Exploiting Temporal Collateral Sensitivity in Tumor Clonal Evolution.

The prevailing approach to addressing secondary drug resistance in cancer focuses on treating the resistance mechanisms at relapse. However, the dynamic nature of clonal evolution, along with potential fitness costs and cost compensations, may present exploitable vulnerabilities-a notion that we term "temporal collateral sensitivity." Using a combined pharmacological screen and drug resistance selection approach in a murine model of Ph(+) acute lymphoblastic leukemia, we indeed find that temporal and/or persistent collateral sensitivity to non-classical BCR-ABL1 drugs arises in emergent tumor subpopulations during the evolution of resistance toward initial treatment with BCR-ABL1-targeted inhibitors. We determined the sensitization mechanism via genotypic, phenotypic, signaling, and binding measurements in combination with computational models and demonstrated significant overall survival extension in mice. Additional stochastic mathematical models and small-molecule screens extended our insights, indicating the value of focusing on evolutionary trajectories and pharmacological profiles to identify new strategies to treat dynamic tumor vulnerabilities.

Machine Learning Identifies Chemical Characteristics That Promote Enzyme Catalysis.

Despite tremendous progress in understanding and engineering enzymes, knowledge of how enzyme structures and their dynamics induce observed catalytic properties is incomplete, and capabilities to engineer enzymes fall far short of industrial needs. Here, we investigate the structural and dynamic drivers of enzyme catalysis for the rate-limiting step of the industrially important enzyme ketol-acid reductoisomerase (KARI) and identify a region of the conformational space of the bound enzyme-substrate complex that, when populated, leads to large increases in reactivity. We apply computational statistical mechanical methods that implement transition interface sampling to simulate the kinetics of the reaction and combine this with machine learning techniques from artificial intelligence to select features relevant to reactivity and to build predictive models for reactive trajectories. We find that conformational descriptors alone, without the need for dynamic ones, are sufficient to predict reactivity with greater than 85% accuracy (90% AUC). Key descriptors distinguishing reactive from almost-reactive trajectories quantify substrate conformation, substrate bond polarization, and metal coordination geometry and suggest their role in promoting substrate reactivity. Moreover, trajectories constrained to visit a region of the reactant well, separated from the rest by a simple hyperplane defined by ten conformational parameters, show increases in computed reactivity by many orders of magnitude. This study provides evidence for the existence of reactivity promoting regions within the conformational space of the enzyme-substrate complex and develops methodology for identifying and validating these particularly reactive regions of phase space. We suggest that identification of reactivity promoting regions and re-engineering enzymes to preferentially populate them may lead to significant rate enhancements.

Rational design of thiolase substrate specificity for metabolic engineering applications.

Metabolic engineering efforts require enzymes that are both highly active and specific toward the synthesis of a desired output product to be commercially feasible. The 3-hydroxyacid (3HA) pathway, also known as the reverse ß-oxidation or coenzyme-A-dependent chain-elongation pathway, can allow for the synthesis of dozens of useful compounds of various chain lengths and functionalities. However, this pathway suffers from byproduct formation, which lowers the yields of the desired longer chain products, as well as increases downstream separation costs. The thiolase enzyme catalyzes the first reaction in this pathway, and its substrate specificity at each of its two catalytic steps sets the chain length and composition of the chemical scaffold upon which the other downstream enzymes act. However, there have been few attempts reported in the literature to rationally engineer thiolase substrate specificity. In this study, we present a model-guided, rational design study of ordered substrate binding applied to two biosynthetic thiolases, with the goal of increasing the ratio of C6/C4 products formed by the 3HA pathway, 3-hydroxy-hexanoic acid and 3-hydroxybutyric acid. We identify thiolase mutants that result in nearly 10-fold increases in C6/C4 selectivity. Our findings can extend to other pathways that employ the thiolase for chain elongation, as well as expand our knowledge of sequence-structure-function relationship for this important class of enzymes.

Strong Enrichment of Aromatic Residues in Binding Sites from a Charge-neutralized Hyperthermostable Sso7d Scaffold Library.

