Dead-end elimination for multistate protein design

Generating new protein sequences by using dense network and attention mechanism

Protein engineering uses de novo protein design technology to change the protein gene sequence, and then improve the physical and chemical properties of proteins. These newly generated proteins will meet the needs of research better in properties and functions. The Dense-AutoGAN model is based on GAN, which is combined with an Attention mechanism to generate protein sequences. In this GAN architecture, the Attention mechanism and Encoder-decoder can improve the similarity of generated sequences and obtain variations in a smaller range on the original basis. Meanwhile, a new convolutional neural network is constructed by using the Dense. The dense network transmits in multiple layers over the generator network of the GAN architecture, which expands the training space and improves the effectiveness of sequence generation. Finally, the complex protein sequences are generated on the mapping of protein functions. Through comparisons of other models, the generated sequences of Dense-AutoGAN verify the model performance. The new generated proteins are highly accurate and effective in chemical and physical properties.

Algorithms for protein design

Computational Protein Design has the potential to contribute to major advances in enzyme technology, vaccine design, receptor-ligand engineering, biomaterials, nanosensors, and synthetic biology. Although Protein Design is a challenging problem, proteins can be designed by experts in Protein Design, as well as by non-experts whose primary interests are in the applications of Protein Design. The increased accessibility of Protein Design technology is attributable to the accumulated knowledge and experience with Protein Design as well as to the availability of software and online resources. The objective of this review is to serve as a guide to the relevant literature with a focus on the novel methods and algorithms that have been developed or applied for Protein Design, and to assist in the selection of algorithms for Protein Design. Novel algorithms and models that have been introduced to utilize the enormous amount of experimental data and novel computational hardware have the potential for producing substantial increases in the accuracy, reliability and range of applications of designed proteins.

Rosetta:MSF:NN: Boosting performance of multi-state computational protein design with a neural network

Rational protein design aims at the targeted modification of existing proteins. To reach this goal, software suites like Rosetta propose sequences to introduce the desired properties. Challenging design problems necessitate the representation of a protein by means of a structural ensemble. Thus, Rosetta multi-state design (MSD) protocols have been developed wherein each state represents one protein conformation. Computational demands of MSD protocols are high, because for each of the candidate sequences a costly three-dimensional (3D) model has to be created and assessed for all states. Each of these scores contributes one data point to a complex, design-specific energy landscape. As neural networks (NN) proved well-suited to learn such solution spaces, we integrated one into the framework Rosetta:MSF instead of the so far used genetic algorithm with the aim to reduce computational costs. As its predecessor, Rosetta:MSF:NN administers a set of candidate sequences and their scores and scans sequence space iteratively. During each iteration, the union of all candidate sequences and their Rosetta scores are used to re-train NNs that possess a design-specific architecture. The enormous speed of the NNs allows an extensive assessment of alternative sequences, which are ranked on the scores predicted by the NN. Costly 3D models are computed only for a small fraction of best-scoring sequences; these and the corresponding 3D-based scores replace half of the candidate sequences during each iteration. The analysis of two sets of candidate sequences generated for a specific design problem by means of a genetic algorithm confirmed that the NN predicted 3D-based scores quite well; the Pearson correlation coefficient was at least 0.95. Applying Rosetta:MSF:NN:enzdes to a benchmark consisting of 16 ligand-binding problems showed that this protocol converges ten-times faster than the genetic algorithm and finds sequences with comparable scores.

Protein Design by Provable Algorithms

Protein design algorithms can leverage provable guarantees of accuracy to provide new insights and unique optimized molecules.

Positive multistate protein design

Motivation

Structure-based computational protein design (CPD) plays a critical role in advancing the field of protein engineering. Using an all-atom energy function, CPD tries to identify amino acid sequences that fold into a target structure and ultimately perform a desired function. The usual approach considers a single rigid backbone as a target, which ignores backbone flexibility. Multistate design (MSD) allows instead to consider several backbone states simultaneously, defining challenging computational problems.

Results

We introduce efficient reductions of positive MSD problems to Cost Function Networks with two different fitness definitions and implement them in the Pompd (Positive Multistate Protein design) software. Pompd is able to identify guaranteed optimal sequences of positive multistate full protein redesign problems and exhaustively enumerate suboptimal sequences close to the MSD optimum. Applied to nuclear magnetic resonance and back-rubbed X-ray structures, we observe that the average energy fitness provides the best sequence recovery. Our method outperforms state-of-the-art guaranteed computational design approaches by orders of magnitudes and can solve MSD problems with sizes previously unreachable with guaranteed algorithms.

