Statistical theory of combinatorial libraries of folding proteins: energetic discrimination of a target structure

Protein Design: From the Aspect of Water Solubility and Stability

Water solubility and structural stability are key merits for proteins defined by the primary sequence and 3D-conformation. Their manipulation represents important aspects of the protein design field that relies on the accurate placement of amino acids and molecular interactions, guided by underlying physiochemical principles. Emulated designer proteins with well-defined properties both fuel the knowledge-base for more precise computational design models and are used in various biomedical and nanotechnological applications. The continuous developments in protein science, increasing computing power, new algorithms, and characterization techniques provide sophisticated toolkits for solubility design beyond guess work. In this review, we summarize recent advances in the protein design field with respect to water solubility and structural stability. After introducing fundamental design rules, we discuss the transmembrane protein solubilization and de novo transmembrane protein design. Traditional strategies to enhance protein solubility and structural stability are introduced. The designs of stable protein complexes and high-order assemblies are covered. Computational methodologies behind these endeavors, including structure prediction programs, machine learning algorithms, and specialty software dedicated to the evaluation of protein solubility and aggregation, are discussed. The findings and opportunities for Cryo-EM are presented. This review provides an overview of significant progress and prospects in accurate protein design for solubility and stability.

Computational Design of Single-Peptide Nanocages with Nanoparticle Templating

Protein complexes perform a diversity of functions in natural biological systems. While computational protein design has enabled the development of symmetric protein complexes with spherical shapes and hollow interiors, the individual subunits often comprise large proteins. Peptides have also been applied to self-assembly, and it is of interest to explore such short sequences as building blocks of large, designed complexes. Coiled-coil peptides are promising subunits as they have a symmetric structure that can undergo further assembly. Here, an α-helical 29-residue peptide that forms a tetrameric coiled coil was computationally designed to assemble into a spherical cage that is approximately 9 nm in diameter and presents an interior cavity. The assembly comprises 48 copies of the designed peptide sequence. The design strategy allowed breaking the side chain conformational symmetry within the peptide dimer that formed the building block (asymmetric unit) of the cage. Dynamic light scattering (DLS) and transmission electron microscopy (TEM) techniques showed that one of the seven designed peptide candidates assembled into individual nanocages of the size and shape. The stability of assembled nanocages was found to be sensitive to the assembly pathway and final solution conditions (pH and ionic strength). The nanocages templated the growth of size-specific Au nanoparticles. The computational design serves to illustrate the possibility of designing target assemblies with pre-determined specific dimensions using short, modular coiled-coil forming peptide sequences.

DNA barcoding of five Japanese encephalitis mosquito vectors (Culex fuscocephala, Culex gelidus, Culex tritaeniorhynchus, Culex pseudovishnui and Culex vishnui)

Culex mosquitoes can act as vectors of several important diseases, including Japanese encephalitis, West Nile virus, St. Louis encephalitis and equine encephalitis. Besides the neurological sequelae caused in humans, Japanese encephalitis can lead to abortion in sows and encephalitis in horses. Effective vector control and early diagnosis, along with continuous serosurveillance in animals, are crucial to fight this arboviral disease. However, the success of vector control operations is linked with the fast and reliable identification of targeted species, and knowledge about their biology and ecology. Since the DNA barcoding of Culex vectors of Japanese encephalitis is scarcely explored, here we evaluated the efficacy of this tool to identify and analyze the variations among five overlooked Culex vectors of Japanese encephalitis, Culex fuscocephala, Culex gelidus, Culex tritaeniorhynchus, Culex pseudovishnui and Culex vishnui, relying to the analysis of mitochondrial CO1 gene. Variations in their base pair range were elucidated by the entropy H_x plot. The differences among individual conspecifics and on base pair range across the same were studied. The C (501-750 bp) region showed a moderate variation among all the selected species. C. tritaeniorhynchus exhibited the highest variation in all the ranges. The observed genetic divergence was partially non-discriminatory. i.e., the overall intra- and inter nucleotide divergence was 0.0920 (0.92%) and 0.125 (1.25%), respectively. However, 10X rule fits accurately intraspecies divergence <3% for the five selected Culex species. The analysis of individual scatter plots showed threshold values (10X) of 0.008 (0.08%), 0.005 (0.05%), 0.123 (1.23%), 0.033 (0.33%) and 0.019 (0.19%) for C. fuscocephala, C. gelidus, C. tritaeniorhynchus, C. pseudovishnui and C. vishnui, respectively. The C. tritaeniorhynchus haplotypes KU497604, KU497603, AB690847 and AB690854 exhibited the highest divergence range, i.e., from 0.465 -0.546. Comparatively, the intra-divergence among the other haplotypes of C. tritaeniorhynchus ranged from 0-0.056. The maximum parsimony tree was formed by distinctive conspecific clusters with appreciable branch values illustrating their close congruence and extensive genetic deviations. Overall, this study adds valuable knowledge to the molecular biology and systematics of five overlooked mosquito species acting as major vectors of Japanese encephalitis in Asian countries.

