Abstract
Despite the central role that antibodies play in the adaptive immune system and in biotechnology, much remains unknown about the quantitative relationship between an antibody’s amino acid sequence and its antigen binding affinity. Here we describe a new experimental approach, called TiteSeq, that is capable of measuring binding titration curves and corresponding affinities for thousands of variant antibodies in parallel. The measurement of titration curves eliminates the confounding effects of antibody expression and stability that arise in standard deep mutational scanning assays. We demonstrate Tite-Seq on the CDR1H and CDR3H regions of a well-studied scFv antibody. Our data shed light on the structural basis for antigen binding affinity and suggests a role for secondary CDR loops in establishing antibody stability. Tite-Seq fills a large gap in the ability to measure critical aspects of the adaptive immune system, and can be readily used for studying sequence-affinity landscapes in other protein systems.
I. Introduction
During an infection, the immune system must recognize and neutralize invading pathogens. B-cells contribute to immune defense by producing antibodies, proteins that bind specifically to foreign antigens. The astonishing capability of antibodies to recognize virtually any foreign molecule has been repurposed by scientists in wide variety of experimental techniques (immunofluorescence, western blots, ELISA, ChIP-Seq, etc.). Antibody based therapeutic drugs have also been developed for treating many different diseases, including cancer [1].
Much is known about the qualitative mechanisms of antibody generation and function [2]. The antigenic specificity of antibodies in humans, mice, and most jawed vertebrates is primarily governed by six complementarity determining regions (CDRs), each roughly 10 amino acids (aa) long. Three CDRs (denoted CDR1H, CDR2H, and CDR3H) are located on the antibody heavy chain, and three are on the light chain. During B-cell differentiation, these six sequences are randomized through V(D)J recombination, then selected for functionality as well as against the ability to recognize host antigens. Upon participation in an immune response, CDR regions can further undergo somatic hypermutation and selection, yielding higher-affinity antibodies for specific antigens. Among the CDRs, CDR3H is the most highly variable and typically contributes the most to antigen specificity; less clear are the functional roles of the other CDRs, which often do not interact with the target antigen directly.
Many high-throughput techniques, including phage display [3⇓–5], ribosome display [6],yeast display [7, 8],and mammalian cell display [9], have been developed for optimizing antibodies ex vivo. Advances in DNA sequencing technology have also made it possible to effectively monitor both antibody and T-cell receptor diversity within immune repertoires, e.g. in healthy individuals [10⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓–21], in specific tissues [22], in individuals with diseases [23] or following vaccination [24⇓⇓⇓–28]. Yet many questions remain about basic aspects of the quantitative relationship between antibody sequence and antigen binding affinity. How many different antibodies will bind a given antigen with specified affinity? How large of a role do epistatic interactions between amino acid positions within the CDRs have on antigen binding affinity? How is this sequence-affinity landscape navigated by the V(D)J recombination process, or by somatic hypermutation? Answering these and related questions is likely to prove critical for developing a systems-level understanding of the adaptive immune system, as well as for using antibody repertoire sequencing to diagnose and monitor disease.
Recently developed “deep mutational scanning” (DMS) assays [29] provide one potential method for measuring binding affinities with high enough throughput to effectively explore antibody sequence-affinity landscapes. In DMS experiments, one begins with a library of variants of a specific protein. Proteins that have high levels of a particular activity of interest are then enriched via one or more rounds of selection, which can be carried out in a variety of ways. The set of enriched sequences is then compared to the initial library, and protein sequences (or mutations within these sequences) are scored according to how much this enrichment procedure increases their prevalence.
Multiple DMS assays have been described for investigating protein-ligand binding affinity. But no DMS assay has yet been shown to provide quantitative binding affinity measurements, i.e., dissociation constants in molar units. For example, one of the first DMS experiments[30] used phage display technology to measure how mutations in a WW domain affect the affinity of this domain for its peptide ligand. These data were sufficient to compute enrichment ratios and corresponding sequence logos, but they did not yield quantitative affinities. Analogous experiments have since been performed on antibodies using yeast display [31, 32] and mammalian cell display [9], but these approaches do not provide quantitative affinity values either. SORTCERY [31, 33], a DMS assay that combines yeast display and quantitative modeling, has been shown to provide approximate rank-order values for the affinity of a specific protein for short unstructured peptides of varying sequence. Determining quantitative affinities from SORTCERY data, however, requires separate low-throughput calibration measurements [31]. Moreover, it is unclear how well SORTCERY, if applied to a library of folded proteins rather than unstructured peptides, can distinguish sequence-dependence effects on affinity from sequence-dependent effects on protein expression and stability.
To enable massively parallel measurements of absolute binding affinities for antibodies and other structured proteins, we have developed an assay called “Tite-Seq.” Tite-Seq, like SORTCERY, builds on the capabilities of Sort-Seq, an experimental strategy that was first developed for studying transcriptional regulatory sequences in bacteria [34]. Sort-Seq combines fluorescence-activated cell sorting (FACS) with high-throughput sequencing to provide massively parallel measurements of cellular fluorescence. In the Tite-Seq assay, Sort-Seq is applied to antibodies displayed on the surface of yeast cells and incubated with antigen at a wide range of concentrations. From the resulting sequence data, thousands of antibodyantigen binding titration curves and their corresponding absolute dissociation constants (here denoted KD) can be inferred. By assaying full binding curves, Tite-Seq is able to measure affinities over many orders of magnitude [35]. Moreover, the resulting sequence-dependent affinity values are not confounded by potential sequence-dependent variation in protein expression or stability, as is the case with SORTCERY and other DMS assays.
