Designing protein energy landscapes

In silico design of misfolding resistant proteins: the role of structural similarity of a competing conformational ensemble in the optimization of frustration

Most state-of-the-art in silico design methods fail due to misfolding of designed sequences to a conformation other than the target. Thus, a method to design misfolding resistant proteins will provide a better understanding of the misfolding phenomenon and will also increase the success rate of in silico design methods. In this work, we optimize the conformational ensemble to be selected for negative design purposes based on the similarity of the conformational ensemble to the target. Five ensembles with different degrees of similarity to the target are created and destabilized and the target is stabilized while designing sequences using mean field theory and Monte Carlo simulation methods. The results suggest that the degree of similarity of the non-native conformations to the target plays a prominent role in designing misfolding resistant protein sequences. The design procedures that destabilize the conformational ensemble with moderate similarity to the target have proven to be more promising. Incorporation of either highly similar or highly dissimilar conformations to the target conformation into the non-native ensemble to be destabilized may lead to sequences with a higher misfolding propensity. This will significantly reduce the conformational space to be considered in any protein design procedure. Interestingly, the results suggest that a sequence with higher frustration in the target structure does not necessarily lead to a misfold prone sequence. A successful design method may purposefully choose a frustrated sequence in the target conformation if that sequence is even more frustrated in the competing non-native conformations.

Identification of an optimal foldability criterion to design misfolding resistant protein

Proteins achieve their functional, active, and operative three dimensional native structures by overcoming the possibility of being trapped in non-native energy minima present in the energy landscape. The enormous and intricate interactions that play an important role in protein folding also determine the stability of the proteins. The large number of stabilizing/destabilizing interactions makes proteins to be only marginally stable as compared to the other competing structures. Therefore, there are some possibilities that they become trapped in the non-native conformations and thus get misfolded. These misfolded proteins lead to several debilitating diseases. This work performs a comparative study of some existing foldability criteria in the computational design of misfold resistant protein sequences based on self-consistent mean field theory. The foldability criteria selected for this study are E_f, Δ, and Φ that are commonly used in protein design procedures to determine the most efficient foldability criterion for the design of misfolding resistant proteins. The results suggest that the foldability criterion Δ is significantly better in designing a funnel energy landscape stabilizing the target state. The results also suggest that inclusion of negative design features is important for designing misfolding resistant proteins, but more information about the non-native conformations in terms of Φ leads to worse results compared to even simple positive design. The sequences designed using Δ show better resistance to misfolding in the Monte Carlo simulations performed in the study.

Analysis of Heterodimeric "Mutual Synergistic Folding"-Complexes

Several intrinsically disordered proteins (IDPs) are capable to adopt stable structures without interacting with a folded partner. When the folding of all interacting partners happens at the same time, coupled with the interaction in a synergistic manner, the process is called Mutual Synergistic Folding (MSF). These complexes represent a discrete subset of IDPs. Recently, we collected information on their complexes and created the MFIB (Mutual Folding Induced by Binding) database. In a previous study, we compared homodimeric MSF complexes with homodimeric and monomeric globular proteins with similar amino acid sequence lengths. We concluded that MSF homodimers, compared to globular homodimeric proteins, have a greater solvent accessible main-chain surface area on the contact surface of the subunits, which becomes buried during dimerization. The main driving force of the folding is the mutual shielding of the water-accessible backbones, but the formation of further intermolecular interactions can also be relevant. In this paper, we will report analyses of heterodimeric MSF complexes. Our results indicate that the amino acid composition of the heterodimeric MSF monomer subunits slightly diverges from globular monomer proteins, while after dimerization, the amino acid composition of the overall MSF complexes becomes more similar to overall amino acid compositions of globular complexes. We found that inter-subunit interactions are strengthened, and additionally to the shielding of the solvent accessible backbone, other factors might play an important role in the stabilization of the heterodimeric structures, likewise energy gain resulting from the interaction of the two subunits with different amino acid compositions. We suggest that the shielding of the β-sheet backbones and the formation of a buried structural core along with the general strengthening of inter-subunit interactions together could be the driving forces of MSF protein structural ordering upon dimerization.