Availability and implementation

https://forgemia.inra.fr/thomas.schiex/pompd as documented Open Source.

Supplementary information

Supplementary data are available at Bioinformatics online.

PLUG (Pruning of Local Unrealistic Geometries) removes restrictions on biophysical modeling for protein design

Protein design algorithms must search an enormous conformational space to identify favorable conformations. As a result, those that perform this search with guarantees of accuracy generally start with a conformational pruning step, such as dead-end elimination (DEE). However, the mathematical assumptions of DEE-based pruning algorithms have up to now severely restricted the biophysical model that can feasibly be used in protein design. To lift these restrictions, I propose to prune local unrealistic geometries (PLUG) using a linear programming-based method. PLUG's biophysical model consists only of well-known lower bounds on interatomic distances. PLUG is intended as preprocessing for energy-based protein design calculations, whose biophysical model need not support DEE pruning. Based on 96 test cases, PLUG is at least as effective at pruning as DEE for larger protein designs-the type that most require pruning. When combined with the LUTE protein design algorithm, PLUG greatly facilitates designs that account for continuous entropy, large multistate designs with continuous flexibility, and designs with extensive continuous backbone flexibility and advanced nonpairwise energy functions. Many of these designs are tractable only with PLUG, either for empirical reasons (LUTE's machine learning step achieves an accurate fit only after PLUG pruning), or for theoretical reasons (many energy functions are fundamentally incompatible with DEE).

iCFN: an efficient exact algorithm for multistate protein design

Motivation

Multistate protein design addresses real-world challenges, such as multi-specificity design and backbone flexibility, by considering both positive and negative protein states with an ensemble of substates for each. It also presents an enormous challenge to exact algorithms that guarantee the optimal solutions and enable a direct test of mechanistic hypotheses behind models. However, efficient exact algorithms are lacking for multistate protein design.

Results

We have developed an efficient exact algorithm called interconnected cost function networks (iCFN) for multistate protein design. Its generic formulation allows for a wide array of applications such as stability, affinity and specificity designs while addressing concerns such as global flexibility of protein backbones. iCFN treats each substate design as a weighted constraint satisfaction problem (WCSP) modeled through a CFN; and it solves the coupled WCSPs using novel bounds and a depth-first branch-and-bound search over a tree structure of sequences, substates, and conformations. When iCFN is applied to specificity design of a T-cell receptor, a problem of unprecedented size to exact methods, it drastically reduces search space and running time to make the problem tractable. Moreover, iCFN generates experimentally-agreeing receptor designs with improved accuracy compared with state-of-the-art methods, highlights the importance of modeling backbone flexibility in protein design, and reveals molecular mechanisms underlying binding specificity.

Availability and implementation

https://shen-lab.github.io/software/iCFN.

Supplementary information

Supplementary data are available at Bioinformatics online.

In silico methods for design of biological therapeutics

It has been twenty years since the first rationally designed small molecule drug was introduced into the market. Since then, we have progressed from designing small molecules to designing biotherapeutics. This class of therapeutics includes designed proteins, peptides and nucleic acids that could more effectively combat drug resistance and even act in cases where the disease is caused because of a molecular deficiency. Computational methods are crucial in this design exercise and this review discusses the various elements of designing biotherapeutic proteins and peptides. Many of the techniques discussed here, such as the deterministic and stochastic design methods, are generally used in protein design. We have devoted special attention to the design of antibodies and vaccines. In addition to the methods for designing these molecules, we have included a comprehensive list of all biotherapeutics approved for clinical use. Also included is an overview of methods that predict the binding affinity, cell penetration ability, half-life, solubility, immunogenicity and toxicity of the designed therapeutics. Biotherapeutics are only going to grow in clinical importance and are set to herald a new generation of disease management and cure.

Rosetta:MSF: a modular framework for multi-state computational protein design

Computational protein design (CPD) is a powerful technique to engineer existing proteins or to design novel ones that display desired properties. Rosetta is a software suite including algorithms for computational modeling and analysis of protein structures and offers many elaborate protocols created to solve highly specific tasks of protein engineering. Most of Rosetta’s protocols optimize sequences based on a single conformation (i. e. design state). However, challenging CPD objectives like multi-specificity design or the concurrent consideration of positive and negative design goals demand the simultaneous assessment of multiple states. This is why we have developed the multi-state framework MSF that facilitates the implementation of Rosetta’s single-state protocols in a multi-state environment and made available two frequently used protocols. Utilizing MSF, we demonstrated for one of these protocols that multi-state design yields a 15% higher performance than single-state design on a ligand-binding benchmark consisting of structural conformations. With this protocol, we designed de novo nine retro-aldolases on a conformational ensemble deduced from a (βα)₈-barrel protein. All variants displayed measurable catalytic activity, testifying to a high success rate for this concept of multi-state enzyme design.

