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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 \(\varepsilon \)-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 \(K^{*}\) (\({ MARK}^{*}\)), that tightens bounds not on single conformations, but instead on distinct regions of the conformation space. We compare the performance of iMinDEE-\(A^*\)-\(K^*\) vs. \({ MARK}^{*}\) by running the \(BBK^*\) 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 two 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 the HIV-1 capsid protein C-terminal domain in complex with camelid V\(_{\mathrm{{H}}}\)H, 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.

PDZ domains are small protein-binding domains that interact with short, mostly C-terminal peptides and play important roles in cellular signaling and the trafficking and localization of ion channels. The CFTR-associated ligand PDZ domain (CALP) binds to the cystic fibro-sis transmembrane conductance regulator (CFTR) and mediates degradation of mature CFTR through lysosomal pathways. Inhibition of the CALP:CFTR interaction has been explored as a potential therapeutic avenue for cystic fibrosis (CF).1Previously, we reported2the ensemble-based computational design of a novel 6-residue peptide inhibitor of CALP, which resulted in the most binding-efficient inhibitor of CALP to date. This inhibitor, kCAL01, was designed using OSPREY3and displayed significant biological activity inin vitrocell-based assays. Here, we report a crystal structure of kCAL01 bound to CALP (PDB ID: 6OV7). To elucidate the structural basis for the enhanced binding efficiency of kCAL01, we compare this structure to that of a previously developed inhibitor of CALP, iCAL36 (PDB ID: 4E34). In addition to per-forming traditional structural analysis, we compute the side-chain energy landscapes for each structure using the recently developedMARK*partition function approximation algorithm.4Analysis of these energy landscapes not only enables approximation of binding thermodynamics for these structural models of CALP:inhibitor binding, but also foregrounds important structural features and reveals dynamic features, both of which contribute to the comparatively efficient binding of kCAL01. The investigation of energy landscapes complements traditional analysis of the few low-energy conformations found in crystal structures, and provides information about the entire conformational ensemble that is accessible to a protein structure model. Finally, we compare the previously reported NMR-based design model ensemble for kCAL01 vs. the new crystal structure and show that, despite the notable differences between the CALP NMR model and crystal structure, many significant features are successfully captured in the design ensemble. This suggests not only that ensemble-based design captured thermodynamically significant features observedin vitro, but also that a design algorithm eschewing ensembles would likely miss the kCAL01 sequence entirely.Graphical TOC Entry

TYRO3 belongs to the TAM (TYRO3, AXL, and MER) receptor family, a unique subfamily of the receptor tyrosine kinases. Members of TAM family share the same ligand, growth arrest-specific 6, and protein S. Although the signal transduction pathways of TYRO3 have not been evaluated in detail, overexpression and activation of TYRO3 receptor tyrosine kinase have been reported to promote cell proliferation, survival, tumorigenesis, migration, invasion, epithelial-mesenchymal transition, or chemoresistance in several human cancers. Targeting TYRO3 could break the kinase signaling, stimulate antitumor immunity, reduce tumor cell survival, and regain drug sensitivity. To date, there is no specific TYRO3-targeted drug, the effectiveness of targeting TYRO3 in cancer is worthy of further investigations. In this review, we present an update on molecular biology of TYRO3, summarize the development of potential inhibitors of TAM family members, and provide new insights in TYRO3-targeted treatment.Impact statementCancer is among the leading causes of death worldwide. In 2016, 8.9 million people are estimated to have died from various forms of cancer. The current treatments, including surgery with chemotherapy and/or radiation therapy, are not effective enough to provide full protection from cancer, which highlights the need for developing novel therapy strategies. In this review, we summarize the molecular biology of a unique member of a subfamily of receptor tyrosine kinase, TYRO3 and discuss the new insights in TYRO3-targeted treatment for cancer therapy.