The Sso7d protein from the hyperthermophilic archaeon Sulfolobus solfataricus is an attractive binding scaffold because of its small size (7 kDa), high thermal stability (Tm of 98 °C), and absence of cysteines and glycosylation sites. However, as a DNA-binding protein, Sso7d is highly positively charged, introducing a strong specificity constraint for binding epitopes and leading to nonspecific interaction with mammalian cell membranes. In the present study, we report charge-neutralized variants of Sso7d that maintain high thermal stability. Yeast-displayed libraries that were based on this reduced charge Sso7d (rcSso7d) scaffold yielded binders with low nanomolar affinities against mouse serum albumin and several epitopes on human epidermal growth factor receptor. Importantly, starting from a charge-neutralized scaffold facilitated evolutionary adaptation of binders to differentially charged epitopes on mouse serum albumin and human epidermal growth factor receptor, respectively. Interestingly, the distribution of amino acids in the small and rigid binding surface of enriched rcSso7d-based binders is very different from that generally found in more flexible antibody complementarity-determining region loops but resembles the composition of antibody-binding energetic hot spots. Particularly striking was a strong enrichment of the aromatic residues Trp, Tyr, and Phe in rcSso7d-based binders. This suggests that the rigidity and small size of this scaffold determines the unusual amino acid composition of its binding sites, mimicking the energetic core of antibody paratopes. Despite the high frequency of aromatic residues, these rcSso7d-based binders are highly expressed, thermostable, and monomeric, suggesting that the hyperstability of the starting scaffold and the rigidness of the binding surface confer a high tolerance to mutation.

Symmetric signaling by an asymmetric 1 erythropoietin: 2 erythropoietin receptor complex.

Via sites 1 and 2, erythropoietin binds asymmetrically to two identical receptor monomers, although it is unclear how asymmetry affects receptor activation and signaling. Here we report the design and validation of two mutant erythropoietin receptors that probe the role of individual members of the receptor dimer by selectively binding either site 1 or site 2 on erythropoietin. Ba/F3 cells expressing either mutant receptor do not respond to erythropoietin, but cells co-expressing both receptors respond to erythropoietin by proliferation and activation of the JAK2-Stat5 pathway. A truncated receptor with only one cytosolic tyrosine (Y343) is sufficient for signaling in response to erythropoietin, regardless of the monomer on which it is located. Similarly, only one receptor in the dimer needs a juxtamembrane hydrophobic L253 or W258 residue, essential for JAK2 activation. We conclude that despite asymmetry in the ligand-receptor interaction, both sides are competent for signaling, and appear to signal equally.

Intramolecular Hydrogen Bonding Restricts Gd-Aqua-Ligand Dynamics.

Aqua ligands can undergo rapid internal rotation about the M-O bond. For magnetic resonance contrast agents, this rotation results in diminished relaxivity. Herein, we show that an intramolecular hydrogen bond to the aqua ligand can reduce this internal rotation and increase relaxivity. Molecular modeling was used to design a series of four Gd complexes capable of forming an intramolecular H-bond to the coordinated water ligand, and these complexes had anomalously high relaxivities compared to similar complexes lacking a H-bond acceptor. Molecular dynamics simulations supported the formation of a stable intramolecular H-bond, while alternative hypotheses that could explain the higher relaxivity were systematically ruled out. Intramolecular H-bonding represents a useful strategy to limit internal water rotational motion and increase relaxivity of Gd complexes.

Molecular mechanisms and design principles for promiscuous inhibitors to avoid drug resistance: lessons learned from HIV-1 protease inhibition.

Molecular recognition is central to biology and ranges from highly selective to broadly promiscuous. The ability to modulate specificity at will is particularly important for drug development, and discovery of mechanisms contributing to binding specificity is crucial for our basic understanding of biology and for applications in health care. In this study, we used computational molecular design to create a large dataset of diverse small molecules with a range of binding specificities. We then performed structural, energetic, and statistical analysis on the dataset to study molecular mechanisms of achieving specificity goals. The work was done in the context of HIV-1 protease inhibition and the molecular designs targeted a panel of wild-type and drug-resistant mutant HIV-1 protease structures. The analysis focused on mechanisms for promiscuous binding to bind robustly even to resistance mutants. Broadly binding inhibitors tended to be smaller in size, more flexible in chemical structure, and more hydrophobic in nature compared to highly selective ones. Furthermore, structural and energetic analyses illustrated mechanisms by which flexible inhibitors achieved binding; we found ligand conformational adaptation near mutation sites and structural plasticity in targets through torsional flips of asymmetric functional groups to form alternative, compensatory packing interactions or hydrogen bonds. As no inhibitor bound to all variants, we designed small cocktails of inhibitors to do so and discovered that they often jointly covered the target set through mechanistic complementarity. Furthermore, using structural plasticity observed in experiments, and potentially in simulations, is suggested to be a viable means of designing adaptive inhibitors that are promiscuous binders.

