Generalized dead-end elimination algorithms make large-scale protein side-chain structure prediction tractable: implications for protein design and structural genomics

Molecular Information Theory Meets Protein Folding

We propose an application of molecular information theory to analyze the folding of single domain proteins. We analyze results from various areas of protein science, such as sequence-based potentials, reduced amino acid alphabets, backbone configurational entropy, secondary structure content, residue burial layers, and mutational studies of protein stability changes. We found that the average information contained in the sequences of evolved proteins is very close to the average information needed to specify a fold ∼2.2 ± 0.3 bits/(site·operation). The effective alphabet size in evolved proteins equals the effective number of conformations of a residue in the compact unfolded state at around 5. We calculated an energy-to-information conversion efficiency upon folding of around 50%, lower than the theoretical limit of 70%, but much higher than human-built macroscopic machines. We propose a simple mapping between molecular information theory and energy landscape theory and explore the connections between sequence evolution, configurational entropy, and the energetics of protein folding.

Development of an Indole-Amide-Based Photoswitchable Cannabinoid Receptor Subtype 1 (CB1R) "Cis-On" Agonist

Activation of the human cannabinoid receptor type 1 (hCB₁R) with high spatiotemporal control is useful to study processes involved in different pathologies related to nociception, metabolic alterations, and neurological disorders. To synthesize new agonist ligands for hCB₁R, we have designed different classes of photoswitchable molecules based on an indole core. The modifications made to the central core have allowed us to understand the molecular characteristics necessary to design an agonist with optimal pharmacological properties. Compound 27a shows high affinity for CB₁R (K_i (cis-form) = 0.18 μM), with a marked difference in affinity with respect to its inactive "trans-off" form (CB₁R K_i trans/cis ratio = 5.4). The novel compounds were evaluated by radioligand binding studies, receptor internalization, sensor receptor activation (GRABeCB2.0), Western blots for analysis of ERK1/2 activation, NanoBiT βarr2 recruitment, and calcium mobilization assays, respectively. The data show that the novel agonist 27a is a candidate for studying the optical modulation of cannabinoid receptors (CBRs), serving as a new molecular tool for investigating the involvement of hCB₁R in disorders associated with the endocannabinoid system.

Protein Assembly by Design

Proteins are nature's primary building blocks for the construction of sophisticated molecular machines and dynamic materials, ranging from protein complexes such as photosystem II and nitrogenase that drive biogeochemical cycles to cytoskeletal assemblies and muscle fibers for motion. Such natural systems have inspired extensive efforts in the rational design of artificial protein assemblies in the last two decades. As molecular building blocks, proteins are highly complex, in terms of both their three-dimensional structures and chemical compositions. To enable control over the self-assembly of such complex molecules, scientists have devised many creative strategies by combining tools and principles of experimental and computational biophysics, supramolecular chemistry, inorganic chemistry, materials science, and polymer chemistry, among others. Owing to these innovative strategies, what started as a purely structure-building exercise two decades ago has, in short order, led to artificial protein assemblies with unprecedented structures and functions and protein-based materials with unusual properties. Our goal in this review is to give an overview of this exciting and highly interdisciplinary area of research, first outlining the design strategies and tools that have been devised for controlling protein self-assembly, then describing the diverse structures of artificial protein assemblies, and finally highlighting the emergent properties and functions of these assemblies.

"Photo-Rimonabant": Synthesis and Biological Evaluation of Novel Photoswitchable Molecules Derived from Rimonabant Lead to a Highly Selective and Nanomolar "Cis-On" CB1R Antagonist

Human cannabinoid receptor type 1 (hCB₁R) plays important roles in the regulation of appetite and development of addictive behaviors. Herein, we describe the design, synthesis, photocharacterization, molecular docking, and in vitro characterization of "photo-rimonabant", i.e., azo-derivatives of the selective hCB₁R antagonist SR1411716A (rimonabant). By applying azo-extension strategies, we yielded compound 16a, which shows marked affinity for CB₁R (K_{i (cis form)} = 29 nM), whose potency increases by illumination with ultraviolet light (CB₁R K_itrans/cis ratio = 15.3). Through radioligand binding, calcium mobilization, and cell luminescence assays, we established that 16a is highly selective for hCB₁R over hCB₂R. These selective antagonists can be valuable molecular tools for optical modulation of CBRs and better understanding of disorders associated with the endocannabinoid system.

