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With over 270 unique occurrences in the human genome, peptide-recognizing PDZ domains play a central role in modulating polarization, signaling, and trafficking pathways. Mutations in PDZ domains lead to diseases such as cancer and cystic fibrosis, making PDZ domains attractive targets for therapeutic intervention. D-peptide inhibitors offer unique advantages as therapeutics, including increased metabolic stability and low immunogenicity. Here, we introduce DexDesign, a novel OSPREY-based algorithm for computationally designing de novo D-peptide inhibitors. DexDesign leverages three novel techniques that are broadly applicable to computational protein design: the Minimum Flexible Set, K*-based Mutational Scan, and Inverse Alanine Scan. We apply these techniques and DexDesign to generate novel D-peptide inhibitors of two biomedically important PDZ domain targets: CAL and MAST2. We introduce a framework for analyzing de novo peptides-evaluation along a replication/restitution axis-and apply it to the DexDesign-generated D-peptides. Notably, the peptides we generated are predicted to bind their targets tighter than their targets' endogenous ligands, validating the peptides' potential as lead inhibitors. We also provide an implementation of DexDesign in the free and open source computational protein design software OSPREY., (© The Author(s) 2024. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.)

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.

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.

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.

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.

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.)

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 A* to produce conformations in increasing order of energy, we defined new A* strategies combining CFN lower bounds, with new side-chain positioning-based branching scheme. Beyond the speedups obtained in the new A*-CFN combination, this novel branching scheme enables a much faster enumeration of suboptimal sequences, far beyond what is reachable without it. Together with the immediate and important speedups provided by CFN technology, these developments directly benefit to all the algorithms that previously relied on the DEE/ A* combination inside Osprey* and make it possible to solve larger CPD problems with provable algorithms., (© 2016 Wiley Periodicals, Inc.)

Methods to accurately predict potential drug target mutations in response to early-stage leads could drive the design of more resilient first generation drug candidates. In this study, a structure-based protein design algorithm (K* in the OSPREY suite) was used to prospectively identify single-nucleotide polymorphisms that confer resistance to an experimental inhibitor effective against dihydrofolate reductase (DHFR) from Staphylococcus aureus. Four of the top-ranked mutations in DHFR were found to be catalytically competent and resistant to the inhibitor. Selection of resistant bacteria in vitro reveals that two of the predicted mutations arise in the background of a compensatory mutation. Using enzyme kinetics, microbiology, and crystal structures of the complexes, we determined the fitness of the mutant enzymes and strains, the structural basis of resistance, and the compensatory relationship of the mutations. To our knowledge, this work illustrates the first application of protein design algorithms to prospectively predict viable resistance mutations that arise in bacteria under antibiotic pressure.

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: We have developed a suite of protein redesign algorithms that improves realistic in silico modeling of proteins. These algorithms are based on three characteristics that make them unique: (1) improved flexibility of the protein backbone, protein side-chains, and ligand to accurately capture the conformational changes that are induced by mutations to the protein sequence; (2) modeling of proteins and ligands as ensembles of low-energy structures to better approximate binding affinity; and (3) a globally optimal protein design search, guaranteeing that the computational predictions are optimal with respect to the input model. Here, we illustrate the importance of these three characteristics. We then describe OSPREY, a protein redesign suite that implements our protein design algorithms. OSPREY has been used prospectively, with experimental validation, in several biomedically relevant settings. We show in detail how OSPREY has been used to predict resistance mutations and explain why improved flexibility, ensembles, and provability are essential for this application., Availability: OSPREY is free and open source under a Lesser GPL license. The latest version is OSPREY 2.0. The program, user manual, and source code are available at www.cs.duke.edu/donaldlab/software.php., Contact: osprey@cs.duke.edu., (Copyright © 2013 Elsevier Inc. All rights reserved.)

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., (Copyright © 2012 Wiley Periodicals, Inc.)

