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The K* algorithm provably approximates partition functions for a set of states (e.g., protein, ligand, and protein-ligand complex) to a user-specified accuracy ε. Often, reaching an ε-approximation for a particular set of partition functions takes a prohibitive amount of time and space. To alleviate some of this cost, we introduce two new algorithms into the osprey suite for protein design: fries, a Fast Removal of Inadequately Energied Sequences, and EWAK*, an Energy Window Approximation to K*. fries pre-processes the sequence space to limit a design to only the most stable, energetically favorable sequence possibilities. EWAK* then takes this pruned sequence space as input and, using a user-specified energy window, calculates K* scores using the lowest energy conformations. We expect fries/EWAK* to be most useful in cases where there are many unstable sequences in the design sequence space and when users are satisfied with enumerating the low-energy ensemble of conformations. In combination, these algorithms provably retain calculational accuracy while limiting the input sequence space and the conformations included in each partition function calculation to only the most energetically favorable, effectively reducing runtime while still enriching for desirable sequences. This combined approach led to significant speed-ups compared to the previous state-of-the-art multi-sequence algorithm, BBK*, while maintaining its efficiency and accuracy, which we show across 40 different protein systems and a total of 2,826 protein design problems. Additionally, as a proof of concept, we used these new algorithms to redesign the protein-protein interface (PPI) of the c-Raf-RBD:KRas complex. The Ras-binding domain of the protein kinase c-Raf (c-Raf-RBD) is the tightest known binder of KRas, a protein implicated in difficult-to-treat cancers. fries/EWAK* accurately retrospectively predicted the effect of 41 different sets of mutations in the PPI of the c-Raf-RBD:KRas complex. Notably, these mutations include mutations whose effect had previously been incorrectly predicted using other computational methods. Next, we used fries/EWAK* for prospective design and discovered a novel point mutation that improves binding of c-Raf-RBD to KRas in its active, GTP-bound state (KRasGTP). We combined this new mutation with two previously reported mutations (which were highly-ranked by osprey) to create a new variant of c-Raf-RBD, c-Raf-RBD(RKY). fries/EWAK* in osprey computationally predicted that this new variant binds even more tightly than the previous best-binding variant, c-Raf-RBD(RK). We measured the binding affinity of c-Raf-RBD(RKY) using a bio-layer interferometry (BLI) assay, and found that this new variant exhibits single-digit nanomolar affinity for KRasGTP, confirming the computational predictions made with fries/EWAK*. This new variant binds roughly five times more tightly than the previous best known binder and roughly 36 times more tightly than the design starting point (wild-type c-Raf-RBD). This study steps through the advancement and development of computational protein design by presenting theory, new algorithms, accurate retrospective designs, new prospective designs, and biochemical validation., Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: BRD, MSF, and JDJ are founders of Ten63 Therapeutics. All other authors have declared that no competing interests exist.

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.

Drug resistance in protein targets is an increasingly common phenomenon that reduces the efficacy of both existing and new antibiotics. However, knowledge of future resistance mutations during pre-clinical phases of drug development would enable the design of novel antibiotics that are robust against not only known resistant mutants, but also against those that have not yet been clinically observed. Computational structure-based protein design (CSPD) is a transformative field that enables the prediction of protein sequences with desired biochemical properties such as binding affinity and specificity to a target. The use of CSPD to predict previously unseen resistance mutations represents one of the frontiers of computational protein design. In a recent study (Reeve et al. Proc Natl Acad Sci U S A 112(3):749-754, 2015), we used our OSPREY (Open Source Protein REdesign for You) suite of CSPD algorithms to prospectively predict resistance mutations that arise in the active site of the dihydrofolate reductase enzyme from methicillin-resistant Staphylococcus aureus (SaDHFR) in response to selective pressure from an experimental competitive inhibitor. We demonstrated that our top predicted candidates are indeed viable resistant mutants. Since that study, we have significantly enhanced the capabilities of OSPREY with not only improved modeling of backbone flexibility, but also efficient multi-state design, fast sparse approximations, partitioned continuous rotamers for more accurate energy bounds, and a computationally efficient representation of molecular-mechanics and quantum-mechanical energy functions. Here, using SaDHFR as an example, we present a protocol for resistance prediction using the latest version of OSPREY. Specifically, we show how to use a combination of positive and negative design to predict active site escape mutations that maintain the enzyme's catalytic function but selectively ablate binding of an inhibitor.