We demonstrated Tite-Seq on a protein library derived from a well-studied single-chain variable fragment (scFv) antibody specific to the small molecule fluorescein [7, 36]. Mutations were restricted to CDR1H and CDR3H regions, which are known to play an important role in the antigen recognition of this scFv [36, 37]. The resulting affinity measurements were validated with binding curves for a handful of clones measured using standard low-throughput flow cytometry. Our Tite-Seq measurements reveal both expected and unexpected differences between the effects of mutations in CDR1H and CDR3H. These data also shed light on structural aspects of antigen recognition that are independent of effects on antibody stability.
II. Results
A. Overview of Tite-Seq
Our general strategy is illustrated in Fig. 1. First, a library of variant antibodies is displayed on the surface of yeast cells (Fig. 1A). The composition of this library is such that each cell displays a single antibody variant, and each variant is expressed on the surface of multiple cells. Cells are then incubated with the antigen of interest, bound antigen is fluroescently labeled, and fluorescence-activated cell sorting (FACS) is used to sort cells one-by-one into multiple “bins” based on this fluorescent readout (Fig. 1B). Deep sequencing is then used to survey the antibody variants present in each bin. Because each variant antibody is sorted multiple times, it will be associated with a histogram of counts spread across one or more bins (Fig. 1C). The spread in each histogram is due to cell-to-cell variability in antibody expression, and to the inherent noisiness of flow cytometry measurements. Finally, the histogram corresponding to each antibody variant is used to compute an “average bin number” (Fig. 1C, dots), which serves as a proxy measurement for the average amount of bound antigen per cell.
It has previously been shown that KD values can be accurately measured using yeast-displayed antibodies by taking binding titration curves, i.e., by measuring the average amount of bound antigen as a function of antigen concentration [8, 38]. The median fluorescence f of labeled cells is expected to be related to antigen concentration via where A is proportional to the number of functional antibodies displayed on the cell surface, B accounts for background fluorescence, and c is the concentration of free antigen in solution. Fig. 1D illustrates the shape of curves having this form. By using flow cytometry to measure f on clonal populations of yeast at different antigen concentrations c, one can infer curves having the sigmoidal form shown in Eq. 1 and thereby learn KD. Such measurements, however, can only be performed in a low-throughput manner.
Tite-Seq allows thousands of binding titration curves to be measured in parallel. The Sort-Seq procedure illustrated in Fig. 1A-C is performed at multiple antigen concentrations, and the resulting average bin number for each variant antibody is plotted against concentration. Sigmoidal curves are then fit to these proxy measurements, enabling KDvalues to be inferred for each variant.
We emphasize that KDvalues cannot, in general, be accurately inferred from Sort-Seq experiments performed at a single antigen concentration. Because the relationship between binding and KD is sigmoidal, the amount of bound antigen provides a quantitative readout of KDonly when the concentration of antigen used in the labeling procedure is comparable in magnitude to KD. However, single mutations within a protein binding domain often change KDby multiple orders of magnitude. SortSeq experiments used to measure sequence-affinity landscapes must therefore be carried out over a range of concentrations large enough to encompass this variation.
Furthermore, as illustrated in Figs. 1C and 1D, different antibody variants often lead to different levels of functional antibody expression on the yeast cell surface. If one performs Sort-Seq at a single antigen concentration, high affinity (low KD) variants with low expression (blue variant) may bind less antigen than low affinity (high KD) variants with high expression (orange variant). Only by measuring full titration curves can the effect that sequence has on affinity be deconvolved from sequence-dependent effects on functional protein expression.
B. Proof-of-principle Tite-Seq experiments
To test the feasibility of Tite-Seq, we used a wellcharacterized antibody-antigen system: the 4-4-20 single chain variable fragment (scFv) antibody [7], which binds the small molecule fluorescein with KD = 1.2 nM [8]. This system was used in early work to establish the capabilities of yeast display [7], and a high resolution co-crystal structure of the 4-4-20 antibody bound to fluorescein, shown in Fig. 2A, has been determined [39]. An ultra-high-affinity (KD = 270 fM) variant of this scFv, called 4m5.3, has also been found [36]. In what follows, we refer to the 4-4-20 scFv from [7] as WT, and the 4m5.3 variant from [36] as OPT.
The scFv was expressed on the surface of yeast as part of the multi-domain construct illustrated in Fig. 2B and previously described in [7]. Following [36], we used fluorescein-biotin as the antigen and labeled scFv-bound antigen with streptavidin-RPE (PE). The amount of surface-expressed protein was separately quantified by labeling the C-terminal c-Myc tag using anti-c-Myc primary antibodies, followed by secondary antibodies conjugated to Brilliant Violet 421 (BV). See Appendix B for details on this labeling procedure.
Two different scFv libraries were assayed simultaneously. In the “1H” library, a 10 aa region encompasing the CDR1H region of the WT scFv (see Fig. 2C) was mutagenized using a microarray-synthesized oligos (see Appendix C for details on library generation). The resulting 1H library consisted of all 600 single-codon variants of this 10 aa region, 1100 randomly chosen 2-codon variants, and 150 random 3-codon variants (Fig. 2D). An analogous “3H” library was generated for a 10 aa region containing the CDR3H region of this scFv. In all of the Tite-Seq experiments described below, these two libraries were pooled together and supplemented with WT and OPT scFvs, as well with a nonfunctional scFv referred to as Δ.
