Model for the nucleation mechanism of protein folding

A nucleation-like pathway of protein folding involves the formation of a cluster containing native residues that grows by including residues from the unfolded part of the protein. This pathway is examined by using a heteropolymer as a protein model. The model heteropolymer consists of hydrophobic and hydrophilic beads with fixed bond lengths and bond angles. The total energy of the heteropolymer is determined by the pairwise repulsive/attractive interactions between nonlinked beads and by the contribution from the dihedral angles involved. The parameters of these interactions can be rigorously defined, unlike the ill-defined surface tension of a cluster of protein residues that constitutes the basis of a previous nucleation model. The main idea underlying the new model consists of averaging the dihedral potential of a selected residue over all possible configurations of all neighboring residues along the protein chain. The resulting average dihedral potential depends on the distance between the selected residue and the cluster center. Its combination with the average pairwise potential of the selected residue and with a confining potential caused by the bonds between the residues leads to an overall potential around the cluster that has a double-well shape. Residues in the inner (closer to the cluster) well are considered as belonging to the folded cluster, whereas those in the outer well are treated as belonging to the unfolded part of the protein. Transitions of residues from the inner well into the outer one and vice versa are considered as elementary emission and absorption events, respectively. The double-well character of the potential well around the cluster allows one to determine the rates of both emission and absorption of residues by the cluster using a first passage time analysis. Once these rates are found as functions of the cluster size, one can develop a self-consistent kinetic theory for the nucleation mechanism of folding of a protein. The model allows one to evaluate the size of the nucleus and the protein folding time. The latter is evaluated as the sum of the times necessary for the first nucleation event to occur and for the nucleus to grow to the maximum size (of the folded protein). Depending on the diffusion coefficients of the native residues in the range from 10(-6) to 10(-8) cm2/s, numerical calculations for a protein of 2500 residues suggest that the folding time ranges from several seconds to several hundreds of seconds.     

A ternary nucleation model for the nucleation pathway of protein folding

Recently [Y. S. Djikaev and E. Ruckenstein, J. Phys. Chem. B 111, 886 (2007)], the authors proposed a kinetic model for the nucleation mechanism of protein folding where a protein was modeled as a heteropolymer consisting of hydrophobic and hydrophilic beads and the composition of the growing cluster of protein residues was assumed to be constant and equal to the overall protein composition. Here, they further develop the model by considering a protein as a three-component heteropolymer and by allowing the composition of the growing cluster of protein residues to vary independently of the overall one. All the bonds in the heteropolymer (now consisting of hydrophobic, hydrophilic, and neutral beads) have the same constant length, and all the bond angles are equal and fixed. As a crucial idea of the model, an overall potential around the cluster wherein a residue performs a chaotic motion is considered to be a combination of the average dihedral and average pairwise potentials assigned to the bead. The overall potential as a function of the distance from the cluster center has a double well shape which allows one to determine its emission and absorption rates by using a first passage time analysis. Knowing these rates as functions of three independent variables of a ternary cluster, one can develop a self-consistent kinetic theory for the nucleation mechanism of folding of a protein using a ternary nucleation formalism and evaluate the size and composition of the nucleus and the protein folding time. As an illustration, the model is applied to the folding of bovine pancreatic ribonuclease consisting of 124 amino acids whereof 40 are hydrophobic, 81 hydrophilic, and 3 neutral. With a reasonable choice of diffusion coefficients of the residues in the native state and potential parameters, the model predicts folding times in the range of 1-100 s.     

