Equilibrium thermal transitions of collagen model peptides

Authors

  • Anton V. Persikov,

    1. University of Medicine and Dentistry of New Jersey (UMDNJ)–Robert Wood Johnson Medical School, Piscataway, New Jersey 08854, USA
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  • Yujia Xu,

    1. University of Medicine and Dentistry of New Jersey (UMDNJ)–Robert Wood Johnson Medical School, Piscataway, New Jersey 08854, USA
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    • Present address: Department of Chemistry, Hunter College, 695 Park Avenue, New York, NY 10021, USA.

  • Barbara Brodsky

    Corresponding author
    1. University of Medicine and Dentistry of New Jersey (UMDNJ)–Robert Wood Johnson Medical School, Piscataway, New Jersey 08854, USA
    • UMDNJ–Robert Wood Johnson Medical School, 675 Hoes Lane, Piscataway, NJ 08854, USA; fax: (732) 235-4783.
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Abstract

The folding of collagen in vitro is very slow and presents difficulties in reaching equilibrium, a feature that may have implications for in vivo collagen function. Peptides serve as good model systems for examining equilibrium thermal transitions in the collagen triple helix. Investigations were carried out to ascertain whether a range of synthetic triple-helical peptides of varying sequences can reach equilibrium, and whether the triple helix to unfolded monomer transition approximates a two-state model. The thermal transitions for all peptides studied are fully reversible given sufficient time. Isothermal experiments were carried out to obtain relaxation times at different temperatures. The slowest relaxation times, on the order of 10–15 h, were observed at the beginning of transitions, and were shown to result from self-association limited by the low concentration of free monomers, rather than cis–trans isomerization. Although the fit of the CD equilibrium transition curves and the concentration dependence of Tm values support a two-state model, the more rigorous comparison of the calorimetric enthalpy to the van't Hoff enthalpy indicates the two-state approximation is not ideal. Previous reports of melting curves of triple-helical host–guest peptides are shown to be a two-state kinetic transition, rather than an equilibrium transition.

The folding of multimeric fibrous proteins is complicated, in contrast with the classic experiments of Anfinsen, that demonstrated reversible refolding of monomer globular proteins (Anfinsen 1973; Jaenicke and Lilie 2000). Many small globular proteins undergo very fast unfolding and refolding, leading to rapid establishment of equilibrium. When these conditions apply and only the native and unfolded states are significantly populated, thermodynamic analysis for a two-state model can be applied to clarify stabilizing interactions. Fibrous proteins are more complicated because of their multichain nature, their length, and the linear nature of their superhelical motifs (Beck and Brodsky 1998). The coiled-coil α-helical domain of tropomyosin consists of multiple cooperative units of different stability, and the triple-helical region of collagen molecule contains multiple cooperative units with similar stability (Privalov 1982). Although the coiled-coil tropomyosin molecule reaches equilibrium very quickly, the reversibility of transitions of the collagen triple helix is controversial (Miles 1993; Engel and Bächinger 2000; Bächinger and Engel 2001). The nature of the collagen triple helix to unfolded monomer transition is approached here through studies on collagen-like model peptides.

The collagen triple helix has unique sequence and conformational features that could influence folding and unfolding, as well as the ability to reach equilibrium. The family of collagens includes at least 27 distinct genetic types that are united by their common triple-helix motif (Kielty and Grant 2002). The native conformation of collagen consists of three left-handed polyproline II-like helices supercoiled into a right-handed triple helix. The close packing of the three chains requires that Gly occupy every third position, giving a Gly-X-Y repeating sequence. Imino acids stabilize the extended polyproline II nature of the individual chains, and typically about 20% of the X and Y positions are occupied by proline or hydroxyproline (Hyp), respectively.

