Thermodynamic parameters for unfolding and refolding of ACF I by GdnHCl at 25 C, monitored by measurement of fluorescence at 340nm
1. Introduction
The mechanism by which proteins fold to their unique native conformations from an initially disorganized form is one of the fundamental problems in molecular biology. In the study of proteins fold or refold standard Gibbs free energy,
The history of evaluation of the quantity known as standard Gibbs free energy spans more than four decades, and at least three procedures involving strong solvent denaturation have been used in evaluation of this quantity. The three procedures are known as the transfer model of Tanford, the denaturant binding model, and the linear extrapolation method. Of the three methods employed in evaluation of
The linear extrapolation method is the most frequently used method of determining protein unfolding free energy changes induced by urea or guanidine hydrochloride (GdnHCl). It is based upon the premise that unfolding free energy changes are linearly dependent on denaturant concentration and that extrapolation to zero denaturant concentration gives
When the native, partially unfolded (stable intermediate) and unfolded forms of protein are present in significant concentrations at equilibrium,
2. Assumptions
1. The protein unfolding process is determined by the structural element, Ei. Ei can change from a native state, Ei(F) to a denatured, unfolded state Ei(U), in two-state model.
The equilibrium between Ei(F) and Ei(U) is described in eq (1).
Figure 1A shows that the observed signals of the various experimental techniques (optical rotation, viscosity, UV-Vis absorption, fluorescence, circular dichroism, dynamic light scattering, nuclear magnetic resonance, etc) for structural element, Ei vary with the denaturant concentrations. At low denaturant concentrations (from [D] = 2.0 to [D] = 3.0) the measured signals are constant and can be considered as
where
According to the linear extrapolation method the unfolding curve of Ei can be fitted based on eq (3).
where
The free energy difference,
From Figure 1B the plot of
When
where [D]1/2 is the midpoint concentration of denaturant required for unfolding of structural element. It means that we can use ether mi and [D]1/2 as two parameters or
At [D]1/2 = 4.57M the variations of
2. Protein is consisted of structural elements connected by chemical bonds that there is no contribution to measured signal. When protein contains two kinds of structural elements, Ei and Ej, the three-state unfolding behavior may be observed. The observed three-state unfolding curve
If the number of structural elements is n, the protein can be express as scheme 1. Typical 1 of protein is consisted of same structural elements and typical 2 and 3 of proteins are consisted of different structural elements.
It is known that the unfolding of structural element, Ei obeys two-state model. The stability can be expressed as
Denaturant-induced unfolding of the protein is found to be a two-state process, just as that of the structural element, E1.
There is a protein, in which the structural element, E1 appears for n1 times and E2 does for n2 times. The sum of n1 and n2 is n. The measured unfolding data (O) of the protein are presented in Figure 4B. Denaturant-induced unfolding of the protein is found to be a two-step process with accumulation of an intermediate state at around 3.5~5.5 M denaturant concentration. Therefore, denaturant-induced denaturation may be considered as a three-state transition and the mechanism for unfolding of the protein may be represented as:
where F, I and U are the folding, intermediate and unfolding states of the protein, respectively. The first transition which corresponded to the transformation of F state to the I state started at around at 1.5 M denaturant concentration and completed at 3.5 M denaturant with a midpoint occurring at 2.57 M denaturant. In fact the transition corresponds to the unfolding of E1 in the protein.
The second transition, which corresponded to the unfolding of the I state, started at around 5.5 M denaturant concentration and finally sloped off to the U state at 7.7 M denaturant with a midpoint occurring at 5.57 M denaturant. The transition corresponds to the unfolding of E2 in the protein. The intermediate state of the protein is a partial unfolding state, in which E1 exists in completely unfolding form and E2 does in completely folding form. The three-state unfolding process can be considered to be composed of two sequential two-state unfolding processes. Then the measured unfolding data (O) of the protein in Figure 4B can be fitted by using eq(8).
where f1 and f2 are molar fractions of structural elements E1 and E2 in the protein.