Combined model of intrinsic and extrinsic variability for computational network design with application to synthetic biology.

Biological systems are inherently variable, with their dynamics influenced by intrinsic and extrinsic sources. These systems are often only partially characterized, with large uncertainties about specific sources of extrinsic variability and biochemical properties. Moreover, it is not yet well understood how different sources of variability combine and affect biological systems in concert. To successfully design biomedical therapies or synthetic circuits with robust performance, it is crucial to account for uncertainty and effects of variability. Here we introduce an efficient modeling and simulation framework to study systems that are simultaneously subject to multiple sources of variability, and apply it to make design decisions on small genetic networks that play a role of basic design elements of synthetic circuits. Specifically, the framework was used to explore the effect of transcriptional and post-transcriptional autoregulation on fluctuations in protein expression in simple genetic networks. We found that autoregulation could either suppress or increase the output variability, depending on specific noise sources and network parameters. We showed that transcriptional autoregulation was more successful than post-transcriptional in suppressing variability across a wide range of intrinsic and extrinsic magnitudes and sources. We derived the following design principles to guide the design of circuits that best suppress variability: (i) high protein cooperativity and low miRNA cooperativity, (ii) imperfect complementarity between miRNA and mRNA was preferred to perfect complementarity, and (iii) correlated expression of mRNA and miRNA--for example, on the same transcript--was best for suppression of protein variability. Results further showed that correlations in kinetic parameters between cells affected the ability to suppress variability, and that variability in transient states did not necessarily follow the same principles as variability in the steady state. Our model and findings provide a general framework to guide design principles in synthetic biology.

Substrate Turnover Dynamics Guide Ketol-Acid Reductoisomerase Redesign for Increased Specific Activity.

The task of adapting enzymes for specific applications is often hampered by our incomplete ability to tune and tailor catalytic functions, particularly when seeking increased activity. Here, we develop and demonstrate a rational approach to address this challenge, applied to ketol-acid reductoisomerase (KARI), which has uses in industrial-scale isobutanol production. While traditional structure-based computational enzyme redesign strategies typically focus on the enzyme-bound ground state (GS) and transition state (TS), we postulated that additionally treating the underlying dynamics of complete turnover events that connect and pass through both states could further elucidate the structural properties affecting catalysis and help identify mutations that lead to increased catalytic activity. To examine the dynamics of substrate conversion with atomistic detail, we adapted and applied computational methods based on path sampling techniques to gather thousands of QM/MM simulations of attempted substrate turnover events by KARI: both productive (reactive) and unproductive (nonreactive) attempts. From these data, machine learning models were constructed and used to identify specific conformational features (interatomic distances, angles, and torsions) associated with successful, productive catalysis. Multistate protein redesign techniques were then used to select mutations that stabilized reactive-like structures over nonreactive-like ones while also meeting additional criteria consistent with enhanced specific activity. This procedure resulted in eight high-confidence enzyme mutants with a significant improvement in calculated specific activity relative to wild type (WT), with the fastest variant's increase in calculated k cat being (2 ± 1) × 104-fold. Collectively, these results suggest that introducing mutations designed to increase the population of reaction-promoting conformations of the enzyme-substrate complex before it reaches the barrier can provide an effective approach to engineering improved enzyme catalysts.

Combining metabolic and protein engineering of a terpenoid biosynthetic pathway for overproduction and selectivity control.

