Evidences for the unfolding mechanism of three-dimensional domain swapping

The full or partial unfolding of proteins is widely believed to play an essential role in three-dimensional domain swapping. However, there is little research that has rigorously evaluated the association between domain swapping and protein folding/unfolding. Here, we examined a kinetic model in which domain swapping occurred via the denatured state produced by the complete unfolding of proteins. The relationships between swapping kinetics and folding/unfolding thermodynamics were established, which were further adopted as criteria to show that the proposed mechanism dominates in three representative proteins: Cyanovirin-N (CV-N), the C-terminal domain of SARS-CoV main protease (Mpro-C), and a single mutant of oxidized thioredoxin (Trx_W28Aox).


Introduction
Three-dimensional domain swapping is a special form of protein oligomerization, where monomers exchange one or more identical structural elements (ranging from secondary structure elements to whole structural domains) to form complexes. 1 Currently, more than 500 domain-swapped structures have been solved. 2 An analysis in the protein structural space suggested that domain swapping is a general property of proteins. 2 Domain swapping possesses many potential biological implications. 1,3 It acts as a mechanism for regulating protein function, and as an evolutionary strategy to create protein complexes. This process is also involved in protein misfolding and aggregation.
In comparison with conventional protein-protein interactions, 4 domain swapping has two distinct kinetic features. First, the interconversion between the monomer and the domain-swapped dimer is generally very slow. [5][6][7] The equilibrium process may take days or even months. Second, the interconversion rate is very sensitive to temperature. 5,6,8,9 An increase in temperature by 3À4 C is sufficient to produce an overall increase of the conversion rate by 10-fold. 8,9 The extracted enthalpy component of the activation barrier is larger than 100 kcal/mol. These behaviors are closely related to the folding/unfolding process of proteins. In an extreme model (the unfolding mechanism for domain swapping), 6,8,10 it was proposed that domain swapping proceeds via complete unfolding, so the swapping kinetics can be explained in terms of the equilibrium folding/unfolding properties of proteins. Very recently, a study on Cyanovirin-N indeed verified that the energy barrier of domain swapping is very close to the equilibrium unfolding enthalpy of the protein. 8 However, there were also some doubts on the feasibility of the unfolding mechanism of domain swapping. 9,11 The main concern is that the population of the fully unfolded state is too low to account for the observed swapping rate. 9,11 In addition, careful examination with rigorous formalism is necessary to distinguish domain-swapping via fully unfolded states from domain-swapping via partially unfolded states. For example, the rigorous derivation of the unfolding mechanism for domain swapping predicts that the enthalpy barrier of domain swapping is two times that of the equilibrium unfolding enthalpy of the protein monomer (will be given below), and not onefold as that defined previously. 8 Here, we examined the kinetic properties of domain swapping under the unfolding mechanism and analyzed the experimental swapping data in combination with the folding/unfolding data of three proteins: Cyanovirin-N (CV-N), the C-terminal domain of SARS-CoV main protease (M pro -C), and a single mutant of oxidized thioredoxin (Trx_W28A ox ). The results showed that domain swapping in all three systems are well described by the unfolding mechanism when the heat capacity difference between the native and denatured states in protein folding/ unfolding is appropriately addressed.

