Testing a new Monte Carlo algorithm for protein folding

We demonstrate that the recently proposed pruned-enriched Rosenbluth method (PERM) (Grassberger, Phys. Rev. E 56:3682, 1997) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare it to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences. Proteins 32:52–66, 1998. © 1998 Wiley-Liss, Inc.     

Accelerated simulation of unfolding and refolding of a large single chain globular protein

We have developed novel strategies for contracting simulation times in protein dynamics that enable us to study a complex protein with molecular weight in excess of 34 kDa. Starting from a crystal structure, we produce unfolded and then refolded states for the protein. We then compare these quantitatively using both established and new metrics for protein structure and quality checking. These include use of the programs Concoord and Darvols. Simulation of protein-folded structure well beyond the molten globule state and then recovery back to the folded state is itself new, and our results throw new light on the protein-folding process. We accomplish this using a novel cooling protocol developed for this work.     

Exhaustive enumeration of protein conformations using experimental restraints.

We present an efficient new algorithm that enumerates all possible conformations of a protein that satisfy a given set of distance restraints. Rapid growth of all possible self-avoiding conformations on the diamond lattice provides construction of alpha-carbon representations of a protein fold. We investigated the dependence of the number of conformations on pairwise distance restraints for the proteins crambin, pancreatic trypsin inhibitor, and ubiquitin. Knowledge of between one and two contacts per monomer is shown to be sufficient to restrict the number of candidate structures to approximately 1,000 conformations. Pairwise RMS deviations of atomic position comparisons between pairs of these 1,000 structures revealed that these conformations can be grouped into about 25 families of structures. These results suggest a new approach to assessing alternative protein folds given a very limited number of distance restraints. Such restraints are available from several experimental techniques such as NMR, NOESY, energy transfer fluorescence spectroscopy, and crosslinking experiments. This work focuses on exhaustive enumeration of protein structures with emphasis on the possible use of NOESY-determined distance restraints.     

Fast tree search for a triangular lattice model of protein folding

Using a triangular lattice model to study the designability of protein folding, we overcame the parity problem of previous cubic lattice model and enumerated all the sequences and compact structures on a simple two-dimensional triangular lattice model of size 4 5 6 5 4. We used two types of amino acids, hydrophobic and polar, to make up the sequences, and achieved 223W212 different sequences excluding the reverse symmetry sequences. The total string number of distinct compact structures was 219,093, excluding reflection symmetry in the self-avoiding path of length 24 triangular lattice model. Based on this model, we applied a fast search algorithm by constructing a cluster tree. The algorithm decreased the computation by computing the objective energy of non-leaf nodes. The parallel experiments proved that the fast tree search algorithm yielded an exponential speed-up in the model of size 4 5 6 5 4. Designability analysis was performed to understand the search result.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

A branch and bound algorithm for the protein folding problem in the HP lattice model

A branch and bound algorithm is proposed for the two-dimensional protein folding problem in the HP lattice model. In this algorithm, the benefit of each possible location of hydrophobic monomers is evaluated and only promising nodes are kept for further branching at each level. The proposed algorithm is compared with other well-known methods for 10 benchmark sequences with lengths ranging from 20 to 100 monomers. The results indicate that our method is a very efficient and promising tool for the protein folding problem.     

Detection of native-like models for amino acid sequences of unknown three-dimensional structure in a data base of known protein conformations.

We present an approach which can be used to identify native-like folds in a data base of protein conformations in the absence of any sequence homology to proteins in the data base. The method is based on a knowledge-based force field derived from a set of known protein conformations. A given sequence is mounted on all conformations in the data base and the associated energies are calculated. Using several conformations and sequences from the globin family we show that the native conformation is identified correctly. In fact the resolution of the force field is high enough to discriminate between a native fold and several closely related conformations. We then apply the procedure to several globins of known sequence but unknown three dimensional structure. The homology of these sequences to globins of known structures in the data base ranges from 49 to 17%. With one exception we find that for all globin sequences one of the known globin folds is identified as the most favorable conformation. These results are obtained using a force field derived from a data base devoid of globins of known structure. We briefly discuss useful applications in protein structural research and future development of our approach.     

Reversible unfolding and refolding behavior of a monomeric aldolase from Staphylococcus aureus.

