Thermodynamics of Conformational Ordering of Î¹-Carrageenan in KCl

Biomacromolecules 2001, 2, 864-873

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Thermodynamics of Conformational Ordering of ι-Carrageenan in KCl Solutions Using High-Sensitivity Differential Scanning Calorimetry Valerij Ya. Grinberg,*,† Natalia V. Grinberg,† Anatoly I. Usov,‡ Nadezhda P. Shusharina,§ Alexei R. Khokhlov,§ and Kees G. de Kruif| Institute of Biochemical Physics, Russian Academy of Sciences, Vavilov St. 28, 117813 Moscow GSP-1, Russia; Institute of Organic Chemistry, Russian Academy of Sciences, Leninsky Av. 37, 117913 Moscow, Russia; Physics Department, Moscow State University, 117234 Moscow, Russia; and NIZO Food Research, Kernhemseweg 2, NL-6718, Ede, The Netherlands Received February 28, 2001

Thermodynamic properties of aqueous solutions of ι-carrageenan as affected by KCl (0.15-1.2 M) or ι-carrageenan (0.5-6 mg/mL) content were studied by high-sensitivity differential scanning calorimetry. The polysaccharide was found to undergo two consecutive cooperative conformational transitions, which can be represented by the scheme: [H2]2 T 2H2 T 4C where C is the random coil, H2 is the double helix, and [H2]2 is the double helix dimer. The first transition follows by the “all or none” mechanism. The profile of the second transition resembles that of a second-order phase transition. The parameter σ (of order 1), estimated for this latter transition, suggests that the stacking effect in helices of ι-carrageenan is rather small. The cooperativity of the transition is mainly defined by the loop factor. Free energies of both transitions at 273 K were calculated as a function of salt concentration. These experimental data were found to agree with Manning’s theory. 1. Introduction Considerable uncertainty surrounds the in vivo function of some polysaccharides, e.g., polysaccharides of seaweeds and bacteria.1 Knowledge regarding the energetics of the variety of ordered conformations for these polysaccharides (of either a single or multiple helix type) and of the interaction between them and other cell components is essential to deepen our understanding of their behavior including structure formation, protective barrier role, binding, or detoxication of metal ions.2 Thermodynamic analysis of helix-to-coil type conformational transitions provides quantitative information on the relative stability of the ordered conformations of polysaccharides, e.g., determination of the free energy of biopolymer transition under various conditions. Comparing this experimental datum with results of conformational calculations, a model of the ordered conformation of a polysaccharide could be developed. ι-Carrageenan is one of the most important seaweed polysaccharides.3 This is a high-molecular weight linear polymer consisting principally of an alternating sequence of 3-linked β-D-galactose 4-sulfate and 4-linked 3,6-anhydroβ-D-galactose 2-sulfate. Thus, each monosaccharide unit in the ideal polysaccharide structure carries one sulfate group, and therefore ι-carrageenan behaves in aqueous solutions as * Corresponding author. E-mail: [email protected]. † Institute of Biochemical Physics, Russian Academy of Sciences. ‡ Institute of Organic Chemistry, Russian Academy of Sciences. § Moscow State University. | NIZO Food Research.

a highly charged polyanion with the linear charge density ξ(25 °C) ) 1.386 in the extended conformation.4 According to X-ray fiber diffraction data, the polysaccharide has a double helix conformation in the solid state,5-7 while its calcium salt takes a 3-fold right-handed double helix with parallel strands and a helix pitch of 2.66 nm. It is assumed that in solution ι-carrageenan can readily and reversibly transform from an ordered to a disordered conformation, with high ionic strength and temperature favoring the former state. This concept is supported by structural information obtained by optical rotation analysis.8 On heating, the helices melt cooperatively, and the polysaccharide assumes a random coil conformation.9 Intermolecular double helix formation should result in a doubling in the observed molecular weight of the polysaccharide; a phenomenon that has been observed in several studies,10-13 but not in others,14 where monomolecular single-helix ordering was proposed.15 It appears that the formation of the ι-carrageenan double-helix follows secondorder reaction kinetics while the back reaction is a first-order process. A secondary process, which is connected with gel formation, is assumed to involve polymer annealing and aggregation.9 Recently, it has been shown that the change in the mechanism of ι-carrageenan conformational ordering from an intermolecular to an intramolecular multistrand state may occur on lowering the concentration of the polymer.16 There are numerous data on the phenomenology, structural aspects, and kinetics of the conformational double helix-tocoil transition in ι-carrageenan.17-29 However, thermodynamic interpretation of these data is rather complicated because of the lack of sufficiently precise data on the

10.1021/bm0100460 CCC: $20.00 © 2001 American Chemical Society Published on Web 07/10/2001