Results
Formalism of the unfolding mechanism for domain swapping In general, domain swapping is described by a dimerization reaction: with the equilibrium dissociation constant The time evolution of monomer and dimer concentrations is given as (see Supporting Information): Equation (2) is generally applicable to various domain swapping processes no matter whether they proceed via complete or partial unfolding. It can be used to fit the experimental kinetic data of domain swapping to extract the constants k on , k off, and K d . It is noted that , the denominator on the right side of Eq. (2) is approximately a constant independent on time t, and thus, the kinetics can be described by a single exponential as observed previously. 8,9 When domain swapping occurs by the unfolding mechanism, i.e., swapping proceeds via complete unfolding, the process is subdivided as: where k u and k f are the unfolding and folding rate constants, respectively, and the superscripts ''(M)'' and ''(D)'' denote the monomer and dimer proteins. U is the denatured monomer and U*U is an encounter complex where two monomers come close to each other but do not essentially interact. The equilibrium dissociation constant of the global domain swapping process is thus: where K are the unfolding equilibrium constants for monomer and dimer, respectively, while K ðUÞ d is the dissociation constant for the step 2U $ U*U . Under the steadystate assumption and the condition that folding rates are fast (which operates when the denatured states are highly unstable), the time evolution of process (4) can be reduced into process (1) with the corresponding parameters (see Supporting Information): This is the main results for the unfolding mechanism of domain swapping. It relates the kinetics of domain swapping to the equilibrium of protein folding/unfolding. By introducing variations (e.g., temperature, denaturant, and mutation) that change the protein stability, Eq. (6) can be critically assessed by examining the quantitative relation between the swapping kinetics and the unfolding thermodynamics. For example, when the temperature is raised to change the domain-swapping rate, Eq. (6) gives that: where DH ‡ on is the enthalpy barrier of k on and DH ‡ off is the enthalpy barrier of k off . DH On the other hand, the temperature dependence of K d is usually much smaller than that of k on and k off , so it is derived from K d ¼ k off /k on that: The relationships can be summarized as: Therefore, the kinetic barrier of domain swapping is two times the equilibrium unfolding enthalpy of the monomer and one time the equilibrium unfolding enthalpy change of the dimer. This provides a criterion for the unfolding mechanism of domain swapping. The k ðUÞ on and k ðUÞ off can also be extracted from Eq. (6) to see whether they lie in a reasonable range.
Equations (6) and (10) apply for domain swapping which proceeds via complete unfolding. When swapping proceeds via partial unfolding, there would be no correlation between the swapping kinetics and the global protein stability, and thus Eqs. (6) and (10) are not applicable. Swapping via partial unfolding is still described by Eqs. (2,3), but the thermodynamics of partial unfolding should be instead used to relate to the swapping kinetics of domain swapping. Because the free energy for partial unfolding is usually not as high as that for complete unfolding under native conditions, the interconversion rate for swapping via partial unfolding should be faster and less sensitive to the temperature.
In the following sections, we examined three domain-swapped proteins whose swapping kinetics and folding/unfolding thermodynamics are available in the literature, and showed an agreement between the predictions and the experimental data.
Case study 1: Cyanovirin-N The protein CV-N is a potent inhibitor of the human immunodeficiency virus and many other viruses. 12 CV-N is composed of 101 amino acids and exists in both a monomer and a domain-swapped dimer. 13 Recently, Liu et al. 8 found that the swapping enthalpy barrier is very large and of similar magnitude to the equilibrium unfolding enthalpy of the monomer and dimer, and concluded that domain swapping proceeds via the unfolding mechanism. However, although DH ‡ % DH ðDÞ u was verified, a relation of DH ‡ % DH ðMÞ u was observed in their work rather than the predicted DH ‡ % 2DH ðMÞ u presented in Eq. (10). In addition, they observed that the domain swapping reaction exhibited a single exponential time dependence, which was then used to support the suggestion that the rate-limiting step is M!U. Consequently, we decided to re-examine their data.
In fact, the kinetic data of Liu et al. 8 can be well described by Eq. (2). In Figure 1, we refit the conversion data of Liu et al. 8 from the wild-type (wt) CV-N domain-swapped dimer to the monomer using Eq.
(2) and the enthalpy barrier relation: where T 0 is a reference temperature. It can be seen from Figure 1 that the agreement between the experimental data and Eq. (2) is excellent even if only four parameters were used to globally fit six curves. The discrepancy of Eq. (2) from single exponential behaviors is reflected in the factor The ratio of D ½ t¼0 À D ½ eq . ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is calculated to be only 0.024, so it is not surprising that the factor y is very close to 1, as shown in the inset of Figure 1. This explains why the experimental data can also be fitted by a single exponential in Liu et al. 8 Such a property is expected to apply also to other proteins when experiment conditions strongly favor the formation of the monomer ([M] total ¼ 2[D] total ( K d ). As a result, the enthalpy barrier DH ‡ extracted from our fitting (151 kcal/mol) is very close to that derived from the single exponential fitting (145/153 kcal/mol). 8 On the problem why DH ‡ % DH ðMÞ u instead of DH ‡ % 2DH ðMÞ u was observed by Liu et al., 8 we found that the answer lies in the large heat capacity difference (DC p ) between the denatured and native proteins. 14 The equilibrium unfolding enthalpy (DH ðMÞ u ) was usually measured from thermal melting curves so that its value is applicable near the melting temperature (T m ), while the domain swapping kinetics was measured at lower temperatures, where, according to the equation of: the corresponding DH ðMÞ u should be lower than that at T m . By incorporating the effect of DC p , we recovered the relation of DH ‡ % 2DH ðMÞ u for CV-N as follows: 1 For the CV-N P51G monomer, Table II of Liu et al. 8 gave DH u (T m ) ¼ 130 kcal/mol, and Ref. 15 gave T m ¼ 71.2 C. We did not find the corresponding DC p in the literature, so we made use of the experimental fact 16 of DG u (20 C) ¼ 9.8 kcal/mol and the equation: to estimate DC p to be 2.38 kcal/(molÁK). Therefore, DH ðMÞ u at the temperature of the swapping measurement ($329 K) is determined to be 93.5 kcal/ mol, and thus 2DH ðMÞ u ¼ 187 kcal/mol, which is close to the observed DH ‡ (162 kcal/mol) for swapping kinetics. 8 8 3 For the dimer, DH u (T m ) of CV-N P51G and CV-N DQ50 were reported by Liu et al. 8 However, for dimers which are less stable than monomers, their unfolding is usually coupled with a dimer-monomer transition and the extracted unfolding thermodynamics may be problematic. We have ignored the less stable CV-N P51G dimer, and only discussed CV-N DQ50 that exists solely as a domain-swapped dimer. The T m of CV-N DQ50 dimer is 50.2 C, which is close to the swapping temperature ($325 K) of wt CV-N. Thus, we directly estimated the DH ðDÞ u of the wt CV-N dimer at the swapping temperature as the DH u (T m ) value (142 kcal/mol) of CV-N DQ50 , which is almost identical to the experimental DH ‡ value (145/153 kcal/mol) 8

