Single-domain Globular Proteins Research Articles

Estimating ruggedness of free-energy landscapes of small globular proteins from principal component analysis of molecular dynamics trajectories.

The internal dynamics of biomolecules, and hence their function, is governed by the structure of their free-energy landscape. Early flash-photolysis experiments on myoglobin suggested that the free-energy landscapes of proteins are hierarchically structured, with a characteristic distribution of free-energy barriers which gives rise to anomalous diffusion. Analytical results have been derived for one-dimensional or high-dimensional hierarchical free-energy landscapes. Recent improvements in methods and computer performance enable generating sufficiently long molecular dynamics (MD) trajectories to extract dynamics information covering many orders of magnitude, such that the broad distributions of energy barriers of proteins become accessible to quantitative studies of intermediate dimensions. In this work, we present a nonequilibrium method to estimate barrier height distributions from microsecond-long MD simulations. It infers barrier height distributions from anomalous diffusion exponents derived from principal component analysis and by comparison to simple hierarchical lattice models. These models are d-dimensional lattices of states separated by free-energy barriers, the heights of which are distributed as p(ΔG)=1/γexp(-ΔG/γ). The parameter γ quantifies the "ruggedness" of the free-energy landscape in such models. We show that both parameters, i.e., ruggedness and effective dimensionality d, can be inferred from anomalous diffusion exponents. Assuming a similar dependency of anomalous diffusion exponents on γ and d for proteins, we estimate the ruggedness of the free-energy landscapes of 500 small, single-domain globular proteins between 15 and 20 kT per dimension with an estimated accuracy of 4.2 kT and dimensionality between 40 and 60 with an estimated accuracy of 10 dimensions. Remarkably, neither effective dimensionality nor the ruggedness correlates with protein size and both ruggedness and effective dimensionality are much smaller than the scatter of protein sizes. From this finding, we conclude that these two properties of the free-energy landscape of a protein are rather adapted to the particular function of each single protein and that, quite generally, are functionally relevant for globular proteins.

PFDB: A standardized protein folding database with temperature correction

We constructed a standardized protein folding kinetics database (PFDB) in which the logarithmic rate constants of all listed proteins are calculated at the standard temperature (25 °C). A temperature correction based on the Eyring–Kramers equation was introduced for proteins whose folding kinetics were originally measured at temperatures other than 25 °C. We verified the temperature correction by comparing the logarithmic rate constants predicted and experimentally observed at 25 °C for 14 different proteins, and the results demonstrated improvement of the quality of the database. PFDB consists of 141 (89 two-state and 52 non-two-state) single-domain globular proteins, which has the largest number among the currently available databases of protein folding kinetics. PFDB is thus intended to be used as a standard for developing and testing future predictive and theoretical studies of protein folding. PFDB can be accessed from the following link: http://lee.kias.re.kr/~bala/PFDB.

Transient intermediates are populated in the folding pathways of single-domain two-state folding protein L.

Small single-domain globular proteins, which are believed to be dominantly two-state folders, played an important role in elucidating various aspects of the protein folding mechanism. However, recent single molecule fluorescence resonance energy transfer experiments [H. Y. Aviram et al. J. Chem. Phys. 148, 123303 (2018)] on a single-domain two-state folding protein L showed evidence for the population of an intermediate state and it was suggested that in this state, a β-hairpin present near the C-terminal of the native protein state is unfolded. We performed molecular dynamics simulations using a coarse-grained self-organized-polymer model with side chains to study the folding pathways of protein L. In agreement with the experiments, an intermediate is populated in the simulation folding pathways where the C-terminal β-hairpin detaches from the rest of the protein structure. The lifetime of this intermediate structure increased with the decrease in temperature. In low temperature conditions, we also observed a second intermediate state, which is globular with a significant fraction of the native-like tertiary contacts satisfying the features of a dry molten globule.

Coarse-Grained Modeling of the Interplay between Secondary Structure Propensities and Protein Fold Assembly.