Computer-aided design of amino acid-based therapeutics: a review

During the last two decades, the pharmaceutical industry has progressed from detecting small molecules to designing biologic-based therapeutics. Amino acid-based drugs are a group of biologic-based therapeutics that can effectively combat the diseases caused by drug resistance or molecular deficiency. Computational techniques play a key role to design and develop the amino acid-based therapeutics such as proteins, peptides and peptidomimetics. In this study, it was attempted to discuss the various elements for computational design of amino acid-based therapeutics. Protein design seeks to identify the properties of amino acid sequences that fold to predetermined structures with desirable structural and functional characteristics. Peptide drugs occupy a middle space between proteins and small molecules and it is hoped that they can target "undruggable" intracellular protein-protein interactions. Peptidomimetics, the compounds that mimic the biologic characteristics of peptides, present refined pharmacokinetic properties compared to the original peptides. Here, the elaborated techniques that are developed to characterize the amino acid sequences consistent with a specific structure and allow protein design are discussed. Moreover, the key principles and recent advances in currently introduced computational techniques for rational peptide design are spotlighted. The most advanced computational techniques developed to design novel peptidomimetics are also summarized.

A Deterministic Optimization Approach to Protein Sequence Design Using Continuous Models

Determining the sequence of amino acid residues in a heteropolymer chain of a protein with a given conformation is a discrete combinatorial problem that is not generally amenable for gradient-based continuous optimization algorithms. In this paper we present a new approach to this problem using continuous models. In this modeling, continuous “state functions” are proposed to designate the type of each residue in the chain. Such a continuous model helps define a continuous sequence space in which a chosen criterion is optimized to find the most appropriate sequence. Searching a continuous sequence space using a deterministic optimization algorithm makes it possible to find the optimal sequences with much less computation than many other approaches. The computational efficiency of this method is further improved by combining it with a graph spectral method, which explicitly takes into account the topology of the desired conformation and also helps make the combined method more robust. The continuous modeling used here appears to have additional advantages in mimicking the folding pathways and in creating the energy landscapes that help find sequences with high stability and kinetic accessibility. To illustrate the new approach, a widely used simplifying assumption is made by considering only two types of residues: hydrophobic (H) and polar (P). Self-avoiding compact lattice models are used to validate the method with known results in the literature and data that can be practically obtained by exhaustive enumeration on a desktop computer. We also present examples of sequence design for the HP models of some real proteins, which are solved in less than five minutes on a single-processor desktop computer. Some open issues and future extensions are noted.

Designing peptide sequences in flexible chain conformations to bind RNA: a search algorithm combining Monte Carlo, self-consistent mean field and concerted rotation techniques

A search algorithm combining Monte Carlo, self-consistent mean field, and concerted rotation techniques was developed to discover peptide sequences that are reasonable HIV drug candidates due to their exceptional binding to human tRNAUUU(Lys3), the primer of HIV replication. The search algorithm allows for iteration between sequence mutations and conformation changes during sequence evolution. Searches conducted for different classes of peptides identified several potential peptide candidates. Analysis of the energy revealed that the asparagine and cysteine at residues 11 and 12 play important roles in "recognizing" tRNA(Lys3) via van der Waals interactions, contributing to binding specificity. Arginines preferentially attract the phosphate linkage via charge-charge interaction, contributing to binding affinity. Evaluation of the RNA/peptide complex's structure revealed that adding conformation changes to the search algorithm yields peptides with better binding affinity and specificity to tRNA(Lys3) than a previous mutation-only algorithm.

De novo design and experimental characterization of ultrashort self-associating peptides

Self-association is a common phenomenon in biology and one that can have positive and negative impacts, from the construction of the architectural cytoskeleton of cells to the formation of fibrils in amyloid diseases. Understanding the nature and mechanisms of self-association is important for modulating these systems and in creating biologically-inspired materials. Here, we present a two-stage de novo peptide design framework that can generate novel self-associating peptide systems. The first stage uses a simulated multimeric template structure as input into the optimization-based Sequence Selection to generate low potential energy sequences. The second stage is a computational validation procedure that calculates Fold Specificity and/or Approximate Association Affinity (K*association) based on metrics that we have devised for multimeric systems. This framework was applied to the design of self-associating tripeptides using the known self-associating tripeptide, Ac-IVD, as a structural template. Six computationally predicted tripeptides (Ac-LVE, Ac-YYD, Ac-LLE, Ac-YLD, Ac-MYD, Ac-VIE) were chosen for experimental validation in order to illustrate the self-association outcomes predicted by the three metrics. Self-association and electron microscopy studies revealed that Ac-LLE formed bead-like microstructures, Ac-LVE and Ac-YYD formed fibrillar aggregates, Ac-VIE and Ac-MYD formed hydrogels, and Ac-YLD crystallized under ambient conditions. An X-ray crystallographic study was carried out on a single crystal of Ac-YLD, which revealed that each molecule adopts a β-strand conformation that stack together to form parallel β-sheets. As an additional validation of the approach, the hydrogel-forming sequences of Ac-MYD and Ac-VIE were shuffled. The shuffled sequences were computationally predicted to have lower K*association values and were experimentally verified to not form hydrogels. This illustrates the robustness of the framework in predicting self-associating tripeptides. We expect that this enhanced multimeric de novo peptide design framework will find future application in creating novel self-associating peptides based on unnatural amino acids, and inhibitor peptides of detrimental self-aggregating biological proteins.

