Method and system for predicting binding affinity and method for generating candidate protein-binding peptides

Abstract

According to a first aspect of the present invention, there is provided a computer-implemented method for predicting a binding affinity value of a query binding agent molecule to a query target molecule, wherein the query binding agent molecule has a first amino acid sequence and the query target molecule has a second amino acid sequence, the method comprising: co-encoding the first and second amino acid sequences as a plurality of data elements to generate coded amino acid pairs, each data element of the coded pair representing which amino acids of the first and second amino acid sequences pair at respective contact points between the first and second amino acid sequences to form a contact point pair, a contact point pair being a pairing of amino acids of the binder molecule and the target molecule that are in close proximity to each other to affect binding; and applying a machine learning or statistical model to the coded amino acid pairs to predict the binding affinity value, wherein the machine learning or statistical model represents at least The prediction method includes: using one processor to access a reference data store of reference binder-target pairs, the data store including each paired reference binder sequence and each reference target sequence, each reference binder-target pair having an associated measured binding value; and encoding each reference binder-target pair as a plurality of data elements, each data element of the encoded reference binder-target pair representing which amino acids of each paired reference binder sequence and reference target sequence are paired at each contact point to form a contact point pair, such that the predicted binding affinity value represents the contribution of each contact point pair to binding between the query binder molecule and the query target molecule.

Description

[Background technology]

[0001] 2. Background of the Invention Biological molecular binding is of interest throughout biomedical sciences, including bioinformatics, genomics, proteomics, medicine, and pharmacology. Understanding molecular binding helps characterize biological processes in healthy and diseased tissues, organs, and subjects, in diagnostic, prognostic, and predictive tasks, and in drug development, evaluation, and selection. Without loss of generality, one example is the role of binding in identifying immunogenic antigens for vaccine development.

[0002] In this scenario, candidate peptides can be selected based on the binding affinity values ​​of the peptides binding to the target molecule for use in the vaccine. Candidate peptides can be selected from the candidate set based on predicted binding, accelerating personalized vaccine development while ensuring the accuracy and efficacy of the antigen or neoantigen.

[0003] Identification of immunogenic antigens from pathogens and tumors has played a central role in vaccine development for decades. Over the past 15-20 years, this process has been simplified and enhanced by the adoption of computational approaches that reduce the number of antigens that need to be tested. Although the key features that determine immunogenicity are not fully understood, it is known that most immunogenic class I peptides (antigens) arise in a typical pathway by proteasomal cleavage of their parent polypeptide / protein in the cytosol, followed by transport into the endoplasmic reticulum by TAP transporters, which then package them into empty MHC molecules (major histocompatibility complexes, also called human leukocyte antigens [HLA] in humans), which are then transported to the cell surface for presentation to circulating CD8+ T cells.

[0004] The ability of a peptide to bind to an MHC molecule corresponds to the most critical step in determining immunogenicity, since only MHC-binding peptides are capable of binding and activating circulating T cells. There are now publicly available databases of rich data, such as the Immune Epitope Database and Analysis Resource (IEDB, http: / / www.iedb.org / , accessed June 2017), which provides experimentally validated measures of binding affinity for the most common MHC alleles, along with standard predefined cross-validation data sets that have been used in the scientific literature to benchmark and compare binding affinity predictors. There are also publicly available databases of rich data on the composition of certain classes of biological molecules, such as the Immuno Polymorphism Database ImMunoGeneTics HLA database (IPD-IMGT / HLA, https: / / www.ebi.ac.uk / ipd / imgt / hla / , accessed June 2017), which provides the DNA sequences of many class I and II HLA alleles. Such databases have been used to train various types of models that attempt to predict binding between de novo, untested biological molecules. Although the sources of measured data are ever-expanding, many alleles remain unrepresented in the data.

[0005] Approaches to the peptide-MHC binding problem have been divided into three categories: position-specific scoring matrices (PSSM), machine learning methods, and structural methods (Luo, et al., 2015). In PSSM approaches, binding predictions are calculated by combining values ​​taken from one or more matrices defined for each peptide residue position. As larger databases became available, PSSM approaches were largely supplanted by machine learning methods, in which potentially complex and arbitrarily flexible functions are fitted to examples from a potentially large database. Structural methods model binding through the three-dimensional structure of the molecule using data from crystal structure databases and approximations that fit the underlying physics. PSSM methods are interpretable because they are based on relatively simple mechanistic models, but tend to make poorer predictions compared to machine learning methods. Machine learning methods generally are not easily interpretable because they are not based on a mechanistic understanding of binding, but achieve state-of-the-art prediction quality. Structural methods have a clear mechanistic interpretation, but predictions are generally not as fast or accurate as with machine learning methods.

[0006] Providing high-quality predictions of binding affinity while also having a relatively simple mechanistic interpretation remains a key challenge for the industry. The earliest attempts to use statistical and machine learning models to predict binding affinity focused on individual MHC alleles, resulting in the current so-called allele-specific models in which only the role of amino acids in the peptide is considered. The current leading allele-specific methods for MHC class I are probably NetMHC4.0 (Andreatta & Nielsen, 2015) and mhcflurry (https: / / github.com / hammerlab / mhcflurry, accessed July 2017), which are machine learning models that use artificial neural networks to fit arbitrary functions to example data and use the fitted functions to make predictions. Allele-specific methods for MHC class II have also been published.

[0007] Subsequently, the increasing availability of experimental data for a wider range of common alleles prompted the development of pan-allele and pan-specific models that attempt to predict binding affinity for any allele or any particular set of alleles using a single model, respectively. Unlike allele-specific models, "pan" models implicitly or explicitly consider the amino acids that form the MHC molecule and the peptide. Pan-allele and pan-specific models generally predict binding or binding affinity less well than allele-specific models, but are applicable to alleles for which there is insufficient data to train the allele-specific model and novel alleles that may arise due to mutations (e.g., in the case of cancer). The current leading MHC class I pan model is probably NetMHCpan4.0 (Jurtz, et al., 2017), which, like its equivalent allele-specific model, is based on an artificial neural network. Pan methods for MHC class II have also been published.

[0008] Given a sufficiently large training set, machine learning methods tend to make better binding predictions than PSSMs or structural models, but the lack of interpretable mechanistic models of binding may limit their immediate commercial biomedical applications outside academic research. There is a large and growing literature on the properties that may be required to be demonstrated in automated prediction systems in addition to making good predictions, such as confidentiality, transparency, accountability, and fairness (NIPS Symposium Organizing Committee, 2016). The legal context requiring such properties of automated systems is also evolving. For example, with regard to automated decisions that significantly affect the health of natural persons, the European Union (EU) General Data Protection Regulation provides EU citizens with the right to human intervention in such decisions and to an explanation for them (European Parliament & Council, 2016). Such requirements may be easier to meet if more interpretable models are used. Summary of the Invention [Problem to be solved by the invention]

[0009] Given the importance in biological science of understanding and predicting binding and binding affinity between biological molecule pairs, particularly in the automated development of immunotherapies, there is a need in the art for methods that can provide high quality predictions on read retrieved data based on plausible mechanistic models that facilitate human interpretation and intervention, and that can provide estimates of uncertainty regarding the predictions so that downstream consumers of the predictions can act rationally on those predictions. Similarly, there is a need to identify candidate peptides from a peptide set that are suitable for binding to a target molecule for use in a vaccine, while providing a human-interpretable measure of the prediction and how it was derived. [Means for solving the problem]

[0010] Summary of the Invention In general terms, the present disclosure presents the concept of predicting pan-allelic binding affinity for MHC classes I and II by amino acid pairs that correspond to contact points between a peptide and an MHC molecule. A linear model of the contact point amino acid pairs results in a model whose parameters can be interpreted.

[0011] According to a first aspect of the present invention, there is provided a computer-implemented method for predicting a binding affinity value of a query binding agent molecule to a query target molecule, the query binding agent molecule having a first amino acid sequence and the query target molecule having a second amino acid sequence, the method comprising: encoding the first and second amino acid sequences together as a plurality of data elements to generate coded amino acid pairs, each data element of the coded pair representing which amino acids of the first and second amino acid sequences are paired at respective contact points of the first and second amino acid sequences to form a contact point pair, a contact point pair being a pairing of amino acids of the binding agent molecule and the target molecule that are in close proximity to each other to affect binding; and applying a machine learning or statistical model to the coded amino acid pairs to predict the binding affinity value, the machine learning or statistical model representing at least The method includes: accessing, with one processor, a reference data store of reference binder-target pairs including respective paired reference binder sequences and reference target sequences, each reference binder-target pair having an associated measured binding value; and encoding each reference binder-target pair as a plurality of data elements, each data element of the encoded reference binder-target pair representing which amino acids of the respective paired reference binder sequence and reference target sequence are paired at a respective contact point to form a contact point pair, such that a predicted binding affinity value represents a contribution to binding of each contact point pair of a query binder molecule and a query target molecule. Close to each other means sufficiently close to each other.

[0012] Thus, predictions of binding affinity can be determined and the models used to perform the predictions can be interpreted. In addition to providing high quality point estimates of binding affinity or binding, the invention may also provide rigorous uncertainty estimates for such point estimates. Rigorous estimates of uncertainty for predictions may facilitate rational use of predictions by downstream consumers and may aid in the interpretation or intervention of automated decisions. For example, some predictions indicate that a molecular pair will definitely bind but are unlikely and may be overturned by a skeptical expert, while other predictions indicate that a molecular pair will definitely bind but are likely but may be treated differently by the same expert. Automated downstream consumers of binding predictions may be able to make predictions or decisions that rigorously take into account the uncertainties of the inputs.

[0013] A predictor according to the present invention is capable of providing high quality predictions based on plausible mechanistic models that facilitate human interpretation and intervention, and can provide estimates of uncertainty regarding the predictions so that downstream consumers of the predictions can act rationally on the predictions.

[0014] The measured binding affinity value can be, for example, an exact value determined from laboratory experiments, an approximate value, or a value greater than or less than the experimentally determined value. In certain instances, the measured binding affinity value is Cancellation It can be done and Cancellation Information may be provided.

[0015] The invention may further provide for outputting an estimate of the probability of the accuracy of the predicted binding affinity value.

[0016] Preferably, the encoded amino acid pairs are encoded as a vector of data elements. Encoding the data elements in this manner facilitates application of a function to each of the contact point pairs to identify how each contributes to the binding affinity value. More preferably, each data element is a value indicative of the presence of amino acid pairing at each contact point. Possibly, the value is a binary value indicative of whether amino acid pairing exists at the contact point such that there is only one positive binary value for each contact point in the vector. Alternatively, the data elements may be symbols representing amino acid pairs or a matrix of possible amino acid pairs.

[0017] Applying the trained machine learning or statistical model may include retrieving a set of model coefficients from a data store. The data store may be remote or nearby the location where the method is performed and may be secret or encrypted. The coefficients may represent the magnitude and direction of the contribution of each possible pairing of amino acids to the binding affinity. Preferably, the coefficients may represent the deviation from the overall average binding affinity.

[0018] In certain embodiments, applying the trained machine learning or statistical model may involve linear combination of the retrieved coefficients with the encoded amino acid pairs, which is computationally efficient and allows for quick and easy prediction of the query data with regularity, allowing for quick and easy conversion of the query molecule into candidate peptides with high binding potential when incorporated into the vaccine development pathway.

[0019] The coefficients can be derived by applying a Bayesian inference algorithm to the coded reference binder-target pairs and their associated measured binding values. The statistical distribution can be parameterized. The Bayesian inference algorithm provides accurate predictions of the binding affinity accuracy with interpretable probabilities and clear likelihood values, so that users can interpret the likelihood of the binding affinity value accuracy and make informed decisions regarding its use. Similarly, if a binding affinity has a likelihood value below a threshold, its use can be rejected.

[0020] Each reference binder-target pair can be encoded as a sparse matrix, where each row represents a reference binder-target pair and each row is associated with a measured binding value. Such encoding during the training process facilitates computational efficiency and data storage, for example, storage in a compressed sparse row storage structure. When training on data, sparse matrix encoding improves space and time complexity.

[0021] Each row of the matrix may contain a series of bits, where each bit corresponds to a possible pairing of amino acids at each contact point and is an index of the specific amino acid present in the contact point pair. Thus, there may be one positive value at each contact point, which results in, for example, a 441-dimensional binary vector for each binder-target pair. Such encoding reduces the dimensionality, for example, to reduce the run time of model fitting and prediction procedures. This significantly reduces storage and computational efficiency.

[0022] By partitioning the rows of the matrix, the amino acid pairs can be encoded as feature vectors describing the pairing of amino acids in the reference binder sequence with amino acids in the target binder sequence, so that all the training data can be represented by one matrix for efficient storage and computation of partitioning the required data into matrices.

[0023] The machine learning or statistical model may be trained by estimating a set of coefficients that fit the encoded reference binding agent-target pairs and their associated measured binding affinity values. Fitting techniques may include, for example, maximum likelihood estimation or regularized estimation or hierarchical Bayesian estimation.

[0024] The method may further include outputting a set of parameters associated with the model such that a user may interpret whether the model is appropriate using known molecules and binding affinity values ​​for the known molecules. Such an output may provide an intervention task in the process.