Tite-Seq was carried out as follows. Yeast cells expressing scFv from the mixed library were incubated with fluorescein-biotin at one of eleven concentrations: 0 M, 10−9.5 M, 10−9 M, 10−8.5 M, 10−8 M, 10−7.5 M, 10−7 M, 10−6.5 M, 10−6 M, 10−5.5 M, and 10−5 M. After subsequent PE labeling of bound antigen, cells were sortedinto four bins using FACS (Fig. 3A). Separately, BVlabeled cells were sorted according to measured scFv expression levels (Fig. 3B). The number of cells sorted into each bin is shown in Fig. 3C. Each bin of cells was regrown and bulk DNA was extracted. The 1H and 3H variable regions were then PCR amplified and sequenced using paired-end Illumina sequencing, as described in Appendix D. The final data set consisted of an average of 2.6 × 106 sequences per bin across all 48 bins (Fig. 3D). Three independent replicates of this experiment were performed on three different days.
For each variant scFv gene, a KD value was inferred by fitting a binding curve to the resulting Tite-Seq data, with separate curves independently fit to data from each Tite-Seq experiment (Fig. 4A). As illustrated in Fig. 1E, this fitting procedure uses the sigmoidal function in Eq. 1 to model mean bin number as a function of antigen concentration. However, the need to account for multiple sources of noise in the Tite-Seq experiment necessitates a more complex procedure than Fig. 1E might suggest; the details of this inference procedure are described in Appendix E.
The Sort-Seq data obtained by sorting the BV-labeled libraries were used to separately determine the expression level of each scFv. In what follows we use E to denote the mean bin computed for each scFv gene in the library. These E values are scaled so that the mean of such measurements for all synonymous WT scFv gene variants is 1.0.
C. Low-throughput validation experiments
To judge the accuracy of Tite-Seq, we separately measured binding curves for individual scFv clones as described for Fig. 1D. In addition to the WT, OPT, and Δ scFvs, we assayed eight clones from the 1H library (named C3, C5, C7, C18, C22, C132, C133 and C144) and eight clones from the 3H library (C39, C45, C93, C94, C102, C103, C107, C112). Each clone underwent the same labeling procedure as in the Tite-Seq experiment, after which median fluorescence values were measured using standard flow cytometry. KDvalues were then inferred by fitting binding curves of the form in Eq. 1 using the procedure described in Appendix F. These curves, which can be directly compared to the Tite-Seq measurement (Fig.4A), are plotted in Fig. 4B; at least three replicate binding curves were measured for each clone. See Fig. S4 for the titration curves of all the tested clones.
D. Tite-Seq can measure dissociation constants
Fig. 4C reveals a strong correspondence between the KDvalues measured by Tite-Seq and those measured using low-throughput flow cytometry. The robustness of Tite-Seq is further illustrated by the consistency of KDvalues measured for the WT scFv. Using TiteSeq, and averaging the results from the 33 synonymous variants and over all three replicates, we determined KD = 10−8.87±0.02 M for the WT scFv. These measurements are consistent with the measurement of KD = 10−8.61±0.07 M obtained by averaging low-throughput flow cytometry measurements across 10 replicates, and coincides with the previously measured value of 1.2 nM = 10−8.9 M reported in [8]. The three independent replicate Tite-Seq experiments give reproducible results (Fig. S5 and S6) with Pearson coefficients ranging from r = 0.82 to r = 0.89 for all the measured KDvalues. The error bars for KDvalues in Fig. 4C calculated from the variability of the fits to different replicates support the reproducibility of the experiment.
The necessity of performing KDmeasurements over a wide range of antigen concentrations is illustrated in Fig. S7. At each antigen concentration used in our Tite-Seq experiments, the enrichment of scFvs in the high-PE bins correlated poorly with the KDvalues inferred from full titration curves. Moreover, at each antigen concentration used, a detectable correlation between KDand enrichment was found only for scFvs with KDvalues close to that concentration.
Fig. S8 suggests a possible reason for the weak correlation between KDvalues and enrichment in high-PE bins. We found that, at saturating concentrations of fluorescein (2 μ M), cells expressing the OPT scFv bound twice as much fluorescein as cells expressing the WT scFv. This difference was not due to variation in the total amount of displayed scFv, which one might control for by labeling the c-Myc epitope as in [33]. Rather, this difference in binding reflects a difference in the fraction of displayed scFvs that are competent to bind antigen. Yeast display experiments performed at a single antigen concentration cannot distinguish such differences in the fraction of displayed scFv molecules that function properly from differences in scFv affinity.
To further test the capability of Tite-Seq to infer dissociation constants from sequencing data over a wide range of values, as well as to validate our analysis procedures, we simulated Tite-Seq data in silico and analyzed the results using the same analysis pipeline that we used for our experiments. Details about the simulations are given in Appendix G. The simulated data is illustrated in Fig. S9. KDvalues inferred from these simulated data agreed to high accuracy with the KDused in the simulation (Fig. S10), thus validating our analysis pipeline.
