively showed the presence of minor relaxation modes j ) 2 and 3. The squared residual values of ε′ and ε′′ data, (ε′ - ε′fit)2 and (ε′′ - ε′′fit)2, for all the determined fit curves were less than 10-3 over the entire ω range examined. j P) of PPG10 in 20 To determine the partial molar volumes (V mM aqueous acetic acid, the solution densities were measured at 25.0 °C using an Anton Paar DMA5000 digital density meter (Graz, Austria).

Figure 1. Frequency, ω, dependencies of the real and imaginary parts, ε′ and ε′′, of the electric permittivity for aqueous PPG10 solutions at c ) 3.9 mM in 11 mM acetic acid, plotted together with εW′ and εW′′ (black chains) for pure water at 25 °C. The constituent relaxation modes j ) 1-4 (dotted lines) and the total fit curves (ε′fit and ε′′fit, solid orange lines) for ε′ and ε′′ are also shown.

Results Overview of Dielectric Spectra at 25 °C. Figure 1 shows typical dielectric relaxation spectra, ε′ and ε′′ versus ω, for a PPG10 solution in 20 mM acetic acid at c ) 3.9 mM and 25 °C. Dielectric relaxation spectra for pure water are also plotted for comparison. The PPG10 solution had a remarkable DR process for an ω range 1010 s-1. The fast relaxation process is assigned to free water molecules similar to bulk water on the basis of similarities to εW′ and εW′′ for pure water in the same ω range. These two major DR processes observed in distinct frequency ranges are essential characteristics for aqueous PPG10 solutions in 20 mM acetic acid and pure water. The relaxation process found in the low ω region corresponds to the dynamics and dissociation state of PPG10 triple helices and is discussed later in detail. According to the linear response theory,23 the DR spectra can be decomposed into constituent Debye-type relaxation modes described by

′ ) εfit

ε

∑ 1 + ωj 2τ 2 + ε∞ j)1

j

and

″ εfit )

ε ωτ

∑ 1 +j ω2jτ 2 j)1

j

(1) where τj and εj are the mean relaxation time and strength for a mode j (where j ) 1-4), and ε∞ is an ω-independent electric permittivity. Figure 1 shows the ω dependence of the individual relaxation modes, and consequent fits for ε′ and ε′′. Each constituent relaxation mode will be attributed to a distinct dynamic mode via qualitative or quantitative arguments. Relaxation Processes in Low and Middle Frequency Ranges. The DR difference spectra in the low to middle ω range at T ) 25 °C are shown in Figure 2 for PPG10 in 20 mM acetic acid at several concentrations ranging from 0.40 to 11 mM. The spectra show only the contribution of the slow modes, which were obtained by subtraction of the two fast relaxation modes, j ) 1 and 2, and ε∞ from the ε′ and ε′′ data. The PPG10 solutions always showed a pronounced DR relaxation mode at ω ∼ 1.7 × 107 s-1 with a relaxation time of τ4 ∼ 60 ns, irrespective of c. The relaxation strength of this mode, ε4, increased with increasing c; however, the form of proportionality was not identified, as seen in Figure 3. The DR spectra plotted in Figure 2 also possessed another small relaxation mode, j ) 3, at ω ∼

14506

J. Phys. Chem. B, Vol. 113, No. 43, 2009

Shikata et al. According to the hydrodynamic theory, τrod is given by

τrod )

Figure 2. Frequency, ω, dependencies of the differential DR spectra, ∆εS′ and ∆εS′′, in the low to middle ω range for PPG10 solutions in 20 mM acetic acid at c ) 0.4, 1.2, and 11 mM and 25 °C.

Figure 3. Concentration, c, dependence of the concentration reduced dielectric strength for the slow relaxation modes, ε3c-1 and ε4c-1, and a ratio of their strengths, ε3ε4-1, for PPG10 solutions in 20 mM acetic acid at 25 °C.

1.4 × 108 s-1 with a relaxation time of τ3 ∼ 7 ns, irrespective of c. Although there was no clear functional form for the relationship, ε3 and c, the ratio ε3ε4-1 was found to decrease with increasing c, as seen in Figure 3. These observations reveal that the populations corresponding to the dynamic processes in modes j ) 3 and 4 depend on c, and the two modes result from different dynamic origins. It is well-known that PPG10 forms triple helices in aqueous acetic acid at moderate concentrations, such as the 20 mM used in this study,4-6 and that some of the carboxy and amino termini may ionize to provide a large dipole along the long axis of the helix. Therefore, evaluating a characteristic DR time (τrod) for a rod bearing an electric dipole moment and with dimensions comparable to the triple helix formed by PPG10 may provide an interesting comparison to τ4. The length and diameter of the triple helix, determined from X-ray diffraction data of single crystals of PPG10, are L ) 8.6 and d ) 1.5 nm,6-8 which should be taken as a first approximation. Furthermore, the X-ray analysis6-8 has revealed that the three PPG10 molecules comprising the helix wind parallel in the right-hand direction, with NH · · · OdC hydrogen bonds remaining nearly perpendicular to the long axes of the helix, as schematically depicted in Figure 4.6-8 Because the sum of the carbonyl group dipoles sums to zero for long triple helices, the origin of the dipole moments for triple helices of PPG10 is undoubtedly attributed to ionized C- and N-termini.