The Framework of Computational Protein Design

Computational protein design (CPD) has established itself as a leading field in basic and applied science with a strong coupling between the two. Proteins are computationally designed from the level of amino acids to the level of a functional protein complex. Design targets range from increased thermo- (or other) stability to specific requested reactions such as protein-protein binding, enzymatic reactions, or nanotechnology applications. The design scheme may encompass small regions of the proteins or the entire protein. In either case, the design may aim at the side-chains or at the full backbone conformation. Herein, the main framework for the process is outlined highlighting key elements in the CPD iterative cycle. These include the very definition of CPD, the diverse goals of CPD, components of the CPD protocol, methods for searching sequence and structure space, scoring functions, and augmenting the CPD with other optimization tools. Taken together, this chapter aims to introduce the framework of CPD.

Globular–disorder transition in proteins: a compromise between hydrophobic and electrostatic interactions?

Protein disorder, like protein folding, satisfies the principle of minimal frustration.

The role of site-directed point mutations in protein misfolding

Mutations inducing higher clashing and lower matching residue pairs lead to misfolding.

Kinetic and thermodynamic analysis of the conformational folding process of SS-reduced bovine pancreatic ribonuclease A using a selenoxide reagent with high oxidizing ability

Redox-coupled folding pathways of bovine pancreatic ribonuclease A (RNase A) with four intramolecular disulfide (SS) bonds comprise three phases: (I) SS formation to generate partially oxidized intermediate ensembles with no rigid folded structure; (II) SS rearrangement from the three SS intermediate ensemble (3S) to the des intermediates having three native SS linkages; (III) final oxidation of the last native SS linkage to generate native RNase A. We previously demonstrated that DHS^ox, a water-soluble selenoxide reagent for rapid and quantitative SS formation, allows clear separation of the three folding phases. In this study, the main conformational folding phase (phase II) has been extensively analyzed at pH 8.0 under a wide range of temperatures (5–45 °C), and thermodynamic and kinetic parameters for the four des intermediates were determined. The free-energy differences (ΔG) as a function of temperature suggested that the each SS linkage has different thermodynamic and kinetic roles in stability of the native structure. On the other hand, comparison of the rate constants and the activation energies for 3S → des with those reported for the conformational folding of SS-intact RNase A suggested that unfolded des species (desU) having three native SS linkages but not yet being folded are involved in very small amounts (<1%) in the 3S intermediate ensemble and the desU species would gain the native-like structures via X-Pro isomerization like SS-intact RNase A. It was revealed that DHS^ox is useful for kinetic and thermodynamic analysis of the conformational folding process on the oxidative folding pathways of SS-reduced proteins.

Characterization of kinetic and thermodynamic phases in the prefolding process of bovine pancreatic ribonuclease A coupled with fast SS formation and SS reshuffling

In the redox-coupled oxidative folding of a protein having several SS bonds, two folding phases are usually observed, corresponding to SS formation (oxidation) with generation of weakly stabilized heterogeneous structures (a chain-entropy losing phase) and the subsequent intramolecular SS rearrangement to search for the native SS linkages (a conformational folding phase). By taking advantage of DHS(ox) as a highly strong and selective oxidant, the former SS formation phase was investigated in detail in the oxidative folding of RNase A. The folding intermediates obtained at 25 °C and pH 4.0 within 1 min (1S°-4S°) showed different profiles in the HPLC chromatograms from those of the intermediates obtained at pH 7.0 and 10.0 (1S-4S). However, upon prolonged incubation at pH 4.0 the profiles of 1S°-3S° transformed slowly to those similar to 1S-3S intermediate ensembles via intramolecular SS reshuffling, accompanying significant changes in the UV and fluorescence spectra but not in the CD spectrum. Similar conversion of the intermediates was observed by pH jump from 4.0 to 8.0, while the opposite conversion from 1S-4S was observed by addition of guanidine hydrochloride to the folding solution at pH 8.0. The results demonstrated that the preconformational folding phase coupled with SS formation can be divided into two distinct subphases, a kinetic (or stochastic) SS formation phase and a thermodynamic SS reshuffling phase. The transition from kinetically formed to thermodynamically stabilized SS intermediates would be induced by hydrophobic nucleation as well as generation of the native interactions.

