Designing amino acid sequences to fold with good hydrophobic cores

Lattice simulations of aggregation funnels for protein folding

A computer model of protein aggregation competing with productive folding is proposed. Our model adapts techniques from lattice Monte Carlo studies of protein folding to the problem of aggregation. However, rather than starting with a single string of residues, we allow independently folding strings to undergo collisions and consider their interactions in different orientations. We first present some background into the nature and significance of protein aggregation and the use of lattice Monte Carlo simulations in understanding other aspects of protein folding. The results of a series of simulation experiments involving simple versions of the model illustrate the importance of considering aggregation in simulations of protein folding and provide some preliminary understanding of the characteristics of the model. Finally, we discuss the value of the model in general and of our particular design decisions and experiments. We conclude that computer simulation techniques developed to study protein folding can provide insights into protein aggregation, and that a better understanding of aggregation may in turn provide new insights into and constraints on the more general protein folding problem.

Computational protein design

A 'protein design cycle', involving cycling between theory and experiment, has led to recent advances in rational protein design. A reductionist approach, in which protein positions are classified by their local environments, has aided development of an appropriate energy expression. The computational principles and practicalities of the protein design cycle are discussed.

Hydrophobic core packing and protein design

Over the past few years, we have witnessed exciting advances in protein design. Several groups have reported success in the design of hydrophobic cores, and the principles developed in these studies have been recently applied to the full sequence design of a small protein motif and the design of a catalytically active metal center. These successes suggest that designing large, functional proteins in computero is more feasible than ever before.

A simple model for evolution of proteins towards the global minimum of free energy

BACKGROUND

Proteins seem to have their native structure in a global minimum of free energy. No mechanism is known, however, for ensuring this property. Furthermore, computational complexity studies suggest that such a mechanism is not feasible. These seemingly contradictory observations can be reconciled by the suggestion that evolutionary selection can yield proteins whose native conformation is in the global minimum of free energy. The aim of this study is to investigate such evolutionary processes in a simple model of protein folding.

RESULTS

Three possible evolutionary processes are explored.First, if the free energy of the chain is kept below a fixed threshold there is no improvement towards the global minimum. Second, if free energy is minimized directly, sequences emerge whose native conformation is in the global minimum of free energy. Third, when evolutionary pressure is applied within a small set of close homologs, sequences emerge whose functional conformation is in the global minimum of free energy.

CONCLUSIONS

Although minimizing free energy does select for sequences whose functional conformation is in the global free energy minimum, we argue that for most proteins, which typically have free energy values of only 5-15 kcal/mol, such evolutionary pressure cannot be considered biologically plausible. In contrast, by repeatedly forcing sequences to avoid drifting towards competing "non-native" conformations, sequences emerge whose native conformation becomes very close to the global minimum of free energy. We argue that such a mechanism is both efficient and biologically plausible.

Design, structure and stability of a hyperthermophilic protein variant

Here we report the use of an objective computer algorithm in the design of a hyperstable variant of the Streptococcal protein Gbeta1 domain (Gbeta1). The designed seven-fold mutant, Gbeta1-c3b4, has a melting temperature in excess of 100 degrees C and an enhancement in thermodynamic stability of 4.3 kcal mol(-1) at 50 degrees C over the wild-type protein. Gbeta1-c3b4 maintains the Gbeta1 fold, as determined by nuclear magnetic resonance spectroscopy, and also retains a significant level of binding to human IgG in qualitative comparisons with wild type. The basis of the stability enhancement appears to have multiple components including optimized core packing, increased burial of hydrophobic surface area, more favorable helix dipole interactions, and improvement of secondary structure propensity. The design algorithm is able to model such complex contributions simultaneously using empirical physical/chemical potential functions and a combinatorial optimization algorithm based on the dead-end elimination theorem. Because the design methodology is based on general principles, there is the potential of applying the methodology to the stabilization of other unrelated protein folds.

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.

Protein folding in the landscape perspective: chevron plots and non-Arrhenius kinetics

We use two simple models and the energy landscape perspective to study protein folding kinetics. A major challenge has been to use the landscape perspective to interpret experimental data, which requires ensemble averaging over the microscopic trajectories usually observed in such models. Here, because of the simplicity of the model, this can be achieved. The kinetics of protein folding falls into two classes: multiple-exponential and two-state (single-exponential) kinetics. Experiments show that two-state relaxation times have "chevron plot" dependences on denaturant and non-Arrhenius dependences on temperature. We find that HP and HP+ models can account for these behaviors. The HP model often gives bumpy landscapes with many kinetic traps and multiple-exponential behavior, whereas the HP+ model gives more smooth funnels and two-state behavior. Multiple-exponential kinetics often involves fast collapse into kinetic traps and slower barrier climbing out of the traps. Two-state kinetics often involves entropic barriers where conformational searching limits the folding speed. Transition states and activation barriers need not define a single conformation; they can involve a broad ensemble of the conformations searched on the way to the native state. We find that unfolding is not always a direct reversal of the folding process.