The folding process is best characterized for fibril-forming collagens, including type I collagen found in fibrils in bone, tendon, and skin, and type III collagen found in fibrils of skin and blood vessels (Bächinger et al. 1980; McLaughlin and Bulleid 1998). In vivo, chain selection and trimerization is directed by C-terminal globular propeptides. Triple-helix folding is nucleated at a C-terminal Gly-Pro-Hyp rich sequence and propagated from the C terminus to the N terminus in a zipper-like manner (Engel and Prockop 1991). The rate-limiting step in collagen folding was shown to be cis–trans isomerization of the large number of imino acids in the sequence (Bächinger et al. 1978). Following triple-helix folding, procollagen molecules are secreted, and propeptides are cleaved prior to self-assembly into characteristic collagen fibers.

It is practically impossible to refold collagen to its native structure in vitro. Type I collagen is a heterotrimer consisting of two α1(I) and one α2(I) chains, and after propeptide removal, the α1(I) and α2(I) chains combine randomly rather than recreating the original native chain composition (Leikina et al. 2002). Type III collagen is a homotrimer consisting of three α1(III) chains, but type III collagen did not show reversible folding, even with its native disulfide crosslink at the C terminus (Engel and Bächinger 2000). However, when homotrimeric type III collagen was crosslinked at both the N- and C-terminal ends (pN type III collagen), equilibrium could be reached when samples were equilibrated up to 24 h at each temperature, indicating it is possible for the collagen triple-helix to reach equilibrium given sufficient time (Bächinger and Engel 2001). Some researchers support the applicability of equilibrium thermodynamics for studying collagen, because it can eventually reach a reversible transition (Bächinger and Engel 2001; Leikina et al. 2002). Others argue that it is invalid to apply equilibrium thermodynamics to a system like collagen with extremely slow folding, and a kinetic approach must be applied to study this process (Miles 1993; Miles et al. 1995). Extensive thermodynamic and kinetic studies have also been carried out on CNBr collagen peptides, showing complete reversibility for the two shortest peptides with lengths of 36 and 47 residues, but not for longer peptides (Piez and Sherman 1970; Saygin et al. 1978).

A recent study on human type I collagen showed that it unfolds slowly over a period of several days even at 35°C, which is below the body temperature (Leikina et al. 2002). There is also evidence for local microunfolding in collagen molecules at temperatures just below body temperature (Ryhanen et al. 1983; Kadler et al. 1988), and it is indicated that this microunfolding process plays a critical role in promoting self-association of collagen into fibrils (Leikina et al. 2002). The very slow folding and unfolding of collagen have implications for its biological function. It is known that collagen thermal stability correlates with the habitat temperature of animals, having an apparent denaturation temperature close to the environmental temperature (Rigby 1971; Privalov 1982). This fine tuning of Tm values gives the collagen molecule sufficient stability to not unfold rapidly at the body temperature, yet sufficient flexibility to form fibrils, which are necessary for biological function (Leikina et al. 2002; Persikov and Brodsky 2002).

Short synthetic peptides are good models for collagen structure, folding, and stability (Goodman et al. 1998; Baum and Brodsky 1999; Jenkins and Raines 2002). Peptide designs include simple repeating tripeptides, for example, (PPG)10 and (POG)10, host–guest peptides, and peptides that contains stretches of collagen sequences (Shah et al. 1997; Persikov et al. 2003; Xu et al. 2003). The folding and unfolding behavior of a range of synthetic peptides of various sequences is reported here to shed the light on the transition between the native and the unfolded states of the collagen triple helix. In particular, investigations were carried out to ascertain whether peptides of different sequences can reach equilibrium, and whether the equilibrium process approximates a two-state model.

