Integrated prediction of protein folding and unfolding rates from only size and structural class

Protein stability, folding and unfolding rates are all determined by the multidimensional folding free energy surface, which in turn is dictated by factors such as size, structure, and amino-acid sequence. Work over the last 15 years has highlighted the role of size and 3D structure in determining folding rates, resulting in many procedures for their prediction. In contrast, unfolding rates are thought to depend on sequence specifics and be much more difficult to predict. Here we introduce a minimalist physics-based model that computes one-dimensional folding free energy surfaces using the number of aminoacids (N) and the structural class (α-helical, all-β, or α-β) as only protein-specific input. In this model N sets the overall cost in conformational entropy and the net stabilization energy, whereas the structural class defines the partitioning of the stabilization energy between local and non-local interactions. To test its predictive power, we calibrated the model empirically and implemented it into an algorithm for the PREdiction of Folding and Unfolding Rates (PREFUR). We found that PREFUR predicts the absolute folding and unfolding rates of an experimental database of 52 proteins with accuracies of ±0.7 and ±1.4 orders of magnitude, respectively (relative to experimental spans of 6 and 8 orders of magnitude). Such prediction uncertainty for proteins vastly varying in size and structure is only two-fold larger than the differences in folding (±0.34) and unfolding rates (±0.7) caused by single-point mutations. Moreover, PREFUR predicts protein stability with an accuracy of ±6.3 kJ mol(-1), relative to the 5 kJ mol(-1) average perturbation induced by single-point mutations. The remarkable performance of our simplistic model demonstrates that size and structural class are the major determinants of the folding landscapes of natural proteins, whereas sequence variability only provides the final 10-20% tuning. PREFUR is thus a powerful bioinformatic tool for the prediction of folding properties and analysis of experimental data.     

Magnetic susceptibility of CfCl3 and its dependence on crystal structure

Magnetic measurements are presented for polycrystalline samples of californium trichloride in both a hexagonal (UC1₃ type; californium(III) CN = 9) and an orthorhombic (PuBr₃ type; californium(III) CN = 8) crystal form. In the Curie-Weiss temperature regions (orthorhombic, 100–340 K, hexagonal, 60–340 K) the Weiss constant θ_p is significantly larger for the orthorhombic form. As the temperature decreases, the susceptibility of the orthorhombic form begins to deviate from Curie-Weiss behavior at a higher temperature than the hexagonal form indicating a larger crystal-field splitting in the orthorhombic form. At temperatures below 15 K a field-dependent transition is observed. In a field of 5 kG an antiferromagnetic maximum in the susceptibility is observed at 7 K and 13 K for the hexagonal and orthorhombic forms respectively. For 30 kG both types exhibit monotonically increasing susceptibilities with decreasing temperature and the hexagonal form shows saturation behavior in the susceptibility vs. temperature plots with a saturation moment of about 6_μB atom⁻¹.     

Vibrational spectra,packing calculations and crystal structure of 1,2-diiodobenzene

The vibrational spectra of crystalline 1,2-diiodobenzene are presented. Spectroscopic evidence in combination with packing and lattice frequence calculations point to a tetramolecular unit cell, space group C⁵_2h- Approximate molecular positions are given.     

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.     

Improving protein structural class prediction using novel combined sequence information and predicted secondary structural features

Protein structural class prediction solely from protein sequences is a challenging problem in bioinformatics. Numerous efficient methods have been proposed for protein structural class prediction, but challenges remain. Using novel combined sequence information coupled with predicted secondary structural features (PSSF), we proposed a novel scheme to improve prediction of protein structural classes. Given an amino acid sequence, we first transformed it into a reduced amino acid sequence and calculated its word frequencies and word position features to combine novel sequence information. Then we added the PSSF to the combine sequence information to predict protein structural classes. The proposed method was tested on four benchmark datasets in low homology and achieved the overall prediction accuracies of 83.1%, 87.0%, 94.5%, and 85.2%, respectively. The comparison with existing methods demonstrates that the overall improvements range from 2.3% to 27.5%, which indicates that the proposed method is more efficient, especially for low-homology amino acid sequences.     

Scaling laws in simple and complex proteins: size scaling effects associated with domain number and folding class

The native states of the most compact globular proteins have been described as being in the so-called “collapsed-polymer regime,” characterized by the scaling law R _g ~ n ^ν, where R _g is radius of gyration, n is the number of residues, and ν ≈ 1/3. However, the diversity of folds and the plasticity of native states suggest that this law may not be universal. In this work, we study the scaling regimes of: (i) one to four-domain protein chains, and (ii) their constituent domains, in terms of the four major folding classes. In the case of complete chains, we show that size scaling is influenced by the number of domains. For the set of domains belonging to the all-α, all-β, α/β, and α?+?β folding classes, we find that size-scaling exponents vary between 0.3?≤?ν?≤?0.4. Interestingly, even domains in the same folding class show scaling regimes that are sensitive to domain provenance, i.e., the number of domains present in the original intact chain. We demonstrate that the level of compactness, as measured by monomer density, decreases when domains originate from increasingly complex proteins.     

