Biology subjects

McCandlish, D. M.

Publications and source records attributed to McCandlish, D. M..

At least 19 recordsLinked to original sources

bioRxiv2026

Dynamical consequences of context-dependent mutation: visualizing antibody sequence evolution during somatic hypermutation

Context-dependent mutation models describe how local sequence context affects individual substitution rates, but how these biases shape sequence evolution over multiple mutational steps remains challenging to characterize. Here, we develop a framework for analyzing and visualizing long-term sequence dynamics arising from context-dependent, non-reversible mutation processes. We apply it to somatic hypermutation during antibody affinity maturation, using previously inferred context-dependent mutation rates. Our analysis recovers conventional hypermutation hot- and cold-spot patterns while exposing substantial heterogeneity in mutability within these categories. We also identify sequences with low mutability that lack conventional cold-spot motifs. Applying the framework to antigen-binding regions from different antibody-encoding gene families reveals how differences in sequence composition lead to distinct mutational trajectories through sequence space, suggesting that hypermutation biases constrain how these regions diversify. We further show how mutational biases defined at the level of 5-nucleotide contexts propagate to the codon and amino acid levels, producing low stationary frequencies for stop codons and tyrosine and high stationary frequencies for proline. Changes in amino acid composition between naive and memory B cells are qualitatively consistent with these predictions. Together, our results provide a general framework for connecting local context-dependent mutation rates to long-term sequence evolution and demonstrate how intrinsic somatic hypermutation biases shape the relative accessibility of different regions of sequence space during affinity maturation.

evolutionary biology↗

bioRxiv2026

Inference of fitness landscapes with heterogeneous patterns of epistasis across sites

Fitness landscapes provide a framework for understanding how genetic variation shapes evolutionary outcomes. Although these landscapes were long treated as abstract conceptual objects, recent advances in genetic engineering and high-throughput phenotyping have enabled the empirical measurement of phenotypic values across large combinatorial sequence spaces. These developments create a need for statistical frameworks that can summarize, infer, and interpret fitness landscapes in the presence of complex genetic interactions. Here, we introduce a framework for summarizing the structure of genetic interactions across sites based on the average squared local k-way epistatic coefficients between mutations at different subsets of sites, and derive the precise manner in which the variance in these local k-way epistatic coefficients across backgrounds relates to epistasis of orders higher than k. These statistics can be computed exactly for complete combinatorial landscapes and are related to classical statistics in the fitness landscape literature. Moreover, they can be estimated from empirical correlations when data are incomplete or noisy, and used to define an empirical Bayes prior for fitness landscape inference that differentially penalizes interactions involving different subsets of sites. We apply this inference method to diverse high-throughput protein and RNA combinatorial mutagenesis datasets and find that fitness landscapes often show highly structured patterns of genetic interactions across positions. Finally, we use this model to infer a fitness landscape for a dynamic self-splicing intron comprising 65,536 genotypes, and describe in detail the main genetic interactions that shape the structure of this landscape and how they relate to the underlying molecular mechanism. Together, these results provide new tools for summarizing and modeling complex fitness landscapes, and for linking large-scale empirical data to the mathematical theory of fitness landscapes.

evolutionary biology↗

bioRxiv2026

Genetic background shapes AI-predicted variant effects

Predicting the consequences of genetic variants remains a major goal in biomedicine. Conventional approaches typically assess single-nucleotide variants in the context of a single reference genome, without accounting for genetic diversity that can modulate variant effects. Here we introduce the personalized variant effect predictor (pVEP) framework, which quantifies how genetic background across thousands of human genomes from globally diverse populations shapes computational predictions of clinical variant effects. Across deep learning models spanning protein structure, splicing, and noncoding regulation, pVEP reveals that many clinical variants exhibit heterogeneous predicted effects across haplotypes, with the same variant predicted to be pathogenic in some genetic backgrounds and benign in others. We find support for underlying molecular mechanisms, including shifts in predicted protein contacts and changes in splice-site recognition. Overall, personalized genomic context emerges as a systematically underappreciated variable in variant annotation and clinical interpretation, with particular implications for genetically diverse populations.