Hybrid MC/MD for protein design

Computational protein design relies on simulations of a protein structure, where selected amino acids can mutate randomly, and mutations are selected to enhance a target property, such as stability. Often, the protein backbone is held fixed and its degrees of freedom are modeled implicitly to reduce the complexity of the conformational space. We present a hybrid method where short molecular dynamics (MD) segments are used to explore conformations and alternate with Monte Carlo (MC) moves that apply mutations to side chains. The backbone is fully flexible during MD. As a test, we computed side chain acid/base constants or pK_a's in five proteins. This problem can be considered a special case of protein design, with protonation/deprotonation playing the role of mutations. The solvent was modeled as a dielectric continuum. Due to cost, in each protein we allowed just one side chain position to change its protonation state and the other position to change its type or mutate. The pK_a's were computed with a standard method that scans a range of pH values and with a new method that uses adaptive landscape flattening (ALF) to sample all protonation states in a single simulation. The hybrid method gave notably better accuracy than standard, fixed-backbone MC. ALF decreased the computational cost a factor of 13.

OPUS-Rota2: An Improved Fast and Accurate Side-Chain Modeling Method

Side-chain modeling plays a critical role in protein structure prediction. However, in many current methods, balancing the speed and accuracy is still challenging. In this paper, on the basis of our previous work OPUS-Rota (Protein Sci. 2008, 17, 1576-1585), we introduce a new side-chain modeling method, OPUS-Rota2, which is tested on both a 65-protein test set (DB65) in the OPUS-Rota paper and a 379-protein test set (DB379) in the SCWRL4 paper. If the main chain is native, OPUS-Rota2 is more accurate than OPUS-Rota, SCWRL4, and OSCAR-star but slightly less accurate than OSCAR-o. Also, if the main chain is non-native, OPUS-Rota2 is more accurate than any other method. Moreover, OPUS-Rota2 is significantly faster than any other method, in particular, 2 orders of magnitude faster than OSCAR-o. Thus, the combination of higher accuracy and speed of OPUS-Rota2 in modeling side chains on both the native and non-native main chains makes OPUS-Rota2 a very useful tool in protein structure modeling.

Trends in therapeutic antibody affinity maturation: From in-vitro towards next-generation sequencing approaches

Current advances in antibody engineering driving the strongest growth area in biotherapeutic agents development. Affinity improvement that is mainly important for biological activity and clinical efficacy of therapeutic antibodies, has still remained a challenging task. In the human body, during a course of immune response affinity maturation increase antibody activity by several rounds of somatic hypermutation and clonal selection in the germinal center. The final outputs are antibodies representing higher affinity and specificity against a particular antigen. In the realm of biotechnology, exploring of mutations which improve antibody affinity while preserving its specificity and stability is an extremely time-consuming and laborious process. Recent advances in computational algorithms and DNA sequencing technologies help researchers to redesign antibody structure to achieve desired properties such as improved binding affinity. In this review, we briefly described the principle of affinity maturation and different corresponding in vitro techniques. Also, we recapitulated the most recent advancements in the field of antibody affinity maturation including computational approaches and next-generation sequencing (NGS).

Structural Basis of Substrate Recognition and Covalent Inhibition of Cdu1 from Chlamydia trachomatis

Based on the similarity between the active sites of the deubiquitylating and deneddylating enzyme ChlaDub1 (Cdu1) and the evolutionarily related protease adenain, a target-hopping screening approach on a focused set of adenain inhibitors was investigated. The cyanopyrimidine-based inhibitors identified represent the first active-site-directed small-molecule inhibitors of Cdu1. High-resolution crystal structures of Cdu1 in complex with two covalently bound cyanopyrimidines, as well as with its substrate ubiquitin, were obtained. These structural data were complemented by enzymatic assays and covalent docking studies to provide insight into the substrate recognition of Cdu1, active-site pocket flexibility and potential hotspots for ligand interaction. Combined, these data provide a strong basis for future structure-guided medicinal chemistry optimization of this cyanopyrimidine scaffold into more potent and selective Cdu1 inhibitors.

ProPOSE: Direct Exhaustive Protein-Protein Docking with Side Chain Flexibility

Despite decades of development, protein-protein docking remains a largely unsolved problem. The main difficulties are the immense space spanned by the translational and rotational degrees of freedom and the prediction of the conformational changes of proteins upon binding. FFT is generally the preferred method to exhaustively explore the translation-rotation space at a fine grid resolution, albeit with the trade-off of approximating force fields with correlation functions. This work presents a direct search alternative that samples the states in Cartesian space at the same resolution and computational cost as standard FFT methods. Operating in real space allows the use of standard force field functional forms used in typical non-FFT methods as well as the implementation of strategies for focused exploration of conformational flexibility. Currently, a few misplaced side chains can cause docking programs to fail. This work specifically addresses the problem of side chain rearrangements upon complex formation. Based on the observation that most side chains retain their unbound conformation upon binding, each rigidly docked pose is initially scored ignoring up to a limited number of side chain overlaps which are resolved in subsequent repacking and minimization steps. On test systems where side chains are altered and backbones held in their bound state, this implementation provides significantly better native pose recovery and higher quality (lower RMSD) predictions when compared with five of the most popular docking programs. The method is implemented in the software program ProPOSE (Protein Pose Optimization by Systematic Enumeration).

