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Computational strategies for dissecting the high-dimensional complexity of adaptive immune repertoires

Enkelejda Miho, Alexander Yermanos, Cédric R. Weber, Christoph T. Berger, Sai T. Reddy, Victor Greiff

arXiv:1711.11070v1q-bio.QM

TL;DR

AIRR-seq has revealed the high-dimensional complexity of immune repertoires, but computational synthesis across repertoire dimensions remains missing. This review surveys computational approaches to repertoire analysis and reports that the field has matured, yielding insights into immune development and disease profiling.

  • Problem

    A computational approach synthesizing multiple dimensions of repertoire complexity is missing, hindering high-dimensional understanding.

    Source: Conclusion · p. 13

  • Method

    The review surveys computational, mathematical, and statistical approaches for analyzing, measuring, and predicting immune repertoire complexity.

    Source: Introduction · p. 2

  • Results

    The computational immunology toolbox has matured, yielding insights into B- and T-cell development and disease and infection profiling.

    Source: Conclusion · p. 13

  • Takeaways & Limitations

    AIRR-seq has catalyzed computational and systems immunology by providing molecular insight into repertoire complexity.

    Source: Introduction · p. 2

    A computational approach synthesizing many dimensions of repertoire space is missing, limiting high-dimensional understanding.

    Source: Conclusion · p. 13

Abstract

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The adaptive immune system recognizes antigens via an immense array of antigen-binding antibodies and T-cell receptors, the immune repertoire. The interrogation of immune repertoires is of high relevance for understanding the adaptive immune response in disease and infection (e.g., autoimmunity, cancer, HIV). Adaptive immune receptor repertoire sequencing (AIRR-seq) has driven the quantitative and molecular-level profiling of immune repertoires thereby revealing the high-dimensional complexity of the immune receptor sequence landscape. Several methods for the computational and statistical analysis of large-scale AIRR-seq data have been developed to resolve immune repertoire complexity in order to understand the dynamics of adaptive immunity. Here, we review the current research on (i) diversity, (ii) clustering and network, (iii) phylogenetic and (iv) machine learning methods applied to dissect, quantify and compare the architecture, evolution, and specificity of immune repertoires. We summarize outstanding questions in computational immunology and propose future directions for systems immunology towards coupling AIRR-seq with the computational discovery of immunotherapeutics, vaccines, and immunodiagnostics.

Introduction

AIRR-seq has exposed the immense, dynamic diversity of adaptive immune repertoires and enabled computational analysis of their complexity. This review surveys downstream computational, mathematical, and statistical methods for analyzing repertoire diversity, architecture, evolution, and convergence.

Introduction

  • V(D)J recombination and nucleotide deletion and addition generate >10^13 potential B- and T-cell receptor sequences, while clonal expansion, selection, and immune memory shape dynamic repertoires (1,2) (3–8).Repertoire dynamics span germline genes to clonal diversity, molecular to cellular processes, and short-lived responses to memory lasting decades (9–14).Source: Introduction · p. 2
  • Since 2009, AIRR-seq datasets have grown to 100 millions to billions of reads, driving computational methods to dissect repertoire complexity (6,21,22) (23).Methods address diversity generation, repertoire architecture, antibody evolution, and molecular convergence; the review illustrates this growth in Figures 1 and 2.Source: Introduction · p. 2
  • The review covers downstream computational, mathematical, and statistical methods for analyzing, measuring, and predicting repertoire complexity, chiefly applicable to both antibody and T-cell studies.It excludes data preprocessing, for which standard operating procedures lack consensus, and notes exceptions to cross-application where relevant (2,17,24).Source: Introduction · p. 2

Measuring immune repertoire diversity

Immune repertoire diversity spans germline gene variation, VDJ recombination, and clonal composition, but only a fraction of potential diversity is represented in an individual. AIRR-seq enables these dimensions to be quantified, compared, and related to antigen-driven responses, while important questions remain about measurement and antigen-specific repertoires.

