Mechanism of the multiphasic kinetics in the folding and unfolding of globular proteins

All-Electron Calculations of the Nucleation Structures in Metal-Induced Zinc-Finger Folding: Role of the Peptide Backbone

Although the folding of individual protein domains has been extensively studied both experimentally and theoretically, protein folding induced by a metal cation has been relatively understudied. Almost all folding mechanisms emphasize the role of the side-chain interactions rather than the peptide backbone in the protein folding process. Herein, we focus on the thermodynamics of the coupled metal binding and protein folding of a classical zinc-finger (ZF) peptide, using all-electron calculations to obtain the structures of possible nucleation centers and free energy calculations to determine their relative stability in aqueous solution. The calculations indicate that a neutral Cys first binds to hexahydrated Zn2+ via its ionized sulfhydryl group and neutral backbone oxygen, with the release of four water molecules and a proton. Another nearby Cys then binds in the same manner as the first one, yielding a fully dehydrated Zn2+. Subsequently, two His ligands from the C-terminal part of the peptide successively dislodge the Zn-bound backbone oxygen atoms to form the native-like Zn-(Cys)2(His)2 complex. Each successive Zn complex accumulates increasingly favorable and native interactions, lowering the energy of the ZF polypeptide, which concomitantly becomes more compact, reducing the search volume, thus guiding folding to the native state. In the protein folding process, not only the side chains but also the backbone peptide groups play a critical role in stabilizing the nucleation structures and promoting the hydrophobic core formation.

How do biomolecular systems speed up and regulate rates?

The viability of a biological system depends upon careful regulation of the rates of various processes. These rates have limits imposed by intrinsic chemical or physical steps (e.g., diffusion). These limits can be expanded by interactions and dynamics of the biomolecules. For example, (a) a chemical reaction is catalyzed when its transition state is preferentially bound to an enzyme; (b) the folding of a protein molecule is speeded up by specific interactions within the transition-state ensemble and may be assisted by molecular chaperones; (c) the rate of specific binding of a protein molecule to a cellular target can be enhanced by mechanisms such as long-range electrostatic interactions, nonspecific binding and folding upon binding; (d) directional movement of motor proteins is generated by capturing favorable Brownian motion through intermolecular binding energy; and (e) conduction and selectivity of ions through membrane channels are controlled by interactions and the dynamics of channel proteins. Simple physical models are presented here to illustrate these processes and provide a unifying framework for understanding speed attainment and regulation in biomolecular systems.

Protein folding in the landscape perspective: chevron plots and non-Arrhenius kinetics

We use two simple models and the energy landscape perspective to study protein folding kinetics. A major challenge has been to use the landscape perspective to interpret experimental data, which requires ensemble averaging over the microscopic trajectories usually observed in such models. Here, because of the simplicity of the model, this can be achieved. The kinetics of protein folding falls into two classes: multiple-exponential and two-state (single-exponential) kinetics. Experiments show that two-state relaxation times have "chevron plot" dependences on denaturant and non-Arrhenius dependences on temperature. We find that HP and HP+ models can account for these behaviors. The HP model often gives bumpy landscapes with many kinetic traps and multiple-exponential behavior, whereas the HP+ model gives more smooth funnels and two-state behavior. Multiple-exponential kinetics often involves fast collapse into kinetic traps and slower barrier climbing out of the traps. Two-state kinetics often involves entropic barriers where conformational searching limits the folding speed. Transition states and activation barriers need not define a single conformation; they can involve a broad ensemble of the conformations searched on the way to the native state. We find that unfolding is not always a direct reversal of the folding process.