Nuclear magnetic resonance (NMR) spectroscopy is a primary tool to perform structural studies of proteins in physiologically-relevant solution conditions. Restraints on distances between pairs of nuclei in the protein, derived from the nuclear Overhauser effect (NOE), provide information about the structure of the protein in its folded state. NMR studies of symmetric protein homo-oligomers present a unique challenge. Using X-filtered NOESY experiments, it is possible to determine whether an NOE restrains a pair of protons across different subunits or within a single subunit, but current experimental techniques are unable to determine in which subunits the restrained protons lie. Consequently, it is difficult to assign NOEs to particular pairs of subunits with certainty, thus hindering the structural analysis of the oligomeric state. Computational approaches are needed to address this subunit ambiguity, but traditional solutions often rely on stochastic search coupled with simulated annealing and simulations of simplified molecular dynamics, which have many tunable parameters that must be chosen carefully and can also fail to report structures consistent with the experimental restraints. In addition, these traditional approaches rarely provide guarantees on running time or solution quality. We reduce the structure determination of homo-oligomers with cyclic symmetry to computing geometric arrangements of unions of annuli in a plane. Our algorithm, disco, runs in expected O(n²) time, where n is the number of distance restraints, potentially assigned ambiguously. disco is guaranteed to report the exact set of oligomer structures consistent with the distance restraints and also with orientational restraints from residual dipolar couplings (RDCs). We demonstrate our method using two symmetric protein complexes: the trimeric E. coli diacylglycerol kinase (DAGK) and a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G (GB1). In both cases, disco computes oligomer structures with high precision and also finds distance restraints that are either mutually inconsistent or inconsistent with the RDCs. The entire protocol DISCO has been completely automated in a software package that is freely available and open-source at www.cs.duke.edu/donaldlab/software.php.

Drug resistance resulting from mutations to the target is an unfortunate common phenomenon that limits the lifetime of many of the most successful drugs. In contrast to the investigation of mutations after clinical exposure, it would be powerful to be able to incorporate strategies early in the development process to predict and overcome the effects of possible resistance mutations. Here we present a unique prospective application of an ensemble-based protein design algorithm, K*, to predict potential resistance mutations in dihydrofolate reductase from Staphylococcus aureus using positive design to maintain catalytic function and negative design to interfere with binding of a lead inhibitor. Enzyme inhibition assays show that three of the four highly-ranked predicted mutants are active yet display lower affinity (18-, 9-, and 13-fold) for the inhibitor. A crystal structure of the top-ranked mutant enzyme validates the predicted conformations of the mutated residues and the structural basis of the loss of potency. The use of protein design algorithms to predict resistance mutations could be incorporated in a lead design strategy against any target that is susceptible to mutational resistance.

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., ((c) 2008 Wiley Periodicals, Inc. J Comput Chem, 2008.)

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.

High-throughput structure determination based on solution Nuclear Magnetic Resonance (NMR) spectroscopy plays an important role in structural genomics. One of the main bottlenecks in NMR structure determination is the interpretation of NMR data to obtain a sufficient number of accurate distance restraints by assigning nuclear Overhauser effect (NOE) spectral peaks to pairs of protons. The difficulty in automated NOE assignment mainly lies in the ambiguities arising both from the resonance degeneracy of chemical shifts and from the uncertainty due to experimental errors in NOE peak positions. In this paper we present a novel NOE assignment algorithm, called HAusdorff-based NOE Assignment (HANA), that starts with a high-resolution protein backbone computed using only two residual dipolar couplings (RDCs) per residue, employs a Hausdorff-based pattern matching technique to deduce similarity between experimental and back-computed NOE spectra for each rotamer from a statistically diverse library, and drives the selection of optimal position-specific rotamers for filtering ambiguous NOE assignments. Our algorithm runs in time O(tn3 + tn log t), where t is the maximum number of rotamers per residue and n is the size of the protein. Application of our algorithm on biological NMR data for three proteins, namely, human ubiquitin, the zinc finger domain of the human DNA Y-polymerase Eta (pol eta) and the human Set2-Rpb1 interacting domain (hSRI) demonstrates that our algorithm overcomes spectral noise to achieve more than 90% assignment accuracy. Additionally, the final structures calculated using our automated NOE assignments have backbone RMSD < 1.7 A and all-heavy-atom RMSD < 2.5 A from reference structures that were determined either by X-ray crystallography or traditional NMR approaches. These results show that our NOE assignment algorithm can be successfully applied to protein NMR spectra to obtain high-quality structures.