A search for energy minimized sequences of proteins

In this paper, we present numerical evidence that supports the notion of minimization in the sequence space of proteins for a target conformation. We use the conformations of the real proteins in the Protein Data Bank (PDB) and present computationally efficient methods to identify the sequences with minimum energy. We use edge-weighted connectivity graph for ranking the residue sites with reduced amino acid alphabet and then use continuous optimization to obtain the energy-minimizing sequences. Our methods enable the computation of a lower bound as well as a tight upper bound for the energy of a given conformation. We validate our results by using three different inter-residue energy matrices for five proteins from protein data bank (PDB), and by comparing our energy-minimizing sequences with 80 million diverse sequences that are generated based on different considerations in each case. When we submitted some of our chosen energy-minimizing sequences to Basic Local Alignment Search Tool (BLAST), we obtained some sequences from non-redundant protein sequence database that are similar to ours with an E-value of the order of 10^-7. In summary, we conclude that proteins show a trend towards minimizing energy in the sequence space but do not seem to adopt the global energy-minimizing sequence. The reason for this could be either that the existing energy matrices are not able to accurately represent the inter-residue interactions in the context of the protein environment or that Nature does not push the optimization in the sequence space, once it is able to perform the function.

Localizing frustration in native proteins and protein assemblies

We propose a method of quantifying the degree of frustration manifested by spatially local interactions in protein biomolecules. This method of localization smoothly generalizes the global criterion for an energy landscape to be funneled to the native state, which is in keeping with the principle of minimal frustration. A survey of the structural database shows that natural proteins are multiply connected by a web of local interactions that are individually minimally frustrated. In contrast, highly frustrated interactions are found clustered on the surface, often near binding sites. These binding sites become less frustrated upon complex formation.

Statistical theory for protein ensembles with designed energy landscapes

Combinatorial protein libraries provide a promising route to investigate the determinants and features of protein folding and to identify novel folding amino acid sequences. A library of sequences based on a pool of different monomer types are screened for folding molecules, consistent with a particular foldability criterion. The number of sequences grows exponentially with the length of the polymer, making both experimental and computational tabulations of sequences infeasible. Herein a statistical theory is extended to specify the properties of sequences having particular values of global energetic quantities that specify their energy landscape. The theory yields the site-specific monomer probabilities. A foldability criterion is derived that characterizes the properties of sequences by quantifying the energetic separation of the target state from low-energy states in the unfolded ensemble and the fluctuations of the energies in the unfolded state ensemble. For a simple lattice model of proteins, excellent agreement is observed between the theory and the results of exact enumeration. The theory may be used to provide a quantitative framework for the design and interpretation of combinatorial experiments.

Protein design based on the relative entropy

An approach to protein design is proposed based on the relative entropy and a reduced amino acid alphabet. In this approach, the relative entropy is used as a minimization object function. The method has been tested on a real protein's off-lattice model successfully, and the results are similar to those obtained from other design studies. It can be applied as a uniform frame for both folding and inverse folding of protein. An iterative calculation method of the ensemble average of the contact strength is proposed at the same time.

A novel flow cytometry-based method for analysis of expression levels in Escherichia coli, giving information about precipitated and soluble protein

A high throughput method for screening of protein expression is described. By using a flow cytometer, levels of both soluble and precipitated protein can simultaneously be assessed in vivo. Protein fragments were fused to the N-terminus of enhanced GFP and the cell samples were analysed using a flow cytometer. Data concerning whole cell fluorescence and light scattering was collected. The whole cell fluorescence is probing intracellular concentrations of soluble fusion proteins. Concurrently, forward scattered light gives data about inclusion body formation, valuable information in process optimisation. To evaluate the method, the cells were disrupted, separated into soluble and non-soluble fractions and analysed by gel electrophoresis. A clear correlation between fluorescence and soluble target protein was shown. Interestingly, the distribution of the cells regarding forward scatter (standard deviation) correlates with the amount of inclusion bodies formed. Finally, the newly developed method was used to evaluate two different purification tags, His(6) and Z(basic), and their effect on the expression pattern.

Chain-length-dependent helical motifs and self-association of beta-peptides with constrained side chains

Homo-oligomers constructed by using trans-2-aminocyclohexanecarboxylic acid monomers without protecting groups were studied. Both ab initio theory and NMR measurements showed that the tetramer tends to adopt a 10-helix motif, while the pentamer and hexamer form the known 14-helix. It was concluded that the conformationally constrained backbone is flexible enough to afford both 10-helical and 14-helical motifs, this observation in turn providing evidence of the true folding process. Self-association of the helical units was also detected, and the results of variable-temperature diffusion NMR measurements strongly suggested the presence of helical bundles in methanol solution.