Protein engineering, i. e. the targeted modification or design of proteins has tremendous potential for medical and industrial applications. One generally applicable strategy for protein engineering is rational protein design: based on detailed knowledge of structure and function, computer programs like Rosetta propose the sequence of a protein possessing the desired properties. So far, most computer protocols have used rigid structures for design, which is a simplification because a protein’s structure is more accurately specified by a conformational ensemble. We have now implemented a framework for computational protein design that allows certain design protocols of Rosetta to make use of multiple design states like structural ensembles. An in silico assessment simulating ligand-binding design showed that this new approach generates more reliably native-like sequences than a single-state approach. As a proof-of-concept, we introduced de novo retro-aldolase activity into a scaffold protein and characterized nine variants experimentally, all of which were catalytically active.

Computationally optimized deimmunization libraries yield highly mutated enzymes with low immunogenicity and enhanced activity

Therapeutic proteins of wide-ranging function hold great promise for treating disease, but immune surveillance of these macromolecules can drive an antidrug immune response that compromises efficacy and even undermines safety. To eliminate widespread T-cell epitopes in any biotherapeutic and thereby mitigate this key source of detrimental immune recognition, we developed a Pareto optimal deimmunization library design algorithm that optimizes protein libraries to account for the simultaneous effects of combinations of mutations on both molecular function and epitope content. Active variants identified by high-throughput screening are thus inherently likely to be deimmunized. Functional screening of an optimized 10-site library (1,536 variants) of P99 β-lactamase (P99βL), a component of ADEPT cancer therapies, revealed that the population possessed high overall fitness, and comprehensive analysis of peptide-MHC II immunoreactivity showed the population possessed lower average immunogenic potential than the wild-type enzyme. Although similar functional screening of an optimized 30-site library (2.15 × 10⁹ variants) revealed reduced population-wide fitness, numerous individual variants were found to have activity and stability better than the wild type despite bearing 13 or more deimmunizing mutations per enzyme. The immunogenic potential of one highly active and stable 14-mutation variant was assessed further using ex vivo cellular immunoassays, and the variant was found to silence T-cell activation in seven of the eight blood donors who responded strongly to wild-type P99βL. In summary, our multiobjective library-design process readily identified large and mutually compatible sets of epitope-deleting mutations and produced highly active but aggressively deimmunized constructs in only one round of library screening.

A critical analysis of computational protein design with sparse residue interaction graphs

Protein design algorithms enumerate a combinatorial number of candidate structures to compute the Global Minimum Energy Conformation (GMEC). To efficiently find the GMEC, protein design algorithms must methodically reduce the conformational search space. By applying distance and energy cutoffs, the protein system to be designed can thus be represented using a sparse residue interaction graph, where the number of interacting residue pairs is less than all pairs of mutable residues, and the corresponding GMEC is called the sparse GMEC. However, ignoring some pairwise residue interactions can lead to a change in the energy, conformation, or sequence of the sparse GMEC vs. the original or the full GMEC. Despite the widespread use of sparse residue interaction graphs in protein design, the above mentioned effects of their use have not been previously analyzed. To analyze the costs and benefits of designing with sparse residue interaction graphs, we computed the GMECs for 136 different protein design problems both with and without distance and energy cutoffs, and compared their energies, conformations, and sequences. Our analysis shows that the differences between the GMECs depend critically on whether or not the design includes core, boundary, or surface residues. Moreover, neglecting long-range interactions can alter local interactions and introduce large sequence differences, both of which can result in significant structural and functional changes. Designs on proteins with experimentally measured thermostability show it is beneficial to compute both the full and the sparse GMEC accurately and efficiently. To this end, we show that a provable, ensemble-based algorithm can efficiently compute both GMECs by enumerating a small number of conformations, usually fewer than 1000. This provides a novel way to combine sparse residue interaction graphs with provable, ensemble-based algorithms to reap the benefits of sparse residue interaction graphs while avoiding their potential inaccuracies.