Background Colorectal carcinoma (CRC) is the third most common cancer in the world and also the third leading cause of cancer-related mortality in Taiwan. CRC tumorigenesis is a multistep process, starting from mutations causing loss of function of tumor suppressor genes, canonically demonstrated in adenomatous polyposis coli pathogenesis. Although many genes or chromosomal alterations have been shown to be involved in this process, there are still unrecognized molecular events within CRC tumorigenesis. Elucidating these mechanisms may help improve the management and treatment. Methods In this study, we aimed to identify copy number alteration of the smallest chromosomal regions that is significantly associated with sporadic CRC tumorigenesis using high-resolution array-based Comparative Genomic Hybridization (aCGH) and quantitative Polymerase chain reaction (qPCR). In addition, microsatellite instability assay and sequencing-based mutation assay were performed to illustrate the initiation event of CRC tumorigenesis. Results A total of 571 CRC patients were recruited and 377 paired CRC tissues from sporadic CRC cases were used to define the smallest regions with chromosome copy number changes. In addition, 198 colorectal polyps from 160 patients were also used to study the role of 20q13.33 gain in CRC tumorigenesis. We found that gain in 20q13.33 is the main chromosomal abnormalities in this patient population and counts 50.9 and 62.8% in CRC and colon polyps, respectively. Furthermore, APC and KRAS gene mutations were profiled simultaneously and co-analyzed with microsatellite instability and 20q13.33 gain in CRC patients. Our study showed that the frequency of 20q13.33 copy number gain was highest among all reported CRC mutations. Conclusion As APC or KRAS mutations are currently identified as the most important targets for CRC therapy, this study proposes that 20q13.33 copy number gain and the associated chromosomal genes function as promising biomarkers for both early stage detection and targeted therapy of sporadic CRCs in the future.

The short isoform of human TIAM2 has been shown to promote proliferation and invasion in various cancer cells. However, the roles of TIAM2S in immune cells in relation to tumor development have not been investigated. To characterize the effects of TIAM2S, we generated TIAM2S-overexpressing mouse lines and found that aged TIAM2S-transgenic (TIAM2S-TG) developed significantly higher occurrence of lymphocytic infiltration and tumorigenesis in various organs, including colon. In addition, TIAM2S-TG is more sensitized to AOM-induced colon tumor development, suggesting a priming effect toward tumorigenesis. In the light of our recent findings that TIAM2S functions as a novel regulator of cellular serotonin level, we found that serotonin, in addition to Cox2, is a unique inflammation marker presented in the colonic lesion sites in the aged TG animals. Furthermore, our results demonstrated that ectopic TIAM2S altered immunity via the expansion of T lymphocytes, this was especially pronounced in CD8+ T cells in combination with CXCL13/BCA-1 pro-inflammatory chemokine in the serum of TIAM2S-TG mice. Consequently, T lymphocytes and B cells were recruited to the lesion sites and stimulated IL-23/IL17A expression to form the tertiary lymphoid organs. Collectively, our research suggests that TIAM2S provokes a pro-inflammatory immune microenvironment permissive to colorectal tumorigenesis through the serotonin-induced immunomodulatory effects.

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.

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(H)H, 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.

Summary Background Acute respiratory distress syndrome (ARDS) is a lung inflammatory process caused mainly by sepsis. Most previous studies that identified genetic risks for ARDS focused on candidates with biological relevance. We aimed to identify novel genetic variants associated with ARDS susceptibility and to provide complementary functional evidence of their effect in gene regulation. Methods We did a case-control genome-wide association study (GWAS) of 1935 European individuals, using patients with sepsis-associated ARDS as cases and patients with sepsis without ARDS as controls. The discovery stage included 672 patients admitted into a network of Spanish intensive care units between January, 2002, and January, 2017. The replication stage comprised 1345 individuals from two independent datasets from the MESSI cohort study (Sep 22, 2008–Nov 30, 2017; USA) and the VISEP (April 1, 2003–June 30, 2005) and MAXSEP (Oct 1, 2007–March 31, 2010) trials of the SepNet study (Germany). Results from discovery and replication stages were meta-analysed to identify association signals. We then used RNA sequencing data from lung biopsies, in-silico analyses, and luciferase reporter assays to assess the functionallity of associated variants. Findings We identified a novel genome-wide significant association with sepsis-associated ARDS susceptibility (rs9508032, odds ratio [OR] 0·61, 95% CI 0·41–0·91, p=5·18 × 10−8) located within the Fms-related tyrosine kinase 1 (FLT1) gene, which encodes vascular endothelial growth factor receptor 1 (VEGFR-1). The region containing the sentinel variant and its best proxies acted as a silencer for the FLT1 promoter, and alleles with protective effects in ARDS further reduced promoter activity (p=0·0047). A literature mining of all previously described ARDS genes validated the association of vascular endothelial growth factor A (VEGFA; OR 0·55, 95% CI 0·41–0·73; p=4·69 × 10−5). Interpretation A common variant within the FLT1 gene is associated with sepsis-associated ARDS. Our findings support a role for the vascular endothelial growth factor signalling pathway in ARDS pathogenesis and identify VEGFR-1 as a potential therapeutic target. Funding Instituto de Salud Carlos III, European Regional Development Funds, Instituto Tecnologico y de Energias Renovables.

