Influence of the native topology on the folding barrier for small proteins

The possibility of downhill instead of two-state folding for proteins has been a very controversial topic which arose from recent experimental studies. From the theoretical side, this question has also been accomplished in different ways. Given the experimental observation that a relationship exists between the native structure topology of a protein and the kinetic and thermodynamic properties of its folding process, Gō-type potentials are an appropriate way to approach this problem. In this work, we employ an interaction potential from this family to get a better insight on the topological characteristics of the native state that may somehow determine the presence of a thermodynamic barrier in the folding pathway. The results presented here show that, indeed, the native topology of a small protein has a great influence on its folding behavior, mostly depending on the proportion of local and long range contacts the protein has in its native structure. Furthermore, when all the interactions present contribute in a balanced way, the transition results to be cooperative. Otherwise, the tendency to a downhill folding behavior increases.     

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.     

Understanding the folding rates and folding nuclei of globular proteins

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

Analyzing energy landscapes for folding model proteins

A new benchmark 20-bead HP model protein sequence (on a square lattice), which has 17 distinct but degenerate global minimum (GM) energy structures, has been studied using a genetic algorithm (GA). The relative probabilities of finding particular GM conformations are determined and related to the theoretical probability of generating these structures using a recoil growth constructor operator. It is found that for longer successful GA runs, the GM probability distribution is generally very different from the constructor probability, as other GA operators have had time to overcome any initial bias in the originally generated population of structures. Structural and metric relationships (e.g., Hamming distances) between the 17 distinct GM are investigated and used, in conjunction with data on the connectivities of the GM and the pathways that link them, to explain the GM probability distributions obtained by the GA. A comparison is made of searches where the sequence is defined in the normal (forward) and reverse directions. The ease of finding mirror image solutions are also compared. Finally, this approach is applied to rationalize the ease or difficulty of finding the GM for a number of standard benchmark HP sequences on the square lattice. It is shown that the relative probabilities of finding particular members of a set of degenerate global minima depend critically on the topography of the energy landscape in the vicinity of the GM, the connections and distances between the GM, and the nature of the operators used in the chosen search method.     

A new folding paradigm for repeat proteins

The folding/unfolding transitions of a series of designed consensus tetratricopeptide repeat proteins are quantitatively described by the classical one-dimensional Ising model, which thus represents a new folding paradigm for repeat proteins. Moreover, for the first time for any protein, a theoretical model predicts the folding/unfolding transition midpoint and the width of the transition.     

Novel characterization of the folding of proteins

In this paper, we consider a characterization of the folding of 3D model proteins. In this characterization, we describe the different kinds of 3‐step path conformation, then construct an augmented Hasse matrix which reflects some properties of the protein folding. This method can characterize the folding degree of 3D model proteins and evaluate the similarity/diversity of these five model proteins. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A ruler for determining the position of proteins in membranes

Both the oxygen diffusion rate and the oxygen solubility vary with depth into the interior of biological membranes. The product of these two gradients generates a single gradient, a permeability gradient, which is a smooth continuous function of the distance from the center of the membrane. Using electron paramagnetic resonance and the spin-probe method, the relaxation gradient of oxygen, which is directly proportional to the permeability gradient, is the quantity that can be directly measured in membranes under physiological conditions. The gradient obtained provides a calibrated ruler for determining the membrane depth of residues either from loop regions of membrane-binding proteins or from the membrane-exposed residues of transmembrane proteins. We have determined the relaxation gradient of oxygen in zwitterionic and anionic phospholipid membranes by attaching a single nitroxide probe to a transmembrane alpha-helical polypeptide at specific residues. The peptide ruler was used to determine the depth of penetration of the calcium-binding loops of the C2 domain of cytosolic phospholipase A(2). The positions of selected residues of this membrane-binding protein that penetrate into the membrane, determined using this ruler, compared favorably with previous determinations using more complex methods. The relaxation gradient constrains the possible values of the membrane-dependent oxygen concentration and the oxygen diffusion gradients. The average oxygen diffusion coefficient is estimated to be at least 2-fold smaller in the membrane than that in water.     