genomics↗

bioRxiv2025

GaugeFixer: overcoming parameter non-identifiability in models of sequence-function relationships

BackgroundMathematical models of sequence-function relationships are widely used in computational biology. A key challenge when interpreting these models is that many different choices for model parameters can encode the same sequence-function relationship. These ambiguities, called "gauge freedoms," must be removed before parameter values can be meaningfully interpreted. Doing this requires imposing additional mathematical constraints on parameter values, a process called "fixing the gauge." We recently developed mathematical methods for fixing the gauge of a large class of commonly used models. The most direct computational implementation of these methods is often impractical, however, because it requires a projection matrix whose size scales quadratically with the number of model parameters. ResultsHere we introduce GaugeFixer, a Python package that exploits the mathematical structure of gauge-fixing projections to achieve log-linear scaling in computation time and linear scaling in memory usage. GaugeFixer thus requires orders of magnitude less time and memory than standard matrix multiplication, and can fix the gauge of models having millions of parameters in seconds. To demonstrate its utility, we used GaugeFixer to analyze an empirical fitness landscape for translation initiation in bacteria. This analysis revealed striking similarities (but also fine-scale differences) in ribosome-binding preferences at different positions relative to the start codon, thereby aiding the interpretation of this otherwise unwieldy landscape. ConclusionsGaugeFixer thus fills an important gap in the computational tools available for interpreting quantitative models of sequence-function relationships.

bioinformatics↗

bioRxiv2025

Weakest link epistasis and the geometry of genetic load

Because natural selection must optimise multiple traits at once, previous work has suggested that phenotypic dimensionality can substantially worsen the equilibrium fitness defect of a population relative to the phenotypic optimum. However, it remains unclear how conclusions drawn from classical theoretical phenotype-fitness maps extend to models grounded in explicit biological mechanisms. Here we introduce weakest-link epistasis (WLE), a framework in which fitness is determined by the least-fit phenotypic component, an extreme form of diminishing returns epistasis. We show that in this framework, increasing dimensionality amplifies the load in a manner comparable to, but surprisingly not more than, Fishers geometric model (FGM). Building on this similarity, we demonstrate why genetic load is often invariant across different rules for combining trait-specific fitness components into an overall organismal fitness. We explore these ideas by considering the family of models where the organismal fitness is determined based on the{ell} p-norm of the vector of trait-specific fitness defects, a framework that includes both FGM and WLE, but also captures a continuum of genetic architectures, ranging from generalist to specialist regimes. Altogether, our approach proposes a new perspective on the geometry of adaptive landscapes, and may help provide quantitative insight into the cost of complexity.

evolutionary biology↗

bioRxiv2025

Uncovering the Mechanistic Landscape of Regulatory DNA with Deep Learning

The regulatory genome encodes the logic that governs gene expression, enabling cells to respond to developmental, environmental, and evolutionary cues. This logic arises from complex cis-regulatory mechanisms that integrate transcription factor motifs, their syntactical arrangement, and surrounding sequence context, features that remain challenging to decode. Here, we present SEAM (Systematic Explanation of Attribution-based Mechanisms), a computational framework that combines deep learning with explainable AI to map the mechanistic impact of genetic mutations. Applied to human and Drosophila regulatory loci, SEAM uncovers functional binding sites at sequences of interest and identifies which mutations preserve, disrupt, or create novel binding sites. SEAM also reveals that two qualitatively distinct classes of regulatory signal are operative at many loci: signals that are robust to mutation and signals that are readily reprogrammable. These results clarify the inherent ability of regulatory DNA to evolve. They also position SEAM as a versatile framework for interpreting non-coding variants and for informing the mechanism-aware design of synthetic sequences.

