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bioRxivEvolutionary BiologyPreprint

Inference and visualization of complex genotype-phenotype maps with gpmap-tools

Carlos Martí‐GómeziD, Juannan ZhouiD, Wei-Chia CheniD, Arlin StoltzfusiD, Justin B. KinneyiD, David M. McCandlishiD

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In-depth summary

Claude Opus 5.5 · xhigh effort · 8 Nov 2026 · from the full text of version 3 (26 Aug 2025) · CC BY 4.0

gpmap-tools uses Gaussian processes to infer and visualize genotype-phenotype maps with higher-order epistasis; across 262,144 Shine-Dalgarno variants it reveals register-specific peaks linked by three-nucleotide-offset ridges.

Genotype-phenotype maps are hard to characterize because sequence space is vast and mutation effects depend on genetic background, and earlier Shine-Dalgarno models ignored higher-order interactions. gpmap-tools combines interpretable Gaussian process priors, calibrated uncertainty, site-level epistasis decomposition and evolutionary visualization of millions of genotypes in a memory-efficient library for multiplex assay of variant effect (MAVE) data or natural sequences.

Key results

  1. ShownGenome-derived and MAVE-derived Shine-Dalgarno (SD) landscapes share one architecture: isolated peaks for anti-SD (aSD) binding at distinct spacings from the start codon, with functional ridges joining registers three nucleotides apart and valleys separating one-nucleotide shifts.

    E. coli SeqDEFT map: AGGAG peaks at consecutive registers; B. subtilis (4,328 5' UTRs) log-probabilities vs E. coli Spearman ρ = 0.94 with the same peaks and ridges; E. coli probability vs MAVE log(GFP) Spearman ρ = 0.55, yet same structure; A-10G, G-8A, A-7G are deleterious in UUAAGGAGC but beneficial in UAAGGAGCA (95% credible intervals). · Visualizing the probability distribution of the…; Comparing sequence probability across different…; Comparing sequence probability and functional…; Uncertainty quantification for genetic…

  2. ShownVariance component (VC) regression imputes the complete 4^9 SD landscape from MAVE data with high held-out accuracy and calibrated uncertainty, and generally outperforms minimum epistasis interpolation (MEI), which does better only under extremely sparse sampling.

    257,565 measured genotypes, 0.1% held out: R^2 = 0.94 (training) and 0.87 (held-out test); credible intervals near-nominal over 274 test points; additive plus pairwise terms explain 57.6% of prior variance; phenotype correlation falls to 0.25 at three mutations; MEI vs VC learning curves use 3 training subsets per fraction. · Inferring the genotype-phenotype map of the…; Analysis of the experimental fitness landscape…; Figure legends

  3. ShownSeqDEFT applied to E. coli 5' UTRs achieves its best held-out likelihood at an intermediate value of the epistasis-penalty hyperparameter, beating both the independent-site and empirical-frequency limits, which supports substantial epistasis in natural SD sequences.

    5,311 E. coli 5' UTRs yielded 3,690 unique 9-nt sequences of 262,144 possible; 5-fold cross-validation peaks at intermediate a; MAP root mean square local epistatic coefficient 0.32 vs root mean square mutational effect 0.78; unobserved sequences span 4 orders of magnitude in inferred probability. · Inferring the probability distribution of the…; Figure legends

  4. ShownDecomposing VC-inferred variance by site and interaction order shows that SD positions play very different roles, and that epistasis is largely local: interactions seldom couple sites more than four nucleotides apart.

    Positions −13 to −10: strong additive and epistatic variance; −9 to −7: mostly higher-order; −6 and −5: weak overall; pairwise terms confined to sites within 3 nt, higher-order terms reach 4 nt, and sites 5 or more nt apart rarely interact (VC regression MAP estimate). · Position-specific contributions to epistasis; B. Variance explained by interactions among sets…

  5. ShownGuided by the visualization, a 27-parameter thermodynamic model with register-independent additive aSD binding energies reproduces the peaks-and-ridges structure and predicts better than an RNAcofold base-pair stacking calibration model.

    Maximum-likelihood fit to MAVE data: R^2 = 0.59 (training) and 0.64 (held-out); RNAcofold v2.4.9 ensemble-energy calibration model reported at R^2 = 0.44; inferred ΔΔG for A4G is 0.84 kcal/mol (mild) whereas A4C is strongly destabilizing; SD positions 2-5 carry the largest energetic contributions. · A biophysical model recapitulates the…; Thermodynamic model of the Shine-Dalgarno…

Methods, data and reproducibility

Gaussian process models (minimum epistasis interpolation, VC regression, SeqDEFT) with Gaussian or multinomial likelihoods infer complete maps with posterior uncertainty; projection operators split variance by order and site set, and a weak-mutation evolutionary embedding visualizes landscapes, using sparse matrices and matrix-free linear operators to avoid building dense matrices.