A conformationally constrained nucleotide analogue controls the folding topology of a DNA g-quadruplex

Guanine-rich DNA and RNA sequences can fold into unique structures known as G-quadruplexes. The structures of G-quadruplexes can be divided into several classes, depending on the parallel or antiparallel nature of the strands and the number of G-rich tracts present in an oligonucleotide. Oligonucleotides with single tracts of guanines form intermolecular parallel tetrameric G-quadruplexes. Oligonucleotides with two tracts of guanosines separated by two or more bases can form both intermolecular antiparallel fold-back dimeric and parallel tetrameric G-quadruplexes, and those with four tracts of guanosines can form both intramolecular parallel and antiparallel structures. Intramolecular G-qaudruplexes can fold into several folding topologies including antiparallel crossover basket, antiparallel chair, and parallel propeller. The ability to control the folding of G-quadruplexes would allow the physical, biochemical, and biological properties of these various folding topologies to be studied. Previously, the known methods to control the folding topology of G-quadruplexes included changing the buffer by varying the mono- and divalent cations that are present, and by changing the DNA sequence. Because the glycosidic bonds in the G-quartets of G-quadruplexes with parallel strands are in the anti conformation, we reasoned that incorporation of nucleoside analogues that prefer the anti conformation of the glycosidic bond into G-rich sequences would increase the preference for parallel G-quadruplex formation. As predicted, by positioning the conformationally constrained nucleotide analogue 2'-O-4'-C-methylene-linked ribonucleotide into specific positions of a DNA G-quadruplex we were able to shift the thermodynamically favored structure of a G-quadruplex from an antiparallel to a parallel structure.     

A new method for rapid characterization of the folding pathways of multidisulfide-containing proteins

Oxidative folding is a composite process that consists of both the conformational folding to the native three-dimensional structure and the regeneration of the native disulfide bonds of a protein, frequently involving over 100 disulfide intermediate species. Understanding the oxidative folding pathways of a multiple-disulfide-containing protein is a very difficult task that often requires years of devoted research due to the high complexity of the process and the very similar features of the large number of intermediates. Here we developed a method for rapidly delineating the major features of the oxidative folding pathways of a protein. The method examines the temperature dependence of the oxidative folding rate of the protein in combination with reduction pulses. Reduction pulses expose the presence of structured intermediates along the pathways. The correlation between the regeneration rate at different temperatures and the stability of the structured intermediates reveals the role that the intermediates play in determining the pathway. The method was first tested with bovine pancreatic ribonuclease A whose folding pathways were defined earlier. Then, it was explored to discern some of the major features of the folding pathways of its homologue, frog Onconase. The results suggest that the stability of the three-dimensional structure of the native protein is a major determinant of the folding rate in oxidative folding.     

Perturbation theory of Phi-value analysis of two-state protein folding: relation between p fold and Phi values

In protein folding, the transition state ensemble is defined as the set of conformations with p(fold)=12, where the p(fold) of a conformation is the probability that starting from this conformation the protein folds before it unfolds. Experimentally, this ensemble is probed by the Phi-value analysis, where Phi is the ratio of the changes in the logarithms of the folding rate and the equilibrium constant when the system is perturbed by a mutation. We show that for a two-state protein the Phi value can be expressed in terms of the perturbation and only the first two eigenfunctions of the evolution operator (e.g., a rate matrix) of the wild-type protein. The first eigenfunction is the equilibrium probability distribution while the second is proportional to p(fold), thus establishing a formal relation between p(fold) and Phi values. In addition to providing insight into the theoretical foundation of the Phi-value analysis, our results may prove practically useful in performing such analyses within the framework of models containing a large number of states.     

Thermodynamics of folding and association of lattice-model proteins

Closely related to the "protein folding problem" is the issue of protein misfolding and aggregation. Protein aggregation has been associated with the pathologies of nearly 20 human diseases and presents serious difficulties during the manufacture of pharmaceutical proteins. Computational studies of multiprotein systems have recently emerged as a powerful complement to experimental efforts aimed at understanding the mechanisms of protein aggregation. We describe the thermodynamics of systems containing two lattice-model 64-mers. A parallel tempering algorithm abates problems associated with glassy systems and the weighted histogram analysis method improves statistical quality. The presence of a second chain has a substantial effect on single-chain conformational preferences. The melting temperature is substantially reduced, and the increase in the population of unfolded states is correlated with an increase in interactions between chains. The transition from two native chains to a non-native aggregate is entropically favorable. Non-native aggregates receive approximately 25% of their stabilizing energy from intraprotein contacts not found in the lowest-energy structure. Contact maps show that for non-native dimers, nearly 50% of the most probable interprotein contacts involve pairs of residues that form native contacts, suggesting that a domain-swapping mechanism is involved in self-association.     