Thermodynamics of Conformational Ordering

energetics of the transition.30-33 A HS-DSC study of the transition of ι-carrageenan is clearly needed. The aim of the current study was to obtain calorimetric evaluation of the energetics of order-disorder transitions in ι-carrageenan using the HS-DSC technique. From the experimental data, we elucidated the thermodynamic stability of the ordered conformations of ι-carrageenan, which were found to correlate with some features of the chemical structure of ι-carrageenan. In this paper, we will present results of HS-DSC measurements of the apparent partial heat capacity of ι-carrageenan in diluted aqueous solutions at varied concentrations of polysaccharide and KCl. The heat capacity will be analyzed over the temperature range 5-80 °C. We will give detailed thermodynamic descriptions of conformational transitions of the polysaccharide occurring in the chosen ranges of thermodynamic variables. Mechanisms of the transitions will be also discussed. It should be specially noted that over all ranges of the variables we will deal with liquid homogeneous solutions of the polysaccharide. 2. Experimental Section ι-Carrageenan (lot 12946) was purchased from SKW Biosystems. The sample involved 92% of ι-carrageenan, 4% of κ-carrageenan, and 4% unidentified material according to data of 13C NMR. Contents of both impurities were rather minor and close to detection limits of the technique.34 It was characterized by the SEC-MALLS method as outlined by Tuiner et al.35 The measurements were performed in 0.1 M LiCl at 60 °C. The following molecular parameters were determined: Mn ) 287 kDa, Mw ) 446 kDa, and Mz ) 605 kDa. Potassium chloride was of reagent grade quality. Fresh bidistilled water was used for the preparation of stock polysaccharide and salt solutions. Stock solutions of the polysaccharide were prepared at room temperature through the incremental addition of the sample to water with careful stirring. Conventionally, the polysaccharide solutions less than 4 mg/mL were stirred for 3-4 h and kept at ambient temperature overnight (∼16 h), while more concentrated solutions were stirred overnight at ambient temperature. All stock solutions were subsequently stored at 6 °C. The polysaccharide concentration in the stock solutions was determined by dry weight at 105 °C. Samples for calorimetric measurements were prepared by slowly adding the corresponding stock KCl solution to the stock solution of the polysaccharide, while stirring vigorously. The stirring lasted for 30-60 min. The solution vial was hermetically sealed and held at 70 °C for 30 min prior to analysis. Calorimetric measurements were carried out with a differential adiabatic scanning microcalorimeter DASM-4A (NPO BIOPRIBOR) under an excess pressure of 6 bar in the temperature range 5-80 °C. The heating rate was 1.0 deg/min. In each experiment, the measuring cell of the instrument was filled with the sample at a temperature of 30-50 °C depending on the polysaccharide concentration. The first scan, aimed at a standardization of thermal history of the sample, was made from 2-4 to 80 °C. Then, the

Biomacromolecules, Vol. 2, No. 3, 2001 865

Figure 1. Thermograms of ι-carrageenan in 0.5 M KCl during the first (1), second (2) and sixth (3) scans. A number of points of curve 3 are omitted for clarity of presentation. The polysaccharide concentration is 1 mg/mL; the heating rate is 1.0 deg/min.

system was cooled to 0 °C and kept in the isothermal mode of the instrument for 45 min before analysis. This protocol provided a very good reproducibility of the measurements for several subsequent scans. As a rule, results of the second scan were used for data processing. The software “Nairta” (Institute of Biochemical Physics, Moscow) was used for primary data processing. The transition baseline was approximated by the spline interpolation. Conventionally, the heat capacity peak temperature was accepted as the transition temperature. Other calculations were done using Origin-5, PeakFit-4, SigmaPlot-5, or MathCad-8 programs. For the analysis of the heat capacity profile of the conformational transition, the experimental thermograms were corrected for the limited time response of the calorimeter according to an established procedure.36 However, note that these corrections were rather small because of the excellent dynamic properties of the instrument (time constant is about 20 s). 3. Results To ensure the reproducibility of calorimetric measurements, a sample preparation protocol with specific timetemperature regimes was followed. The sample was held at 70 °C for the defined time, preheated at a constant heating rate over the temperature range of interest, and then incubated at 0 °C to facilitate the structure formation processes. Figure 1 shows the results of such an experimental procedure. It can be seen that from the second scan onward the thermograms are reproducible, which illustrates the reversible nature of ι-carrageenan’s temperature-dependent conformational transition. In the first series of calorimetric experiments, the effect of KCl concentration at 0.15-1.2 M on the excess heat capacity functions of ι-carrageenan (2.0 mg/mL) was determined (Figure 2). At low salt concentrations (0.15 to 0.5 M KCl), only one peak is detected, the shape of which is similar to that typical of a second-order phase transition;37,38 i.e., the initial slow increase in the heat capacity is followed by a sharp drop. The sharpness of the transition is somewhat smoothed due to the limited time response of the instrument,

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Figure 2. Excess heat capacity functions of ι-carrageenan at various concentrations (M) of KCl: 0.15 (A), 0.3 (B), 0.5 (C), 0.6 (D), 0.8 (E), and 1.0 (F). The polysaccharide concentration is 2 mg/mL.

which possibly is the reason for the absence of the singularity in the heat capacity at the transition temperature. The peak shifts to higher temperatures with increasing salt concentration, which is commonly observed for conformational transitions of highly charged biopolymers.39-41 Surprisingly, at a salt concentration of 0.6 M, an additional and more symmetrical peak appears, which also shifts to higher temperatures with increasing salt concentration. It is significant that under these specific conditions the system remains a liquid, homogeneous and optically isotropic at all temperatures to the left of the peak. Here no phase separation was observed. Hereafter the high- and low-temperature transitions will be referred to as the primary and secondary transitions, respectively. Thermodynamic parameters of both transitions as a function of the KCl concentration are presented in Figure 3. In both cases, the dependence of the transition temperature on salt concentration can be approximated by the usual logarithmic law42 (Figure 3, panel A). With decreasing salt concentration, the transition temperature of the secondary transition markedly decreases and may become lower than the starting temperature of the instrument (about 5 °C), which presumably is why the secondary transition could not be detected at KCl concentrations less than 0.6 M (Figure 2). In addition, data on the double helix-to-coil transition temperature of ι-carrageenan, obtained as a function of KCl concentration from polarimetric measurements by Rinaudo et al.43 and Piculell et al.,44 are also given in Figure 3 (panel A). They are in a rather good agreement with our calorimetric data on the transition 1. Therefore, the primary transition can be considered as the double helix-to-coil transition.

Grinberg et al.

Figure 3. Thermodynamic parameters of the conformational transitions 1 and 2 of ι-carrageenan vs salt concentration (polysaccharide concentration is 2 mg/mL). Curves 3 and 4 are data of Rinaudo et al.43 and of Piculell et al.44 on the double helix-to-coil transition of ι-carrageenan. Solid lines were obtained in result of approximation of the dependence of Tt on [KCl] by a logarithmic function. Its extrapolation for transition 1 to lower salt concentrations is given by the dashed line. The start up temperature of the calorimetric measurements is indicated by the dash-dot line. Dashed lines (B) display confidence limits of the average values.