Antibody Affinity Maturation by Computational Design

The immune systems protect our bodies from foreign molecules or antigens, where antibodies play important roles. Antibodies evolve over time upon antigen encounter by somatically mutating their genome sequences. The end result is a series of antibodies that display higher affinities and specificities to specific antigens. This process is called affinity maturation. Recent improvements in computer hardware and modeling algorithms now enable the rational design of protein structures and functions, and several works on computer-aided antibody design have been published. In this chapter, we briefly describe computational methods for antibody affinity maturation, focusing on methods for sampling antibody conformations and for scoring designed antibody variants. We also discuss lessons learned from the successful computer-aided design of antibodies.

Deterministic Search Methods for Computational Protein Design

One main challenge in Computational Protein Design (CPD) lies in the exploration of the amino-acid sequence space, while considering, to some extent, side chain flexibility. The exorbitant size of the search space urges for the development of efficient exact deterministic search methods enabling identification of low-energy sequence-conformation models, corresponding either to the global minimum energy conformation (GMEC) or an ensemble of guaranteed near-optimal solutions. In contrast to stochastic local search methods that are not guaranteed to find the GMEC, exact deterministic approaches always identify the GMEC and prove its optimality in finite but exponential worst-case time. After a brief overview on these two classes of methods, we discuss the grounds and merits of four deterministic methods that have been applied to solve CPD problems. These approaches are based either on the Dead-End-Elimination theorem combined with A* algorithm (DEE/A*), on Cost Function Networks algorithms (CFN), on Integer Linear Programming solvers (ILP) or on Markov Random Fields solvers (MRF). The way two of these methods (DEE/A* and CFN) can be used in practice to identify low-energy sequence-conformation models starting from a pairwise decomposed energy matrix is detailed in this review.

Automated protein design: Landmarks and operational principles

Protein design has an eventful history spanning over three decades, with handful of success stories reported, and numerous failures not reported. Design practices have benefited tremendously from improvements in computer hardware and advances in scientific algorithms. Though protein folding problem still remains unsolved, the possibility of having multiple sequence solutions for a single fold makes protein design a more tractable problem than protein folding. One of the most significant advancement in this area is the implementation of automated design algorithms on pre-defined templates or completely new folds, optimized through deterministic and heuristic search algorithms. This progress report provides a succinct presentation of important landmarks in automated design attempts, followed by brief account of operational principles in automated design methods.

Comparing three stochastic search algorithms for computational protein design: Monte Carlo, replica exchange Monte Carlo, and a multistart, steepest-descent heuristic

Computational protein design depends on an energy function and an algorithm to search the sequence/conformation space. We compare three stochastic search algorithms: a heuristic, Monte Carlo (MC), and a Replica Exchange Monte Carlo method (REMC). The heuristic performs a steepest-descent minimization starting from thousands of random starting points. The methods are applied to nine test proteins from three structural families, with a fixed backbone structure, a molecular mechanics energy function, and with 1, 5, 10, 20, 30, or all amino acids allowed to mutate. Results are compared to an exact, "Cost Function Network" method that identifies the global minimum energy conformation (GMEC) in favorable cases. The designed sequences accurately reproduce experimental sequences in the hydrophobic core. The heuristic and REMC agree closely and reproduce the GMEC when it is known, with a few exceptions. Plain MC performs well for most cases, occasionally departing from the GMEC by 3-4 kcal/mol. With REMC, the diversity of the sequences sampled agrees with exact enumeration where the latter is possible: up to 2 kcal/mol above the GMEC. Beyond, room temperature replicas sample sequences up to 10 kcal/mol above the GMEC, providing thermal averages and a solution to the inverse protein folding problem. © 2016 Wiley Periodicals, Inc.