genomics↗

bioRxiv2025

Molecular adaptation reflects taxon-specific mutational biases

A fundamental question in molecular evolution is the extent to which patterns of adaptive change are shaped by mutational biases that make some variants more likely than others to arise. Past studies provide support for important effects of mutation bias on adaptive change, but leave open the empirical question of how strongly and how broadly evolutionary patterns depend on taxon-specific mutational tendencies. To characterize this effect quantitatively, we aggregated frequency spectra of adaptive amino acid changes from 14 species, comprising over 5000 total adaptive events, primarily from adaptive laboratory evolution studies. We then paired each species-specific spectrum of adaptive changes with independent measurements of the mutation spectrum of that same species. Across the 14 species, we find considerable heterogeneity in the relative frequencies of the six possible types of single-nucleotide changes, for both the mutational and adaptive spectra. Comparing these spectra across species, we find that, for any given mutation type, the stronger the bias toward or against that type in a species mutation spectrum, the more enriched or depleted it tends to be in that species adaptive spectrum. We conclude that, for the adaptation of proteins via amino acid changes, taxon-specific evolutionary preferences are strongly responsive to taxon-specific mutational preferences over their observed range. Significance statementThe rates at which different types of mutation occur vary widely, both for different types of mutations within a single species and across species. Historically, a strong concordance between patterns of sequence evolution and mutational biases was used to support the thesis that most sequence evolution is caused by variants that do not affect fitness. However, more recent evidence shows that mutational biases can also influence adaptive evolution. Using data from 14 species, we find a strong relationship between the rate at which different kinds of nucleotide mutations emerge and their frequency among adaptive amino acid changes during protein evolution. These results suggest that processes that bias the production of variation may have a strong impact even during adaptive evolution.

evolutionary biology↗

bioRxiv2025

Learning sequence-function relationships with scalable, interpretable Gaussian processes

AbstractUnderstanding the relationship between biological sequences, such as DNA, RNA or protein sequences, and their resulting phenotypes is one of the central goals of genetics. This task is complicated by epistasis, i.e., the context dependence of mutational effects. Advances in high-throughput phenotyping now make it possible to study these relationships at unprecedented scale, generating large datasets that measure phenotypes for tens or hundreds of thousands of sequences. However, standard regression models for analyzing such datasets often make unrealistic assumptions about the generalizability of mutational effects and epistatic coefficients across genetic backgrounds. Deep neural networks offer greater flexibility but suffer from limited interpretability and lack uncertainty quantification. Here, we introduce a family of interpretable Gaussian process models for sequence-function relationships that capture epistasis through flexible prior distributions that generalize classical theoretical models from the fitness landscape literature. In particular, these priors are parameterized by interpretable site-, allele-, and mutation-specific factors controlling the degree to which specific mutations decrease the predictability of the effects of other mutations. Using GPU acceleration to scale to large protein, RNA, and genome-wide SNP datasets, our models consistently deliver superior predictive performance while yielding interpretable parameters that both recover known features and uncover novel epistatic interactions. Overall, our methods provide new insights into the structure of the genotype-phenotype map and offer scalable, interpretable approaches for exploring complex genetic interactions across diverse biological systems.

systems biology↗

bioRxiv2025

Positive genetic interactions: high impact, but underrepresented in theliterature

Genetic interactions, where the combined effect of perturbing two genes leads to a phenotype that deviates from the expectation based on the effects of the individual perturbations, often provide important information about the functional architecture of biological systems. These interactions are commonly classified as negative or positive based on whether the phenotype of the double mutant is less than or greater than what would be expected based on the single mutant effects. When the trait in question is fitness, systematic studies of pairwise deletions have shown that negative interactions typically link genes with similar functional annotations, while positive interactions typically link genes that are less obviously related and thus often viewed as less informative. However, research in the sociology of science suggests that transformative discoveries often arise from unexpected, cross-domain linkages. To evaluate these competing perspectives, we integrated large-scale genetic interaction data in yeast with literature annotations from the Saccharomyces Genome Database and citation data from iCite. We found that positive genetic interactions are associated with greater scientific impact, as measured by citation metrics, contrary to prevailing assumptions. Despite their greater impact, positive interactions are significantly underrepresented in the scientific literature. Interestingly, the advent of an unbiased mapping technology capable of detecting positive and negative interactions with equal facility did not alleviate this bias, implicating factors beyond mere discoverability. We also find that the research building on positive interactions forms a more interconnected body of follow-on work. Together, our analyses reveal the underappreciated value of positive genetic interactions and suggest that investigating cross-domain genetic links represents an under-exploited opportunity deserving of greater attention.

