Refolding kinetic constants

The results from studies of the kinetics of refolding of various oligomeric proteins are summarized in Table 11.1. Also listed are the kinetic constants for renaturation of the different enzymes studied by Jaenicke and co-workers as well as the activity of the monomeric unit (if any) fitting with the irreversible unimolecular-bimolecular model (Jaenicke, 1979 Jaenicke and Rudolph, 1980). 

The role of Ca2+ in inducing refolding of a-lactalbumin is reflected in clean two-stage kinetics, with rate constants 6.0 and 1.3 s-1. The maximum concentration of the intermediate, monitored by stopped-flow fluorescence and time-resolved photo-CIDNP NMR, occurs at about 200 ms (327). 

Biochemical processes such as protein unfolding/refold-ing and supramolecular assembly/disassembly take place on a time scale of seconds to minutes after readjusting the temperature of a system. Most commercially available glass-jacketed cuvettes are not suitable for temperature jumps on this time scale, as a result of the slow kinetics of heat transfer across substances with characteristically high dielectric constants, and their use can convolute the time scale of the temperature change onto the time scale... 

Scheme II. Kinetic model for the slow-refolding reactions of RNase T1 under strongly native conditions, U stands for unfolded species, I for intermediates of refolding, and N is the native protein. The superscript and the subscript indicate the isomeric states of Pro39 and Pro55, respectively, in the correct, nativelike cis (c) and in the incorrect, nonnative trans (t) isomeric state. As an example, 155 stands for an intermediate with Pro55 in the correct cis and Pro39 in the incorrect trans state. The time constants given for the individual steps refer to folding conditions of 0.15 M GdmCl, 0.1 M Tris-HCl, pH 8.0, at 10°C. From Kiefhaber et al. (1990b,c).

Fig. 8. Acceleration of the oxidative refolding of RNase T1 by PPI and PDI. The increase in fluorescence at 320 nm is shown as a function of the time of reoxidation. The final conditions were 2.5 fiM RNase T1 in 0.1 Af Tris-HCl, 0.2 M GdmCl, 2 mM EDTA, 3 mAf glycine, 0.4 mAf oxidized glutathione, and 4 mAf reduced glutathione at pH 7.8 and 25°C. Reoxidation ( ) in the absence of PPI and PDI, (O) in the presence of 1.4 tiM PPI, (A) in the presence of 1.6 fiM PDI, and (A) in the presence of both 1.6 fiM PDI and 1.4 /uAf PPI. In all experiments more than 90% of the observed kinetics were well approximated by single first-order processes, as indicated by the continuous lines. The respective time constants (t) are ( ) t = 4300 sec, (O) r = 2270 sec, (A) t = 1500 sec, (A) T = 650 sec. In all cases the initial fluorescence signal was about 10% of the final emission of the native protein. From Schonbrunner and Schmid (1992).

Refolding yield optimimization. Equations (3) through (7) describe the kinetics of hCAB refolding under a given set of environmental conditions. However, when diafiltration is employed to remove the denaturant, the denaturant concentration is a function of time. For a constant volume, constant filtration rate diafiltration system, the equation describing the rate of denaturant agent removal is ... 

Fig. 7. Conservation of the unfolding/folding mechanism of cold-shock proteins (Csp) from B. subtilis (Bs), B. caldolyticus (fid), and Thermotoga maritima (Tm). (a) Equilibrium unfolding transitions of Csp from Bs (A), Be ( ), and Tm ( ) induced by GdmCI at 25° and monitored by intrinsic fluorescence. Least-squares fit analyses based on the two-state model yield stabilization energies AGstab = 11.3,20.1, and 26.2 kJ/mol for Csp from Bs, Be, and Tm, respectively, (b) Kinetics of unfolding (open symbols) and refolding (closed symbols) of Bs (A, A), Be ( , ) and T Csp (O, ), respectively. The apparent rate constants, X, are plotted against the GdmCI concentration. The fits are on the basis of the linear two-state model. ...

Therefore, kinetic criteria for a two-state process were considered to be fulfilled. However, if temperature dependence of the unfolding rate constant varied linearly indicating independence of the activation energy, anomalous temperature dependence was observed for the refolding. Figure 7.2 indicates the different temperature dependence for unfolding and folding rate constants. 

Both fast and slow refolding species yield native enzyme possessing both ability to bind 2 CMP and catalytic activity (hydrolysis of CpA). The binding constant of RNase formed by fast refolding process for 2 CMP is identical to that of native RNase. Further, the presence of 2 CMP does not affect the kinetics of refolding as followed by the exposure of tyrosine groups. 

Staphylococcal nuclease undergoes a reversible transition between pH 3 and 4. Kinetics of refolding of the acidified enzyme was studied by a stopped-flow method by measuring the increase of fluorescence of Trp 140 (Schechter et ai, 1970 Epstein et ai, 1971a). Biphasic kinetics were observed as shown in Fig. 7.5. Two first-order processes correctly describe the kinetics with rate constants of 12.4 and 1.9 sec , respectively for fast and slow processes. The two processes are not so broadly separated in the time scale as is the... 

Under conditions of the equilibrium for unfolding-refolding and dissociation-association processes, side reactions become preponderant. For this reason, conditions for kinetic studies are generally chosen far from this equilibrium so that the reactions are practically irreversible (i.e., the rate constants for reverse reactions are negligible). In the critical range of the monomer-oligomer transition, a kind of hysteresis, i.e., a noncoincidence of, on the one hand, deactivation-denaturation, on the other hand. 

Denaturation of LDH-H4 was induced by various methods including 6 M GuHCl, 6 M urea, and low pH. An irreversible unimolecular-bimolecular kinetic mechanism correctly describes refolding and reactivation (Fig. 11.5), with only a first-order rate constant kj = (1.45 0.45) x 10" sec" and a second-order reaction rate constant 2 = (5 1) mM sec" These two constants are identical regardless of the denaturant employed. Irreversible steps in the kinetic mechanism are only operational that means rate constants of the reversible process are very small under the experimental... 

A sequential unimolecular-bimolecular process was proposed to account for refolding and reactivation of tryptophan synthetase P2 subunit previously denatured in 4.5 M GuHCl at pH 2.3. The return of enzymatic activity can be described by first-order kinetics over a large concentration range (3-0.04 fiM) with a kinetic rate constant k = 6 1 x 10 " sec This was explained by a slow reshuffling process occurring after the first association... 

---