Computational structure-based protein design (CSPD) is an important problem in computational biology, which aims to design or improve a prescribed protein function based on a protein structure template. It provides a practical tool for real-world protein engineering applications. A popular CSPD method that guarantees to find the global minimum energy solution (GMEC) is to combine both dead-end elimination (DEE) and A* tree search algorithms. However, in this framework, the A* search algorithm can run in exponential time in the worst case, which may become the computation bottleneck of large-scale computational protein design process. To address this issue, we extend and add a new module to the OSPREY program that was previously developed in the Donald lab (Gainza et al., Methods Enzymol 523:87, 2013) to implement a GPU-based massively parallel A* algorithm for improving protein design pipeline. By exploiting the modern GPU computational framework and optimizing the computation of the heuristic function for A* search, our new program, called gOSPREY, can provide up to four orders of magnitude speedups in large protein design cases with a small memory overhead comparing to the traditional A* search algorithm implementation, while still guaranteeing the optimality. In addition, gOSPREY can be configured to run in a bounded-memory mode to tackle the problems in which the conformation space is too large and the global optimal solution cannot be computed previously. Furthermore, the GPU-based A* algorithm implemented in the gOSPREY program can be combined with the state-of-the-art rotamer pruning algorithms such as iMinDEE (Gainza et al., PLoS Comput Biol 8:e1002335, 2012) and DEEPer (Hallen et al., Proteins 81:18-39, 2013) to also consider continuous backbone and side-chain flexibility.

Computational structure-based protein design programs are becoming an increasingly important tool in molecular biology. These programs compute protein sequences that are predicted to fold to a target structure and perform a desired function. The success of a program's predictions largely relies on two components: first, the input biophysical model, and second, the algorithm that computes the best sequence(s) and structure(s) according to the biophysical model. Improving both the model and the algorithm in tandem is essential to improving the success rate of current programs, and here we review recent developments in algorithms for protein design, emphasizing how novel algorithms enable the use of more accurate biophysical models. We conclude with a list of algorithmic challenges in computational protein design that we believe will be especially important for the design of therapeutic proteins and protein assemblies., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Despite significant successes in structure-based computational protein design in recent years, protein design algorithms must be improved to increase the biological accuracy of new designs. Protein design algorithms search through an exponential number of protein conformations, protein ensembles, and amino acid sequences in an attempt to find globally optimal structures with a desired biological function. To improve the biological accuracy of protein designs, it is necessary to increase both the amount of protein flexibility allowed during the search and the overall size of the design, while guaranteeing that the lowest-energy structures and sequences are found. DEE/A*-based algorithms are the most prevalent provable algorithms in the field of protein design and can provably enumerate a gap-free list of low-energy protein conformations, which is necessary for ensemble-based algorithms that predict protein binding. We present two classes of algorithmic improvements to the A* algorithm that greatly increase the efficiency of A*. First, we analyze the effect of ordering the expansion of mutable residue positions within the A* tree and present a dynamic residue ordering that reduces the number of A* nodes that must be visited during the search. Second, we propose new methods to improve the conformational bounds used to estimate the energies of partial conformations during the A* search. The residue ordering techniques and improved bounds can be combined for additional increases in A* efficiency. Our enhancements enable all A*-based methods to more fully search protein conformation space, which will ultimately improve the accuracy of complex biomedically relevant designs., (© 2015 Wiley Periodicals, Inc.)

Motivation: Structure-based computational protein design (SCPR) is an important topic in protein engineering. Under the assumption of a rigid backbone and a finite set of discrete conformations of side-chains, various methods have been proposed to address this problem. A popular method is to combine the dead-end elimination (DEE) and A* tree search algorithms, which provably finds the global minimum energy conformation (GMEC) solution., Results: In this article, we improve the efficiency of computing A* heuristic functions for protein design and propose a variant of A* algorithm in which the search process can be performed on a single GPU in a massively parallel fashion. In addition, we make some efforts to address the memory exceeding problem in A* search. As a result, our enhancements can achieve a significant speedup of the A*-based protein design algorithm by four orders of magnitude on large-scale test data through pre-computation and parallelization, while still maintaining an acceptable memory overhead. We also show that our parallel A* search algorithm could be successfully combined with iMinDEE, a state-of-the-art DEE criterion, for rotamer pruning to further improve SCPR with the consideration of continuous side-chain flexibility., Availability: Our software is available and distributed open-source under the GNU Lesser General License Version 2.1 (GNU, February 1999). The source code can be downloaded from http://www.cs.duke.edu/donaldlab/osprey.php or http://iiis.tsinghua.edu.cn/∼compbio/software.html., (© The Author 2014. Published by Oxford University Press.)