E. Properties of the affinity and expression landscapes
Fig. 5 shows the effect that every single-amino-acid substitution mutation within the 1H and 3H variable regions has on affinity and on expression; histograms of these effects are provided in Fig. S11. In both regions, the large majority of mutations weaken antigen binding (1H: 88%; 3H: 93%), with many mutations increasing KD above our detection threshold of 10−5 M (1H: 36%; 3H: 52%). Far fewer mutations reduced KD(1H: 12%; 3H: 7%), and very few dropped KDbelow our detection limit of 10−9.5 M (1H: 0%; 3H: 3%). Histograms of the effect of 2 or 3 amino acid changes relative to WT, shown in Fig. S12A, show that multiple random mutations tend to further deteriorate affinity. We also observed that mutations within the 3H variable region have a larger effect on affinity than do mutations in the 1H variable region. Specifically, single amino acid mutations in 3H were seen to increased KDmore than mutations in 1H (1H median KD = 10−6.84; 3H median KD~10−5.0; P = 4.7 * 10−4, one-sided Mann-Whitney U test). This result suggests that binding affinity is more sensitive to variation in CDR3H than to variation in CDR1H, a finding that is consistent with the conventional understanding of these antibody CDR regions [40, 41].
Our observations are thus fully consistent with the hypothesis that the amino acid sequences of the CDR1H and CDR3H regions of the WT scFv have been selected for high affinity binding to fluorescein. We know this to be true, of course; still, this result provides an important validation of our Tite-Seq measurements.
To further validate our Tite-Seq affinity measurements, we examined positions in the high affinity OPT scFv (from [36]) that differ from WT and that lie within the 1H and 3H variable regions. As illustrated in Figs. 5A and 5B, five of the six OPT-specific mutations reduce KDor are nearly neutral. Previous structural analysis [37] has suggested that D106E, the only OPT mutation that we find significantly increases KD, may indeed disrupt antigen binding on its own while still increasing affinity in the presence of the S101A mutation.
Next, we used our measurements to build a “matrix model” [42] (also known as a “position-specific affinity matrix,” or PSAM [43]) describing the sequence-affinity landscape of these two regions. Our model assumed that the log10 KDvalue for an arbitrary amino acid sequence could be computed from the log10 KDvalue of the WT scFv, plus the measured change in log10 KDproduced by each amino acid substitution away from WT. We evaluated our matrix models on the 1H and 3H variable regions of OPT, finding an affinity of 10−9.16 M. Our simple model for the sequence affinity landscape of this scFv therefore correctly predicts that OPT has higher affinity than WT. The quantitative affinity predicted by our model does not match the known affinity of the OPT scFv (KD = 10−12.6 M), but this is unsurprising for three reasons. First the OPT scFv differs from WT in 14 residues, only 6 of which are inside the 1H and 3H variable regions assayed here. Second, one of the OPT mutations (W108L) reduces KD below our detection threshold of 10−9.5 M; in building our matrix model, we set this value equal to 10−9.5, knowing it would likely underestimate the affinity-increasing effect of the mutation. Third, our additive model ignores potential epistatic interactions. Still, we thought it worth asking how likely it it would be for 6 random mutations within the 1H and 3H variable regions to reduce affinity as much as our model predicts for OPT. We therefore simulated a large number (107) of variants having a total of 6 substitution mutations randomly scattered across the 1H and 3H variable regions. The fraction of these random sequences that had an affinity at or below our predicted affinity for OPT was 4.7 10−5. This finding is fully consistent with the fact that the mutations in OPT relative to WT were selected for increased affinity, an additional confirmation of the validity of our Tite-Seq measurements.
The sequence-expression landscape measured in our separate Sort-Seq experiment yielded qualitatively different results (Figs. 5C and 5D). We observed no significant difference in the median effect that mutations in the variable regions of 1H (median E = 0. 826) versus 3H (median E = 0. 822) have on expression (P = 0. 96, two-sided Mann-Whitney U test); see also Fig. S11. The variance in these effects, however, was larger in 3H than in 1H (P = 9. 9 10−16, Levene’s test). These results suggest two things. First, the 3H variable region appears to have a larger effect on scFv expression than the 1H variable region has. At the same time, since we observe fewer beneficial mutations in 1H (Fig. 5C) than in 3H (Fig. 5D), the WT sequence appears to be more highly optimized for expression in CDR1H than in CDR3H. The effect of double or triple mutations further reduced expression in both CDRs (Fig. S12B), similar to what was observed for affinity.
F. Structural correlates of the sequence-affinity landscape
We asked if the sensitivity of the antibody to mutations could be understood from a structural perspective. To quantify sensitivity of affinity and expression at each position i, we computed two quantities:
Here, and respectively denote the dissociation constant and expression level measured for the WT scFv, and Eia denote analogous quantities for the scFv with a single substitution mutation of amino acid a at position i, and 〈·〉a |i denotes an average computed over the 19 non-WT amino acids at that position.
Fig. 6A shows the known structure [39] of the 1H and 3H variable regions of the WT scFv in complex with fluorescein. Each residue is colored according to the SK and SE values computed for its position. To get a better understanding of what aspects of the structure might govern affinity, we plotted SK values against two other quantities: the number of amino acid contacts made by the WT residue within the antibody structure (Fig. 6B), and the distance between the WT residue and the antigen (Fig. 6C). We found a strong correlation between SK and the number of contacts, but no significant correlation between SK and distance to antigen. By contrast, SE did not correlate significantly with either of these structural quantities (Figs. 6D and 6E).