From eq(8) it is known that f1 or f2,
Protein is consisted of structural elements, E1, E2, E3, , En-1, which appears n1, n2, n3, , nn-1 times in the protein. The unfolding curves corresponding to E1, E2, E3, , En-1 are
So the four-state, five-state unfolding curves can be fitted by using eq(10).
3. The unfolding free energy represented by the curve (
Protein is consisted of structural elements, E1, E2, E3, , En-1, which appears n1, n2, n3, , nn-1 times in the protein. The unfolding free energies corresponding to E1, E2, E3, , En-1 are
When n is 4 the four-state unfolding free energy,
It can be seen that
Although the unfolding curve of a protein, which is composed of same structural elements, i.e. Ei appears n times in the protein, is same with that of Ei, the
According to thermodynamics the
3. Typical multistate unfolding curves
Three-state unfolding curves
From eq(8) three-state unfolding curve is dependence on
Of course, if the difference of
When n is 4 the unfolding curve appears three transitions from eq(10). The four-state unfolding curve is a function of
4. Structural element
Structural element is a smallest structural unit in native protein, of which the unfolding obeys two-state model.
Native proteins are only marginally entities under physiological conditions. There are various no covalent bonds to which protein is subject—electrostatic interactions (both attractive and repulsive), hydrogen bonding (both intramolecular and to water), and hydrophobic force, over an entire protein molecule. The low conformational stabilities of native proteins make them easily susceptible to denaturation by altering the balance of the weak nonbonding forces that maintain the native conformation. Native protein structure unfolds in a highly cooperative manner: Any partial unfolding of the structure destabilizes the remaining structure, which must simultaneously collapse to the random coil.
It has been shown that the unfolding or folding of small globular proteins occurs via a two-state process, whereas the unfolding or folding of larger proteins is complex and often involves the formation of intermediate [9]. Thioredoxin is characterized by an active site containing two cysteine residues separated by two other residues. The reversible oxidation of these cysteine residues to the disulfide form serves as a redox couple for a number of biological reactions. It was first characterized in yeast for its role in the reduction of methionine sulfoxide and inorganic sulphate[10, 11]. The backbone of oxidized form and ribbon model of reduced form for Escherichia coli thioredoxin are shown in Figure 9. The protein consists of single polypeptide chain of 108 amino acid residues. Either the oxidized or the reduced forms the protein is a compact molecule with 90% of its residues in -helices, -strands or reverse turns, which a core of twisted -strand is flanked on either side by -helices. The conversion between the oxidized and the reduced forms is accompanied by a change in conformation that is reflected in the fluorescence properties of Trp28.
The equilibrium unfolding of the oxidized form of Escherichia coli thioredoxin at pH 7 was studied by Santoro and Bolen [1] using guanidine hydrochloride (GdnHCl) and urea as denaturant at 25 C by monitoring the changes in ellipticity at 222nm.
The GdnHCl- or urea-induced unfolding of thioredoxin is a two-state process. The unfolding free energy change is 7.8±0.2 kcal/mole (32.64±0.84 kJ/mole) in the absence of (GdnHCl) or 8.6±0.9 kcal/mole (35.98±3.77 kJ/mole) in the absence of urea. Thermal unfolding measurements give G0(H2O) being 8.1±0.1 kcal/mole (33.89±0.42 kJ/mole) by using differential scanning calorimetry. Within error, G0(H2O) values obtained from GdnHCl- and urea-induced, and thermal unfolding are in agreement, meaning that GdnHCl, urea, and thermal unfolding involve the same native form to unfolding form equilibrium in oxidized form of Escherichia coli thioredoxin.
The free energy required to denature a protein is ~ 0.4 kJ/mole of amino acid residues so that 100-residue protein is typically stable by only around 40 kJ/mole [12]. Since the measured G0(H2O) of thioredoxin is close to 40 kJ/mole, the compact protein molecule can be considered as a structural element.