Results

Collagen-like peptides reach equilibrium after long time periods

Experiments were carried out to determine whether a variety of collagen-like peptides are in equilibrium during thermal transitions. Peptides of different lengths and sequences were studied, including three host–guest peptides of the form (GPO)3-(GPY)-(GPO)4: GPR (the most stable; see Persikov et al. 2000), GPD (average stability), and GPW (the least stable); and 30-mer peptides: T1–892, (POG)10, and (PPG)10 (Table 1). The reversibility of the thermal transitions between native triple helix and unfolded monomer was followed by circular dichroism spectroscopy. At heating rates equal to or faster than 0.1°C/min, the Tm values were independent of concentration, which is not for a monomer–trimer equilibrium transition. Thermal unfolding and refolding experiments at an average heating/cooling rate of 0.1°C/min are not superimposable in the transition region (see example in Fig. 1A). With increasing concentrations, the difference between folding and unfolding curves at this heating rate becomes smaller. These peptides either reach equilibrium at a very slow rate or the process is inherently irreversible.

To further investigate this apparent hysteresis, isothermal experiments were performed, monitoring the CD signal after the sample is transferred to a defined temperature from warmer and cooler starting points (Fig. 1B). These experiments are similar to those previously described for collagen CNBr peptides (Piez and Sherman 1970; Saygin et al. 1978). For a given temperature, the CD signal reaches a final value independent of the initial state. Thus, given sufficient time, there is a single equilibrium ellipticity value at each temperature (Fig. 1). For all peptides studied, these values generate a true equilibrium transition curve, in which the folding and unfolding curves are superimposable (Fig. 1A).

Investigations of curve fitting, concentration dependence, and calorimetry were carried out to examine whether the peptides fit a two-state trimer-to-monomer model under equilibrium conditions. The equilibrium transition curves, expressed as fraction folded versus temperature, fit well to a simple two-state model (equation 6) for the host–guest peptides and T1–892 in PBS (Fig. 2A). The fitting was also good for (PPG)10 and (POG)10 in 0.1 M HAc, but not in PBS. Concentration dependence of the equilibrium melting temperature is expected for a trimer dissociation/association process (equation 5). Determination of the equilibrium transition curves at different concentrations carried out for various host–guest and 30-mer peptides showed an inverse linear dependence of Tm versus the logarithm of total peptide concentration, in good agreement with equation 5 (Fig. 2B). An independent method for assessing the validity of a two-state model is the agreement between calorimetric (ΔHcal) and van't Hoff enthalpies (ΔHvH). The ΔHvH values were determined using two different methods of analysing the CD equilibrium thermal transition curves. First, the individual equilibrium CD thermal transitions were fit to equation 6 (Table 1). Second, the Tm dependence on the total peptide concentration was fit with equation 5. The calorimetric transitions were not used for calculating the ΔHvH values because the slowest scanning rates used are far from equilibrium, making extrapolation to zero scanning rate problematic. Values of ΔHcal were obtained from DSC experiments. The ΔHcal values were independent of the heating rate over the practical range of the calorimeter (Fig. 3, Table 1), indicating ΔCp is equal to zero. There is good agreement between ΔHcal and ΔHvH for (POG)10 in 0.1 M HAc, but ΔHvHHcal values were 0.7–0.8 for host–guest peptides (GPR, GPD, and GPW), T1–892 and (PPG)10 (Table 1).

Analysis of relaxation times for collagen peptide equilibration

The CD measurements described above generate information on how long it takes to reach equilibrium, as well as the final equilibrium value. Each isothermal experiment yields relaxation data, and the relaxation kinetics fit well to a first-order exponential decay (equation 7, Fig. 1B). For all collagen-like peptides studied, the relaxation times (τ) near the beginning of the transition curve are very long, while the τ values are smaller near the end of the transition. For example, for the host–guest peptide GPR, (Tmeq = 40.6°C, 1 mg/mL), changing the temperature from 25°C to 30°C, where the transition is just starting, results in a very slow drop in fraction folded, which is only complete after more than 10 h (Fig. 4). At temperatures higher than the midpoint of the transition, for example, going from 45°C to 50°C, equilibrium is reached more quickly, with a τ value of about an hour (Fig. 4).