Effect of ionized protein residues on the nucleation pathway of protein folding

Using a ternary nucleation formalism, we have recently [Y. S. Djikaev and E. Ruckenstein, J. Chem. Phys. 126, 175103 (2007)] proposed a kinetic model for the nucleation mechanism of protein folding. A protein was considered as a heteropolymer consisting of hydrophobic, hydrophilic, and neutral beads with all the bonds having the same constant length and all the bond angles equal and fixed. In this paper, we further develop that model by taking into account of the ionizability of some of the protein residues. As previously, an overall potential around the cluster wherein a protein residue performs a chaotic motion is considered to be a combination of the average dihedral and average pairwise potentials (the latter now including an electrostatic contribution for ionized residues) assigned to the residue and the confining potential due to the polymer connectivity constraint. The overall potential as a function of the distance from the cluster has a double well shape (even for ionized beads) which allows one to determine the rates of emission and absorption of residues by the cluster by using a first passage time analysis. Assuming the equality of the ratios of the numbers of negatively and positively ionized residues in the cluster and in the entire protein, one can keep the modified model within the framework of the ternary nucleation formalism and evaluate the size and composition of the nucleus and the protein folding time as in the previous model. As an illustration, the model is again applied to the folding of bovine pancreatic ribonuclease consisting of 124 amino acids, whereof 40 are hydrophobic, 81 hydrophilic (of which 10 are negatively and 18 positively ionizable), and 3 neutral. Numerical calculations at pH=6.3, pH=7.3, and pH=8.3 show that for this protein the time of folding via nucleation is significantly affected by electrostatic interactions only for the unusually low pH of 6.3 and that among all pH's considered pH=7.3 provides the lowest folding time.     

Molecular simulation of protein dynamics in nanopores. I. Stability and folding

Discontinuous molecular dynamics simulations, together with the protein intermediate resolution model, an intermediate-resolution model of proteins, are used to carry out several microsecond-long simulations and study folding transition and stability of alpha-de novo-designed proteins in slit nanopores. Both attractive and repulsive interaction potentials between the proteins and the pore walls are considered. Near the folding temperature T(f) and in the presence of the attractive potential, the proteins undergo a repeating sequence of folding/partially folding/unfolding transitions, with T(f) decreasing with decreasing pore sizes. The unfolded states may even be completely adsorbed on the pore's walls with a negative potential energy. In such pores the energetic effects dominate the entropic effects. As a result, the unfolded state is stabilized, with a folding temperature T(f) which is lower than its value in the bulk and that, compared with the bulk, the folding rate decreases. The opposite is true in the presence of a repulsive interaction potential between the proteins and the walls. Moreover, for short proteins in very tight pores with attractive walls, there exists an unfolded state with only one alpha-helical hydrogen bond and an energy nearly equal to that of the folded state. The proteins have, however, high entropies, implying that they cannot fold onto their native structure, whereas in the presence of repulsive walls the proteins do attain their native structure. There is a pronounced asymmetry between the two termini of the protein with respect to their interaction with the pore walls. The effect of a variety of factors, including the pore size and the proteins' length, as well as the temperature, is studied in detail.     

Denatured-state ensemble and the early-stage folding of the G29A mutant of the B-domain of protein A

The folding mechanism of the G29A mutant of the B-domain of protein A (BdpA) has been studied by all-atom molecular dynamics simulation using AMBER force field (ff03) and generalized Born continuum solvent model. Started from the extended chain conformation, a total of 16 simulations (400 ns each) at 300 K captured some early folding events of the G29A mutant of BdpA. In one of the 16 trajectories, the G29A mutant folded within 2.8 A (root mean square) of the wild-type NMR structure. We observed that the fast burial of hydrophobic residues was the driving force to bring the distant residues into close proximity. The initiation of the helix I and III occurred during the stage of hydrophobic collapse. The initiation and growth of the helix II was slow. Both the secondary structure formation and the development of the native tertiary contacts suggested a multistage folding process. Clustering analysis indicated that two helix species (helices I and III) could be intermediates. Further analysis revealed that the hydrophobic residues of partially folded helix II formed nativelike hydrophobic contacts with helices I and III that stabilized a nativelike state and delayed the completion of folding of the entire protein. The details of the early folding process were compared with other theoretical and experimental studies. It was found that a nativelike hydrophobic cluster was formed by residues including F(30), I(31), L(34), L(44), L(45), and A(48) that prevented further development of the native structures, and breaking the hydrophobic cluster like this one contributed to the rate-limiting step. This was in complete agreement with the recent kinetic measurements in which mutations of these residues to Gly and Ala substantially increased the folding rates by as much as 60 times. Apparently, destabilization of nonnative states dramatically enhanced the folding rates.     