Forced folding and structural analysis of metastable proteins

A significant fraction of the proteins encoded by the human and other genomes appears to be significantly unfolded in vitro. This will undoubtedly hamper attempts to characterize their structure by classical crystallographic or solution NMR methods. Here we show that encapsulation of a metastable protein within the restricted volume a reverse micelle can be used to force fold the protein and allow its characterization by modern methods of NMR spectroscopy. This may have significant utility in the context of structural proteomics. In addition, variation of the inner volume of the reverse micelle can be used to probe the character of the manifold of unfolded states.     

Communication: folding of glycosylated proteins under confinement

Conjugating flexible polymers (such as oligosaccharides) to proteins or confining a protein in a restricted volume often increases protein thermal stability. In this communication, we investigate the interplay between conjugation and confinement which is not trivial as the magnitude and the mechanism of stabilization are different in each instance. Using coarse-grained computational approach the folding biophysics is studied when the protein is placed in a sphere of variable radius and is conjugated to 0-6 mono- or penta-saccharides. We observe a synergistic effect on thermal stability when short oligosaccharides are attached and the modified protein is confined in a small cage. However, when large oligosaccharides are added, a conflict between confinement and glycosylation arises as the stabilizing effect of the cage is dramatically reduced and it is almost impossible to further stabilize the protein beyond the mild stabilization induced by the sugars.     

Importance of gas-phase proton affinities in determining the electrospray ionization response for analytes and solvents

The effect of gas-phase proton transfer reactions on the mass spectral response of solvents and analytes with known gas-phase proton affinities was evaluated. Methanol, ethanol, propanol and water mixtures were employed to probe the effect of gas-phase proton transfer reactions on the abundance of protonated solvent ions. Ion-molecule reactions were carried out either in an atmospheric pressure electrospray ionization source or in the central quadrupole of a triple-quadrupole mass spectrometer. The introduction of solvent vapor with higher gas-phase proton affinity than the solvent being electrosprayed caused protons to transfer to the gas-phase solvent molecules. In mixed solvents, protonated solvent clusters of the solvent with higher gas-phase proton affinity dominated the resulting mass spectra. The effect of solvent gas-phase proton affinity on analyte response was also investigated, and the analyte response was suppressed or eliminated in solvents with gas-phase proton affinities higher than that of the analyte.     

Heuristic-based tabu search algorithm for folding two-dimensional AB off-lattice model proteins

The protein structure prediction problem is a classical NP hard problem in bioinformatics. The lack of an effective global optimization method is the key obstacle in solving this problem. As one of the global optimization algorithms, tabu search (TS) algorithm has been successfully applied in many optimization problems. We define the new neighborhood conformation, tabu object and acceptance criteria of current conformation based on the original TS algorithm and put forward an improved TS algorithm. By integrating the heuristic initialization mechanism, the heuristic conformation updating mechanism, and the gradient method into the improved TS algorithm, a heuristic-based tabu search (HTS) algorithm is presented for predicting the two-dimensional (2D) protein folding structure in AB off-lattice model which consists of hydrophobic (A) and hydrophilic (B) monomers. The tabu search minimization leads to the basins of local minima, near which a local search mechanism is then proposed to further search for lower-energy conformations. To test the performance of the proposed algorithm, experiments are performed on four Fibonacci sequences and two real protein sequences. The experimental results show that the proposed algorithm has found the lowest-energy conformations so far for three shorter Fibonacci sequences and renewed the results for the longest one, as well as two real protein sequences, demonstrating that the HTS algorithm is quite promising in finding the ground states for AB off-lattice model proteins.     

A rapid electrochemical method for determining rate coefficients for copper-catalyzed polymerizations

Copper(I) polyamine complexes have emerged as excellent atom-transfer radical polymerization catalysts. The rate of their reaction with organic halide initiators (the so-called activation step) varies across a broad range, depending on both the structure of the copper complex and the initiator. Herein, we report a new technique for determining the rate of copper-catalyzed activation (k(act)) using cyclic voltammetry coupled with electrochemical simulation. This method is applied to measuring k(act) for one of the most active catalysts, [Cu(I)(Me(6)tren)](+) (Me(6)tren = N,N,N-tris-(2-(dimethylamino)ethyl)amine), in reaction with ethyl bromoisobutyrate.