  • E. coli 5' UTRs (20 bp upstream of annotated start codons) from Ensembl bacteria release 51; 9-nt region 4 nt upstream modeled with SeqDEFT · E. coli · n = 5,311 genes; 3,690 unique 9-nt sequences · ASM160652v1
  • B. subtilis 5' UTRs from a GenBank assembly; 9-nt region 6 bp upstream of the start codon modeled with SeqDEFT · B. subtilis · n = 4,328 genes · ASM904v1
  • Previously published SD MAVE: GFP reporter expression for a near-complete 9-nt variant library in the dmsC context (processed replicate data) · n = 257,565 measured sequences; 3 replicates
Methods & tools
gpmap-tools (Python library), SeqDEFT, Minimum epistasis interpolation (MEI), Empirical variance component regression with kernel alignment, Laplace approximation for MAP posterior, scipy LinearOperator with Conjugate Gradient, matplotlib, plotly and datashader plotting back-ends, PyTorch (Adam optimizer), RNAcofold v2.4.9, pysam, logomaker
Software & environment
Python library built on scipy LinearOperators; plotting via matplotlib, plotly and datashader; PyTorch Adam (learning rate 0.02, 1500 iterations); RNAcofold v2.4.9 with -p0; Ensembl bacteria release 51.
Experimental conditions
No hardware or wall-clock runtimes stated; a naive 4^9 × 4^9 matrix would need 512GB and a CSR Laplacian about 450MB for 9-nt DNA, which matrix-free operators avoid; datashader rendering is nearly an order of magnitude faster.
Reproducibility gaps
The SD MAVE dataset is reused from a prior study with no URL or accession given in the text; genomes are cited by assembly name only; apart from RNAcofold v2.4.9, no software versions or container are specified.
Limitations (5)
  • MEI and VC regression are phenomenological and lack an explicit term for global (nonspecific) epistasis caused by nonlinear measurement scales; they instead absorb it as pervasive specific interactions. · stated by the authors
  • SeqDEFT treats observed sequences as independent draws; this may hold for motifs repeated across one genome such as the SD sequence, but its robustness to phylogenetically related sequences in protein-family alignments is unknown. · stated by the authors
  • Inference and visualization keep every possible genotype and its phenotype in memory, which grows exponentially with length and restricts gpmap-tools to short fixed-length spaces (5 amino acids, 12 nucleotides, 24 biallelic sites). · stated by the authors
  • Inference methods are benchmarked only against each other (MEI vs VC regression, SeqDEFT vs its limiting models); no head-to-head comparison is reported with the neural network or latent-variable models cited as alternatives. · noted in this summary
  • Agreement across data sources rests largely on visual similarity of the landscapes, with Spearman ρ = 0.55 between genomic and MAVE maps; only one MAVE in a single dmsC flanking context was analyzed, and that context produced an extra GAG ridge. · noted in this summary

Read this if you analyze combinatorial MAVE libraries or natural sequence collections for short regulatory elements or peptides and want epistasis-aware imputation with uncertainty plus interpretable landscape visualization.

Citations
4

Abstract

Understanding how biological sequences give rise to observable traits, that is, how genotype maps to phenotype, is a central goal in biology. Yet our knowledge of genotype-phenotype maps in natural systems is limited due to the high dimensionality of sequence space and the context-dependent effects of mutations. The emergence of Multiplex assays of variant effect (MAVEs), along with large collections of natural sequences, offer new opportunities to empirically characterize these maps at an unprecedented scale. However, tools for statistical and exploratory analysis of these high-dimensional data are still needed. To address this gap, we developed gpmaptools https://github.com/cmarti/gpmap-tools), a python library that integrates a series of models for inference, phenotypic imputation, and error estimation from MAVE data or collections of natural sequences in the presence of genetic interactions of every possible order. gpmap-tools also provides methods for summarizing patterns of epistasis and visualization of genotype-phenotype maps containing up to millions of genotypes. To demonstrate its utility, we used gpmap-tools to infer genotype-phenotype maps containing 262,144 variants of the Shine-Dalgarno sequence from both genomic 5UTR sequences and experimental MAVE data. Visualization of the inferred landscapes consistently revealed high-fitness ridges that link core motifs at different distances from the start codon. In summary, gpmap-tools provides a flexible, interpretable framework for studying complex genotype-phenotype maps, opening new avenues for understanding the architecture of genetic interactions and their evolutionary consequences.

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