Unlabelled: Optimizing amino acid conformation and identity is a central problem in computational protein design. Protein design algorithms must allow realistic protein flexibility to occur during this optimization, or they may fail to find the best sequence with the lowest energy. Most design algorithms implement side-chain flexibility by allowing the side chains to move between a small set of discrete, low-energy states, which we call rigid rotamers. In this work we show that allowing continuous side-chain flexibility (which we call continuous rotamers) greatly improves protein flexibility modeling. We present a large-scale study that compares the sequences and best energy conformations in 69 protein-core redesigns using a rigid-rotamer model versus a continuous-rotamer model. We show that in nearly all of our redesigns the sequence found by the continuous-rotamer model is different and has a lower energy than the one found by the rigid-rotamer model. Moreover, the sequences found by the continuous-rotamer model are more similar to the native sequences. We then show that the seemingly easy solution of sampling more rigid rotamers within the continuous region is not a practical alternative to a continuous-rotamer model: at computationally feasible resolutions, using more rigid rotamers was never better than a continuous-rotamer model and almost always resulted in higher energies. Finally, we present a new protein design algorithm based on the dead-end elimination (DEE) algorithm, which we call iMinDEE, that makes the use of continuous rotamers feasible in larger systems. iMinDEE guarantees finding the optimal answer while pruning the search space with close to the same efficiency of DEE., Availability: Software is available under the Lesser GNU Public License v3. Contact the authors for source code.

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(alpha)-C(beta) 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 < or = 0.9 A 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.

Motivation: Structure-based protein redesign can help engineer proteins with desired novel function. Improving computational efficiency while still maintaining the accuracy of the design predictions has been a major goal for protein design algorithms. The combinatorial nature of protein design results both from allowing residue mutations and from the incorporation of protein side-chain flexibility. Under the assumption that a single conformation can model protein folding and binding, the goal of many algorithms is the identification of the Global Minimum Energy Conformation (GMEC). A dominant theorem for the identification of the GMEC is Dead-End Elimination (DEE). DEE-based algorithms have proven capable of eliminating the majority of candidate conformations, while guaranteeing that only rotamers not belonging to the GMEC are pruned. However, when the protein design process incorporates rotameric energy minimization, DEE is no longer provably-accurate. Hence, with energy minimization, the minimized-DEE (MinDEE) criterion must be used instead., Results: In this paper, we present provably-accurate improvements to both the DEE and MinDEE criteria. We show that our novel enhancements result in a speedup of up to a factor of more than 1000 when applied in redesign for three different proteins: Gramicidin Synthetase A, plastocyanin, and protein G., Availability: Contact authors for source code.

Antimicrobial resistance presents a significant health care crisis. The mutation F98Y in Staphylococcus aureus dihydrofolate reductase (SaDHFR) confers resistance to the clinically important antifolate trimethoprim (TMP). Propargyl-linked antifolates (PLAs), next generation DHFR inhibitors, are much more resilient than TMP against this F98Y variant, yet this F98Y substitution still reduces efficacy of these agents. Surprisingly, differences in the enantiomeric configuration at the stereogenic center of PLAs influence the isomeric state of the NADPH cofactor. To understand the molecular basis of F98Y-mediated resistance and how PLAs' inhibition drives NADPH isomeric states, we used protein design algorithms in the osprey protein design software suite to analyze a comprehensive suite of structural, biophysical, biochemical, and computational data. Here, we present a model showing how F98Y SaDHFR exploits a different anomeric configuration of NADPH to evade certain PLAs' inhibition, while other PLAs remain unaffected by this resistance mechanism. Author summary: Antimicrobial resistance is a major healthcare crisis. While we were developing novel enzyme inhibitors to combat methicillin-resistant Staphylococcus aureus (MRSA), we found that the chirality of both inhibitor and cofactor can have a large influence on inhibitor potency. Our detailed study of enantiomeric propargyl-linked antifolates (PLAs) shows that the chiral state of inhibitors can affect the chiral state of the cofactor. Moreover, the bacterial enzyme target can exploit cooperative chirality to evade inhibitor binding. We call this phenomenon chiral evasion. Using crystal structures, biochemical assays, computational protein design algorithms, and statistical mechanics, a detailed mechanism for chiral evasion is proposed. While the concept that different enantiomers have different biology is well known, MRSA is unique: we do not know of any other cases where a single mutation (F98Y) flips the chirality preference for cofactor binding and induces stereospecificity for drug binding. Thus, we illuminate the effect of this clinically relevant resistance mutation on the obligate cofactor binding site. These new insights will be useful to develop more durable antibiotics that are resilient to resistance. [ABSTRACT FROM AUTHOR]