A common strategy of metabolic engineering is to increase the endogenous supply of precursor metabolites to improve pathway productivity. The ability to further enhance heterologous production of a desired compound may be limited by the inherent capacity of the imported pathway to accommodate high precursor supply. Here, we present engineered diterpenoid biosynthesis as a case where insufficient downstream pathway capacity limits high-level levopimaradiene production in Escherichia coli. To increase levopimaradiene synthesis, we amplified the flux toward isopentenyl diphosphate and dimethylallyl diphosphate precursors and reprogrammed the rate-limiting downstream pathway by generating combinatorial mutations in geranylgeranyl diphosphate synthase and levopimaradiene synthase. The mutant library contained pathway variants that not only increased diterpenoid production but also tuned the selectivity toward levopimaradiene. The most productive pathway, combining precursor flux amplification and mutant synthases, conferred approximately 2,600-fold increase in levopimaradiene levels. A maximum titer of approximately 700 mg/L was subsequently obtained by cultivation in a bench-scale bioreactor. The present study highlights the importance of engineering proteins along with pathways as a key strategy in achieving microbial biosynthesis and overproduction of pharmaceutical and chemical products.

Delineation of lipopolysaccharide (LPS)-binding sites on hemoglobin: from in silico predictions to biophysical characterization.

Hemoglobin (Hb) functions as a frontline defense molecule during infection by hemolytic microbes. Binding to LPS induces structural changes in cell-free Hb, which activates the redox activity of the protein for the generation of microbicidal free radicals. Although the interaction between Hb and LPS has implications for innate immune defense, the precise LPS-interaction sites on Hb remain unknown. Using surface plasmon resonance, we found that both the Hb α and ß subunits possess high affinity LPS-binding sites, with K(D) in the nanomolar range. In silico analysis of Hb including phospho-group binding site prediction, structure-based sequence comparison, and docking to model the protein-ligand interactions showed that Hb possesses evolutionarily conserved surface cationic patches that could function as potential LPS-binding sites. Synthetic Hb peptides harboring predicted LPS-binding sites served to validate the computational predictions. Surface plasmon resonance analysis differentiated LPS-binding peptides from non-binders. Binding of the peptides to lipid A was further substantiated by a fluorescent probe displacement assay. The LPS-binding peptides effectively neutralized the endotoxicity of LPS in vitro. Additionally, peptide B59 spanning residues 59-95 of Hbß attached to the surface of Gram-negative bacteria as shown by flow cytometry and visualized by immunogold-labeled scanning electron microscopy. Site-directed mutagenesis of the Hb subunits further confirmed the function of the predicted residues in binding to LPS. In summary, the integration of computational predictions and biophysical characterization has enabled delineation of multiple LPS-binding hot spots on the Hb molecule.

Exploring the gap between dynamic and constraint-based models of metabolism.

Systems biology provides new approaches for metabolic engineering through the development of models and methods for simulation and optimization of microbial metabolism. Here we explore the relationship between two modeling frameworks in common use namely, dynamic models with kinetic rate laws and constraint-based flux models. We compare and analyze dynamic and constraint-based formulations of the same model of the central carbon metabolism of Escherichia coli. Our results show that, if unconstrained, the space of steady states described by both formulations is the same. However, the imposition of parameter-range constraints can be mapped into kinetically feasible regions of the solution space for the dynamic formulation that is not readily transferable to the constraint-based formulation. Therefore, with partial kinetic parameter knowledge, dynamic models can be used to generate constraints that reduce the solution space below that identified by constraint-based models, eliminating infeasible solutions and increasing the accuracy of simulation and optimization methods.

Distinct mechanisms act in concert to mediate cell cycle arrest.

In response to DNA damage, cells arrest at specific stages in the cell cycle. This arrest must fulfill at least 3 requirements: it must be activated promptly; it must be sustained as long as damage is present to prevent loss of genomic information; and after the arrest, cells must re-enter into the appropriate cell cycle phase to ensure proper ploidy. Multiple molecular mechanisms capable of arresting the cell cycle have been identified in mammalian cells; however, it is unknown whether each mechanism meets all 3 requirements or whether they act together to confer specific functions to the arrest. To address this question, we integrated mathematical models describing the cell cycle and the DNA damage signaling networks and tested the contributions of each mechanism to cell cycle arrest and re-entry. Predictions from this model were then tested with quantitative experiments to identify the combined action of arrest mechanisms in irradiated cells. We find that different arrest mechanisms serve indispensable roles in the proper cellular response to DNA damage over time: p53-independent cyclin inactivation confers immediate arrest, whereas p53-dependent cyclin downregulation allows this arrest to be sustained. Additionally, p21-mediated inhibition of cyclin-dependent kinase activity is indispensable for preventing improper cell cycle re-entry and endoreduplication. This work shows that in a complex signaling network, seemingly redundant mechanisms, acting in a concerted fashion, can achieve a specific cellular outcome.