Both transition enthalpies are independent of salt concentration (Figure 3, panel B): ∆tH1 ) 22.9 ( 0.7 J/g for the primary transition and ∆tH2 ) 7.8 ( 1.3 J/g for the secondary transition. Thus, when the salt concentration is varied, the transition enthalpies of both transitions remain constant while their transition temperatures change over wide ranges: about 30 and 20 °C for primary and secondary transitions, respectively. This comparison allows one to point out that for both transitions the heat capacity increment, defined as ∆tCp ) (∂∆tH/∂Tt),45 is close to zero. In the second series of calorimetric experiments, the concentration of the polysaccharide was varied from 0.5 to 6.0 mg/mL at a constant salt concentration of 0.5 M. The results are presented in Figures 4 and 5. The polysaccharide concentration does not have any significant impact on transition 1 up to polysaccharide concentration of 4 mg/mL (Figure 4, panels A-E). At higher polysaccharide concentrations, the low-temperature transition, i.e., the transition 2, reappears (panels F and G). Figure 5 illustrates that the transition temperature and enthalpy of transition 1 do not depend significantly on polysaccharide concentration. Their averages are equal to Tt,1 ) 72.0 ( 0.7 °C and ∆tH1 ) 23.7 ( 1.6 J/g. The presented standard deviations are comparable with the experimental errors for the determination of the transition parameters. Polysaccharide concentration has little effect on the enthalpy of the secondary transition but does markedly affect the transition temperature. On decreasing the concen-


Figure 4. Excess heat capacity functions of ι-carrageenan at various polysaccharide concentrations (mg/mL): 0.5 (A), 1.0 (B), 2.0 (C), 3.0 (D), 4.0 (E), 5.0 (F), and 6.0 (G). Potassium chloride concentration is 0.5 M.

Figure 5. Thermodynamic parameters of the conformational transitions 1 and 2 of ι-carrageenan vs polysaccharide concentration. Dashed lines in panels A and B display confidence limits of the average values. The start up temperature of the calorimetric measurements is indicated by the dash-dot line (A). Potassium chloride concentration is 0.5 M.

tration from 5 to 4 mg/mL, the transition temperature is reduced by 4-5 °C and then falls outside the temperature range accessible for measurements with the calorimeter used. However, at a polysaccharide concentration of 4.5 mg/mL it was possible to detect only the transition temperature as a


Figure 6. Excess heat capacity functions of the conformational transitions 1 (A) and 2 (B) of ι-carrageenan, reduced to the transition temperature (Tt), at different concentrations (M) of KCl: 0.15 (A, 1), 0.3 (A, 2), 0.5 (A, 3), 0.6 (A, 4; B, 1), 0.8 (A, 5; B, 2), 1.0 (A, 6; B, 3), and 1.2 (B, 4). Curve 7 in panel A represents the average reduced function for the salt concentration range 0.15-1.0 M. A number of points of the curves are omitted for clarity of presentation. The polysaccharide concentration is 2 mg/mL.

peak temperature of the thermogram. The main part of the thermogram was located in a lower temperature region inaccessible to measurements. For this reason, the transition enthalpy at this polysaccharide concentration could not be estimated. To specify how changes in the system variables affect profiles of the primary and secondary transition, the excess heat capacity functions obtained at the different conditions were reduced using the difference, T - Tt, as a generalized variable. The results of such a reduction for the first experimental series are shown in Figure 6. Within a KCl concentration of 0.15-1.0 M the primary transition may be approximated by a master curve (Figure 6, curve 7), which is also compatible with the reduced excess heat capacity functions obtained at various concentrations of the polysaccharide (data not shown). From these data, it may be deduced that the profile of the helix-to-coil transition of ι-carrageenan does not change within a rather large range of the system variables. In contrast, the profile of the secondary transition is dramatically affected by salt (Figure 6, panel B). When the salt concentration is increased, the transition broadens significantly, thereby becoming less cooperative. The most interesting thermodynamic function of the transition is its free energy relating directly to the structure of biopolymer. It is important for further analysis to estimate the transition free energy for both transitions of ι-carrageenan (∆tG) as a function of the salt concentration at the reference temperature, T0 ) 273 K. Since according to the obtained experimental data ∆tCp ) 0 for both transitions, the first approximation of thermochemistry was applied:46

868


∆tG(T0) ) ∆tH(1 - T0/Tt)

Grinberg et al.

(1)

where Tt is the peak temperature for transition 1 and the midpoint temperature for transition 2. The results of calculations for different salt concentrations, Cs, are summarized in Figure 7. It is significant that dependences ∆tG(T0, Cs) for both transitions are linear functions of ln Cs. The slopes of these dependences are 0.499 ( 0.004 and 0.352 ( 0.003 kJ/mol for transitions 1 and 2, respectively. 4. Discussion Morris et al.12,30 and Rees et al. 3 proposed the so-called domain model for the ordering of ι-carrageenan in solutions and gels. According to this model, there are two levels of ordering of the polysaccharide, being the double helix and clusters of the double helices. In the simplest case, the clusters may be dimers. This concept can be represented by the following scheme [H2]2 T 2H2 T 4C where C is the random coil, H2 is the double helix, and [H2]2 is the double helix dimer. Apparently, our data provide clear support for this scheme. In fact, transition 1 is undoubtedly the double helix-to-coil transition. This follows from a good agreement our calorimetric and chiroptical43,44 data. Moreover, the profile of transition and its independence on the polysaccharide concentration are typical of a second-order phase transition, which is the double helix-to-coil transition.38,47,48 The secondary transition can be considered as a cooperative dissociation of dimers of double helices. Actually, polysaccharide concentration affects strongly this transition displaying its intermolecular nature. Furthermore, secondary transition is observed only at rather high ionic strengths, as would be expected for dimerization of double helices. The double helices would have a very high charge density,4 which induces strong electrostatic repulsion between them. Evidently, one needs an adequately high ionic strength in order to diminish the repulsion to a level allowing close contact between the double helices during the dimer formation. According to the domain model,12 one of the important driving forces for the dimerization of double helices is specific cation binding at the contact area between two double helices. Considering the three-dimensional structure of the double helix of ι-carrageenan6 suggests that hydrogen bonding (between hydroxyl groups at position 6 of Dgalactose residues and oxygen atoms of 3,6-anhydro rings located at the outer surface of the helix) may also play a role in the dimerization process. Below we will provide additional arguments to substantiate this proposed scheme. This evidence is obtained from theoretical analysis of the transition profiles and salt effects on the stability of the ordered forms of ι-carrageenan. 4.1. The Double Helix-to-Coil Transition. The theory of helix-to-coil transitions in single- and double-stranded homopolymers was developed by Zimm47 and Lifson and Zimm.49 Subsequently, this theory was generalized by Applequist50 and Vedenov et al.48 The extended description