Symmetric protein architecture in protein design: top-down symmetric deconstruction

Top-down symmetric deconstruction (TDSD) is a joint experimental and computational approach to generate a highly stable, functionally benign protein scaffold for intended application in subsequent functional design studies. By focusing on symmetric protein folds, TDSD can leverage the dramatic reduction in sequence space achieved by applying a primary structure symmetric constraint to the design process. Fundamentally, TDSD is an iterative symmetrization process, in which the goal is to maintain or improve properties of thermodynamic stability and folding cooperativity inherent to a starting sequence (the "proxy"). As such, TDSD does not attempt to solve the inverse protein folding problem directly, which is computationally intractable. The present chapter will take the reader through all of the primary steps of TDSD-selecting a proxy, identifying potential mutations, establishing a stability/folding cooperativity screen-relying heavily on a successful TDSD solution for the common β-trefoil fold.

The role of site-directed point mutations in protein misfolding

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

A computationally designed water-soluble variant of a G-protein-coupled receptor: the human mu opioid receptor

G-protein-coupled receptors (GPCRs) play essential roles in various physiological processes, and are widely targeted by pharmaceutical drugs. Despite their importance, studying GPCRs has been problematic due to difficulties in isolating large quantities of these membrane proteins in forms that retain their ligand binding capabilities. Creating water-soluble variants of GPCRs by mutating the exterior, transmembrane residues provides a potential method to overcome these difficulties. Here we present the first study involving the computational design, expression and characterization of water-soluble variant of a human GPCR, the human mu opioid receptor (MUR), which is involved in pain and addiction. An atomistic structure of the transmembrane domain was built using comparative (homology) modeling and known GPCR structures. This structure was highly similar to the subsequently determined structure of the murine receptor and was used to computationally design 53 mutations of exterior residues in the transmembrane region, yielding a variant intended to be soluble in aqueous media. The designed variant expressed in high yield in Escherichia coli and was water soluble. The variant shared structural and functionally related features with the native human MUR, including helical secondary structure and comparable affinity for the antagonist naltrexone (K_d  = 65 nM). The roles of cholesterol and disulfide bonds on the stability of the receptor variant were also investigated. This study exemplifies the potential of the computational approach to produce water-soluble variants of GPCRs amenable for structural and functionally related characterization in aqueous solution.

Quality assessment of protein model-structures based on structural and functional similarities

Background

Experimental determination of protein 3D structures is expensive, time consuming and sometimes impossible. A gap between number of protein structures deposited in the World Wide Protein Data Bank and the number of sequenced proteins constantly broadens. Computational modeling is deemed to be one of the ways to deal with the problem. Although protein 3D structure prediction is a difficult task, many tools are available. These tools can model it from a sequence or partial structural information, e.g. contact maps. Consequently, biologists have the ability to generate automatically a putative 3D structure model of any protein. However, the main issue becomes evaluation of the model quality, which is one of the most important challenges of structural biology.

Results

GOBA - Gene Ontology-Based Assessment is a novel Protein Model Quality Assessment Program. It estimates the compatibility between a model-structure and its expected function. GOBA is based on the assumption that a high quality model is expected to be structurally similar to proteins functionally similar to the prediction target. Whereas DALI is used to measure structure similarity, protein functional similarity is quantified using standardized and hierarchical description of proteins provided by Gene Ontology combined with Wang's algorithm for calculating semantic similarity. Two approaches are proposed to express the quality of protein model-structures. One is a single model quality assessment method, the other is its modification, which provides a relative measure of model quality. Exhaustive evaluation is performed on data sets of model-structures submitted to the CASP8 and CASP9 contests.

Conclusions

The validation shows that the method is able to discriminate between good and bad model-structures. The best of tested GOBA scores achieved 0.74 and 0.8 as a mean Pearson correlation to the observed quality of models in our CASP8 and CASP9-based validation sets. GOBA also obtained the best result for two targets of CASP8, and one of CASP9, compared to the contest participants. Consequently, GOBA offers a novel single model quality assessment program that addresses the practical needs of biologists. In conjunction with other Model Quality Assessment Programs (MQAPs), it would prove useful for the evaluation of single protein models.