Probing the role of packing specificity in protein design

By using a protein-design algorithm that quantitatively considers side-chain packing, the effect of specific steric constraints on protein design was assessed in the core of the streptococcal protein G beta1 domain. The strength of packing constraints used in the design was varied, resulting in core sequences that reflected differing amounts of packing specificity. The structural flexibility and stability of several of the designed proteins were experimentally determined and showed a trend from well-ordered to highly mobile structures as the degree of packing specificity in the design decreased. This trend both demonstrates that the inclusion of specific packing interactions is necessary for the design of native-like proteins and defines a useful range of packing specificity for the design algorithm. In addition, an analysis of the modeled protein structures suggested that penalizing for exposed hydrophobic surface area can improve design performance.

Neutral networks in protein space: a computational study based on knowledge-based potentials of mean force

BACKGROUND

Many protein sequences, often unrelated, adopt similar folds. Sequences folding into the same shape thus form subsets of sequence space. The shape and the connectivity of these sets have implications for protein evolution and de novo design.

RESULTS

We investigate the topology of these sets for some proteins with known three-dimensional structure using inverse folding techniques. First, we find that sequences adopting a given fold do not cluster in sequence space and that there is no detectable sequence homology among them. Nevertheless, these sequences are connected in the sense that there exists a path such that every sequence can be reached from every other sequence while the fold remains unchanged. We find similar results for restricted amino acid alphabets in some cases (e. g. ADLG). In other cases, it seems impossible to find sequences with native-like behavior (e.g. QLR). These findings seem to be independent of the particular structure considered.

CONCLUSIONS

Amino acid sequences folding into a common shape are distributed homogeneously in sequence space. Hence, the connectivity of the set of these sequences implies the existence of very long neutral paths on all examined protein structures. Regarding protein design, these results imply that sequences with more or less arbitrary chemical properties can be attached to a given structural framework. But we also observe that designability varies significantly among native structures. These features of protein sequence space are similar to what has been found for nucleic acids.

Conformational stabilities of Escherichia coli RNase HI variants with a series of amino acid substitutions at a cavity within the hydrophobic core

Escherichia coli ribonuclease HI has a cavity within the hydrophobic core. Two core residues, Ala52 and Val74, resided at both ends of this cavity. We have constructed a series of single mutant proteins at Ala52, and double mutant proteins, in which Ala52 was replaced by Gly, Val, Ile, Leu, or Phe, and Val74 was replaced by Ala or Leu. All of these mutant proteins, except for A52W, A52R, and A52G/V74A, were overproduced and purified. Measurement of the thermal denaturations of the proteins at pH 3.2 by CD suggests that the cavity is large enough to accommodate three methyl or methylene groups without creating serious strains. A correlation was observed between the protein stability and the hydrophobicity of the substituted residue. As a result, a number of the mutant proteins were more stable than the wild-type protein. The stabilities of the mutant proteins with charged or extremely bulky residues at the cavity were lower than those expected from the hydrophobicities of the substituted residues, suggesting that considerable strains are created at the mutation sites in these mutant proteins. However, examination of the far- and near-UV CD spectra and the enzymatic activities suggest that all of the mutant proteins have structures similar to that of the wild-type protein. These results suggest that the cavity in the hydrophobic core of E. coli RNase HI is conformationally fairly stable. This may be the reason why the cavity-filling mutations effectively increase the thermal stability of this protein.

Protein folding and fold recognition for square lattice models

Protein folding and inverse protein folding problems are examined for the extremely simplified model of short self-avoiding square lattice walks involving only two or three residue types. Simple interresidue contact free energy functions are given and are used to determine which sequences fold uniquely to which conformations. Contrary to general theories of protein folding, this model system shows little correlation between free energy and conformational distance from the native, nor is there any marked energy gap between the native and the best non-native structures. Furthermore, even the given free energy function sometimes fails to identify which sequences fold to a particular target structure. If current ideas about protein folding and structure/sequence compatibility fail in this model system, it is unclear why they should be valid for real proteins.

Comparing folding codes for proteins and polymers

Proteins fold to unique compact native structures. Perhaps other polymers could be designed to fold in similar ways. The chemical nature of the monomer "alphabet" determines the "energy matrix" of monomer interactions-which defines the folding code, the relationship between sequence and structure. We study two properties of energy matrices using two-dimensional lattice models: uniqueness, the number of sequences that fold to only one structure, and encodability, the number of folds that are unique lowest-energy structures of certain monomer sequences. For the simplest model folding code, involving binary sequences of H (hydrophobic) and P (polar) monomers, only a small fraction of sequences fold uniquely, and not all structures can be encoded. Adding strong repulsive interactions results in a folding code with more sequences folding uniquely and more designable folds. Some theories suggest that the quality of a folding code depends only on the number of letters in the monomer alphabet, but we find that the energy matrix itself can be at least as important as the size of the alphabet. Certain multi-letter codes, including some with 20 letters, may be less physical or protein-like than codes with smaller numbers of letters because they neglect correlations among inter-residue interactions, treat only maximally compact conformations, or add arbitrary energies to the energy matrix.