We recently developed a new coarse-grained model of protein structure and dynamics [ Dawid et al. J. Chem. Theory Comput. 2017 , 13 ( 11 ), 5766 - 5779 ]. The model assumed a single bead representation of amino acid residues, where positions of such united residues were defined by centers of mass of four amino acid fragments. Replica exchange Monte Carlo sampling of the model chains provided good pictures of modeled structures and their dynamics. In its generic form the statistical knowledge-based force field of the model has been dedicated for single-domain globular proteins. Sequence-specific interactions are defined by three-letter secondary structure data. In the present work we demonstrate that different assignments and/or predictions of secondary structures are usually sufficient for enforcing cooperative formation of native-like folds of SURPASS chains for the majority of single-domain globular proteins. Simulations of native-like structure assembly for a representative set of globular proteins have shown that the accuracy of secondary structure data is usually not crucial for model performance, although some specific errors can strongly distort the obtained three-dimensional structures.

50+ Years of Protein Folding.

The ability of proteins to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured rates of spontaneous folding of single-domain globular proteins range from microseconds to hours: the difference - 10-11 orders of magnitude - is the same as between the lifespan of a mosquito and the age of the Universe. This review (based on the literature and some personal recollections) describes a winding road to understanding spontaneous folding of protein structure. The main attention is given to the free-energy landscape of conformations of a protein chain - especially to the barrier separating its unfolded (U) and the natively folded (N) states - and to physical theories of rates of crossing this barrier in both directions: from U to N, and from N to U. It is shown that theories of both these processes come to essentially the same result and outline the observed range of folding and unfolding rates for single-domain globular proteins. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control, and explain the observed maximal size of "foldable" protein domains.

SURPASS Low-Resolution Coarse-Grained Protein Modeling.

Coarse-grained modeling of biomolecules has a very important role in molecular biology. In this work we present a novel SURPASS (Single United Residue per Pre-Averaged Secondary Structure fragment) model of proteins that can be an interesting alternative for existing coarse-grained models. The design of the model is unique and strongly supported by the statistical analysis of structural regularities characteristic for protein systems. Coarse-graining of protein chain structures assumes a single center of interactions per residue and accounts for preaveraged effects of four adjacent residue fragments. Knowledge-based statistical potentials encode complex interaction patterns of these fragments. Using the Replica Exchange Monte Carlo sampling scheme and a generic version of the SURPASS force field we performed test simulations of a representative set of single-domain globular proteins. The method samples a significant part of conformational space and reproduces protein structures, including native-like, with surprisingly good accuracy. Future extension of the SURPASS model on large biomacromolecular systems is briefly discussed.

Golden triangle for folding rates of globular proteins

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured rates of spontaneous folding of single-domain globular proteins range from microseconds to hours: the difference (11 orders of magnitude) is akin to the difference between the life span of a mosquito and the age of the universe. Here, we show that physical theory with biological constraints outlines a "golden triangle" limiting the possible range of folding rates for single-domain globular proteins of various size and stability, and that the experimentally measured folding rates fall within this narrow triangle built without any adjustable parameters, filling it almost completely. In addition, the golden triangle predicts the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control. It also predicts the maximal allowed size of the "foldable" protein domains, and the size of domains found in known protein structures is in a good agreement with this limit.

Coarse-Grained Strategy for Modeling Protein Stability in Concentrated Solutions

We present a coarse-grained approach for modeling the thermodynamic stability of single-domain globular proteins in concentrated aqueous solutions. Our treatment derives effective protein-protein interactions from basic structural and energetic characteristics of the native and denatured states. These characteristics, along with the intrinsic (i.e., infinite dilution) thermodynamics of folding, are calculated from elementary sequence information using a heteropolymer collapse theory. We integrate this information into Reactive Canonical Monte Carlo simulations to investigate the connections between protein sequence hydrophobicity, protein-protein interactions, protein concentration, and the thermodynamic stability of the native state. The model predicts that sequence hydrophobicity can affect how protein concentration impacts native-state stability in solution. In particular, low hydrophobicity proteins are primarily stabilized by increases in protein concentration, whereas high hydrophobicity proteins exhibit richer nonmonotonic behavior. These trends appear qualitatively consistent with the available experimental data. Although factors such as pH, salt concentration, and protein charge are also important for protein stability, our analysis suggests that some of the nontrivial experimental trends may be driven by a competition between destabilizing hydrophobic protein-protein attractions and entropic crowding effects.