An energy-based conformer library for side chain optimization: improved prediction and adjustable sampling

Side chain optimization is a fundamental component of protein modeling applications such as docking, structural prediction, and design. In these applications side chain flexibility is often provided by rotamer or conformer libraries, which are collections of representative side chain conformations. Here we demonstrate that the sampling provided by the library can be substantially improved by adding an energetic criterion to its creation. The result of the new procedure is the Energy-Based library, a conformer library selected according to the propensity of its elements to fit energetically into natural protein environments. The new library performs outstandingly well in side chain optimization, producing structures with significantly lower energies and resulting in improved side chain conformation prediction. In addition, because the library was created as an ordered list, its size can be adjusted to any desired level. This feature provides unprecedented versatility in tuning sampling. It allows to precisely balance the number of conformers required by each amino acid type, equalizing their chances to fit into structural environments. It also allows to scale the amount of sampling to the specific requirement of any given side optimization problem. A rotameric version of the library was also produced with the same method to support applications that require a dihedral-only description of side chain conformation. The libraries are available at http://seneslab.org/EBL.

Computational design of a protein crystal

Protein crystals have catalytic and materials applications and are central to efforts in structural biology and therapeutic development. Designing predetermined crystal structures can be subtle given the complexity of proteins and the noncovalent interactions that govern crystallization. De novo protein design provides an approach to engineer highly complex nanoscale molecular structures, and often the positions of atoms can be programmed with sub-Å precision. Herein, a computational approach is presented for the design of proteins that self-assemble in three dimensions to yield macroscopic crystals. A three-helix coiled-coil protein is designed de novo to form a polar, layered, three-dimensional crystal having the P6 space group, which has a "honeycomb-like" structure and hexameric channels that span the crystal. The approach involves: (i) creating an ensemble of crystalline structures consistent with the targeted symmetry; (ii) characterizing this ensemble to identify "designable" structures from minima in the sequence-structure energy landscape and designing sequences for these structures; (iii) experimentally characterizing candidate proteins. A 2.1 Å resolution X-ray crystal structure of one such designed protein exhibits sub-Å agreement [backbone root mean square deviation (rmsd)] with the computational model of the crystal. This approach to crystal design has potential applications to the de novo design of nanostructured materials and to the modification of natural proteins to facilitate X-ray crystallographic analysis.

Probing designability via a generalized model of helical bundle geometry

Because the space of folded protein structures is highly degenerate, with recurring secondary and tertiary motifs, methods for representing protein structure in terms of collective physically relevant coordinates are of great interest. By collapsing structural diversity to a handful of parameters, such methods can be used to delineate the space of designable structures (i.e., conformations that can be stabilized with a large number of sequences)-a crucial task for de novo protein design. We first demonstrate this on natural α-helical coiled coils using the Crick parameterization. We show that over 95% of known coiled-coil structures are within  1-Å C(α) root mean square deviation of a Crick-ideal backbone. Derived parameters show that natural geometric space of coiled coils is highly restricted and can be represented by "allowed" conformations amidst a potential continuum of conformers. Allowed structures have (1) restricted axial offsets between helices, which differ starkly between parallel and anti-parallel structures; (2) preferred superhelical radii, which depend linearly on the oligomerization state; (3) pronounced radius-dependent a- and d-position amino acid propensities; and (4) discrete angles of rotation of helices about their axes, which are surprisingly independent of oligomerization state or orientation. In all, we estimate the space of designable coiled-coil structures to be reduced at least 160-fold relative to the space of geometrically feasible structures. To extend the benefits of structural parameterization to other systems, we developed a general mathematical framework for parameterizing arbitrary helical structures, which reduces to the Crick parameterization as a special case. The method is successfully validated on a set of non-coiled-coil helical bundles, frequent in channels and transporter proteins, which show significant helix bending but not supercoiling. Programs for coiled-coil parameter fitting and structure generation are provided via a web interface at http://www.gevorggrigoryan.com/cccp/, and code for generalized helical parameterization is available upon request.

Characterization of the cofactor-induced folding mechanism of a zinc-binding peptide using computationally designed mutants

Metals are the most commonly encountered protein cofactors, and they play important structural and functional roles in biology. In many cases, metal binding provides a major driving force for a polypeptide chain to fold. While there are many studies on the structure, stability, and function of metal-binding proteins, there are few studies focusing on understanding the kinetic mechanism of metal-induced folding. Herein, the Zn(2+)-induced folding kinetics of a small zinc-binding protein are studied; the CH1(1) peptide is derived from the first cysteine/histidine-rich region (CH1 domain) of the protein interaction domains of the transcriptional coregulator CREB-binding protein. Computational design is used to introduce tryptophan and histidine mutations that are structurally consistent with CH1(1); these mutants are studied using stopped-flow tryptophan fluorescence experiments. The Zn(2+)-induced CH1(1) folding kinetics are consistent with two parallel pathways, where the initial binding of Zn(2+) occurs at two sites. However, the initially formed Zn(2+)-bound complexes can proceed either directly to the folded state where zinc adopts a tetrahedral coordination or to an off-pathway misligated intermediate. While elimination of those ligands responsible for misligation simplifies the folding kinetics, it also leads to a decrease in the zinc binding constant. Therefore, these results suggest why these nonnative zinc ligands in the CH1(1) motif are conserved in several distantly related organisms and why the requirement for function can lead to kinetic frustration in folding. In addition, the loop closure rate of the CH1(1) peptide is determined based on the proposed model and temperature-dependent kinetic measurements.

