MEnTaT: A machine-learning approach for the identification of mutations to increase protein stability.

Enhancing protein thermal stability is important for biomedical and industrial applications as well as in the research laboratory. Here, we describe a simple machine-learning method which identifies amino acid substitutions that contribute to thermal stability based on comparison of the amino acid sequences of homologous proteins derived from bacteria that grow at different temperatures. A key feature of the method is that it compares the sequences based not simply on the amino acid identity, but rather on the structural and physicochemical properties of the side chain. The method accurately identified stabilizing substitutions in three well-studied systems and was validated prospectively by experimentally testing predicted stabilizing substitutions in a polyamine oxidase. In each case, the method outperformed the widely used bioinformatic consensus approach. The method can also provide insight into fundamental aspects of protein structure, for example, by identifying how many sequence positions in a given protein are relevant to temperature adaptation.

A conserved core region of the scaffold NEMO is essential for signal-induced conformational change and liquid-liquid phase separation.

Scaffold proteins help mediate interactions between protein partners, often to optimize intracellular signaling. Herein, we use comparative, biochemical, biophysical, molecular, and cellular approaches to investigate how the scaffold protein NEMO contributes to signaling in the NF-κB pathway. Comparison of NEMO and the related protein optineurin from a variety of evolutionarily distant organisms revealed that a central region of NEMO, called the Intervening Domain (IVD), is conserved between NEMO and optineurin. Previous studies have shown that this central core region of the IVD is required for cytokine-induced activation of IκB kinase (IKK). We show that the analogous region of optineurin can functionally replace the core region of the NEMO IVD. We also show that an intact IVD is required for the formation of disulfide-bonded dimers of NEMO. Moreover, inactivating mutations in this core region abrogate the ability of NEMO to form ubiquitin-induced liquid-liquid phase separation droplets in vitro and signal-induced puncta in vivo. Thermal and chemical denaturation studies of truncated NEMO variants indicate that the IVD, while not intrinsically destabilizing, can reduce the stability of surrounding regions of NEMO due to the conflicting structural demands imparted on this region by flanking upstream and downstream domains. This conformational strain in the IVD mediates allosteric communication between the N- and C-terminal regions of NEMO. Overall, these results support a model in which the IVD of NEMO participates in signal-induced activation of the IKK/NF-κB pathway by acting as a mediator of conformational changes in NEMO.

The anti-Müllerian hormone prodomain is displaced from the hormone/prodomain complex upon bivalent binding to the hormone receptor.

Noncovalent complexes of transforming growth factor-ß family growth/differentiation factors with their prodomains are classified as latent or active, depending on whether the complexes can bind their respective receptors. For the anti-Müllerian hormone (AMH), the hormone-prodomain complex is active, and the prodomain is displaced upon binding to its type II receptor, AMH receptor type-2 (AMHR2), on the cell surface. However, the mechanism by which this displacement occurs is unclear. Here, we used ELISA assays to measure the dependence of prodomain displacement on AMH concentration and analyzed results with respect to the behavior expected for reversible binding in combination with ligand-induced receptor dimerization. We found that, in solution, the prodomain has a high affinity for the growth factor (GF) (Kd = 0.4 pM). Binding of the AMH complex to a single AMHR2 molecule does not affect this Kd and does not induce prodomain displacement, indicating that the receptor binding site in the AMH complex is fully accessible to AMHR2. However, recruitment of a second AMHR2 molecule to bind the ligand bivalently leads to a 1000-fold increase in the Kd for the AMH complex, resulting in rapid release of the prodomain. Displacement occurs only if the AMHR2 is presented on a surface, indicating that prodomain displacement is caused by a conformational change in the GF induced by bivalent binding to AMHR2. In addition, we demonstrate that the bone morphogenetic protein 7 prodomain is displaced from the complex with its GF by a similar process, suggesting that this may represent a general mechanism for receptor-mediated prodomain displacement in this ligand family.

High Accuracy Prediction of PROTAC Complex Structures.