III. DISCUSSION
We have described a massively parallel assay, called Tite-Seq, for measuring the sequence-affinity landscape of antibodies. The range of affinities measured in our Tite-Seq experiments (10−9.5 M to 10−5.0 M) includes a large fraction of the physiological range relevant to affinity maturation (10−10 M to 10−6 M to) [44⇓–46]. Expanding the measured range of affinities below 10−9.5 M might require larger volume labeling reactions, but would be straight-forward. Tite-Seq therefore provides a potentially powerful method for mapping the sequence-affinity trajectories of antibodies during the affinity maturation process, as well as for studying other aspects of the adaptive immune response.
Tite-Seq fundamentally differs from prior DMS experiments in that full binding titration curves, not enrichment statistics, are used to determine binding affinities. The measurement of binding curves provides three major advantages. First, binding curves provide absolute KD values in molar units, not just rank-order affinities like those provided by SORTCERY [31]. Second, because ligand binding is a sigmoidal function of affinity, DMS experiments performed at a single ligand concentration are insensitive to receptor KDs that differ substantially from this ligand concentration. Yet mutations within a protein’s binding domain often change KD by multiple orders of magnitude. Binding curves, by contrast, integrate measurements over a wide range of concentrations and are therefore sensitive to a wide range of KDs. Third, protein sequence determines not just ligandbinding affinity, but also the amount of surface-displayed protein, as well as the fraction of this protein that is functional. Our data demonstrate that these confounding effects can strongly distort yeast display affinity measurements made at a single antigen concentration, and that the binding curves measured by Tite-Seq successfully deconvolve these effects from affinity measurements.
More generally, changing a protein’s amino acid sequence can be expected to change multiple biochemical properties of that protein. Our work emphasizes the importance of designing massively parallel assays that can disentangle these multiple effects so that measurements of a specific activity of interest can be obtained. TiteSeq provides a general solution to this problem for massively parallel studies of protein-ligand binding. Indeed, the Tite-Seq procedure described here can be readily applied to any protein binding assay that is compatible with yeast display and FACS. Many such assays have been developed [47]. We expect that Tite-Seq can also be readily adapted for use with other expression platforms, such as mammalian cell display [9].
Our Tite-Seq measurements reveal interesting distinctions between the effects of mutations in the CDR1H and CDR3H regions of the anti-fluorescein scFv antibody studied here. As expected, we found that variation in and around CDR3H had a larger effect on affinity than variation in and around CDR1H. We also found that CDR1H is more optimized for protein expression than is CDR3H, an unexpected finding that appears to be novel. Yeast display expression levels are known to correlate with thermostability [48]. Our data is limited in scope, and we remain cautious about generalizing our observations to arbitrary antibody-antigen interactions. Still, this finding suggests the possibility that secondary CDR regions (such as CDR1H) might be evolutionarily optimized to help ensure antibody stability, thereby freeing up CDR3H to encode antigen specificity. If this hypothesis holds, it could provide a biochemical rationale for why CDR3H is more likely than CDR1H to be mutated in functioning receptors [41] and why variation in CDR3H is often sufficient to establish antigen specificity [40].
Tite-Seq can also potentially shed light on the structural basis for antibody-antigen recognition. By comparing the effects of mutations with the known antibodyfluorescein co-crystal structure [39], we identified a strong correlation between the effect that a position has on affinity and the number of molecular contacts that the residue at that position makes within the antibody. By contrast, no such correlation of expression with this number of contacts is observed. Again, we are cautious about generalizing from observations made on a single antibody. If our observation were to hold for other antibodies, however, it would suggest that paratopes might represent protein “sectors” [49], with antigen specificity (but not antibody stability) governed by tightly interacting networks of residues.
IV. METHODS
Tite-Seq was performed as follows. Variant 3H and 1H regions were generated using microarray-synthesized oligos (LC Biosciences, Houston TX. USA). These were inserted into the 4-4-20 scFv of [7] using cassette replacement restriction cloning as in [34]; see Appendix C. Yeast display experiments were performed as previously described [36] with modifications; see Appendix B. Sorted cells were regrown and bulk DNA was extracted using standard techniques, and amplicons containing the 1H and 3H variable regions were amplified using PCR and sequenced using the Illumina NextSeq platform; see Appendix D. Three replicate experiments were performed on different days. Raw sequencing data has been posted on the Sequence Read Archive under BioProject ID PRJNA344711. Low-throughput flow cytometry measurements were performed on clones randomly picked from the Tite-Seq library. Sequence data and flow cytometry data were analyzed using custom Python scripts, as described in Appendices E and F. Processed data and analysis scripts are available at github.com/jbkinney/ 16_titeseq.
Acknowledgements.
We would like to thank Jacklyn Jansen, Amy Keating, Lother Reich, and Bruce Stillman for helpful discussions. We would also like to thank Dane Wittrup for sharing plasmids and yeast strains. RMA, TM and AMW were supported by European Research Council Starting Grant n. 306312. JBK was supported by the Simons Center for Quantitative Biology at Cold Spring Harbor Laboratory.
The authors declare that they have no conflict of interests.