Variationally determined free energy profiles for structural models of proteins: characteristic temperatures for folding and trapping

Characterizing the phase diagram for proteins is important both for laboratory studies and for the development of structure prediction algorithms. Using a variational scheme, we calculated the generic features of the protein thermostability over a large range of temperatures for a set of more than 50 different proteins using a model based on native structure alone. Focusing on a specific system, protein G, we further examined, using a more realistic model that includes the nonnative interaction, the thermostability of both the native state and a collection of trap structures. By surveying the native structures for many proteins and by paying closer attention to the various trap structures of protein G, we obtained an overall understanding of the folding dynamics far from the conditions usually focused on; namely, those near the folding temperature alone. Two characteristic temperatures (shown to scale with folding temperature in general) signal drastic changes in the folding mechanism. The variational calculations suggest that most proteins would, indeed, fold in a barrierless manner below a critical temperature analogous to a spinodal in crystallization. For fixed interaction strengths, this temperature, however, seems to be generally very low, approximately 50% of the equilibrium folding temperature. Likewise, native proteins, in general, would unfold in a completely barrierless way at a temperature 25% above folding temperature according to these variational calculations. We also studied the distribution of free energy profiles for escape from a set of trap structures generated by simulations.     

A high-resolution probe of protein folding

Protein folding is a central problem in the biological sciences. To generate residue-specific information on the equilibrium folding of cytochrome c, we have semisynthesized the protein with specifically deuterated residues. The C-D bonds may be easily visualized in an otherwise transparent region of the IR spectra, even at high protein and denaturant concentrations. Plotted as a function of added guanidine hydrochloride denaturant, the absorption intensities reveal that the protein undergoes a conformational change at the protein-based ligand, Met80, which is then followed by a more global unfolding at 2.3 M denaturant. Deuteration and characterization of other residues in cytochrome c, or other protein of interest, should provide complete views of folding with residue specific detail that is capable of resolving even the most rapidly interconverting intermediates.     

Folding kinetics of a lattice protein via a forward flux sampling approach

We implement a forward flux sampling approach [R. J. Allen et al., J. Chem. Phys. 124, 194111 (2006)] for calculating transition rate constants and for sampling paths of protein folding events. The algorithm generates trajectories for the transition between the unfolded and folded states as chains of partially connected paths, which can be used to obtain the transition-state ensemble and the properties that characterize these intermediates. We apply this approach to Monte Carlo simulations of a model lattice protein in open space and in confined spaces of varying dimensions. We study the effect of confinement on both protein thermodynamic stability and folding kinetics; the former by mapping free-energy landscapes and the latter by the determination of rate constants and mechanistic details of the folding pathway. Our results show that, for the range of temperatures where the native state is stable, confinement of a protein destabilizes the unfolded state by reducing its entropy, resulting in increased thermodynamic stability of the folded state. Relative to the folding in open space, we find that the kinetics can be accelerated at temperatures above the temperature at which the unconfined protein folds fastest and that the rate constant increases with the number of constrained dimensions. By examining the statistical properties of the transition-state ensemble, we detect signs of a classical nucleation folding mechanism for a core of native contacts formed at an early stage of the process. This nucleus acts as folding foci and is composed of those residues that have higher probability to form native contacts in the transition-state intermediates, which can vary depending on the confinement conditions of the system.     

New scenarios of protein folding can occur on the ribosome

Identifying and understanding the differences between protein folding in bulk solution and in the cell is a crucial challenge facing biology. Using Langevin dynamics, we have simulated intact ribosomes containing five different nascent chains arrested at different stages of their synthesis such that each nascent chain can fold and unfold at or near the exit tunnel vestibule. We find that the native state is destabilized close to the ribosome surface due to an increase in unfolded state entropy and a decrease in native state entropy; the former arises because the unfolded ensemble tends to behave as an expanded random coil near the ribosome and a semicompact globule in bulk solution. In addition, the unfolded ensemble of the nascent chain adopts a highly anisotropic shape near the ribosome surface and the cooperativity of the folding-unfolding transition is decreased due to the appearance of partially folded structures that are not populated in bulk solution. The results show, in light of these effects, that with increasing nascent chain length folding rates increase in a linear manner and unfolding rates decrease, with larger and topologically more complex folds being the most highly perturbed by the ribosome. Analysis of folding trajectories, initiated by temperature quench, reveals the transition state ensemble is driven toward compaction and greater native-like structure by interactions with the ribosome surface and exit vestibule. Furthermore, the diversity of folding pathways decreases and the probability increases of initiating folding via the N-terminus on the ribosome. We show that all of these findings are equally applicable to the situation in which protein folding occurs during continuous (non-arrested) translation provided that the time scales of folding and unfolding are much faster than the time scale of monomer addition to the growing nascent chain, which results in a quasi-equilibrium process. These substantial ribosome-induced perturbations to almost all aspects of protein folding indicate that folding scenarios that are distinct from those of bulk solution can occur on the ribosome.     