Design and STM Investigation of Intramolecular Folding in Self-Assembled Monolayers on the Surface

The rational design of catechol bis-amides rendered molecular structures that fold into beta-turn mimics at the interface of HOPG and 1-octanol as demonstrated by STM. These self-assembled monolayers provide a prototypical model for linear sequences containing more turn mimics, which will allow for true synthetic surface confined foldamers.

Folding versus Self-Assembling

Model foldable polymers with sequences of rigid hydrophobic chromophores and flexible hydrophilic tetra(ethylene glycol) were synthesized and used as a paradigm for studying molecular-folding and self-assembly phenomena. Our results demonstrate that intramolecular association or folding prevails over intermolecular interaction or self-assembling in the concentration region from 1 microM to 0.1 M. Importantly, folded polymeric nanostructures have absorption and fluorescence properties that are distinct from those of unfolded polymers or free monomers. We hypothesize that the origins of folding and self-assembly come from interactions between molecular units, and that the key parameter that regulates the on-and-off of such interactions is the distance R separating the two molecular units. Each molecular unit produces a characteristic force field, and when another molecular unit enters this field, the probability that the two units will interact increases significantly. A preliminary estimate of the radius of such a force field for the perylene tetracarboxylic diimide chromophore is about 90-120 A. As a result, phenomena associated with folding or self-assembly of molecular species are observed when these conditions are met in solution.

De novo design of foldable proteins with smooth folding funnel: automated negative design and experimental verification

De novo sequence design of foldable proteins provides a way of investigating principles of protein architecture. We performed fully automated sequence design for a target structure having a three-helix bundle topology and synthesized the designed sequences. Our design principle is different from the conventional approach, in that instead of optimizing interactions within the target structure, we design the global shape of the protein folding funnel. This includes automated implementation of negative design by explicitly requiring higher free energy of the denatured state. The designed sequences do not have significant similarity to those of any natural proteins. The NMR and CD spectroscopic data indicated that one designed sequence has a well-defined three-dimensional structure as well as alpha-helical content consistent with the target.

Testing the relationship between foldability and the early folding events of dihydrofolate reductase from Escherichia coli

A "folding element" is a contiguous peptide segment crucial for a protein to be foldable and is a new concept that could assist in our understanding of the protein-folding problem. It is known that the presence of the complete set of folding elements of dihydrofolate reductase (DHFR) from Escherichia coli is essential for the protein to be foldable. Since almost all of the amino acid residues known to be involved in the early folding events of DHFR are located within the folding elements, a close relationship between the folding elements and early folding events is hypothesized. In order to test this hypothesis, we have investigated whether or not the early folding events are preserved in circular permutants and topological mutants of DHFR, in which the order of the folding elements is changed but the complete set of folding elements is present. The stopped-flow circular dichroism (CD) measurements show that the CD spectra at the early stages of folding are similar among the mutants and the wild-type DHFR, indicating that the presence of the complete set of folding elements is sufficient to preserve the early folding events. We have further examined whether or not sequence perturbation on the folding elements by a single amino acid substitution affects the early folding events of DHFR. The results show that the amino acid substitutions inside of the folding elements can affect the burst-phase CD spectra, whereas the substitutions outside do not. Taken together, these results indicate that the above hypothesis is true, suggesting a close relationship between the foldability of a protein and the early folding events. We propose that the folding elements interact with each other and coalesce to form a productive intermediate(s) early in the folding, and these early folding events are important for a protein to be foldable.

To fold or to assemble?

We introduce a new class of foldable oligomers consisting of alternating rigid and flexible regions. The rigid segments overlap to give pi-stacked folded conformers whose formation is driven mostly by pi-pi molecular orbital overlaps. As the oligomer concentration increases, the folded molecular structures further self-assemble into larger nanostructures. The dynamic processes of folding and self-organization are monitored with absorption, fluorescence, and NMR spectroscopies. Our results show that folding dominates at low concentrations (< approximately 1 mM) and precedes self-assembly, which occurs over the initial concentration range of approximately 1-100 mM.

Combinatorial protein design

Combinatorial protein libraries permit the examination of a wide range of sequences. Such methods are being used for denovo design and to investigate the determinants of protein folding. The exponentially large number of possible sequences, however, necessitates restrictions on the diversity of sequences in a combinatorial library. Recently, progress has been made in developing theoretical tools to bias and characterize the ensemble of sequences that fold into a given structure - tools that can be applied to the design and interpretation of combinatorial experiments.