The design of PROteolysis-TArgeting Chimeras (PROTACs) requires bringing an E3 ligase into proximity with a target protein to modulate the concentration of the latter through its ubiquitination and degradation. Here, we present a method for generating high-accuracy structural models of E3 ligase-PROTAC-target protein ternary complexes. The method is dependent on two computational innovations: adding a "silent" convolution term to an efficient protein-protein docking program to eliminate protein poses that do not have acceptable linker conformations and clustering models of multiple PROTACs that use the same E3 ligase and target the same protein. Results show that the largest consensus clusters always have high predictive accuracy and that the ensemble of models can be used to predict the dissociation rate and cooperativity of the ternary complex that relate to the degrading activity of the PROTAC. The method is demonstrated by applications to known PROTAC structures and a blind test involving PROTACs against BRAF mutant V600E. The results confirm that PROTACs function by stabilizing a favorable interaction between the E3 ligase and the target protein but do not necessarily exploit the most energetically favorable geometry for interaction between the proteins.

Recapitulating the Binding Affinity of Nrf2 for KEAP1 in a Cyclic Heptapeptide, Guided by NMR, X-ray Crystallography, and Machine Learning.

Macrocycles, including macrocyclic peptides, have shown promise for targeting challenging protein-protein interactions (PPIs). One PPI of high interest is between Kelch-like ECH-Associated Protein-1 (KEAP1) and Nuclear Factor (Erythroid-derived 2)-like 2 (Nrf2). Guided by X-ray crystallography, NMR, modeling, and machine learning, we show that the full 20 nM binding affinity of Nrf2 for KEAP1 can be recapitulated in a cyclic 7-mer peptide, c[(D)-ß-homoAla-DPETGE]. This compound was identified from the Nrf2-derived linear peptide GDEETGE (KD = 4.3 µM) solely by optimizing the conformation of the cyclic compound, without changing any KEAP1 interacting residue. X-ray crystal structures were determined for each linear and cyclic peptide variant bound to KEAP1. Despite large variations in affinity, no obvious differences in the conformation of the peptide binding residues or in the interactions they made with KEAP1 were observed. However, analysis of the X-ray structures by machine learning showed that locations of strain in the bound ligand could be identified through patterns of subangstrom distortions from the geometry observed for unstrained linear peptides. We show that optimizing the cyclic peptide affinity was driven partly through conformational preorganization associated with a proline substitution at position 78 and with the geometry of the noninteracting residue Asp77 and partly by decreasing strain in the ETGE motif itself. This approach may have utility in dissecting the trade-off between conformational preorganization and strain in other ligand-receptor systems. We also identify a pair of conserved hydrophobic residues flanking the core DxETGE motif which play a conformational role in facilitating the high-affinity binding of Nrf2 to KEAP1.

Exploring the structural origins of cryptic sites on proteins.

Molecular dynamics (MD) simulations of proteins reveal the existence of many transient surface pockets; however, the factors determining what small subset of these represent druggable or functionally relevant ligand binding sites, called "cryptic sites," are not understood. Here, we examine multiple X-ray structures for a set of proteins with validated cryptic sites, using the computational hot spot identification tool FTMap. The results show that cryptic sites in ligand-free structures generally have a strong binding energy hot spot very close by. As expected, regions around cryptic sites exhibit above-average flexibility, and close to 50% of the proteins studied here have unbound structures that could accommodate the ligand without clashes. Nevertheless, the strong hot spot neighboring each cryptic site is almost always exploited by the bound ligand, suggesting that binding may frequently involve an induced fit component. We additionally evaluated the structural basis for cryptic site formation, by comparing unbound to bound structures. Cryptic sites are most frequently occluded in the unbound structure by intrusion of loops (22.5%), side chains (19.4%), or in some cases entire helices (5.4%), but motions that create sites that are too open can also eliminate pockets (19.4%). The flexibility of cryptic sites frequently leads to missing side chains or loops (12%) that are particularly evident in low resolution crystal structures. An interesting observation is that cryptic sites formed solely by the movement of side chains, or of backbone segments with fewer than five residues, result only in low affinity binding sites with limited use for drug discovery.

Interaction Energetics and Druggability of the Protein-Protein Interaction between Kelch-like ECH-Associated Protein 1 (KEAP1) and Nuclear Factor Erythroid 2 Like 2 (Nrf2).