Appendix A: Schematic simulations
For panels D and E of Fig. 1, data was simulated (using Eq. 1) for two hypothetical scFvs: one similar to WT, with KD = 1.2 10−9 M, A = 300, and B = 10, and one similar to a typical mutant, with KD = 10−6 M, A = 1000, B = 10. Simulated sorts were performed at the eleven antigen concentrations used in our experiments (c = 0 M, 10−9.5 M, 10−9.0 M, …, 10−5.0 M). For each clone at each antigen concentration, fluorescence signals were simulated for 1000 cells by multiplying the f quantity in Eq. 1 by a factor of exp(η) where η is a normally distributed random number. Fig. 1D shows the mean values of these simulated fluorescence signals. Curves of the form in Eq. 1 were fit to these data by minimizing the square deviation between predicted log10 f values and the log10 mean of the simulated fluoresence values. The Tite-Seq measurements illustrated in Fig. 1E were simulated by sorting 1000 cells, using fluorescence values generated in the same manner as above, into three bins defined by the following fluorescence boundaries: (0, 30) for bin 0, (30, 300) for bin 1, and (300,∞) for bin 2. The mean bin number for each clone at each antigen concentration was then computed. Curves having the form in Eq. 1 were then fit to these data by minimizing the square deviation of predicted log10 f values from these mean bin values.
Appendix B: Yeast display
To help ensure consistency across samples, the yeast display cultures used in our low-throughput flow cytometry measurements and in our Tite-Seq experiments were inoculated with carefully prepared frozen liquid culture inocula. Specifically, inoculation cultures were grown at 30?C in SC-trp + 2% glucose to an OD600 value between 0.9 and 1.1, then stored at −80? in aliquots containing 10% glycerol and either 0.4 ml·OD of cells (for clones) or 1 ml·OD of cells (for libraries).
The expression of yeast-displayed scFvs was induced as follows. Liquid cultures of SC-trp + 2% glucose were inoculated using single frozen inocula, yielding an approximate starting OD of 0.05. These cultures were grown at 30?C for 8 hours; the final OD of these cultures was approximately 0.7. Cells were then spun down at 1932 g for 8 minutes at 4?C, resuspended in SC-trp + 2% galactose + 0.1% glucose at 0.2 OD, and incubated for 16 hr at 20?C. We note that adding 0.1% glucose to these galactose induction cultures was essential for reliably achieving scFv expression in a large fraction of yeast cells.
Induced yeast were fluorescently labeled as follows. Galactose induction cultures were spun down and washed with ice cold TBS-BSA (0.2 mg/ml BSA, 50 mM Tris, 25 mM NaCl, pH 8). This yielded approximately 5.3 ml OD of cells for tite-seq FACS. For antigen binding reactions, cells were then resuspended in a primary labeling reaction containing 40 ml TBS-BSA and biotinylated fluorescein (ThermoFisher B1370) at a concentration between 0 M and 10−5 M, then incubated with shaking for 1 hour at room temperature. Reaction volumes were large enough to ensure that ~ 10 antigen molecules per scFv were present, assuming ~105 scFvs per cell [7]. Cells were then washed twice with 40 ml ice cold TBS-BSA, suspended in a secondary labeling reaction containing 1 ml ice-cold TBS-BSA and 7 μg/ml streptavidin R-PE (ThermoFisher S866), and incubated for 30 min at 4?C while shaking. Cells were then spun down and resuspended in ice cold TBS-BSA and saved for FACS later that day. Expression labeling reactions proceeded in the same manner, except that the primary labeling reaction contained 1.4 μg/ml rabbit anti-c-Myc antibody (SigmaAldrich C3956) in place of the antigen, and the secondary labeling reaction contained 0.8 μg/ml BV421-conjugated donkey anti-rabbit antibody (BioLegend 406410) in place of streptavidin R-PE. The labeling reactions used to filter out improperly cloned scFvs (as described in Appendix C) proceeded in the same manner as the expression labeling reaction, except that 0.8 μg/ml mouse anti-HA antibody (Roche 11583816001) was added to the primary labeling reaction, while 0.4 μg/ml APC-conjugated antimouse antibody (BD Biosciences 550826) was added to the secondary labeling reaction. For clonal flow cytometry measurements, excluding secondary labeling we kept reagent and cell concentrations the same as described above, but reduced reaction volumes 27-fold. Secondary labeling reactions with streptavidin R-PE were done at 4 μg/ml 112.5 μ l to facilitate mixing. Secondary labeling reactions with 0.8 μg/ml BV421-conjugated donkey anti-rabbit antibody were performed in 60 μ l.
Appendix C: Cloning strategy
Amplicons containing variable CDR1H or CDR3H regions were generated as follows. An oligonucleotide library containing mutagenized 1H and 3H variable regions (see Table II) was generated by LC Sciences using microarray-based synthesis. The specific oligos used are provided at github.com/jbkinney/16_ titeseq. 1H and 3H library oligos were separately amplified via PCR using primers oRAL10 and oRAR10 (for 1H) or oRAL11 and oRAR11 (for 3H). Oligos containing the WT sequence were amplified from plasmid pCT302 [7] using primers 1H2F and 1H1R (for the 1H region) or 3H1F and 3H2R (for the 3H region). Overlap-extension PCR using primers oRA10 and oRA11, one oligo library (1H or 3H) and the complementary WT oligo (3H or 1H, respectively), and plasmid pCT302, were then used to create the iRA11 amplicon library (Fig. S1A). Note that each amplicon in this library has mutations only in the 1H variable region or in the 3H variable region, but not in both of these regions.