The Hydrophobicity of the H3 Histone Fold differs from the Hydrophobicity of the other three Folds

The eukaryotic histone dimers, H3-H4 and H2A-H2B, are formed in the cytosol prior to being transported into the nucleus and assembled into the nucleosome. Residue side-chain distances from the interior of the histone dimers are obtained with an ellipsoidal spatial metric and structural information provided by X-ray analyses at atomic resolution of the nucleosome core particles. While the spatial hydrophobic moment profiles of the dimers are comparable with profiles obtained previously that characterize the hydrophobic core of single-chain, single-domain globular soluble proteins, correlation coefficients between the side-chain hydrophobicities and distances from the interior of the H3-H4 dimer and H2A-H2B dimer differ significantly. This difference is traced to the H3 histone fold, which segregates fewer hydrophobic residues within the protein interior than the three other folds. Examination of the correlation coefficient between residue hydrophobicity and side-chain distance from the dimer interior over local regions of the fold sequence shows that the region of reduced correlation is associated mainly with the residues at the carboxyl end of the H3 histone fold, the helical region of the fold involved in the H3-H3' binding of the (H3-H4)(2) tetramer of the nucleosome. Hydrophobic interactions apparently contribute to the binding of this fourfold helical bundle and this evolutionary requirement may trade off against the requirement for H3-H4 dimer stability. The present results provide a different view than previously proposed, albeit of similar origin, to account for the reduced stability of the H3-H4 dimer compared with the H2A-H2B dimer.

Landscape approaches for determining the ensemble of folding transition states: success and failure hinge on the degree of frustration.

We present a method for determining structural properties of the ensemble of folding transition states from protein simulations. This method relies on thermodynamic quantities (free energies as a function of global reaction coordinates, such as the percentage of native contacts) and not on "kinetic" measurements (rates, transmission coefficients, complete trajectories); consequently, it requires fewer computational resources compared with other approaches, making it more suited to large and complex models. We explain the theoretical framework that underlies this method and use it to clarify the connection between the experimentally determined Phi value, a quantity determined by the ratio of rate and stability changes due to point mutations, and the average structure of the transition state ensemble. To determine the accuracy of this thermodynamic approach, we apply it to minimalist protein models and compare these results with the ones obtained by using the standard experimental procedure for determining Phi values. We show that the accuracy of both methods depends sensitively on the amount of frustration. In particular, the results are similar when applied to models with minimal amounts of frustration, characteristic of rapid-folding, single-domain globular proteins.

Barriers in protein folding reactions

This chapter focuses on the experimental thermodynamic and structural characterization of the barriers in the folding of single-domain globular proteins. The chapter also focuses on the structural aspects of the transition state of folding reactions, primarily, on mutational analyses and other protein engineering studies in which folding and/or unfolding kinetics have been investigated. The thermodynamic properties and the dynamics of the barrier crossings are also discussed. Studies of the elementary events in protein folding through simple model systems and a comparative overview of insights obtained from experimental and computational results are presented in the chapter. Many single-domain proteins, typically composed of 300 or fewer amino acids, exhibit intermediates in their folding reactions. Studies in which the properties of the intermediates have been the focus, as opposed to the transition states, are discussed. The chapter concludes that the merging of computational and experimental studies offers the prospect of unprecedented insight into the structure and dynamics of barriers in protein folding reactions.

Nativelike structure and stability in a truncation mutant of a protein minidomain: the peripheral subunit-binding domain.

Despite its small size, the peripheral subunit-binding domain from the dihydrolipoamide acetyltransferase component of the Bacillus stearothermophilus pyruvate dehydrogenase multienzyme complex adopts a unique, compact structure. To determine whether the full 43 residue sequence is required for the domain to adopt a stable, nativelike structure, 3 proteins of different lengths were prepared. Psbd41 corresponds to residues 3-43 of the domain, psbd36 spans residues 6-41, and psbd33 comprises residues 7-39. Psbd41 folds in a cooperative, two-state fashion with a Tm of 53 degrees C and a stability at 25 degrees C of 2.2 kcal mol-1. Psbd36 is nearly as stable with a Tm of 48 degrees C and a stability of 1.8 kcal mol-1. Similar m-values and heat capacities suggest that psbd36 and psbd41 bury approximately the same surface area. Minimal differences in CalphaH and NH chemical shifts between psbd41 and psbd36 show that the two sequences adopt the same tertiary fold. On a per residue basis, DeltaH degrees and DeltaC degrees p fall within the range typical for single-domain globular proteins. Psbd33 is significantly less stable. It is not fully folded at 25 degrees C, and at all temperatures it shows broadened NMR lines. ANS titrations provide evidence that this is due to an equilibrium between nativelike and unfolded molecules rather than formation of a molten globule. The fraction of psbd33 molecules which are folded appear to adopt the same structure as the full-length domain. Thus, although more than the 33 residue core is required to form a fully stable native structure, the entire sequence is not required for folding.