of wt CV-N.
Case study 2: M pro -C M pro , the main protease of the SARS coronavirus (SARS-CoV), is a key target for structure-based drug design against SARS. 17 The C-terminal domain of M pro (M pro -C) was found to exist in both monomeric and domain-swapped dimeric forms. 18 Unlike many other domain-swapped proteins, the swapped element of M pro -C is fully buried inside the hydrophobic core rather than at the protein surface, which makes the unfolding mechanism of domain swapping more probable to occur in this system. 19 On the other hand, Kang et al. 9 recently measured the swapping kinetics and the folding/unfolding thermodynamics, and concluded that it is thermodynamically impossible for M pro -C to swap through fully unfolded states.
A main reason for this suggestion is that k ðUÞ on calculated from Eq. (6) greatly exceeds the typical protein association rate constants. 9 However, after considering the influence of DC p , we found that the conclusion may change. From Kang et al. 9   ðUÞ on is determined from Eq. (6) to be 7.7 Â 10 5 M À1 s À1 , which is a typical protein association rate limited by diffusion. 4 Consequently, the doubt on the feasibility of the unfolding mechanism may be dismissed.
Kang et al. have also constructed various mutants of M pro -C and measured their thermal stability and domain swapping kinetics. 9 By redrawing their data in Figure 2, it is clearly demonstrated that, despite some fluctuations, there is a tight correlation between k on and T m . This result strongly suggests that the change in the swapping kinetics of the mutants is simply because of a change in the protein thermal stability. A linear fitting to ln k on $ 1/T m gives an effective enthalpy difference of 388 kJ/mol, which is very similar to the observed swapping DH ‡ value (373/433 kJ/mol). 9 The calculated k ðUÞ on for the mutants falls in the range of 1.0-16.9 Â 10 5 M À1 s À1 (Supporting Information Table S1), the majority of which are close to that for the wide-type. The consistence among k ðUÞ on for the wide-type and various mutants of M pro -C lends support to the unfolding mechanism, i.e., swapping proceeds via complete unfolding.
It is noted that the state U*U in Eq. (4) is not well established, so the physicochemical meaning of the parameters such as k ðUÞ on may depend on the system. In the unfolding mechanism we discussed, U*U is assumed to be made of two completely unfolded monomers. If swapping proceeds via partial unfolding, then U*U should be composed of partially unfolded monomers and the derived swapping kinetics would relate to the thermodynamics of partial unfolding. Thus, there does not exist a tight correlation between the swapping kinetics and the global protein stability for swapping proceeds via partial unfolding.
Case study 3: Trx_W28A ox Thioredoxin (Trx) plays an essential role in many biological processes, including cellular redox balance, promotion of cell growth, and inhibition of apoptosis. 20 Garcia-Pino et al. showed that a single active-site mutation on the oxidized form (Trx_W28A ox ) converts the protein into a biologically inactive domain-swapped dimer. 21 The swapped dimer of Trx_W28A ox is a kinetically trapped species. Its unfolding is not reversible, i.e., it spontaneously refolds to the monomer after thermal unfolding. (In Garcia-Pino et al., 21 the transition was written as S 2 !2I, which is synonymous to our notation of D!2M here. For the unfolding of monomer, the van't Hoff enthalpy instead of the calorimetric enthalpy was assigned to DH ðMÞ u since van't Hoff enthalpy better reflects the properties of denatured population.) In other words, the K d is very large in this system and the measured swapping kinetics is mainly determined by k off . Based on Table III  value is very similar to the measured swapping kinetic barrier DH ‡ (120 kcal/ mol), 21 suggesting the unfolding mechanism to be responsible for the domain swapping of Trx_W28A ox . Figure 2. Correlation between the domain-swapping association rate (k on ) at 37 C and the melting temperature (T m ) for wt and mutants of M pro -C. The experimental data were taken from Table I of Kang et al. 9 The wild-type is high-lighted by using an open circle. The solid line is a linear fit to the data.