Thermal and GdmCl-induced unfolding transitions of aldolase from Staphylococcus aureus are reversible under a variety of solvent conditions. Analysis of the transitions reveals that no partially folded intermediates can be detected under equilibrium conditions. The stability of the enzyme is very low with a delta G0 value of -9 +/- 2 kJ/mol at 20 degrees C. The kinetics of unfolding and refolding of aldolase are complex and comprise at least one fast and two slow reactions. This complexity arises from prolyl isomerization reactions in the unfolded chain, which are kinetically coupled to the actual folding reaction. Comparison with model calculations shows that at least two prolyl peptide bonds give rise to the observed slow folding reactions of aldolase and that all of the involved bonds are presumably in the trans conformation in the native state. The rate constant of the actual folding reaction is fast with a relaxation time of about 15 s at the midpoint of the folding transition at 15 degrees C. The data presented on the folding and stability of aldolase are comparable to the properties of much smaller proteins. This might be connected with the simple and highly repetitive tertiary structure pattern of the enzyme, which belongs to the group of alpha/beta barrel proteins.     

SnapDRAGON: a method to delineate protein structural domains from sequence data

We describe a method to identify protein domain boundaries from sequence information alone based on the assumption that hydrophobic residues cluster together in space. SnapDRAGON is a suite of programs developed to predict domain boundaries based on the consistency observed in a set of alternative ab initio three-dimensional (3D) models generated for a given protein multiple sequence alignment. This is achieved by running a distance geometry-based folding technique in conjunction with a 3D-domain assignment algorithm. The overall accuracy of our method in predicting the number of domains for a non-redundant data set of 414 multiple alignments, representing 185 single and 231 multiple-domain proteins, is 72.4 %. Using domain linker regions observed in the tertiary structures associated with each query alignment as the standard of truth, inter-domain boundary positions are delineated with an accuracy of 63.9 % for proteins comprising continuous domains only, and 35.4 % for proteins with discontinuous domains. Overall, domain boundaries are delineated with an accuracy of 51.8 %. The prediction accuracy values are independent of the pair-wise sequence similarities within each of the alignments. These results demonstrate the capability of our method to delineate domains in protein sequences associated with a wide variety of structural domain organisation.     

Accurate general method for lattice approximation of three-dimensional structure of a chain molecule

An algorithm based on dynamic programming gives the lattice models having the minimal RMS deviations from the actual folds of protein (RNA, etc.) chains for a given lattice and a given orientation of the macromolecule relative to the lattice. The algorithm is applicable for 3-D lattices of any kind. The accuracy of the lattice approximation increases when the distance between neighbor chain links is not rigidly fixed. Special repulsive potentials facilitate generation of self-avoiding lattice chains. The results of model building show the efficiency and precisionof this proposed general method when compared with others. © 1995 Wiley-Liss, Inc.     

Secondary structure prediction and folding of globular protein: refolding of ferredoxin

The physicochemical mechanism of protein folding has been elucidated by the island model, describing a growth type of folding. The folding pathway is closely related with nucleation on the polypeptide chain and thus the formation of small local structures or secondary structures at the earliest stage of folding is essential to all following steps. The island model is applicable to any protein, but a high precision of secondary structure prediction is indispensable to folding simulation. The secondary structures formed at the earliest stage of folding are supposed to be of standard form, but they are usually deformed during the folding process, especially at the last stage, although the degree of deformation is different for each protein. Ferredoxin is an example of a protein having this property. According to X-ray investigation (1FDX), ferredoxin is not supposed to have secondary structures. However, if we assumed that in ferredoxin all the residues are in a coil state, we could not attain the correct structure similar to the native one. Further, we found that some parts of the chain are not flexible, suggesting the presence of secondary structures, in agreement with the recent PDB data (1DUR). Assuming standard secondary structures (-helices and -strands) at the nonflexible parts at the early stage of folding, and deforming these at the final stage, a structure similar to the native one was obtained. Another peculiarity of ferredoxin is the absence of disulfide bonds, in spite of its having eight cysteines. The reason cysteines do not form disulfide bonds became clear by applying the lampshade criterion, but more importantly, the two groups of cysteines are ready to make iron complexes, respectively, at a rather later stage of folding. The reason for poor prediction accuracy of secondary structure with conventional methods is discussed.     