πηL3 L 6kBT ln 2d

( )

(2)

where η and kBT indicate the viscosity of the suspending medium and the product of Boltzmann’s constant and the absolute temperature.24 When a rod with L ) 8.6 and d ) 1.5 nm is dispersed in aqueous media of viscosity, η ) 0.89 mPas at 25 °C, τrod is calculated to be ∼68 ns. Because of the reasonable agreement between τ4 and τrod, one can assign the slowest relaxation mode, j ) 4, to the rotational mode of the triple helix, (PPG10)3. The calculated L values for triple helices via eq 2 at 25 °C assuming d ) 1.5 nm are tabulated in Table 1. If the triple helix has additional dielectric relaxation modes, such as bending or flexural motions that generate fluctuations in the ionized C- and N-termini, the strength of these modes should be proportional to the concentration of the triple helices, similar to the relaxation mode j ) 4. Thus, the mode j ) 3 should be attributed to dynamics that do not belong to the triple helix. If the flexural motions of the triple helix are essential to the mode j ) 3, the characteristic times of the flexural motions correspond to τ3. However, the estimated fundamental flexural time is much shorter than the τ3 and on the order of 10-11 s, assuming the persistence length of the triple helix to be 170 nm as a usual value of triple helices of collagen.25 Here, we estimate a characteristic DR time (τcoil) for an isolated single coil of PPG10. According to previous studies on the solution properties of collagen model peptides, the radius of rotation (〈>S2〉1/2) for a single-coil polypeptide with 10 repeating units, such as PPG10, has been determined to be ∼1.4 nm.18 According to the Stokes-Einstein-Debye theory,26 the average radius, 〈S2〉1/2, gives τcoil as

τcoil )

4πη〈S2〉3/2 kBT

(3)

This equation provides a value of τcoil ∼ 9 ns for the single coil in aqueous media at 25 °C. The fair agreement between τcoil and τ3 strongly suggests the presence of a small amount of single coils with ionized C- and N-termini at 25 °C. As discussed in detail later, single coils of PPG10 in aqueous media are well approximated by the bead-spring model.27,28 The relaxation time given by eq 3 corresponds to the first normal mode of conformation fluctuations of PPG10 in the bead-spring model

Figure 4. Schematic depiction of the crystalline structure for a triple helix, (PPG10)3. Blue, green, and red molecular species represent parts of individual PPG10 molecules, and light-blue dotted lines mean hydrogen bonds between two amide groups.

PPG10 in Aqueous Media

J. Phys. Chem. B, Vol. 113, No. 43, 2009 14507

TABLE 1: Calculated Length of a Triple Helix, L; Mean Square Values of Dipole Moments of a Triple Helix, 〈µth2〉; and Single Coil, 〈µcoil2〉, of PPG10 and Degrees of Charge Dissociation of the C-Termini of PPG10 in the Triple Helix State, DDth; Single Coil State, DDcoil; and Average Evaluated from pH Values, DDpH, in Solutions of Pure Water and 20 mM Acetic Acid c/mM 0.4 1.2 0.4 1.2 3.9 7.6 11 a

solvent pure water pure water acetic acidc acetic acidc acetic acidc acetic acidc acetic acidc

L/nma 8.2 8.0 8.7 8.6 8.0 8.6 9.1

〈µth2〉/C2cm2

〈µcoil2〉/C2cm2

DDth

DDcoil

pH

DDpHb

-49

-51

0.95 0.78 0.87 0.62 0.51 0.50 0.48

0.92 0.83 0.82 0.62 0.42 0.42 0.39

∼6 ∼6 3.2 3.3 3.7 3.9 4.0

0.99 0.99 0.61 0.67 0.84 0.89 0.91

1.44 × 10 1.05 × 10-49 1.29 × 10-49 6.60 × 10-50 4.35 × 10-50 4.29 × 10-50 3.96 × 10-50

2.33 × 10 2.17 × 10-51 2.36 × 10-51 1.77 × 10-51 1.40 × 10-51 1.40 × 10-51 1.33 × 10-51

Calculated via eq 2 at 25 °C assuming d ) 1.5 nm. b Calculated assuming pKa ) 3 for C-termini. c 20 mM acetic acid.

Figure 5. Temperature, T, dependence of the differential DR spectra, ∆εS′ and ∆εS′′ vs ω, in the slow mode for PPG10 solutions in 20 mM acetic acid at c ) 7.6 mM.

Figure 6. Temperature, T, dependence of relaxation times for the modes j ) 3 and 4, plotted on a semilogarithmic scale, τ4 and τ3 vs T-1, for PPG10 solutions in 20 mM acetic acid at c ) 7.6 mM, obtained from the spectra in Figure 5.