genetics↗

bioRxiv2025

On learning functions over biological sequence space: relating Gaussian process priors, regularization, and gauge fixing

Mappings from biological sequences (DNA, RNA, protein) to quantitative measures of sequence functionality play an important role in contemporary biology. We are interested in the related tasks of (i) inferring predictive sequence-to-function maps and (ii) decomposing sequence-function maps to elucidate the contributions of individual subsequences. Because each sequence-function map can be written as a weighted sum over subsequences in multiple ways, meaningfully interpreting these weights requires "gauge-fixing," i.e., defining a unique representation for each map. Recent work has established that most existing gauge-fixed representations arise as the unique solutions to L2-regularized regression in an overparameterized "weight space" where the choice of regularizer defines the gauge. Here, we establish the relationship between regularized regression in overparameterized weight space and Gaussian process approaches that operate in "function space," i.e. the space of all real-valued functions on a finite set of sequences. We disentangle how weight space regularizers both impose an implicit prior on the learned function and restrict the optimal weights to a particular gauge. We show how to construct regularizers that correspond to arbitrary explicit Gaussian process priors combined with a wide variety of gauges and characterize the implicit function space priors associated with the most common weight space regularizers. Finally, we derive the posterior distribution of a broad class of sequence-to-function statistics, including gauge-fixed weights and multiple systems for expressing higher-order epistatic coefficients. We show that such distributions can be efficiently computed for product-kernel priors using a kernel trick.

bioinformatics↗

bioRxiv2025

Inference and visualization of complexgenotype-phenotype with gpmap-tools

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.

evolutionary biology↗

bioRxiv2025

Cryptic variation fuels plant phenotypic change through hierarchical epistasis

Cryptic genetic variants exert minimal or no phenotypic effects alone but have long been hypothesized to form a vast, hidden reservoir of genetic diversity that drives trait evolvability through epistatic interactions. This classical theory has been reinvigorated by pan-genome sequencing, which has revealed pervasive variation within gene families and regulatory networks, including extensive cis-regulatory changes, gene duplication, and divergence between paralogs. Nevertheless, empirical testing of cryptic variations capacity to fuel phenotypic diversification has been hindered by intractable genetics, limited allelic diversity, and inadequate phenotypic resolution. Here, guided by natural and engineered cis-regulatory cryptic variants in a recently evolved paralogous gene pair, we identified an additional pair of redundant trans regulators, establishing a regulatory network that controls tomato inflorescence architecture. By combining coding mutations with a cis-regulatory allelic series in populations segregating for all four network genes, we systematically constructed a collection of 216 genotypes spanning the full spectrum of inflorescence complexity and quantified branching in over 27,000 inflorescences. Analysis of the resulting high-resolution genotype-phenotype map revealed a layer of dose-dependent interactions within paralog pairs that enhances branching, culminating in strong, synergistic effects. However, we also uncovered an unexpected layer of antagonism between paralog pairs, where accumulating mutations in one pair progressively diminished the effects of mutations in the other. Our results demonstrate how gene regulatory network architecture and complex dosage effects from paralog diversification converge to shape phenotypic space under a hierarchical model of epistatic interactions. Given the prevalence of paralog evolution in genomes, we propose that paralogous cryptic variation within regulatory networks elicits hierarchies of epistatic interactions, catalyzing bursts of phenotypic change. Keyword: cryptic mutations, paralogs, redundancy, cis-regulatory, tomato, inflorescence, gene regulatory network, modeling, epistasis