[0025] The reference data store may further include reference binder-target pairs having associated indices of binding or non-binding, and the machine learning model or statistical model may estimate each reference binder-target pair associated with an indices of binding or non-binding. Cancellation I C 50 The model may be trained by associating a value with a binding peptide that is less than a threshold value, for example. The value may be less than a threshold value, so that the putative binding peptides can be used to improve the accuracy of the model and its associated predictions. The training data may contain examples from assays where binding or non-binding can be inferred, but binding affinity cannot be measured.

[0026] This example, in which training is performed on data from an assay that provides binding / non-binding results for a very large number of distinct MHC-peptide complexes, may provide a way to dramatically increase sample size, and thus result in models that make better predictions. Cancellation The approach could, in principle, combine such data with traditional binding assay data to determine binding affinity (IC 50 It also makes it possible to predict the value of

[0027] The machine learning model or statistical model estimates each reference binder-target pair with an indication of binding or non-binding. Cancellation I C 50 Associating values ​​and estimating Cancellation I C 50 For each reference binder-target pair associated with a value, the binding contribution can be calculated by integrating the associated statistical distribution over the set of possible binding affinity values. The calculation can be performed based on candidate values ​​of the model parameters proposed during model fitting.

[0028] Thus, the binding predictor may be trained using training data that may contain reference binder-target pairs, where the binding affinity is known or estimated to be below or above a certain value. In one particular example, a model trained using training data in which the binding affinity is measured may: Cancellation It was observed that they made poorer predictions compared to models trained by supplementing the same dataset with an approximately equal number of additional reference binder-target pairs for which only binding affinity values ​​were available.

[0029] In a further example, the machine learning model or statistical model may be used to derive a subset of the measured binding affinity values. Cancellation and integrating the associated statistical distribution over the set of possible binding affinity values, Cancellation calculating a likely binding affinity value corresponding to the binding affinity value; Cancellation The method can be trained by associating each reference binder-target pair associated with a measured binding affinity value with a calculated likely binding affinity value.

[0030] The query binding agent molecule may be a peptide and / or the second amino acid sequence may be an MHC or HLA protein sequence. As such, the present invention is particularly useful for determining immunogenicity.

[0031] In certain embodiments, the method may further include comparing the predicted binding affinity value to a threshold value, and the conclusion of the query binding agent molecule is bounded by the threshold value and / or the conclusion of the query binding agent molecule may be used with the target and is a suitable candidate.

[0032] The present invention is applicable to both MHC class I and MHC class II molecules.

[0033] According to a further aspect of the invention, there may be provided a method for generating at least one candidate protein-binding peptide, the method comprising obtaining the amino acid sequence of a plurality of peptides and the amino acid sequence of a protein, determining for each peptide a predicted binding affinity to the protein by a method according to any one of the above aspects of the invention, and selecting one or more candidate peptides from the plurality of peptides based on their respective predicted binding affinities.

[0034] The amino acid sequence of the protein may be obtained by one of serological antibody tests, oligonucleotide hybridization methods, nucleic acid amplification-based methods (including but not limited to polymerase chain reaction-based methods), DNA or RNA sequencing-based automated prediction, de novo peptide sequencing, Edman sequencing-based, or mass spectrometry.

[0035] The method may further include synthesizing one or more candidate peptides.

[0036] Alternatively, the method may further include encoding the candidate peptide into a corresponding DNA or RNA sequence. Additionally, the method may include incorporating the sequence into the genome of a bacterial or viral delivery system to generate a vaccine.

[0037] Therefore, peptide, DNA, or RNA-based vaccines can be more reliably tailored to individual patients, as binding affinities can be effectively predicted and the data interpreted.

[0038] According to a further aspect of the present invention, there may be provided a binding affinity prediction system for predicting the binding affinity of a query binding agent molecule to a query target molecule, the query binding agent molecule having a first amino acid sequence and the query target molecule having a second amino acid sequence, the system comprising at least one processor in communication with at least one memory device, the at least one memory device storing instructions for causing the at least one processor to perform a method according to any one of the above aspects of the present invention.

[0039] According to a further aspect of the present invention, a computer-implemented method for training a machine learning model for use in predicting a binding affinity value of a query binding agent molecule to a query target molecule may be provided. The method includes: accessing, with at least one processor, a reference data store of reference binder-target pairs including respective paired reference binder sequences and reference target sequences, each reference binder-target pair having an associated measured binding value; encoding each reference binder-target pair as a plurality of data elements, each data element of the encoded reference binder-target pair representing which amino acids of the respective paired reference binder sequences and reference target sequences are paired at respective contact points to form a contact point pair, the contact point pair being a pairing of amino acids of the binder molecule and the target molecule that are in close proximity to each other to affect binding; and training a machine learning model or a statistical model on the encoded reference binder-target pair and the measured binding value associated with each reference binder-target pair. Preferably, the method further includes outputting a set of model coefficients for use in predicting the binding affinity value of the query binding agent molecule and the query target molecule. Preferably, the machine learning model or statistical model is an average binding affinity function that models how each pairing of amino acids contributes to binding affinity. Preferably, the statistical model fits coded reference binder-target pairs to associated measured binding affinity values.

[0040] A computer readable medium may be provided that, when executed by a processor, causes the processor to perform the method of any of the above aspects.

[0041] BRIEF DESCRIPTION OF THE DRAWINGS Embodiments will now be described in detail, by way of example only, with reference to the accompanying drawings, in which: FIG. [Brief description of the drawings]

[0042] [Figure 1] A peptide that binds to a target molecule is shown. [Diagram 2] 1 illustrates an embodiment for constructing a training data set. [Diagram 3] 1 illustrates an embodiment of a method for predicting the binding affinity of a binding agent to a target. [Figure 4] 13 shows an example of a sparse matrix implemented in the example that encodes contact point pairs of a binder-target pair. [Figure 5A] 1 illustrates a conceptual matrix visualization diagram. [Figure 5B] 1 illustrates a conceptual matrix visualization diagram. [Figure 6] 1 illustrates a schematic diagram of a peptide synthesis system. [Figure 7] 1 illustrates a schematic diagram of a server. [Figure 8] Scatter plots and ROC plots are shown for an experiment in which the model was trained on IEDB2009 data and tested on IEDB2013 data. [Figure 9] Scatter plots and ROC plots for a five-fold cross-validation experiment using IEDB2009 and 2013 data are shown. [Figure 10A] 1 shows an array of heatmaps, where each heatmap provides an estimate of the model parameter β corresponding to one of the 62 contact points. [Figure 10B] Shown is a subset of Figure 10A. [Figure 11] Shown are the estimated binding probabilities ("p_bind") as a function of predicted binding affinity ("y_hat") and marginal histograms of their quantities. [Figure 12] 1 shows the results of modeling and prediction of binding affinity for variable length sequences (uncensored and censored data). DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0043] Detailed Description of the Invention The methods according to certain embodiments described herein allow for computational prediction of binding affinity values ​​of a query binder molecule, such as a peptide, to a query target molecule, such as a protein. The prediction is particularly useful for identifying candidate peptides from a candidate set capable of binding to a MHC major histocompatibility complex (MHC) molecule for personalized vaccine identification, i.e., cancer immunotherapy.

[0044] By way of example, the binding affinity can be between a peptide and an MHC molecule. Binding to MHC class I and II molecules is required for activation of CD8+ and CD4+ T cells, respectively. This scenario is consistent with HLA-A * This is exemplified by FIG. 1, which shows a ribbon diagram of the nonameric peptide 101 SLYNTIATL bound to the 02 MHC class I molecule 102 (1, 2, 3).

[0045] Although binding affinity can be measured in vitro (e.g., using competitive assays), such methods are laborious, expensive, and time-consuming. They do not feasibly identify all possible antigens among the many candidates that arise in any given proteome. This problem is particularly acute in the rapid manufacture of vaccines for infectious diseases or personalized neoantigen-based cancer vaccines. In such scenarios, high-throughput, nearly automated, and reliable predictions are required, motivating in silico approaches.

[0046] The query binding agent molecule and the query target molecule of the proposed technology each have a respective amino acid sequence. The prediction is based on reference data including reference binding agent-target pairs, each pair having a known (measured) binding value, e.g., IC2 measured in nM. 50Value or IC 50 , or other values ​​based on the reference data. The reference data may also be referred to herein as training data.

[0047] The measured binding affinity value need not be a direct measure of binding affinity, so long as it reflects the relative binding strength between the binder and the target (i.e., relative to other binder-target pairs).Typically, reference data can be obtained, at least in part, from public databases such as the Immune Epitope Database (IEDB) (www.iedb.org), GPCRdb (www.gpcrdb.org), BRENDA (http: / / www.brenda-enzymes.org), etc.

[0048] In the example reference data, each observation is recorded with the allele name (MHC class I) or name pair (MHC class II), species, peptide sequence, peptide length, and IC in nM. 50 The binding affinity between the MHC and the peptide molecule, expressed as a value, and IC 50 Inequalities on values ​​( Cancellation ) information.

[0049] From this reference data, the technology proposed herein allows training a machine learning model which can then be applied to the input data set, i.e. the query peptide and the target module described above, in order to identify candidate peptides for subsequent vaccine synthesis, in particular for cancer immunotherapy.

[0050] The proposed technique is based on the principle of considering each specific contact point pair and equating the binding affinity with the sum of the binding contributions of these pairs. A contact point pair can be considered as a pairing of amino acids of the binder molecule and the target molecule that are close to each other and affect the binding. Previously proposed techniques do not consider the specific pairing of peptide and MHC amino acids. Even if they did, the known techniques would be computationally expensive. In order to accurately train the neural network, known techniques in the art code each peptide-MHC complex as a pseudosequence, i.e., code the peptide amino acid sequence and the MHC amino acid sequence that is thought to contact the peptide.

[0051] In the background, it is known that molecular pairs bind due to complex dynamic interactions in the electromagnetic field resulting from the electronic configuration of the molecules. The usual model of binding between two biological molecules assumes the existence of contact points. A contact point includes a pair of nucleotides or amino acids, one member of the pair originating from a first molecule and the other member of the pair originating from a second molecule. Each pair of nucleotides or amino acids at a contact point is considered to be in close spatial proximity, so that there exists a sufficiently strong electromagnetic force between the nucleotides or amino acids to affect the binding between the two molecules. A contact point between the known sequences of two molecules can be described by a set of sequence position pairs.

[0052] The role of contact points in the peptide-MHC binding problem was taken into account in the development of NetMHCpan (Nielsen, et al., 2007). In a pan-allelic model, variation between peptides (as in the allele-specific model) and polymorphisms in the MHC molecules must be considered. In NetMHCpan, pairs of peptides and MHC molecules are encoded as pseudosequences that contain the peptide amino acid sequence and the MHC amino acid sequences that are thought to contact the peptide. Importantly, this encoding does not explicitly model the specific pairing of peptide and MHC amino acids at the contact points, but merely adds the relevant variation available to the artificial neural network; the effect of each specific contact point on the binding affinity may or may not be inferred.

[0053] In the literature, molecules are often classified as bound if some measure of binding affinity is below or above a certain value. However, it is known that even the best binding predictors do not always predict binding correctly, and there are no known methods that, in addition to providing high-quality point estimates of binding affinity or binding, also provide rigorous uncertainty estimates for such point estimates. Rigorous estimates of uncertainty for predictions can facilitate rational use of predictions by downstream consumers and can aid in the interpretation or intervention of automated decisions. For example, some predictions indicate that a molecule pair will bind but with a low probability that can be overturned by a skeptical expert, while other predictions indicate that a molecule pair will bind and with a high probability that can be treated differently by the same expert. An automated downstream consumer of binding predictions may be able to make predictions or decisions that rigorously consider the uncertainty of the inputs.

[0054] An embodiment of the present invention will now be described with reference to figures 2 and 3. The proposed technique can be considered as two-step: first, building a model and second, making predictions from the model. The method first comprises accessing a reference data store of reference binder-target pairs (step 201). Each reference binder-target pair comprises a reference binder amino acid sequence, such as a peptide sequence, and a reference target amino acid sequence, such as an MHC protein sequence. The following discussion focuses on peptide-MHC binding, but it will be understood that the methods and systems discussed below can be easily adapted to other data sets in which paired binder and target sequences and corresponding measured binding values ​​are available.

[0055] In the reference data, each reference binder-target pair can be associated with a measured binding value. As above, this value can be, for example, an IC 50 It can be exposed as a value.

[0056] However, it will be understood that a measured binding value can mean an exact value determined by laboratory experiment, an approximation of the binding value, an indication of binding or non-binding, or a value greater or less than the experimentally determined value. As indicated, binding affinity is typically measured using a competitive assay to determine IC 50 The IC value (in nM) is determined as the concentration of the query peptide that displaces 50% of the reference peptide bound to the query MHC molecule (or vice versa). 50 The value can take on a wide range of values, and for modeling purposes, the transformation y=1-logbIC is typically used. 50 where b is a sufficiently large logarithm base) (Nielsen, et al., Reliable prediction of T-cell epitopes using neural networks with novel sequence representations, 2003). We use this transformed scale to measure IC 50 and conversions to and from this scale are typically implicit throughout this disclosure.

[0057] As an example, a data store may contain representations of peptides that have been deconvoluted from HLA molecules and identified using mass spectrometry, which have been confirmed to bind, but for which the absolute binding affinity is never known.

[0058] In step 202, the reference data store can be used to code each reference binder-target pair as a set of contact point amino acid pairs. Contact points are pairings of amino acids of different sequences that are close to each other and affect binding. Each coded pair is associated with a binding affinity value, such as a measured binding affinity value or an inequality expression of the binding affinity (e.g., <500 nM or >500 nM).