The pRA10 cloning vector (Fig. S1B) was assembled using Gibson cloning [50] with template plasmids pCT302 [7] and pJK14 [34]. pCT302 is the yeast display expression plasmid containing the WT scFv. pJK14 contains a ccdB cloning cassette flanked by outwardfacing BsmBI restriction sites. pRA10 closely resembles pCT302, except that it contains the ccdB cassette from pJK14 in place of the region of the scFv gene that we aimed to mutagenize. Multiple spurious BsmBI restriction sites present pCT302 were also removed in pRA10. pRA10 was propagated in Escherichia coli strain DB3.1, which is resistant to the CcdB toxin.
The pRA11 plasmid library (Fig. S1C) was generated by digesting pRA10 with BsmBI, digesting the iRA11 amplicon library with BsaI, and subsequent ligation with T4 DNA ligase. Ligation reactions were desalted and transformed into DH10B E. coli via electroporation, yielding ~ 108 transformants. The 1H and 3H libraries were cloned separately.
The pRA11 libraries were introduced into the EBY100 strain of Saccharomyces cerevisiae using high-efficiency LiAc transformation [51]. This yielded ~ 105 transformants. To filter out yeast containing improperly cloned scFvs, we induced scFv expression, immuno-affinity labeled the HA and c-Myc epitopes on the scFv, and used FACS to recover 8 105 2 106 cells that registered positive for both epitopes. The scFv induction and labeling procedures used to do this are described in Appendix B. 144 yeast clones were picked at random from this library and submitted for low-throughput Sanger sequencing of the 1H and 3H variable regions of the scFv. Based on preliminary Tite-Seq experiments, 19 of these clones were then chosen for low-throughput KD measurements.
Appendix D: Tite-Seq procedure
The inocula used for our Tite-Seq experiments comprised yeast harboring the 1H and 3H pRA11 plasmid libraries, mixed in equal proportions, and spiked at 0.625% with OPT-containing yeast (as a positive control) and at 0.625% with ?-containing yeast (negative control). Cells were then grown, induced, and labeled with antigen at eleven different concentrations (0 M, 10−9.5 M, 10−9.0 M, …, 10−5.0 M) as described in Appendix B.
Each batch of labeled cells was then sorted, using FACS, over a period of approximately 20 min. During FACS, cells were first filtered based on forward scatter and side scatter to help ensure exactly one live cell per droplet. Cells passing this criterion were sorted into 4 bins based on R-PE fluorescence. The fluorescence gates used in these sorts were kept the same across all antigen concentrations (see Figs. 3, S2, and S3). Cells were sorted into a rounded 5 ml polypropylene tube containing 1 ml 2X YPAD media. In our separate Sort-Seq experiments assaying scFv expression levels, cells were prepared and sorted in the same way, save for the changes to the labeling reaction described in Appendix B and the use of gates on BV421 fluorescence instead of R-PE fluorescence.
Each of the 48 bins of sorted cells, as well as a sample of unsorted cells, were then deposited in 5 ml of SC-trp + 2% glucose and regrown overnight at 30?C. Approximately 25 ml OD of cells were spun down, resuspended in a lysis reaction containing 200 μ l 0.5 mm glass beads, 200 μ l of Phenol/chloroform/isoamyl alcohol and 200 μ l of yeast lysis buffer (10 mM NaCl, 1 mM Tris, 0.1 mM EDTA, 0.2% Triton X-100, 0.1% SDS), and vortexed for 30 min. 200 μ l of water was added, cells were spun down, and the aqueous layer was extracted. Four subsequent extractions were performed, the first two using 200 μ l of Phenol/chloraform/isoamyl alcohol, the second two using 200 μ l for chloroform/isoamyl alcohol. Bulk nucleic acid was then ethanol precipitated and resuspended in 100 μ l of IDTE (Integrated DNA Technologies).
Two rounds of PCR were then performed on each of the 49 samples of bulk nucleic acid. In the first round of PCR, primers L1AF XX and L2AF XX were used to amplify the 1H-to-3H region and to add a bin-specific barcode (numbered XX = 01, 02, …, 64) on either end of the 1H-to-3H region; see Fig. S1. To keep PCR crossover to a minimum, only 15 PCR cycles were used. These 49 PCR reactions were then pooled, purified using a QIAquick PCR purification kit (Qiagen), and used as template for second round of PCR with primers PE1v3ext and PE2v3. Again, to keep crossover to a minimum, only 25 PCR cycles were used. This PCR reaction was again purified, mixed with PhiX DNA (at ~ 25% molarity) and submitted for sequencing using the Illumina NextSeq platform. Analysis of the resulting sequence data revealed some of the 49 FACS bins to be highly under-sampled. PCR amplicons were therefore prepared for the under-sampled bins from all three replicate experiments (using different barcodes than before) and submitted for a fourth round of sequencing.
Appendix E: Inference of KD from Tite-Seq data
We modeled the binding titration curve of each sequence – i.e., the curve describing how mean cellular fluorescence depends on antigen concentration – using a non-cooperative Hill function. Making the dependence on scFv sequence s and antigen concentration c explicit, Eq. 1 of the main text becomes where fsc denotes the mean fluorescence of cells carrying sequence s and labeled with antigen at concentration c. B represents the autofluorescence of cells, and was set equal to the mean fluorescence of cells labeled at 0 M antigen. A>s is the increase in fluorescence due to saturation of all surface-displayed scFvs, and KD,s is the dissociation constant for sequence s. We inferred As and KD,s for all sequences s, as follows.