plant biology↗

bioRxiv2024

A fitness distribution law for amino-acid replacements

The effect of replacing the amino acid at a given site in a protein is difficult to predict. Yet, evolutionary comparisons have revealed highly regular patterns of interchangeability between pairs of amino acids, and such patterns have proved enormously useful in a range of applications in bioinformatics, evolutionary inference, and protein design. Here we reconcile these apparently contradictory observations using fitness data from over 350,000 experimental amino acid replacements. Almost one-quarter of the 20 x 19 = 380 types of replacements have broad distributions of fitness effects (DFEs) that closely resemble the background DFE for random changes, indicating an overwhelming influence of protein context in determining mutational effects. However, we also observe that the 380 pair-specific DFEs closely follow a maximum entropy distribution, specifically a truncated exponential distribution. The shape of this distribution is determined entirely by its mean, which is equivalent to the chance that a replacement of the given type is fitter than a random replacement. In this type of distribution, modest deviations in the mean correspond to much larger changes in the probability of falling in the far right tail, so that modest differences in mean exchangeability may result in much larger differences in the chance of a highly fit mutation. Indeed, we show that under the assumption that purifying selection filters out the vast majority of mutations, the maximum entropy distributions of fitness effects inferred from deep mutational scanning experiments predict the characteristic patterns of amino acid change observed in molecular evolution. These maximum entropy distributions of mutational effects not only provide a tuneable model for molecular evolution, but also have implications for mutational effect prediction and protein engineering.

evolutionary biology↗

bioRxiv2024

Gauge fixing for sequence-function relationships

Quantitative models of sequence-function relationships are ubiquitous in computational biology, e.g., for modeling the DNA binding of transcription factors or the fitness landscapes of proteins. Interpreting these models, however, is complicated by the fact that the values of model parameters can often be changed without affecting model predictions. Before the values of model parameters can be meaningfully interpreted, one must remove these degrees of freedom (called "gauge freedoms" in physics) by imposing additional constraints (a process called "fixing the gauge"). However, strategies for fixing the gauge of sequence-function relationships have received little attention. Here we derive an analytically tractable family of gauges for a large class of sequence-function relationships. These gauges are derived in the context of models with all-order interactions, but an important subset of these gauges can be applied to diverse types of models, including additive models, pairwise-interaction models, and models with higher-order interactions. Many commonly used gauges are special cases of gauges within this family. We demonstrate the utility of this family of gauges by showing how different choices of gauge can be used both to explore complex activity landscapes and to reveal simplified models that are approximately correct within localized regions of sequence space. The results provide practical gauge-fixing strategies and demonstrate the utility of gauge-fixing for model exploration and interpretation. Significance StatementComputational biology relies heavily on mathematical models that predict biological activities from DNA, RNA, or protein sequences. Interpreting the parameters of these models, however, remains difficult. Here we address a core challenge for model interpretation-the presence of gauge freedoms, i.e., ways of changing model parameters without affecting model predictions. The results unify commonly used methods for eliminating gauge freedoms and show how these methods can be used to simplify complex models in localized regions of sequence space. This work thus overcomes a major obstacle in the interpretation of quantitative sequence-function relationships.

biophysics↗

bioRxiv2024

Symmetry, gauge freedoms, and the interpretability of sequence-function relationships

Quantitative models that describe how biological sequences encode functional activities are ubiquitous in modern biology. One important aspect of these models is that they commonly exhibit gauge freedoms, i.e., directions in parameter space that do not affect model predictions. In physics, gauge freedoms arise when physical theories are formulated in ways that respect fundamental symmetries. However, the connections that gauge freedoms in models of sequence-function relationships have to the symmetries of sequence space have yet to be systematically studied. In this work we study the gauge freedoms of models that respect a specific symmetry of sequence space: the group of position-specific character permutations. We find that gauge freedoms arise when model parameters transform under redundant irreducible matrix representations of this group. Based on this finding, we describe an "embedding distillation" procedure that enables both analytic calculation of the number of independent gauge freedoms and efficient computation of a sparse basis for the space of gauge freedoms. We also study how parameter transformation behavior affects parameter interpretability. We find that in many (and possibly all) nontrivial models, the ability to interpret individual model parameters as quantifying intrinsic allelic effects requires that gauge freedoms be present. This finding establishes an incompatibility between two distinct notions of parameter interpretability. Our work thus advances the understanding of symmetries, gauge freedoms, and parameter interpretability in models of sequence-function relationships.

