Solvent-induced forces in protein folding reflections on the protein folding problem

It is shown that the solvent induced forces on hydrophilic groups are the strongest ones. The relevance of this finding to protein folding is discussed.     

Conformation-transitional rate in protein folding

Based on the conformation dynamics of macromolecules, the rate of conformational transition is deduced from the nonadiabaticity operator method which can be used to explain the time scale of milliseconds for protein folding. It is proved that (1) the dependence of the transition rate on inertial moment I of the atomic group obeys the I^?2.5 law; (2) its dependence on numbers n of torsional angles participating in the transition obeys the n^1.5 law; and (3) the temperature dependence of the transitional rate shows an abnormal character in the high- temperature region. © 1995 John Wiley & Sons, Inc.     

Understanding the role of the topology in protein folding by computational inverse folding experiments

Recent studies suggest that protein folding should be revisited as the emergent property of a complex system and that the nature allows only a very limited number of folds that seem to be strongly influenced by geometrical properties. In this work we explore the principles underlying this new view and show how helical protein conformations can be obtained starting from simple geometric considerations. We generated a large data set of C-alpha traces made of 65 points, by computationally solving a backbone model that takes into account only topological features of the all-alpha proteins; then, we built corresponding tertiary structures, by using the sequences associated to the crystallographic structures of four small globular all-alpha proteins from PDB, and analysed them in terms of structural and energetic properties. In this way we obtained four poorly populated sets of structures that are reasonably similar to the conformational states typical of the experimental PDB structures. These results show that our computational approach can capture the native topology of all-alpha proteins; furthermore, it generates backbone folds without the influence of the side chains and uses the protein sequence to select a specific fold among the generated folds. This agrees with the recent view that the backbone plays an important role in the protein folding process and that the amino acid sequence chooses its own fold within a limited total number of folds.     

On the kinematics of protein folding

We offer simple solutions to three kinematic problems that occur in the folding of proteins. We show how to construct suitably local elementary Monte Carlo moves, how to close a loop, and how to fold a loop without breaking the bond that closes it.     

Stochastic protein folding simulation in the three-dimensional HP-model

We present results from three-dimensional protein folding simulations in the HP-model on ten benchmark problems. The simulations are executed by a simulated annealing-based algorithm with a time-dependent cooling schedule. The neighbourhood relation is determined by the pull-move set. The results provide experimental evidence that the maximum depth D of local minima of the underlying energy landscape can be upper bounded by D相似文献   

Mechanism of protein folding

The first stage of protein self-organization—the formation of a fluctuating secondary structure in the unfolded protein chain—is considered. The stereochemical theory is presented enabling one to calculate helix-coil and β-structure-coil equilibrium constants. It is shown that the most probable localization of fluctuating α- and β-structure in the unfolded protein chain corresponds to the native localization of these structures. The formation of large α- and β-structural blocks is observed, each of them including several native α-helices or β-strands.     

Self-organization in protein folding and the hydrophobic interaction

Self-organization is a critical aspect of living systems. During the folding of protein molecules, the hydrophobic interaction plays an important role in the collapse of the peptide chain to a compact shape. As the hydrophobic core tightens and excludes water, not only does the number of hydrophobic side chain contacts increase, but stabilization is further enhanced by an increase in strength of each hydrophobic interaction between side chains in the core. Thus, the self-organization of the protein folding process augments itself by enhancing the stability of the core against large-scale motions that would unfold the protein. Through calculations and computer simulations on a model four-helix bundle protein, we show how the strengthening of the hydrophobic interaction is crucial for stabilizing the core long enough for completion of the folding process and quantitatively manifests self-organizing dynamical behavior.     

Engineering the protein folding landscape in gram-negative bacteria

Gram-negative bacteria, especially Escherichia coli, are often the preferred hosts for recombinant protein production because of their fast doubling times, ability to grow to high cell density, propensity for high recombinant protein titers and straightforward protein purification techniques. The utility of simple bacteria in such studies continues to improve as a result of an ever-increasing body of knowledge regarding their native protein biogenesis machinery. From translation on the ribosome to interaction with cytosolic accessory factors to transport across the inner membrane into the periplasmic space, cellular proteins interact with many different types of cellular machinery and each interaction can have a profound effect on the protein folding process. This review addresses key aspects of cellular protein folding, solubility and expression in E. coli with particular focus on the elegant biological machinery that orchestrates the transition from nascent polypeptide to folded, functional protein. Specifically highlighted are a variety of different techniques to intentionally alter the folding environment of the cell as a means to understand and engineer intracellular protein folding and stability.     