Goat -lactoglobulin consists of single polypeptide chain of 101 amino acid residues. The protein contains - helices (red) and - sheets (yellow) as shown in Figure 10. The measured G0(H2O) is 11.7±0.8 kcal/mole (48.95±3.35 kJ/mole) at 25 C by measuring optical rotation [13]. -lactoglobulin can be considered as a structural element. Although -chymotrypsin consists of single polypeptide chain of 178 amino acid residues the G0(H2O) is only 8.3±0.4 kcal/mole (34.73±1.67 kJ/mole) at 25 C by measuring optical rotation [13]. If the G0(H2O) of a 100-residue protein were 40 kJ/mole, the G0(H2O) of -chymotrypsin would have been around 70 kJ/mole at 25 C. It means that -chymotrypsin contains same structural elements at least two.
Human serum albumin (HSA) has been used as a model protein for protein folding and ligand-binding studies over many decades [5, 14-19]. The protein is a single chain protein with 585 amino acids, with a molecular weight of ~67,000 Da. Serum albumin homologs with very similar properties are found in other mammals. The protein contains only - helices. The structure of this protein has been determined by X-ray crystallography of high resolution (Figure 11); it includes three homologous domains (I-III) that assemble a heart-shaped molecule. Each domain is formed by two subdomains that possess common structural motifs. Only one cysteine residue located at position 34 (in domain I) with a free sulfhydryl group. HSA plays a special role in transporting metabolites and drugs throughout the vascular system and also in maintaining the pH and osmotic pressure of plasma. Interestingly, the structure and dynamics of HAS are known to be influenced by a number of factors, like pH, temperature, and binding of different ligands.
Denaturation of HSA has been studied by several workers using different methods like absorption difference at 287nm, fluorescence at 340nm upon excitation at 282nm, tryptophan fluorescence upon excitation at 295nm, ellipticity at 222nm, 1-anilinonaphthalene-8-sulfonate fluorescence, differential calorimetry, etc. Denaturation of HSA has been suggested to follow a single-step transition as well as two- or multiple-step transitions depending upon the reaction conditions and probes used. For example, urea denaturation of HSA has been shown to follow a two-step, three-state transition involving one intermediate when studied by fluorescence and ellipticity measurements but became single-step, two-state transition when studied by UV difference spectroscopy. Similarly, guanidine hydrochloride (GdnHCl) denaturation of serum albumin has been reported to follow both single-step and two-step transitions [16]. Meanwhile the measured G0(H2O) has big difference. The measured G0(H2O) is 5.98 kcal/mole (25.02 kJ/mole) and 6.00 kcal/mole (25.10 kJ/mole) at 25 C, 1M KCl pH 7.0 by measuring circular dichroism and fluorescence, respectively [5]. In the presence of 2,2,2-trifluoroethanol the measured G0(H2O) is 8.04 kcal/mole (33.64 kJ/mole) and 8.06 kcal/mole (33.72 kJ/mole) [15]. 2,2,2-trifluoroethanol makes the G0(H2O) increase around 2 kcal/mole. Halim et al [16] used bromophenol blue as a probe the G0(H2O) of bovine serum albumin is 4.04 and 4.60 kcal/mole, respectively, from urea and GdnHCl two-state denaturation curves at pH 8.0, 25 C. However, the G0(H2O) of HSA is 146.7 kJ/mole from sodium dodecyl sulphate two-state denaturation curves at pH 7.0, 35 C [17]. It means that HAS is a multi-element protein. When the structural elements are same at the experimental conditions the unfolding of HAS is a two-state process, and when the structural elements are different at another experimental conditions the unfolding behaves as a three-state process.