expression. The normal modes with odd mode numbers (p ) 1, 3, 5, ...) show a steep decrease in relaxation strengths and times with increasing mode number, p, and are detectable by DR techniques. A careful examination of the differential DR spectra in Figure 2 reveals the minor contribution of relaxation modes faster than τcoil (p ) 1) in the frequency range of ω ) 109 ∼ 1010 s-1. Temperature Dependence of Relaxation Processes in Low and Middle Frequency Ranges. DR spectra for PPG10 solutions in pure water and 20 mM acetic acid were highly temperature-dependent. Figure 5 shows typical temperaturedependent, differential DR spectra for the PPG10 in 20 mM acetic acid at c ) 7.6 mM over a temperature range from 10 to 60 °C. DR spectra observed for T e 25 °C exhibited the distinctive dielectric relaxation mode corresponding to the rotational relaxation mode of (PPG10)3 triple helices (j ) 4). This mode decreased in magnitude with increasing temperature, T > 40 °C. With a decrease in the strength of the mode j ) 4, the mode j ) 3, possibly corresponding to the rotational relaxation of single coils of PPG10, is markedly intense by T ) 60 °C. Essentially the same temperature-dependent DR spectra plotted in Figure 5 were observed for all PPG10 solutions, irrespective of the concentration and presence of acetic acid. The temperature dependencies of τ3 and τ4 for the PPG10 solution in 20 mM acetic acid are shown in Figure 6 as typical examples. The slopes of the τ3 and τ4 lines vs T-1on a semilogarithmic scale yield values for activation energies (E*3 and E*4 ) for these processes. The activation energies were almost identical each other, and also the same as those for the viscosity and τW of pure water: E*W ) 19 kJ mol-1. This agreement between E*W and E*3 , and E*4 was always in all of the PPG10 solutions examined. This observation implies that rotational

relaxation modes for both the triple helices and single coils are governed simply by the temperature dependence of the viscosity of water. It has been well-known that a DR process due to the presence of solute molecules (εsm) observed in solutions is proportional to the product of the concentration, c, and the mean square of their dipole moments (〈µsm2〉); however, the proportionality constant depends on the local electric fields in the solution. For most nonpolar solutions, the expression for the local electric field proposed by Lorentz holds approximately.23 On the other hand, for solutions in highly polar solvents, the local electric field is well described by Onsager’s expression (OE), and the relationship proposed by Oncley29 (eq 4) based on OE is one of the most reliable formulas,13-16

εsm )

2 cNA〈µsm 〉 2εvkBT

(4)

where NA and εv indicate Avogadro’s number and the electric permittivity of a vacuum. Applying this equation, one can evaluate the product of the concentrations and mean square dipole moments for DR modes of ε4 and ε3, assuming that these correspond to the relaxation modes of triple helices (cth〈µth2〉) and single coils (ccoil〈µcoil2〉), respectively. Figure 7a shows the temperature dependence of ε4 and ε3 for the PPG10 solution in 20 mM acetic acid at c ) 7.6 mM. Figure 7b also shows the relationship between 〈µth2〉cthc-1 and 〈µcoil2〉ccoilc-1, and T, converted from the ε4 and ε3 data of Figure 7a using eq 4. Because it is assumed that 〈µth2〉 and 〈µcoil2〉 are negligibly dependent on T, cth was found to decrease with increasing T, whereas ccoil increased to approach an asymptotic value. If one assumes that PPG10 molecules exist in only two

14508

J. Phys. Chem. B, Vol. 113, No. 43, 2009

Shikata et al.

Figure 7. (a) Temperature, T, dependence of relaxation strength, ε4 and ε3, for PPG10 solutions in 20 mM acetic acid at c ) 7.6 mM, obtained from spectra in Figure 5. (b) Temperature, T, dependence of concentration-reduced relaxation strength for the triple helix, 〈µth2〉cthc-1; the single coil, 3〈µcoil2〉ccoilc-1; and molar faction of single coil, fcoil, determined from both modes j ) 3 and 4 for PPG10 solutions in 20 mM acetic acid at c ) 7.6 mM, evaluated from data in Figure 7a.

Figure 8. (a) Temperature, T, dependence of equilibrium constant, K, for PPG10 solutions in pure water and (b) that for PPG10 solutions in 20 mM acetic acid plotted on a semilogarithmic scale, ln K vs T-1.

states, namely, the single coil and triple helix, the fraction or population of the coil state (fcoil) is provided by the relationships ccoil ) cfcoil and cth ) c(1- fcoil)/3. Moreover, if one knows the value of 〈µcoil2〉, the population can be evaluated. The fact that 〈µcoil2〉ccoilc-1 () 〈µcoil2〉fcoil) approached an asymptotic value and 〈µth2〉cthc-1 diminished to a negligible level in the high temperature limit (T g 50 °C) reveals that fcoil approaches unity at high T. Then, the value of 〈µcoil2〉ccoilc-1 at T ∼ 60 °C, ∼1.40 × 10-51 C2 cm2, provides 〈µcoil2〉. Consequently, the temperature dependence of fcoil is determined from the ε3 data for the single coil state, as seen in Figure 7b. A similar argument for the determination of fcoil is possible in the triple helix state. The value of 〈µth2〉 allows one to determine fcoil from the ε4 data for the triple helix via the relationship fcoil ) 1 - 3cthc-1. From these relationships, the value of 〈µth2〉 can be determined by choosing a value that allows the T dependence of fcoil to match that obtained above from the ε3 data. This was accomplished with 〈µth2〉 ) 4.29 × 10-50 C2 cm2, as seen in Figure 7b. The same procedure allowed 〈µcoil2〉, 〈µth2〉, and the T dependence of fcoil to be determined for all of the PPG10 solutions examined. When eq 4 is not valid for PPG10 solutions in pure water and 20 mM acetic acid, the values for 〈µcoil2〉 and 〈µth2〉 tabulated in Table 1 are not correct. However, the dependence of fcoil on T for the solutions (cf. Figure 7b) is correct irrespective of the validity of eq 4. Consequently, one might conclude that fcoil is not zero, but has a finite value that increases with decreasing

concentration, c, even in the low temperature range around T ∼ 10 °C, and approaches unity above T g 50 °C. It must be noted that a time scale for the equilibration of the TH-SC transition is on the order of 103 s 21 and much longer than that for relaxation modes j ) 3 and 4. This distinctive difference in the time scales between molecular events of PPG10 allows us the consideration above. Chemical Reaction between Triple Helix and Single Coil. If it is assumed that PPG10 molecules exist only in triple helix and single coil states (a two-state model), the equilibrium constant for the reaction (PPG10)3 a 3PPG10 is given in terms of the molar fraction of PPG10 (xc ) c/55.6),30