NMR studies of a channel protein without membranes: structure and dynamics of water-solubilized KcsA

Structural studies of polytopic membrane proteins are often hampered by the vagaries of these proteins in membrane mimetic environments and by the difficulties in handling them with conventional techniques. Designing and creating water-soluble analogues with preserved native structures offer an attractive alternative. We report here solution NMR studies of WSK3, a water-soluble analogue of the potassium channel KcsA. The WSK3 NMR structure (PDB ID code 2K1E) resembles the KcsA crystal structures, validating the approach. By more stringent comparison criteria, however, the introduction of several charged residues aimed at improving water solubility seems to have led to the possible formations of a few salt bridges and hydrogen bonds not present in the native structure, resulting in slight differences in the structure of WSK3 relative to KcsA. NMR dynamics measurements show that WSK3 is highly flexible in the absence of a lipid environment. Reduced spectral density mapping and model-free analyses reveal dynamic characteristics consistent with an isotropically tumbling tetramer experiencing slow (nanosecond) motions with unusually low local ordering. An altered hydrogen-bond network near the selectivity filter and the pore helix, and the intrinsically dynamic nature of the selectivity filter, support the notion that this region is crucial for slow inactivation. Our results have implications not only for the design of water-soluble analogues of membrane proteins but also for our understanding of the basic determinants of intrinsic protein structure and dynamics.

Structure and dynamics of an extended conjugated NLO chromophore within an amphiphilic 4-helix bundle peptide by molecular dynamics simulation

Incorporation of extended conjugated chromophores into amphiphilic 4-helix bundle peptides has been shown experimentally to be an effective means to orient the chromphores vectorially in 2-D ensembles with high in-plane density. The designed microscopic hyperpolarizabilty of the chromophore is preserved in the macroscopic NLO response of the ensemble. We show via molecular dynamics simulation that the designed coiled-coil structure of the bundle controls the conformation and dynamics of the chromophore that are critical to optimizing its hyperpolarizability.

Toward full-sequence de novo protein design with flexible templates for human beta-defensin-2

In this article, we introduce and apply our de novo protein design framework, which observes true backbone flexibility, to the redesign of human beta-defensin-2, a 41-residue cationic antimicrobial peptide of the innate immune system. The flexible design templates are generated using molecular dynamics simulations with both Generalized Born implicit solvation and explicit water molecules. These backbone templates were employed in addition to the x-ray crystal structure for designing human beta-defensin-2. The computational efficiency of our framework was demonstrated with the full-sequence design of the peptide with flexible backbone templates, corresponding to the mutation of all positions except the native cysteines.

Modeling backbone flexibility to achieve sequence diversity: the design of novel alpha-helical ligands for Bcl-xL

Computational protein design can be used to select sequences that are compatible with a fixed-backbone template. This strategy has been used in numerous instances to engineer novel proteins. However, the fixed-backbone assumption severely restricts the sequence space that is accessible via design. For challenging problems, such as the design of functional proteins, this may not be acceptable. Here, we present a method for introducing backbone flexibility into protein design calculations and apply it to the design of diverse helical BH3 ligands that bind to the anti-apoptotic protein Bcl-xL, a member of the Bcl-2 protein family. We demonstrate how normal mode analysis can be used to sample different BH3 backbones, and show that this leads to a larger and more diverse set of low-energy solutions than can be achieved using a native high-resolution Bcl-xL complex crystal structure as a template. We tested several of the designed solutions experimentally and found that this approach worked well when normal mode calculations were used to deform a native BH3 helix structure, but less well when they were used to deform an idealized helix. A subsequent round of design and testing identified a likely source of the problem as inadequate sampling of the helix pitch. In all, we tested 17 designed BH3 peptide sequences, including several point mutants. Of these, eight bound well to Bcl-xL and four others showed weak but detectable binding. The successful designs showed a diversity of sequences that would have been difficult or impossible to achieve using only a fixed backbone. Thus, introducing backbone flexibility via normal mode analysis effectively broadened the set of sequences identified by computational design, and provided insight into positions important for binding Bcl-xL.

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.