Motivation: Dead-End Elimination (DEE) is a powerful algorithm capable of reducing the search space for structure-based protein design by a combinatorial factor. By using a fixed backbone template, a rotamer library, and a potential energy function, DEE identifies and prunes rotamer choices that are provably not part of the Global Minimum Energy Conformation (GMEC), effectively eliminating the majority of the conformations that must be subsequently enumerated to obtain the GMEC. Since a fixed-backbone model biases the algorithm predictions against protein sequences for which even small backbone movements may result in a significantly enhanced stability, the incorporation of backbone flexibility can improve the accuracy of the design predictions. If explicit backbone flexibility is incorporated into the model, however, the traditional DEE criteria can no longer guarantee that the flexible-backbone GMEC, the lowest-energy conformation when the backbone is allowed to flex, will not be pruned., Results: We derive a novel DEE pruning criterion, flexible-backbone DEE (BD), that is provably accurate with backbone flexibility, guaranteeing that no rotamers belonging to the flexible-backbone GMEC are pruned; we also present further enhancements to BD for improved pruning efficiency. The results from applying our novel algorithms to redesign the beta1 domain of protein G and to switch the substrate specificity of the NRPS enzyme GrsA-PheA are then compared against the results from previous fixed-backbone DEE algorithms. We confirm experimentally that traditional-DEE is indeed not provably-accurate with backbone flexibility and that BD is capable of generating conformations with significantly lower energies, thus confirming the feasibility of our novel algorithms., Availability: Contact authors for source code.

Assignment of nuclear Overhauser effect (NOE) data is a key bottleneck in structure determination by NMR. NOE assignment resolves the ambiguity as to which pair of protons generated the observed NOE peaks, and thus should be restrained in structure determination. In the case of intersubunit NOEs in symmetric homo-oligomers, the ambiguity includes both the identities of the protons within a subunit, and the identities of the subunits to which they belong. This paper develops an algorithm for simultaneous intersubunit NOE assignment and C(n) symmetric homo-oligomeric structure determinations, given the subunit structure. By using a configuration space framework, our algorithm guarantees completeness, in that it identifies structures representing, to within a user-defined similarity level, every structure consistent with the available data (ambiguous or not). However, while our approach is complete in considering all conformations and assignments, it avoids explicit enumeration of the exponential number of combinations of possible assignments. Our algorithm can draw two types of conclusions not possible under previous methods: (1) that different assignments for an NOE would lead to different structural classes, or (2) that it is not necessary to uniquely assign an NOE, since it would have little impact on structural precision. We demonstrate on two test proteins that our method reduces the average number of possible assignments per NOE by a factor of 2.6 for MinE and 4.2 for CCMP. It results in high structural precision, reducing the average variance in atomic positions by factors of 1.5 and 3.6, respectively.

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.