Urea-induced unfolding of bovine serum albumin and one of its fragments containing domain II+III has been studied by difference spectral and fluorescence emission measurements. The unfolding-refolding curves of both the proteins showed the presence of at least one stable intermediate when the transition was monitored at 288 nm. The presence of the intermediate was not detectable at 293 nm where only tryptophan contributed towards the protein absorption. However, both the proteins did show the presence of intermediate when the denaturation was monitored fluorometrically. Since domain III of the albumin is devoid of tryptophan, it is concluded that the formation of intermediate in the unfolding-refolding transition of serum albumin involves (i) unfolding of domain III, (ii) minor structural transformations in domain II, and/or (iii) the separation of the sub-domains of domain III from each other [15-17].
5. The factors affected structural element
Acquisition of native globular conformation (3D structure) of a protein is governed by its structural elements and biological environment surrounding it. The stability of protein’s 3D structure is endorsed by various intramolecular forces, such as hydrogen bonds, van der Waals, electrostatic and hydrophobic interactions involving various amino acid side chains as well as their milieu in the native structure. So protein structure is affected by factors such as experiment conditions (extreme temperature, pH and pressure) and presence of destabilizing agents (salt, alkali, denaturant and surfactant), and of stabilizing agents (metal ions, anions and small organic molecules) [15-19]. In fact they are the factors which structural element is affected. A few examples are given to show the effect of stabilizing agents on structural element.
Anticoagulation factor I (ACF I) isolated from the venom of
[D]1/2/M | -m/(kcal/M/mole) | |||||
Holo-ACF I | F↔Ia | Ia↔Ib | Ib↔U | F↔Ia | Ia↔Ib | Ib↔U |
Unfolding | 0.66±0.02 | 1.60±0.04 | 2.52±0.05 | 3.76±0.09 | 3.63±0.04 | 2.59±0.02 |
Refolding | 0.67±0.03 | 1.59±0.02 | 2.55±0.06 | 3.70±0.05 | 3.79±0.10 | 2.77±0.08 |
G0/(kcal/mole) | ||||||
Holo-ACF I | F↔Ia | Ia↔Ib | Ib↔U | total | ||
Unfolding | 2.51±0.04 | 2.21±0.02 | 1.29±0.03 | 6.01±0.09 | ||
Refolding | 2.60±0.07 | 2.16±0.03 | 1.31±0.02 | 6.07±0.12 |
The guanidine hydrochloride induced unfolding of apo-ACF I is a two-state process with no detectable intermediate state, whereas the unfolding of holo-ACF I follows a three-step transition, with intermediate state Ia and intermediate state Ib. The thermodynamic parameters for unfolding and refolding of ACF I are shown in Table 1 [6]. The unfolding data can be fitted by using eq (3) for two-state process of apo-ACF I and eq (10) for four-state process of holo-ACF I, respectively.
Using the new method it can be thought that ACF I is consisted of multi-structural elements, and the structural elements are same in apo-ACF I in guanidine hydrochloride. The stability of structural element can be described by parameters [D]1/2 (1.22M) and m (-4.06 kcal/M/mole), i.e. G0(H2O) is 4.96 kcal/mole. After binding Ca2+ the structural elements are changed. At least three-kind structural elements appear in holo-ACF I. Their stability is 4.22 kcal/mole, 7.07 kcal/mole, and 5.95 kcal/mole, for structural element 1, 2, and 3, respectively.
Parameters of [D]1/2 and m values are 0.85M and -4.96 kcal/M/mole, 1.56M and -4.53 kcal/M/mole, 2.56M and -2.32 kcal/M/mole, for structural element 1, 2, and 3, respectively. The unfolding of holo-ACF I
where
If using the stability of structural element in apo-ACF I as standard the binding of Ca2+ makes structural element 1 be destabilized and 2 and 3 be stabilized. Of the various forces, hydrogen bonding and hydrophobic effect have been shown to make significant contribution to the protein stability. Being secondary contributor to protein’s stability through salt bridges, charged residues have also been found important in manipulating protein stability [20]. It is that Ca2+ binding breaks the balance of charged residues makes the charged residues in apo-ACF I re-distribute and form new structural elements in holo-ACF I.