Figure 7. Free energies of the conformational transitions 1 and 2 of ι-carrageenan at 273 K calculated per residue vs concentration of KCl.

of the theory is given in the book of Grosberg and Khokhlov.51 The basic idea of the double helix-to-coil transition model is that each link of the helix-forming chain can be regarded as a system with two clearly defined states: the “helical” and the “molten” (coil). A marginal area between the helical and coil sections leads to a junction point due to the cooperative effects. Of course, this junction is thermodynamically unfavorable. The theory of helix-to-coil transition is based on the method of generating function Z(p),51 where p is the activity of a chain link. This function may be treated as a grand partition function of the chain of N links. The partition function and thermodynamic characteristics of the system are determined by the singularities of the generating function. The singularities of Z(p) correspond to the roots of the equation: σsp2 ) (1 - sp)(1 - p)

(2)

Here, s and σ are the so-called Bragg-Zimm parameters defined as s ) exp(-∆f/kBT); σ ) exp(-2∆fs/kBT)

(3)

where ∆f is the free energy of the helical link (having chosen the coil state of the link as a reference point), ∆fs is the free energy of the junction between the helix and coil, T is the temperature, and kB is the Boltzmann constant. The parameter σ is a quantitative measure of cooperativity. In a single-stranded polymer, the link conformations of a nonhelical section are as free as well as those of an ordinary coil. This is not the case for a double-stranded polymer where the conformations of the coil section are restricted by the fact that the chains converge at the ends forming a closed loop.



Consequently, instead of the constant value of σ the partition function of the coil section in the double-stranded polymer depends on the section length c (see ref 51): σef(c) ) σc-3/2

σef(c) ) σc-R

(5)

It has been shown38 that if R > 1, a real phase helix-to-coil transition occurs. However, if 1 < R < 2, a second-order phase transition is predicted. In the current study calculations were based on the assumption that the chains are ideal; i.e., the value of R should be equal to 3/2. Experimental data for polynucleotides52 suggest that this value of the exponent R can be used as a good approximation for the real chains. The equation for the singularities of the generating function can be rewritten in the form: 1 - p ) σpφ3/2(p) s

(6)

where ∞

pcc-3/2 ∑ c)1

(7)

It is convenient to make a re-definition of the variable p as p ) e-δ and present the function φ3/2(δ) as an integral 1/2

∫0∞ex+δx - 1 dx

1 Γ(3/2)

φ3/2(δ) )

(8)

where Γ(3/2) is the γ-function. After simple transformations, we obtain φ3/2(δ) )

1 Γ(3/2)

{∫ [( ∞

1

) ] }

1 1 - (ln x)2 dx -δ x x-e

(9)

Then eq 6 can be rewritten in the following form kσpΦ(p) + p )

1 s

(10)

where k ) 1/Γ(3/2) and Φ(p) )

[(

∫1∞

)

]

1 1 - (ln x)1/2 dx lnp x x-e

(11)

An important parameter of the model that could be compared with experimental results is the fraction of residues in the ordered state, designed f. The theory37 yields this quantity as f)-

p (∂ln ∂ln s )

f)

(4)

Equation 4, known as the Jacobson-Stockmayer formula, shows the power dependence of σef(c) (the so-called loop factor) on the length c. It is clear that an entropic disadvantage of long loops leads to an increase in cooperativity of the transition. Equation 4 was obtained through the assumption of an ideal nature of both chains; it is worthwhile to write the loop factor as

φ3/2(p) t

By definition, 1 e f e 0 at T e Tt and f ) 0 at T > Tt. Application of this transform to eq 10 gives

(12)

1 + kσΦ(p) 1 + kσ[Φ(p) + Φ′(p)]

(13)

where Φ′(p) )

[ ]

∂Φ(p) ) ∂ln p

∫1∞(x -p p)2ln x0.5 dx

(14)

In principle, data of HS-DSC allow one to calculate the integral curve of transition, f(T), and the partition function p(T). In this case, the analysis of experimental data in terms of the model would come to study a correlation between f(T) and p(T) via eqs 13, 11, and 14. The quantity f can be simply expressed in terms of the current and total transition enthalpies, ∆tH(T) and ∆tH(Tt), respectively: f(T) ) 1 -

∆tH(T) ∆tH(Tt)

(15)