Protein side chain conformation predictions with an MMGBSA energy function

The prediction of protein side chain conformations from backbone coordinates is an important task in structural biology, with applications in structure prediction and protein design. It is a difficult problem due to its combinatorial nature. We study the performance of an "MMGBSA" energy function, implemented in our protein design program Proteus, which combines molecular mechanics terms, a Generalized Born and Surface Area (GBSA) solvent model, with approximations that make the model pairwise additive. Proteus is not a competitor to specialized side chain prediction programs due to its cost, but it allows protein design applications, where side chain prediction is an important step and MMGBSA an effective energy model. We predict the side chain conformations for 18 proteins. The side chains are first predicted individually, with the rest of the protein in its crystallographic conformation. Next, all side chains are predicted together. The contributions of individual energy terms are evaluated and various parameterizations are compared. We find that the GB and SA terms, with an appropriate choice of the dielectric constant and surface energy coefficients, are beneficial for single side chain predictions. For the prediction of all side chains, however, errors due to the pairwise additive approximation overcome the improvement brought by these terms. We also show the crucial contribution of side chain minimization to alleviate the rigid rotamer approximation. Even without GB and SA terms, we obtain accuracies comparable to SCWRL4, a specialized side chain prediction program. In particular, we obtain a better RMSD than SCWRL4 for core residues (at a higher cost), despite our simpler rotamer library. Proteins 2016; 84:803-819. © 2016 Wiley Periodicals, Inc.

Flat-Bottom Strategy for Improved Accuracy in Protein Side-Chain Placements

We present a new strategy for protein side-chain placement that uses flat-bottom potentials for rotamer scoring. The extent of the flat bottom depends on the coarseness of the rotamer library and is optimized for libraries ranging from diversities of 0.2 Å to 5.0 Å. The parameters reported here were optimized for forcefields using Lennard-Jones 12-6 van der Waals potential with DREIDING parameters but are expected to be similar for AMBER, CHARMM, and other forcefields. This Side-Chain Rotamer Excitation Analysis Method is implemented in the SCREAM software package. Similar scoring function strategies should be useful for ligand docking, virtual ligand screening, and protein folding applications.

Pairwise decomposition of an MMGBSA energy function for computational protein design

Computational protein design (CPD) aims at predicting new proteins or modifying existing ones. The computational challenge is huge as it requires exploring an enormous sequence and conformation space. The difficulty can be reduced by considering a fixed backbone and a discrete set of sidechain conformations. Another common strategy consists in precalculating a pairwise energy matrix, from which the energy of any sequence/conformation can be quickly obtained. In this work, we examine the pairwise decomposition of protein MMGBSA energy functions from a general theoretical perspective, and an implementation proposed earlier for CPD. It includes a Generalized Born term, whose many-body character is overcome using an effective dielectric environment, and a Surface Area term, for which we present an improved pairwise decomposition. A detailed evaluation of the error introduced by the decomposition on the different energy components is performed. We show that the error remains reasonable, compared to other uncertainties.

Protein side-chain modeling with a protein-dependent optimized rotamer library

Despite years of effort, the problem of predicting the conformations of protein side chains remains a subject of inquiry. This problem has three major issues, namely defining the conformations that a side chain may adopt within a protein, developing a sampling procedure for generating possible side-chain packings, and defining a scoring function that can rank these possible packings. To solve the former of these issues, most procedures rely on a rotamer library derived from databases of known protein structures. We introduce an alternative method that is free of statistics. We begin with a rotamer library that is based only on stereochemical considerations; this rotamer library is then optimized independently for each protein under study. We show that this optimization step restores the diversity of conformations observed in native proteins. We combine this protein-dependent rotamer library (PDRL) method with the self-consistent mean field (SCMF) sampling approach and a physics-based scoring function into a new side-chain prediction method, SCMF-PDRL. Using two large test sets of 831 and 378 proteins, respectively, we show that this new method compares favorably with competing methods such as SCAP, OPUS-Rota, and SCWRL4 for energy-minimized structures.

Comparative Modeling of Drug Target Proteins☆

In this perspective, we begin by describing the comparative protein structure modeling technique and the accuracy of the corresponding models. We then discuss the significant role that comparative prediction plays in drug discovery. We focus on virtual ligand screening against comparative models and illustrate the state-of-the-art by a number of specific examples.

Expanded explorations into the optimization of an energy function for protein design

Nature possesses a secret formula for the energy as a function of the structure of a protein. In protein design, approximations are made to both the structural representation of the molecule and to the form of the energy equation, such that the existence of a general energy function for proteins is by no means guaranteed. Here, we present new insights toward the application of machine learning to the problem of finding a general energy function for protein design. Machine learning requires the definition of an objective function, which carries with it the implied definition of success in protein design. We explored four functions, consisting of two functional forms, each with two criteria for success. Optimization was carried out by a Monte Carlo search through the space of all variable parameters. Cross-validation of the optimized energy function against a test set gave significantly different results depending on the choice of objective function, pointing to relative correctness of the built-in assumptions. Novel energy cross terms correct for the observed nonadditivity of energy terms and an imbalance in the distribution of predicted amino acids. This paper expands on the work presented at the 2012 ACM-BCB.