Development of small molecule inhibitors of protein-protein interactions (PPIs) is hampered by our poor understanding of the druggability of PPI target sites. Here, we describe the combined application of alanine-scanning mutagenesis, fragment screening, and FTMap computational hot spot mapping to evaluate the energetics and druggability of the highly charged PPI interface between Kelch-like ECH-associated protein 1 (KEAP1) and nuclear factor erythroid 2 like 2 (Nrf2), an important drug target. FTMap identifies four binding energy hot spots at the active site. Only two of these are exploited by Nrf2, which alanine scanning of both proteins shows to bind primarily through E79 and E82 interacting with KEAP1 residues S363, R380, R415, R483, and S508. We identify fragment hits and obtain X-ray complex structures for three fragments via crystal soaking using a new crystal form of KEAP1. Combining these results provides a comprehensive and quantitative picture of the origins of binding energy at the interface. Our findings additionally reveal non-native interactions that might be exploited in the design of uncharged synthetic ligands to occupy the same site on KEAP1 that has evolved to bind the highly charged DEETGE binding loop of Nrf2. These include π-stacking with KEAP1 Y525 and interactions at an FTMap-identified hot spot deep in the binding site. Finally, we discuss how the complementary information provided by alanine-scanning mutagenesis, fragment screening, and computational hot spot mapping can be integrated to more comprehensively evaluate PPI druggability.

Benchmark Sets for Binding Hot Spot Identification in Fragment-Based Ligand Discovery.

Binding hot spots are regions of proteins that, due to their potentially high contribution to the binding free energy, have high propensity to bind small molecules. We present benchmark sets for testing computational methods for the identification of binding hot spots with emphasis on fragment-based ligand discovery. Each protein structure in the set binds a fragment, which is extended into larger ligands in other structures without substantial change in its binding mode. Structures of the same proteins without any bound ligand are also collected to form an unbound benchmark. We also discuss a set developed by Astex Pharmaceuticals for the validation of hot and warm spots for fragment binding. The set is based on the assumption that a fragment that occurs in diverse ligands in the same subpocket identifies a binding hot spot. Since this set includes only ligand-bound proteins, we added a set with unbound structures. All four sets were tested using FTMap, a computational analogue of fragment screening experiments to form a baseline for testing other prediction methods, and differences among the sets are discussed.

A Central Region of NF-κB Essential Modulator Is Required for IKKß-Induced Conformational Change and for Signal Propagation.

NF-κB essential modulator (NEMO) regulates NF-κB signaling by acting as a scaffold for the kinase IKKß to direct its activity toward the NF-κB inhibitor, IκBα. Here, we show that a highly conserved central region of NEMO termed the intervening domain (IVD, amino acids 112-195) plays a key role in NEMO function. We determined a structural model of full-length NEMO by small-angle X-ray scattering and show that full-length, wild-type NEMO becomes more compact upon binding of a peptide comprising the NEMO binding domain of IKKß (amino acids 701-745). Mutation of conserved IVD residues (9SG-NEMO) disrupts this conformational change in NEMO and abolishes the ability of NEMO to propagate NF-κB signaling in cells, although the affinity of 9SG-NEMO for IKKß compared to that of the wild type is unchanged. On the basis of these results, we propose a model in which the IVD is required for a conformational change in NEMO that is necessary for its ability to direct phosphorylation of IκBα by IKKß. Our findings suggest a molecular explanation for certain disease-associated mutations within the IVD and provide insight into the role of conformational change in signaling scaffold proteins.

Ligand deconstruction: Why some fragment binding positions are conserved and others are not.

Fragment-based drug discovery (FBDD) relies on the premise that the fragment binding mode will be conserved on subsequent expansion to a larger ligand. However, no general condition has been established to explain when fragment binding modes will be conserved. We show that a remarkably simple condition can be developed in terms of how fragments coincide with binding energy hot spots--regions of the protein where interactions with a ligand contribute substantial binding free energy--the locations of which can easily be determined computationally. Because a substantial fraction of the free energy of ligand binding comes from interacting with the residues in the energetically most important hot spot, a ligand moiety that sufficiently overlaps with this region will retain its location even when other parts of the ligand are removed. This hypothesis is supported by eight case studies. The condition helps identify whether a protein is suitable for FBDD, predicts the size of fragments required for screening, and determines whether a fragment hit can be extended into a higher affinity ligand. Our results show that ligand binding sites can usefully be thought of in terms of an anchor site, which is the top-ranked hot spot and dominates the free energy of binding, surrounded by a number of weaker satellite sites that confer improved affinity and selectivity for a particular ligand and that it is the intrinsic binding potential of the protein surface that determines whether it can serve as a robust binding site for a suitably optimized ligand.

Progress towards the broad use of non-peptide synthetic macrocycles in drug discovery.