Potentially slow steps in the folding of the collagen triple helix include cis–trans isomerization of the numerous imino acids in the unfolded state, the self-association of monomers, and out-of-register misfolding. The cis–trans isomerization has a very high activation energy, and the isomerization rate is known to increase dramatically with increasing temperature (Bächinger et al. 1978; Jaenicke and Lilie 2000). To better understand the origin of the extremely slow equilibration times, studies were carried out on peptides of different stabilities to investigate whether relaxation is limited by a temperature dependent reaction, such as cis–trans isomerization. A more stable peptide reaches a given fraction folded value at a higher temperature than a less stable peptide, and would be expected to have faster relaxation times at each fraction folded value. Comparison of results from peptides of different sequence and stability indicates that they all follow the same pattern, with extremely slow equilibration when fraction folded is near 1, and faster equilibration when fraction folded approaches 0, regardless of their Tm values. For instance, GPD and GPR peptides (c = 1 mg/mL) reach F = 0.7 at different temperatures, 25°C and 36°C, respectively, yet the relaxation times for both peptides are similar (about 9 h). This indicates the dominant cause of long equilibration time is not a temperature dependent process such as cis–trans isomerization.

During an equilibrium transition, folding and unfolding are taking place, and both folding and unfolding rates determine the relaxation time at any temperature. A concentration dependence is expected for chain association involved in folding, which dominates at low temperatures. The unfolding rate is concentration independent, and has a major influence in the relaxation time at higher temperatures. Relaxation times were determined for a given host–guest GPR peptide at different concentrations as a function of temperature (Fig. 5A). At each concentration, relaxation is faster at higher temperatures, and the higher the concentration, the more quickly equilibrium is reached. This concentration effect is less pronounced near the end of the transition curve (Fig. 5A). Because chain association depends on the monomer concentration, relaxation times for GPR at different total peptide concentrations were plotted against the concentration of free monomers in solution (Fig. 5B). This analysis resulted in a single curve of relaxation values for samples of different concentrations. This indicates low monomer concentration is a key factor in the very slow equilibration near the beginning of the transition.

The relaxation curves were analyzed using the two-state kinetic model described by equations 8–12. The integrated rate equation 9 implies a reversible process with first-order kinetics for the unfolding reaction and n-order kinetics for the refolding. The individual sets of relaxation data were fit to equation 12, varying the reaction order n, the unfolding rate kunf, and the equilibrium fraction folded Feq and confirmed n = 3 reaction order.

Comparison of equilibrium melting temperatures with nonequilibrium values

Previously, a heating rate of 0.1°C/min (average) was used to compare the thermal stabilities of an extensive set of host–guest triple-helical peptides, as well as other collagen model peptides (Persikov et al. 2000, 2002). Comparison of apparent Tm values obtained under these conditions with equilibrium Tmeq values are given in Table 1 for peptides of varying thermal stability. The apparent Tm values were all significantly higher than the Tmeq values by 4–8°C. Varying the concentration has little effect on apparent Tm values, but significantly affected Tmeq values. Even though Tmeq values are lower than apparent values, the order of stability for the host–guest peptides studied remains unchanged (Table 1).

Discussion

The data presented here indicate that thermal transitions for all collagen model peptides studied are fully reversible given sufficient time. Isothermal experiments were used to obtain true equilibrium values of fraction folded, which can be reached at any temperature studied regardless of the direction of temperature change. Evaluation of whether the equilibrium transitions follow a two-state model was carried out using several different approaches. First, the CD transition curves for all peptides fit well to a trimer-to-monomer model, except for (PPG)10 and (POG)10 in PBS. Second, the concentration dependence of Tm values obtained from equilibrium CD transition curves was studied for three peptides, and agreed well with the two-state model. Thus, analysis of CD data supports the two-state approximation.

