Role of foldability and stability in designing real protein sequences

This work explores the effects of two different fitness criteria, the free energy of folding (ΔG(folding)) and foldability (Φ) of mutated sequences, by measuring the designed protein's robustness via cumulative random point mutations. The results of a self-consistent mean-field based theory are used to design 'wild type' protein sequences corresponding to a specified target structure for a given foldability criteria Φ. The theory is applied on three 36-mer real protein conformations and the 'wild type' sequences are identified in terms of site specific monomer probabilities corresponding to a given foldability. Unlike the stability criteria, ΔG(folding) < 0, the foldability criteria Φ(mutated) < -1 effectively identifies sequences of different site-specific monomer identities by specifying the mean and variance of the energy of the unfolded state ensemble. The results depict a distinct difference in the pattern of mutational robustness of the neutral sequence space, Φ(mutated) < -1 scans more number of neutral sequences compared to ΔG(folding) < 0 to find the evolutionary fit sequences. Φ(mutated) < -1 also accounts for marginally stable sequences which are not effectively scanned by ΔG(folding) < 0 to determine evolutionary fitness. The results clearly point out that viable mutated sequences that are foldable, may not always conform to ΔG(fold) < 0, hence assessing the role of foldability in addition to stability for determining protein's robustness towards cumulative random point mutations. These observations may be used in engineering and designing de novo protein sequences which are more robust towards random point mutations.     

The Energetics of a Three‐State Protein Folding System Probed by High‐Pressure Relaxation Dispersion NMR Spectroscopy

The energetic and volumetric properties of a three‐state protein folding system, comprising a metastable triple mutant of the Fyn SH3 domain, have been investigated using pressure‐dependent ¹⁵N‐relaxation dispersion NMR from 1 to 2500 bar. Changes in partial molar volumes (ΔV) and isothermal compressibilities (Δκ_T) between all the states along the folding pathway have been determined to reasonable accuracy. The partial volume and isothermal compressibility of the folded state are 100 mL mol^?1 and 40 μL mol^?1 bar^?1, respectively, higher than those of the unfolded ensemble. Of particular interest are the findings related to the energetic and volumetric properties of the on‐pathway folding intermediate. While the latter is energetically close to the unfolded state, its volumetric properties are similar to those of the folded protein. The compressibility of the intermediate is larger than that of the folded state reflecting the less rigid nature of the former relative to the latter.     

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.     

Measuring pK(a) values in protein folding transition state ensembles by NMR spectroscopy

Protein folding kinetic data have been obtained for the marginally stable N-terminal SH3 domain of the Drosophila protein drk as a function of pH in order to investigate the electrostatic properties of Asp8 in the folding transition state ensemble. The slow exchange between folded and unfolded forms of the protein gives rise to separate NMR resonances for both folded and unfolded states at equilibrium. As a result, kinetic data can be derived from magnetization transfer between these two states without the need for denaturants. Using the fact that ionization of Asp8 dominates the electrostatic behavior of the protein between pH 2 and 3, along with pKa values for titrating groups in both folded and unfolded states that have been determined in a previous study, values of 2.9 +/- 0.1 and 3.3 +/- 0.2 are obtained for the pKa of Asp8 in the transition state for the wild-type protein and for a His7Ala mutant, respectively. The data are consistent with the partial formation in the transition state ensemble of an Asp8 side chain carboxylate-a Lys21 backbone amide interaction that represents a highly conserved contact in folded SH3 domains.     