Least activation path for protein folding: investigation of staphylococcal nuclease folding by stopped-flow circular dichroism

Is the pathway of protein folding determined by the relative stability of folding intermediates, or by the relative height of the activation barriers leading to these intermediates? This is a fundamental question for resolving the Levinthal paradox, which stated that protein folding by a random search mechanism would require a time too long to be plausible. To answer this question, we have studied the guanidinium chloride (GdmCl)-induced folding/unfolding of staphylococcal nuclease [(SNase, formerly EC 3.1.4.7; now called microbial nuclease or endonuclease, EC 3.1.31.1] by stopped-flow circular dichroism (CD) and differential scanning microcalorimetry (DSC). The data show that while the equilibrium transition is a quasi-two-state process, kinetics in the 2-ms to 500-s time range are triphasic. Data support the sequential mechanism for SNase folding: U3 <--> U2 <--> U1 <--> N0, where U1, U2, and U3 are substates of the unfolded protein and N0 is the native state. Analysis of the relative population of the U1, U2, and U3 species in 2.0 M GdmCl gives delta-G values for the U3 --> U2 reaction of +0.1 kcal/mol and for the U2 --> U1 reaction of -0.49 kcal/mol. The delta-G value for the U1 --> N0 reaction is calculated to be -4.5 kcal/mol from DSC data. The activation energy, enthalpy, and entropy for each kinetic step are also determined. These results allow us to make the following four conclusions. (i) Although the U1, U2, and U3 states are nearly isoenergetic, no random walk occurs among them during the folding. The pathway of folding is unique and sequential. In other words, the relative stability of the folding intermediates does not dictate the folding pathway. Instead, the folding is a descent toward the global free-energy minimum of the native state via the least activation path in the vast energy landscape. Barrier avoidance leads the way, and barrier height limits the rate. Thus, the Levinthal paradox is not applicable to the protein-folding problem. (ii) The main folding reaction (U1 --> N0), in which the peptide chain acquires most of its free energy (via van der Waals' contacts, hydrogen bonding, and electrostatic interactions), is a highly concerted process. These energy-acquiring events take place in a single kinetic phase. (iii) U1 appears to be a compact unfolded species; the rate of conversion of U2 to U1 depends on the viscosity of solution. (iv) All four relaxation times reported here depend on GdmCl concentrations: it is likely that none involve the cis/trans isomerization of prolines. Finally, a mechanism is presented in which formation of sheet-like chain conformations and a hydrophobic condensation event precede the main-chain folding reaction.

Protein folding dynamics: the diffusion-collision model and experimental data

The diffusion-collision model of protein folding is assessed. A description is given of the qualitative aspects and quantitative results of the diffusion-collision model and their relation to available experimental data. We consider alternative mechanisms for folding and point out their relationship to the diffusion-collision model. We show that the diffusion-collision model is supported by a growing body of experimental and theoretical evidence, and we outline future directions for developing the model and its applications.

Comparison of kinetics of formation of helices and hydrophobic core during the folding of staphylococcal nuclease from acid

Our previous kinetic study of the acid and base-induced folding/unfolding transitions of staphylococcal nuclease (SNase) has monitored Trp-140 fluorescence. Trp-140 is located near the flexible COOH terminus and whether or not its fluorescence reflects the overall conformation of the protein has yet to be established. Here we show that the fluorescence intensity of Try-140 correlated closely with the thermal stability (i.e., the calorimetric enthalpy, delta Hcal, of unfolding) of the protein in the pH range 7 to 2.5, confirming that it is a good measure of the overall protein structure. Circular dichroism (CD) at 222 nm, which reflects the helical content of the protein molecule, was used to follow the same folding/unfolding transition in order to compare kinetics of the helix formation and of the appearance of the hydrophobic core. In addition to the three kinetic phases reported earlier with the fluorescence detection, there were a rapid reaction (completed within the 25 ms mixing time of the instrument), which comprised 15% of the signal, and a very slow reaction (time constant > 300 s), which comprised 19% of the signal. With the fluorescence detection for the folding from acid, only 5% of the signal occurred in the rapid phase and there was no reaction slower than 300 s. By comparing kinetics of folding at pH 7 by the CD and fluorescence detection methods, we concluded that: (a) Roughly 15% of the helix content of SNase accumulated before significant changes in the hydrophobic environment (< 5%) of Trp-140 could be detected. The rapid appearance of CD signal reminiscent of helix formation within 25ms would be consistent with the framework model of protein folding. Note, however, that, 15% of the 22% helix content of the protein amounts to an equivalent of fewer than 5 amino acid residues. (b) For the time-resolved signal between 2 ms and 300s, kinetics measured by both properties are consistent with the sequential model, D4 = D3 = D2 = D1 = No (the four Ds are the four substates of the denatured protein and No is the native state). The major folding step by both signals is the D1 to No transition, which gave approximately a 50% change in fluorescence and CD and had a time constant of 160 ms at 25 degree C, pH7.0. (c) The slow phase with the CD signal (>300 s), which is insensitive to Trp-140 fluorescence, has been assigned to be the cis/trans isomerization of Pro-1 17 by other studies. (d) Kinetics in the unfolding direction are consistent with the above interpretation.