Fluorescence correlation spectroscopic study of serpin depolymerization by computationally designed peptides

Members of the serine proteinase inhibitor (serpin) family play important roles in the inflammatory and coagulation cascades. Interaction of a serpin with its target proteinase induces a large conformational change, resulting in insertion of its reactive center loop (RCL) into the main body of the protein as a new strand within beta-sheet A. Intermolecular insertion of the RCL of one serpin molecule into the beta-sheet A of another leads to polymerization, a widespread phenomenon associated with a general class of diseases known as serpinopathies. Small peptides are known to modulate the polymerization process by binding within beta-sheet A. Here, we use fluorescence correlation spectroscopy (FCS) to probe the mechanism of peptide modulation of alpha(1)-antitrypsin (alpha(1)-AT) polymerization and depolymerization, and employ a statistical computationally-assisted design strategy (SCADS) to identify new tetrapeptides that modulate polymerization. Our results demonstrate that peptide-induced depolymerization takes place via a heterogeneous, multi-step process that begins with internal fragmentation of the polymer chain. One of the designed tetrapeptides is the most potent antitrypsin depolymerizer yet found.

Structural determinants of the rate of protein evolution in yeast

We investigate how a protein's structure influences the rate at which its sequence evolves. Our basic hypothesis is that proteins with highly designable structures (structures that are encoded by many sequences) will evolve more rapidly. Recent theoretical advances argue that structures with a higher density of interresidue contacts are more designable, and we show that high contact density is correlated with an increased rate of sequence evolution in yeast. In addition, we investigate the correlations between the rate of sequence evolution and several other structural descriptors, carefully controlling for the strong effect of expression level on evolutionary rate. Overall, we find that the structural descriptors that we consider appear to explain roughly 10% of the variation in rates of protein evolution in yeast. We also show that despite the well-known trend for buried residues to be more conserved, proteins with a higher fraction of buried residues, nonetheless, tend to evolve their sequences more rapidly. We suggest that this effect is due to the increased designability of structures with more buried residues. Our results provide evidence that protein structure plays an important role in shaping the rate of sequence evolution and provide evidence to support recent theoretical advances linking structural designability to contact density.

Characterization of a membrane protein folding motif, the Ser zipper, using designed peptides

Polar residues play important roles in the association of transmembrane helices and the stabilities of membrane proteins. Although a single Ser residue in a transmembrane helix is unable to mediate a strong association of the helices, the cooperative interactions of two or more appropriately placed serine hydroxyl groups per helix has been hypothesized to allow formation of a "serine zipper" that can stabilize transmembrane helix association. In particular, a heptad repeat Sera Xxx Xxx Leud Xxx Xxx Xxx (Xxx is a hydrophobic amino acid) appears in both antiparallel helical pairs of polytopic membrane proteins as well as the parallel helical dimerization motif found in the murine erythropoietin receptor. To examine the intrinsic conformational preferences of this motif independent of its context within a larger protein, we synthesized a peptide containing three copies of a SeraLeud heptad motif. Computational results are consistent with the designed peptide adopting either a parallel or antiparallel structure, and conformational search calculations yield the parallel dimer as the lowest energy configuration, which is also significantly more stable than the parallel trimer. Analytical ultracentrifugation indicated that the peptide exists in a monomer-dimer equilibrium in dodecylphosphocholine micelles. Thiol disulfide interchange studies showed a preference for forming parallel dimers in micelles. In phospholipid vesicles, only the parallel dimer was formed. The stability of the SerZip peptide was studied in vesicles prepared from phosphatidylcholine (PC) lipids of different chain length: POPC (C16:0C18:1 PC) and DLPC (C12:0PC). The stability was greater in POPC, which has a good match between the length of the hydrophobic region of the peptide and the bilayer length. Finally, mutation to Ala of the Ser residues in the SerZip motif gave rise to a relatively small decrease in the stability of the dimer, indicating that packing interactions rather than hydrogen-bonding provided the primary driving force for association.

Molecular Dynamics Simulation of WSK-3, a Computationally Designed, Water-Soluble Variant of the Integral Membrane Protein KcsA

Poor solubility and low expression levels often make membrane proteins difficult to study. An alternative to the use of detergents to solubilize these aggregation-prone proteins is the partial redesign of the sequence so as to confer water solubility. Recently, computationally assisted membrane protein solubilization (CAMPS) has been reported, where exposed hydrophobic residues on a protein's surface are computationally redesigned. Herein, the structure and fluctuations of a designed, water-soluble variant of KcsA (WSK-3) were studied using molecular dynamics simulations. The root mean square deviation of the protein from its starting structure, where the backbone coordinates are those of KcsA, was 1.8 angstroms. The structure of salt bridges involved in structural specificity and solubility were examined. The preferred configuration of ions and water in the selectivity filter of WSK-3 was consistent with the reported preferences for KcsA. The structure of the selectivity filter was maintained, which is consistent with WSK-3 having an affinity for agitoxin2 comparable to that of wild-type KcsA. In contrast to KcsA, the central cavity's side chains were observed to reorient, allowing water diffusion through the side of the cavity wall. These simulations provide an atomistic analysis of the CAMPS strategy and its implications for further investigations of membrane proteins.