Molecular mechanisms for cooperative folding of proteins

The folding of single-domain globular proteins exhibits the character of first-order or two-state thermodynamics. The origin of such high cooperativity in relatively small polymer systems is still not well understood. Recently, the statistical mechanics of protein folding has been studied extensively with simple protein models such as short cubic-lattice chains with contact-based interactions. While many valuable insights about protein folding were gained with such models, some concerns have also arisen, viz. that they lack the character of protein backbones whose interactions would limit the folding patterns of proteins. Here, a comparative study of the conventional cubic-lattice chain model and a fine-grained more realistic lattice protein model with both backbone and side-chain interactions is carried out. It is found that, even though both types of models exhibit a cooperative two-state folding transition to the native structure with optimized force fields, the character and origin of cooperativity of the two models are different. In the simple contact-based model, the free-energy barrier occurs at the low end of the energy scale, and the cooperativity arises from a concerted formation of native contacts among many residues in a compact state. In the other more complicated model, the free-energy barrier occurs in the intermediate energy region, and the folding cooperativity arises from collective orientational arrangements of locally structured units in semi-open conformational states. On the basis of these results, two limiting molecular mechanisms for protein folding emerge, which can be used for analyzing the folding process of real proteins.

Stability and oligosaccharide binding of the N1 cellulose-binding domain of Cellulomonas fimi endoglucanase CenC.

Differential scanning calorimetry has been used to study the thermal stability and oligosaccharide-binding thermodynamics of the N-terminal cellulose-binding domain of Cellulomonas fimi beta-1,4-glucanase CenC (CBDN1). CBDN1 has a relatively low maximum stability (delta Gmax = 33 kJ/mol = 216 J/residue at 1 degree C and pH 6.1) compared to other small single-domain globular proteins. The unfolding is fully reversible between pH 5.5 and 9 and in accordance with the two-state equilibrium model between pH 5.5 and 11. When the single disulfide bond in CBDN1 is reduced, the protein remains unfolded at all conditions, as judged by NMR spectroscopy. This indicates that the intramolecular cross-link makes a major contribution to the stability of CBDN1. The measured heat capacity change of unfolding (delta Cp = 7.5 kJ mol-1 K-1) agrees well with that calculated from the predicted changes in the solvent accessible nonpolar and polar surface areas upon unfolding. Extrapolation of the specific enthalpy and entropy of unfolding to their respective convergence temperature indicates that per residue unfolding energies for CBDN1, an isolated domain, are in accordance with those found by Privalov (1) for many single-domain globular proteins. DSC thermograms of the unfolding of CBDN1 in the presence of various concentrations of cellopentaose were fit to a thermodynamic model describing the linkage between protein-ligand binding and protein unfolding. A global two-dimensional minimization routine is used to regress the binding enthalpy, binding constant, and unfolding thermodynamics for the CBDN1-cellopentaose system. Extrapolated binding constants are in quantitative agreement with those determined by isothermal titration calorimetry at 35 degrees C.

A method for the prediction of surface “U”-turns and transglobular connections in small proteins

A simple method for predicting the location of surface loops/turns that change the overall direction of the chain that is, "U" turns, and assigning the dominant secondary structure of the intervening transglobular blocks in small, single-domain globular proteins has been developed. Since the emphasis of the method is on the prediction of the major topological elements that comprise the global structure of the protein rather than on a detailed local secondary structure description, this approach is complementary to standard secondary structure prediction schemes. Consequently, it may be useful in the early stages of tertiary structure prediction when establishment of the structural class and possible folding topologies is of interest. Application to a set of small proteins of known structure indicates a high level of accuracy. The prediction of the approximate location of the surface turns/loops that are responsible for the change in overall chain direction is correct in more than 95% of the cases. The accuracy for the dominant secondary structure assignment for the linear blocks between such surface turns/loops is in the range of 82%.