pH-induced folding/unfolding of staphylococcal nuclease: determination of kinetic parameters by the sequential-jump method

On the basis of previous stopped-flow pH-jump experiments, we have proposed that the acid- and alkaline-induced folding/unfolding transition of staphylococcal nuclease, in the time range 2 ms to 300 s, follows the pathway N0 in equilibrium with D1 in equilibrium with D2 in equilibrium with D3, in which D1, D2, and D3 are three substates of the unfolded state and N0 is the native state. The stopped-flow "double-jump" technique has been employed to test this mechanism and to determine the rate constants which would not be accessible by the direct pH jump because of the lack of fluorescence signal, i.e., the rates for the conversion of D1 to D2 and of D2 to D3. In the forward jump, a protein solution kept at pH 7.0 was mixed with an acidic or alkaline solution to the final pH of 3.0 or 12.2, respectively. The mixed solution was kept for varying periods of time, called the delay time, tD. A second mixing (the back jump) was launched to bring the protein solution back to pH 7.0. The time course of the Trp-140 fluorescence signals recovered in the back jump was analyzed as a function of tD. Kinetics of the unfolding were found to be triphasic by the double-jump method, contrary to the monophasic kinetics observed by the direct pH jump. Complex kinetics of unfolding are expected with the proposed kinetic scheme.(ABSTRACT TRUNCATED AT 250 WORDS)

Kinetic analysis of the acid and the alkaline unfolded states of staphylococcal nuclease

Thermodynamic analysis by differential scanning calorimetry shows that the folding/unfolding transition of staphylococcal nuclease is consistent with the two-state process. Stopped-flow kinetic measurements, monitoring the Trp140 fluorescence and covering five decades in time (2 ms to 300 s), indicate that the unfolding from pH 7.0 to 3.1 is monophasic (time constant 1.15 s) and from pH 7.0 to 12.2 is biphasic (time constants: one less than 2 ms and the other 0.6 s). However, the folding, either from pH 3.1 to 7.0 or from pH 12.2 to 7.0, is triphasic (time constants 150 ms, 850 ms and 30 s from acid, 90 ms, 565 ms and 33 s from alkaline). A simple sequential model, which agrees with the above observations for acidic folding/unfolding is, D3 in equilibrium D2 in equilibrium D1 in equilibrium N. The three Ds denote three sub-states of the unfolded state and N denotes the native state. These sub-states of D have similar enthalpy and tryptophan fluorescence, and their equilibrium cannot be shifted by temperature changes. However, they are kinetically distinctive. Data do not favor alternative mechanisms assuming parallel transitions of the three Ds to N, or complexity of the N state, or parallel transitions of sub-states of N1, N2 and N3 to D. Other more complex, branched or cyclic, kinetics are not considered because of the lack of evidence, pH dependence of the unfolding kinetics suggests that the unfolding is triggered by protonation of 0.8(+/- 0.3) ionizable groups, with a pKa of 3.9 or by deprotonation of 1.6(+/- 0.4) ionizable groups with pKa values near 10.5. Circular dichroisms indicate that these three D states retain nonrandom chain conformation. Possible role of these "chain conformation" in the protein folding is discussed.

Nucleation in protein folding--confusion of structure and process

The term 'nucleation' is currently used to denote two distinctly different aspects of folding: the kinetic and the structural. This gives rise to ambiguity in the use of the word 'nucleation', which is compounded by the fact that the word 'nuclei', as used in the structural sense, has more aliases than cats have lives.