Evidently, a dimension of the transition enthalpy is not of importance in this case. From practical point of view, it is convenient to use the specific transition enthalpy obtained directly from experimental data. Alternatively, there is a problem how to express the partition function p(T) in terms of experimental thermodynamic quantities, normally specific, obtained by HS-DSC. To do this, the expression needs to go from specific thermodynamic quantities to appropriate molar ones which the theory demands. It is possible to express the molar quantities per pair of residues. In this case, a residue should be considered as a principal element of the chain. However, it would be valid only if a macromolecule behaves as an ideal random flight chain. This condition results from the fact that the theory considers loops formed during the melting of the double helix as Gaussian chains describing the Jacobson-Stockmeyer formula (eq 4). In practice, any flexible macromolecule is not the ideal random flight chain. Nevertheless, it can be treated as a Gaussian chain in terms of Kuhn segments. Hence, in this case it would be reasonable to express the thermodynamic quantities of the transition per pair of Kuhn segments of the macromolecule in the coil state. Unfortunately, we did not find data on the Kuhn segment length for ι-carrageenan in the coil state. For this reason, we were forced to use a number of residues per the Kuhn segment of ι-carrageenan in the coil state, nK, as an adjustable parameter. In so doing, the partition function calculated per pair of the Kuhn segments can be expressed in terms of nK and the partition function calculated per pair of residues, pres: p ) presnk

(16)

The theory was applied to analyze the experimental data for the polysaccharide at 2 mg/mL in 0.5 M KCl. The excess heat capacity function per residue, Cp,res(T), was corrected to account for the limited time response of the calorimeter

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Grinberg et al.

Figure 9. Schematic presentation of the macromolecular pairing according to the zipper model (see text). Figure 8. Comparison of experimental (1) and theoretical (2) integral transition curves for the double helix-to-coil transition of ι-carrageenan at 0.5 M KCl. Optimal values of the parameters are σ ) 0.94 ( 0.01 and nK ) 10 ( 1; the standard fit error is (0.018.

and converted into the function pres(T) using the following transforms 〈H〉res(T) )

∫TTCp,res(T) dT

〈G〉res(T) ) -T

(17)

t

∫TT

t

〈H〉res(T) T2

dT

(18)

where 〈H〉res(T) and 〈G〉res(T) are the enthalpy and free energy of the polysaccharide in the helical state, respectively (calculated with the random coil as a reference state). Evidently, they are zero at T g Tt with Tt as the transition temperature where pres reduces to 1, and pres(T) ) exp

(

)

〈G〉res(T) RT

(19)

A fitting procedure was applied using eqs 16, 11, 14, and 13, with experimental values of f, T, and pres as variables and σ and nK as adjustable parameters. Results of the fitting are compared with experimental data in Figure 8. It shows that the model for the double helix-to-coil transition fits well to the experimental data. A standard fit error is of (0.018. Optimal values of the parameters are σ ) 0.93 ( 0.01 and nK ) 10 ( 1. The obtained value of σ is rather high but still realistic. Similar σ values were reported for one-stranded helices of polyadenylic53 and polycytidylic54acids. To our knowledge, there are no direct data on the Kuhn segment length for ι-carrageenan in the coil state. Nevertheless, values nK ∼ 755-57 obtained for poly(U) and DNA coils, having the chain stereochemistry roughly similar to that of ι-carrageenan, point out that our estimate of nK for ι-carrageenan appears to be reasonable. Examining the fitting results, it should be noted that the obtained σ value is of about 1. This indicates that the stacking effect seems to be negligible for the ordered state of ι-carrageenan. Possibly, it may be due to electrostatic repulsion between sulfate groups in the ordered state as well as an appreciable freedom of their internal rotation in the

random coil state.53 Therefore, the loop factor is likely to be considered as a primary source of the cooperativity of the double helix-to-coil transition of ι-carrageenan. 4.2. The Dissociation Transition. The dissociation transition can be considered in terms of the zipper model for coupling of macromolecules,58 as it is principally concerned with the effect of polymer concentration. This model is particularly strongly affected by the polysaccharide concentration. The zipper model initially applied to describe the pairing of short polynucleotides and is based on the concept that no more than one uninterrupted bonded sequence can exist in any species. Presumably, it would be the case for relatively rigid macromolecules when the persistence length of the chain (l) is comparable with its contour length (L), a property that has not been investigated for the double helix of ι-carrageenan. However, taking into account data for κ-carrageenan59 (l ∼ 75 nm) and the geometry of the double helix of ι-carrageenan6 we estimated the ratio l/L for our ι-carrageenan sample as ∼0.1. Therefore, the double helix of ι-carrageenan can be actually considered as a rather rigid chain. According to the zipper model, the pairing of macromolecules involves the nucleation step and subsequent growth of the bonded sequence. The first step is treated as a bimolecular reaction with the equilibrium constant βs and all subsequent steps are of the first order with the equilibrium constant s (Figure 9). The total concentration of macromolecules (C) is dealt with in the model via the parameter γ ) βC. For simplicity, we will use the model at the infinite dilution approximation. This approximation is appropriate in our case because the experimental data were obtained at a rather low concentration of ι-carrageenan (2 mg/mL). In addition, even a qualitative inspection shows that the model48 agrees with the experimental data (Figure 6B): the transition is broadened with increasing transition temperature. It was shown58 that the zipper model is reduced to the “all or none” model at the infinite dilution limit. In this case it is convenient to present an equation for the fraction of bonded residues, f, in a form which does not include the biopolymer concentration



Figure 10. Results of the analysis of the conformational transition 2 of ι-carrageenan at 1.2 M KCl in terms of the zipper model: (O) experimental data; (s) calculated curve. A number of points of the experimental curve are omitted for a more clear presentation. The polysaccharide concentration is 2 mg/mL. The inset shows parameters of the zipper model vs the salt concentration: (O) ratio of the experimental and theoretical enthalpies (rH, left ordinate axis); (0) average number of residues per one cooperative domain (N, right ordinate axis). The thermodynamic quantities are calculated per pair of residues of the polysaccharide.