The role of plastic beta-hairpin and weak hydrophobic core in the stability and unfolding of a full sequence design protein

In this study, the thermal stability of a designed alpha/beta protein FSD (full sequence design) was studied by explicit solvent simulations at three moderate temperatures, 273 K, 300 K, and 330 K. The average properties of the ten trajectories at each temperature were analyzed. The thermal unfolding, as judged by backbone root-mean-square deviation and percentage of native contacts, was displayed with increased sampling outside of the native basin as the temperature was raised. The positional fluctuation of the hairpin residues was significantly higher than that of the helix residues at all three temperatures. The hairpin segment displayed certain plasticity even at 273 K. Apart from the terminal residues, the highest fluctuation was shown in the turn residues 7-9. Secondary structure analysis manifested the structural heterogeneity of the hairpin segment. It was also revealed by the simulation that the hydrophobic core was vulnerable to thermal denaturation. Consistent with the experiment, the I7Y mutation in the double mutant FSD-EY (FSD with mutations Q1E and I7Y) dramatically increased the protein stability in the simulation, suggesting that the plasticity of the hairpin can be partially compensated by a stronger hydrophobic core. As for the unfolding pathway, the breathing of the hydrophobic core and the separation of the two secondary structure elements (alpha helix and beta hairpin) was the initiation step of the unfolding. The loss of global contacts from the separation further destabilized the hairpin structure and also led to the unwinding of the helix.     

Interaction of a Rhodococcus sp. trehalose lipid biosurfactant with model proteins: thermodynamic and structural changes

One major application of surfactants is to prevent aggregation during various processes of protein manipulation. In this work, a bacterial trehalose lipid (TL) with biosurfactant activity, secreted by Rhodococcus sp., has been identified and purified. The interactions of this glycolipid with selected model proteins have been studied by using differential scanning calorimetry (DSC), Fourier-transform infrared (FTIR) spectroscopy, isothermal titration calorimetry (ITC), and fluorescence spectroscopy. Bovine serum albumin (BSA) and cytochrome c (Cyt-c) have been chosen because of their quite different secondary structures: BSA contains essentially no β-sheets and an average 66% α-helix, whereas Cyt-c possesses up to 25% β-sheets and up to 45% α-helical structure. Differential scanning calorimetry shows that addition of TL to BSA at concentrations below the critical micelle concentration (cmc) shifts the thermal unfolding temperature to higher values. FTIR indicates that TL does not alter the secondary structure of native BSA, but the presence of TL protects the protein toward thermal denaturation, mainly by avoiding formation of β-aggregates. Studies on the intrinsic Trp fluorescence of BSA show that addition of TL to the native protein results in conformational changes. BSA unfolding upon thermal denaturation in the absence of TL makes the Trp residues less accessible to the quencher, as shown by a decrease in the value of Stern-Volmer dynamic quenching constant, whereas denaturation in the presence of the biosurfactant prevents unfolding, in agreement with FTIR results. In the case of Cyt-c, interaction with TL gives rise to a new thermal denaturation transition, as observed by DSC, at temperatures below that of the native protein, therefore facilitating thermal unfolding. Binding of TL to native BSA and Cyt-c, as determined by ITC, suggests a rather nonspecific interaction of the biosurfactant with both proteins. FTIR indicates that TL slightly modifies the secondary structure of native Cyt-c, but protein denaturation in the presence of TL results in a higher proportion of β-aggregates than in its absence (20% vs 3.9%). The study of Trp fluorescence upon TL addition to Cyt-c results in a completely opposite scenario to that described above for BSA. In this case, addition of TL considerably increases the value of the dynamic quenching constant, both in native and denatured protein; that is, the interaction with the glycolipid induces conformational changes which facilitate the exposure of Trp residues to the quencher. Considering the structures of both proteins, it could be derived that the characteristics of TL interactions, either promoting or avoiding thermal unfolding, are highly dependent on the protein secondary structure. Our results also suggest the rather unspecific nature of these interactions. These might well involve protein hydrophobic domains which, being buried into the protein native structures, become exposed upon thermal unfolding.     