Antibody humanization by redesign of complementarity-determining region residues proximate to the acceptor framework

Antibodies are key components of the adaptive immune system and are well-established protein therapeutic agents. Typically high-affinity antibodies are obtained by immunization of rodent species that need to be humanized to reduce their immunogenicity. The complementarity-determining regions (CDRs) contain the residues in a defined loop structure that confer antigen binding, which must be retained in the humanized antibody. To design a humanized antibody, we graft the mature murine CDRs onto a germline human acceptor framework. Structural defects due to mismatches at the graft interface can be fixed by mutating some framework residues to murine, or by mutating some residues on the CDRs' backside to human or to a de novo designed sequence. The first approach, framework redesign, can yield an antibody with binding better than the CDR graft and one equivalent to the mature murine, and reduced immunogenicity. The second approach, CDR redesign, is presented here as a new approach, yielding an antibody with binding better than the CDR graft, and immunogenicity potentially less than that from framework redesign. Application of both approaches to the humanization of anti-α4 integrin antibody HP1/2 is presented and the concept of the hybrid humanization approach that retains "difficult to match" murine framework amino acids and uses de novo CDR design to minimize murine amino acid content and reduce cell-mediated cytotoxicity liabilities is discussed.

Computational Enzyme Design: Advances, hurdles and possible ways forward

This mini review addresses recent developments in computational enzyme design. Successful protocols as well as known issues and limitations are discussed from an energetic perspective. It will be argued that improved results can be obtained by including a dynamic treatment in the design protocol. Finally, a molecular dynamics-based approach for evaluating and refining computational designs is presented.

Computer-aided antibody design

Recent clinical trials using antibodies with low toxicity and high efficiency have raised expectations for the development of next-generation protein therapeutics. However, the process of obtaining therapeutic antibodies remains time consuming and empirical. This review summarizes recent progresses in the field of computer-aided antibody development mainly focusing on antibody modeling, which is divided essentially into two parts: (i) modeling the antigen-binding site, also called the complementarity determining regions (CDRs), and (ii) predicting the relative orientations of the variable heavy (V(H)) and light (V(L)) chains. Among the six CDR loops, the greatest challenge is predicting the conformation of CDR-H3, which is the most important in antigen recognition. Further computational methods could be used in drug development based on crystal structures or homology models, including antibody-antigen dockings and energy calculations with approximate potential functions. These methods should guide experimental studies to improve the affinities and physicochemical properties of antibodies. Finally, several successful examples of in silico structure-based antibody designs are reviewed. We also briefly review structure-based antigen or immunogen design, with application to rational vaccine development.

Residues with similar hexagon neighborhoods share similar side-chain conformations

We present in this study a new approach to code protein side-chain conformations into hexagon substructures. Classical side-chain packing methods consist of two steps: first, side-chain conformations, known as rotamers, are extracted from known protein structures as candidates for each residue; second, a searching method along with an energy function is used to resolve conflicts among residues and to optimize the combinations of side chain conformations for all residues. These methods benefit from the fact that the number of possible side-chain conformations is limited, and the rotamer candidates are readily extracted; however, these methods also suffer from the inaccuracy of energy functions. Inspired by threading and Ab Initio approaches to protein structure prediction, we propose to use hexagon substructures to implicitly capture subtle issues of energy functions. Our initial results indicate that even without guidance from an energy function, hexagon structures alone can capture side-chain conformations at an accuracy of 83.8 percent, higher than 82.6 percent by the state-of-art side-chain packing methods.

Rational and computational design of stabilized variants of cyanovirin-N that retain affinity and specificity for glycan ligands

Cyanovirin-N (CVN) is an 11 kDa pseudosymmetric cyanobacterial lectin that has been shown to inhibit infection by the human immunodeficiency virus by binding to high-mannose oligosaccharides on the surface of the viral envelope glycoprotein gp120. In this work, we describe rationally designed CVN variants that stabilize the protein fold while maintaining high affinity and selectivity for their glycan targets. Poisson-Boltzmann calculations and protein repacking algorithms were used to select stabilizing mutations in the protein core. By substituting the buried polar side chains of Ser11, Ser20, and Thr61 with aliphatic groups, we stabilized CVN by nearly 12 °C against thermal denaturation, and by 1 M GuaHCl against chemical denaturation, relative to a previously characterized stabilized mutant. Glycan microarray binding experiments confirmed that the specificity profile of carbohydrate binding is unperturbed by the mutations and is identical for all variants. In particular, the variants selectively bound glycans containing the Manα(1→2)Man linkage, which is the known minimal binding unit of CVN. We also report the slow denaturation kinetics of CVN and show that they can complicate thermodynamic analysis; in particular, the unfolding of CVN cannot be described as a fixed two-state transition. Accurate thermodynamic parameters are needed to describe the complicated free energy landscape of CVN, and we provide updated values for CVN unfolding.

