Design of epitope-specific probes for sera analysis and antibody isolation

Novel, provable algorithms for efficient ensemble-based computational protein design and their application to the redesign of the c-Raf-RBD:KRas protein-protein interface

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 (KRas^GTP). 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 KRas^GTP, 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.

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.

Minimization-Aware Recursive K*: A Novel, Provable Algorithm that Accelerates Ensemble-Based Protein Design and Provably Approximates the Energy Landscape

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 V_HH, 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.

OSPREY 3.0: Open-source protein redesign for you, with powerful new features

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.

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).

CATS (Coordinates of Atoms by Taylor Series): protein design with backbone flexibility in all locally feasible directions

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.

Availability and implementation

Our code is available as free software at https://github.com/donaldlab/OSPREY_refactor.

Supplementary information

Supplementary data are available at Bioinformatics online.

BBK* (Branch and Bound Over K*): A Provable and Efficient Ensemble-Based Protein Design Algorithm to Optimize Stability and Binding Affinity Over Large Sequence Spaces

Computational protein design (CPD) algorithms that compute binding affinity, K_a, 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 K_a 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 K_a 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 K_a up to 1982-fold faster than the previous state-of-the-art iMinDEE/[Formula: see text]/[Formula: see text] 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.

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.

OSPREY Predicts Resistance Mutations Using Positive and Negative Computational Protein Design

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.

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.

cOSPREY: A Cloud-Based Distributed Algorithm for Large-Scale Computational Protein Design

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.

Compact Representation of Continuous Energy Surfaces for More Efficient Protein Design

In macromolecular design, conformational energies are sensitive to small changes in atom coordinates; thus, modeling the small, continuous motions of atoms around low-energy wells confers a substantial advantage in structural accuracy. However, modeling these motions comes at the cost of a very large number of energy function calls, which form the bottleneck in the design calculations. In this work, we remove this bottleneck by consolidating all conformational energy evaluations into the pre-computation of a local polynomial expansion of the energy about the "ideal" conformation for each low-energy, "rotameric" state of each residue pair. This expansion is called "energy as polynomials in internal coordinates" (EPIC), where the internal coordinates can be side-chain dihedrals, backrub angles, and/or any other continuous degrees of freedom of a macromolecule, and any energy function can be used without adding any asymptotic complexity to the design. We demonstrate that EPIC efficiently represents the energy surface for both molecular-mechanics and quantum-mechanical energy functions, and apply it specifically to protein design for modeling both side chain and backbone degrees of freedom.

Fast search algorithms for computational protein design

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.

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.

BWM*: A Novel, Provable, Ensemble-based Dynamic Programming Algorithm for Sparse Approximations of Computational Protein Design

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([Formula: see text]) time and enumerates each additional conformation in merely O([Formula: see text]) 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.

Fast gap-free enumeration of conformations and sequences for protein design

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.