We discuss progress towards addressing three key questions pertaining to the design of screening libraries of synthetic non-peptidic macrocycles (MCs) for drug discovery: What structural and physicochemical properties of MCs maximize the likelihood of achieving strong and specific binding to protein targets? What features render a protein target suitable for binding MCs, and can this information be used to identify suitable targets for inhibition by MCs? What properties of synthetic MCs confer good pharmaceutical properties, and particularly good aqueous solubility coupled with passive membrane permeability? We additionally discuss how the criteria that define a meaningful MC screening hit are linked to the size of the screening library and the synthetic methodology employed in its preparation.

Quantitative analysis of receptor tyrosine kinase-effector coupling at functionally relevant stimulus levels.

A major goal of current signaling research is to develop a quantitative understanding of how receptor activation is coupled to downstream signaling events and to functional cellular responses. Here, we measure how activation of the RET receptor tyrosine kinase on mouse neuroblastoma cells by the neurotrophin artemin (ART) is quantitatively coupled to key downstream effectors. We show that the efficiency of RET coupling to ERK and Akt depends strongly on ART concentration, and it is highest at the low (∼100 pM) ART levels required for neurite outgrowth. Quantitative discrimination between ERK and Akt pathway signaling similarly is highest at this low ART concentration. Stimulation of the cells with 100 pM ART activated RET at the rate of ∼10 molecules/cell/min, leading at 5-10 min to a transient peak of ∼150 phospho-ERK (pERK) molecules and ∼50 pAkt molecules per pRET, after which time the levels of these two signaling effectors fell by 25-50% while the pRET levels continued to slowly rise. Kinetic experiments showed that signaling effectors in different pathways respond to RET activation with different lag times, such that the balance of signal flux among the different pathways evolves over time. Our results illustrate that measurements using high, super-physiological growth factor levels can be misleading about quantitative features of receptor signaling. We propose a quantitative model describing how receptor-effector coupling efficiency links signal amplification to signal sensitization between receptor and effector, thereby providing insight into design principles underlying how receptors and their associated signaling machinery decode an extracellular signal to trigger a functional cellular outcome.

How proteins bind macrocycles.

The potential utility of synthetic macrocycles (MCs) as drugs, particularly against low-druggability targets such as protein-protein interactions, has been widely discussed. There is little information, however, to guide the design of MCs for good target protein-binding activity or bioavailability. To address this knowledge gap, we analyze the binding modes of a representative set of MC-protein complexes. The results, combined with consideration of the physicochemical properties of approved macrocyclic drugs, allow us to propose specific guidelines for the design of synthetic MC libraries with structural and physicochemical features likely to favor strong binding to protein targets as well as good bioavailability. We additionally provide evidence that large, natural product-derived MCs can bind targets that are not druggable by conventional, drug-like compounds, supporting the notion that natural product-inspired synthetic MCs can expand the number of proteins that are druggable by synthetic small molecules.

Inhibition of Oncogenic Transcription Factor REL by the Natural Product Derivative Calafianin Monomer 101 Induces Proliferation Arrest and Apoptosis in Human B-Lymphoma Cell Lines.

Increased activity of transcription factor NF-κB has been implicated in many B-cell lymphomas. We investigated effects of synthetic compound calafianin monomer (CM101) on biochemical and biological properties of NF-κB. In human 293 cells, CM101 selectively inhibited DNA binding by overexpressed NF-κB subunits REL (human c-Rel) and p65 as compared to NF-κB p50, and inhibition of REL and p65 DNA binding by CM101 required a conserved cysteine residue. CM101 also inhibited DNA binding by REL in human B-lymphoma cell lines, and the sensitivity of several B-lymphoma cell lines to CM101-induced proliferation arrest and apoptosis correlated with levels of cellular and nuclear REL. CM101 treatment induced both phosphorylation and decreased expression of anti-apoptotic protein Bcl-XL, a REL target gene product, in sensitive B-lymphoma cell lines. Ectopic expression of Bcl-XL protected SUDHL-2 B-lymphoma cells against CM101-induced apoptosis, and overexpression of a transforming mutant of REL decreased the sensitivity of BJAB B-lymphoma cells to CM101-induced apoptosis. Lipopolysaccharide-induced activation of NF-κB signaling upstream components occurred in RAW264.7 macrophages at CM101 concentrations that blocked NF-κB DNA binding. Direct inhibitors of REL may be useful for treating B-cell lymphomas in which REL is active, and may inhibit B-lymphoma cell growth at doses that do not affect some immune-related responses in normal cells.

