2.1 Protein purification

Wild-type cmFDH was prepared and purified as described previously [6]. SDS–PAGE and Coomassie Brilliant Blue staining showed the protein to be >95% pure after purification. Protein concentration was estimated at 280 nm from its specific extinction coefficient, 49 170 cm⁻¹ M⁻¹, and expressed in terms of the monomeric protein concentration using monomer mass of 42 000 Da.

2.2 Equilibrium unfolding assay of cmFDH

Unfolding experiments were performed by using 0.1 and 1 μM protein. Protein samples were incubated in 20 mM Tris, pH 8 at a series of GdnHCl concentrations at 25 °C in previous experiments. According to results of preliminary experiments unfolding studies were carried on with 0.1 μM protein, samples were incubated at different temperatures (25, 30, 35, 40, 45 °C) for 4 h. The protein fluorescence intensity of each sample was measured between 300 and 400 nm using an excitation wavelength of 285 nm in a Spex Fluoromax spectrofluorometer. Maximum emission was obtained at 350 nm. For each sample three scans were averaged for final spectrum. Denaturation curves were analysed by assuming a two-state mechanism. Data were fitted Eq. (1) to calculate K_w by fixing the m at the mean value for all transitions with Grafit 5.

K= K w ·exp(m·D)((1))

where K _w is the D/M in water, sig _D is the signal for folded state, sig _M is the signal for unfolded state and Mo is the monomer concentration as a constant. For the analysis of equilibrium data, guanidinium hydrochloride concentration ([GdnHCl]) is converted to molar denaturant activity (D), according to the following relationship:

D = ([GdnHCl] · C _0.5)/([GdnHCl] + C _0.5), where C _0.5 is a denaturation constant with a value of 7.5 M [7].

The change in free energy between the folded and unfolded states in the absence of denaturant, ΔG_w , was calculated for each temperature (25, 30, 35, 40, 45 °C), using the ΔG = −RT ln K_w relationship. For the free-energy change associated with a particular transition with temperature, data were fitted to the following equation:

ΔG=ΔH+Δ C p ·(T‐ T o )‐T·ΔS‐Δ C p ·T·ln(T/ T o ),((2))

where ΔH(T_o ), ΔS(T_o ) and ΔC_p are the enthalpy, entropy and heat capacity changes, respectively, at a defined reference temperature (T_o ). All data were fitted using the Grafit 5 analysis software (Erithracus Software, UK).

2.3 Stopped flow unfolding experiments of cmFDH

The rate constant for unfolding at a particular concentration of GdnHCl was measured using stopped flow fluorometer (Applied Photophysics (05-109) pbp Spectra Kinetic Monochromator). One micromolar protein is jumped into 4, 4.5, 5, 5.5 and 6 M GdnHCl concentrations and fluorescence decay was measured against time. Protein was excited by monochromatic light at 285 nm and the resulting fluorescence was selected with a WG320 cut-off filter. Each recorded transient was an average of at least three individual reactions. Reactions were recorded at 25 °C. Data were fitted to single exponential decay pattern. The rate constants were plotted as a function of denaturant activity to extract the rate constant for unfolding in the absence of denaturant (k_{u ( w )}) according to the following equation:

K u = k u ( w ) ·exp(‐m·D)((3))

2.4 Refolding activity assay

cmFDH enzyme was unfolded in the unfolding buffer containing 4 M GdnHCl and 20 mM DTT in 20 mM Tris pH 8, at room temperature for 2 h. Refolding assay was initiated by the dilution of 16.6 μM unfolded FDH to 0.1, 0.2, 0.3, 0.5 and 1 μM concentration in the refolding assay buffer containing 20 mM Tris pH 8, 5 mM DTT, 20 mM formate, 1 mM nicotinamide adenine dinucleotide (NAD). The production of NADH was monitored by following the increase in absorption at 340 nm spectrophotometrically to assess the refolding yield of different concentrations of FDH. Measurements were performed by using UV/VIS Spectrometer Lambda 2 for 60 min in 1 ml cuvette. For numerical analysis of the refolding curves data were globally fitted using a numerical method [8] to the system 2U → 2M → D.