A re-examination of the crystal structure and molecular packing of α-nylon 6

During studies of polymorphism of polyamides with an even number of carbon atoms, it was thought worthwhile to re-examine the crystal structure and molecular packing of the α-form of nylon 6 by more advanced instrumentation and computing facilities. X-ray diffraction measurements on mono-oriented fibres confirm that nylon 6 crystallizes in the monoclinic system, with crystallographic parameters: $\text{a = 9.71}\text{A}\text{?}\text{, b = 8.19}\text{A}\text{?}\text{, c = 17.40}\text{A}\text{?}$ (fibre axis), γ = 115°, 8 monomeric units in the unit cell and space group P2₂. The crystal packing can be represented by parallel sheets of hydrogen-bonded antiparallel chains; the sheets are all oriented in the same sense and alternately displaced 3.73 Å along the c axis. The hydrogen bond distance is 2.98 Å. Although the structure was substantially similar to that previously found, some differences were observed; they are discussed on the basis of theoretical calculations.     

Predicting structural class for protein sequences of 40% identity based on features of primary and secondary structure using Random Forest algorithm

At present, tertiary structure discovery growth rate is lagging far behind discovery of primary structure. The prediction of protein structural class using Machine Learning techniques can help reduce this gap. The Structural Classification of Protein – Extended (SCOPe 2.07) is latest and largest dataset available at present. The protein sequences with less than 40% identity to each other are used for predicting α, β, α/β and α + β SCOPe classes. The sensitive features are extracted from primary and secondary structure representations of Proteins. Features are extracted experimentally from secondary structure with respect to its frequency, pitch and spatial arrangements. Primary structure based features contain species information for a protein sequence. The species parameters are further validated with uniref100 dataset using TaxId. As it is known, protein tertiary structure is manifestation of function. Functional differences are observed in species. Hence, the species are expected to have strong correlations with structural class, which is discovered in current work. It enhances prediction accuracy by 7%–10%. The subset of SCOPe 2.07 is trained using 65 dimensional feature vector using Random Forest classifier. The test result for the rest of the set gives consistent accuracy of better than 95%. The accuracy achieved on benchmark datasets ASTRAL 1.73, 25PDB and FC699 is better than 86%, 91% and 97% respectively, which is best reported to our knowledge.     

Effect of finite size on cooperativity and rates of protein folding

We analyze the dependence of cooperativity of the thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, N, using lattice models with side chains, off-lattice Go models, and the available experimental data. A dimensionless measure of cooperativity, Omega(c) (0 < Omega(c) < infinity), scales as Omega(c) approximately N(zeta). The results of simulations and the analysis of experimental data further confirm the earlier prediction that zeta is universal with zeta = 1 + gamma, where exponent gamma characterizes the susceptibility of a self-avoiding walk. This finding suggests that the structural characteristics in the denaturated state are manifested in the folding cooperativity at the transition temperature. The folding rates k(F) for the Go models and a dataset of 69 proteins can be fit using k(F) = k(F)0 exp(-cN(beta)). Both beta = 1/2 and 2/3 provide a good fit of the data. We find that k(F) = k(F)0 exp(-cN(1/2)), with the average (over the dataset of proteins) k(F)0 approximately (0.2 micros)(-1) and c approximately 1.1, can be used to estimate folding rates to within an order of magnitude in most cases. The minimal models give identical N dependence with c approximately 1. The prefactor for off-lattice Go models is nearly 4 orders of magnitude larger than the experimental value.     

The structure of crystalline monoethanolamine and a model of its structural rearrangement on crystal melting

A model of structural rearrangement upon melting of crystalline monoethanolamine (MEA) was proposed on the basis of analysis of literature data on the structure of crystalline and liquid monoethanolamine (MEA), the structure and conformation of MEA molecule in gas, liquid, and solid state, and a number of physicochemical properties of liquid MEA. The results were compared with the model of crystalline ethylene glycol melting suggested by the authors earlier.     

2D representation of protein secondary structure sequences and its applications

In terms of the classification of the protein secondary structures, we propose a 2D representation of protein secondary structure sequences. The representation are used to display, analyze, and compare the secondary structure sequences. Based on this representation, we assign the structural class to the protein, and verify the advantage or disadvantage of the methods of predicted protein second structure.     