Structural Analysis of a Helical Peptide Unfolding Pathway

The analysis of the folding mechanism in peptides adopting well‐defined secondary structure is fundamental to understand protein folding. Herein, we describe the thermal unfolding of a 15‐mer vascular endothelial growth factor mimicking α‐helical peptide (QK_L10A) through the combination of spectroscopic and computational analyses. In particular, on the basis of the temperature dependencies of QK_L10A H_α chemical shifts we show that the first phase of the thermal helix unfolding, ending at around 320 K, involves mainly the terminal regions. A second phase of the transition, ending at around 333 K, comprises the central helical region of the peptide. The determination of high‐resolution QK_L10A conformational preferences in water at 313 K allowed us to identify, at atomic resolution, one intermediate of the folding–unfolding pathway. Molecular dynamics simulations corroborate experimental observations detecting a stable central helical turn, which represents the most probable site for the helix nucleation in the folding direction. The data presented herein allows us to draw a folding–unfolding picture for the small peptide QK_L10A compatible with the nucleation–propagation model. This study, besides contributing to the basic field of peptide helix folding, is useful to gain an insight into the design of stable helical peptides, which could find applications as molecular scaffolds to target protein–protein interactions.     

Understanding the folding rates and folding nuclei of globular proteins

The first part of this paper contains an overview of protein structures, their spontaneous formation ("folding"), and the thermodynamic and kinetic aspects of this phenomenon, as revealed by in vitro experiments. It is stressed that universal features of folding are observed near the point of thermodynamic equilibrium between the native and denatured states of the protein. Here the "two-state" ("denatured state" <--> "native state") transition proceeds without accumulation of metastable intermediates, but includes only the unstable "transition state". This state, which is the most unstable in the folding pathway, and its structured core (a "nucleus") are distinguished by their essential influence on the folding/unfolding kinetics. In the second part of the paper, a theory of protein folding rates and related phenomena is presented. First, it is shown that the protein size determines the range of a protein's folding rates in the vicinity of the point of thermodynamic equilibrium between the native and denatured states of the protein. Then, we present methods for calculating folding and unfolding rates of globular proteins from their sizes, stabilities and either 3D structures or amino acid sequences. Finally, we show that the same theory outlines the location of the protein folding nucleus (i.e., the structured part of the transition state) in reasonable agreement with experimental data.     

Temperature dependent equilibrium native to unfolded protein dynamics and properties observed with IR absorption and 2D IR vibrational echo experiments

Dynamic and structural properties of carbonmonoxy (CO)-coordinated cytochrome c(552) from Hydrogenobacter thermophilus (Ht-M61A) at different temperatures under thermal equilibrium conditions were studied with infrared absorption spectroscopy and ultrafast two-dimensional infrared (2D IR) vibrational echo experiments using the heme-bound CO as the vibrational probe. Depending on the temperature, the stretching mode of CO shows two distinct bands corresponding to the native and unfolded proteins. As the temperature is increased from low temperature, a new absorption band for the unfolded protein grows in and the native band decreases in amplitude. Both the temperature-dependent circular dichroism and the IR absorption area ratio R(A)(T), defined as the ratio of the area under the unfolded band to the sum of the areas of the native and unfolded bands, suggest a two-state transition from the native to the unfolded protein. However, it is found that the absorption spectrum of the unfolded protein increases its inhomogeneous line width and the center frequency shifts as the temperature is increased. The changes in line width and center frequency demonstrate that the unfolding does not follow simple two-state behavior. The temperature-dependent 2D IR vibrational echo experiments show that the fast dynamics of the native protein are virtually temperature independent. In contrast, the fast dynamics of the unfolded protein are slower than those of the native protein, and the unfolded protein fast dynamics and at least a portion of the slower dynamics of the unfolded protein change significantly, becoming faster as the temperature is raised. The temperature dependence of the absorption spectrum and the changes in dynamics measured with the 2D IR experiments confirm that the unfolded ensemble of conformers continuously changes its nature as unfolding proceeds, in contrast to the native state, which displays a temperature-independent distribution of structures.     