A more rigorous test of the two-state model involves comparison of thermodynamic parameters obtained from spectroscopy with those obtained from calorimetry (Dragan and Privalov 2002). The van't Hoff enthalpy calculated from the CD equilibrium transitions agrees with the calorimetric enthalpy for (POG)10 in 0.1 M acetic acid. For other peptides studied, the ratio ΔHcalHvH is 0.7–0.8 (Table 1), which is outside the experimental error and indicates the two-state approximation is less than ideal. A ΔHcalHvH ratio less than 1 is unlikely to be due to the existence of intermediate states or independently melting domains, which typically leads to ΔHvH values smaller then ΔHcal (Privalov 1982). The ΔHcalHvH ratio less then 1 usually indicates the existence of protein association during the denaturation process (Sanchez-Ruiz 1992, 1995). The breakdown in the two-state approximation can be attributed to the presence of significantly populated states other than the fully triple helical or fully monomer forms. It is possible that the very long time scale required for equilibration may result in the formation of aggregates of loosened trimers (or monomers), which distorts the two-state process. Alternatively, repetitive sequences of the triple helix are susceptible to misalignment during association (Weidner 1975) and such misfolded triple helices could represent a significantly populated off-pathway state.

The long equilibration times together with the relaxation curves indicate very slow folding and/or unfolding rates, which may be a result of unique features of collagen folding. Collagen triple-helix folding consists at least of two slow steps: nucleation and zipper-like propagation (Bächinger et al. 1978). Both steps require the cis–trans isomerization of numerous prolines/hydroxyprolines, a process with a high activation energy and temperature dependence (Bächinger et al. 1978; Xu et al. 2003). However, peptides with different stability show similar relaxation times at the beginning of their melts, indicating although cis–trans isomerization is taking place, it is not the rate-limiting factor in the relaxation process. At the peptide concentrations used in this study, the relaxation rate is dependent on the concentration of free monomers in solution. Thus, it appears the self-association of chains, presumably in the nucleation step, is the rate-limiting step in the relaxation process. The three-stranded nature of the collagen triple helix does not inherently dictate slow folding, because three-stranded coiled coils can fold on second time scale (Dürr and Bosshard 2000), but coiled coils have the potential to form stable dimers prior to trimer formation and can undergo sliding. In collagen, trimerization can only occur from single monomers, as confirmed by the observed good fit of relaxation data in the transition temperature region to the combination of third-order folding and first-order unfolding reactions. At higher peptide concentrations, the trimerization rate will increase and the cis–trans isomerization step may become the rate-limiting step (Buevich et al. 2000).

Another feature of collagen folding that may contribute to its long relaxation times is the potential for misalignment of chains within the triple helix. The repeating nature of the collagen sequence allows out-of-register alignment during refolding (Weidner 1975), unless there are propeptides or crosslinks that dictate the proper chain registration. The collagen triple helix is stabilized by interchain hydrogen bonds, which prevent the sliding of the single chains to correct the alignment. The misfolded triple helix has to dissociate to monomers before correct folding can begin (Weidner et al. 1974). Difficulty in folding of long triple helices to equilibrium has been reported, and this may be due to out-of-register folding (Weidner et al. 1974). Previous studies showed that short CNBr peptides of collagen fold reversibly, while the transitions of longer CNBr peptides, as well as full-length collagens, are not reversible (Piez and Sherman 1970; Saygin et al. 1978; Engel and Bächinger 2000). In theory, the crosslinking of three chains would facilitate the chain association and eliminate the free monomer concentration and out-of-register effects. Such covalently linked collagen peptide have been showed to fold faster (Feng et al 1997; Goodman et al. 1998) and double crosslinked type III pN-collagen experiences reversible folding/unfolding (Bächinger and Engel 2001).