Computational structure-based protein design algorithms have successfully redesigned proteins to fold and bind target substrates in vitro, and even in vivo. Because the complexity of a computational design increases dramatically with the number of mutable residues, many design algorithms employ cutoffs (distance or energy) to neglect some pairwise residue interactions, thereby reducing the effective search space and computational cost. However, the energies neglected by such cutoffs can add up, which may have nontrivial effects on the designed sequence and its function. To study the effects of using cutoffs on protein design, we computed the optimal sequence both with and without cutoffs, and showed that neglecting long-range interactions can significantly change the computed conformation and sequence. Designs on proteins with experimentally measured thermostability showed the benefits of computing the optimal sequences (and their conformations), both with and without cutoffs, efficiently and accurately. Therefore, we also showed that a provable, ensemble-based algorithm can efficiently compute the optimal conformation and sequence, both with and without applying cutoffs, by enumerating a small number of conformations, usually fewer than 1000. This provides a novel way to combine cutoffs with provable, ensemble-based algorithms to reap the computational efficiency of cutoffs while avoiding their potential inaccuracies.

Multistate Computational Protein Design with Backbone Ensembles

The ability of computational protein design (CPD) to identify protein sequences possessing desired characteristics in vast sequence spaces makes it a highly valuable tool in the protein engineering toolbox. CPD calculations are typically performed using a single-state design (SSD) approach in which amino-acid sequences are optimized on a single protein structure. Although SSD has been successfully applied to the design of numerous protein functions and folds, the approach can lead to the incorrect rejection of desirable sequences because of the combined use of a fixed protein backbone template and a set of rigid rotamers. This fixed backbone approximation can be addressed by using multistate design (MSD) with backbone ensembles. MSD improves the quality of predicted sequences by using ensembles approximating conformational flexibility as input templates instead of a single fixed protein structure. In this chapter, we present a step-by-step guide to the implementation and analysis of MSD calculations with backbone ensembles. Specifically, we describe ensemble generation with the PertMin protocol, execution of MSD calculations for recapitulation of Streptococcal protein G domain β1 mutant stability, and analysis of computational predictions by sequence binning. Furthermore, we provide a comparison between MSD and SSD calculation results and discuss the benefits of multistate approaches to CPD.

LUTE (Local Unpruned Tuple Expansion): Accurate Continuously Flexible Protein Design with General Energy Functions and Rigid Rotamer-Like Efficiency

Most protein design algorithms search over discrete conformations and an energy function that is residue-pairwise, that is, a sum of terms that depend on the sequence and conformation of at most two residues. Although modeling of continuous flexibility and of non-residue-pairwise energies significantly increases the accuracy of protein design, previous methods to model these phenomena add a significant asymptotic cost to design calculations. We now remove this cost by modeling continuous flexibility and non-residue-pairwise energies in a form suitable for direct input to highly efficient, discrete combinatorial optimization algorithms such as DEE/A* or branch-width minimization. Our novel algorithm performs a local unpruned tuple expansion (LUTE), which can efficiently represent both continuous flexibility and general, possibly nonpairwise energy functions to an arbitrary level of accuracy using a discrete energy matrix. We show using 47 design calculation test cases that LUTE provides a dramatic speedup in both single-state and multistate continuously flexible designs.

comets (Constrained Optimization of Multistate Energies by Tree Search): A Provable and Efficient Protein Design Algorithm to Optimize Binding Affinity and Specificity with Respect to Sequence

Practical protein design problems require designing sequences with a combination of affinity, stability, and specificity requirements. Multistate protein design algorithms model multiple structural or binding "states" of a protein to address these requirements. comets provides a new level of versatile, efficient, and provable multistate design. It provably returns the minimum with respect to sequence of any desired linear combination of the energies of multiple protein states, subject to constraints on other linear combinations. Thus, it can target nearly any combination of affinity (to one or multiple ligands), specificity, and stability (for multiple states if needed). Empirical calculations on 52 protein design problems showed comets is far more efficient than the previous state of the art for provable multistate design (exhaustive search over sequences). comets can handle a very wide range of protein flexibility and can enumerate a gap-free list of the best constraint-satisfying sequences in order of objective function value.