K)

3xc2fcoil3 1 - fcoil

(5)

Arrhenius type plots of the relationship between ln K and T-1 are shown in Figure 8a and b for all the PPG10 solutions examined. Distinctive changes in slopes were always found around T ∼ 30 °C (T-1 ∼ 3.3 × 10-3 K-1), which is close to the temperature for the triple helix-to-single coil transition previously reported using optical rotational and circular dichroism experiments.4,5,19-22 It is concluded that the triple helix-tosingle coil transition is relevant to the dramatic change in the slope of ln K on T-1. As discussed in detail later, K is related

PPG10 in Aqueous Media

J. Phys. Chem. B, Vol. 113, No. 43, 2009 14509

to the standard Gibbs energy change (∆G+) between the triplehelix and single-coil states in the relationship K ) exp{-∆G+(RT)-1}, where R ) NAkB. When the physicochemical features of both the single coil and triple helix, such as ionization of the C- and N-termini, are unaffected by the presence and concentration of acetic acid, K should only be a function of temperature. This was observed for the PPG10 solutions in 20 mM acetic acid at c > 4.0 mM, indicating that ionization of the termini does not significantly vary in the solutions at c > 4.0 mM. Because the pH values of the solutions were lower than 7, it can be well-approximated that the N-termini were always protonated to be positively ionized. Ionization of the C-termini would then depend on the concentration, c, and the addition of acetic acid. Dissociation of C-Termini of PPG10. In the case of dipolar rods bearing opposite electric charges of eq+ and -eq-, where e, q+, and q-indicate the elementary electric charge, the number of positive charges at the N-terminus, and the number of negative charges at the C-terminus (eq+ ) 3), the dipole moment is given by 〈µrod2〉1/2 ) Leq-. The simplest case for triple helices is to assume full ionization of the C-terminus (q) q+ ) 3) to yield 〈µrod-f2〉1/2 ) 3Le. From these arguments, the degree of charge dissociation of the C-terminus in triple helices (DDth) is given by DDth ) q-/3 ) 〈µth2〉1/2(3Le)-1. The DDth values for all solutions are summarized in Table 1. In dilute aqueous solutions (c < 1.2 mM), the highest DDth value was close to unity, corresponding to full dissociation, and was expected on the basis of the pH. This observation strongly supports the validity of eq 4. The DDth decreased and approached an asymptotic value of 0.5 with increasing c, even in the same 20 mM acetic acid solvent. The average degrees of charge dissociation at the C-termini, calculated from pH values for each PPG10 solution (DDpH) assuming pKa ) 3, are also summarized in Table 1. The degree of charge dissociation at the C-termini of single coils (DDcoil) is also obtainable. In the case of a dipolar, zwitterionic coil bearing opposite electric charges, eq+ and -eqat its two termini, its molecular motion or dynamics is well approximated by that of a sequential chain of N beads, with a friction coefficient (ζ), connected by N - 1 springs (namely, segments or subchains) with a mean square extension of b2 and a spring constant of κ ) 3kBTb-2.27,28 According to our previous study on PPG5 in aqueous media, PPG10 is long enough for the bead-spring model approximation to predict Gaussian statistics.13,18 The time-dependent conformational fluctuations of this model chain are described by a superposition of fundamental normal modes, p. The relaxation time of the bead-spring model chain for a mode, p, is given by

τbs p )

ζp kp

and

kp )

24kBTN 2

b

πp ( 2N )

sin2

(6)

where ζp means a p-dependent function that is influenced by the presence of hydrodynamic interaction between beads via the medium liquid.27,28,31 When the hydrodynamic interaction is not taken in account, a free-draining condition, the relationship ζp ) 2Nζ provides the relaxation time, τpbs-fd, as31

τbs-fd ) p

b2ζ πp 2N

( )

12kBT sin2

(7)

On the other hand, when the hydrodynamic interaction is fully considered, a nondraining condition, the relationship ζp ) (12π3b2Np)1/2η gives the other relaxation time, τpbs-nd, as31

τbs-nd ) p

b2η√π3p 4kBT√3N sin2

πp 2N

( )

(7a)

According to our previous study on aqueous PPG5 with 15 amino acid residues,13 τcoil ∼ 4 ns was determined, and N was evaluated to be 4. Thus, N is estimated to be ∼7 for PPG10. Consequently, the odd normal modes p ) 1, 3, and 5 should be detected at relaxation times of ∼9 () τcoil), ∼ 1, and ∼ 0.5 ns at 25 °C (cf. Figure 2). In the case of dilute polymer solutions, the hydrodynamic interaction is essential to the estimation of relaxation times in general. When the obtained relation times, τcoil, were compared each other on the basis of the formula, taking account of the nondraining condition, the ratio τcoil(PPG10; N ) 7)/τcoil(PPG5; N ) 4) ∼ 2.2 perfectly agreed with the relationship τ1bs-nd(N ) 7)/τ1bs-nd(N ) 4) ∼ 2.2 for the nondraining condition. However, the other relationship τ1bs-fd(N ) 7)/τ1bs-fd(N ) 4) ∼ 3.0 for the free-draining condition clearly deviated from the ratio of 2.2. These findings strongly sustain that the dynamics of PPG10 in aqueous media in the single coil state observed as the relaxation mode j ) 3 are welldescribed with the bead-spring model chain taking account of the nondraining condition. In the case of zwitterionic coils bearing electric charges of q+ ) q- ) 1, the dielectrically detectable normal modes are the odd number modes in which the terminal beads move in opposite directions. The first normal mode, p ) 1, possesses the largest mean square dipole moment, as given by the following eq 8, and is nine times as large as that of the next detectable, third normal mode p ) 3,