We present osprey 3.0, a new and greatly improved release of the osprey protein design software. Osprey 3.0 features a convenient new Python interface, which greatly improves its ease of use. It is over two orders of magnitude faster than previous versions of osprey when running the same algorithms on the same hardware. Moreover, osprey 3.0 includes several new algorithms, which introduce substantial speedups as well as improved biophysical modeling. It also includes GPU support, which provides an additional speedup of over an order of magnitude. Like previous versions of osprey, osprey 3.0 offers a unique package of advantages over other design software, including provable design algorithms that account for continuous flexibility during design and model conformational entropy. Finally, we show here empirically that osprey 3.0 accurately predicts the effect of mutations on protein–protein binding. Osprey 3.0 is available at http://www.cs.duke.edu/donaldlab/osprey.php as free and open‐source software. © 2018 Wiley Periodicals, Inc. We present the third major release of the OSPREY protein design software, along with comparisons to experimental data that confirm its ability to optimize protein mutants for desired functions. Osprey 3.0 has significant efficiency, ease‐of‐use, and algorithmic improvements over previous versions, including GPU acceleration and a new Python interface. [ABSTRACT FROM AUTHOR]

Motivation: When proteins mutate or bind to ligands, their backbones often move significantly, especially in loop regions. Computational protein design algorithms must model these motions in order to accurately optimize protein stability and binding affinity. However, methods for backbone conformational search in design have been much more limited than for sidechain conformational search. This is especially true for combinatorial protein design algorithms, which aim to search a large sequence space efficiently and thus cannot rely on temporal simulation of each candidate sequence. Results: We alleviate this difficulty with a new parameterization of backbone conformational space, which represents all degrees of freedom of a specified segment of protein chain that maintain valid bonding geometry (by maintaining the original bond lengths and angles and ω dihedrals). In order to search this space, we present an efficient algorithm, CATS, for computing atomic coordinates as a function of our new continuous backbone internal coordinates. CATS generalizes the iMinDEE and EPIC protein design algorithms, which model continuous flexibility in sidechain dihedrals, to model continuous, appropriately localized flexibility in the backbone dihedrals φ and ψ as well. We show using 81 test cases based on 29 different protein structures that CATS finds sequences and conformations that are significantly lower in energy than methods with less or no backbone flexibility do. In particular, we show that CATS can model the viability of an antibody mutation known experimentally to increase affinity, but that appears sterically infeasible when modeled with less or no backbone flexibility. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

One of the main challenges in computational protein design (CPD) is the huge size of the protein sequence and conformational space that has to be computationally explored. Recently, we showed that state-of-the-art combinatorial optimization technologies based on Cost Function Network (CFN) processing allow speeding up provable rigid backbone protein design methods by several orders of magnitudes. Building up on this, we improved and injected CFN technology into the well-established CPD package Osprey to allow all Osprey CPD algorithms to benefit from associated speedups. Because Osprey fundamentally relies on the ability of [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Amino acid substitutions in protein structures often require subtle backbone adjustments that are difficult to model in atomic detail. An improved ability to predict realistic backbone changes in response to engineered mutations would be of great utility for the blossoming field of rational protein design. One model that has recently grown in acceptance is the backrub motion, a low-energy dipeptide rotation with single-peptide counter-rotations, that is coupled to dynamic twostate sidechain rotamer jumps, as evidenced by alternate conformations in very high-resolution crystal structures. It has been speculated that backrubs may facilitate sequence changes equally well as rotamer changes. However, backrubinduced shifts and experimental uncertainty are of similar magnitude for backbone atoms in even high-resolution structures, so comparison of wildtype-vs.-mutant crystal structure pairs is not sufficient to directly link backrubs to mutations. In this study, we use two alternative approaches that bypass this limitation. First, we use a quality-filtered structure database to aggregate many examples for precisely defined motifs with single amino acid differences, and find that the effectively amplified backbone differences closely resemble backrubs. Second, we directly apply a provablyaccurate, backrub-enabled protein design algorithm to idealized versions of these motifs, and discover that the lowestenergy computed models match the average-coordinate experimental structures. These results support the hypothesis that backrubs participate in natural protein evolution and validate their continued use for design of synthetic proteins. [ABSTRACT FROM AUTHOR]