Second example is succinylation-induced conformational destabilization of lysozyme as studied by guanidine hydrochloride denaturation [20]. Figure 13 shows the crystal structure of lysozyme which is made up of a single polypeptide chain of 129 amino acid residues arranged in the form of two domains and stabilized by four disulphide bonds. All six lysine residues are distributed in the molecular surface and all six tryptophan residues are located at -helices and loops. The unfolding of the protein obeys two-state process, meaning that the protein is consisted of same structural element(s). Using fluorescence data upon excitation at 280nm value of
Third example is HAS, whose crystal is shown in Figure 11. In the presence of different concentrations of KCl urea-induced denaturation of HAS displays different pathways. When the concentration of KCl is 1.0M HAS undergoes a single-step transition with no intermediate. At pH 7.0, 25 C the variation of G as a function of urea concentration is presented in Figure 14A (curve 2). According to eq (5)
However, the authors [5] reported
In my views the calculation of
where
According eq (12) the
6. The unfolding of CopC
The protein CopC of
The fluorescence properties of tryptophan residues in protein can be considered as three discrete spectral classes: One is the buried in nonpolar regions of the protein, the fluorescence maximum position appears at 310~330 nm and spectral band width is around 48~49 nm: two is located at the surface of protein and completely exposed to water, maximum peak is in 350~353 nm and half bandwidth is in the range of 59~61 nm; the latter is in limited contact with water which is probably immobilized by bonding at the macromolecular surface, the fluorescence maximum peak is located at 340~342 nm and the half bandwidth is about 53~55 nm.
Figure 16 is the spectra of apoCopC in different experimental conditions. In the presence of 9.4 M urea the fluorescence peak of apoCopC locates at 353 nm and the half bandwidth reaches to 60 nm (Figure 16 spectrum 3), meaning that apoCopC exists in unfolding state. In the absence of urea the fluorescence peak of native apoCopC appears at 320 nm and the half bandwidth is 48 nm (Figure 16 spectrum 1), meaning that the tryptophan residue 83 is buried in nonpolar regions of apoCopC. In the presence of 5.0 M urea the fluorescence peak appears at 331 nm and the half bandwidth reaches to 66 nm (Figure 16 spectrum 2).
Obviously spectrum 2 is the summing of spectra produced by two-class tryptophan residue in protein(s). With the increasing of urea concentration an iso-fluorescence point keeps at 332nm from spectrum 1 to spectrum 3, meaning that there are two species of apoCopC in the presence of 5.0 M urea. Curve 4 (red line) in Figure 16 is fitted from spectrum 1 and 2, in which the contribution of spectrum 1 is 0.73 and that of spectrum 2 is 0.27. It can be seen that the fitted curve is nearly coincided with the measured spectrum. In the presence of 5.0 M urea apoCopC exists in native and completed unfolding forms. The fluorescence property of tryptophan residue 83 in apoCopC is an index to show the protein in either native or unfolding states. It can be deduced that the unfolding of apoCopC would obeys two-state mechanism.
When the tryptophan residue 83 is mutated as leucine residue the protein is nearly immeasurable by fluorescence. Meanwhile the mutagenesis make the ability of binding to Cu(II), the thermal stability of apoCopC be decreased [28]. The important role of the tryptophan residue 83 is not only in using as a fluorescence probe but also in keeping the -sandwich hydrophobic structure. The thermodynamic stability apoCopC can be investigated at pH 7.4 by monitoring the fluorescence intensity at around 405 nm [25, 29, 30]. As known Cu2+-CopC and Hg2+-CopC-Hg2+ are prepared by adding Cu(II) or Hg(II). The unfolding of apoCopC, Cu2+-CopC and Hg2+-CopC-Hg2+ are reversible. According to two-state model, the free energy change can be measured, respectively, and the order of stability is Cu2+-CopC > Hg2+-CopC-Hg2+ ~ apoCopC. The binding of Cu(II) makes the stability of CopC be increased greatly. Although Hg(II) can also binding the Cu(II) site the contribution to the stability can be neglected. The reason is the weak binding of Hg(II) to the sites of apoCopC.