Background Specific common and rare single nucleotide variants (SNVs) increase the likelihood of developing sporadic idiopathic pulmonary fibrosis (IPF). We performed target-enriched sequencing on three loci previously identified by a genome-wide association study to gain a deeper understanding of the full spectrum of IPF genetic risk and performed a two-stage case–control association study. Methods A total of 1.7 Mb of DNA from 181 IPF patients was deep sequenced (>100×) across 11p15.5, 14q21.3 and 17q21.31 loci. Comparisons were performed against 501 unrelated controls and replication studies were assessed in 3968 subjects. Results 36 SNVs were associated with IPF susceptibility in the discovery stage (p, Deep sequencing of genome-wide association study hits identified novel low-frequency variants associated with IPF susceptibility. http://bit.ly/2IF4AT8

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(\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$nw^2 q^ { \frac { 3 } { 2 } w } $$ \end{document}) time and enumerates each additional conformation in merely O(\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$n \log q$$ \end{document}) 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.

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.

Background Infratentorial siderosis (iSS) is a progressive degenerative disorder targeting primarily the cerebellum and cranial nerve eighth; therefore, progressive ataxia and its neuro-otological findings are common. Toxicity from hemosiderin involves selectively vulnerable neurons and glia in these posterior fossa structures. Other neurologic findings may be present, though our focus relates to the cochlea-vestibular cerebellar involvement. Radiographic evidence of siderosis may be the result of recurrent, albeit covert bleeding in the subarachnoid space, or the consequence of an overt post-traumatic or aneurysmal subarachnoid hemorrhage (SAH). The radiographic iSS appearance is identical regardless of the SAH cause. A recent study provides compelling evidence to search and correct possible hemorrhage sources in the spinal canal. The removal of residual existing hemosiderin deposits that may potentially cause clinical symptoms remains as a major therapeutic challenge. Methods We reviewed large data sources and identified salient papers that describe the pathogenesis, clinical and neurotologic manifestations, and the radiographic features of iSS. Results The epidemiology of iSS is unknown. In a recent series, clinically evident iSS was associated with recurrent SAH; by contrast, in a follow-up period ranging from weeks up to 11 years after a monophasic episode of SAH, radiographic siderosis was clinically silent. However, the post-aneurysmal or post-trauma SAH sample size in this single study was small and their observation period relatively short; moreover, the burden of intraneuronal hemosiderin is likely greater with recurrent SAH. There are a few reports of late iSS, several decades after traumatic SAH. A recent report found subjective hearing loss in aneurysmal SAH individuals with radiographic siderosis. Only in recent years, it is safe to perform magnetic resonance imaging (MRI) in post-aneurysmal SAH, because of the introduction of titanium, MRI-compatible aneurysm clips. Conclusion iSS can be associated with significant neurotologic and cerebellar morbidity; the recurrent SAH variant is frequently clinically symptomatic, has a shorter latency and greater neurotologic disability. In these cases, a thorough search and management of a covert source of bleeding may stop clinical progression. The frequency and clinical course of radiographic iSS after traumatic and post-aneurysmal SAH is largely unknown. Detection of radiographic iSS after trauma or aneurysm bleeding suggests that the slower clinical course could benefit from an effective intervention if it became available. The use of cochlear implants is a valid alternative with advanced hearing impairment.

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.

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 10(5)-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.

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., Author summary 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.

Current dynamic programming protein design algorithms that exploit the optimal substructure induced by sparse energy functions compute only the Global Minimum Energy Conformation (GMEC). This disproportionately favors the sequence of a single, static conformation and overlooks better sequences with multiple low-energy conformations. 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(\(nw^2q^{\frac{3}{2}w}\)) time, and enumerates each additional conformation in O(\(n\log q\)) time. BWM\(^*\) outperforms the classical search algorithm A\(^*\) in 49 of 67 protein design problems, computing the full ensemble or a close approximation up to two orders of magnitude faster. Performance of BWM\(^*\) can be predicted cheaply beforehand, allowing selection of the most efficient algorithm for each design problem.

Most protein design algorithms assume that the conformational space of proteins is discrete and that their energy is residue-pairwise, i.e., 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 additional 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 design algorithms like 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 non-pairwise energy functions to an arbitrary level of accuracy using a discrete matrix of effective residue interaction energies. We show using 47 design calculation test cases that LUTE provides a dramatic speedup in both single-state and multistate continuously flexible designs.