We report a computational, structure-based redesign of the phenylalanine adenylation domain of the nonribosomal peptide synthetase enzyme gramicidin S synthetase A (GrsA-PheA) for a set of noncognate substrates for which the wild-type enzyme has little or virtually no specificity. Experimental validation of a set of top- ranked computationally predicted enzyme mutants shows significant improvement in the specificity for the target substrates. We further present enhancements to the methodology for computational enzyme redesign that are experimentally shown to result in significant additional improvements in the target substrate specificity. The mutant with the highest activity for a noncognate substrate exhibits 1/6 of the wild-type enzyme/wild-type substrate activity, further confirming the feasibility of our computational approach. Our results suggest that structure-based protein design can identify active mutants different from those selected by evolution. [ABSTRACT FROM AUTHOR]

One of the main challenges for protein redesign is the efficient evaluation of a combinatorial number of candidate structures. The modeling of protein flexibility, typically by using a rotamer library of commonly-observed low-energy side-chain conformations, further increases the complexity of the redesign problem. A dominant algorithm for protein redesign is dead-end elimination (DEE), which prunes the majority of candidate conformations by eliminating rigid rotamers that provably are not part of the global minimum energy conformation (GMEC). The identified GMEC consists of rigid rotamers (i.e., rotamers that have not been energy-minimized) and is thus referred to as the rigid-GMEC. As a postprocessing step, the conformations that survive DEE may be energy-minimized. When energy minimization is performed after pruning with DEE, the combined protein design process becomes heuristic, and is no longer provably accurate: a conformation that is pruned using rigid-rotamer energies may subsequently minimize to a lower energy than the rigid-GMEC. That is, the rigid-GMEC and the conformation with the lowest energy among all energy-minimized conformations (the minimized-GMEC) are likely to be different. While the traditional DEE algorithm succeeds in not pruning rotamers that are part of the rigid-GMEC, it makes no guarantees regarding the identification of the minimized-GMEC. In this paper we derive a novel, provable, and efficient DEE-like algorithm, called minimized-DEE (MinDEE), that guarantees that rotamers belonging to the minimized-GMEC will not be pruned, while still pruning a combinatorial number of conformations. We show that MinDEE is useful not only in identifying the minimized-GMEC, but also as a filter in an ensemble-based scoring and search algorithm for protein redesign that exploits energy-minimized conformations. We compare our results both to our previous computational predictions of protein designs and to biological activity assays of predicted protein mutants. Our provable and efficient minimized-DEE algorithm is applicable in protein redesign, protein-ligand binding prediction, and computer-aided drug design. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008 [ABSTRACT FROM AUTHOR]

Computational, in silico prediction of resistance-conferring escape mutations could accelerate the design of therapeutics less prone to resistance. This article describes how to use the Resistor algorithm to predict escape mutations. Resistor employs Pareto optimization on four resistance-conferring criteria—positive and negative design, mutational probability, and hotspot cardinality—to assign a Pareto rank to each prospective mutant. It also predicts the mechanism of resistance, that is, whether a mutant ablates binding to a drug, strengthens binding to the endogenous ligand, or a combination of these two factors, and provides structural models of the mutants. Resistor is part of the free and open-source computational protein design software OSPREY. [ABSTRACT FROM AUTHOR]

Computational protein design (CPD) algorithms that compute binding affinity, Ka, search for sequences with an energetically favorable free energy of binding. Recent work shows that three principles improve the biological accuracy of CPD: ensemble-based design , continuous flexibility of backbone and side-chain conformations, and provable guarantees of accuracy with respect to the input. However, previous methods that use all three design principles are single-sequence (SS) algorithms, which are very costly: linear in the number of sequences and thus exponential in the number of simultaneously mutable residues. To address this computational challenge, we introduce BBK* , a new CPD algorithm whose key innovation is the multisequence (MS) bound: BBK* efficiently computes a single provable upper bound to approximate Ka for a combinatorial number of sequences , and avoids SS computation for all provably suboptimal sequences. Thus, to our knowledge, BBK* is the first provable, ensemble-based CPD algorithm to run in time sublinear in the number of sequences. Computational experiments on 204 protein design problems show that BBK* finds the tightest binding sequences while approximating Ka for up to 105-fold fewer sequences than the previous state-of-the-art algorithms, which require exhaustive enumeration of sequences. Furthermore, for 51 protein–ligand design problems, BBK* provably approximates Ka up to 1982-fold faster than the previous state-of-the-art iMinDEE/ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${\curr A^*}$$ \end{document} / \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${\curr K^*}$$ \end{document} algorithm. Therefore, BBK* not only accelerates protein designs that are possible with previous provable algorithms, but also efficiently performs designs that are too large for previous methods. [ABSTRACT FROM AUTHOR]