1+ f)

( ) [ ( )] () s sd

N

- 1+8 4

s sd

s sd

N 0.5

N

(20)

where s ) f(T) is the equilibrium constant of the coupling of residues; sd ) s(Td); Td is the midpoint transition temperature and N is the number of residues per primary chain. Using the van’t Hoff equation60 one gets

[ ( )]

∆bH 1 s 1 ) exp sd RT T Td

(21)

where ∆bH is the standard bonding enthalpy. Obviously, ∆bH ) -∆tH where ∆tH is the enthalpy of the dissociation transition. It is also apparent that a change in enthalpy in the course of the pairing is60 ∆H ) f∆bH

(22)

Differentiating this equation with respect to temperature and assuming that ∆bH * f(T), one gets the general equation for the excess heat capacity of the dissociation transition:

(∂T∂f )

Cp ) -∆tH

p

(23)

Equations 20-23 were fitted to the experimental heat capacity functions of transition 2 (expressed per two residues of the polysaccharide) for a polysaccharide concentration 2 mg/mL and various concentrations of KCl. The parameters ∆tH, Td, and N were adjusting parameters. The model fits to the experimental data rather well under all experimental conditions (Figure 10). The theoretical estimate of the transition enthalpy agrees well with the experimental data. The average ratio of the experimental and theoretical enthalpies rH ) 1.02 ( 0.02. It is interesting that the

parameter N is relatively constant at all salt concentrations studied. Its average value 407 ( 55 can be attributed to a molecular weight of an apparent primary chain of the polysaccharide of 110 kDa. This seems not to contradict to the estimates of molecular weight of the polysaccharide (Mw ∼ 500 kDa) because of the presence of some irregularities (kinks) in the primary structure of ι-carrageenan.3 If a kink content is about 0.8%, as typical of ι-carrageenan, a chain of 500 kDa should involve about four kinks. If these kinks are distributed randomly along the chain, the average molecular weight of a segment between neighboring kinks, that is a cooperative unit of the polysaccharide, would be about 100 kDa. Hence, our estimate of size of the cooperative unit (110 kDa) is rather reasonable for the polysaccharide sample studied. Therefore, the analysis of the profile of the secondary transition suggests that this transition is the cooperative, “all or none”, dissociation of dimers of the double helices. 4.3. Electrostatic Effects on the Stability of Ordered Structures. We noted that the increase in salt concentration causes a strong increase in the transition temperature of both transitions without any noticeable changes in the transition enthalpies. This agrees with the assumption that the effect of salt on the stability of the double helices and their dimers is predominantly entropy-driven. This then agrees closely with theoretical predictions of preferential interactions between electrolyte ions and charged biopolymers.39-41 According to this theory

( )

∂∆tG ) RT∆ti ∂ln as

(24)

where as is the activity of electrolyte and ∆ti is the change in the thermodynamic dissociation degree of biopolymer in result of the transition. Since all forms of ι-carrageenan are thought to have a linear charge density (ξ) > 1,4 the counterion condensation theory of Manning can be applied to express ∆ti via ξ:40 ∆ti ) ∆t(2ξ)-1

(25)

Assuming for simplicity that the activity of electrolyte is equal to its molar concentration and that ξ(0 °C) ) 1.353, 3.398, and 6.797 for ι-carrageenan’s coiled, double helix and double helix dimer conformations, respectively (obtained by a trivial temperature correction of the literature data4), eqs 24 and 25 can be used to analyze the experimental data presented in Figure 7. Results of this analysis are listed in Table 1. Experimental estimate of the transition increment of thermodynamic dissociation degree for the secondary transition agrees well with the prediction of the Manning theory. However, for the double helix-to-coil transition the predicted value of this parameter is noticeably larger than its experimental value. The agreement between theoretical and the experimental data for the dissociation transition originates from the fact that in this case both coexisting conformations can be quite well treated as rodlike polyions of defined geometry for which the calculated ξ values are reasonable.

872


Grinberg et al.

Table 1. Results of the Analysis of Salt Effects on Conformational Transitions in ι-Carrageenan and Some Other Biopolymersa ∆ti no.

biopolymer

transition

exptl

calcd

1 2 3 4 5 6 7

ι-carrageenan ι-carrageenan gellan64 DNA42 DNAb) poly(A)b) poly(U)b)

[H2]2 T 2 H2 H2 T 2 C H2 T 2 C H2 T 2 C H2 T 2 C H2 T 2 C H2 T 2 C

0.07 0.10 0.07 0.17

0.07 0.22 0.16 0.36

app calc bcoil /bcoil

0.66 0.65 0.60 0.63 0.46 0.66

a [H ] is the dimer of double helices; H is the double helix; C is the 2 2 2 random coil state; ∆ti is the transition increment of thermodynamic degree app calc of dissociation of a biopolymer; bcoil and bcoil are the charge separation lengths for the coil state determined experimentally and calculated for the extended chain conformation. b Calculated from data of Record et al.65 calc assuming bcoil ) 6.8 A as for a completely extended conformation of DNA.

In the case of the double helix-to-coil transition only the helix has a strictly rodlike structure with a known ξ parameter. Consequently, it is rather hard to determine the ξ for the coil because of its fluctuating nature. The ξ value used for the description of the coil state corresponds to the so-called “all-trans” or extended conformation of the polysaccharide chain.4 Obviously, it is underestimated, as actually the average distance between neighboring charge projections on the axis of polyion should be less than that for the extended conformation, bcalc coil . This problem was thoroughly calc app 61 discussed for DNA. The ratio bapp coil/bcoil , where bcoil is the apparent charge separation length calculated from the experimental ∆ti value by eq 25 and the definition of ξ,39 can serve as a measure of the deviation of the behavior of the disordered conformation from that of the rodlike polyion (Table 1). In fact, this ratio is constant for ι-carrageenan, calc gellan, DNA, and polynucleotides, bapp coil/bcoil ) 0.61 ( 0.03. The data presented show that the effect of salt on the thermodynamic stability of ι-carrageenan ordered conformations (double helices and their dimers) are in good agreement with predictions of the counterion condensation theory. As this theory deals exclusively with electrostatic phenomena, it is concluded that the effect of salt is predominantly electrostatic. This concept is supported by the fact that the salt affects only the entropy of the transitions considered (Tt ) f(Cs) but ∆tH * f(Cs)). An interesting approach to the analysis of electrostatic effects on the conformational order-disorder transition in carrageenans was elaborated by Nilsson et al.62 and Nilsson and Piculell.63 It is based on application of the PoissonBoltzmann cell model (PBCM) for calculations of the electrostatic contribution to the transition free energy, ∆tGel. This approach makes it possible to calculate the ∆tGel at different ionic strengths from some structural parameters of the ordered and disordered forms of a polysaccharide. In the work63 the approach was used for interpretation of experimental data on the thermal double helix-to-coil transition in segmented ι-carrageenan at varied concentrations of NaCl. The ∆tGel at the transition temperature, Tt, was calculated for different concentrations of the salt. Values of the linear charge densities of the double helix and the coil used in these calculations were the same as we used in the present study.