[0059] In practice, this encoding serves as a translation from an amino acid alphabet of 21 symbols (including X, as described below) to an alphabet of 21 x 21 symbols (i.e., 441 symbols). A given symbol describes a peptide-MHC amino acid pair at a contact point, e.g., the symbol GA represents a glycine-alanine pair. Each binding affinity value is associated with an encoded contact point pair.

[0060] In an implementation described in detail below, each reference binder-target pair can be coded as a matrix of symbols to organize the data for further analysis. Preferably, this matrix can be a multidimensional sparse matrix for ease of implementation.

[0061] From the training data, in step 203, the technique trains a machine learning model or a statistical model based on the coded pairs from step 202 and the associated binding affinities. That is, it builds a function that models the coded contact point pairs into associated binding affinity values. For example, in the specific implementation described below, this function can be a linear sum. In this case, the binding affinity values ​​can be calculated as deviations from the mean of the coded matrix (as row vectors in the specific implementation described). The function thus generates a set of model coefficients that represent the estimated contribution of each contact point pair to the binding affinity. This set of model coefficients is then output in step 204. Again, the binding affinity values ​​can be an index of binding affinity, such as a measured value or an inequality.

[0062] FIG. 3 illustrates a high level process of how binding affinity values ​​can be predicted. In step 301, a representation of a query binding agent molecule is retrieved. In step 302, a representation of a query target molecule is retrieved. As will be understood, the representation can be an indication of the amino acids of the sequence in the molecule and can be referred to as an amino acid sequence. In step 303, following a similar process used to create training data from reference data, the amino acid sequences of the query binding agent molecule and the query target molecule are coded together as a contact point pair set. This can take the form of a vector representing the contact point pairs. In practice, this vector is similar to the row vector of the matrix of coded reference data.

[0063] In step 304, the trained machine learning model or statistical model is applied to the coded contact point pairs. For example, if a linear model is used to create a model coefficient set, this model coefficient set is retrieved (not shown), and then the coded contact point pair vector is multiplied by the model coefficient vector to predict the estimated binding affinity value of the query binding agent molecule and the query target molecule. The predicted binding affinity value can then be output in step 305. The output can also additionally or alternatively be a classification of bound or non-bound, a probability of binding, or an indication of binding affinity, rather than an exact value.

[0064] As discussed elsewhere herein, the output may be utilized in the vaccine development process, although the use of candidate peptides selected using the present technology may be part of a multifactorial selection and may not be selected solely on the basis of predicted binding affinity. In practice, however, the output of predicted binding affinity values ​​may be compared to a threshold and, based on the comparison, binding or no binding may be considered. Similarly, the output may select a peptide or peptide subset from a query peptide set based on the best predicted binding affinity.

[0065] In practice, for example, if the threshold is 500nM and the predicted value is above this threshold, the query peptide may be said to bind, but in more complex systems that may utilize this technology, other factors such as processing may be incorporated. 500nM is chosen here as an arbitrary threshold for illustrative purposes. In practice, the threshold may be different for every allele, so 500nM is just a potential threshold.

[0066] The remainder of this disclosure describes an example implementation of the high-level process illustrated in Figures 2 and 3, provides a more detailed illustration of the coding process proposed to enable implementation of the technology, and then provides a detailed discussion of the technology that has been tested, along with experimental data that demonstrates the efficacy of the concepts described.

[0067] First, we search for a training set based on experimental studies where someone performed a competition assay between MHC molecules, target / query peptides, and reference peptides in a lab. The training set consists of sequences of MHC molecules and sequences of peptides. For each pairing, a measure of binding affinity was empirically measured. The reason peptides bind to MHC molecules is that there is some attraction between them. Research in the field theorizes that this attraction or repulsion is explained by the proximity of peptide amino acids to molecule amino acids. The molecule is based on the principle of contact points (i.e., positions where peptide amino acids are near MHC amino acids), so at each contact point, we see amino acid pairing, one amino acid from the peptide and one amino acid from the molecule.

[0068] From the training data, a sparse matrix is ​​generated that represents each contact point pair of peptide and MHC molecule pairs in the training data. A given row in the matrix may describe the pairing of each amino acid at each contact point. Associated with each row in the matrix are measured binding affinity values ​​for the training set. In a preferred implementation, there is one matrix for the entire encoded training set, but this is not limiting and symbols may be encoded in other ways in implementations. A single sparse matrix implementation allows for computational efficiency during the encoding and training stages.

[0069] Sparsity refers to the notion that many of the values ​​in a matrix are zero or near zero. In a classic definition, a matrix of order n has n 2A matrix is ​​considered sparse if it contains much fewer non-zero elements than x. There are many alternative definitions of a sparse matrix. For the purposes of the present technique, the fact that the matrix is ​​sparse is not relevant. However, the matrix should have a specific encoding that allows the encoding of contact point pairs and the association of symbol vectors with associated measured binding affinity values. This will become practically clear from the following description. The fact that the matrix is ​​inevitably sparse is a direct consequence of the encoding method, and being sparse, this allows efficient storage of sparse matrices with well-known techniques for sparse matrix storage and computation (i.e., multiplication and addition).

[0070] In other alternatives, for example, the single matrix may be a series of matrices, each matrix representing a contact point pair, however, for the sake of brevity, only a single matrix representation is described herein to allow those skilled in the art to understand the principles of the present invention.

[0071] An implementation of a sparse matrix is ​​illustrated in Figure 4, which illustrates how a sparse matrix can be designed to implement the principles of the present disclosure. In the example sparse matrix, rows correspond to specific MHC molecules and specific peptides. Each row contains an indication of each contact point and which amino acid is involved in each pair of that contact point.

[0072] With this encoding, each row can then be split into its contact points, i.e., a row vector can be chopped into smaller row vectors. Splitting is conceptually a way of splitting a matrix. A matrix can be split into a series of vectors (rows or columns), i.e., a one-dimensional list of numbers or smaller matrices.

[0073] In MHC class I, there are 62 contact points. Therefore, each row can be divided into 62 vectors, one for each contact point. Each division is specific to a contact point. Take the first contact point as an example, this division describes which amino acid in the peptide is near which amino acid in the MHC molecule at that contact point. This information needs to be somehow encoded in the vector.

[0074] 20 amino acids are encoded by human DNA. Thus, in each pair, there can be one of the 20 amino acids on the MHC molecule side and one of the 20 amino acids on the peptide side. In the exemplary encoding, X amino acid represents the case where it is not known which amino acid is present, and X can represent an extraordinary attribute. Thus, in each contact point pair, i.e., in the contact point partition of the matrix, there is one of the 21 amino acids on each side. The pairing is one of 21 x 21 possible pairings. Thus, each contact point partition has 441 possible values.

[0075] In the sparse matrix implementation we are describing, only one value is encoded: this one value represents which amino acids in the peptide and which amino acids in the molecule are close to each other.

[0076] The column division of the matrix identifies which column belongs to which contact point and whether the pairing of peptide amino acids and molecule amino acids may be adjacent. Thus, if the column has a value of "0", this indicates that the amino acids in the column are not adjacent. If the column has a value of "1", this indicates that the peptide and molecule amino acids are adjacent.

[0077] While FIG. 4 illustrates each contact point as a number of contact points coded with an amino acid sequence, there are numerous alternatives contemplated for coding each contact point pair; that is, material at each position is not required. As an example, an abbreviated amino acid dictionary (or alphabet) may be used for each pair shown to be beneficial for a particular scenario known in the art. In other examples, each pair may be represented by a binary grouping or a physicochemical property (e.g., charge) and coded using a floating point number (rather than binary coding) for the representation of each property. Similarly, while we show 62 contact points, this number may vary and each pair may not be represented by all 20 (or 21, including unknowns as described elsewhere) amino acids.

[0078] Additionally, the binary representation may be reversed from that shown, with a "0" indicating the presence of the pair and a "1" indicating its absence.

[0079] Moreover, the order of the columns may be rearranged and is shown in this order for visualization purposes only. Preferably, the dimensions are matched between training and prediction. It is not important in which order the peptides and MHC are sorted. For example, the first "A" may come from a peptide and the second "A" from an MHC molecule, but in practice this may be indexed in any order.

[0080] It should be emphasized that FIG. 4 is not a biological example, but merely a coding example.

[0081] Figure 4 suggests that each measured binding affinity value associated with each row can be expressed as an exact value or as an inequality such as <500 nM or >500 nM, as described in more detail elsewhere herein.

[0082] In an alternative implementation, conceptually illustrated in Figure 5A, each contact point may be coded as a matrix such that the matrix is ​​in fact a matrix of embedding matrices. If each element of the matrix is ​​a contact point pair, then each column of the matrix would actually correspond to another matrix. Figure 5B illustrates a further alternative conceptual visualization of a possible implementation. In this case, each contact point is a matrix that is combined with other contact points to generate a multi-dimensional matrix representing each peptide molecule pair.

[0083] Returning to FIG. 5A, to summarize the matrix design, starting from the top left of the matrix, every 441 column represents a contact point, then moves to the next contact point. Each contact point is a 21×21 item in a row that together form one contact point of information. There can only be one long sparse entry per 441 elements and 62 non-sparse entries per row. The non-sparse entries indicate which amino acid pairings are close together, from which an amino acid sequence can be derived.

[0084] The binding affinity values ​​may be associated with each pair set individually and may or may not form part of the matrix, but preferably instead a data store is associated with each row of the matrix, i.e., there is one row in the matrix for each binding affinity measurement.

[0085] In an alternative implementation, the matrix may contain symbols, eg, GA, AB, etc., corresponding to the pairs, rather than binary values ​​representing each possible amino acid pairing of the contact points.

[0086] Each of the above examples is a conceptual visualization of the proposed technique, however what is important is to extract a contact point pair, somehow encode this contribution, and relate it to a measured binding affinity value.

[0087] The visualization in Figures 5A and 5B resembles previous work in the field, such as position-specific scoring matrices (PSSMs) used to capture motifs in biological sequences, but as noted elsewhere in this document, it should be noted at this stage that such methods do not model interactions in the same way as the one proposed here. Such methods do not consider contact point pairing (code contact point pairs) and most are not pan-allelic. That is, the proposed method allows binding predictions for all MHC molecules, not just individual MHC molecules.

[0088] This stage of the technology generated data representations from reference data that could be stored permanently or temporarily in memory.

[0089] The next step of the concrete implementation is to generate a function, in this example a linear sum or a linear regression model. In the function, a multiplication of two vectors is performed. The first vector is the rows of the matrix and the second is a vector of model coefficients estimated from the training data. The sum of the contributions to the binding affinity is only one example of the proposed technique, and is merely an example of a function that maps contact point pairs to binding affinities. Conceptually, any function can be provided. For simplicity, it is assumed that the training data is Cancellation We have not described what information may be contained in these examples; these examples are provided merely to illustrate important concepts.

[0090] Therefore, there must be a set of unknowns that are estimated from the matrix and the training data. Using Bayesian estimation, discussed below, it is possible to determine a set of coefficients that, when used as a product of row vectors, results in an approximation of the binding affinity, or comes as close as possible to it. Being an approximation, it may not be necessary to know the exact binding affinity.

[0091] Therefore, the outcome of the training process is a vector of coefficients, which is preferably stored in a data store.

[0092] Knowing the vector of coefficients, it is possible to predict the binding affinity value of a query binder and a target using the coefficients. First, a query peptide and an MHC molecule are received. Then, the peptide and the MHC molecule are encoded to generate a vector representing a contact point pair as above. If each bit in the vector represents the presence of an amino acid pair formation at a contact point, it is a sparse vector. It will be recalled that there are 62 non-sparse bits and 440x62 sparse bits in the vector. Then, this vector is multiplied by the coefficient vector to generate a predicted binding affinity value.

[0093] As will be appreciated, this column vector of coefficients only needs to be constructed once, and in practice the stored column vector values ​​can be utilized for new peptide queries. The column vector can be encrypted or stored for coefficient security, and can be interpreted privately using a request-response or query-based paradigm.

[0094] Each coefficient can be thought of as a weight, with the presence of a pair represented by a "0" or a "1", and the binding affinity is the weighted sum of the contact point pairs present in the queried combination, i.e., each pair is weighted with a coefficient of "1" to derive a value.

[0095] For each possible pairing of amino acids from the MHC molecule, for each possible amino acid from the peptide, for each contact point, there is a number. The number represents the binding contribution for each pairing at that contact point. In practice, in a linear model or linear regression, there may be a grand average. Each coefficient may represent a deviation from the grand average. Therefore, an additional column may be introduced in the training matrix that represents all "1". An additional single element in the coefficient may represent the grand average. Using the deviation from the average in this way helps with computational efficiency. As will be known to those skilled in the art, other alternatives are possible to address this computational challenge using well-known techniques of linear regression, linear modeling, or other techniques proposed to provide a function between contact point pairs and binding affinity.

[0096] In summary, the present invention can be viewed as a PSSM-like method built to incorporate models of the three-dimensional structure of molecules and leverage recent advances in statistical modeling and machine learning, which is capable of making high-quality predictions while also having a relatively simple mechanistic interpretation.

[0097] Using the proposed encoding of the amino acid pairs at each contact point, any machine learning algorithm can be used. The main idea behind the encoding is to represent the data according to a plausible model of the binding mechanism, so as to facilitate the application of statistical models or machine learning methods.