Protein design algorithms that model continuous sidechain flexibility and conformational ensembles better approximate the in vitro and in vivo behavior of proteins. The previous state of the art, iMinDEE-A*-K*, computes provable ɛ-approximations to partition functions of protein states (e.g., bound vs. unbound) by computing provable, admissible pairwise-minimized energy lower bounds on protein conformations, and using the A* enumeration algorithm to return a gap-free list of lowest-energy conformations. iMinDEE-A*-K* runs in time sublinear in the number of conformations, but can be trapped in loosely-bounded, low-energy conformational wells containing many conformations with highly similar energies. That is, iMinDEE-A*-K* is unable to exploit the correlation between protein conformation and energy: similar conformations often have similar energy. We introduce two new concepts that exploit this correlation: Minimization-Aware Enumeration and Recursive K*. We combine these two insights into a novel algorithm, Minimization-Aware Recursive K* (MARK*), which tightens bounds not on single conformations, but instead on distinct regions of the conformation space. We compare the performance of iMinDEE-A*-K* versus MARK* by running the Branch and Bound over K* (BBK*) algorithm, which provably returns sequences in order of decreasing K* score, using either iMinDEE-A*-K* or MARK* to approximate partition functions. We show on 200 design problems that MARK* not only enumerates and minimizes vastly fewer conformations than the previous state of the art, but also runs up to 2 orders of magnitude faster. Finally, we show that MARK* not only efficiently approximates the partition function, but also provably approximates the energy landscape. To our knowledge, MARK* is the first algorithm to do so. We use MARK* to analyze the change in energy landscape of the bound and unbound states of an HIV-1 capsid protein C-terminal domain in complex with a camelid VHH, and measure the change in conformational entropy induced by binding. Thus, MARK* both accelerates existing designs and offers new capabilities not possible with previous algorithms. [ABSTRACT FROM AUTHOR]

Finding the global minimum energy conformation (GMEC) of a huge combinatorial search space is the key challenge in computational protein design (CPD) problems. Traditional algorithms lack a scalable and efficient distributed design scheme, preventing researchers from taking full advantage of current cloud infrastructures. We design cloud OSPREY (cOSPREY), an extension to a widely used protein design software OSPREY, to allow the original design framework to scale to the commercial cloud infrastructures. We propose several novel designs to integrate both algorithm and system optimizations, such as GMEC-specific pruning, state search partitioning, asynchronous algorithm state sharing, and fault tolerance. We evaluate cOSPREY on three different cloud platforms using different technologies and show that it can solve a number of large-scale protein design problems that have not been possible with previous approaches. [ABSTRACT FROM AUTHOR]

Sparse energy functions that ignore long range interactions between residue pairs are frequently used by protein design algorithms to reduce computational cost. Current dynamic programming algorithms that fully exploit the optimal substructure produced by these energy functions only compute the GMEC. This disproportionately favors the sequence of a single, static conformation and overlooks better binding sequences with multiple low-energy conformations. Provable, ensemble-based algorithms such as A* avoid this problem, but A* cannot guarantee better performance than exhaustive enumeration. We propose a novel, provable, dynamic programming algorithm called Branch-Width Minimization* (BWM*) to enumerate a gap-free ensemble of conformations in order of increasing energy. Given a branch-decomposition of branch-width w for an n-residue protein design with at most q discrete side-chain conformations per residue, BWM* returns the sparse GMEC in O(nw²q3/2w) time and enumerates each additional conformation in merely O(n log q) time. We define a new measure, Total Effective Search Space (TESS), which can be computed efficiently a priori before BWM* or A* is run. We ran BWM* on 67 protein design problems and found that TESS discriminated between BWM*-efficient and A*- efficient cases with 100% accuracy. As predicted by TESS and validated experimentally, BWM* outperforms A* in 73% of the cases and computes the full ensemble or a close approximation faster than A*, enumerating each additional conformation in milliseconds. Unlike A*, the performance of BWM* can be predicted in polynomial time before running the algorithm, which gives protein designers the power to choose the most efficient algorithm for their particular design problem. [ABSTRACT FROM AUTHOR]