Quantifying polypeptide conformational space: sensitivity to conformation and ensemble definition

Quantifying the density of conformations over phase space (the conformational distribution) is needed to model important macromolecular processes such as protein folding. In this work, we quantify the conformational distribution for a simple polypeptide (N-mer polyalanine) using the cumulative distribution function (CDF), which gives the probability that two randomly selected conformations are separated by less than a "conformational" distance and whose inverse gives conformation counts as a function of conformational radius. An important finding is that the conformation counts obtained by the CDF inverse depend critically on the assignment of a conformation's distance span and the ensemble (e.g., unfolded state model): varying ensemble and conformation definition (1 --> 2 A) varies the CDF-based conformation counts for Ala(50) from 10(11) to 10(69). In particular, relatively short molecular dynamics (MD) relaxation of Ala(50)'s random-walk ensemble reduces the number of conformers from 10(55) to 10(14) (using a 1 A root-mean-square-deviation radius conformation definition) pointing to potential disconnections in comparing the results from simplified models of unfolded proteins with those from all-atom MD simulations. Explicit waters are found to roughen the landscape considerably. Under some common conformation definitions, the results herein provide (i) an upper limit to the number of accessible conformations that compose unfolded states of proteins, (ii) the optimal clustering radius/conformation radius for counting conformations for a given energy and solvent model, (iii) a means of comparing various studies, and (iv) an assessment of the applicability of random search in protein folding.     

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.     

Stability of a protein tethered to a surface

Surface-tethered proteins are increasingly being used in a variety of experimental situations, and they are the basis for many new technologies. Nevertheless, a thorough understanding of how a surface can impact the native state stability of an attached protein is lacking. In this work, the authors use molecular dynamics simulations of a model beta-barrel protein to investigate how surface tethering influences native state stability. They find that stability, as measured by the folding temperature Tf, can be either increased, decreased, or remain unchanged as a result of tethering. Observed shifts are highly dependent on the location of residue used as the tether point, and stability is influenced by a number of factors, both energetic and entropic. These factors include native state vibrations, loss of bulk unfolded conformations, changes to the unfolded state ensemble, and the emergence of an entropic term not present for the bulk protein. They discuss each of these contributions in detail and comment on their relative importance and connection to experiment.     

Probing the transition state ensemble of a protein folding reaction by pressure-dependent NMR relaxation dispersion

The F61A/A90G mutant of a redesigned form of apocytochrome b562 folds by an apparent two-state mechanism. We have used the pressure dependence of 15N NMR relaxation dispersion rate profiles to study the changes in volumetric parameters that accompany the folding reaction of this protein at 45 degrees C. The experiments were performed under conditions where the folding/unfolding equilibrium could be studied at each pressure without addition of denaturants. The exquisite sensitivity of the methodology to small changes in folding/unfolding rates facilitated the use of relatively low-pressure values (between 1 and 270 bar) so that pressure-induced changes to the unfolded state ensemble could be minimized. A volume change for unfolding of -81 mL/mol is measured (at 1 bar), a factor of 1.4 larger (in absolute value) than the volume difference between the transition state ensemble (TSE) and the unfolded state. Notably, the changes in the free energy difference between folded and unfolded states and in the activation free energy for folding were not linear with pressure. Thus, the difference in the isothermal compressibility upon unfolding (-0.11 mL mol(-1) bar(-1)) and, for the first time, the compressibility of the TSE relative to the unfolded state (0.15 mL mol(-1) bar(-1)) could be calculated. The results argue for a TSE that is collapsed but loosely packed relative to the folded state and significantly hydrated, suggesting that the release of water occurs after the rate-limiting step in protein folding. The notion of a collapsed and hydrated TSE is consistent with expectations based on earlier temperature-dependent folding studies, showing that the barrier to folding at 45 degrees C is entropic (Choy, W. Y.; Zhou, Z.; Bai, Y.; Kay, L. E. J. Am. Chem. Soc. 2005, 127, 5066-5072).     

The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations

Using over 75 mus of molecular dynamics simulation, we have generated several thousand folding simulations of the 20-residue Trp cage at experimental temperature and solvent viscosity. A total of 116 independent folding simulations reach RMSDcalpha values below 3 A RMSDcalpha, some as close as 1.4 A RMSDcalpha. We estimate a folding time of 5.5+/-3.5 mus, a rate that is in reasonable agreement with experimental kinetics. Finally, we characterize both the folded and unfolded ensemble under native conditions and note that the average topology of the unfolded ensemble is very similar to the topology of the native state.     