Structural biology of the cell adhesion protein CD2: from molecular recognition to protein folding and design

CD2 (cluster of differentiation 2) is a cell adhesion molecule expressed on T cells and is recognized as a target for CD48 (rats) and CD58 (humans). Tremendous progress has been achieved in understanding the function of CD2, the mechanism of molecular recognition and protein folding, thus, leading towards the use of this protein as a scaffold for protein design. CD2 has been shown to set quantitative thresholds in T cell activation both in vivo and in vitro. Further, intracellular CD2 signaling pathways and networks are being discovered by the identification of several cytosolic tail binding proteins. In addition, a new method for directly measuring heterophilic adhesion has been developed. The functional "hot spot" for the adhesion surface of CD2 and CD58 has been dissected. Detailed NMR studies reveal that rat CD2 weakly self-associates to form a homodimeric structure in solution. Dynamic interaction of CD2 with the GYF and SH3 domains has been investigated. CD2 has been shown to form fibrils in the presence of 2,2,2-trifluoroethanol (TFE) and at low pH. Furthermore, kinetic studies have been completed to monitor the effect of surface hydrophobic residues and intramolecular bridges on the folding pathways of CD2. Our lab has de novo designed single calcium-binding sites into domain 1 of rat CD2 (CD2-D1) with strong metal selectivity. In addition, the EF-hand motifs have been grafted into CD2 to understand the site-specific calcium-binding affinity of calmodulin and calcium-dependent cell adhesion.     

Diffusion models of protein folding

In theory and in the analysis of experiments, protein folding is often described as diffusion along a single coordinate. We explore here the application of a one-dimensional diffusion model to interpret simulations of protein folding, where the parameters of a model that "best" describes the simulation trajectories are determined using a Bayesian analysis. We discuss the requirements for such a model to be a good approximation to the global dynamics, and several methods for testing its accuracy. For example, one test considers the effect of an added bias potential on the fitted free energies and diffusion coefficients. Such a bias may also be used to extend our approach to determining parameters for the model to systems that would not normally explore the full coordinate range on accessible time scales. Alternatively, the propagators predicted from the model at different "lag" times may be compared with observations from simulation. We then present some applications of the model to protein folding, including Kramers-like turnover in folding rates of coarse-grained models, the effect of non-native interactions on folding, and the effect of the chosen coordinate on the observed position-dependence of the diffusion coefficients. Lastly, we consider how our results are useful for the interpretation of experiments, and how this type of Bayesian analysis may eventually be applied directly to analyse experimental data.     

Two-state folding observed in individual protein molecules

The folding dynamics of small proteins are often described in terms of a simple two-state kinetic model. Within this notion, the behavior of individual molecules is expected to be stochastic, with a protein molecule residing in either the unfolded or the folded state for extended periods of time, with intermittent rapid jumps across the free energy barrier. However, a direct observation of this bistable behavior has not been made to date. Rather, previous reports of folding trajectories of individual proteins have shown an unexpected degree of complexity. This raises the question whether the simple kinetic properties derived from classical experiments on large ensembles of molecules are reflected in the folding paths taken by individual proteins. Here we report single-molecule folding/unfolding trajectories observed by fluorescence resonance energy transfer for a protein that meets all criteria of a two state-system. The trajectories, measured on molecules immobilized in lipid vesicles, demonstrate the anticipated bistable behavior, with steplike transitions between folded and unfolded conformations. They further allow us to put an upper bound on the barrier crossing time.     

Nanoscale dewetting transition in protein complex folding

In a previous study, a surprising drying transition was observed to take place inside the nanoscale hydrophobic channel in the tetramer of the protein melittin. The goal of this paper is to determine if there are other protein complexes capable of displaying a dewetting transition during their final stage of folding. We searched the entire protein data bank (PDB) for all possible candidates, including protein tetramers, dimers, and two-domain proteins, and then performed the molecular dynamics (MD) simulations on the top candidates identified by a simple hydrophobic scoring function based on aligned hydrophobic surface areas. Our large scale MD simulations found several more proteins, including three tetramers, six dimers, and two two-domain proteins, which display a nanoscale dewetting transition in their final stage of folding. Even though the scoring function alone is not sufficient (i.e., a high score is necessary but not sufficient) in identifying the dewetting candidates, it does provide useful insights into the features of complex interfaces needed for dewetting. All top candidates have two features in common: (1) large aligned (matched) hydrophobic areas between two corresponding surfaces, and (2) large connected hydrophobic areas on the same surface. We have also studied the effect on dewetting of different water models and different treatments of the long-range electrostatic interactions (cutoff vs PME), and found the dewetting phenomena is fairly robust. This work presents a few proteins other than melittin tetramer for further experimental studies of the role of dewetting in the end stages of protein folding.     

Frustration and hydrophobicity interplay in protein folding and protein evolution

A lattice model is used to study mutations and compacting effects on protein folding rates and folding temperature. In the context of protein evolution, we address the question regarding the best scenario for a polypeptide chain to fold: either a fast nonspecific collapse followed by a slow rearrangement to form the native structure or a specific collapse from the unfolded state with the simultaneous formation of the native state. This question is investigated for optimized sequences, whose native state has no frustrated contacts between monomers, and also for mutated sequences, whose native state has some degree of frustration. It is found that the best scenario for folding may depend on the amount of frustration of the native structure. The implication of this result on protein evolution is discussed.     