Measuring immune repertoire diversity

  • Only a fraction of potential immune receptor diversity is present in any individual, and diversity analysis spans germline building blocks, VDJ generation, and repertoire frequencies.The number of cells and clones constrains the diversity represented at a given time; these analyses have expanded quantitative insight into naïve and antigen-driven diversity.Source: Measuring immune repertoire diversity · p. 3
  • Accurate diversity measurement depends on read annotation and germline references that match the individual, since mismatches can distort gene assignments and somatic hypermutation estimates.IgDiscover reconstructs V-gene databases de novo (40), TiGER detects novel alleles from mutation patterns (37), Lym1K aggregates validated and novel alleles (41,42), and probabilistic annotation has revealed segment- and allele-dependent mutation processes (4,43–46).Source: Measuring immune repertoire diversity · pp. 3–4
  • VDJ recombination is biased, and this bias can generate public clonotypes and predetermined sequence signatures in both public and private clones (4,5,44,54,56).The signatures occur across naïve and antigen-selected compartments, while recombination statistics may help distinguish antigen-specific public clonotypes from naïvely predetermined ones (46,55).Source: Measuring immune repertoire diversity · p. 4
  • Clonotype definitions vary, and diversity profiles can capture clonal frequency-distribution shape more faithfully than a single index (62,63,64,69).Hill-Diversity includes richness (α = 0), exponential Shannon-Weiner (α → 1), inverse Simpson (α = 2), and Berger-Parker (α → ∞); the clonal plane represents richness and evenness to distinguish polyclonal from oligoclonal samples (71).Source: Measuring immune repertoire diversity · pp. 4–5
  • Clonal frequency distributions are often power-law distributed, and repertoire diversity can contain antigen-associated information about host immune status (63,72–76).Zipf-like distributions may arise naturally when fluctuating unobserved variables, such as external antigen environments, affect the system (75).Source: Measuring immune repertoire diversity · p. 5
  • Open questions include integrating distinct diversity dimensions into a universal metric, modeling arbitrary-length interactions beyond probabilistic models’ short-range scope, and explaining antigen-specific repertoires and chain-pairing rules when large-scale data become available.Strategies allow confidence areas around each diversity profile across differently sized repertoires (64,77); precision under incomplete sampling matters because human studies often isolate limited numbers of peripheral-blood B and T cells (17,78–80).Source: Measuring immune repertoire diversity · p. 6

Resolving the sequence similarity architecture of immune repertoires

Immune repertoire similarity architecture captures frequency-independent sequence relationships that shape antigen-recognition breadth, complementing diversity analysis. Network methods and similarity indices enable increasingly quantitative analysis, while comparison across people, similarity layers, and antibody measurement levels remains unresolved.

Resolving the sequence similarity architecture of immune repertoires

  • Similarity architecture describes frequency-independent relationships among immune receptor sequences, and greater receptor dissimilarity corresponds to broader antigen space coverage.Its characterization is relevant to designing naïve antibody libraries and synthetic repertoires that recapitulate natural repertoires (87).Source: Resolving the sequence similarity… · p. 6
  • Clonal networks encode sequences as nodes and similarity-threshold matches as edges, but all-by-all distances become costly beyond 10^5 clones; imNet enables large-scale construction and antibody networks resist subsampling (87).Network visualizations become uninformative beyond 10^3 nodes, motivating quantitative graph analysis.Source: Resolving the sequence similarity… · pp. 6–7
  • Global degree distributions distinguish power-law networks associated with antigen-driven expansion from more even exponential distributions reflective of naïve repertoires, while local metrics characterize clone relationships (87).Local parameters include degree, authority, closeness, betweenness, and PageRank; they can be related to clone frequency and antigen specificity.Source: Resolving the sequence similarity… · p. 7
  • Similarity indices provide continuous repertoire-wide scores from 0 to 100% similarity, and the Strauli–Hernandez index additionally normalizes pairwise similarity by sequence frequency (102).These indices complement network-based descriptions of repertoire architecture (6,102).Source: Resolving the sequence similarity… · p. 7
  • Quantitative network analysis has revealed reproducibility, robustness, and redundancy, but biological interpretation remains early and key questions about cross-person comparison, layered evolution, and serum-level structure remain open (87,103–109).Open questions include combining discrete and continuous representations without information loss, linking similarity layers to antigen-driven evolution, and testing whether antibody network structure persists at phenotypic and immunoproteomic levels.Source: Resolving the sequence similarity… · p. 8