Using guanidine hydrochloride as chemical denaturant the unfolding profiles are presented in Figure 17 by monitoring the changes of fluorescence ratio at 400nm and 320nm. ApoCopC unfolds in two-state equilibrium reaction. It means that apoCopC is consisted of a kind of structural element(s). The
The corresponding GdnHCl-induced unfolding with Cu2+-CopC reveals some difference. If the unfolding were considered as two-state process the GdnHCl-concentration at transition midpoint would have been 2.06 M which is higher than 1.55 M, and the dependence of ∆G on GdnHCl concentrations would have been as inset in Figure 17. Indeed the binding of Cu(II) makes the transition midpoint of apoCopC from 1.55 M shift to 2.06 M and stabilize the protein. However, there are evidently two slopes in dependence of ∆G on GdnHCl concentrations (Inset of Figure 17). This indicates that the equilibrium-unfolding reaction is three-state process, involving an intermediate species populated at 1.4 to 1.7 M guanidine hydrochloride [7].
Protein | Denaturant | -m kJ/M/mole | [D]1/2 M | kJ/mole | |
apoCopC | GdnHCl | 16.16±0.22 | 1.55 | 24.98±0.31 | |
Urea | 4.32±0.18 | 5.61 | 24.24±1.04 | ||
CopC-Ag+ | GdnHCl | 15.74±0.27 | 1.55 | 24.33±0.41 | |
-mFI kJ/M/mole | -mIU kJ/M/mole | kJ/mole | kJ/mole | kJ/mole | |
Cu2+-CopC | 8.83±0.31 | 19.86±0.18 | 12.83±0.31 | 42.52±0.30 | 36.82 |
Cu2+-CopC-Ag+ | 7.67±0.25 | 18.930±0.23 | 10.54±0.28 | 45.08±0.43 | 36.71 |
Cu2+-Y79W-W83F | 9.78±0.36 | 21.27±0.31 | 12.33±0.39 | 44.22±0.66 | 37.80 |
Urea –induced | |||||
Cu2+-CopC | 2.21±0.03 | 4.35±0.07 | 9.71±0.13 | 36.70±0.54 | 29.36 |
According to the new model the structural element(s) of apoCopC is changed by the binding of Cu(II), from one-kind structural element(s) changing to two-kind structural elements, which one is more stable than another. Naturally the equilibrium-unfolding reaction of the protein displays three-state behavior. The data (●) measured guanidine hydrochloride experiment with Cu2+-CopC are fitted well in eq (19).
where
Cu2+-CopC is consisted of two-kind structural elements. Thus the unfolding profile appears to involve two sequential transitions. The first transition corresponds to the unfolding of structural element one, whose free energy change is 12.83 kJ/mole and the guanidine hydrochloride concentration at the transition midpoint is 1.53 M, close to 1.55 M of apoCopC or apoCopC-Ag+. The second transition corresponds to the unfolding of another, whose free energy change is 42.52 kJ/mole and the guanidine hydrochloride concentration at the transition midpoint is 2.12 M. The probability of one appeared in the protein is 0.19 and another is 0.81. This indicates that the binding of Cu(II) makes the secondary structure of 81% integrative apo-CopC be stabilized. The stabilized energy ∆∆G0Cu(II) is 11.84 kJ/mole. Since Cu(II) binds at N-terminal of apoCopC the first transition corresponds to the partial unfolding of apoCopC and it is the part the C-terminal of apoCopC.
Using urea as chemical denaturant the unfolding of Cu2+-CopC shows three-state process. The free energy change is calculated to be 29.16 kJ/mole by using the new model. The stabilized energy ∆∆G0Cu(II) is only 4.18 kJ/mole. At pH 7.4 apoCopC is a protein charged positively since the pI of the protein is 8.27. After binding of Cu(II) the positive charges of the protein is increased and anion ions would make Cu2+-CopC be stable. As an ionic denaturant, guanidine hydrochloride makes Cu2+-CopC be stable.