[0098] However, the encoding results in a rather high-dimensional sparse design matrix. Several statistical models and machine learning methods have properties that mean they can "tackle" such design matrices. One example is a linear model fitted using the well-known least squares method. The horseshoe estimator employed is one (Bayesian) way of dealing with the problem. Although others exist, the horseshoe has several pleasing properties.

[0099] For example, an alternative to the Horseshoe is Ridge Regression. However, this requires the researcher to specify the value of a parameter that controls an aspect of the model fit. That parameter is difficult to discuss, and in practice it is chosen by trial and error. The Horseshoe addresses this issue by tying its version of this parameter to the "noise level" of the quantity being predicted (binding affinity in this example). The researcher does not need to choose the value of this quantity, since the method estimates it from the training data.

[0100] In general, model fitting is typically considered a one-time task, so the time it takes to generate the coefficients is not important. In practice, it is known to fit models using many computing devices running in parallel via cloud computing. However, linear models (Bayesian or other) such as those described herein used in the technology are typically very fast at the prediction stage (typically run multiple times when used in product). Optionally, when using the technology to develop patient-specific immunotherapies, the process can be easily repeated to evaluate multiple candidate peptides using the stored coefficients.

[0101] In fields where the exact mechanisms underlying a process are not well understood or where it is difficult to simulate such processes with the required fidelity (e.g., due to economic, time, or other constraints), statistical and machine learning methods are beneficial because they can learn useful approximations to the process using training data (Hastie, Tibshirani, & Friedman, 2009). There is no significant difference between machine learning methods and statistical models, but machine learning methods are often used to model processes when a fundamental understanding of the mechanisms involved in the process is lacking, whereas statistical models are often used when approximations to the mechanisms can be assumed and interpretation and prediction of the model is desired.

[0102] When a particular input is known to lead to a particular outcome and a mechanism can be hypothesized, a statistical model can often be developed, and the parameter values ​​of the model can be estimated to explain the outcome under the model and its parameter values ​​as inputs. In both machine learning methods and statistical models, the estimated model parameter values ​​can be used in the model to predict outcomes for de novo inputs. The estimated parameter values ​​of the statistical model are often interpretable with respect to the hypothesized mechanism, aiding in the understanding of the model and the hypothesized or actual mechanism. The ability to interpret facilitates the development of falsifiable hypotheses that may allow for improvements to the model or have other immediate applications. For example, in the context of vaccine development, the estimated parameter values ​​can be used to determine how to modify the vaccine to improve its efficacy. In other examples, model parameter estimates that estimate uncertainty can be used to rationally choose which of many potentially expensive measurements to take to improve training or test sets. The ability to intervene facilitates some applications. For example, in the context of personalized medicine, patients with life-threatening diseases may argue against an automated decision that a specific therapy is unlikely to work. A person skilled in the art would be able to intervene to validate the automated calculations or to override the automated decisions using his or her own expert knowledge of the disease, therapy, or model.

[0103] A statistical model may be fitted to a data set containing many representative examples of the process being modeled (this is known as estimating the model parameters or training the model). A coding step is typically required to convert the representative samples into a structured form suitable for use within the statistical model. The chosen mathematical form of the statistical model and coding usually substantially impacts the model's ability to fit the training data, predict, interpret, and facilitate intervention on de novo examples. The solutions described herein provide particularly effective guidance on which coding and which statistical model should be used to predict binding between biological molecule pairs.

[0104] As described above, the encoded nucleotide pairs or amino acid pairs, their corresponding binding affinity values, and corresponding Cancellation The information may be provided as training data for a statistical model. In a particularly preferred implementation, each coded nucleotide or amino acid pair represents a nucleotide or amino acid pair at one of a number of contact points between two molecules, where a first member of the pair is from a first type of molecule and a second member of the pair is from a second type of molecule. The contact points may originate from studies of the structure of binding molecular pairs or may be inferred using statistical or machine learning models.

[0105] The encoded nucleotide or amino acid pairs may be represented as a design matrix. Each row of the design matrix may represent an example containing encoded nucleotide or amino acid pairs for a pair of biological molecules that may bind. The design matrix may be partitioned column-wise such that each partition of a row represents a particular nucleotide or amino acid pair for the example represented by that row. A partition of a given row may encode a nucleotide or amino acid pair as a feature vector that uniquely or non-uniquely describes the pairing of a particular nucleotide or amino acid from a corresponding first molecule with a particular nucleotide or amino acid from a corresponding second molecule. Non-unique encoding allows the use of a simplified nucleotide or amino acid alphabet (Peterson, Kondev, Theriot, & Phillips, 2009) in which two distinguishable nucleotides or amino acids are represented by a common symbol in the alphabet. The encoding of the reduced alphabet may be lower dimensional than the full alphabet. As one skilled in the art will recognize, dimensionality reduction may be advantageous for many reasons, including reducing storage requirements and run-times of model fitting and prediction procedures.

[0106] Preferential encoding uniquely describes pairings as binary vectors where all elements of the vector are zero except for a single element whose index represents the particular nucleotide or amino acid present in the pair (such encodings are often referred to as "one-hot" or "dummy" encodings). As one of skill in the art would be familiar with, many other encodings exist, including one-hot encoding with reference categories, BLOSUM encoding (Nielsen, 2003), and VTSA and VHSE encodings (Li, Li, & Shu, 2008). In an even more preferential encoding of amino acid pairs, using an alphabet of 20 amino acids (alanine [A], arginine [R], ... valine [V]), where the identity of one or both amino acids in each pair may be unknown (usually coded as X), the amino acid pairs may be coded as a (20+1) x (20+1) = 21 x 21 = 441-dimensional binary vector.

[0107] In the preferred case where binary encoding is used, the design matrix will be sparse. To improve the space and time complexity of the method, the design matrix may be stored in a sparse data structure, such as the Compressed Sparse Row (CSR) Stored Data Structure (also known as Compressed Row Store [CRS]). As those skilled in the art will be familiar with, other sparse data structures exist, such as the Compressed Sparse Column Store (CSC) Data Structure (also known as Compressed Column Store [CCS]) and Dictionary of Keys (DOK).

[0108] The binding affinity values ​​may be represented as a vector where the i-th element of the vector gives the binding affinity for the instance represented by the i-th row of the design matrix. Cancellation The information can be represented as a set of L, R, and U, whose elements are the left and right Cancellation ,right Cancellation , and no Cancellation However, those skilled in the art will recognize that the binding affinity values ​​and Cancellation It will be appreciated that there are numerous ways to represent information.

[0109] Binding affinity measurements are often performed using in vitro competition assays, with IC measured in nM. 50 It is expressed as a value IC 50 represents the concentration of a first type of molecule required to displace 50% of the reference molecules bound to a second type of molecule. The binding affinity values ​​may be transformed using a link function. In a preferred embodiment, the link function is: y=1-log b I C 50 (Nielsen, 2003), where log b is the logarithm to the base b, where b is large enough that any magnitude of binding affinity value in the training set can be transformed to the interval [0,1]. The logarithm base b is preferentially 250,000 nM, although those skilled in the art will recognize that other values ​​may be suitable. In another preferred embodiment, the link function is: y=lnIC 50 where ln is the natural logarithm. In yet another preferred embodiment, the link function is the identity function y=IC 50 It is.

[0110] An inverse link function can be defined to calculate the binding affinity that corresponds to the transformed binding affinity. For example, if the link function is y=1-log b I C 50 If , the inverse link function is IC 50 =b 1-y The link function is y=lnIC 50 If , the inverse link function is IC 50 =e y where e is Euler's number, and if the link function is the identity function, then the inverse link function is also the identity function. The link function and inverse link function may be clamped such that the transformed binding affinities are constrained to the interval [0,1] and the binding affinities are constrained to be greater than 0.

[0111] Critically, the link function is IC 50 When it decreases with respect to (y=1-logbIC 50 As in the case of Cancellation The direction must be reversed because, for example, IC50 <1000nM is y>1-log b Because it means 1000nM. Cancellation The information can be reversed by switching the indices of the L and R sets. In what follows, we consider the specific link function used (i.e., IC 50 is expressed) and Cancellation Reversal of direction is implicit unless otherwise stated.

[0112] An average binding affinity function is described that models how encoded nucleotide or amino acid pairs contribute to binding affinity, which is used in statistical models along with other information to parameterize statistical distributions, to predict binding affinities for de novo molecular pairs, and to assess the probability that de novo molecular pairs will bind.

[0113] The average binding function can be parameterized by a "grand average" binding affinity and, for each encoded nucleotide pair or amino acid pair, a coefficient that models the magnitude and direction of deviation from the grand average binding affinity associated with the encoded nucleotide pair or amino acid pair.

[0114] The average binding affinity function is

number

number

[0115] The vector β is x T A design matrix (i.e., x T ) can be split in a similar manner to the splitting of columns in x T and the division of β corresponds to the contact points between the first type of molecule and the second type of molecule.

[0116] β and other parameters θ can be estimated by fitting a model to the training data. The obvious way to fit a model to the training data is maximum likelihood. However, β can contain many elements (44,100 in this example), considering that each partition of x and β can be as large as 441 elements and that the number of contact points (partitions) can be approximately 100. The dimension of θ can be comparable to that of β. If the number of training examples is small compared to the dimension of (β, θ), traditional estimation methods such as maximum likelihood may not be successful. Methods based on explicit or implicit regularization can be used to estimate β and other parameters θ. Regularization methods can be understood as imposing the assumption that the observed data can be well modeled via parameters such as β that contain many values ​​that are small enough that their magnitude is negligible (i.e., in practical terms, β is sparse). Regularization methods transform estimation problems that have many inherently intractable solutions into tractable problems whose solutions generalize well to de novo examples, and there is currently a large body of literature on this topic (Jin, Maas, & Scherzer, 2017). Those skilled in the art will be aware of numerous regularized estimation methods, such as ridge regression, lasso, elastic net, compressive sensing, and matching pursuit algorithms. In a preferred implementation, β and the other parameters θ may be estimated via hierarchical Bayesian estimation, as described below.

[0117] Hierarchical Bayesian inference for high-dimensional models can be performed using optimization methods such as limited-memory Broyden-Fletcher-Goldfarb-Shannot (L-BFGS) (Byrd, Hansen, Nocedal, & Singer, 2016) or stochastic gradient ascent (Robbins & Monro, 1951) to compute maximum a posteriori (MAP) point estimates of β and other parameters. Alternatively, approximate samples from the joint posterior distribution of β and θ can be drawn using automatic differential variational inference (ADVI) (Kucukelbir, Tran, Ranganath, Gelman, & Blei, 2017) or Markov chain Monte Carlo (MCMC) methods such as the No U-Turn (NUTS) sampler (Hoffman & Gelman, 2014).

[0118] Each of these methods requires the ability to compute a posterior likelihood or log likelihood value (optionally excluding the constant term) given training data and proposed values ​​for β, θ. The following can be formulated in terms of likelihood or log likelihood, but those skilled in the art will recognize that for computational reasons it may be advantageous to work with probability masses and densities on a logarithmic scale. Given a design matrix X, binding affinity y, and censorship information L, R, U, the posterior log likelihood of parameters β, θ is logf(β,θ|X,y,L,R,U)=logf(y|X,L,R,U,β,θ)+logf(β,θ)-logf(X,y,L,R,U) where f(y|X,L,R,U,β,θ) is the likelihood function (probability mass or probability density of y conditional on X,L,R,U,β,θ), f(β,θ) is the prior probability mass or density function of β,θ, and f(X,y,L,R,U) is the probability mass or density of X,y,L,R,U. Since X,y,L,R,U are constant for a given training set, the logf(X,y,L,R,U) term can be eliminated such that logf(β,θ|X,y,L,R,U) can be computed up to a constant additive term.

[0119] The likelihood function may be calculated via a probability mass or density function that models the probability of observing y given the predicted mean μ. The likelihood function models the stochastic variation of the amount measured by the assay from the predicted value that is not subject to stochastic variation (e.g. measurement error).

[0120] The binding affinity values ​​in the training set are Cancellation When the binding affinity is low (e.g., when only the upper or lower bounds of the binding affinity are known), Cancellation The likelihood corresponding to the binding affinity is Cancellation The binding predictor may be calculated by integrating its associated statistical distribution over the possible binding affinity values ​​allowed by . Thus, the binding predictor may be trained with training data that may contain examples where the binding affinity is known or assumed to be below or above a certain value. Moreover, the training data may contain examples from assays where binding or non-binding can be inferred but binding affinity cannot be measured. Examples of training data include mass spectrometry data. In the MHC class I peptide binding example, data from a competitive assay that allows the measurement of binding affinity could be supplemented with data from peptide eluate tests where it is only known whether the peptide binds or does not bind. As an example, where the binding affinity cannot be measured but it can be assumed that binding occurs, the binding peptides may have a binding affinity of less than 500 nM. Cancellation I C 50 value, or alternatively, allele-specific Cancellation The values ​​can be used to model the observation that distinct MHC alleles can have different binding properties.

[0121] The machine learning model or statistical model estimates each reference binder-target pair with an indication of binding or non-binding. Cancellation The model can be trained by associating IC50 values ​​with the binding affinity values ​​of each pair and, for each such pair, calculating a contribution to the likelihood by integrating the associated statistical distribution over the set of possible binding affinity values, given the candidate values ​​of the model parameters proposed during model fitting.