There are many recent reports comparing stabilities of collagen-like peptides of different length and sequence (Goodman et al. 1998; Persikov et al. 2000, 2002; Malkar et al. 2002; Doi et al. 2003; Hodges and Raines 2003). A range of experimental conditions are used in these investigations. The present study raises issues about the most practical way of determining peptide stability such that useful comparisons can be made among sets of peptides. The typical conditions of the melting experiments previously reported from this laboratory (average heating rate ≈0.1°C/min, c = 0.3 mM) are shown here not to result in equilibrium. The dependence of the apparent Tm on the heating rate and the lack of concentration dependence of the apparent Tm indicate a kinetic rather than equilibrium measure of stability. However, it has been indicated that nonequilibrium behavior can still be consistent with a true two-state transition with no intermediates or aggregates (Sanchez-Ruiz 1992), and such a two-state kinetic model may be applicable to standardize stability measurements of collagen-like peptides, because the folding rates are very slow. All the initial states in our typical conditions were confirmed to be in equilibrium and completely folded. The presence of significant populations for only the trimer and monomer states is supported by the overlap of NMR and CD thermal transitions and the general lack of observable NMR intermediates at equilibrium (Li et al. 1993; Liu et al. 1998). Although, ideally, it is best to compare stabilities from equilibrium melts when the two-state approximation is valid, this approximation is very good for the equilibrium transitions of only a very small fraction of triple-helical peptides studied. In practice, the use of typical melting conditions (heating rates ≈0.1°C/min) leads to a better approximation of a two-state model, even though the peptide transitions are kinetic rather than equilibrium. Such typical conditions results in experimental data more useful for practical stability measurements that can be applied in comparative studies, as long as the same heating conditions are used in all cases. The kinetic stabilities of GXY triplets derived from the typical melting curves on host–guest peptides have been applied successfully to predict the stability of short triple-helical peptides of different sequences as measured in standardized melting conditions (Persikov et al. 2000, 2002; A. Persikov, unpubl.). This supports the empirical usefulness of using kinetic standardized melting conditions in comparative studies.

Materials and methods

Peptides

The peptides (Pro-Pro-Gly)10 and (Pro-Hyp-Gly)10 were obtained from Peptide International Inc. The T1–892 peptide Ac-Gly-Pro-Ala-Gly-Pro-Ala-Gly-Pro-Val-Gly-Pro-Ala-Gly-Ala-Arg-Gly-Pro-Ala-(Gly-Pro-Hyp)4-Gly-Tyr-CONH2 was synthesized by Synpep Corporation. The host–guest peptides had a uniform sequence of Ac-(Gly-Pro-Hyp)3-Gly-X-Y-(Gly-Pro-Hyp)4-Gly-Gly-CONH2, and were synthesized by solid-phase chemistry as described previously (Persikov et al. 2000, 2002). Each host–guest peptide is designated by the sequence of its guest triplet using a one-letter amino acid code. All peptides were purified to >90% purity using a reverse-phase HPLC system (Shimadzu) on a C-18 column and eluted in 0.1% trifluoroacetic acid with a binary gradient of 0%–40% (v/v) water/acetonitrile. The peptide identity was confirmed by laser desorption mass spectrometry. The peptide concentration was determined by absorbance at 214 nm using the ε214 = 2200 cm−1 •M−1 per peptide bond.

Circular dichroism spectroscopy

CD measurements were made on an Aviv Model 62DS spectrometer (Aviv Biomedical, Inc.). Peptide solutions in PBS buffer (0.15 M NaCl, 10 mM sodium phosphate [pH 7.0]) or 0.1 M acetic acid (pH 2.9) were used. Prior to all melting experiments, the peptides were incubated at 5°C for 48 h. For equilibrium transition experiments, the ellipticity at 225 nm was monitored while the sample temperature was increased or decreased. The conditions designated as “standard” use a temperature step of 0.3°C with 2-min equilibration time at each temperature and 10-sec data collection time for each of five samples in the multicell holder. This procedure results in faster heating rates at higher temperatures, but gives an average heating rate of 0.1°C/min. The fraction folded was calculated from CD melting curves as

equation image

where θ is the observed ellipticity and θN and θM are the ellipticities for the native and monomer forms, respectively, at temperature T. The melting temperature (Tm) was obtained as a midpoint of the transition, that is, F(Tm) = 1/2. From repeated experiments on independently prepared samples, the error of determination of the melting temperature is estimated to be ±0.5°C.