Studies of irreversible heat denaturation of green fluorescent protein by differential scanning microcalorimetry

Heat denaturation of green fluorescent protein (the GFP-cycle3 mutant) was studied by the method of differential scanning microcalorimetry. Activation energy values for two stages of GFP unfolding were calculated from the calorimetric data using the model of irreversible denaturation. Dependences of activation energy and denaturation enthalpy on the temperature of the maxima of corresponding stages of denaturation were obtained, which allow estimating the corresponding increments of heat capacity. Based on the known correlations of the structure and energy parameters, it was concluded that the first transition state is close to the native state, whereas the second transition state is close to the denatured state, judging by the exposure of hydrophobic groups to the solvent.     

Comparison of chemical and thermal protein denaturation by combination of computational and experimental approaches. II

Chemical and thermal denaturation methods have been widely used to investigate folding processes of proteins in vitro. However, a molecular understanding of the relationship between these two perturbation methods is lacking. Here, we combined computational and experimental approaches to investigate denaturing effects on three structurally different proteins. We derived a linear relationship between thermal denaturation at temperature T(b) and chemical denaturation at another temperature T(u) using the stability change of a protein (ΔG). For this, we related the dependence of ΔG on temperature, in the Gibbs-Helmholtz equation, to that of ΔG on urea concentration in the linear extrapolation method, assuming that there is a temperature pair from the urea (T(u)) and the aqueous (T(b)) ensembles that produces the same protein structures. We tested this relationship on apoazurin, cytochrome c, and apoflavodoxin using coarse-grained molecular simulations. We found a linear correlation between the temperature for a particular structural ensemble in the absence of urea, T(b), and the temperature of the same structural ensemble at a specific urea concentration, T(u). The in silico results agreed with in vitro far-UV circular dichroism data on apoazurin and cytochrome c. We conclude that chemical and thermal unfolding processes correlate in terms of thermodynamics and structural ensembles at most conditions; however, deviations were found at high concentrations of denaturant.     

Effects of pH on the kinetic reaction

In most cases, kinetic unfolding reactions of proteins follow a simple one-step mechanism that does not involve any detectable intermediates. One example for a more complicated unfolding reaction is the acid-induced denaturation of holo-myoglobin (hMb). This reaction proceeds through a transient intermediate and can be described by a sequential two-step mechanism (Konermann et al. Biochemistry 1997, 36, 6448-6454). Time-resolved electrospray ionization mass spectrometry (ESI MS) is a new technique for monitoring the kinetics of protein folding and unfolding in solution. Different protein conformations can be distinguished by the different charge state distributions that they generate during ESI. At the same time this technique allows monitoring the loss or binding of noncovalent protein ligands. In this work, time-resolved ESI MS is used to study the dependence of the kinetic unfolding mechanism of hMb on the specific solvent conditions used in the experiment. It is shown that hMb unfolds through a short-lived intermediate only at acidic pH. Under basic conditions no intermediate is observed. These findings are confirmed by the results of optical stopped-flow absorption experiments. This appears to be the first time that a dependence of the kinetic mechanism for protein unfolding on external conditions such as pH has been observed.     

Design of functional ferritin-like proteins with hydrophobic cavities

Ferritin four-helix bundle subunits self-assemble to create a stable multimer with a large central hydrophilic cavity where metal ions bind. To explore the versatility of this reaction vessel, computational design was used to generate cavities with increasingly apolar surface areas inside a dodecameric ferritin-like protein, Dps. Cavity mutants, in which as many as 120 surface accessible hydrophilic residues were replaced with hydrophobic amino acids, were shown to still assemble properly using size-exclusion chromatography and dynamic light scattering measurements. Wild-type Dps exhibited highly cooperative subunit folding and assembly, which was monitored by changes in Trp fluorescence and UV circular dichroism. The hydrophobic cavity mutants showed distinctly less cooperative unfolding behavior, with one mutant forming a partially assembled intermediate upon guanidine denaturation. Although the stability of Dps to such denaturation decreased with increasing apolar surface area, all proteins exhibited high melting temperatures, T(m) = 74-90 degrees C. Despite the large number of mutations, near-native ability to mineralize iron was maintained. This work illustrates the versatility of the ferritin scaffold for engineering large protein cavities with novel properties.