Residue-specific real-time NMR diffusion experiments define the association states of proteins during folding

Characterizing the association states of proteins during folding is critical for understanding the nature of protein-folding intermediates and protein-folding pathways, protein aggregation, and disease-related aggregation. To study the association states of unfolded, folded, and intermediate species during protein folding, we have introduced a novel residue-specific real-time NMR diffusion experiment. This experiment, a combination of NMR real-time folding experiments and 3D heteronuclear pulsed field gradient NMR diffusion experiments (LED-HSQC), measures hydrodynamic properties, or molecular sizes, of kinetic species directly during the folding process. Application of the residue-specific real-time NMR diffusion experiments to characterize the folding of the collagen triple helix motif shows that this experiment can be used to determine the association states of unfolded, folded, and kinetic intermediates with transient lifetimes simultaneously. The ratio of the apparent translational diffusion coefficients of the unfolded to the folded form of the triple helix is 0.59, which correlates very well with a theoretical ratio for monomer to linear trimer. The apparent diffusion coefficients of the kinetic intermediates formed during triple helix folding indicate the formation of trimer-like associates which is consistent with previously published kinetic and relaxation data. The residue-specific time dependence of apparent diffusion coefficients of monomer and trimer peaks also illustrates the ability to use diffusion data to probe the directionality of triple helix formation. NMR diffusion experiments provide a new strategy for the investigation of protein-folding mechanisms, both to understand the role of kinetic intermediates and to determine the time-dependent aggregation processes in human diseases.     

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.     

A statistical model for predicting protein folding rates from amino acid sequence with structural class information

Prediction of protein folding rates from amino acid sequences is one of the most important challenges in molecular biology. In this work, I have related the protein folding rates with physical-chemical, energetic and conformational properties of amino acid residues. I found that the classification of proteins into different structural classes shows an excellent correlation between amino acid properties and folding rates of two- and three-state proteins, indicating the importance of native state topology in determining the protein folding rates. I have formulated a simple linear regression model for predicting the protein folding rates from amino acid sequences along with structural class information and obtained an excellent agreement between predicted and experimentally observed folding rates of proteins; the correlation coefficients are 0.99, 0.96 and 0.95, respectively, for all-alpha, all-beta and mixed class proteins. This is the first available method, which is capable of predicting the protein folding rates just from the amino acid sequence with the aid of generic amino acid properties and structural class information.     

A minimum-reaction-flux solution to master-equation models of protein folding

Master equations are widely used for modeling protein folding. Here an approximate solution to such master equations is presented. The approach used may be viewed as a discrete variational transition-state theory. The folding rate constant kf is approximated by the outgoing reaction flux J, when the unfolded set of macrostates assumes an equilibrium distribution. Correspondingly the unfolding rate constant ku is calculated as Jpu(1-pu), where pu is the equilibrium fraction of the unfolded state. The dividing surface between the unfolded and folded states is chosen to minimize the reaction flux J. This minimum-reaction-flux surface plays the role of the transition-state ensemble and identifies rate-limiting steps. Test against exact results of master-equation models of Zwanzig [Proc. Natl. Acad. Sci. USA 92, 9801 (1995)] and Munoz et al. [Proc. Natl. Acad. Sci. USA 95, 5872 (1998)] shows that the minimum-reaction-flux solution works well. Macrostates separated by the minimum-reaction-flux surface show a gap in p(fold) values. The approach presented here significantly simplifies the solution of master-equation models and, at the same time, directly yields insight into folding mechanisms.     

Direct measurement of tertiary contact cooperativity in RNA folding

All structured biological macromolecules must overcome the thermodynamic folding problem to populate a unique functional state among a vast ensemble of unfolded and alternate conformations. The exploration of cooperativity in protein folding has helped reveal and distinguish the underlying mechanistic solutions to this folding problem. Analogous dissections of RNA tertiary stability remain elusive, however, despite the central biological importance of folded RNA molecules and the potential to reveal fundamental properties of structured macromolecules via comparisons of protein and RNA folding. We report a direct quantitative measure of tertiary contact cooperativity in a folded RNA. We precisely measured the stability of an independently folding P4-P6 domain from the Tetrahymena thermophila group I intron by single molecule fluorescence resonance energy transfer (smFRET). Using wild-type and mutant RNAs, we found that cooperativity between the two tertiary contacts enhances P4-P6 stability by 3.2 +/- 0.2 kcal/mol.     