Adapting Poisson-Boltzmann to the self-consistent mean field theory: application to protein side-chain modeling

We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ(1) for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.

THE DIFFERENTIAL GEOMETRY OF PROTEINS AND ITS APPLICATIONS TO STRUCTURE DETERMINATION

Understanding the three-dimensional structure of proteins is critical to understand their function. While great progress is being made in understanding the structures of soluble proteins, large classes of proteins such as membrane proteins, large macromolecular assemblies, and partially organized or heterogeneous structures are being comparatively neglected. Part of the difficulty is that the coordinate models we use to represent protein structure are discrete and static, whereas the molecules themselves are flexible and dynamic. In this article, we review methods to develop a continuous description of proteins more general than the traditional coordinate models and which can describe smooth changes in form. This description can be shown to be strictly equivalent to the traditional atomic coordinate description.

A Bayesian approach for determining protein side-chain rotamer conformations using unassigned NOE data

A major bottleneck in protein structure determination via nuclear magnetic resonance (NMR) is the lengthy and laborious process of assigning resonances and nuclear Overhauser effect (NOE) cross peaks. Recent studies have shown that accurate backbone folds can be determined using sparse NMR data, such as residual dipolar couplings (RDCs) or backbone chemical shifts. This opens a question of whether we can also determine the accurate protein side-chain conformations using sparse or unassigned NMR data. We attack this question by using unassigned nuclear Overhauser effect spectroscopy (NOESY) data, which records the through-space dipolar interactions between protons nearby in three-dimensional (3D) space. We propose a Bayesian approach with a Markov random field (MRF) model to integrate the likelihood function derived from observed experimental data, with prior information (i.e., empirical molecular mechanics energies) about the protein structures. We unify the side-chain structure prediction problem with the side-chain structure determination problem using unassigned NMR data, and apply the deterministic dead-end elimination (DEE) and A* search algorithms to provably find the global optimum solution that maximizes the posterior probability. We employ a Hausdorff-based measure to derive the likelihood of a rotamer or a pairwise rotamer interaction from unassigned NOESY data. In addition, we apply a systematic and rigorous approach to estimate the experimental noise in NMR data, which also determines the weighting factor of the data term in the scoring function derived from the Bayesian framework. We tested our approach on real NMR data of three proteins: the FF Domain 2 of human transcription elongation factor CA150 (FF2), the B1 domain of Protein G (GB1), and human ubiquitin. The promising results indicate that our algorithm can be applied in high-resolution protein structure determination. Since our approach does not require any NOE assignment, it can accelerate the NMR structure determination process.

Protein side-chain resonance assignment and NOE assignment using RDC-defined backbones without TOCSY data

One bottleneck in NMR structure determination lies in the laborious and time-consuming process of side-chain resonance and NOE assignments. Compared to the well-studied backbone resonance assignment problem, automated side-chain resonance and NOE assignments are relatively less explored. Most NOE assignment algorithms require nearly complete side-chain resonance assignments from a series of through-bond experiments such as HCCH-TOCSY or HCCCONH. Unfortunately, these TOCSY experiments perform poorly on large proteins. To overcome this deficiency, we present a novel algorithm, called NASCA: (NOE Assignment and Side-Chain Assignment), to automate both side-chain resonance and NOE assignments and to perform high-resolution protein structure determination in the absence of any explicit through-bond experiment to facilitate side-chain resonance assignment, such as HCCH-TOCSY. After casting the assignment problem into a Markov Random Field (MRF), NASCA: extends and applies combinatorial protein design algorithms to compute optimal assignments that best interpret the NMR data. The MRF captures the contact map information of the protein derived from NOESY spectra, exploits the backbone structural information determined by RDCs, and considers all possible side-chain rotamers. The complexity of the combinatorial search is reduced by using a dead-end elimination (DEE) algorithm, which prunes side-chain resonance assignments that are provably not part of the optimal solution. Then an A* search algorithm is employed to find a set of optimal side-chain resonance assignments that best fit the NMR data. These side-chain resonance assignments are then used to resolve the NOE assignment ambiguity and compute high-resolution protein structures. Tests on five proteins show that NASCA: assigns resonances for more than 90% of side-chain protons, and achieves about 80% correct assignments. The final structures computed using the NOE distance restraints assigned by NASCA: have backbone RMSD 0.8-1.5 Å from the reference structures determined by traditional NMR approaches.