The problem of protein folding and dynamics: time-resolved dynamic nonradiative excitation energy transfer measurements

The proteins are molecular machines that are self-assembled infinitely diverse, give rise to complex structures of any size, and have well-controlled vectorial modes of conformational changes, driven by thermal motions. Numerous experiments show that the pathway of folding of globular proteins, from the un-ordered state to the native conformations, and their modes of intramolecular motions, are determined by the sequence of the amino acyl residues (the monomers) in the polypeptide chain (the genetic information) of each protein. Attempts to decipher the mechanism by which the multiple transitions, on a wide range of time and distance scales are directed, depend on development of new methods for determination of distributions of intermolecular distances in flexible molecules and their time dependence. Methods based on time resolved measurements of intramolecular dynamic nonradiative excitation energy transfer, combined with protein engineering and site directed labeling were developed. Global analysis of data sets obtained by these measurements yield distributions of probabilities of segments end-to-end distances (EEDP) (in the range of 8 to 80 W chain). Methods for AMP determination of rates of conformational fluctuations and of the folding transitions, down to picosecond time scale, by means of this approach were also developed. Application of this experimental approach in the study of the denatured state of single-domain globular proteins, show that even in the denatured states, these proteins have compact structures. The bovine pancreatic trypsin inhibitor (BPTI) showed in the denatured state at least two conformational subpopulations, one was native-like and the other was characterized by EEDP distributions corresponding to an unfolded polypeptide chain.

Core domain of hirudin from the leech Hirudinaria manillensis: chemical synthesis, purification, and characterization of a Trp3 analog of fragment 1-47.

Hirudin is a small (approximately 7 kDa) disulfide-cross-linked polypeptide known as the most potent and specific thrombin inhibitor. We have previously shown that the N-terminal proteolytic fragment 1-47 of hirudin HM2 from Hirudinaria manillensis maintains inhibitory action toward thrombin [Vindigni, A., et al. (1994) Eur. J. Biochem. 226, 323-333]. Here we report the solid-phase chemical synthesis of an analog of fragment 1-47 bearing a Tyr3-->Trp exchange (Y3W analog). The crude, reduced peptide was purified by reverse-phase HPLC and subjected to oxidative folding to the disulfide-cross-linked species. The folding process of the Y3W analog was slower than that of the natural fragment 1-47, but nevertheless still occurred almost quantitatively as the natural species. The overall final yield of the synthetic product was approximately 35%, and its identity and homogeneity was established by a number of analytical techniques, including electrospray mass spectometry. The unique alignment of the three disulfide bridges of the Y3W analog was established by peptide mapping as Cys6-Cys14, Cys16-Cys28, and Cys22-Cys37 and shown to be identical to that of the natural fragment. The results of far- and near-ultraviolet circular dichroism and fluorescence emission measurements provided evidence that the Y3W analog retains the structural features of the natural species. The thermodynamic quantities (delta GD, delta Hm, delta Sm, and delta Cp) characterizing the reversible and cooperative thermal unfolding processes of the Y3W analog (Tm = 60.5 degrees C) and the natural fragment species (Tm = 62.5 degrees C) were evaluated. Despite the relatively high Tm values, the stability of both fragment species at 37 degrees C was only approximately 10 kJ mol-1, well below the average 50 kJ mol-1 typical of single-domain globular proteins. The synthetic Y3W species was found to be approximately 5-fold more active (KI = 30 +/- 5 nM) than the natural fragment 1-47 (KI = 150 +/- 20 nM) in inhibiting thrombin. Of interest was that the difference in the free energies of binding to thrombin at 37 degrees C, delta delta Gb, between the Y3W analog and natural species (4.2 kJ mol-1) was that expected for the difference in hydrophobicity between the two polypeptides resulting from the Tyr-->Trp exchange. The results of this study indicate that solid-phase chemical synthesis represents a convenient and high-yield procedure to prepare analogs of the biologically active, N-terminal core domain of hirudin with improved functional properties.