Ubiquitin: a small protein folding paradigm

For the past twenty years, the small, 76-residue protein ubiquitin has been used as a model system to study protein structure, stability, folding and dynamics. In this time, ubiquitin has become a paradigm for both the experimental and computational folding communities. The folding energy landscape is now uniquely characterised with a plethora of information available on not only the native and denatured states, but partially structured states, alternatively folded states and locally unfolded states, in addition to the transition state ensemble. This Perspective focuses on the experimental characterisation of ubiquitin using a comprehensive range of biophysical techniques.     

Random sequences with power-law correlations exhibit proteinlike behavior

We use a replica approach to investigate the thermodynamic properties of the random heteropolymers with persistent power-law correlations in monomer sequence. We show that this type of sequences possess proteinlike properties. In particular, we show that they can fold into stable unique three-dimensional structure (the "native" structure, in protein terminology) through two different types of pathways. One is a fast folding pathway and leads directly to the native structure. Another one, a more slower pathway, passes through the microphase separated (MPS) state and includes a number of intermediate glassy states. The scale and the magnitude of the MPS are calculated. The frozen state can be reached only by sequences with weak long-range correlations. The critical value for the correlation exponent is found, above which (strong correlations) freezing is impossible.     

The beta-peptide hairpin in solution: conformational study of a beta-hexapeptide in methanol by NMR spectroscopy and MD simulation.

The structural and thermodynamic properties of a 6-residue beta-peptide that was designed to form a hairpin conformation have been studied by NMR spectroscopy and MD simulation in methanol solution. The predicted hairpin would be characterized by a 10-membered hydrogen-bonded turn involving residues 3 and 4, and two extended antiparallel strands. The interproton distances and backbone torsional dihedral angles derived from the NMR experiments at room temperature are in general terms compatible with the hairpin conformation. Two trajectories of system configurations from 100-ns molecular-dynamics simulations of the peptide in solution at 298 and 340 K have been analyzed. In both simulations reversible folding to the hairpin conformation is observed. Interestingly, there is a significant conformational overlap between the unfolded state of the peptide at each of the temperatures. As already observed in previous studies of peptide folding, the unfolded state is composed of a (relatively) small number of predominant conformers and in this case lacks any type of secondary-structure element. The trajectories provide an excellent ground for the interpretation of the NMR-derived data in terms of ensemble averages and distributions as opposed to single-conformation interpretations. From this perspective, a relative population of the hairpin conformation of 20% to 30% would suffice to explain the NMR-derived data. Surprisingly, however, the ensemble of structures from the simulation at 340 K reproduces more accurately the NMR-derived data than the ensemble from the simulation at 298 K, a question that needs further investigation.     

Influence of the chain stiffness on the thermodynamics of a Gō-type model for protein folding

The relative importance of local and long range interactions in the characteristics of the protein folding process has long been a matter of controversy. Computer simulations based on Gō-type models have been widely used to study this topic, but without much agreement on which type of interactions is more relevant for the foldability of a protein. In this work, the authors also employ a topology-based potential and simulation model to analyze the influence of local and long range interactions on the thermodynamics of the folding transition. The former are mainly used to control the degree of flexibility (or stiffness) of the chain, mostly appreciable in the unfolded (noncompact) state. Our results show the different effects that local and nonlocal interactions have on the entropy and the energy of the system. This implies that a balance between both types of interactions is required, so that a free energy barrier exists between the native and the denatured states. The variations in the contribution of both types of interactions have also a direct effect on the stability of the chain conformations, including the possible appearance of thermodynamic folding intermediates.