Understanding cytokine and growth factor receptor activation mechanisms.

Our understanding of the detailed mechanism of action of cytokine and growth factor receptors - and particularly our quantitative understanding of the link between structure, mechanism and function - lags significantly behind our knowledge of comparable functional protein classes such as enzymes, G protein-coupled receptors, and ion channels. In particular, it remains controversial whether such receptors are activated by a mechanism of ligand-induced oligomerization, versus a mechanism in which the ligand binds to a pre-associated receptor dimer or oligomer that becomes activated through subsequent conformational rearrangement. A major limitation to progress has been the relative paucity of methods for performing quantitative mechanistic experiments on unmodified receptors expressed at endogenous levels on live cells. In this article, we review the current state of knowledge on the activation mechanisms of cytokine and growth factor receptors, critically evaluate the evidence for and against the different proposed mechanisms, and highlight other key questions that remain unanswered. New approaches and techniques have led to rapid recent progress in this area, and the field is poised for major advances in the coming years which promise to revolutionize our understanding of this large and biologically and medically important class of receptors.

Disulfide-mediated stabilization of the IκB kinase binding domain of NF-κB essential modulator (NEMO).

Human NEMO (NF-κB essential modulator) is a 419 residue scaffolding protein that, together with catalytic subunits IKKα and IKKß, forms the IκB kinase (IKK) complex, a key regulator of NF-κB pathway signaling. NEMO is an elongated homodimer comprising mostly α-helix. It has been shown that a NEMO fragment spanning residues 44-111, which contains the IKKα/ß binding site, is structurally disordered in the absence of bound IKKß. Herein we show that enforcing dimerization of NEMO1-120 or NEMO44-111 constructs through introduction of one or two interchain disulfide bonds, through oxidation of the native Cys54 residue and/or at position 107 through a Leu107Cys mutation, induces a stable α-helical coiled-coil structure that is preorganized to bind IKKß with high affinity. Chemical and thermal denaturation studies showed that, in the context of a covalent dimer, the ordered structure was stabilized relative to the denatured state by up to 3 kcal/mol. A full-length NEMO-L107C protein formed covalent dimers upon treatment of mammalian cells with H2O2. Furthermore, NEMO-L107C bound endogenous IKKß in A293T cells, reconstituted TNF-induced NF-κB signaling in NEMO-deficient cells, and interacted with TRAF6. Our results indicate that the IKKß binding domain of NEMO possesses an ordered structure in the unbound state, provided that it is constrained within a dimer as is the case in the constitutively dimeric full-length NEMO protein. The stability of the NEMO coiled coil is maintained by strong interhelix interactions in the region centered on residue 54. The disulfide-linked constructs we describe herein may be useful for crystallization of NEMO's IKKß binding domain in the absence of bound IKKß, thereby facilitating the structural characterization of small-molecule inhibitors.

Structural conservation of druggable hot spots in protein-protein interfaces.

Despite the growing number of examples of small-molecule inhibitors that disrupt protein-protein interactions (PPIs), the origin of druggability of such targets is poorly understood. To identify druggable sites in protein-protein interfaces we combine computational solvent mapping, which explores the protein surface using a variety of small "probe" molecules, with a conformer generator to account for side-chain flexibility. Applications to unliganded structures of 15 PPI target proteins show that the druggable sites comprise a cluster of binding hot spots, distinguishable from other regions of the protein due to their concave topology combined with a pattern of hydrophobic and polar functionality. This combination of properties confers on the hot spots a tendency to bind organic species possessing some polar groups decorating largely hydrophobic scaffolds. Thus, druggable sites at PPI are not simply sites that are complementary to particular organic functionality, but rather possess a general tendency to bind organic compounds with a variety of structures, including key side chains of the partner protein. Results also highlight the importance of conformational adaptivity at the binding site to allow the hot spots to expand to accommodate a ligand of drug-like dimensions. The critical components of this adaptivity are largely local, involving primarily low energy side-chain motions within 6 Å of a hot spot. The structural and physicochemical signature of druggable sites at PPI interfaces is sufficiently robust to be detectable from the structure of the unliganded protein, even when substantial conformational adaptation is required for optimal ligand binding.

Mutation of nonessential cysteines shows that the NF-κB essential modulator forms a constitutive noncovalent dimer that binds IκB kinase-ß with high affinity.