Engineering the enolase magnesium II binding site: implications for its evolution

The glycolytic enzyme enolase catalyzes the reversible elimination of water from 2-phosphoglycerate (2-PGA) to form phosphoenolpyruvate (PEP). Two magnesium ions in the active site are thought to facilitate the reaction by activation of the C2 proton of 2-PGA and charge stabilization of the intermediate. The initial abstraction of a proton from a carboxylic acid is common to all members of the enolase superfamily, yet in all other known members of this superfamily, only one magnesium ion (MgI) per active site is sufficient to promote catalysis. We wanted to further investigate the importance of the second magnesium ion (MgII) for the catalytic mechanism of yeast enolase 1. Toward this end, we removed all MgII coordinating residues and replaced substrate-MgII interactions by introducing positively charged side chains. High-resolution crystal structures and activity assays show that the introduced positively charged side chains effectively prohibit MgII binding but fail to promote catalysis. We conclude that enolase is inactive without MgII, yet control mutants without additional positively charged side chains retain basal enolase activity through binding of magnesium to 2-PGA in an open active site without the help of MgII coordinating residues. Thus, we believe that ancestral enolase activity might have evolved in a member of the enolase superfamily that provides only the necessary catalytic residues and the binding site for MgI. Additionally, precatalytic binding of 2-PGA to the apo state of enolase was observed.

De novo backbone scaffolds for protein design

In recent years, there have been significant advances in the field of computational protein design including the successful computational design of enzymes based on backbone scaffolds from experimentally solved structures. It is likely that large-scale sampling of protein backbone conformations will become necessary as further progress is made on more complicated systems. Removing the constraint of having to use scaffolds based on known protein backbones is a potential method of solving the problem. With this application in mind, we describe a method to systematically construct a large number of de novo backbone structures from idealized topological forms in a top–down hierarchical approach. The structural properties of these novel backbone scaffolds were analyzed and compared with a set of high-resolution experimental structures from the protein data bank (PDB). It was found that the Ramachandran plot distribution and relative γ- and β-turn frequencies were similar to those found in the PDB. The de novo scaffolds were sequence designed with RosettaDesign, and the energy distributions and amino acid compositions were comparable with the results for redesigned experimentally solved backbones. Proteins 2010. © 2009 Wiley-Liss, Inc.

An improved hybrid global optimization method for protein tertiary structure prediction

First principles approaches to the protein structure prediction problem must search through an enormous conformational space to identify low-energy, near-native structures. In this paper, we describe the formulation of the tertiary structure prediction problem as a nonlinear constrained minimization problem, where the goal is to minimize the energy of a protein conformation subject to constraints on torsion angles and interatomic distances. The core of the proposed algorithm is a hybrid global optimization method that combines the benefits of the αBB deterministic global optimization approach with conformational space annealing. These global optimization techniques employ a local minimization strategy that combines torsion angle dynamics and rotamer optimization to identify and improve the selection of initial conformations and then applies a sequential quadratic programming approach to further minimize the energy of the protein conformations subject to constraints. The proposed algorithm demonstrates the ability to identify both lower energy protein structures, as well as larger ensembles of low-energy conformations.

Designing artificial enzymes by intuition and computation

The rational design of artificial enzymes, either by applying physico-chemical intuition of protein structure and function or with the aid of computational methods, is a promising area of research with the potential to tremendously impact medicine, industrial chemistry and energy production. Designed proteins also provide a powerful platform for dissecting enzyme mechanisms of natural systems. Artificial enzymes have come a long way from simple α-helical peptide catalysts to proteins that facilitate multistep chemical reactions designed by state-of-the-art computational methods. Looking forward, we examine strategies employed by natural enzymes that could be used to improve the speed and selectivity of artificial catalysts.

Optimization techniques in molecular structure and function elucidation

This paper discusses recent optimization approaches to the protein side-chain prediction problem, protein structural alignment, and molecular structure determination from X-ray diffraction measurements. The machinery employed to solve these problems has included algorithms from linear programming, dynamic programming, combinatorial optimization, and mixed-integer nonlinear programming. Many of these problems are purely continuous in nature. Yet, to this date, they have been approached mostly via combinatorial optimization algorithms that are applied to discrete approximations. The main purpose of the paper is to offer an introduction and motivate further systems approaches to these problems.