2 〈(µbs p) 〉

)

2(N - 1)b2e2(q+ ( q-)2 π2p2

(+, odd p; - , even p) (8)

Other, higher odd-numbered modes have a much smaller contribution than that of the mode p ) 3. Thus, only the first normal mode, 〈(µ1bs)2〉1/2, was used to evaluate DDcoil. Since the bead-and-spring model satisfies Gaussian statistics, the meansquared end-to-end distance of the chain is given by R2 ) (N - 1)b2 ) 6S2. Consequently, the relationship 〈(µ1bs)2〉 ) 4.9e2〈S2〉 is obtained. According to the bead-and-spring model (eq 8), a monopolar single coil bearing an electric charge at only one terminus, for example, q+ ) 1 and q- ) 0, will also show dielectric relaxation at the relaxation time of the first normal mode, but with a meansquared dipole moment only 1/4 that of a dipolar coil with the same N and b. Then the relationship 〈µcoil2〉 ) 4.9e2〈S2〉{DDcoil + (1 - DDcoil)/4} yields DDcoil ) 0.27〈µcoil2〉(e2〈S2〉)-1 - 0.33, and it allows one to evaluate DDcoil from the ε3 value assuming 〈S2〉1/2 ) 1.4 nm. The DDcoil evaluated from the ε3 data from Table 1 agreed fairly well with the value of DDth and DDpH for dilute PPG10 solutions in pure water at c e 1.2 mM. On the other hand, in 20 mM acetic acid, the concentration dependence of DDth and DDcoil displayed an opposite trend from that of DDpH. Moreover, it was observed that DDth > DDcoil at c g 4.0 mM. It is likely that dissociation of the C-termini of PPG10 in aqueous media is more significantly governed by the concentra-

14510

J. Phys. Chem. B, Vol. 113, No. 43, 2009

Shikata et al.

Figure 9. Concentration, c, dependence of a ratio ε3ε4-1 for PPG10 solutions in 20 mM acetic acid at 25 °C.

tion of PPG10 than by pH. This indicates that the C-termini of PPG10 in both the triple helix and single coil states are highly protonated to reduce electric charges with increasing c. This protonation may be necessary for the solubility of PPG10. Hydration Number of Triple Helix. The large, fast relaxation mode j ) 1, observed at ω ∼ 1011 s-1, is assigned to free water molecules in bulk water, since the εW ′and εW′′ for pure water show a similar DR process in the same ω range, as seen in Figure 1. This major DR process includes the contribution of both free and hydrated water molecules to PPG10 in the single coil and triple helix states. The fastest relaxation mode found at τ1 ∼ 8.3 ps (25 °C) was assigned to the relaxation mode of free water molecules,32 as described above. It has been wellknown that the decrease in relaxation strength for the mode j ) 1, ε1, relative to that of pure water, εW, is described by the relationship

j smc ε1 1 - 10-3V j Wcm - 10-3V ) -3 j εW 1 + 10 Vsmc/2

(9)

j sm and V j W indicate the partial molar volume of the solute where V and water molecules, and m indicates the number of hydrated j sm value of water molecules per solute molecule.14-16 The V PPG10 was determined to be 1846 cm3 mol-1 at 25 °C from the density measurements of sample solutions. The c dependence of ε1εW-1 for PPG10 solutions in 20 mM acetic acid at T ) 25 °C is shown in Figure 9 along with lines predicted by m values ranging from 100 to 150. The ε1εW-1 data were not welldescribed by a single m value. Because PPG10 exists in a mixture of single coils and triple helices and the population of single coils, fcoil, depends on c even at one temperature, a single m value fails to explain the observations in Figure 9. In this case, the value of m should be the average value, m ) mcoilfcoil + mth(1 - fcoil), where mcoil and mth represent the hydration number per PPG10 in the single-coil and triple-helix states. Recently, for PPG5 in solutions of pure water and 30 mM acetic acid at 25 °C, we have determined mcoil to be 130 ( 5, irrespective of the addition of acetic acid.13 Because PPG5 does not form triple helices in aqueous solution at this temperature,17 it is an ideal polypeptide to investigate collagen in the single coil state. On the basis of this, the mcoil for PPG10 in the solutions of 20 mM acetic acid at 25 °C might be approximated by mcoil ) 260 ( 10. With this value, m is plotted as a function of fcoil in Figure 10, and the relationship mth ) 65 ( 5 is obtained via extrapolation of the line to fcoil ) 0. More experiments for the PPG10 solution at several temperatures are necessary to

Figure 10. Relationship between the average hydration number, m, per PPG10 molecule and molar fraction of single coil forming components, fcoil, for PPG10 solutions in 20 mM acetic acid at 25 °C. The hydration number for PPG10 in the triple helix state, mth, is evaluated from the intercept of the line at fcoil ) 0.