2.5 Thermal denaturation

The proteins (wild-type and mutant FDHs) were aliquot and incubated at different temperatures with 2 °C intervals for 20 min as triplicate. Remaining activity measurements were performed at 25 °C in a reaction mixture containing 20 mM Tris Buffer at pH 8, 1 mM NAD⁺, 2 mM formate and 0.4 μM enzyme. Rate constants (k) were derived directly from the residual activity (A) by the following relationship:

A= A o ·exp(‐k· t inc )((4))

where t _inc is the period of incubation (in our case 1200s) and A_o is the initial activity. The free-energy barrier for unfolding as a function of temperature is described by the relationship:

k= k o ·exp(‐ΔG/(R·T))((5))

where ΔG = ΔH + ΔC_p · (T − T_o ) − T · ΔS − ΔC_p · T · ln(T/T_o ) and k_o is the rate of an unfolding reaction in the absence of an activation barrier (a value of 10⁷ s⁻¹ was taken for our analysis, see Section 3).

3.1 Equilibrium unfolding

To measure the free energy of folding of this dimeric FDH, we analysed the guanidinium-induced denaturation of the enzyme at equilibrium. Upon unfolding there is a large (∼70%) quench is the native tryptophan fluorescence and the transition to the unfolded state occurs in a single step, without intermediates, as shown in Fig. 1 . As denaturation of the dimer requires dissociation of the component subunits, this transition must be dependent upon protein concentration. To confirm this we collected equilibrium unfolding curves at two protein concentrations an order of magnitude apart and found that at the higher concentration the midpoint of the curve was shifted to higher concentrations of denaturant (Fig. 1). The data have been fitted to Eq. (1) for dimer dissociation. Owing to the equation accounting for the effect of protein concentration on the denaturation transition, both of the fit-lines produce the same value for the apparent association constant (K_a ), i.e. about 10¹³ M⁻¹. Note that this represents the equilibrium: 1 dimer = 2 unfolded monomers, so includes both folding and dissociation processes.

3.2 Thermodynamics of the folding–unfolding transition

The above experiment was performed at a series of temperatures in order to extract the thermal dependence of equilibrium unfolding. The plot in Fig. 2 shows the free-energy change (i.e. −RT · ln K_a ) for this transition as a function of temperature fitted to the Gibbs–Helmholtz equation (Eq. (2)). The data shows that, at the reference temperature of 25 °C the enthalpy change on folding (ΔH) is unfavourable (approximately +27 ± 18 kcal/mol), while the entropy change is favourable (−TΔS = −46 ± 18 kcal/mol). The heat capacity change (ΔC_p ) is −10.5 ± 1.8 kcal/mol/K; a value that is dominated by the degree of desolvation of non-polar surface during the folding process. Hence, ΔC_p is dependent on the chain-length of the protein and can be empirically estimated by the formula [9]:

Δ C p =N×‐0.015+0.13kcal/mol/K

The enzyme unfolds in a single transition involving two subunits of 364 residues hence the expected value is −10.8 kcal/mol/K, extremely close to the value of −10.5 derived from the data shown in Fig. 2.

3.3 Kinetics of folding and unfolding

The rate constant for unfolding in the absence of denaturant can be estimated from the data shown in Fig. 3 . Extrapolation to zero denaturant yield a value for the rate constant of 3.4 (±1.5) × 10⁻⁷ s⁻¹ and the Δm-value for the linear free-energy relationship, which relates to the change in solvent exposure between the folded dimeric ground state and the transition state for unfolding, is 4.6 (±) 0.1.

To analyse the folding kinetics, we measured the rate of regain of enzymatic activity from the fully unfolded state as a function of time (Fig. 4 ). The reactivation curves have a distinct lag phase followed by the acquisition of catalytic activity, showing that refolding process is rate-limited by at least two steps occurring on the same time scale. Further, one of these steps must be multi-molecular since the half-time of refolding is clearly sensitive to the protein concentration. At zero time the tangents to the refolding curves are zero, showing that the intermediate state (or states) lying between the two rate-limiting steps is devoid of activity. In any dimeric system, at least two processes must occur before the individual unfolded chains can form the active state, i.e. folding and association [10]. The simplest model that accounts for the data is an essentially irreversible uni-bi reaction: 2U → 2M → D, where U is the unfolded chain, M the folded monomer, and D is the active dimer.

Using numerical methods we globally, i.e. simultaneously, fitted the progress curves to the above kinetic model which yielded values of 1.9 (±0.4) × 10⁻³ s⁻¹ for the unimolecular folding step and 1.6 (±0.5) × 10⁴ M⁻¹ s⁻¹ for the bimolecular association of subunits. Results show a close agreement between model and data over a wide concentration range.