Rotamer optimization for protein design through MAP estimation and problem-size reduction

The search for the global minimum energy conformation (GMEC) of protein side chains is an important computational challenge in protein structure prediction and design. Using rotamer models, the problem is formulated as a NP-hard optimization problem. Dead-end elimination (DEE) methods combined with systematic A* search (DEE/A*) has proven useful, but may not be strong enough as we attempt to solve protein design problems where a large number of similar rotamers is eligible and the network of interactions between residues is dense. In this work, we present an exact solution method, named BroMAP (branch-and-bound rotamer optimization using MAP estimation), for such protein design problems. The design goal of BroMAP is to be able to expand smaller search trees than conventional branch-and-bound methods while performing only a moderate amount of computation in each node, thereby reducing the total running time. To achieve that, BroMAP attempts reduction of the problem size within each node through DEE and elimination by lower bounds from approximate maximum-a-posteriori (MAP) estimation. The lower bounds are also exploited in branching and subproblem selection for fast discovery of strong upper bounds. Our computational results show that BroMAP tends to be faster than DEE/A* for large protein design cases. BroMAP also solved cases that were not solved by DEE/A* within the maximum allowed time, and did not incur significant disadvantage for cases where DEE/A* performed well. Therefore, BroMAP is particularly applicable to large protein design problems where DEE/A* struggles and can also substitute for DEE/A* in general GMEC search.

Accurate prediction for atomic-level protein design and its application in diversifying the near-optimal sequence space

The task of engineering a protein to assume a target three-dimensional structure is known as protein design. Computational search algorithms are devised to predict a minimal energy amino acid sequence for a particular structure. In practice, however, an ensemble of low-energy sequences is often sought. Primarily, this is performed because an individual predicted low-energy sequence may not necessarily fold to the target structure because of both inaccuracies in modeling protein energetics and the nonoptimal nature of search algorithms employed. Additionally, some low-energy sequences may be overly stable and thus lack the dynamic flexibility required for biological functionality. Furthermore, the investigation of low-energy sequence ensembles will provide crucial insights into the pseudo-physical energy force fields that have been derived to describe structural energetics for protein design. Significantly, numerous studies have predicted low-energy sequences, which were subsequently synthesized and demonstrated to fold to desired structures. However, the characterization of the sequence space defined by such energy functions as compatible with a target structure has not been performed in full detail. This issue is critical for protein design scientists to successfully continue using these force fields at an ever-increasing pace and scale. In this paper, we present a conceptually novel algorithm that rapidly predicts the set of lowest energy sequences for a given structure. Based on the theory of probabilistic graphical models, it performs efficient inspection and partitioning of the near-optimal sequence space, without making any assumptions of positional independence. We benchmark its performance on a diverse set of relevant protein design examples and show that it consistently yields sequences of lower energy than those derived from state-of-the-art techniques. Thus, we find that previously presented search techniques do not fully depict the low-energy space as precisely. Examination of the predicted ensembles indicates that, for each structure, the amino acid identity at a majority of positions must be chosen extremely selectively so as to not incur significant energetic penalties. We investigate this high degree of similarity and demonstrate how more diverse near-optimal sequences can be predicted in order to systematically overcome this bottleneck for computational design. Finally, we exploit this in-depth analysis of a collection of the lowest energy sequences to suggest an explanation for previously observed experimental design results. The novel methodologies introduced here accurately portray the sequence space compatible with a protein structure and further supply a scheme to yield heterogeneous low-energy sequences, thus providing a powerful instrument for future work on protein design.

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.

Challenges in the computational design of proteins

Protein design has many applications not only in biotechnology but also in basic science. It uses our current knowledge in structural biology to predict, by computer simulations, an amino acid sequence that would produce a protein with targeted properties. As in other examples of synthetic biology, this approach allows the testing of many hypotheses in biology. The recent development of automated computational methods to design proteins has enabled proteins to be designed that are very different from any known ones. Moreover, some of those methods mostly rely on a physical description of atomic interactions, which allows the designed sequences not to be biased towards known proteins. In this paper, we will describe the use of energy functions in computational protein design, the use of atomic models to evaluate the free energy in the unfolded and folded states, the exploration and optimization of amino acid sequences, the problem of negative design and the design of biomolecular function. We will also consider its use together with the experimental techniques such as directed evolution. We will end by discussing the challenges ahead in computational protein design and some of their future applications.