[0122] Therefore, the log likelihood function logf(y|X,L,R,U,β,θ) is

number

number

[0123] As would be known to one skilled in the art, there are many probability masses or density functions that can be chosen for f. In a preferred embodiment, f is the density function of a normal distribution, and the link function is y=1-log b I C 50 or f is the probability mass function of the Poisson distribution and the link function is y=lnIC 50 or f is the probability mass function of the negative binomial distribution and the link function is y=lnIC 50 Depending on the support of the function chosen for f, the domain of y may be adjusted, for example, by rounding the true values ​​of y to integers.

[0124] For all i (row index of X and element index of y)

number

[0125] The posterior log likelihood is the parameter

number

number

number

number

[0126] The log likelihood function is, on average,

number

number

[0127] If the training set is large enough, m 1 , s 1 , s 2 Those skilled in the art will observe that the exact values ​​of the constants such as , τ are relatively unimportant and that as φ→∞, the negative binomial distribution tends towards a Poisson distribution, which may be used instead of the negative binomial distribution if overdispersion is not supported by the training data.

[0128] In the example below, there are ways to interpret fitted models or to intervene in the use of such models by presenting estimates of model parameters using an output medium. According to an example of a proposed solution, estimates of β or θ can be presented as an array of heat maps on an output medium such as a computer screen. In such a presentation, each heat map corresponds to a division of β (i.e., contact points), and within each heat map, the rows may correspond to nucleotides or amino acids from a first type of molecule and the columns to nucleotides or amino acids from a second type of molecule, and the hue or intensity of each element of the heat map may correspond to an estimate of the contribution made by the corresponding pairing of nucleotides or amino acids at the corresponding contact point. Such a presentation may enable a suitably qualified person to perform an intervention task such as predicting binding affinity for a molecular pair of known sequence, given the contact point indices used to fit the model and the estimated overall average binding affinity. Those skilled in the art will recognize that there are numerous ways to present such information (e.g., as a table or nomogram) and numerous output media (e.g., paper printout or computer user interface).

[0129] A method is provided for predicting binding affinities for de novo molecular pairs using an estimate of the average binding affinity function and the joint posterior parameters of the model. By forming the design matrix as well as the training data, it is possible to predict binding affinities for de novo molecular pairs. Measured or estimated binding affinity values ​​and censoring information are not required for de novo prediction. The estimate of the joint posterior parameters of the model can be a maximum a posteriori (MAP) point estimate, a sample from the joint posterior distribution of the parameters of the statistical model, or a summary statistic calculated from such samples. In a preferred example, the summary statistic is the mean of the samples from the joint posterior distribution. Given the estimated parameters β, the binding affinity for the molecules represented by the design matrix X can be calculated using the average binding affinity function

number

[0130] Calculating an estimate of the probability that the molecular pair will bind provides a way to quantify the uncertainty in the predicted binding affinity for each de novo molecular pair. In one example, this can be estimated by summarizing a large number of binding affinity predictions. In this case, each prediction can be made with estimates of the parameters of a statistical model drawn from a sample of the joint posterior distribution of the model's parameters. The summary can be the proportion of the large number of predictions that meet a criterion, such as predictions that are below a particular value. In the MHC class I peptide binding example, this proportion can be a percentage of predictions that meet a criterion, such as predictions that are below a certain value. 50 It may be a percentage of a number of predictions.

[0131] In other examples,

number

[0132] In this document, we provide the obvious use of this method in designing vaccines.However, it is understood that the techniques described herein are equally applicable to designing regulated T cells that recognize the identified targets.Similarly, this technique can also be used to identify the neoantigen load in tumors, which is used as a biomarker, i.e., as a predictor of response to therapy.

[0133] 6, an example of a system suitable for implementing embodiments of the present method is shown. The system 600 includes at least one server 610 in communication with a reference data store 620. The server may also be in communication with an automated peptide synthesis device 630, for example, via a communication network 640.

[0134] In certain embodiments, the server may obtain the amino acid sequences of a plurality of peptides and the amino acid sequence of a protein, and for each peptide, determine a predicted binding affinity to the protein using the steps described above. Based on the respective predicted binding affinities, the server may select one or more candidate peptides from the plurality of peptides.

[0135] The candidate peptides can be sent to an automated peptide synthesis device 630 which synthesizes peptides. The automated peptide synthesis device 630 synthetically produces the target epitope, i.e., the target peptide in this example. It will be understood that automated peptide synthesis techniques are well known in the art and any known technique can be used. Typically, the target peptide is synthesized using standard solid-phase synthetic peptide chemistry, purified using reverse-phase high performance liquid chromatography, and then formulated as an aqueous solution. If used, prior to administration, the peptide solution is usually mixed with an adjuvant and then administered to the patient. Similarly, peptides can be encoded into DNA or RNA and used as vaccines as described elsewhere.

[0136] Peptide synthesis technology has been around for over 20 years, but has undergone rapid improvements in recent years. For the sake of brevity, we will not describe such machines in detail, but their operation will be understood by those skilled in the art. Also, such conventional machines can be adapted to receive candidate proteins from a server.

[0137] The server may include the above-described functionality of predicting the binding affinity of the query binding agent molecule to the query target molecule. The respective binding affinities may be sent to a further processing module to identify target epitopes based on the binding affinities suitable for vaccine production. However, the server may also be operable to identify target epitopes for vaccine design. It is understood, of course, that these functions may be subdivided across various processing entities of a computer network and various processing modules that communicate with each other. For example, the server may receive one or more query molecules via a computer network and return suitable binding affinities or a set of candidate epitopes. The query may be received electronically from a computer network or input to a graphic user interface.

[0138] The technology of predicting binding affinity and identifying candidate peptides based on binding affinity can be integrated into a broad ecosystem for customized vaccine development. Although examples of vaccine development ecosystems are well known in the art and have been described at a high level, for the sake of brevity, we will not describe the ecosystem in detail.

[0139] In the example ecosystem, a first sample step may be to isolate DNA from tumor biopsies and matched healthy tissue controls. In a second sequencing step, the data is sequenced and variants or mutations are identified. In an immune profiler step, associated mutant peptides may be generated «in silico».

[0140] Using the related mutant peptides and the techniques described herein, neoantigens are predicted and selected, and target epitopes are identified for vaccine design, i.e., candidate peptide sequences are chosen based on their predicted binding affinity determined using the techniques described herein.

[0141] The target epitope is then synthetically produced using conventional techniques as described above. Prior to administration, the peptide solution is usually mixed with an adjuvant and then administered to the patient (vaccination).

[0142] Suitable target epitopes predicted by the methods described herein can also be used to generate other types of vaccines other than peptide-based vaccines. For example, peptide targets can be encoded in corresponding DNA or RNA sequences and used to vaccinate patients, either directly using naked DNA / RNA or alternatively using delivery vehicles such as microparticles, nanoparticles, bacterial delivery systems, etc. It should be noted that DNA is usually inserted into a plasmid construct. Alternatively, DNA can be integrated into the genome of bacteria or viral delivery systems (depending on the viral delivery system, RNA is also possible), which can be used to vaccinate patients, and thus the vaccines generated are genetically engineered viruses or bacteria that generate the targets in patients after immunization, i.e. in vivo.

[0143] An example of a suitable server 610 is shown in Figure 7. In this example, the server includes at least one microprocessor 700, memory 701, optional input / output devices 702, such as a keyboard and / or display, and an external interface 703, interconnected via a bus 704 as shown. In this example, the external interface 703 can be used to connect the server 610 to peripheral devices, such as a communications network 640, a reference data store 620, other storage devices, etc. Although a single external interface 703 is shown, this is for illustrative purposes only, and in practice multiple interfaces may be provided using a variety of methods (e.g., Ethernet, serial, USB, wireless, etc.).

[0144] In use, the microprocessor 700 executes instructions in the form of application software stored in the memory 701 to enable the performance of required processes, including communicating with the reference data store 620 to receive and process input data and / or client devices to receive sequence data for query binding agent molecules and query target molecules, and performing binding affinity predictions in accordance with the methods described above. The application software may include one or more software modules and may be executed in a suitable execution environment, such as an operating system environment.

[0145] It will therefore be appreciated that server 700 may be formed from any suitable processing system, such as a suitably programmed client device, a PC, a web server, a network server, etc. In one particular example, server 610 is a standard processing system, such as an Intel architecture-based processing system, executing software applications stored on non-volatile (e.g., hard disk) storage (although this is not required). However, it will also be appreciated that the processing system may be any electronic processing device, such as a microprocessor, a microchip processor, logic gate structures, firmware associated with implementing logic, optionally in an FPGA (field programmable gate array), or any other electronic device, system, or arrangement. Thus, although the term server is used, this is for illustrative purposes only and is not intended to be limiting.

[0146] It will be appreciated that although server 610 is shown as a single entity, server 610 may be distributed across several geographic locations, for example, by using a processing system and / or database provided as part of a cloud-based environment, and thus the above described arrangement is not required and other suitable configurations may be used. EXAMPLES

[0147] Materials and Methods Forming the training set Set forth below is a detailed example of the implementation of aspects of the present invention along with a set of results obtained from this example that demonstrate the utility of the present invention in practice.

[0148] The datasets BD2009 and BD2013 described in (Kim, et al., 2014) were downloaded from the Immune Epitope Database and Analysis Resource (IEDB) website (http: / / tools.iedb.org / main / datasets / , accessed August 2016). These datasets are referred to as IEDB2009 and IEDB2013 from here on. A repeatable uniform pseudorandom subset of 1 / 2 to 1 percent of the IEDB2009 and 2013 data was obfuscated (weakly encrypted) and reserved for future use. The datasets contain information about the MHC class I allele name, human or animal species name, peptide sequence, peptide length, and the measured binding affinity between the allele and the peptide molecule (IC in nM). 50 values), and IC 50 In addition, the dataset identifies three different types of 5-fold cross-validation partitions, called cv_rnd, cv_sr, and cv_gs. Based on the results of (Kim, et al., Dataset size and composition impact the reliability of performance benchmarks for peptide-MHC binding predictions, 2014), the cv_rnd partition was adopted for subsequent experiments.

[0149] Release 3.25.0 of the IPD-IMGT / HLA database of human MHC DNA sequences was downloaded in extended mark-up format (XML) from the Anthony Nolan HLA Informatics Group's GitHub repository (https: / / github.com / ANHIG / IMGTHLA / , accessed August 2016). The XML file was a parsed intermediate data structure formed to represent the mapping from human MHC allele names to quality-controlled amino acid sequences of the α1 and α2 domains of MHC class I alleles translated from the DNA sequences encoding those domains. Similar data structures were constructed to represent the mapping from MHC allele names for animal species present in the IEDB2009 and 2013 datasets (chimpanzee, gorilla, horse, macaque, and mouse) to quality-controlled amino acid sequences of the α1 and α2 domains of those alleles. Animal amino acid sequences were accessed in the second half of 2016 and were obtained from sources including the Research Collaboratory for Structural Bioinformatics Protein Data Bank (RCSB PDB, http: / / www.rcsb.org / pdb / home / home.do).

[0150] The IEDB2009 and 2013 datasets were combined with MHC class I amino acid sequence data to form a dataset that, in addition to the data in the IEDB2009 and 2013 datasets, also contained the sequences of the α1 and α2 domains of MHC class I allelic molecules for each peptide. Peptides composed of nine amino acids (nonamers) are of interest for applications involving MHC class I because the binding groove of MHC molecules that bind peptides is structured such that nonamers are preferentially bound. Entries in the combined dataset corresponding to peptides of other lengths were removed, leaving entries for only nonamers.

[0151] Using data published by (Nielsen, et al., 2007), a data structure was created describing 62 pairs of nonamer peptides and contact point indices to the α1 and α2 domain amino acid sequences. Each of the 62 pairings represents an amino acid in the nonamer that is believed to be within 4 Å of one of the 182 amino acids in the α1 and α2 domains of a potential MHC class I molecule, such that the two amino acids may interact to affect the binding of the peptide to the MHC molecule. A 21-symbol amino acid alphabet was used, including the 20 standard amino acids encoded by DNA, plus an X symbol to represent an unknown amino acid. The 62 contact point amino acid pairs were coded as a sparse binary design matrix using one-hot coding and compressed sparse row storage. For computational convenience, Cancellation The information is represented as a vector of indicator values, where the i-th indicator value is the i-th binding affinity Cancellation Identify the information and Cancellation is coded as -1, and Cancellation Code as 0, and then Cancellation was coded as 1. Thus, set L consisted of all indices whose vectors had a value of -1, set R consisted of all indices whose vectors had a value of 1, and set U consisted of all indices whose vectors had a value of 0. In each of the experiments that followed, the binding affinity values ​​were represented as vectors and transformed using the link functions as described above. Conversion of predicted binding affinities back to IC50 scale using the corresponding inverse link function is implicit unless otherwise stated. The decreasing link function (IC 50 ) is used, Cancellation The direction was reversed.

[0152] The result of these steps is a data set suitable for forming a training set, each containing a large number of examples of encoded nucleotide or amino acid sequence pairs, their corresponding binding affinity values, and corresponding censoring information, and for forming a corresponding test set used for validation purposes. The following training and test sets were formed: i) a training set corresponding to the IEDB2009 data and a test set corresponding to the IEDB2013 data; ii) a 5-fold cross-validation training and test set including, for each of the 5 folds defined by the cv_rnd folds, a training set including all examples except those corresponding to the fold, and a test set including all examples corresponding to the fold; and iii) A one-allele-leavaged training set containing all data corresponding to the IEDB 2009 and 2013 data except for the examples corresponding to each plucked allele, and a corresponding test set containing data for the plucked allele. In either case, the training and test sets are disjointed so that the model cannot be evaluated using the data it was trained on.

