arXiv subjects

Allon M. Klein

Publications and source records attributed to Allon M. Klein.

4 recordsLinked to original sources

arXiv2026

A measurement noise scaling law for cellular representation learning

Large genomic and imaging datasets can be used to train models that learn meaningful representations of cellular systems. Across domains, model performance improves predictably with dataset size and compute budget, providing a basis for allocating data and computation. Scientific data, however, is also limited by noise arising from factors such as molecular undersampling, sequencing errors, and image resolution. By fitting 1,670 representation learning models across three data modalities (gene expression, sequence, and image data), we show that noise defines a distinct axis along which performance improves. Noise scaling follows a logarithmic law. We derive the law from a model of noise propagation, and use it to define noise sensitivity and model capacity as benchmarking metrics. We show that protein sequence representations are noise-robust while single cell transcriptomics models are not, with a Transformer-based model showing greater noise robustness but lower saturating performance than a variational autoencoder model. Noise scaling metrics may support future model evaluation and experimental design.

q-bio.QM↗

arXiv2024

Approximating mutual information of high-dimensional variables using learned representations

Mutual information (MI) is a general measure of statistical dependence with widespread application across the sciences. However, estimating MI between multi-dimensional variables is challenging because the number of samples necessary to converge to an accurate estimate scales unfavorably with dimensionality. In practice, existing techniques can reliably estimate MI in up to tens of dimensions, but fail in higher dimensions, where sufficient sample sizes are infeasible. Here, we explore the idea that underlying low-dimensional structure in high-dimensional data can be exploited to faithfully approximate MI in high-dimensional settings with realistic sample sizes. We develop a method that we call latent MI (LMI) approximation, which applies a nonparametric MI estimator to low-dimensional representations learned by a simple, theoretically-motivated model architecture. Using several benchmarks, we show that unlike existing techniques, LMI can approximate MI well for variables with $> 10^3$ dimensions if their dependence structure has low intrinsic dimensionality. Finally, we showcase LMI on two open problems in biology. First, we approximate MI between protein language model (pLM) representations of interacting proteins, and find that pLMs encode non-trivial information about protein-protein interactions. Second, we quantify cell fate information contained in single-cell RNA-seq (scRNA-seq) measurements of hematopoietic stem cells, and find a sharp transition during neutrophil differentiation when fate information captured by scRNA-seq increases dramatically.

q-bio.QM↗

arXiv2007

Mechanism of murine epidermal maintenance: Cell division and the Voter Model

This paper presents an interesting experimental example of voter-model statistics in biology. In recent work on mouse tail-skin, where proliferating cells are confined to a two-dimensional layer, we showed that cells proliferate and differentiate according to a simple stochastic model of cell division involving just one type of proliferating cell that may divide both symmetrically and asymmetrically. Curiously, these simple rules provide excellent predictions of the cell population dynamics without having to address their spatial distribution. Yet, if the spatial behaviour of cells is addressed by allowing cells to diffuse at random, one deduces that density fluctuations destroy tissue confluence, implying some hidden degree of spatial regulation in the physical system. To infer the mechanism of spatial regulation, we consider a two-dimensional model of cell fate that preserves the overall population dynamics. By identifying the resulting behaviour with a three-species variation of the "Voter" model, we predict that proliferating cells in the basal layer should cluster. Analysis of empirical correlations of cells stained for proliferation activity confirms that the expected clustering behaviour is indeed seen in nature.

physics.bio-ph↗

arXiv2007

Kinetics of cell division in epidermal maintenance

The rules governing cell division and differentiation are central to understanding the mechanisms of development, aging and cancer. By utilising inducible genetic labelling, recent studies have shown that the clonal population in transgenic mouse epidermis can be tracked in vivo. Drawing on these results, we explain how clonal fate data may be used to infer the rules of cell division and differentiation underlying the maintenance of adult murine tail-skin. We show that the rates of cell division and differentiation may be evaluated by considering the long-time and short-time clone fate data, and that the data is consistent with cells dividing independently rather than synchronously. Motivated by these findings, we consider a mechanism for cancer onset based closely on the model for normal adult skin. By analysing the expected changes to clonal fate in cancer emerging from a simple two-stage mutation, we propose that clonal fate data may provide a novel method for studying the earliest stages of the disease.

physics.bio-ph↗