The equilibrium transition was generated by recording a number of isothermal experiments, where the CD signal was monitored with time after transferring the sample from high or low temperature to the designated temperature. In most cases, the temperature jump was 5°C. The experiment continued until no changes of CD signal were observed. Every isothermal experiment gave a θeq value or Feq value at that temperature, and the relaxation time τ at every temperature T was determined.

Differential scanning calorimetry

Differential scanning calorimetry (DSC) experiments were performed on a Nano-DSC II, Model 6100 (Calorimetry Sciences Corp.) instrument at scan rates of 0.05–1.0°C/min. Calorimetric enthalpy values were obtained by a temperature integration of excess heat capacity experimental data.

Equilibrium thermodynamics analysis

Given the equilibrium value of fraction folded molecules at each temperature, the equilibrium data set Feq(T) can be treated using thermodynamic analysis for a two-state trimer-to-monomer model:

equation image((1))

where kunf and kfold are rates of unfolding and folding reactions and equilibrium constant K = kunf/kfold If the total concentration of monomers is Co = [U] + 3[N], then concentration of native molecules is [N] = (CoFeq)/3 and concentration of unfolded monomers is [U] = Co•(1−Feq). The equilibrium constant and Gibb's energy are determined from the equilibrium melting experiment as:

equation image((2))
equation image((3))

Calorimetry experiments show that for triple-helical peptides the change of heat capacity during unfolding is negligible, which is confirmed by the independence of calorimetric enthalpy on the temperature obtained at different scanning rates. Therefore, we can assume that ΔH° and ΔS° are constants over temperature range studied (Engel et al. 1977) and

equation image((4))

At the melting temperature (T = Tm), the fraction of folded molecules Feq = 0.5 and3

equation image((5))

Going further and combining equations 2–5, we obtain the relation between fraction folded Feq and temperature:

equation image((6))

The melting temperature and van't Hoff enthalpy values are obtained by fitting the Feq(T) data set with equation 6.

Analysis of relaxation curves for isothermal experiments

Relaxation curves obtained at different concentrations, and different temperatures can be analyzed to obtain triple-helix folding and unfolding rates. The fraction of folded molecules, F, tends to its equilibrium value, Feq, and simple first-order exponential decay gives satisfactory fitting results,

equation image((7))

where Feq is the equilibrium fraction folded at the temperature of the isothermal experiment, ΔF is the difference between the starting and the equilibrium values of the fraction folded, and τ is the relaxation time. As a result of this fitting, τ values are obtained at different temperatures and concentrations.

The data were also analyzed in the context of a two-state kinetic model, similar to that described by Potekhin and Kovrigin (1998). Assuming that unfolding is a kinetic process of the first order and that refolding, including association of n monomers, follows nth order kinetics:

equation image((8))

The kinetic equation for unfolding reaction at given temperature is

equation image((9))

The change of fraction folded with time can be written as:

equation image((10))

From knowing the K = kunf/kfold relation and modified equation 2

equation image((11))

and equation 10 can be rewritten as:

equation image((12))

The fitting of relaxation data with differential equation 12 allows determination of the reaction order and the unfolding rate in any isothermal experiment, when F is approaching Feq.

Table Table 1.. Thermodynamic data for the thermal transitions of collagen-like peptides (c = 1.0 mg/mL)
 Tmapp, °CaTmeq, °CbΔHvH, kJ/molecΔHvH, kJ/moledΔHcal, kJ/moleeΔHcalHvHBuffer
  • a

    a Apparent melting temperatures are determined from the transitions at standard conditions (average heating rate = 0.1°C/min).