The monomeric intermediate of cmFDH forms active dimers at a rate which is slower than expected for a process limited by subunit diffusion in solution. Considerations based on orientational constraints and Brownian diffusion for protein associations have suggested that the basal rate should lie in the range of 10⁵–10⁶ M⁻¹ s⁻¹ [11–13]. Electrostatic attractions can enhance this rate significantly, as shown experimentally in the formation of the barnase:barstar complex [14] and the colicin:Im9 interaction [15]. In addition such charge effects have been predicted with reasonable accuracy by models developed by Alsallaq and Zhou [16]. In these studies association rates greater than 10⁹ M⁻¹ s⁻¹ were observed, which accords with the value for dimerization of the apo form of superoxide dismutase (see Table 1 ) where the second-order rate constant is 2 × 10⁹ M⁻¹ s⁻¹. Comparisons with other large proteins that fold through a unimolecular/bimolecular mechanism and for which all steps have been defined are shown in Table 1 [17–20].

At the level of simple reaction kinetics, there are at least three explanations that can account for the apparently slow association rates of the formate dehydrogenase monomers. Firstly, and most straightforwardly, the bimolecular rate might be genuinely 10⁴ M⁻¹ s⁻¹ owing to some unusually stringent orientational requirement for securing a productive interaction or owing to charge repulsion between monomers. Secondly, the monomer may be an ensemble of conformations in rapid equilibrium with each other. If only a minority population can dimerize then the apparent bimolecular rate will appear to be slower than the real value. For instance if only 1/10th of the population were competent at any one time, then the apparent second-order rate constant would be 100-fold slower than the real bimolecular constant, i.e. a real rate constant of 10⁶ M⁻¹ s⁻¹ would appear to be only 10⁴ M⁻¹ s⁻¹. Thirdly, and least intuitively, an unstable dimeric state might be formed with a rapid bimolecular constant, but be unstable at the experimentally accessible concentration of subunits. If there is a rate-limiting unimolecular isomerization of this encounter complex to form the active dimer, then the progress curve will appear second-order because of the depletion of monomers as the reaction progresses. For instance, if the bimolecular rate constant were 10⁶ M⁻¹ s⁻¹ and the dissociation rate 10¹ s⁻¹, the K_d for this rapid equilibrium would be 10⁻⁵ M. With a unimolecular rate constant for isomerization of 10⁻¹ s⁻¹ and a concentration of 10⁻⁶ M monomer (i.e. the proportion of dimer in the rapid equilibrium is 1/10th), then the renaturation reaction would be closely approximate to a second-order process with an apparent bimolecular rate constant of 10⁴ M⁻¹ s⁻¹.

The relatively slow bimolecular rate constant is combined with a slow rate of dissociation to yield a high stability for the native dimer (ΔG ^o = −14.6 kcal/mol), in keeping with other dimeric proteins of high molecular weight. This level of stability (K_d ∼ 10⁻¹³ M) means that at a micromolar concentration, less than one millionth of the enzyme is in the inactive and unstable monomeric state. It is interesting to note that the rate constant for FDH dissociation (Fig. 3) is so slow that, once formed, the dimer has a dissociative half-life of one and a half years.

3.4 Construction of a quantitative mechanism

For the simplest model there are two steps; a unimolecular folding process defined by k ₁ and k ₋₁ in the forward (U → M) and reverse direction respectively and a bimolecular process defined by k ₂ and k ₋₂. The overall equilibrium constant K_a defines the distribution D/U ², hence is the product of the two steps. However, since it requires two unfolded chains to form the dimer then:

K a =( k 1 / k ‐ 1 ) 2 · k 2 / k ‐ 2 ((6))

Making the assumption that the rate-limiting step in denaturation is dissociation (k ₋₂) then the only value in this system that is not experimentally defined is k ₋₁. This value can be deduced as follows:

k ‐ 1 =(( k 1 2 · k 2 )/( K a · k ‐ 2 ) ) 0.5 ((7))

Given values of 1.5 × 10¹³ M⁻¹ for K_a , 1.9 × 10⁻³ s⁻¹ for k ₁, 1.6 × 10⁴ M⁻¹ s⁻¹ for k ₂ and 3.4 × 10⁻⁷ s⁻¹ for k ₋₂, this relationship provides a value for the M → U step of about 1 × 10⁻⁴ s⁻¹. In this system M has no enzymatic activity and its stability is marginal, the free-energy change for this step being only 1.7 kcal/mol.