Retracing the antigen-driven evolution of antibody repertoires

Antigen challenge drives B-cell expansion and somatic hypermutation from naïve through memory to plasma cells. Phylogenetic methods can retrace this evolution, but antibody-specific mutation patterns and timescales complicate accurate inference and comparison.

Lineage reconstruction

  • Lineage trees trace sequences from a shared recombination event, commonly after grouping identical V and J genes and CDR3 length; Schramm et al.'s software interfaces with BEAST and DNAML (113).A clonal lineage comprises receptor sequences originating from the same recombination event.Source: Retracing the antigen-driven evolution… · p. 8

Phylogenetic methods

  • Distance-based LD and NJ enable fast exploratory analyses, whereas BEAST is practically limited to fewer than 10^3 sequences per tree but yields calendar-time phylogenies and somatic hypermutation rates (118,131,132).Grouping sequences by identical V-J genes and CDR3 length reduces the distance-matrix computational burden.Source: Retracing the antigen-driven evolution… · p. 9

Phylogenetic inference

  • Five reconstruction methods produced different tree topologies, and antibody-specific mutation and timescale assumptions may reduce clade accuracy, warranting caution in interpreting comparisons (17,114,132).The comparison used experimental and simulated sequences and assessed clade overlap and treescape distance.Source: Retracing the antigen-driven evolution… · pp. 8–9

Mutation patterns and models

  • Somatic hypermutation targets 2–7 bp hotspots and CDRs; S5F explained almost half of observed mutation-pattern variance and was highly conserved across individuals (4,114,136,137).Additional models cover mouse and human light chains, while gene-specific amino-acid substitution profiles were unique to each human V-gene and consistent between individuals (138,139).Source: Retracing the antigen-driven evolution… · p. 10

Antibody-specific evolutionary models

  • A hotspot-aware substitution model improved fit across three HIV-neutralizing antibody lineages, while mutability losses were about 60% more frequent than gains in anti-HIV sequences (133,141).The model partially accounts for context-dependent mutability and descent from a known germline sequence; the mutability-loss finding applied to both CDRs and framework regions.Source: Retracing the antigen-driven evolution… · p. 10

Outstanding questions

  • Open problems include integrating clonal expansion into tree inference, comparing topology across differently sized lineages, and linking antigen-specific convergence and affinity across infection contexts (142–146).UniFrac compares samples by the branch length unique to each, but biologically meaningful comparisons of tree topologies remain challenging.Source: Retracing the antigen-driven evolution… · p. 10

Dissecting naïve and antigen-driven repertoire convergence

Repertoire convergence encompasses shared clones and sequence motifs across individuals, and computational approaches quantify or detect these patterns to study immune responses and antigen specificity. The section surveys overlap, sequence-distance, and machine-learning methods, alongside data resources and open challenges.