Stability, denaturation and refolding of Mycobacterium tuberculosis MfpA, a DNA mimicking protein that confers antibiotic resistance

MfpA from Mycobacterium tuberculosis is a founding member of the pentapeptide repeat class of proteins (PRP) that is believed to confer bacterial resistance to the drug fluoroquinolone by mimicking the size, shape and surface charge of duplex DNA. We show that phenylalanine side chain stacking stabilizes the N-terminus of MfpA's pentapeptide thus extending the DNA mimicry analogy. The Lumry-Eyring model was applied to multiple spectral measures of MfpA denaturation revealing that the MfpA dimer dissociates to monomers which undergo a structural transition that leads to aggregation. MfpA retains high secondary and tertiary structure content under denaturing conditions. Dimerization stabilizes MfpA's pentapeptide repeat fold. The high Arrhenius activation energy of the barrier to aggregate formation rationalizes its stability. The mechanism of MfpA denaturation and refolding is a ‘double funnel’ energy landscape where the ‘native’ and ‘aggregate’ funnels are separated by the high barrier that is not overcome during in vitro refolding.     

A screening system for the identification of refolding conditions for a model protein kinase, p38alpha

Protein kinases are key drug targets involved in the regulation of a wide variety of cellular processes. To aid the development of drugs targeting these kinases, it is necessary to express recombinant protein in large amounts. The expression of these kinases in Escherichia coli often leads to the accumulation of the expressed protein as insoluble inclusion bodies. The refolding of these inclusion bodies could provide a route to soluble protein, but there is little reported success in this area. We set out to develop a system for the screening of refolding conditions for a model protein kinase, p38α, and applied this system to denatured p38α derived from natively folded and inclusion body protein. Clear differences were observed in the refolding yields obtained, suggesting differences in the folded state of these preparations. Using the screening system, we have established conditions under which soluble, folded p38α can be produced from inclusion bodies. We have shown that the refolding yields obtained in this screen are suitable for the economic large-scale production of refolded p38α protein kinase.     

Structural and functional conservation of Mycobacterium tuberculosis GroEL paralogs suggests that GroEL1 Is a chaperonin

GroEL is a group I chaperonin that facilitates protein folding and prevents protein aggregation in the bacterial cytosol. Mycobacteria are unusual in encoding two or more copies of GroEL in their genome. While GroEL2 is essential for viability and likely functions as the general housekeeping chaperonin, GroEL1 is dispensable, but its structure and function remain unclear.Here, we present the 2.2-Å resolution crystal structure of a 23-kDa fragment of Mycobacterium tuberculosis GroEL1 consisting of an extended apical domain. Our X-ray structure of the GroEL1 apical domain closely resembles those of Escherichia coli GroEL and M. tuberculosis GroEL2, thus highlighting the remarkable structural conservation of bacterial chaperonins. Notably, in our structure, the proposed substrate-binding site of GroEL1 interacts with the N-terminal region of a symmetry-related neighboring GroEL1 molecule. The latter is consistent with the known GroEL apical domain function in substrate binding and is supported by results obtained from using peptide array technology. Taken together, these data show that the apical domains of M. tuberculosis GroEL paralogs are conserved in three-dimensional structure, suggesting that GroEL1, like GroEL2, is a chaperonin.     

Intra- versus intermolecular interactions in monellin: contribution of surface charges to protein assembly

The relative significance of weak non-covalent interactions in biological context has been much debated. Here, we have addressed the contribution of Coulombic interactions to protein stability and assembly experimentally. The sweet protein monellin, a non-covalently linked heterodimeric protein, was chosen for this study because of its ability to spontaneously reconstitute from separated fragments. The reconstitution of monellin mutants containing large surface charge perturbations was compared to the thermostability of structurally equivalent single-chain monellin containing the same sets of mutations under varying salt concentrations. The affinity between monellin fragments is found to correlate with the thermostability of single chain monellin, indicating the involvement of the same underlying Coulombic interactions. This confirms that there are no principal differences in the interactions involved in folding and binding. Based on comparison with a previous mutational study involving hydrophobic core residues, the relative contribution of Coulombic interactions to stability and affinity is modest. However, the Coulombic perturbations only affect the association rates of reconstitution in contrast to perturbations involving hydrophobic residues, which affect primarily the dissociation rates. These results indicate that Coulombic interactions are likely to be of main importance for the association of protein assembly, relevant for functions of proteins.