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.     

The use of soluble protein structures in modeling helical proteins in a layered membrane

Major advances have been made in the prediction of soluble protein structures, led by the knowledge-based modeling methods that extract useful structural trends from known protein structures and incorporate them into scoring functions. The same cannot be reported for the class of transmembrane proteins, primarily due to the lack of high-resolution structural data for transmembrane proteins, which render many of the knowledge-based method unreliable or invalid. We have developed a method that harnesses the vast structural knowledge available in soluble protein data for use in the modeling of transmembrane proteins. At the core of the method, a set of transmembrane protein decoy sets that allow us to filter and train features recognized from soluble proteins for transmembrane protein modeling into a set of scoring functions. We have demonstrated that structures of soluble proteins can provide significant insight into transmembrane protein structures. A complementary novel two-stage modeling/selection process that mimics the two-stage helical membrane protein folding was developed. Combined with the scoring function, the method was successfully applied to model 5 transmembrane proteins. The root mean square deviations of the predicted models ranged from 5.0 to 8.8?Å to the native structures.     

Disulfide crosslinks to probe the structure and flexibility of a designed four-helix bundle protein.

The introduction of disulfide crosslinks is a generally useful method by which to identify regions of a protein that are close together in space. Here we describe the use of disulfide crosslinks to investigate the structure and flexibility of a family of designed 4-helix bundle proteins. The results of these analyses lend support to our working model of the proteins' structure and suggest that the proteins have limited main-chain flexibility.     

Design of a minimal protein oligomerization domain by a structural approach

Because of the simplicity and regularity of the alpha-helical coiled coil relative to other structural motifs, it can be conveniently used to clarify the molecular interactions responsible for protein folding and stability. Here we describe the de novo design and characterization of a two heptad-repeat peptide stabilized by a complex network of inter- and intrahelical salt bridges. Circular dichroism spectroscopy and analytical ultracentrifugation show that this peptide is highly alpha-helical and 100% dimeric tinder physiological buffer conditions. Interestingly, the peptide was shown to switch its oligomerization state from a dimer to a trimer upon increasing ionic strength. The correctness of the rational design principles used here is supported by details of the atomic structure of the peptide deduced from X-ray crystallography. The structure of the peptide shows that it is not a molten globule but assumes a unique, native-like conformation. This de novo peptide thus represents an attractive model system for the design of a molecular recognition system.     

Switching two-state to three-state kinetics in the helical protein Im9 via the optimisation of stabilising non-native interactions by design

The four-helix protein Im7 folds through an on-pathway intermediate at pH 7.0 and 10 degrees C. By contrast, under these conditions there is no evidence for a populated intermediate in the folding of its more stable homologue, Im9, even in the presence of 0.4 M sodium sulphate. Previous studies using phi-value analysis have shown that the Im7 intermediate is misfolded, in that three of its four native helices are formed, but are docked in a non-native manner. Using knowledge of the structure of the intermediate of Im7, we have used rational design to stabilise an intermediate formed during the folding of Im9 by the introduction of specific stabilising interactions at positions known to stabilise the Im7 folding intermediate through non-native interactions. We show that the redesigned Im9 sequence folds with three-state kinetics at pH 7.0 and have used phi-value analysis to demonstrate that this species resembles the misfolded intermediate populated during Im7 folding. The redesigned Im9 sequence folds 20-fold faster than the wild-type protein under conditions in which folding is two-state. The data show that intermediate formation is an important feature of folding, even for small proteins such as Im9 for which these partially folded states do not become significantly populated. In addition, they show that the introduction of stabilising interactions can lead to rapid refolding, even when the contacts introduced are non-native.     

Characterization of the folding kinetics of a three-helix bundle protein via a minimalist Langevin model.

We use a simple off-lattice Langevin model of protein folding to characterize the folding and unfolding of a fast-folding, 46 residue three-helix bundle. Under conditions at which the C-terminal helix is 30 % stable, we observe a clear three-state folding mechanism. In the on-pathway intermediate state, the middle and C-terminal helices are folded and in contact with each other, while the N-terminal region remains disordered. Nevertheless, under these conditions this intermediate is thermodynamically unstable relative to its unfolded state. The first and highest folding barrier corresponds to the organization of the hinge between the middle and C-terminal helices. A subsequent major barrier corresponds to the organization of the hinge between the middle and N-terminal helices. Hyperstabilizing the hinge regions leads to twice the folding rate that is obtained from hyperstabilizing the helices, even though much fewer contacts are involved in hinge hyperstabilization than in helix hyperstabilization. Unfolding follows single-exponential kinetics, even at temperatures only slightly above the folding transition temperature.     