[0153] Training on IEDB2009 data and testing on IEDB2013 data To assess how well the proposed method can predict binding affinity and binding for de novo pairs of MHC class I and nonamer pairs, a statistical model was fitted to the training set for the IEDB2009 data (i) described above according to the second and third aspects of the present invention. The average binding affinity function

number

[0154] The binding affinity of each nonamer-MHC class I molecule pair in the test set was predicted against the IEDB2013 data (i) above. Logarithmic scale measured and predicted IC 50The quality of the binding affinity predictions was assessed using a scatter plot between the values ​​and by calculating the Pearson correlation coefficient between them. The quality of the binding predictions was assessed by plotting receiver operating characteristic (ROC) curves and calculating the area under the ROC curve (AUC), and true binders were considered to have a measured IC of less than 500 nM. 50 It was defined as having a value.

[0155] 5-fold cross-validation To estimate the effect of sampling error on the summary statistics of prediction quality, we performed a 5-fold cross-validation run using the dataset from cv_rnd fold (ii) above.

[0156] According to the second and third aspects of the invention, a statistical model was fitted to each remaining partition. The mean binding affinity function, log likelihood function, link function and estimation algorithm were as in the previous experiment.

[0157] Binding affinities were predicted for each nonamer-MHC class I molecule pair in each cull. For each cull, log-scaled measured and predicted IC 50 The quality of the binding affinity predictions was assessed using a scatter plot between the values ​​and by calculating the Pearson correlation coefficient between them. For each culled fold, the quality of the binding predictions was assessed by plotting the receiver operating characteristic (ROC) curve and calculating the area under the ROC curve (AUC). True binders had a measured IC of less than 500 nM. 50 The effect of sampling error on correlation coefficients and AUC values ​​was summarized by means and 95% confidence intervals using a t-distribution.

[0158] One-allele cross-validation To estimate the ability of the method to generalize to predict binding affinities for alleles not present in the training data, leave-one-allele cross-validation was performed using dataset (iii) above.

[0159] According to the second and third aspects of the invention, a statistical model was fitted to each remaining partition. The mean binding affinity function, log likelihood function, link function and estimation algorithm were as in the previous experiment.

[0160] Binding affinities were predicted for each nonamer-MHC class I molecule pair in each cull. For each cull, log-scaled measured and predicted IC 50 Generalization was assessed by calculating the Pearson correlation coefficient between values. Binding prediction quality was assessed by calculating the area under the ROC curve (AUC). True binders were defined as those with a measured IC<500 nM. 50 were defined as having an IC value of less than 20. 50 Results of partitions with omitted measurements were discarded, as estimates of correlation coefficients and AUC values ​​may not be reliable in such cases. To test whether the (human) contact points used in the model allow the model to generalize from human to animal alleles, correlation coefficients and AUC values ​​were summarized by allele for each species, with means and 95% confidence intervals.

[0161] Interpreting the model According to the second and third aspects of the invention, a statistical model was fitted to the entire IEDB2009 and 2013 data. The average binding affinity function, log likelihood function, link function, and estimation algorithm were as in the previous experiment. According to the fourth aspect of the invention, an array of heatmaps was generated to visualize the estimates of β. The array was constructed such that each heatmap in the array corresponds to one of the contact points defined in (Nielsen, et al., 2007). The rows of the heatmap correspond to peptide amino acids, the columns correspond to MHC molecule amino acids, and the color of each element corresponded to the estimated binding affinity contribution at the corresponding contact point.

[0162] Estimating Joint Probabilities In the implementation example, the binding probability was estimated for each nonamer-MHC class I molecule pair in the test set for the binding affinity predictions on dataset (i) (IEDB2013 data). Prediction η2 To estimate the variation of σ 2 We used estimates of the variability of each component of β along with the prediction. We used normal distributions parameterized by the prediction and variability to estimate the measured IC 50 The probability that the IC was less than 500 nM was estimated. These probabilities were used to calculate the predicted IC 50 was plotted as a function of

[0163] result Training on IEDB2009 data and testing on IEDB2013 data Figure 8 shows the scatter plot and ROC plot of this experiment. Table 1 shows the Pearson correlation coefficient and area under the ROC curve (AUC) of this experiment.

[0164] 5-fold cross-validation Table 2 shows the results of this experiment. The average Pearson correlation coefficient was 0.782 (95% confidence interval [0.777, 0.787]). The average AUC was 0.933 (95% confidence interval [0.930, 0.936]). Figure 9 shows the scatter plot and ROC plot.

[0165] One-allele cross-validation Table 3 shows the results of this experiment.

[0166] Interpreting the model Figure 10A shows an array of heatmaps presenting estimated parameter values, while Figure 10B shows a subset of the array for clarity.

[0167] Estimating Joint Probabilities FIG. 11 shows a plot of estimated binding predictions ("p_bind") as a function of predicted binding affinity ("y_hat"). A marginal histogram of abundance is also shown. FIG. 11a shows that the estimated binding probabilities [0.312, 0.558] lie across the range of predicted binding affinities [0, 250,000] nM. The sudden decrease in binding probability near 250,000 nM is due to clipping in the link function. FIG. 11b shows the same data for the range of predicted binding affinities [0, 500] nM.

[0168] Training on IEDB2009 data and testing on IEDB2013 data FIG. 12 shows an image similar to FIG. 8, illustrating the evaluation of MHC class I predictions for k-mers instead of 9-mers.

[0169] Consideration Training on IEDB2009 data and testing on IEDB2013 data Training on the EIDB2009 data and testing on the IEDB2013 data facilitated the calculation of point estimates of the Pearson correlation coefficient and the area under the receiver operating characteristic (ROC) curve (AUC), respectively, and the measured IC using de novo examples on which the model was not trained. 50 and predicted IC 50 The Pearson correlation coefficient of 0.801 characterizes the agreement between the measured and predicted IC 50 Indicates that the values ​​are strongly, but not perfectly, correlated.

[0170] The binding affinity predictor can be used as a binding predictor (i.e., classifier) ​​by assigning a "binder" or "non-binder" label to predictions based on a binding affinity threshold. In MHC class I peptide binding problems, a threshold of 500 nM is often used, but any threshold can be chosen to balance the risk of false positive and false negative errors. The AUC value of 0.936 can be interpreted as an estimate of the expected probability that the model will assign a lower predicted binding affinity to a randomly selected binding peptide-MHC pair than to a randomly selected non-binding pair, when the expectation is taken over a uniform distribution of binding affinity thresholds. In practice, a binding predictor based on the present method will typically be operated with a single pre-specified threshold, so the AUC statistic, while useful, is somewhat artificial. The ROC curve itself facilitates rational threshold selection. The ROC curve shows that, for example, if a false positive rate of 0.2 can be tolerated, then the binding affinity threshold can be chosen such that the binding predictor can be operated with a true positive rate of approximately 0.9.

[0171] 5-fold cross-validation The effect of sampling error on summary statistics of prediction quality was estimated by 5-fold cross-validation using the cv_rnd partition of the IEDB data. The average Pearson correlation coefficient was estimated to be 0.782 with a 95% confidence interval of [0.777, 0.787]. The average AUC was estimated to be 0.933 with a 95% confidence interval of [0.930, 0.936]. These values ​​are consistent with the point estimates for the IEDB2013 data in the previous experiment. The shapes of the 5-fold ROC curves are very similar to each other and are consistent with being operable with a true positive rate of approximately 0.9 when a false positive rate of 0.2 is tolerated.

[0172] One-allele cross-validation To estimate the ability of the method to generalize to alleles not present in the training data, we performed leave-one-allele cross-validation. The model demonstrated the ability to generalize to many human alleles. Generalization to the well-characterized human allele HLA-A02-01 was excellent (correlation coefficient of 0.830 and AUC of 0.950), and even better for alleles HLA-A02-199 and HLA-A02-509 (e.g., AUC values ​​of 0.973-0.981). However, generalization to several human alleles, such as HLA-A-01-01, HLA-B-27-03, HLA-B-27-05, and HLA-B-46-01, was poor (AUC values ​​of 0.594, 0.5, and 0.542, respectively).

[0173] The model did not generalize to animal alleles more than to human alleles. On average, the Pearson correlation coefficient and AUC were statistically equivalent to random performance for all mouse alleles except H-2-Ld. On average, generalization to human alleles was statistically significant over all other animal species (without correction for multiple comparisons). This is not surprising considering that the contact points used in the model were determined with human alleles known to be different from the animal alleles. The differences would be expected to be larger for species that are evolutionarily more different from each other. For example, mouse alleles are known to differ from human alleles with respect to "anchor points" (specific peptide sequence positions that have been found to be particularly important in predicting binding affinity). The anchor point model may be considered as a simplification of the contact point model postulated by the present invention. Generalization deteriorates as a function of evolutionary distance across the tested species, from human (mean AUC of 0.830) to chimpanzee (mean AUC of 0.643), to macaque (mean AUC of 0.640), to mouse (mean AUC of 0.575). The poorer generalization to animal alleles compared to human alleles provides evidence that modeling binding contributions at contact points is mechanistically plausible.

[0174] Interpreting the model Presentation of the estimated model parameters may aid one skilled in the art in interpreting the fitted model. 50 The parameter estimates for the model with a link function that decreases with respect to IC 50 A negative estimate of IC corresponds to a peptide and MHC amino acid pairing associated with a small value of IC (i.e., a stronger binder), whereas a negative estimate of IC corresponds to a peptide and MHC amino acid pairing associated with a small value of IC (i.e., a stronger binder). 50 (i.e., weaker binders). The figure also illustrates that the estimates of β obtained using the horseshoe estimation are numerically very sparse (i.e., many values ​​of the parameters are close to zero), but some have very large magnitudes.

[0175] With such a representation, one skilled in the art can infer amino acid pairings that are expected to be preferentially involved in binding. Such inferential hypotheses can then be tested in silico, in vitro, or in vivo.

[0176] Also, as required by law, one skilled in the art can intervene in the prediction of binding affinity given the sequences of a peptide and MHC pair. One can identify the amino acid pairs corresponding to each contact point and for each pair read off the binding affinity contribution from the corresponding heat map. The sum of these values ​​and estimates of the intercept term are then passed through an appropriate inverse link function to obtain the IC 50 The automated predictions can be verified to be correctly calculated, and experiments can be performed in alternative scenarios, for example to see how binding affinity changes when the peptide sequence is altered.

[0177] Estimating Joint Probabilities Although predicted strong binders have an associated binding probability of just over 55%, the ability to obtain an estimate of the uncertainty of the predictions is nevertheless useful because it allows downstream consumers of the predictions to act rationally on the basis of those predictions.

[0178] conclusion We developed a novel, mechanistically plausible model of binding between pairs of biological molecules that enables high-quality predictions of binding and binding affinity, facilitates human interpretation and intervention, and provides uncertainty estimates for those predictions so that downstream consumers of those predictions can act rationally on those predictions.

[0179] Previously proposed techniques do not take into account the specific pairing of peptide and MHC amino acids. To do so would be computationally expensive with known techniques. To accurately train a neural network, known techniques code each peptide-MHC complex as a pseudosequence, i.e., coding the peptide amino acid sequence and the MHC amino acid sequence that is likely to contact the peptide.

[0180] The concept of the present invention is based on the principle of considering each specific contact point pair and equating the binding affinity with the sum of the binding contributions of these pairs.

[0181] To encode this, each combination is equivalent to a unique symbol (212 symbols). The pairs are encoded using a sparse matrix with a single non-sparse element representing the specific amino acid present in the pair. To calculate how each pair contributes to the binding affinity and to generate the training data, the binding affinities are converted to vectors and the deviation from the average binding affinity is determined (using a vector dot product).

[0182] Known Bayesian estimator machine learning techniques (such as probability distribution functions) are used to estimate the deviation from the mean for the new set of contact point pairs, and then the most likely binding affinity is determined accordingly.

[0183] Candidate peptides for use can be selected from the set of most likely binding affinities for the candidate peptides.

[0184] Next, a series of examples will be described, each of which describes a particular aspect of the present disclosure.

[0185] According to a first example, a number of examples of encoded nucleotide or amino acid sequence pairs, their corresponding binding affinity values, and corresponding Cancellation A method can be provided for forming an informative training set, where nucleotide or amino acid pairs are encoded by one or more encoders, and the number of encoded nucleotide or amino acid pairs in each example and their interpretations are invariant across the training set, and corresponding binding affinity values ​​and Cancellation The information is generated from assays or inferred based on the results of assays that can infer binding, and for each binding affinity: Cancellation The information specifies whether the measured binding affinity value is expected to be less than (<) a particular binding affinity, or less than or equal to (≦) a particular binding affinity, or equal to (=) a particular binding affinity, or greater than (≧) a particular binding affinity, or greater than (>) a particular binding affinity.

[0186] According to this example, the encoded nucleotide pairs or amino acid pairs, their corresponding binding affinity values, and the corresponding Cancellation The information can be provided as training data for a statistical model. In a particularly preferred embodiment, each coded nucleotide or amino acid pair represents a nucleotide or amino acid pair at one of a number of contact points between two molecules, the first member of the pair being from a first type of molecule and the second member of the pair being from a second type of molecule. The contact points can originate from studies of the structure of the binding molecule pairs or can be inferred using statistical or machine learning models.