Design of Protein Multi-specificity Using an Independent Sequence Search Reduces the Barrier to Low Energy Sequences

Computational protein design has found great success in engineering proteins for thermodynamic stability, binding specificity, or enzymatic activity in a 'single state' design (SSD) paradigm. Multi-specificity design (MSD), on the other hand, involves considering the stability of multiple protein states simultaneously. We have developed a novel MSD algorithm, which we refer to as REstrained CONvergence in multi-specificity design (RECON). The algorithm allows each state to adopt its own sequence throughout the design process rather than enforcing a single sequence on all states. Convergence to a single sequence is encouraged through an incrementally increasing convergence restraint for corresponding positions. Compared to MSD algorithms that enforce (constrain) an identical sequence on all states the energy landscape is simplified, which accelerates the search drastically. As a result, RECON can readily be used in simulations with a flexible protein backbone. We have benchmarked RECON on two design tasks. First, we designed antibodies derived from a common germline gene against their diverse targets to assess recovery of the germline, polyspecific sequence. Second, we design "promiscuous", polyspecific proteins against all binding partners and measure recovery of the native sequence. We show that RECON is able to efficiently recover native-like, biologically relevant sequences in this diverse set of protein complexes.

A "fuzzy"-logic language for encoding multiple physical traits in biomolecules

To carry out their activities, biological macromolecules balance different physical traits, such as stability, interaction affinity, and selectivity. How such often opposing traits are encoded in a macromolecular system is critical to our understanding of evolutionary processes and ability to design new molecules with desired functions. We present a framework for constraining design simulations to balance different physical characteristics. Each trait is represented by the equilibrium fractional occupancy of the desired state relative to its alternatives, ranging from none to full occupancy, and the different traits are combined using Boolean operators to effect a "fuzzy"-logic language for encoding any combination of traits. In another paper, we presented a new combinatorial backbone design algorithm AbDesign where the fuzzy-logic framework was used to optimize protein backbones and sequences for both stability and binding affinity in antibody-design simulation. We now extend this framework and find that fuzzy-logic design simulations reproduce sequence and structure design principles seen in nature to underlie exquisite specificity on the one hand and multispecificity on the other hand. The fuzzy-logic language is broadly applicable and could help define the space of tolerated and beneficial mutations in natural biomolecular systems and design artificial molecules that encode complex characteristics.

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.

Rational design of a ligand-controlled protein conformational switch

Design of a regulatable multistate protein is a challenge for protein engineering. Here we design a protein with a unique topology, called uniRapR, whose conformation is controlled by the binding of a small molecule. We confirm switching and control ability of uniRapR in silico, in vitro, and in vivo. As a proof of concept, uniRapR is used as an artificial regulatory domain to control activity of kinases. By activating Src kinase using uniRapR in single cells and whole organism, we observe two unique phenotypes consistent with its role in metastasis. Activation of Src kinase leads to rapid induction of protrusion with polarized spreading in HeLa cells, and morphological changes with loss of cell-cell contacts in the epidermal tissue of zebrafish. The rational creation of uniRapR exemplifies the strength of computational protein design, and offers a powerful means for targeted activation of many pathways to study signaling in living organisms.

Dead-end elimination with perturbations (DEEPer): a provable protein design algorithm with continuous sidechain and backbone flexibility

Computational protein and drug design generally require accurate modeling of protein conformations. This modeling typically starts with an experimentally determined protein structure and considers possible conformational changes due to mutations or new ligands. The DEE/A* algorithm provably finds the global minimum-energy conformation (GMEC) of a protein assuming that the backbone does not move and the sidechains take on conformations from a set of discrete, experimentally observed conformations called rotamers. DEE/A* can efficiently find the overall GMEC for exponentially many mutant sequences. Previous improvements to DEE/A* include modeling ensembles of sidechain conformations and either continuous sidechain or backbone flexibility. We present a new algorithm, DEEPer (Dead-End Elimination with Perturbations), that combines these advantages and can also handle much more extensive backbone flexibility and backbone ensembles. DEEPer provably finds the GMEC or, if desired by the user, all conformations and sequences within a specified energy window of the GMEC. It includes the new abilities to handle arbitrarily large backbone perturbations and to generate ensembles of backbone conformations. It also incorporates the shear, an experimentally observed local backbone motion never before used in design. Additionally, we derive a new method to accelerate DEE/A*-based calculations, indirect pruning, that is particularly useful for DEEPer. In 67 benchmark tests on 64 proteins, DEEPer consistently identified lower-energy conformations than previous methods did, indicating more accurate modeling. Additional tests demonstrated its ability to incorporate larger, experimentally observed backbone conformational changes and to model realistic conformational ensembles. These capabilities provide significant advantages for modeling protein mutations and protein-ligand interactions.