Modelling the impact of nucleolin expression level on the activity of F3 peptide-targeted pH-sensitive pegylated liposomes containing doxorubicin.

Strategies targeting nucleolin have enabled a significant improvement in intracellular bioavailability of their encapsulated payloads. In this respect, assessment of the impact of target cell heterogeneity and nucleolin homology across species (structurally and functionally) is of major importance. This work also aimed at mathematically modelling the nucleolin expression levels at the cell membrane, binding and internalization of pH-sensitive pegylated liposomes encapsulating doxorubicin and functionalized with the nucleolin-binding F3 peptide (PEGASEMP), and resulting cytotoxicity against cancer cells from mouse, rat, canine, and human origin. Herein, it was shown that nucleolin expression levels were not a limitation on the continuous internalization of F3 peptide-targeted liposomes, despite the saturable nature of the binding mechanism. Modeling enabled the prediction of nucleolin-mediated total doxorubicin exposure provided by the experimental settings of the assessment of PEGASEMP's impact on cell death. The former increased proportionally with nucleolin-binding sites, a measure relevant for patient stratification. This pattern of variation was observed for the resulting cell death in nonsaturating conditions, depending on the cancer cell sensitivity to doxorubicin. This approach differs from standard determination of cytotoxic concentrations, which normally report values of incubation doses rather than the actual intracellular bioactive drug exposure. Importantly, in the context of development of nucleolin-based targeted drug delivery, the structural nucleolin homology (higher than 84%) and functional similarity across species presented herein, emphasized the potential to use toxicological data and other metrics from lower species to infer the dose for a first-in-human trial.

Evaluating the substrate-envelope hypothesis: structural analysis of novel HIV-1 protease inhibitors designed to be robust against drug resistance.

Drug resistance mutations in HIV-1 protease selectively alter inhibitor binding without significantly affecting substrate recognition and cleavage. This alteration in molecular recognition led us to develop the substrate-envelope hypothesis which predicts that HIV-1 protease inhibitors that fit within the overlapping consensus volume of the substrates are less likely to be susceptible to drug-resistant mutations, as a mutation impacting such inhibitors would simultaneously impact the processing of substrates. To evaluate this hypothesis, over 130 HIV-1 protease inhibitors were designed and synthesized using three different approaches with and without substrate-envelope constraints. A subset of 16 representative inhibitors with binding affinities to wild-type protease ranging from 58 nM to 0.8 pM was chosen for crystallographic analysis. The inhibitor-protease complexes revealed that tightly binding inhibitors (at the picomolar level of affinity) appear to "lock" into the protease active site by forming hydrogen bonds to particular active-site residues. Both this hydrogen bonding pattern and subtle variations in protein-ligand van der Waals interactions distinguish nanomolar from picomolar inhibitors. In general, inhibitors that fit within the substrate envelope, regardless of whether they are picomolar or nanomolar, have flatter profiles with respect to drug-resistant protease variants than inhibitors that protrude beyond the substrate envelope; this provides a strong rationale for incorporating substrate-envelope constraints into structure-based design strategies to develop new HIV-1 protease inhibitors.

Aglycosylated immunoglobulin G1 variants productively engage activating Fc receptors.

Immunoglobulin G plays a vital role in adaptive immunity and antibody-based therapy through engagement of its Fc region by the Fc gamma receptors (Fc gammaRs) on immune cells. In addition to specific protein-protein contacts, N-linked glycosylation of the IgG Fc has been thought to be essential for the recognition of Fc by Fc gammaR. This requirement for the N-linked glycan has limited biomanufacture of therapeutic antibodies by restricting it to mammalian expression systems. We report here aglycosylated Fc domain variants that maintain engagement to Fc gammaRs, both in vitro and in vivo, demonstrating that Fc glycosylation is not strictly required for the activation of immune cells by IgG. These variants provide insight into how the N-linked glycan is used biologically in the recognition of Fc by Fc gammaRs, as well as represent a step toward the production in alternative expression systems of antibody-based therapeutics capable of eliciting immune effector functions.

Entropy of Two-Molecule Correlated Translational-Rotational Motions Using the kth Nearest Neighbor Method.