Dissecting naïve and antigen-driven repertoire convergence

  • Clonotype-overlap measures compare shared clones across samples, while Morisita-Horn indices incorporate clonal frequency and parameterization can reweight abundance ranges (6,47,150,151,58).The Repertoire Dissimilarity Index uses bootstrapped subsampling of binned sequence features and frequencies to account for sequencing-depth variance (49,154).Source: Dissecting naïve and antigen-driven… · p. 11
  • Emerson et al. used Fisher’s exact test to identify CMV-associated public TCRβ clonotypes and a probabilistic classifier to predict CMV status while mitigating HLA variation (147).Source: Dissecting naïve and antigen-driven… · p. 11
  • Sequence-level methods include low-dimensional embedding of pairwise alignments, time-course functional data analysis, and DESeq2 selection of immunization-associated CDR3 clusters (155,102,156,157).The functional data analysis framework accommodates uneven time-point sampling and measurement error; selected clusters showed stereotypic amino acid patterns matching known tetanus-toxoid and measles-specific CDR3 signatures.Source: Dissecting naïve and antigen-driven… · pp. 11–12
  • 80% accuracy was reported for classifying ovalbumin-immunized versus unimmunized mice from TCRβ k-mers and for classifying public versus private clones with gapped-k-mer support vector machines (158,56).Other approaches combine Bayesian feature selection and support-vector machines or add physicochemical properties to machine-learning features (159,160–164).Source: Dissecting naïve and antigen-driven… · p. 12
  • TCRDist uses structure-guided similarity to cluster antigen-specific TCRs, while GLIPH clusters TCR specificity groups; both enabled highly accurate specificity prediction, and GLIPH informed synthetic antigen-specific TCR design (148,169).Source: Dissecting naïve and antigen-driven… · pp. 12–13
  • To address scarce antigen-specific data, VDJDB catalogs over 10,000 TCRs, McPAS-TCR over 5,000 pathogen-associated TCRs, and Abysis over 5,000 antibodies with known function (170–172).VDJDB links sequences to epitopes and MHC context; Abysis includes sequences from more than 15 species and, where available, PDB structural information.Source: Dissecting naïve and antigen-driven… · p. 13
  • Open questions include jointly modeling antigen-driven convergence and phylogenetic evolution, applying VDJ-recombination and selection models to antigen-associated signatures, and testing deep networks for long-range interactions (133,141,4,54,82,173–178).Source: Dissecting naïve and antigen-driven… · p. 13

Conclusion

The repertoire-analysis toolbox has matured and enabled insights and translational advances, but major gaps remain in benchmarking, scalability, multidimensional integration, transcriptomic linkage, and predictive methods.

Conclusion

  • Few benchmarking platforms hinder standardization; expanding bulk and single-cell datasets make scalability crucial, and holistic synthesis across repertoire dimensions remains missing.An AIRR-seq consortium is establishing consensus protocols and simulation frameworks (2,17,33,34,42); scaling advances cover annotation, clustering and networks (62,87,182,183), but phylogenetic inference needs further work (132).Source: Conclusion · p. 13
  • The computational immunology toolbox has yielded insights into B- and T-cell development, disease and infection profiling, and immunodiagnostics and immunotherapeutics (6,179; 76,77; 63,111,180).Source: Conclusion · p. 13
  • Few methods link immune-receptor and transcriptomic data, although tools now extract receptor sequences from bulk and single-cell transcriptomes (184,185; 182,185–189).Linking these data may clarify genetic regulation of antibody and T-cell specificity, with implications for synthetic immunology (190–192).Source: Conclusion · p. 14
  • Many methods capture static repertoire spaces, while few yield predictive quantitative knowledge; improving prediction could advance antibody discovery, vaccine design, and immunodiagnostics (15,19,193–195).Source: Conclusion · p. 14

Funding Statement

The work received support from Swiss, European, and institutional funders, including grants awarded to STR and a Pioneer Fellowship to Enkelejda Miho.

Funding Statement

  • The work was funded by Swiss National Science Foundation Project 31003A_170110, SystemsX.ch–AntibodyX RTD, and European Research Council Starting Grant 679403, all to STR.STR’s professorship was endowed by the S. Leslie Misrock Foundation, and ETH Foundation provided the Pioneer Fellowship to Enkelejda Miho.Source: Funding Statement · p. 14
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