Multistate approaches in computational protein design

Computational protein design (CPD) is a useful tool for protein engineers. It has been successfully applied towards the creation of proteins with increased thermostability, improved binding affinity, novel enzymatic activity, and altered ligand specificity. Traditionally, CPD calculations search and rank sequences using a single fixed protein backbone template in an approach referred to as single-state design (SSD). While SSD has enjoyed considerable success, certain design objectives require the explicit consideration of multiple conformational and/or chemical states. Cases where a "multistate" approach may be advantageous over the SSD approach include designing conformational changes into proteins, using native ensembles to mimic backbone flexibility, and designing ligand or oligomeric association specificities. These design objectives can be efficiently tackled using multistate design (MSD), an emerging methodology in CPD that considers any number of protein conformational or chemical states as inputs instead of a single protein backbone template, as in SSD. In this review article, recent examples of the successful design of a desired property into proteins using MSD are described. These studies employing MSD are divided into two categories--those that utilized multiple conformational states, and those that utilized multiple chemical states. In addition, the scoring of competing states during negative design is discussed as a current challenge for MSD.

Specificity in computational protein design

A long-standing goal of computational protein design is to create proteins similar to those found in Nature. One motivation is to harness the exquisite functional capabilities of proteins for our own purposes. The extent of similarity between designed and natural proteins also reports on how faithfully our models represent the selective pressures that determine protein sequences. As the field of protein design shifts emphasis from reproducing native-like protein structure to function, it has become important that these models treat the notion of specificity in molecular interactions. Although specificity may, in some cases, be achieved by optimization of a desired protein in isolation, methods have been developed to address directly the desire for proteins that exhibit specific functions and interactions.

Design of multispecific protein sequences using probabilistic graphical modeling

In nature, proteins partake in numerous protein- protein interactions that mediate their functions. Moreover, proteins have been shown to be physically stable in multiple structures, induced by cellular conditions, small ligands, or covalent modifications. Understanding how protein sequences achieve this structural promiscuity at the atomic level is a fundamental step in the drug design pipeline and a critical question in protein physics. One way to investigate this subject is to computationally predict protein sequences that are compatible with multiple states, i.e., multiple target structures or binding to distinct partners. The goal of engineering such proteins has been termed multispecific protein design. We develop a novel computational framework to efficiently and accurately perform multispecific protein design. This framework utilizes recent advances in probabilistic graphical modeling to predict sequences with low energies in multiple target states. Furthermore, it is also geared to specifically yield positional amino acid probability profiles compatible with these target states. Such profiles can be used as input to randomly bias high-throughput experimental sequence screening techniques, such as phage display, thus providing an alternative avenue for elucidating the multispecificity of natural proteins and the synthesis of novel proteins with specific functionalities. We prove the utility of such multispecific design techniques in better recovering amino acid sequence diversities similar to those resulting from millions of years of evolution. We then compare the approaches of prediction of low energy ensembles and of amino acid profiles and demonstrate their complementarity in providing more robust predictions for protein design.

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.

Algorithm for backrub motions in protein design

Motivation: The Backrub is a small but kinematically efficient side-chain-coupled local backbone motion frequently observed in atomic-resolution crystal structures of proteins. A backrub shifts the C_α–C_β orientation of a given side-chain by rigid-body dipeptide rotation plus smaller individual rotations of the two peptides, with virtually no change in the rest of the protein. Backrubs can therefore provide a biophysically realistic model of local backbone flexibility for structure-based protein design. Previously, however, backrub motions were applied via manual interactive model-building, so their incorporation into a protein design algorithm (a simultaneous search over mutation and backbone/side-chain conformation space) was infeasible.

Results: We present a combinatorial search algorithm for protein design that incorporates an automated procedure for local backbone flexibility via backrub motions. We further derive a dead-end elimination (DEE)-based criterion for pruning candidate rotamers that, in contrast to previous DEE algorithms, is provably accurate with backrub motions. Our backrub-based algorithm successfully predicts alternate side-chain conformations from ≤0.9 Å resolution structures, confirming the suitability of the automated backrub procedure. Finally, the application of our algorithm to redesign two different proteins is shown to identify a large number of lower-energy conformations and mutation sequences that would have been ignored by a rigid-backbone model.

Availability: Contact authors for source code.

Contact:brd+ismb08@cs.duke.edu