Structure-based design of model proteins

A structure-based, sequence-design procedure is proposed in which one considers a set of decoy structures that compete significantly with the target structure in being low energy conformations. The decoy structures are chosen to have strong overlaps in contacts with the putative native state. The procedure allows the design of sequences with large and small stability gaps in a random-bond heteropolymer model in both two and three dimensions by an appropriate assignment of the contact energies to both the native and nonnative contacts. The design procedure is also successfully applied to the two-dimensional HP model. Proteins 31:10–20, 1998. © 1998 Wiley-Liss, Inc.     

A hierarchic approach to the design of hexameric helical barrels

The design of large macromolecular assemblies is an endeavor with implications for protein engineering as well as nanotechnology. A hierarchic approach was used to design an antiparallel hexameric, tubular assembly of helices. In previous studies, a domain-swapped, dimeric three-helix bundle was designed from first principles. In the crystal lattice, three dimers associate around a 3-fold rotational axis to form a hexameric assembly. Although this hexameric assembly was not observed in solution, it was possible to stabilize its formation by changing three polar residues per monomer to hydrophobic (two Phe and one Trp) residues. Molecular models based on the crystallographic coordinates of DSD (PDB accession code 1G6U) show that these side-chains pack in the central cavity (the "supercore") of the hexameric bundle. Analytical ultracentrifugation, fluorescence spectroscopy, CD spectroscopy, and guanidine-HCl denaturation were used to determine the assembly of the hexamer. To probe the requirements for stabilizing the hexamer, we systematically varied the polarity and steric bulk of one of the Phe residues in the supercore of the hexamer. Depending on the nature of this side-chain, it is possible to modulate the stability of the hexamer in a predictable manner. This family of hexameric proteins may provide a useful framework for the construction of proteins that change their oligomeric states in response to binding of small molecules.     

A model for the structure of a homodimeric prohormone: The precursor to the locust neuropeptide AKH I

We have determined the structure in solution of a homodimeric protein that is a precursor to the locust neuropeptide adipokinetic hormone I using nuclear magnetic resonance spectroscopy. This precursor, called P1, is comprised of two 41 residue strands joined by a single inter-chain disulphide at Cys39. We have also determined the structure of an end product of P1 processing, called APRP1; this is a homodimer comprised of residues 14–41 of PI. Nuclear Overhauser Effect (nOe) data indicate that in both P1 and APRP1, residues 22–37 (numbered with respect to P1) form pairs of α-helices, with no evidence for any other secondary structure. © 1994 Wiley-Liss, Inc.     

Probing dimer interface stabilization within a four-helix bundle of the GrpE protein from Escherichia coli via internal deletion mutants: conversion of a dimer to monomer

Insight into protein stability and folding remains an important area for protein research, in particular protein-protein interactions and the self-assembly of homodimers. The GrpE protein from Escherichia coli is a homodimer with a four-helix bundle at the dimer interface. Each monomer contributes a helix-loop-helix to the bundle. To probe the interface stabilization requirements, in terms of the amount of buried residues in the bundle necessary for dimer formation, internal deletion mutants (IDMs) were created that sequentially truncate each of the two helices in the helix-loop-helix region. Circular dichroism (CD) spectroscopy showed that all IDM's still contained a significant amount of α-helical secondary structure. IDM's that contained 11 or fewer of 22 residues originally present in the helices, or those that lost at least 50% of residues with less than 20% the solvent accessible surfaces (that is, hydrophobic residues) were unable to form a significant amount of dimer species as shown by chemical cross-linking. Gel filtration studies of IDM3.0 (one that retains 10 residues in each helix) show this variant to be mainly monomeric.     

Analysis of protein transmembrane helical regions by a neural network.