NEMO (NF-κB essential modulator) associates with catalytic subunits IKKα and IKKß to form the IκB kinase (IKK) complex and is a key regulator of NF-κB pathway signaling. Biochemical and structural characterization of NEMO has been challenging, however, leading to conflicting data about basic biochemical properties such as the oligomeric state of active NEMO and its binding affinity for IKKß. We show that up to seven of NEMO's 11 cysteine residues can be mutated to generate recombinant full-length NEMO that is highly soluble and active. Using a fluorescence anisotropy binding assay, we show that full-length NEMO binds a 44-mer peptide encompassing residues 701-745 of IKKß with a K(D) of 2.2 ± 0.8 nM. The IKKß binding affinities of mutants with five and seven Cys-to-Ala substitutions are indistinguishable from that of wild-type NEMO. Moreover, when expressed in NEMO -/- fibroblasts, the five-Ala and seven-Ala NEMO mutants can interact with cellular IKKß and restore NF-κB signaling to provide protection against tumor necrosis factor α-induced cell death. Treatment of the NEMO-reconstituted cells with H2O2 led to the formation of covalent dimers for wild-type NEMO and the five-Ala mutant, but not for the seven-Ala mutant, confirming that Cys54 and/or Cys347 can mediate interchain disulfide bonding. However, the IKKß binding affinity of NEMO is unaffected by the presence or absence of interchain disulfide bonding at Cys54, which lies within the IKKß binding domain of NEMO, or at Cys347, indicating that NEMO exists as a noncovalent dimer independent of the redox state of its cysteines. This conclusion was corroborated by the observation that the secondary structure content of NEMO and its thermal stability were independent of the presence or absence of interchain disulfide bonds.

Comprehensive experimental and computational analysis of binding energy hot spots at the NF-κB essential modulator/IKKß protein-protein interface.

We report a comprehensive analysis of binding energy hot spots at the protein-protein interaction (PPI) interface between nuclear factor kappa B (NF-κB) essential modulator (NEMO) and IκB kinase subunit ß (IKKß), an interaction that is critical for NF-κB pathway signaling, using experimental alanine scanning mutagenesis and also the FTMap method for computational fragment screening. The experimental results confirm that the previously identified NEMO binding domain (NBD) region of IKKß contains the highest concentration of hot-spot residues, the strongest of which are W739, W741, and L742 (ΔΔG = 4.3, 3.5, and 3.2 kcal/mol, respectively). The region occupied by these residues defines a potentially druggable binding site on NEMO that extends for ~16 Å to additionally include the regions that bind IKKß L737 and F734. NBD residues D738 and S740 are also important for binding but do not make direct contact with NEMO, instead likely acting to stabilize the active conformation of surrounding residues. We additionally found two previously unknown hot-spot regions centered on IKKß residues L708/V709 and L719/I723. The computational approach successfully identified all three hot-spot regions on IKKß. Moreover, the method was able to accurately quantify the energetic importance of all hot-spot residues involving direct contact with NEMO. Our results provide new information to guide the discovery of small-molecule inhibitors that target the NEMO/IKKß interaction. They additionally clarify the structural and energetic complementarity between "pocket-forming" and "pocket-occupying" hot-spot residues, and further validate computational fragment mapping as a method for identifying hot spots at PPI interfaces.

Determining the affinity and stoichiometry of interactions between unmodified proteins in solution using Biacore.

We describe a general Biacore method for measuring equilibrium binding affinities and stoichiometries for interactions between unmodified proteins and their unmodified ligands free in solution. Mixtures of protein and ligand are preequilibrated at different ratios in solution and then analyzed by Biacore using a sensor chip surface that detects only unbound analyte. Performing the Biacore analysis under mass transport limited conditions allows the concentration of unbound analyte to be determined from the initial velocity of binding. Plots of initial velocity versus the concentration of the varied binding partner are fitted to a quadratic binding equation to give the affinity and stoichiometry of binding. We demonstrate the method using soluble Her2 extracellular domain binding to monovalent, bivalent, and trivalent forms of an anti-Her2 antibody. The affinity we measured agrees with that obtained from conventional Biacore kinetic analysis, and the stoichiometries for the resulting 1:1, 1:2, and 1:3 complexes were confirmed by gel filtration with in-line light scattering. The method is applicable over an affinity range of approximately 100 pM to 1 µM and is particularly useful when there is concern that covalently modifying one or the other binding partner might affect its binding properties or where multivalency might otherwise complicate a quantitative analysis of binding.