biophysics↗

bioRxiv2023

Interpreting cis-regulatory mechanisms from genomic deep neural networks using surrogate models

Deep neural networks (DNNs) have greatly advanced the ability to predict genome function from sequence. Interpreting genomic DNNs in terms of biological mechanisms, however, remains difficult. Here we introduce SQUID, a genomic DNN interpretability framework based on surrogate modeling. SQUID approximates genomic DNNs in user-specified regions of sequence space using surrogate models, i.e., simpler models that are mechanistically interpretable. Importantly, SQUID removes the confounding effects that nonlinearities and heteroscedastic noise in functional genomics data can have on model interpretation. Benchmarking analysis on multiple genomic DNNs shows that SQUID, when compared to established interpretability methods, identifies motifs that are more consistent across genomic loci and yields improved single-nucleotide variant-effect predictions. SQUID also supports surrogate models that quantify epistatic interactions within and between cis-regulatory elements. SQUID thus advances the ability to mechanistically interpret genomic DNNs.

genomics↗

bioRxiv2023

Protein evolvability under rewired genetic codes

The standard genetic code defines the rules of translation for nearly every life form on Earth. It also determines the amino acid changes accessible via single-nucleotide mutations, thus influencing protein evolvability -- the ability of mutation to bring forth adaptive variation in protein function. One of the most striking features of the standard genetic code is its robustness to mutation, yet it remains an open question whether this robustness facilitates or frustrates protein evolvability. To answer this question, we use data from massively-parallel sequence-to-function assays to construct and analyze empirical adaptive landscapes under hundreds of thousands of rewired genetic codes, including those of codon compression schemes relevant to protein engineering and synthetic biology. We find that robust genetic codes tend to enhance protein evolvability by rendering smooth adaptive landscapes with few peaks, which are readily accessible from throughout sequence space. By constructing low-dimensional visualizations of these landscapes, which each comprise more than 16 million mRNA sequences, we demonstrate that alternative genetic codes can radically alter the topological features of the network of high-fitness genotypes. Whereas the genetic codes that optimize evolvability depend to some extent on the detailed relationship between amino acid sequence and protein function, we also uncover general design principles for engineering non-standard genetic codes for enhanced and diminished evolvability, which may facilitate directed protein evolution experiments and the biocontainment of synthetic organisms, respectively. Our findings demonstrate that the standard genetic code, a critical and near-universal cellular information processing system, not only mitigates replication and translation errors as compared to most alternative genetic codes, but also facilitates predictable and directional adaptive evolution by enabling evolving populations to readily find mutational paths to adaptation.

evolutionary biology↗

bioRxiv2023

Mutation and selection induce correlations between selection coefficients and mutation rates

The joint distribution of selection coefficients and mutation rates is a key determinant of the genetic architecture of molecular adaptation. Three different distributions are of immediate interest: (1) the nominal distribution of possible changes, prior to mutation or selection, (2) the de novo distribution of realized mutations, and (3) the fixed distribution of selectively established mutations. Here, we formally characterize the relationships between these joint distributions under the strong selection, weak mutation (SSWM) regime. The de novo distribution is enriched relative to the nominal distribution for the highest rate mutations, and the fixed distribution is further enriched for the most highly beneficial mutations. Whereas mutation rates and selection coefficients are often assumed to be uncorrelated, we show that even with no correlation in the nominal distribution, the resulting de novo and fixed distributions can have correlations with any combination of signs. Nonetheless, we suggest that natural systems with a finite number of beneficial mutations will frequently have the kind of nominal distribution that induces negative correlations in the fixed distribution. We apply our mathematical framework, along with population simulations, to explore joint distributions of selection coefficients and mutation rates from deep mutational scanning and cancer informatics. Finally, we consider the evolutionary implications of these joint distributions together with two additional joint distributions relevant to parallelism and the rate of adaptation.

evolutionary biology↗