The temperature dependence ∆tGel(Tt) was described by the Gibbs-Helmholtz equation. This allowed one to estimate an apparent transition enthalpy. However, it was not compared with a calorimetric transition enthalpy. Therefore, it is rather hard to judge as far as it was successful to use the PBCM for calculations of the electrostatic free energies of ι-carrageenan in the coil and double helix conformations. Nevertheless, it seems that the same problem with the charge separation length for the coil should also arise in this case as in our analysis. For ξ > 1, the PBCM and the Manning’s theory are known to define the same limiting dependence ∆ti(ξ) according to eq 25.40 For this reason, one can expect that the PBCM should give results for ι-carrageenan consistent with those obtained from Manning’s analysis. 5. Conclusions 1. In the presence of K+ ions ι-carrageenan undergoes two consecutive cooperative conformational transitions upon heating: the dissociation of dimers of double helices and, then, the double helix-to-coil transition. 2. The dissociation transition is realized by the “all or none” mechanism since it is quantitatively described by the zipper model at the “all or none” approximation. 3. The double helix-to-coil transition seems to be of a second-order phase transition. 4. The cooperativity of the double helix-to-coil transition is likely to be defined by the loop factor. 5. Effects of KCl on the thermodynamic stability of the ordered conformations of ι-carrageenan are of pure electrostatic origin. Acknowledgment. The research described in this publication was made possible in part due to a NWO collaborative grant. V.Y.G. and N.V.G. also thank the RBRF Foundation (Grant No. 98-03-333709) for partial financial support. The authors are grateful to Dr. T. V. Burova and Prof. A. Yu. Grosberg for useful discussions. References and Notes (1) Polysaccharides: Syntheses. Modification and Structure-Properties Relations; Yalpani, M., Ed.; Elsevier: New York and Tokyo, 1988. (2) Morris, E. R.; Rees, D. A.; Thom, D.; Welsh, E. J. J. Supramol. Struct. 1977, 6, 259. (3) Rees, D. A.; Morris, E. R.; Thom, D.; Madden, J. K. In The Polysaccharides; Aspinall, G. O., Ed.; Academic Press: New York, 1982; pp 195-290. (4) Paoletti, S.; Smidsrod, O.; Grasdalen, H. Biopolymers 1984, 23, 1771. (5) Anderson, N. S.; Campbell, J. W.; Harding, M. M.; Rees, D. A.; Samuel, J. W. J. Mol. Biol. 1969, 45, 85. (6) Arnott, S.; Scott, W. E.; Rees, D. A.; McNab, C. G. J. Mol. Biol. 1974, 90, 253. (7) Lee, I. Polym.-Kor. 1997, 21, 539. (8) Rees, D. A.; Scott, W. E.; Williamson, F. B. Nature 1970, 227, 390. (9) Rees, D. A.; Williamson, F. B.; Frangou, S. A.; Morris, E. R. Eur. J. Biochem. 1982, 122, 71. (10) Austen, K. R. J.; Goodall, D. M.; Norton, I. T. Carbohydr. Res. 1985, 140, 251. (11) Jones, R. A.; Staples, E. J.; Penman, A. J. Chem. Soc., Perkin Trans. 2 1973, 1608. (12) Morris, E. R.; Rees, D. A.; Robinson, G. J. Mol. Biol. 1980, 138, 349. (13) Norton, I. T.; Goodall, D. M.; Morris, E. R.; Rees, D. A. J. Chem. Soc., Perkin Trans. 1 1983, 79, 2489. (14) Smidsrod, O.; Anderson, I. L.; Grasdalen, H.; Larsen, B.; Painter, T. Carbohydr. Res. 1980, 80, C11.