increase the accuracy of extrapolation for the determination of the mth value at fcoil ) 0. X-ray analysis of single crystals of the triple helices, (PPG10)3, revealed that the number of water molecules in the first hydration shell, ∼25, formed by water molecules directly hydrogen bound to amino acid residues of PPG10 and that of the second hydration shell, ∼32, due to water molecules hydrogen bonded to the first hydration shell together give 57.33 This value agrees fairly well with the mth value determined in this study using DR methods. This agreement strongly suggests that the structure of the triple helix in crystals corresponds well to that in aqueous solution, including the location of hydrated water molecules. The DR mode j ) 2 is assigned to an exchange of hydrated water molecules with bulk free ones, since the normalized relaxation strength, ε2(cm)-1 ∼ 1.4 M-1, is only slightly greater j WεW ) 1.3 M-1 and the τ2 is about three than the value of 10-3V times as long as the τ1 () τw) usually observed in aqueous systems, including exchange processes of hydrated water molecules.13-16 Discussion Standard Gibbs Energy Change between Triple Helix and Single Coil. For the reaction of single coils forming triple helices, the equilibrium constant, K, is related to the standard Gibbs energy change, ∆G+, via the fundamental relationships K ) exp(-∆G+/RT) and

ln K ) -

∆H+ ∆S+ + RT R

(10)

where ∆H+ and ∆S+ represent the standard enthalpy and entropy changes. The slopes and intercepts obtained from plots of ln K vs T-1, presented in Figure 8a and b provide ∆H+ and ∆S+ values for the chemical reaction between the triple helix and single coil states for each solution. Changes in the slope corresponding to the transition temperature of the triple helix-to-single coil, Tt, were recognized in the relationship between ln K and T-1, as seen in Figure 8a and b. The standard enthalpy and entropy changes were determined separately in the two temperature ranges below and above Tt: ∆H+L and ∆SL+, and ∆HH+ and ∆SH+, and are summarized in Table 2. The ∆HL+ and ∆SL+ values show a weak dependence on c

PPG10 in Aqueous Media

J. Phys. Chem. B, Vol. 113, No. 43, 2009 14511

TABLE 2: Triple Helix-to-Single Coil Transition Temperatures, Tt; Standard Enthalpy Changes, ∆H+; Standard Entropy Changes, ∆S+; and Differences between Standard Enthalpy Changes, ∆∆H+; above and below Tt in Solutions of Pure Water and 20 mM Acetic Acid c/mM

solvent

0.4 1.2 0.4 1.2 3.9 7.6 11

pure water pure water acetic acidb acetic acidb acetic acidb acetic acidb acetic acidb

a

∆HL+ a/ ∆SL+ a/ ∆HH+ a/ ∆SH+ a/ ∆∆H+ a/ Tt/°C kJmol-1 JK-1mol-1 kJmol-1 JK-1mol-1 kJmol-1 30 30 27 28 27 27 27

5.5 5.5 4.6 6.9 6.9 6.9 6.9

-42 -39 -48 -37 -35 -35 -33

39 37 49 49 66 69 69

71 67 98 100 161 194 194

34 32 44 42 59 62 62

per PPG10 molecule. b 20 mM acetic acid.

and the addition of acetic acid as summarized in Table 2. Moreover, ∆HL+ is close to 0 or slightly positive. These observations indicate that the reaction is driven by the value of ∆SL+, which is much smaller than ∆SH+. In contrast, at higher temperatures, both ∆HH+ and ∆SH+ depend on c and the addition of acetic acid. These parameters reached asymptotic values with increasing c and acetic acid. The determined asymptotic value of ∆HH+ was positive and greater than ∆HL+, whereas the asymptotic ∆SH+ value was positive and much greater than the ∆SL+ (cf. Figure 8a and b). The endothermic reaction is controlled by the positive ∆SH+ and also the ∆HH+ in the range of T > Tt. The behavior of ∆HH+ and ∆SH+ in the range of T > Tt is more comprehensive than that of ∆HL+ and ∆SL+ in the range of T < Tt. According to the chemical reaction formula (PPG10)3a 3PPG10, ∆SH+ should be positive, since the structure of (PPG10)3 is assuredly more compact than that of 3PPG10. Then the determined ∆H+ values were positive, as expected. However, there is no straightforward, simple explanation for the ∆SL+ values according to the above chemical reaction, which were lower than ∆SH+ and negative. We propose the following modified chemical reaction (eq 11), which includes a change in the number of water molecules hydrated to PPG10 to explain the entropy changes,

(ΡΡG10 · mthΗ2Ο)3 + 3(mcoil - mth)Η2Ο a 3(ΡΡG10 · mcoilΗ2Ο) (11) where the molar fraction of solvent water molecules (xW) appears in the equilibrium constant, Khw, as

Khw )

3xc2fcoil3 (1 - fcoil)xW3(mcoil-mth)

(12)