[0187] The encoded nucleotide or amino acid pairs may be represented as a design matrix. Each row of the design matrix may represent an instance containing encoded nucleotide or amino acid pairs for a pair of biological molecules that may bind. The design matrix may be partitioned column-wise such that each partition of a row represents a particular nucleotide or amino acid pair (e.g., represented by the row) for the instance represented by that row. A partition of a given row may encode a nucleotide or amino acid pair as a feature vector that uniquely or non-uniquely describes the pairing of a particular nucleotide or amino acid from a corresponding first molecule with a particular nucleotide or amino acid from a corresponding second molecule.

[0188] Preferential encoding uniquely describes pairings as binary vectors where all elements of the vector are zero except for a single element whose index represents the particular nucleotide or amino acid present in the pair (such encoding is often referred to as "one-hot" or "dummy" encoding). In an even more preferential encoding of amino acid pairs, using an alphabet of 20 amino acids (alanine [A], arginine [R], ... valine [V]), where the identity of one or both amino acids in each of the pairs may be unknown (usually coded as X), amino acid pairs may be coded as a (20+1)x(20+1)=21x21=441-dimensional binary vector.

[0189] In the preferred case where binary encoding is used, the design matrix will be sparse. To improve the space and time complexity of the method, the design matrix may be stored in a sparse data structure, such as a Compressed Sparse Row (CSR) storage data structure (also known as Compressed Row Storage [CRS]).

[0190] The binding affinity values ​​may be represented as a vector where the i-th element of the vector gives the binding affinity for the instance represented by the i-th row of the design matrix. Cancellation The information can be represented as a set of L, R, and U, whose elements are the left and right Cancellation ,right Cancellation , and no Cancellation represents an index of the binding affinity of the target molecule to a binding affinity vector.

[0191] The binding affinity values ​​may be transformed using a link function. In a preferred embodiment, the link function is y=1-log b I C 50 (Nielsen ML, 2003). The base of the logarithm, b, is preferentially 250,000 nM. In another preferred embodiment, the link function is y=lnIC 50 where ln is the natural logarithm. In yet another preferred embodiment, the link function is the identity function y=IC 50 It is.

[0192] An inverse link function can be defined to calculate the binding affinity that corresponds to the transformed binding affinity. For example, if the link function is y=1-log b I C 50 If , the inverse link function is IC 50 =b 1-y The link function is y=lnIC 50 If , the inverse link function is IC 50 =e y where e is Euler's number and if the link function is the identity function, then the inverse link function is also the identity function. The link function and inverse link function may be clamped such that the transformed binding affinities are constrained to the interval [0,1] and the binding affinities are constrained to be greater than 0.

[0193] Critically, the link function is IC 50 When it decreases with respect to (y=1-log b I C 50 As in the case of Cancellation The direction must be reversed because, for example, IC 50 <1000nM is y>1-log b Because it means 1000nM. Cancellation The information can be reversed by switching the indices of the L and R sets. In what follows, we consider the specific link function used (i.e., IC 50is expressed) and Cancellation Reversal of direction is implicit unless otherwise stated.

[0194] In a further example, an average binding affinity function can be provided that models how encoded nucleotide or amino acid pairs contribute to binding affinity, which is used in statistical models along with other information to parameterize statistical distributions, to predict binding affinities for de novo molecular pairs, and to assess the probability that de novo molecular pairs will bind.

[0195] The average binding function can be parameterized by a "grand average" binding affinity and, for each encoded nucleotide pair or amino acid pair, a coefficient that models the magnitude and direction of deviation from the grand average binding affinity associated with the encoded nucleotide pair or amino acid pair.

[0196] The average binding affinity function can be expressed as, for example,

number

number

[0197] The vector β is x T A design matrix (i.e., x T ) in a manner similar to the division of the columns of x Tand the division of β corresponds to the contact points between the first type of molecule and the second type of molecule.

[0198] In a further example, a method may be provided for estimating β and other parameters θ by fitting a model to training data. β and other parameters θ may be estimated by hierarchical Bayesian estimation.

[0199] Hierarchical Bayesian inference for high-dimensional models can be performed using optimization methods such as limited-memory Broyden-Fletcher-Goldfarb-Shannot (L-BFGS) (Byrd, Hansen, Nocedal, & Singer, 2016) or stochastic gradient ascent (Robbins & Monro, 1951) to compute maximum a posteriori (MAP) point estimates of β and other parameters. Alternatively, approximate samples from the joint posterior distribution of β and θ can be drawn using automatic differential variational inference (ADVI) (Kucukelbir, Tran, Ranganath, Gelman, & Blei, 2017) or Markov chain Monte Carlo (MCMC) methods such as the No U-Turn (NUTS) sampler (Hoffman & Gelman, 2014).

[0200] Each of these methods requires the ability to compute a posterior likelihood or log-likelihood value (optionally excluding the constant term) given training data and proposed values ​​for β and θ. Given a design matrix X, binding affinity y, and censoring information L, R, and U, the posterior log-likelihood of parameters β and θ is given by logf(β,θ|X,y,L,R,U)=logf(y|X,L,R,U,β,θ)+logf(β,θ)-logf(X,y,L,R,U) where f(y|X,L,R,U,β,θ) is the likelihood function (probability mass or probability density of y conditional on X,L,R,U,β,θ), f(β,θ) is the prior probability mass or density function of β,θ, and f(X,y,L,R,U) is the probability mass or density of X,y,L,R,U. Since X,y,L,R,U are constant for a given training set, the logf(X,y,L,R,U) term can be eliminated such that logf(β,θ|X,y,L,R,U) can be computed up to a constant additive term.

[0201] The binding affinity values ​​in the training set are Cancellation (i.e., when only the upper or lower bounds of binding affinity are known), Cancellation The likelihood corresponding to the binding affinity is Cancellation The binding predictor may be calculated by integrating its associated statistical distribution over the possible binding affinity values ​​allowed by . Thus, the binding predictor may be trained using training data that may contain examples where the binding affinity is known or estimated to be below or above a certain value.

[0202] Therefore, the log likelihood function logf(y|X,L,R,U,β,θ) is

number

number

[0203] f is the density function of the normal distribution, and the link function is y=1-log b I C 50or f is the probability mass function of the Poisson distribution and the link function is y=lnIC 50 or f is the probability mass function of the negative binomial distribution and the link function is y=lnIC 50 It is.

[0204] For all i (row index of X and element index of y)

number

[0205] The posterior log likelihood is the parameter

number

[0206] Additionally, presenting estimates of model parameters using an output medium may provide a way to interpret the fitted model or to intervene in the use of such a model. According to an example embodiment of the proposed solution, estimates of β or θ may be presented as a heatmap array on an output medium such as a computer screen. Such a presentation may enable a suitably qualified person to perform an intervene task such as predicting binding affinity for a molecular pair of known sequence given the contact point indices used to fit the model and the estimated grand average binding affinity.

[0207] Further, a method may be provided for predicting binding affinities for de novo molecular pairs using the average binding affinity function and estimates of the joint posterior parameters of the model. By forming the design matrix as well as the training data, it is possible to predict binding affinities for de novo molecular pairs. Measured or estimated binding affinity values ​​and censoring information are not required for de novo prediction. The estimates of the joint posterior parameters of the model may be maximum a posteriori (MAP) point estimates, samples from the joint posterior distribution of the parameters of the statistical model, or summary statistics calculated from such samples. In a preferred embodiment, the summary statistics are the average of the samples from the joint posterior distribution. Given the estimated parameters β, the binding affinity for the molecules represented by the design matrix X can be calculated by the average binding affinity function

number

[0208] Also provided may be a method to quantify the uncertainty in the predicted binding affinity for each de novo molecular pair by calculating an estimate of the probability that the molecular pair will bind. In one embodiment, this may be estimated by summarizing a large number of binding affinity predictions, where each prediction may be made with an estimate of a parameter of a statistical model drawn from a sample of the joint posterior distribution of the model's parameters. The summary may be the proportion of a large number of predictions that meet a criterion, such as predictions that are less than a certain value. In other embodiments, a normal approximation may be used, based on the estimate of the parameter that models the uncertainty of β.

[0209] Peptide-MHC binding is central to the study of the adaptive immune system. In vitro binding affinity (IC50) assays cannot be scaled for large-scale epitope prediction applications (e.g., personalized neoantigen vaccines), thus motivating accurate in silico approaches. Leading machine learning methods make good predictions but typically lack mechanistic interpretation and do not provide prediction uncertainty estimates. We developed a mechanistic pan-allelic model covering MHC classes I and II in which IC50 is predicted as a function of amino acid pairs at peptide-MHC contact points. Approximately 40% of IC50 values ​​are consistent with the publicly available binding dataset. Cancellation The present inventors have Cancellation Treating the values ​​as measurements and testing for bias with common prediction quality metrics such as the Pearson correlation coefficient (PCC) showed that this implementation can overestimate PCC by 12% (simulations) and 18% (experiments on class I data). Cancellation When the data were removed to remove such bias from the model metrics, the cross-validated estimates of PCC and area under the receiver operating characteristic curve (AUC) were 0.658 ± 0.01 and 0.834 ± 0.007 (nonamers, class I), 0.668 ± 0.009 and 0.844 ± 0.005 (k-mers, class I), and 0.571 ± 0.02 and 0.779 ± 0.01 (class II). CancellationWith the data included, the PCC and AUC were estimated to be 0.761±0.009 and 0.923±0.005 (nonamer, class I), 0.755±0.006 and 0.915±0.004 (k-mer, class I), and 0.598±0.02 and 0.793±0.01 (class II). We used strict data blinding to test the null hypothesis of no overfitting and observed no evidence of such (P>0.05). Models that accept k-mers often identify nonamer binding cores in longer peptides. Using publicly available X-ray structural data, we demonstrated that class II models can identify binding cores significantly better than chance (P=0.039). Finally, we extended the model to predict contact points between nonamer peptides and MHC class I molecules. Class I models trained with inferred contact points performed nearly identically to those trained with experimentally verified contact points, demonstrating that it is not necessary to rely on X-ray structural data. This disclosure presents a mechanistic model of binding that is competitive with the current state of the art, Cancellation We highlight the importance of careful processing of data and suggest how estimates of predictive uncertainty can be used to facilitate rational vaccine design.

[0210] Description Below are descriptions of embodiments described herein that may provide certain advantages.

[0211] 1. Numerous examples of encoded nucleotide or amino acid sequence pairs, their corresponding binding affinity values, and corresponding Cancellation A method of forming an informative training set, wherein nucleotide pairs or amino acid pairs are encoded by one or more encoders, and the number of encoded nucleotide pairs or amino acid pairs in each instance and their interpretations are invariant across the training set, and corresponding binding affinity values ​​and CancellationInformation is generated from assays or inferred based on the results of assays that can infer binding, and for each binding affinity, indicates whether the measured binding affinity value is expected to be less than (<), or less than or equal to (≦), or equal to (=), or greater than (≧), the specified binding affinity. Cancellation The information identifies the method.

[0212] 2. The method of claim 1, wherein each encoded nucleotide pair or amino acid pair represents a nucleotide pair or amino acid pair at one of a number of contact points between two molecules, a first member of the pair being derived from a first type of molecule and a second member of the pair being derived from a second type of molecule.

[0213] 3. The method of claim 2, wherein the encoded nucleotide pairs or amino acid pairs are represented as a design matrix, with each row of the design matrix representing one example containing encoded nucleotide pairs or amino acid pairs of a biological molecule pair that can bind.

[0214] 4. The method of claim 2 or 3, wherein the column-wise partitioning of the design matrix represents nucleotide or amino acid pairings, and the partitioning of a given row may encode nucleotide or amino acid pairs as feature vectors that uniquely or non-uniquely describe the pairing of a particular nucleotide or amino acid from a corresponding first molecule with a particular nucleotide or amino acid from a corresponding second molecule.

[0215] 5. The method of claim 4, wherein the design matrix may be stored in a sparse data structure.

[0216] 6. A method for calculating an average binding affinity function, which functions models how encoded nucleotide pairs or amino acid pairs contribute to binding affinity, and which binding affinity can be transformed using a link function, which is preferentially the identity function, or more preferentially y=lnx, or even more preferentially y=1-logb wherein b is a sufficiently large constant to ensure that an arbitrarily large portion of the binding affinities are mapped to the interval, which interval is preferentially [0,1], and the link function can be clamped to ensure that all binding affinities are mapped to the interval, and where, if x is measured in nM, b is preferentially 100,000 nM, or 250,000 nM, or 500,000 nM.

[0217] 7. The method of statement 6, wherein the average binding function is parameterized by the grand average binding affinity.

[0218] 8. The method of claim 6, wherein the average binding function is parameterized by coefficients that model the magnitude and direction of deviation from the overall average binding affinity associated with the encoded nucleotide or amino acid pair.

[0219] 9. The average binding affinity function is

number

number

[0220] 10. The method of claim 9, wherein the division of xT and β corresponds to a contact point between a first type of molecule and a second type of molecule.

[0221] 11. A method according to any one of the preceding claims for estimating β and other parameters θ by fitting a model to training data.

[0222] 12. The method of claim 11, wherein explicit or implicit regularization is used to estimate β and the other parameters θ.