Progress in protein structural class prediction and its impact to bioinformatics and proteomics

The structural class is an important attribute used to characterize the overall folding type of a protein or its domain. Since the concept of protein structural class was developed about 3 decades ago based on a visual inspection of polypeptide chain topologies in a dataset of only 31 gloular proteins, the number of structure-known proteins has been increased rapidly. For example, as of 12-July-2005, the entries deposited into RCSB PDB Protein Data Bank for proteins, peptides, and viruses whose 3-dimensional structures were determined by X-ray and NMR techniques have been increased to 28,920. To properly cover more and more structure-known proteins, some modification and expansion from the original structural classification scheme have been developed. Meanwhile, many different approaches have been proposed for predicting the structural class of proteins. In this review, the new classification schemes are briefly introduced. The attention is focused on the progress in structural class prediction and its impact in stimulating the development of identifying the other attributes of proteins. It is interesting to point out that the development of the latter has actually in turn greatly enriched the power of the former. Also, some promising approaches for the further development of protein structural class prediction are also addressed.     

Putting a lid on protein folding: structure and function of the co-chaperonin,GroES

The co-chaperonin GroES is an essential partner in protein folding mediated by the chaperonin, GroEL. Two recent crystal structures of GroES provide a structural basis to understand how GroES forms the lid on the folding-active cis ternary complex, and how the GroEL-GroES complex enhances folding.     

Solvent effect on the folding dynamics and structure of E6-associated protein characterized from ab initio protein folding simulations

Solvent effect on protein conformation and folding mechanism of E6-associated protein (E6ap) peptide are investigated using a recently developed charge update scheme termed as adaptive hydrogen bond-specific charge (AHBC). On the basis of the close agreement between the calculated helix contents from AHBC simulations and experimental results, we observed based on the presented simulations that the two ends of the peptide may simultaneously take part in the formation of the helical structure at the early stage of folding and finally merge to form a helix with lowest backbone RMSD of about 0.9 A? in 40% 2,2,2-trifluoroethanol solution. However, in pure water, the folding may start at the center of the peptide sequence instead of at the two opposite ends. The analysis of the free energy landscape indicates that the solvent may determine the folding clusters of E6ap, which subsequently leads to the different final folded structure. The current study demonstrates new insight to the role of solvent in the determination of protein structure and folding dynamics.     

Synthesis,crystal structure,and hydrogen-bonded displacive-type structural phase transition of guanidine dichloroacetate

Guanidine dichloroacetate was synthesized and separated as crystals. Differential scanning calorimetry (DSC) measurement shows that this compound undergoes a reversible phase transition at about 275 K with a heat hysteresis of 28 K. Step-like dielectric anomaly observed at 274 K further confirms the phase transition. The single-crystal X-ray diffraction data suggested that these was a transition from a room-temperature phase with the space group of P2₁/n (a = 8.030(5), b = 12.014(9), c = 8.124(6) Å, β = 96.089(1)°, V = 779.3(1) Å³, and Z = 4) to a low-temperature one with the space group of P2₁/c (a = 7.941(2), b = 11.828(3), c = 10.614(2) Å, β = 130.985(1)°, V = 752.6(3) Å³, and Z = 4). The displacements of hydrogen bonds induce the structure phase transition.     

A visual representation for RNA secondary structure and its application

The graphical representation of biological sequences is an important subject in the area of genome studies. We propose a novel visual representation for RNA secondary structures. Some symmetric properties and information on the base distribution and compositions can be intuitively reflected by the projection graphs of the points corresponding to the RNA secondary structures. Then our method is applied to compute the similarity of 12 classical samples and 11 real RNA secondary structures. The results indicate that our method can not only effectively analyze the similarity between RNA secondary structures but also show a high consistency with other literatures. Moreover, our method only needs the geometrical center of the characteristic curve of the RNA secondary structure to compute the similarity matrix, which means a low computational complexity. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Influence of ordered backbone structure on protein folding. A study of some simple models

Four series of model molecules, each of which contains a coil section and one or two sections of fixed ordered backbone structure, have been examined to locate their low-energy conformations in water. The four series are: helix-coil, helix-coil-helix, extended-coil, and extended-coil-extended. In each series, the length of the coil is allowed to vary from four to ten residues, while the nuclei (ordered backbone structures) are held fixed at six residues. By comparing these molecules, it is observed that the low-energy conformations of those containing two nuclei can be regarded as being derived from low-energy conformations of molecules containing one nucleus. This suggests that folding of proteins containing preformed nuclei proceeds through interactions between the nuclei and adjacent non-regular sections of the chain rather than between nuclei. It is also observed that helices are better promoters of globularity than extended strands. These results are compared with those from recent studies of various aspects of protein folding.     

X-ray structural investigation of gossypol and its derivatives. VII. Molecular and crystal structure of dianilinegossypol

A complete x-ray structural investigation of the complex of dianilinegossypol with ethyl acetate has been made and it has been shown that in these crystals the dianilinegossypol gossypol has predominantly the quinoid tautomeric form.A. S. Sadykov Institute of Bioorganic Chemistry, Uzbek SSR Academy of Sciences, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 661–666, September–October, 1988.