Thermodynamics of Conformational Ordering (15) Norton, I. T.; Goodall, D. M.; Morris, E. R.; Rees, D. A. J. Chem. Soc., Perkin Trans. 1 1983, 79, 2501. (16) Abeysekera, R. M.; Bergstrom, E. T.; Goodall, D. M.; Norton, I. T.; Robards, A. W. Carbohydr. Res. 1993, 248, 225. (17) Jones, R. A.; Staples, E. J.; Penman, A. J. Chem. Soc., Perkin Trans. 2 1973, 1608. (18) Norton, I. T.; Goodall, D. M.; Morris, E. R.; Rees, D. A. J. Chem. Soc., Chem. Commun. 1978, 515. (19) Morris, E. R.; Norton, I. T. In Aggregation Process in Solution; WynJones, E., Gormally, G., Eds.; Elsevier: Amsterdam, 1983; pp 549593. (20) Piculell, L.; Hakansson, C.; Nilsson, S. Int. J. Biol. Macromol. 1987, 9, 297. (21) Tako, M.; Nakamura, S.; Kohda, Y. Carbohydr. Res. 1987, 161, 247. (22) Piculell, L.; Nilsson, S.; Muhrbeck, P. Carbohydr. Polym. 1992, 18, 199. (23) Abeysekera, R. M.; Bergstrom, E. T.; Goodall, D. M.; Norton, I. T.; Robards, A. W. Carbohydr. Res. 1993, 248, 225. (24) Viebke, C.; Borgstrom, J.; Piculell, L. Carbohydr. Polym. 1995, 27, 145. (25) Denef, B.; Mischenko, N.; Koch, M. H. J.; Reynaers, H. Int. J. Biol. Macromol. 1996, 18, 151. (26) Hjerde, T.; Smidsrod, O.; Christensen, B. E. Carbohydr. Res. 1996, 288, 175. (27) Vanneste, K.; Slootmaekers, D.; Reynaers, H. Food Hydrocolloids 1996, 10, 99. (28) Hossain, K. S.; Nemoto, N. J. Non-Crystalline Solids 1998, 235, 682. (29) Hjerde, T.; Smidsrod, O.; Christensen, B. E. Biopolymers 1999, 49, 71. (30) Morris, E. R.; Rees, D. A.; Norton, I. T.; Goodall, D. M. Carbohydr. Res. 1980, 80, 317. (31) Ridout, M. J.; Garza, S.; Brownsey, G. J.; Morris, V. J. Int. J. Biol. Macromol. 1996, 18, 5. (32) Hossain, K. S.; Nemoto, N.; Nishinari, K. Nihon Reoroji Gakkaishi 1997, 25, 135. (33) Denef, B.; Gamini, A.; Delben, F.; Paoletti, S.; Reynaers, H.; Vanneste, K. Biopolymers 1998, 45, 105. (34) Vanneste, K. Ph.D. Thesis, K. U. Leuven, Leuven, Belgium, 1993. (35) Tuinier, R.; Zoon, P.; Olieman, C.; Cohen Stuart, M. A.; Fleer, G. J.; de Kruif, C. G. Biopolymers 1999, 49, 1. (36) Mayorga, O. L.; Freire, E. Biophys. Chem. 1987, 87, 87. (37) Applequist, J. In Conformation of Biopolymers; Ramachandran, G. N., Ed.; Academic Press Inc.: New York, 1967; pp 403-425.

Biomacromolecules, Vol. 2, No. 3, 2001 873 (38) Applequist, J. J. Chem. Phys. 1969, 50, 600. (39) Manning, G. S. Q. ReV. Biophys. 1978, 11, 179. (40) Anderson, C. F.; Record, M. T., Jr. Annu. ReV. Phys. Chem. 1982, 33, 191. (41) Record, M. T., Jr.; Zhang, W.; Anderson, C. F. AdV. Protein Chem. 1998, 51, 281. (42) Record, M. T., Jr. Biopolymers 1975, 14, 2137. (43) Rinaudo, M.; Kariman, A.; Milas, M. Biopolymers 1979, 18, 1673. (44) Piculell, L.; Hakansson, C.; Nilsson, S. Int. J. Biol. Macromol. 1987, 9, 297. (45) Pfeil, W.; Privalov, P. L. In Biochemical Thermodynamics; Jones, M. M., Ed.; Mir: Moscow, 1982; pp 5-139. (46) Becktel, W. J.; Schellman, J. A. Biopolymers 1987, 26, 1859. (47) Zimm, B. H. J. Chem. Phys. 1960, 33, 1349. (48) Vedenov, A. A.; Dykhne, A. M.; Frank-Kamenetskii, M. D. Usp. Fiz. Nauk 1971, 105, 479 (in Russian). (49) Lifson, S.; Zimm, B. H. Biopolymers 1963, 1, 15. (50) Applequist, J. J. Chem. Phys. 1966, 45, 3459. (51) Grosberg, A. Yu.; Khokhlov, A. R. Statistical Physics of Macromolecules; AIP Press: New York, 1994. (52) Oliver, A. L.; Wartell, R. M. Biopolymers 1977, 16, 1115. (53) Applequist, J.; Damle, V. J. Am. Chem. Soc. 1966, 88, 3895. (54) Freier, S. M.; Hill, K. O.; Dewey, T. G.; Marky, L. A.; Breslauer, K. J.; Turner, D. H. Biochemistry 1981, 20, 1419. (55) Inners, L. D.; Felsenfeld, G. J. Mol. Biol. 1970, 50, 373. (56) Shugalii, A. V.; Frank-Kamenetskii, M. D.; Lazurkin, Yu. S. Mol. Biol. (Mosk) 1969, 3, 133 (in Russian). (57) Veselkov, A. N.; Moroshkin, V. A.; Poliakova, I. D.; Shpungin, I. L.; Frisman, Z. V. Mol. Biol. (Mosk) 1976, 10, 1050 (in Russian). (58) Applequist, J.; Damle, V. J. Am. Chem. Soc. 1965, 87, 1450. (59) Borgstrom, J.; Egermayer, M.; Sparrman, T.; Quist, P. O.; Piculell, L. Langmuir 1998, 14, 4935. (60) Prigogine, I.; Defay, R. Chemical Thermodynamics; Longmans Green & Co.: London, New York, Toronto, 1954. (61) Olson, W.; Manning, G. S. Biopolymers 1976, 15, 2391. (62) Nilsson, S.; Piculell, L.; Joensson, B. Macromolecules 1989, 22, 2367. (63) Nilsson, S.; Piculell, L. Macromolecules 1989, 22, 3011. (64) Burova, T. V.; Grinberg, N. V.; Mashkevich, A. Ya.; Plashchina, I. G.; Usov, A. I.; Shusharina, N. P.; Khokhlov, A. R.; Grinberg, V. Ya.; Cesaro, A. Biopolymers 2001, to be published. (65) Record, M. T., Jr.; Anderson, C. F.; Lohman, T. M. Q. ReV. Biophys. 1978, 11, 103.

BM0100460

Thermodynamics of Conformational Ordering of Î¹-Carrageenan in KCl

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