Markoffian description of the process of protein folding

A long record of computer simulation of folding-unfolding transition in a two-dimensional lattice model of protein as monitored by one conformational order parameter was studied to see if it could be approximated by a markoffian process. For this purpose the normalized time correlation functions of the order parameter were calculated (i) directly from the record of simulation and (ii) by assuming the markoffian behavior of the record. Both of them can be well approximated by a sum of two simple exponential terms. The relaxation time of the slow relaxing term, which corresponds to the overall folding-unfolding transition, becomes very short when the markoffian assumption is made. From this observation we conclude that intermediate states defined by one more-or-less arbitrarily chosen conformational parameter are, in general, collections of very heterogeneous conformations and therefore transitions between them cannot be markoffian. This indicates the importance of multi-parameter observation of dynamic process of folding. Characteristic features of the method of trapping disulfide intermediates are discussed.

Intramolecular α-helix-β-structure-random coil transition in polypeptides

The conformational changes of polypeptides which are capable of forming the alpha-helix. beta-structure and random coil (or the unordered) conformations are discussed. The kinetics of this system are studied as the time evolution of the probabilities describing the conformational states of the system. The time behavior of the average numbers of the alpha-helix and the beta-structure reveals the existence of intermediate states which are not found and not stable at equilibrium. These intermediates make the kinetics of this system more complex. Such situations can occur in protein folding and unfolding processes in such a way that a conformation absent in the tertiary structure appears in the intermediate stages and disappears finally, and the time course of the reaction is described by the sum of two or more exponential terms, in other words, the protein folding and unfolding processes display multiphasic kinetics. These intermediates, which are formed by short-range interactions, may usually be destroyed but sometimes can be stabilized by medium- and long-range interactions and remain stable for a fairly long time in the process of renaturation in real proteins.

Regeneration of RNase A from the reduced protein: models of regeneration pathways

Two models of protein-folding pathways are proposed on the basis of equilibrium and kinetic data in the literature. One is a growth-type model--i.e., nucleation of the native-like structure occurs in the folding process, in the rate-limiting step(s), and subsequent folding around the nucleation sites proceeds smoothly to form the native disulfide bonds and conformation. The other is a rearrangement-type model--i.e., proper nucleation does not occur in the folding process; instead, non-native interactions play a significant role in the folding pathways and lead to metastable intermediate species. Such non-native interactions, including incorrect disulfide bonds and proline cis-trans isomerization, must be disrupted or rearranged to nucleate the native interactions [a process that is included in the rate-limiting step(s)] for the protein to fold. The rate-limiting steps in the pathways for regeneration of RNase A from the reduced protein are classified as growth- or rearrangement-type pathways. The growth-type pathway is the one accompanying the formation of an intramolecular disulfide bond in the rate-limiting step. The rearrangement-type pathway is the one accompanying the reshuffling or disruption of a disulfide bond in the rate-limiting step. The folding of other proteins, accompanying oxidation of the reduced form, and the folding of denatured proteins with intact disulfide bonds are discussed in terms of the growth- and rearrangement-type models.

Hydrophobic basis of packing in globular proteins

The self-assembly of globular proteins is often portrayed as a nucleation process in which the hydrogen bonding in segments of secondary structure is the precondition for further folding. We show here that this concept is unlikely because both the buried interior regions and the peptide chain turns of the folded protein (i.e., inside and outside) are predicted solely by the hydrophobicity of the residues, taken in sequential order along the chain. The helices and strands span the protein, and this observed secondary structure is seen to coincide with the regions predicted to be buried from hydrophobicity considerations alone. Our evidence suggests that linear chain regions rich in hydrophobic residues serve as small clusters that fold against each other, with concomitant or even later fixation of secondary structure. A helix or strand would arise in this folding process as one of a few energetically favorable alternatives for a given cluster, followed by a shift in the equilibrium between secondary structure conformers upon cluster association. the linera chain hydrophobicity alternates between locally maximal and minimal values, and these extrema partition the polypeptide chain into structural segments. This partitioning is seen in the x-ray structure as isodirectional segments bracketed between peptide chain-turns, with the segments expressed most often as helices and strands. the segment interactions define the geometry of the molecular interior and the chain-turns describe the predominant features of the molecular coastline. The segmentation of the molecule by linear chain hydrophobicity imposes a major geometric constraint upon possible folding events.