Realization of novel molecular function requires the ability to alter molecular complex formation. Enzymatic function can be altered by changing enzyme-substrate interactions via modification of an enzyme's active site. A redesigned enzyme may either perform a novel reaction on its native substrates or its native reaction on novel substrates. A number of computational approaches have been developed to address the combinatorial nature of the protein redesign problem. These approaches typically search for the global minimum energy conformation among an exponential number of protein conformations. We present a novel algorithm for protein redesign, which combines a statistical mechanics-derived ensemble-based approach to computing the binding constant with the speed and completeness of a branch-and-bound pruning algorithm. In addition, we developed an efficient deterministic approximation algorithm, capable of approximating our scoring function to arbitrary precision. In practice, the approximation algorithm decreases the execution time of the mutation search by a factor of ten. To test our method, we examined the Phe-specific adenylation domain of the nonribosomal peptide synthetase gramicidin synthetase A (GrsA-PheA). Ensemble scoring, using a rotameric approximation to the partition functions of the bound and unbound states for GrsA-PheA, is first used to predict binding of the wildtype protein and a previously described mutant (selective for leucine), and second, to switch the enzyme specificity toward leucine, using two novel active site sequences computationally predicted by searching through the space of possible active site mutations. The top scoring in silico mutants were created in the wetlab and dissociation/binding constants were determined by fluorescence quenching. These tested mutations exhibit the desired change in specificity from Phe to Leu. Our ensemble-based algorithm, which flexibly models both protein and ligand using rotamer-based partition functions, has application in enzyme redesign, the prediction of protein-ligand binding, and computer-aided drug design.

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. Author summary: Computational structure-based protein design is an innovative tool for redesigning proteins to introduce a particular or novel function. One such function is improving the binding of one protein to another, which can increase our understanding of important protein systems. Herein we introduce two novel, provable algorithms, fries and EWAK*, for more efficient computational structure-based protein design as well as their application to the redesign of the c-Raf-RBD:KRas protein-protein interface. These new algorithms speed-up computational structure-based protein design while maintaining accurate calculations, allowing for larger, previously infeasible protein designs. Additionally, using fries and EWAK* within the osprey suite, we designed the tightest known binder of KRas, a heavily studied cancer target that interacts with a number of different proteins. This previously undiscovered variant of a KRas-binding domain, c-Raf-RBD, has potential to serve as a tool to further probe the protein-protein interface of KRas with its effectors and its discovery alone emphasizes the potential for more successful applications of computational structure-based protein design. [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]

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 [ABSTRACT FROM AUTHOR]

We present designs, theory, and results of fabrication and testing for a novel parallel microrobotic assembly scheme using stress-engineered MEMS microrobots. The robots are 240-280 μm x 60 μm x 7-20 μm in size and can be controlled to dock compliantly together, forming planar structures several times this size. The devices are classified into species based on the design of their steering arm actuators, and the species are further classified as independent if they can be maneuvered independently using a single global control signal. In this paper, we show that microrobot species are independent if the two transition voltages of their steering arms, i.e., the voltages at which the arms are raised or lowered, form a unique pair. We present control algorithms that can be applied to groups of independent microrobot species to direct their motion from arbitrary nondeadlock configurations to desired planar microassemblies. We present designs and fabrication for four independent microrobot species, each with a unique transition voltage. The fabricated microrobots are used to demonstrate directed assembly of five types of planar structures from two classes of initial conditions. We demonstrate an average docking accuracy of 5 μm and use self-aligning compliant interaction between the microrobots to further align and stabilize the intermediate assemblies. The final assemblies match their target shapes on average 96%, by area. [ABSTRACT FROM AUTHOR]

Molecular replacement (MR) often plays a prominent role in determining initial phase angles for structure determination by X-ray crystallography. In this paper, an efficient quaternion-based algorithm is presented for analyzing peaks from a cross-rotation function in order to identify model orientations consistent with proper non-crystallographic symmetry (NCS) and to generate proper NCS-consistent orientations missing from the list of cross-rotation peaks. The algorithm, CRANS, analyzes the rotation differences between each pair of cross-rotation peaks to identify finite subgroups. Sets of rotation differences satisfying the subgroup axioms correspond to orientations compatible with the correct proper NCS. The CRANS algorithm was first tested using cross-rotation peaks computed from structure-factor data for three test systems and was then used to assist in the de novo structure determination of dihydrofolate reductase-thymidylate synthase (DHFR-TS) from Cryptosporidium hominis. In every case, the CRANS algorithm runs in seconds to identify orientations consistent with the observed proper NCS and to generate missing orientations not present in the cross-rotation peak list. The CRANS algorithm has application in every molecular-replacement phasing effort with proper NCS. [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]