Because xW is well-approximated by unity in most dilute aqueous solutions, the relationship Khw ) K holds, and the quantitative discussion above on the basis of fcoil and K still holds using Khw, irrespective of the mcoil - mth values. When mcoil = mth, a low ∆S+ is not expected; however, mcoil > mth provides a small or negative value for ∆S+ due to fixing 3(mcoil - mth) water molecules to single coils. Mrevlishvili34 calorimetrically investigated the entropic cost of hydrated water molecules in some proteins, including collagen in the triple helix state and DNA, and concluded that the hydrated water molecule to collagen has entropy much lower than that of the bulk water molecule by ∼67 J mol-1 K-1. The hydrated water molecules to collagen in the triple helix state

are deprived of both translational and rotational degrees of freedom.34 Although the value of entropy of a hydrated water molecule to single coils is not so low as that of the water molecule hydrated to the triple helices, the value would not be higher than that of the bulk water molecule. From these considerations, in the T < Tt temperature region, a small or negative ∆SL+ is observed only when mcoil > mth. The experimental results at T ) 25 °C; mcoil ) 260 ( 10 > mth ) 65 ( 5 (Figure 10) are consistent with this prediction. On the other hand, in the higher temperature region of T > Tt, the approximate equality of mcoil and mth is enough to explain a value of ∆SH+ higher than ∆SL+. Because the triple helix (PPG10)3 possesses a much more ordered structure than the single coil, its mth would be less influenced by a temperature change. Therefore, it is likely that mcoil decreases with increasing temperature to a value close to mth in the vicinity of the transition temperature, Tt. ∆HH+ indicates the heat energy necessary for the system to dissociate (PPG10)3 into isolated PPG10 coils because the magnitude of dehydration, mcoil - mth, is small in the high temperature range. Nevertheless, ∆HL+ indicates the energy necessary to decompose (PPG10)3 and additionally hydrate PPG10 in the low temperature range. Consequently, the difference between the standard enthalpy changes (∆∆H+ ) ∆HH+ - ∆HL+) roughly represents the heat necessary for the dehydration of PPG10. The values of ∆∆H+ were evaluated to be ∆∆H+ = 32 and 62 kJ mol-1 for PPG10 solutions in pure water (c ) 0.4-1.2 mM) and 20 mM acetic acid (c ) 3.9 and 11 mM), respectively, as summarized in Table 2. These values satisfied the relationship ∆∆H+ ) Tt∆∆S+ and agreed fairly well with the calorimetrically determined values (∆∆Hcal): 29 kJ mol-1 in pure water (c ) 0.33 mM),20 75 kJ mol-1 in 20 mM acetic acid (c ) 2 mM),20 60 kJ mol-1 in 100 mM acetic acid (c ) 0.4 mM),21 and 68 kJ mol-1 in 1.6 M acetic acid (c ) 1.3 mM),19 reported as the endothermic transition enthalpy values of the triple helix-to-single coil transition for PPG10 solutions. Therefore, the calorimetrically determined endothermic heat values, ∆∆Hcal during the triple helix-to-single coil transition procedure should be identical to ∆∆H+. Persikov and Brodsky21 also discussed the triple helix-tosingle coil transition of PPG10, (L-prolyl-4(R)-hydroxyprolylglycine)10 (POG10), and other collagen model polypeptides in aqueous media on the basis of the idea of chemical equilibrium such as (PPG10)3 a 3PPG10. They found that the difference between the standard enthalpy change, ∆∆H+, for PPG10 was slightly greater than the ∆∆Hcal by a factor of ∼20%, but perfect agreement between ∆∆H+ and ∆∆Hcal was seen for POG10. They used temperature-dependent circular dichroism spectra to obtain the fcoil values, assuming fcoil ) 0 at 0 °C.21 Because this work found fcoil values higher than 0.1 for PPG10 in acetic acid, depending on c, even at 10 °C, the assumption was that fcoil ) 0 at low temperature explains the disagreement between ∆∆H+and ∆∆Hcal. Because the dehydration of single coil PPG10 at Tt with increasing temperature alters the values of ∆H+ and ∆S+, it is the essential trigger for the triple helix-to-single coil transition. The triple helix-to-single coil transition has been widely observed in aqueous solutions of other collagen model polypeptides.19-22 For example, aqueous POG10 shows the sharp triple helix-to-single coil transition at ca. 60 °C, which is much higher than the Tt of PPG10. In POG10, dehydration may begin at a temperature close (or equal) to its Tt, and the dehydration parameters of POG10, such as mcoil - mth, ∆∆H+, and ∆∆S+, govern the transition.

14512

J. Phys. Chem. B, Vol. 113, No. 43, 2009

Conclusions It is found that a collagen model polypeptide, (L-prolyl-Lprolylglycyl)10, dissolved in pure water and dilute acetic acid solution forms into a mixture of monodisperse triple helical rods, (PPG10)3, with a length and diameter of 8.6 and 1.5 nm, respectively, and random coils of isolated PPG10 with radii of ∼1.4 nm. The fraction of random coils (fcoil) was found to depend on temperature (T) and also the concentration of PPG10 (c). Although fcoil was small in the low-temperature range, it dramatically increased at the triple helix-to-single coil transition temperature (Tt) and reached full occupancy, fcoil ) 1, at temperatures higher than 50 °C, irrespective of c. This triple helix-to-single coil transition was discussed on the basis of the kinetics of the chemical reaction, (PPG10)3a 3PPG10, with an equilibrium constant given by K ) 3xc2fcoil3(1 - fcoil)-1, where xc is the molar fraction of PPG10 given by xc ) c/55.6. The Arrhenius plots of ln K vs T-1 showed dramatic changes in the slopes at Tt. This means that the slopes corresponding to the standard enthalpy change (∆H+) for the chemical reaction alters at Tt. Our analysis of the equilibrium and the calculated differences between the ∆H+ values above and below Tt (∆∆H+ ) ∆HH+ - ∆HL+) were validated by fairly consistent agreement with the transition enthalpies obtained separately by a calorimetric method. The average hydration numbers (m) per PPG10 for the triple helix and random coil state at 25 °C were evaluated to be mth ) 60-70 and mcoil ) 250-270, respectively. The mth value reasonably agrees with the number of hydrated water molecules in crystals of (PPG10)3, which has been evaluated to be the sum of the number of water molecules in the first and second hydration shells. The difference between mth and mcoil implies that the dehydration of PPG10 in the coil state is necessary to begin the formation of triple helices and is likely relevant to the value of ∆∆H+. Acknowledgment. This work was supported by KAKENHI (Grant-in-Aid for Scientific Research on Priority Area “Soft Matter Physics”) from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and also other KAKENHI (Grant-in-Aid for Scientific Research (B)21350064 and (B)19350059) from Japan Society for the Promotion of Science. References and Notes (1) Privalov, P. L. AdV. Protein Chem. 1982, 35, 1–104.