Solvent viscosity dependence of the protein folding dynamics

Solvent viscosity has been frequently adopted as an adjustable parameter in various computational studies (e.g., protein folding simulations) with implicit solvent models. A common approach is to use low viscosities to expedite simulations. While using viscosities lower than that of aqueous is unphysical, such treatment is based on observations that the viscosity affects the kinetics (rates) in a well-defined manner as described by Kramers' theory. Here, we investigate the effect of viscosity on the detailed dynamics (mechanism) of protein folding. On the basis of a simple mathematical model, we first show that viscosity may indeed affect the dynamics in a complex way. By applying the model to the folding of a small protein, we demonstrate that the detailed dynamics is affected rather pronouncedly especially at unphysically low viscosities, cautioning against using such viscosities. In this regard, our model may also serve as a diagnostic tool for validating low-viscosity simulations. It is also suggested that the viscosity dependence can be further exploited to gain information about the protein folding mechanism.     

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.     

The protein folding network indicates that the ultrafast folding mutant of villin headpiece subdomain has a deeper folding funnel

Protein folding is a dynamic process with continuous transitions among different conformations. In this work, the dynamics in the protein folding network of villin headpiece subdomain (HP35) has been investigated based on multiple reversible folding trajectories of HP35 and its ultrafast folding mutant where sub-angstrom folding was achieved. The four folding states were clearly separated on the network, validating the classification of the states. Examination of the eight conformers with different formation of the individual helices revealed high plasticity of the three helices in all the four states. A consistent feature between the wild type and mutant protein is the dominant conformer 111 (all three helices formed) in the folded state and conformers 111 and 011 (helices II and III formed) in the major intermediate state, indicating the critical role of helices II and III in the folding mechanism. When compared to the wild type, the folding landscape of the ultrafast folding mutant exhibited a deeper folding funnel towards the folded state. The very beginning of the folding (0-10 ns) was very similar for both protein variants but it soon diverged and displayed different folding pathways. Although going through the major intermediate state is the dominant pathway for both, it was also observed that some folding went through the minor intermediate state for the mutant. The intriguing difference resulting from the mutation at two residues in helix III has been carefully analyzed and discussed in details.     

Role of cofactors in folding of the blue-copper protein azurin

Many proteins in living cells coordinate cofactors, such as metal ions, to attain their activity. Since the cofactors in such cases often can interact with their corresponding unfolded polypeptides in vitro, it is important to unravel how cofactors modulate protein folding. In this review, I will discuss the role of cofactors in folding of the blue-copper protein Pseudomonas aeruginosa azurin. In the case of both copper (Cu(II) and Cu(I)) and zinc (Zn(II)), the metal can bind to unfolded azurin. The residues involved in copper (Cu(II) and Cu(I)) coordination in the unfolded state have been identified as Cys112, His117, and Met121. The affinities of Cu(II), Cu(I), and Zn(II) are all higher for the folded than for the unfolded azurin polypeptide, resulting in metal stabilization of the native state as compared to the stability of apo-azurin. Cu(II), Zn(II), and several apo forms of azurin all fold in two-state kinetic reactions with roughly identical polypeptide-folding speeds. This suggests that the native-state beta-barrel topology, not cofactor interactions or thermodynamic stability, determines azurin's folding barrier. Nonetheless, copper binds much more rapidly (i.e., 4 orders of magnitude) to unfolded azurin than to folded azurin. Therefore, the fastest route to functional azurin is through copper binding before polypeptide folding; this sequence of events may be the relevant biological pathway.     

Simulating temperature jumps for protein folding

We present a new computational methodology aimed to calculate the thermodynamics and kinetics of peptide folding. We focus in particular on temperature jump experiments of folding rates and show how a combination of replica exchange molecular dynamics (REMD) followed by multiplexed molecular dynamics starting from structures taken from the REMD runs can be used to extract properties in line with experiments. A model system, alanine20, is studied in this article as a proof of principle and used to describe the methodology.     

Towards protein folding with evolutionary techniques

We present design details and first tests of a new evolutionary algorithm approach to ab initio protein folding. It does not focus on dihedral angles exclusively, but mainly operates on introduction, extension, break-up, and destruction of secondary structure elements, given as correlated dihedral angle values. In first test applications to polyalanines (up to 60 residues) and random primary sequences (up to 40 residues), we demonstrate that this use of prior knowledge is well balanced: On the one hand, it ensures quick introduction of secondary structure elements if they are favorable for a given primary sequence, but still allows for efficient location of pure random coil solutions without enforcing any secondary structure elements, if folds of this type are preferred by the given primary sequence. Furthermore, the algorithm is clearly able to pack several secondary structure elements into favorable tertiary structure arrangements, although no part of the algorithm is explicitly designed to do this. In first test examples on real-life peptides between 21 and 44 residues from the Protein Data Bank, the quality of the results depends on the force field used (as expected); nevertheless, we can show that the algorithm is able to find structures in good agreement with the targets easily and consistently, if the force field allows for that.