Sequence optimization and designability of enzyme active sites

We recently found that many residues in enzyme active sites can be computationally predicted by the optimization of scoring functions based on substrate binding affinity, subject to constraints on the geometry of catalytic residues and protein stability. Here, we explore the generality of this surprising observation. First, the impact of hydrogen-bonding networks necessary for catalysis on the accuracy of sequence optimization is assessed; incorporation of these networks, where relevant, into the set of catalytic constraints is found to be essential. Next, the impact of multiple substrate selectivity on sequence optimization is probed by carrying out independent calculations for complexes of deoxyribonucleoside kinases with various cognate ligands, revealing how simultaneous selection pressures determined active-site sequences of these enzymes. Including previous calculations on simpler enzymes, computational sequence optimization correctly predicts 76% of all active-site residues tested (86% correct, with 93% similar, for naturally conserved residues). In these studies, the ligand is fixed in its native conformation. To assess the applicability of these methods to de novo active-site design, the effect of small ligand motions around the native pose is also examined. Robustness of sequence accuracy for topologically similar poses is demonstrated for selected kinases, but not for a model peptidase. Based on these observations, we introduce the notion of the designability of an enzyme active site, a metric that may be used to guide the search for protein scaffolds suitable for the introduction of de novo activity for a desired chemical reaction.

Protein sequence entropy is closely related to packing density and hydrophobicity

We investigated the correlation between the Shannon information entropy, 'sequence entropy', with respect to the local flexibility of native globular proteins as described by inverse packing density. These are determined at each residue position for a total set of 130 query proteins, where sequence entropies are calculated from each set of aligned residues. For the accompanying aggregate set of 130 alignments, a strong linear correlation is observed between the calculated sequence entropy and the corresponding inverse packing density determined at an associated residue position. This region of linearity spans the range of C(alpha) packing densities from 12 to 25 amino acids within a sphere of 9 angstrom radius. Three different hydrophobicity scales all mimic the behavior of the sequence entropies. This confirms the idea that the ability to accommodate mutations is strongly dependent on the available space and on the propensity for each amino acid type to be buried. Future applications of these types of methods may prove useful in identifying both core and flexible residues within a protein.

Energy Functions for Protein Design: Adjustment with Protein–Protein Complex Affinities, Models for the Unfolded State, and Negative Design of Solubility and Specificity

The development of the EGAD program and energy function for protein design is described. In contrast to most protein design methods, which require several empirical parameters or heuristics such as patterning of residues or rotamers, EGAD has a minimalist philosophy; it uses very few empirical factors to account for inaccuracies resulting from the use of fixed backbones and discrete rotamers in protein design calculations, and describes the unfolded state, aggregates, and alternative conformers explicitly with physical models instead of fitted parameters. This approach unveils important issues in protein design that are often camouflaged by heuristic-emphasizing methods. Inter-atom energies are modeled with the OPLS-AA all-atom forcefield, electrostatics with the generalized Born continuum model, and the hydrophobic effect with a solvent-accessible surface area-dependent term. Experimental characterization of proteins designed with an unmodified version of the energy function revealed problems with under-packing, stability, aggregation, and structural specificity. Under-packing was addressed by modifying the van der Waals function. By optimizing only three parameters, the effects of >400 mutations on protein-protein complex formation were predicted to within 1.0 kcal mol(-1). As an independent test, this modified energy function was used to predict the stabilities of >1500 mutants to within 1.0 kcal mol(-1); this required a physical model of the unfolded state that includes more interactions than traditional tripeptide-based models. Solubility and structural specificity were addressed with simple physical approximations of aggregation and conformational equilibria. The complete energy function can design protein sequences that have high levels of identity with their natural counterparts, and have predicted structural properties more consistent with soluble and uniquely folded proteins than the initial designs.

Computational design of water-soluble analogues of the potassium channel KcsA

Although the interiors of membrane and water-soluble proteins are similar in their physicochemical properties, membrane proteins differ in having larger fractions of hydrophobic residues on their exteriors. Thus, it should be possible to water-solubilize membrane proteins by mutating their lipid-contacting side chains to more polar groups. Here, a computational approach was used to generate water-soluble variants of the potassium channel KcsA. As a probe of the correctness of the fold, the proteins contain an agitoxin2 binding site from a mammalian homologue of the channel. The resulting proteins express in high yield in Escherichia coli and share the intended functional and structural properties with KcsA, including secondary structure, tetrameric quaternary structure, and tight specific binding to both agitoxin2 and a small molecule channel blocker.