Discussion
Although there is currently no unifying molecular mechanism describing domain swapping, it is generally believed that the monomer should be fully or partially unfolded in swapping. However, criteria should be developed to rigorously test any proposed mechanism. In this article, we established the formalism of the (fully) unfolding mechanism for domain swapping and used the obtained criteria to analyze the properties of three representative proteins. We are not suggesting that the unfolding mechanism is universal for all swapped proteins since each protein may behave in a distinct manner; however, the criteria presented were met in the examined proteins. Therefore, the unfolding mechanism probably dominates in these example systems.
The developed formalism can be extended to describe other experiments of domain swapping. For example, when denaturants are used to increase the rate of the swapping kinetics, it is predicted from the unfolding mechanism that the slope of the logarithmic swapping rate as a function of the denaturant concentration is two times as that of the unfolding equilibrium constants for the monomer. This remains to be verified in future work.
It should also be interesting to explore the mechanism where proteins are partially unfolded in swapping. By measuring the equilibrium of the partially unfolded forms by techniques such as native-state hydrogen exchange, 22 the connection between swapping kinetics and the partial unfolding thermodynamics may be established and be tested similarly.

Materials and Methods
Details on the formalism of the unfolding mechanism for domain swapping are described in the Supporting Information.

Conclusions
In conclusion, we have established formulism of domain swapping under the unfolding mechanism, and used the obtained criteria to test a number of protein systems by combining their swapping kinetics with available folding/unfolding equilibrium data. The results suggest that the domain swapping of CV-N, M pro -C, and Trx_W28A ox is dominated by the unfolding mechanism.