In a similar way the unfolding of Cu2+-CopC-Ag+ is studied by measuring the fluorescence ratio at 320 nm and 400 nm. Two transitions appear in the unfolding profile (Figure 17). Corresponding to the unfolding of C-terminal the first transition midpoint is shifted from 1.53 M to lower guanidine hydrochloride concentration (1.42 M), while the second transition midpoint is shifted from 2.12 M to higher guanidine hydrochloride concentration (2.38 M). Comparing with Cu2+-CopC the binding of Ag(I) makes structural element one be unstable and structural element two be stable. This means that the structural element one and two are affected by the binding of Ag(I). Although the structural elements are marked as structural element one and two in Cu2+-CopC-Ag+, they are different with that in Cu2+-CopC.
The data (■) of Cu2+-CopC-Ag+ are fitted well in eq (21).
It is noticed that
Hydrogen bonding and hydrophobic forces have major influence to the structure of native protein. Some molecules are often used in researching stability of native proteins since their perturbation on the hydrogen bonding and hydrophobic forces [31, 32]. Apo-Y79W-W83F is a mutant of apoCopC, in which tyrosine residue 79 is mutated as tryptophan and tryptophan residue is did as phenylalanine. As shown in Figure 18A the fluorescence spectrum of apoY79W-W83F is dominated by tryptophan residue at position 79 and centered at 328 nm. Comparing the fluorescence spectrum of apoCopC the maximum peak is shifted toward to red around 8 nm and the tryptophan residue is yet a typical for buried tryptophyl side chains in apolar environment. The protein binds one equivalent of Cu(II) with high affinity and the fluorescence at 328 nm is quenched[33].
Since the hydrogen bonding and hydrophobic forces in apoCopC are changed, the GdnHCl-induced unfolding profile of apo-Y79W-W83F shows an obvious two transitions. According to the new model apo-Y79W-W83F is consisted of two-kind structural elements, the unfolding curve can be fitted from
Figure 18B shows GdnHCl-induced unfolding of Cu2+-Y79W-W83F (O). Analyzing the unfolding data according to two-state unfolding model, the free energy changes plotted as a function of denaturant concentration are an obviously inflection point, suggesting that GdnHCl-induced unfolding of Cu2+-Y79W-W83F does not proceed via a simple two-state process but involves one intermediate state. Using eq (8) the unfolding data of Cu2+-Y79W-W83F in Figure 18B can be fitted well.
Tryptophan residue 83 locates at N-terminal and tyrosine residue 79 locates at C-terminal of apoCopC. After binding Cu(II) the positions of the residues have no large change (Figure 15). Two transitions are observed in GdnHCl-induced unfolding profiles of Cu2+-CopC-Ag+, Cu2+-CopC, and Cu2+-Y79W-W83F. The first transition corresponds to the unfolding of C-terminal and second does to that of N-terminal. It can be seen that the mutation from tryptophan to phenylalanine residue at position of 83 makes the N-terminal stability be increased, while the mutation from tyrosine to tryptophan residue makes the C-terminal stability be decreased a little. This indicates that the aromatic ring stacking at position 83 plays an important role in keeping the secondary native structure of apoCopC.
7. Summary
A new model to calculate the free energy change of proteins unfolding is presented. In the new proposed model proteins are consisted of different structural elements; the unfolding of structural element obeys two-state mechanism and the free energy change of the element can be obtained by using linear extrapolation method; if the protein is consisted of same structural elements unfolding of the protein displays a two-state process, while the unfolding of the protein shows a multi-state behavior; A least-square fitting is used to analyze the contribution of structural element to the protein and free energy change of the protein is the probable summing of all structural element. The model can be used to analyze and compare the stability of proteins, which are similar in size and structure.
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