Computational design and characterization of a monomeric helical dinuclear metalloprotein

The de novo design of di-iron proteins is an important step towards understanding the diversity of function among this complex family of metalloenzymes. Previous designs of due ferro (DF) proteins have resulted in tetrameric and dimeric four-helix bundles having crystallographically well-defined structures and active-site geometries. Here, the design and characterization of DFsc, a 114 residue monomeric four-helix bundle, is presented. The backbone was modeled using previous oligomeric structures and appropriate inter-helical turns. The identities of 26 residues were predetermined, including the primary and secondary ligands in the active site, residues involved in active site accessibility, and the gamma beta gamma beta turn between helices 2 and 3. The remaining 88 amino acid residues were determined using statistical computer aided design, which is based upon a recent statistical theory of protein sequences. Rather than sampling sequences, the theory directly provides the site-specific amino acid probabilities, which are then used to guide sequence design. The resulting sequence (DFsc) expresses well in Escherichia coli and is highly soluble. Sedimentation studies confirm that the protein is monomeric in solution. Circular dichroism spectra are consistent with the helical content of the target structure. The protein is structured in both the apo and the holo forms, with the metal-bound form exhibiting increased stability. DFsc stoichiometrically binds a variety of divalent metal ions, including Zn(II), Co(II), Fe(II), and Mn(II), with micromolar affinities. 15N HSQC NMR spectra of both the apo and Zn(II) proteins reveal excellent dispersion with evidence of a significant structural change upon metal binding. DFsc is then a realization of complete de novo design, where backbone structure, activity, and sequence are specified in the design process.

Natural selection of more designable folds: a mechanism for thermophilic adaptation

An open question of great interest in biophysics is whether variations in structure cause protein folds to differ in the number of amino acid sequences that can fold to them stably, i.e., in their designability. Recently, we have shown that a novel quantitative measure of a fold's tertiary topology, called its contact trace, strongly correlates with the fold's designability. Here, we investigate the relationship between a fold's contact trace and its relative frequency of usage in mesophilic vs. thermophilic eubacteria. We observe that thermophilic organisms exhibit a bias toward using folds of higher contact trace when compared with mesophiles. We establish this difference both for the distributions of folds at the whole-proteome level and also through more focused structural comparisons of orthologous proteins. Our findings suggest that thermophilic adaptation in bacterial genomes occurs in part through natural selection of more designable folds, pointing to designability as a key component of protein fitness.

Identifying residue-residue clashes in protein hybrids by using a second-order mean-field approach

In this article, a second-order mean-field-based approach is introduced for characterizing the complete set of residue-residue couplings consistent with a given protein structure. This information is subsequently used to classify protein hybrids with respect to their potential to be functional based on the presenceabsence and severity of clashing residue-residue interactions. First, atomistic representations of both the native and denatured states are used to calculate rotamer-backbone, rotamer-intrinsic, and rotamer-rotamer conformational energies. Next, this complete conformational energy table is coupled with a second-order mean-field description to elucidate the probabilities of all possible rotamer-rotamer combinations in a minimum Helmholtz free-energy ensemble. Computational results for the dihydrofolate reductase family reveal correlation in substitution patterns between not only contacting but also distal second-order structural elements. Residue-residue clashes in hybrid proteins are quantified by contrasting the ensemble probabilities of protein hybrids against the ones of the original parental sequences. Good agreement with experimental data is demonstrated by superimposing these clashes against the functional crossover profiles of bidirectional incremental truncation libraries for Escherichia coli and human glycinamide ribonucleotide transformylases.

Statistical formulae of the energy distribution among a globular protein structure ensemble

In prediction of a protein main-chain structure into which a query sequence of amino acids folds, one evaluates the relative stability of a candidate structure against reference structures. We developed a statistical theory for calculating the energy distribution over a main-chain structure ensemble, only with an amino acid composition given as a single argument. Then, we obtained a statistical formulae of the ensemble mean <E> and ensemble variance V[E] of the reference structural energies, as explicit functions of the amino acid composition. The mean <E> and the variance V[E] calculated from the formulae were well or roughly consistent with those resulting from a gapless threading simulation. We can use the formulae not only to perform the high-through-put screening of sequences in the inverse folding problem, but also to handle the problem analytically.

Thoroughly sampling sequence space: large-scale protein design of structural ensembles

Modeling the inherent flexibility of the protein backbone as part of computational protein design is necessary to capture the behavior of real proteins and is a prerequisite for the accurate exploration of protein sequence space. We present the results of a broad exploration of sequence space, with backbone flexibility, through a novel approach: large-scale protein design to structural ensembles. A distributed computing architecture has allowed us to generate hundreds of thousands of diverse sequences for a set of 253 naturally occurring proteins, allowing exciting insights into the nature of protein sequence space. Designing to a structural ensemble produces a much greater diversity of sequences than previous studies have reported, and homology searches using profiles derived from the designed sequences against the Protein Data Bank show that the relevance and quality of the sequences is not diminished. The designed sequences have greater overall diversity than corresponding natural sequence alignments, and no direct correlations are seen between the diversity of natural sequence alignments and the diversity of the corresponding designed sequences. For structures in the same fold, the sequence entropies of the designed sequences cluster together tightly. This tight clustering of sequence entropies within a fold and the separation of sequence entropy distributions for different folds suggest that the diversity of designed sequences is primarily determined by a structure's overall fold, and that the designability principle postulated from studies of simple models holds in real proteins. This has important implications for experimental protein design and engineering, as well as providing insight into protein evolution.