Shikata et al. (2) Gustavson, K. H. The Chemistry and ReactiVity of Collagen; Academic Press: New York, 1956. (3) Ramachandran, G. N.; Ramakrishnan, C. Biochemistry of Collagen; Ranmchandran, G. N., Reddi, A. H., Eds.; Plenum: New York, 1976; pp 45-84. (4) Sasakibara, S.; Kishida, Y.; Kikuchi, Y.; Sakai, R.; Kakiuchi, K. Bull. Chem. Soc. Jpn. 1968, 41, 1273. (5) Kobayashi, Y.; Sakai, R.; Kakiuchi, K.; Isemura, T. Biopolymers 1970, 9, 415–425. (6) Okuyama, K.; Tanaka, N.; Ashida, T.; Kakudo, M.; Sakakibara, S. J. Mol. Biol. 1972, 72, 571–576. (7) Okuyama, K.; Okuyama, K.; Arnot, S.; Takayanagi, M.; Kakudo, M. J. Mol. Biol. 1981, 152, 427–443. (8) Okuyama, K. Connect. Tissue Res. 2008, 49, 299–310. (9) Ramachandran, G. N.; Charandrasekharan, R. Biopolymers 1968, 6, 1649–1658. (10) Grigera, J. R.; Berendsen, H. J. C. Biopolymers 1979, 18, 47–57. (11) Grigera, J. R.; Vericat, F. Biopolymers 1979, 18, 35–45. (12) Umemura, S.; Sakamoto, M.; Hayakawa, R.; Wada, Y. Biopolymers 1979, 18, 25–34. (13) Shikata, T.; Yoshida, N.; Minakawa, A.; Okuyama, K. J. Phys. Chem. B 2009, 113, 9055–9058. (14) Ono, Y.; Shikata, T. J. Am. Chem. Soc. 2006, 128, 10030–10031. (15) Ono, Y.; Shikata, T. J. Phys. Chem. B 2006, 110, 9426–9433. (16) Satokawa, Y.; Shikata, T. Macromolecules 2008, 41, 2908–2913. (17) Berg, R. A.; Olsen, B. R.; Prockop, D. J. J. Biol. Chem. 1970, 21, 5759–5763. (18) Terao, K.; Mizuno, K.; Murashima, M.; Kita, Y.; Hongo, C.; Okuyana, K.; Norisuye, T.; Ba¨chinger, H. P. Macromolecules 2008, 41, 7203–7210. (19) Engel, J.; Chen, H.-T.; Prockop, d. J. Biopolymers 1977, 16, 601– 622. (20) Uchiyama, S.; Kai, T.; Kajiyama, K.; Kobayashi, Y.; Tomiyama, T. Chem. Phys. Lett. 1997, 281, 92–96. (21) Persikov, A. V.; Xu, Y.; Brodsky, B. Protein Sci. 2004, 13, 893– 902. (22) Nishi, Y.; Uchiyama, S.; Doi, M.; Nishiuchi, Y.; Nakazawa, T.; Ohkubo, T.; Kobayashi, Y. Biochemistry 2005, 44, 6034–6042. (23) Daniel, V. V. Dielectric Relaxation; Academic Press: New York, 1967; pp 72-73. (24) Doi, M.; Edwards, S. F. The Theory of Polymer Physics; Oxford Scientific Publication: Oxford, 1986; Chapter 8. (25) Nestler, F. H. M.; Ferry, J. D. Biopolymers 1983, 22, 1747–1758. (26) Debye, P. Polar Molecules; Dover: New York, 1945; pp 77-89. (27) Stockmayer, W. H.; Baur, M. E. J. Am. Chem. Soc. 1964, 86, 3485– 3489. (28) Stockmayer, W. H. Pure Appl. Chem. 1967, 15, 539–554. (29) Oncley, J. L. Chem. ReV. 1942, 30, 433–450. (30) Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: Oxford, 1998; Chapter 9. (31) Doi, M.; Edwards, S. F. The Theory of Polymer Physics; Oxford Scientific Publication: Oxford, 1986; Chapter 4. (32) Kaatze, U. J. Chem. Eng. Data 1989, 34, 371–374. (33) Okuyama, K.; Hongo, C.; Wu, G.; Noguchi, K.; Ebisuzaki, S.; Tanaka, Y.; Ba¨chinger, H. P. Biopolymers 2009, 91, 361–372. (34) Mrevlishvili, G. M. Thermochim. Acta 1998, 308, 49–54.

JP906719F