Neural networks were used to generalize common themes found in transmembrane-spanning protein helices. Various-sized databases were used containing nonoverlapping sequences, each 25 amino acids long. Training consisted of sorting these sequences into 1 of 2 groups: transmembrane helical peptides or nontransmembrane peptides. Learning was measured using a test set 10% the size of the training set. As training set size increased from 214 sequences to 1,751 sequences, learning increased in a nonlinear manner from 75% to a high of 98%, then declined to a low of 87%. The final training database consisted of roughly equal numbers of transmembrane (928) and nontransmembrane (1,018) sequences. All transmembrane sequences were entered into the database with respect to their lipid membrane orientation: from inside the membrane to outside. Generalized transmembrane helix and nontransmembrane peptides were constructed from the maximally weighted connecting strengths of fully trained networks. Four generalized transmembrane helices were found to contain 9 consensus residues: a K-R-F triplet was found at the inside lipid interface, 2 isoleucine and 2 other phenylalanine residues were present in the helical body, and 2 tryptophan residues were found near the outside lipid interface. As a test of the training method, bacteriorhodopsin was examined to determine the position of its 7 transmembrane helices.     

De novo backbone and sequence design of an idealized alpha/beta-barrel protein: evidence of stable tertiary structure

We have designed, synthesized, and characterized a 216 amino acid residue sequence encoding a putative idealized alpha/beta-barrel protein. The design was elaborated in two steps. First, the idealized backbone was defined with geometric parameters representing our target fold: a central eight parallel-stranded beta-sheet surrounded by eight parallel alpha-helices, connected together with short structural turns on both sides of the barrel. An automated sequence selection algorithm, based on the dead-end elimination theorem, was used to find the optimal amino acid sequence fitting the target structure. A synthetic gene coding for the designed sequence was constructed and the recombinant artificial protein was expressed in bacteria, purified and characterized. Far-UV CD spectra with prominent bands at 222nm and 208nm revealed the presence of alpha-helix secondary structures (50%) in fairly good agreement with the model. A pronounced absorption band in the near-UV CD region, arising from immobilized aromatic side-chains, showed that the artificial protein is folded in solution. Chemical unfolding monitored by tryptophan fluorescence revealed a conformational stability (DeltaG(H2O)) of 35kJ/mol. Thermal unfolding monitored by near-UV CD revealed a cooperative transition with an apparent T(m) of 65 degrees C. Moreover, the artificial protein did not exhibit any affinity for the hydrophobic fluorescent probe 1-anilinonaphthalene-8-sulfonic acid (ANS), providing additional evidence that the artificial barrel is not in the molten globule state, contrary to previously designed artificial alpha/beta-barrels. Finally, 1H NMR spectra of the folded and unfolded proteins provided evidence for specific interactions in the folded protein. Taken together, the results indicate that the de novo designed alpha/beta-barrel protein adopts a stable three-dimensional structure in solution. These encouraging results show that de novo design of an idealized protein structure of more than 200 amino acid residues is now possible, from construction of a particular backbone conformation to determination of an amino acid sequence with an automated sequence selection algorithm.     

Self-association of helical peptides in a lipid environment

The self-association of two model transmembrane helical peptides, differing in their surface topography, was compared in mixed micelles containing 3-([3-cholamidopropyl]dimethylammonio)-1-propanesulfonate (CHAPS) and dimyristoylphosphatidylcholine (DMPC). One peptide, Ac-KKL₂₄KK-amide (L₂₄), has large, rotationally mobile leucine side chains and a relatively rough surface. The other peptide, Ac-KKLLLLLLAALLALLAALLALLLLLLKK-amide (L₁₈A₆), has a patch of small alanines on one side of the helix that forms a smooth surface. The aggregation state of the peptides was sampled by chemical cross-linking with bis-sulfosuccinimidyl suberate (B53). A monomer-aggregate association constant was obtained from the cross-linking results in the range of 2 × 10⁵ M^–1 to 3 × 10⁵ M^–1 for both peptides. Kinetics of formation of cross-linked dimers indicated that the ratio of dimerization constants for L₁₈A₆ to L₂₄ was between 10 and 20. This suggests that the alanine patch contributes about 1.5 Kcal/mol more stabilization free energy to dimer formation of L₁₈A₆ compared to L₂₄.     

Dynamic rheology of agar gels: theory and experiments. Part I. Development of a rheological model

A theoretical rheological model for agar gels is proposed, based on the bead and spring model for linear flexible random coils and the model for crosslinked polymers. The model introduces the concept of a temperature dependence of the monomeric friction coefficient, ζ₀, of the agar molecule. The model has a random coil-like behavior at high temperatures (close to 373 K), and contributions from a three-dimensional network at low temperatures (close to 273 K). A proposed temperature dependence of the net association rate allows the calculation of the fraction of associated molecules as a function of time and temperature. The proposed model predicts the gelation behavior of agar gels utilizing time–temperature data (cooling curves).