Tite-Seq does not provide direct measurements of the fluorescence fsc. Instead, we approximated this quantity using a weighted averaged over sorting bins. Specifically, we assumed that
Here, Fbc is the mean log fluorescence of the cells that were sorted at concentration c into bin b, and pb |sc is the probability that a cell having sequence s and labeled at concentration c, if sorted, would be found in bin b. Values for Fbc were computed directly from the FACS data log. The probabilities pb |sc, by contrast, were inferred from Tite-Seq read counts. These probabilities are closely related to Rbsc, the number of sequence reads for each sequence s from bin b at antigen concentration c. This relationship is complicated by additional factors that arise from variability in sequencing depth from bin to bin. Moreover, because there were often a small num ber of reads for any particular sequence in a given bin, it was necessary in our inference procedure to treat the relationship between pb |sc and Rbsc probabilistically.
We therefore inferred values for the probabilities pb |sc through the following maximum likelihood procedure. First, we assumed that the number of reads Rbsc is re-lated to an“expected” number of reads rbsc via a Poisson distribution. The log likelihood of observing a specific set of read counts Rbsc over all bins b and concentrations c for a given sequence s is therefore given by
The expected number of reads rbsc is, in turn, related to the probability pb |sc via
Here, is the total number of reads from bin b at antigen concentration c, Cbc is the number of cells sorted into bin b at antigen concentration c (obtained from the FACS data log), is the total number of cells sorted at concentration c, and Ps is the fraction of cells in the library with sequence s. The factor RbcCc /Cbc in Eq. E4 accounts for differences in the depth with which each bin was sequenced. Note: Eq. E3 assumes that each final read arose from a different sorted cell. This assumption is clearly violated if Rbc > Cbc. In cases where this inequality was found to hold, we rescaled all Rbsc → hRbsc where h = Cbc /Rbc before undertaking further analysis.
For each sequence s, we inferred KD,s, As, Ps, and all probabilities pb |sc by maximizing the likelihood Ls subject to the constraint that at every concentration c. Note that, in this procedure, the sorting probabilities pb|sc are not modeled explicitly as a function of the putative mean fluorescence. Instead, they are inferred from the data along with the parameters of the non-cooperative Hill function. Doing this dispenses with the need for a detailed characterization of the noise in the Tite-Seq sorting procedure. The validity of this procedure is evinced by the analysis of simulated data, shown in Fig. S10.
The maximum likelihood optimization problem described above was solved as follows. For each concentration c, we created a grid of 100 equally spaced points for ln fsc ∈ [F0a, F3a]. For each possible value of fsc, we then used Nelder-Mead optimization of pb |sc to minimize Ls under the constraint in Eq. E5. Akima interpolation was then used to create a function of the optimized probability as a function of fsc. We then scanned a 321 * 201 grid of values for the pair (KD,s, As) and selected the pair that minimized . We repeated this scan by varying Ps over 95 different values. The final inferred values for KD,s, As, and Ps were those so found to maximize Ls. Python code for this inference procedure is provided at github.com/jbkinney/16_titeseq.
Appendix F: Inference of KD from flow cytometry experiments on individual clones
Low-throughput flow cytometry measurements performed on clonal cell populations were used to measure fsc,flow, the mean fluoresence of cells carrying sequence s and labeled at antigen concentration c. As for the TiteSeq inference procedure described in Appendix E, it was assumed that fsc,flow could be modeled using the noncooperative Hill function Asc /(c + KD,s) + B, where As is the increase in mean fluorescence due to fully labeled scFvs of sequence s, KD,s is the corresponding dissociation constant, and B is background fluorescence. B was computed from the average fluorescein of clone s at 0 M fluorescein. As and KD,s were then inferred by minimizing the square deviation between measured ln fsc,flow values and log Hill function predictions, i.e.,
This optimization procedure was performed using a grid search algorithm in which KD,s was restricted to the interval [10−10M, 10−3M] and As was restricted to the interval [Â, 100Â] where  denotes the average range of fluorescence values over the 4-to-8 clones assayed per flow cytometry session.
Appendix G: Realistic Tite-Seq simulations
In order to test our analysis pipeline, we simulated realistic Tite-Seq data and analyzed it with the same scripts that we used on real data. For each sequence s, a KD,s value was randomly drawn from the interval [10−10M, 10−4M] using a uniform distribution in log space, and an As value was drawn uniformly from a uniform distribution spanning the bulk of experimentally observed A values. At each of the eleven antigen concentrations c, we then modeled the distribution of cellular uorescence using a Gaussian Mixture Model (GMM) in log space. Specifically, letting x denote log10 cellular uorescence values, we assumed that the probability density describing x to be where α = 0.2 is the fraction of non-expressing cells, μ0 = 4.77 and σ0 = 1 are the mean and standard deviation of x values for dark cells, and σ1 = 0.5 is the standard deviation of x values for scFv-expressing cells. The mean x value of scFv-expressing cells, here denoted μcs, was chosen so that the population average of x is given by the Hill function in Eq. E1, i.e., so that
The left hand side of Eq. G2 can be computed analytically using Eq. G1. Doing this and solving for μsc gives this is the specific formula we used to compute μsc as a function of c, As, and KD,s. Next we computed exact pb |sc values using where b+ and b- are the upper and lower fluorescence bounds used for bin b in our Tite-Seq experiment (replicate number 1). These values were then used to draw read counts Rbsc for each sequence s values via where ks is a random variable, uniformly distributed on a log scale between 0. 01 and 100, used to represent noise due to PCR jackpotting. Data thus simulated for WT values of KD and A are shown in Fig. S9.