3.5 A simplified analytical method for approximating folding and assembly rates

The formal analytical equation for fitting a uni–bi kinetic systems is extremely unwieldy, therefore to extract the values for rate constants in the renaturation reaction we have used numerical fitting procedures. The numerical fitting technique employed to extract the forward rate constants in the renaturation process required good time-resolution in the data and a simultaneous analysis of the progress curves. However, in the analysis of such data, it is interesting to note that summing the individual half-lives for a bi-molecular step (t _1/2 = 1/(k _bi × M_o ) and a unimolecular step (t _1/2 = ln 2 × k _uni) provides a tolerably close approximation to the overall half-time of refolding. If we use the approximation that the measured t _1/2 = 1/(k _bi × M_o ) + ln 2 × k _uni then the data sets shown in Fig. 4 can be re-analysed in terms of t _1/2 versus total monomer concentration. Such a plot is shown in Fig. 5 and the fitting procedure yields a value for k _bi of 2.4 × 10⁴ M⁻¹ s⁻¹ and a value for k _uni of 1.6 × 10⁻³ s⁻¹; remarkably close to the values arrived at from global numerical fitting, i.e. 1.6 × 10⁴ M⁻¹ s⁻¹ and 1.9 × 10⁻³ s⁻¹, respectively. The k _uni measured in such reactions might be a compound of two or more unimolecular steps in a more complex mechanism; in this case 1/k _uni = τ _uni = τ ₁ + τ ₂ +⋯τ_n .

3.6 Thermal denaturation

Shown in Fig. 6 A are denaturation data derived from an experiment in which the enzyme was incubated at a series of temperatures for a period of 20 min and the residual activity recorded. The heat inactivation of cmFDH, as for most proteins, is not reversible and follows a first-order decay [21–23]. As a result of this, denaturation cannot be formally treated as an equilibrium system to which the orthodox analysis can be applied, rather it should be thought of as being defined by a temperature-sensitive rate constant for the irreversible step. These data can be treated as representing rate constants of denaturation as a function of temperature, i.e. the rate constant (k) can be derived directly from the residual activity (A) by the following relationship:

A= A o ·exp(‐k· t inc )((8))

where t _inc is the period of incubation (in our case 1200s) and A_o is the initial activity. The variation of rate constant with temperature can be described by the Arrhenius relationship: k = k_o · exp(E_a /RT) where E_a is the activation enthalpy. When the data in Fig. 6A are fitted to this relationship we obtain a value for k_o of 2 × 10⁵⁷ s⁻¹ and for E_a a value of 91 kcal/mol.

However, in the knowledge that protein folding involves large changes in heat capacity, it is more realistic to fit the data to the integrated form of the van't Hoff relationship where the free-energy barrier for unfolding is related to temperature by the equation:

k= k o ·exp(‐ΔG/(R·T))((9))

where ΔG is the free energy of activation and k_o is the rate of an unfolding reaction in the absence of an activation barrier. For the purposes of this analysis, we take a value of 10⁷ s⁻¹ as the upper rate of rearrangements involved in protein folding or unfolding [24].

In Fig. 6B the deduced ΔG for activation is plotted against the temperature. The relationship between the height of the free-energy barrier and the temperature defines the changes in heat capacity, enthalpy and entropy between the folded state and the transition state according to Eq. (2). Combining the above equations allows a direct fit of residual activity against ΔH, ΔC_p and ΔS as shown by the fit line in Fig. 6A which is superimposed on the original data. This analysis gives an enthalpic barrier of 25 kcal/mol, a favourable entropic term (−5.5 kcal/mol at 298 K) and a heat capacity change of 2.0 kcal/mol/K. [Measurements of unfolding rate constants as a function of temperature yielded similar values for ΔH, ΔC_p and ΔS i.e. 31 kcal/mol, 1.6 kcal/mol/K. and −11 kcal/mol at 298 K (see Supplementary Fig. S1)].

Interestingly, these values are comparable to those for the barrier to the unfolding of phosphoglycerate kinase (N-domain) (N-PGK) which shows a favourable entropy term (−6.3 kcal/mol −298 K) and an unfavourable enthalpy (+18.4 kcal/mol) [24]. A further similarity can be seen in the heat capacity change in attaining the transition state in unfolding–folding which in the case of FDH and N-PGK is about 20% of the ΔC_p for complete unfolding, i.e. the transition state is about 80% folded as measured by solvent exposure. It is also intriguing to note that for chemical denaturation of FDH, according to the Δm-value for the transition state (∼4.5, Fig. 3) and the overall Δm value for unfolding (∼17.5, Fig. 1), the transition state is about 75% folded. Indeed, using the thermodynamic parameters derived from the rates of thermal denaturation, we would predict the rate of unfolding at 25 °C to be 6 × 10⁻⁷ s⁻¹, a value remarkably close to 3 × 10⁻⁷ s⁻¹ derived from orthodox denaturant analysis.

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.febslet.2009.07.048.