The entropy associated with rotations, translations, and their coupled motions provides an important contribution to the free energy of many physicochemical processes such as association and solvation. The kth nearest neighbor method, which offers a convenient way to estimate the entropy in high-dimensional spaces, has been previously applied for translational-rotational entropy estimation. Here, we explore the possibility of extending the kth nearest neighbor method to the computation of the entropy of correlated translation-rotations of two molecules, i.e., in the product space of two translation-rotations, both referred to the same independent reference system, which is relevant for all cases in which the correlated translational-rotational motion of more than two molecules is involved. Numerical tests show that, albeit the relatively high dimensionality (12) of the space, the kth nearest neighbor approach provides an accurate estimate for the entropy of two correlated translational-rotational motions, even when computed from a limited number of samples.

MIST: Maximum Information Spanning Trees for dimension reduction of biological data sets.

MOTIVATION: The study of complex biological relationships is aided by large and high-dimensional data sets whose analysis often involves dimension reduction to highlight representative or informative directions of variation. In principle, information theory provides a general framework for quantifying complex statistical relationships for dimension reduction. Unfortunately, direct estimation of high-dimensional information theoretic quantities, such as entropy and mutual information (MI), is often unreliable given the relatively small sample sizes available for biological problems. Here, we develop and evaluate a hierarchy of approximations for high-dimensional information theoretic statistics from associated low-order terms, which can be more reliably estimated from limited samples. Due to a relationship between this metric and the minimum spanning tree over a graph representation of the system, we refer to these approximations as MIST (Maximum Information Spanning Trees). RESULTS: The MIST approximations are examined in the context of synthetic networks with analytically computable entropies and using experimental gene expression data as a basis for the classification of multiple cancer types. The approximations result in significantly more accurate estimates of entropy and MI, and also correlate better with biological classification error than direct estimation and another low-order approximation, minimum-redundancy-maximum-relevance (mRMR). AVAILABILITY: Software to compute the entropy approximations described here is available as Supplementary Material. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Computational design of antibody-affinity improvement beyond in vivo maturation.

Antibodies are used extensively in diagnostics and as therapeutic agents. Achieving high-affinity binding is important for expanding detection limits, extending dissociation half-times, decreasing drug dosages and increasing drug efficacy. However, antibody-affinity maturation in vivo often fails to produce antibody drugs of the targeted potency, making further affinity maturation in vitro by directed evolution or computational design necessary. Here we present an iterative computational design procedure that focuses on electrostatic binding contributions and single mutants. By combining multiple designed mutations, a tenfold affinity improvement to 52 pM was engineered into the anti-epidermal growth factor receptor drug cetuximab (Erbitux), and a 140-fold improvement in affinity to 30 pM was obtained for the anti-lysozyme model antibody D44.1. The generality of the methods was further demonstrated through identification of known affinity-enhancing mutations in the therapeutic antibody bevacizumab (Avastin) and the model anti-fluorescein antibody 4-4-20. These results demonstrate computational capabilities for enhancing and accelerating the development of protein reagents and therapeutics.

Evaluation of an inverse molecular design algorithm in a model binding site.

Computational molecular design is a useful tool in modern drug discovery. Virtual screening is an approach that docks and then scores individual members of compound libraries. In contrast to this forward approach, inverse approaches construct compounds from fragments, such that the computed affinity, or a combination of relevant properties, is optimized. We have recently developed a new inverse approach to drug design based on the dead-end elimination and A* algorithms employing a physical potential function. This approach has been applied to combinatorially constructed libraries of small-molecule ligands to design high-affinity HIV-1 protease inhibitors (Altman et al., J Am Chem Soc 2008;130:6099-6013). Here we have evaluated the new method using the well-studied W191G mutant of cytochrome c peroxidase. This mutant possesses a charged binding pocket and has been used to evaluate other design approaches. The results show that overall the new inverse approach does an excellent job of separating binders from nonbinders. For a few individual cases, scoring inaccuracies led to false positives. The majority of these involve erroneous solvation energy estimation for charged amines, anilinium ions, and phenols, which has been observed previously for a variety of scoring algorithms. Interestingly, although inverse approaches are generally expected to identify some but not all binders in a library, due to limited conformational searching, these results show excellent coverage of the known binders while still showing strong discrimination of the nonbinders.