[0223] 13. The method of claim 12, wherein β and other parameters θ are estimated by hierarchical Bayesian estimation.

[0224] 14. The method described in description 13, where an optimization method such as limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) or stochastic gradient ascent is used to compute maximum a posteriori (MAP) point estimates of β and other parameters.

[0225] 15. The method of claim 13, wherein approximate samples from the joint posterior distribution of β, θ are drawn using an automated differential and variational inference (ADVI) or a Markov chain Monte Carlo (MCMC) method, such as the No U-Turns (NUTS) sampler.

[0226] 16. The method of claim 13, wherein a posterior likelihood value or a log likelihood value (optionally excluding a constant term) is calculated given the training data and proposed values ​​of β, θ.

[0227] 17. A method according to any one of the preceding statements, wherein one or more likelihoods or log-likelihoods corresponding to one or more censored binding affinities are calculated by integrating one or more statistical distributions over the possible binding affinity values ​​allowed by the censorship information, or the integration is performed implicitly using a cumulative probability mass or density function.

[0228] 18. A method according to any one of the preceding statements, wherein data from one or more assays allowing the measurement of binding affinity are supplemented with data where it is known, inferred or assumed that binding of the molecules does or does not occur.

[0229] 19. The method of claim 18, wherein binding of a molecule that is known, suspected, or hypothesized to occur or not occurs is assigned a censored binding affinity below or above one or more specified values.

[0230] 20. The method of any one of the preceding statements, wherein the molecules are nonameric peptides and MHC molecules.

[0231] 21. The method of claim 19 or 20, wherein the censored binding affinity value is assumed to be below 500 nM or 1000 nM.

[0232] 22. The method of claim 19 or 20, wherein censored binding affinity values ​​are assigned based on MHC alleles represented in the training data.

[0233] 23. The log likelihood function is

number

number

[0234] 24. f is the density function of the normal distribution and the link function is y=1-log b I C 50 24. The method of claim 6 or 23,

[0235] 25. If f is the probability mass function of the Poisson distribution and the link function is y=lnIC 50 or the method according to statement 6 or 23.

[0236] 26. f is the probability mass function of the negative binomial distribution and the link function is y=lnIC 50 24. The method of claim 6 or 23,

[0237] 27. A method according to any one of the preceding statements, wherein the domains of transformed or untransformed binding affinity are adjusted to match the support of the statistical distribution used according to statement 23.

[0238] 28. Average binding affinity function for all i

number

[0239] 29. The method of claim 28, wherein the matrix-vector product Xβ is computed using a sparse linear algebra routine.

[0240] 30. The method of claim 23, wherein the posterior likelihood or log likelihood is specified by a hierarchy of prior distributions.

[0241] 31.

number

number

[0242] 32. One or more likelihood or log-likelihood functions have an average

number

[0243] 33. m 1 is preferentially 1 / 2, and s 1 is preferentially 1 and s 2 33. The method according to claim 32, wherein:

[0244] 34. One or more likelihood or log-likelihood functions have an average

number

number

[0245] 35. m 1 35. The method according to claim 34, wherein: is preferentially 1 / 2, s1 is preferentially 5, and τ is preferentially 5 / 2.

[0246] 36. A method according to any one of the preceding statements for interpreting the fitted model by presenting estimates of the model parameters using an output medium.

[0247] 37. The method of claim 36, wherein one or more estimates of β or θ are presented using an output medium.

[0248] 38. The method of statement 37, wherein one or more estimates of one or both of β and θ are presented as one or more graphs or tables, and in a preferred embodiment the graphs may be one or more heat maps or nomograms.

[0249] 39. The method of claim 37, wherein the output medium is paper or a computer screen or an audio device.

[0250] 40. A method according to any one of the preceding statements for predicting binding affinity for a de novo molecular pair using estimates of the average binding affinity function and joint posterior parameters of the model.

[0251] 41. The method of claim 40, wherein the design matrix is ​​formed as is the training data used to train the model.

[0252] 42. The method of statement 40, wherein the estimates of the joint posterior parameters of the model are one or more of a maximum a posteriori (MAP) point estimate, a sample from the joint posterior distribution of the parameters of the statistical model, or a summary statistic calculated from such a sample.

[0253] 43. The method of claim 42, wherein the summary statistic is the mean of samples drawn from the joint posterior distribution.

[0254] 44. Given an estimated parameter β, what is the binding affinity for a molecule represented by the design matrix X?

number

[0255] 45. A method for estimating the uncertainty in the predicted binding affinity for one or more de novo molecular pairs by calculating an estimate of the probability that one or more molecular pairs will bind.

[0256] 46. ​​The method of claim 45, wherein the probability is estimated by aggregating multiple binding affinity predictions.

[0257] 47. The method of statement 46, wherein each prediction is made using estimates of parameters of a statistical model drawn from a sample from the joint posterior distribution of the parameters of the model.

[0258] 48. The method of any of statements 45, 46, and 47, wherein the summary can be a percentage of a number of predictions that meet the criteria.

[0259] 49. The method of statement 48, wherein the criterion is that the predicted binding affinity is below, above, or within a particular range of values.

[0260] 50. The method of statement 49, wherein the molecules of interest are nonameric peptides and MHC allele molecules, and the criterion is the proportion of a majority of predictions of binding affinity below or above a given threshold or within a particular threshold range.

[0261] 51. The method of statement 50, wherein the allele is an MHC class I allele and the criterion is a majority prediction percentage of IC50 values ​​below 500 nM or a majority prediction percentage of IC50 values ​​above 500 nM.

[0262] 52. If the joint probability is F(κ|μ i ,η i ) and F is normally distributed N(μ i ,η i ) is the cumulative distribution function of μ i is the average predicted binding affinity of the i-th pair of molecules, and η i η 2 = σ 2 +λ Tis the i-th element of Xλ, σ is the standard deviation, and λ is μ i 46. ​​The method of claim 45, wherein X is a design matrix and κ is a binding affinity threshold.

[0263] 53. The method of statement 52, wherein the molecules of interest are nonameric peptides and MHC allele molecules.

[0264] 54. The method of statement 52 or 53, wherein the allele is an MHC class I allele and κ is 500 nM.

[0265] 55. One or more processors; a memory containing instructions that, when executed by one or more processors, cause the apparatus to perform any of the methods described above; one or more storage devices that can be used to store instructions executable by one or more processors, or training, or testing, or de novo data, or results; zero or more connections that can be used to initiate a method according to any of the above descriptions or to transmit one or more results to one or more other devices; 13. An apparatus comprising:

[0266] References Byrd, RH, Hansen, SL, Nocedal, J., & Singer, Y. (2016). A Stochastic Quasi-Newton Method for Large-Scale Optimization. SIAM Journal on Optimization, 26(2), 1008-1031. Carvalho, CM, Polson, NG, & Scott, JG (2010). The horseshoe estimator for sparse signals. Biometrika, 97(2), 465-480. Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd Edition ed.). Springer. Hoffman, M. D., & Gelman, A. (2014). The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15(1), 1593-1623. Jin, B., Maas, P., & Scherzer, O. (2017, June). Special issue on sparsity regularization in inverse problems. Inverse Problems, 33(6). Kim, Y., Sidney, J., Buus, S., Sette, A., Nielsen, M., & B., P. (2014). Dataset size and composition impact the reliability of performance benchmarks for peptide-MHC binding predictions. BMC Bioinformatics, 15(214). Kim, Y., Sidney, J., Buus, S., Sette, A., Nielsen, M., & Peters, B. (2014). Dataset size and composition impact the reliability of performance benchmarks for peptide-MHC binding predictions. BMC Bioinformatics, 15(241). Kucukelbir, A., Tran, D., Ranganath, R., Gelman, A., & Blei, D. M. (2017). Automatic Differentiation Variational Inference. Journal of Machine Learning Research, 18(14), 1-45. Li, Z., Li, G., & Shu, M. e. (2008). A novel vector of topological and structural information for amino acids and its QSAR applications for peptides and analogues. Science in China Series B: Chemistry, 51(10), 946-957. Nielsen, M. L. (2003). Reliable prediction of T-cell epitopes using neural networks with novel sequence representations. Protein Science, 12, 1007-1017. Nielsen, M., Lundegaard, C., Blicher, T., Lamberth, K., Harndahl, M., Justesen, S., . . . Buus, S. (2007). NetMHCpan, a method for quantitative predictions of peptide binding to any HLA-A and-B locus protein of known sequence. PLOS ONE, 2(8), e796. Peterson, E. L., Kondev, J., Theriot, J. A., & Phillips, R. (2009). Reduced amino acid alphabets exhibit an improved sensitivity and selectivity in fold assignment. Bioinformatics, 25(11), 1356-1362. Robbins, H., & Monro, S. (1951). A Stochastic Approximation Method. Annals of Mathematical Statistics, 22(3), 400-407.

[0267] Table

Table 1

[0268]

Table 2

[0269]

Table 3

[0270]

Table 4

[0271]

Table 5

[0272]

Table 6

Claims

1. 1. A computer-implemented method for predicting a binding affinity value of a query binding agent molecule to a query target molecule, the query binding agent molecule having a first amino acid sequence and the query target molecule having a second amino acid sequence, the method comprising: encoding said first and second amino acid sequences together as a plurality of data elements to generate coded amino acid pairs, each data element of said coded pairs representing which amino acids of said first and second amino acid sequences pair at respective contact points of said first and second amino acid sequences to form contact point pairs, a contact point pair being a pairing of amino acids of a binder molecule and a target molecule that are in close proximity to each other to affect binding; applying a trained machine learning or statistical model to the encoded amino acid pairs to predict binding affinity values, the machine learning or statistical model comprising: accessing, with at least one processor, a reference data store of reference binder-target pairs including respective paired reference binder sequences and reference target sequences, each reference binder-target pair having an associated measured binding value; encoding each reference binder-target pair as a plurality of data elements, each data element of the encoded reference binder-target pair representing which amino acids of a respective paired reference binder sequence and reference target sequence are paired at a respective contact point to form a contact point pair; the model is trained by estimating a set of coefficients that fit the encoded reference binding agent-target pairs and their associated measured binding affinity values; applying the trained machine learning model or statistical model includes retrieving a set of model coefficients from a data store, and applying the trained machine learning model or statistical model includes a linear combination of the retrieved coefficients and the encoded amino acid pairs. and predicting, which is trained by Including, A computer-implemented method, wherein the predicted binding affinity value represents the contribution to binding of each contact point pair between the query binding agent molecule and the query target molecule.

2. 2. The computer-implemented method of claim 1, wherein the encoded amino acid pairs are encoded as a vector of data elements.

3. 3. The computer-implemented method of claim 1, wherein each data element is a value indicative of the presence of an amino acid pairing at each contact point.

4. The computer-implemented method of claim 1 , wherein the associated measured binding values ​​are censored.

5. The computer-implemented method of claim 1 , further comprising outputting an estimate of the probability of accuracy of the predicted binding affinity value.

6. 6. The computer-implemented method of claim 1, wherein the coefficients are derived by applying a Bayesian estimation algorithm to the coded reference binding agent-target pairs and the associated measured binding values.

7. 7. The computer-implemented method of claim 1, wherein each reference binder-target pair is encoded as a sparse matrix, each row representing a reference binder-target pair and each row associated with a measured binding value.

8. 8. The computer-implemented method of claim 7, wherein each row of the matrix contains a series of bits, each bit corresponding to a possible pairing of amino acids at each contact point and indexing a specific amino acid present in the contact point pair, and division of the rows of the matrix encodes amino acid pairs as feature vectors describing pairings between amino acids of the reference binding agent sequence and amino acids of the reference target sequence.

9. 9. The computer-implemented method of any one of claims 1 to 8, wherein the reference data store further comprises reference binder-target pairs having associated binding or non-binding indicators, and the machine learning or statistical model can be further trained by associating an estimated cut-off IC50 value with each reference binder-target pair associated with the binding or non-binding indicator.

10. 10. The computer-implemented method of claim 9, further comprising: for each reference binder-target pair associated with an estimated censored IC50 value, calculating the contribution to binding by integrating an associated statistical distribution over the set of possible binding affinity values.

11. 11. The computer-implemented method of claim 1, further comprising outputting a set of parameters associated with the model such that a user may interpret whether the model is appropriate using known molecules and binding affinity values ​​for known molecules.

12. The computer-implemented method of any one of claims 1 to 11, wherein the query binding agent molecule is a peptide and / or the second amino acid sequence is an MHC protein sequence or an HLA protein sequence.

13. 1. A method for generating at least one candidate protein-binding peptide, comprising: obtaining amino acid sequences of a plurality of peptides and an amino acid sequence of a protein; determining for each peptide its predicted binding affinity to said protein by a method according to any one of claims 1 to 12; selecting one or more candidate peptides from the plurality of peptides based on their respective predicted binding affinities; The method includes:

14. The method of claim 13, further comprising synthesizing the one or more candidate peptides or encoding the candidate peptides into corresponding DNA or RNA sequences and / or incorporating the sequences into the genome of a bacterial or viral delivery system to design a vaccine.

15. 13. A binding affinity prediction system for predicting the binding affinity of a query binding agent molecule to a query target molecule, wherein the query binding agent molecule has a first amino acid sequence and the query target molecule has a second amino acid sequence, the system comprising at least one processor in communication with at least one memory device, the at least one memory device storing instructions for causing the at least one processor to perform a method according to any one of claims 1 to 12.

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