Compact Representation of Continuous Energy Surfaces for More Efficient Protein Design

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.

Dynamics, a Powerful Component of Current and Future in Silico Approaches for Protein Design and Engineering

Computational prediction has become an indispensable aid in the processes of engineering and designing proteins for various biotechnological applications. With the tremendous progress in more powerful computer hardware and more efficient algorithms, some of in silico tools and methods have started to apply the more realistic description of proteins as their conformational ensembles, making protein dynamics an integral part of their prediction workflows. To help protein engineers to harness benefits of considering dynamics in their designs, we surveyed new tools developed for analyses of conformational ensembles in order to select engineering hotspots and design mutations. Next, we discussed the collective evolution towards more flexible protein design methods, including ensemble-based approaches, knowledge-assisted methods, and provable algorithms. Finally, we highlighted apparent challenges that current approaches are facing and provided our perspectives on their further development.

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.

Computational Analysis of Energy Landscapes Reveals Dynamic Features That Contribute to Binding of Inhibitors to CFTR-Associated Ligand

The CFTR-associated ligand PDZ domain (CALP) binds to the cystic fibrosis transmembrane conductance regulator (CFTR) and mediates lysosomal degradation of mature CFTR. Inhibition of this interaction has been explored as a therapeutic avenue for cystic fibrosis. Previously, we reported the ensemble-based computational design of a novel peptide inhibitor of CALP, which resulted in the most binding-efficient inhibitor to date. This inhibitor, kCAL01, was designed using osprey and evinced significant biological activity in in vitro cell-based assays. Here, we report a crystal structure of kCAL01 bound to CALP and compare structural features against iCAL36, a previously developed inhibitor of CALP. We compute side-chain energy landscapes for each structure to not only enable approximation of binding thermodynamics but also reveal ensemble features that contribute to the comparatively efficient binding of kCAL01. Finally, we compare the previously reported design ensemble for kCAL01 vs the new crystal structure and show that, despite small differences between the design model and crystal structure, significant biophysical features that enhance inhibitor binding are captured in the design ensemble. This suggests not only that ensemble-based design captured thermodynamically significant features observed in vitro, but also that a design eschewing ensembles would miss the kCAL01 sequence entirely.

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).

Strategies for designing non-natural enzymes and binders

The design of tailor-made enzymes is a major goal in biochemical research that can result in wide-range applications and will lead to a better understanding of how proteins fold and function. In this review we highlight recent advances in enzyme and small molecule binder design. A focus is placed on novel strategies for the design of scaffolds, developments in computational methods, and recent applications of these techniques on receptors, sensors, and enzymes. Further, the integration of computational and experimental methodologies is discussed. The outlined examples of designed enzymes and binders for various purposes highlight the importance of this topic and underline the need for tailor-made proteins.

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.

Algorithms for protein design

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.

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

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