  • b

    b Melting temperatures are determined from the equilibrium melting curves at F = 0.5.

  • c

    c van't Hoff enthalpies are calculated from fitting the equilibrium melting curves to equation 6. The standard error is about 7%. Values could not be calculated for (PPG)10 and (POG)10 in PBS because the equilibrium melting curves did not give a good fit to a two-state model.

  • d

    d van't Hoff enthalpies are calculated from the fitting of the concentration dependence of equilibrium melting temperatures to equation 5.

  • e

    e Calorimetric enthalpies were confirmed to be independent on the scanning rate within the experimental error of 5%.

Host–guest peptides
    GPW26.122.83533862670.77PBS
    GPD34.028.14052790.69PBS
    GPR47.240.63493832780.80PBS
30-mers
    TI-89227.521.74364843590.82PBS
    (PPG)1027.926.8156PBS
    (PPG)1032.424.52293011790.78HAc
    (POG)1058.856.9376PBS
    (POG)1060.257.03824243901.02HAc
Figure Figure 1..

(A) Unfolding and folding transitions for the GPD host–guest peptide as monitored by the circular dichroism maximum at 225 nm. The arrows indicate the direction of heating at an average rate of 0.1°C/min, while the squares indicate equilibrium values obtained through isothermal experiments (c = 1.0 mg/mL in PBS [pH 7.0]). (B) Relaxation of GPD host–guest peptide monitored by CD ellipticity value at 225 nm, when sample is transferred from 25°C to 30°C (filled squares) and from 35°C to 30°C (empty squares).

Figure Figure 2..

(A) Fraction folded temperature dependence for collagen-like peptides (c = 1.0 mg/mL). (B) Concentration dependence of melting temperatures for collagen-like peptides. The peptides studied are GPR (circles), GPD (squares), and T1–892 (down triangles), all in PBS (pH 7.0); and (POG)10 (up triangles) in HAc (pH 2.9).

Figure Figure 3..

(A) DSC melting curves showing the temperature dependence of excess heat capacity for collagen-like peptides (c = 1.0 mg/mL): GPW (diamonds), GPR (circles), GPD (squares), T1–892 (down triangles), all in PBS (pH 7.0); and (POG)10 (up triangles) in HAc (pH 2.9). (B) Calorimetric enthalpy dependence on the scanning rate in DSC experiment for (POG)10 (triangles) and (PPG)10 (circles).

Figure Figure 4..

Relaxation curves for GPR peptide (c = 1.0 mg/mL in PBS [pH 7.0]), showing the decrease in fraction folded upon the temperature jump from 25°C to 30°C (squares), from 30°C to 35°C (circles), from 35°C to 40°C (up triangles), from 40°C to 45°C (down triangles), and from 45°C to 50°C (diamonds). The final temperature is indicated next to each curve.

Figure Figure 5..

(A) Temperature dependence of relaxation times of GPR peptide at different concentrations in PBS (pH 7.0). (B) Relaxation time dependence on concentration of free monomers for GPR peptide at different total peptide concentrations in PBS (pH 7.0). The total peptide concentrations used are 0.5 mg/mL (squares), 1.0 mg/mL (circles), 2.0 mg/mL (up triangles), 3.0 mg/mL (down triangles), and 3.4 mg/mL (diamonds).

Acknowledgements

This work was supported by NIH Grant GM60048 (B.B.), and A.P. is a recipient of the Michael Geisman Research Fellowship from the Osteogenesis Imperfecta Foundation. We thank Dr. Peter Privalov for encouragement, discussions, and allowing us to obtain early calorimetric data in his laboratory. We are grateful to Dr. Sergey Potekhin and Dr. Daniel Pilch for helpful discussions. Dr. John Ramshaw and Mr. Alan Kirkpatrick generously provided the host–guest peptides and gave helpful comments.

The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 USC section 1734 solely to indicate this fact.

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