Remarkably common statistical laws characterize the diversity scaling and its fluctuations across a wide range of complex "component systems". These regularities are often interpreted as signatures of an underlying innovation mechanism driving the growth of component diversity, but the basic ingredients necessary for their emergence remain poorly understood. In particular, from language and technological artifacts to genomes and gene expression patterns, the number of distinct components grows sublinearly with system size, while its variance scales approximately as the square of its mean. This behavior is consistent across diverse systems, raising the question of whether general constraints or emergent principles underlying diversity and innovation define the architectures of realizations with different numbers of components. To address this question, we derive analytical conditions for the joint emergence of these two diversity laws within a broad class of growth models, showing that they require a specific asymptotic dependence of the innovation probability on diversity and system size. We then demonstrate that the same macroscopic laws arise in a different class of models with latent heterogeneity, where quadratic fluctuation scaling always emerges asymptotically as a consequence of general statistical principles, essentially the law of total variance, without explicitly assuming an innovation mechanism or any specific rule for system assembly. We compare these predictions with empirical data from language, genomes, LEGO constructions, and texts generated by large language models. Our results show that empirical diversity scaling laws strongly constrain generative models but do not uniquely identify the mechanisms generating diversity, revealing a close correspondence between innovation-driven growth models and latent-variable descriptions.

Recent advances in single-cell biology enable the profiling of multiple molecular layers, such as the transcriptome, epigenome, and surface proteins, within a single cell. Tackling the complexity of these data from different perspectives allows researchers to get the most complete insights into the biological properties of cells. Here, we propose a graph-based topic modelling method called bionSBM. Our method leverages well-known community-detection methods for multipartite graphs and the interpretability of topic modelling to cluster and explain high-dimensional, sparse, and noisy single-cell matrices. We applied our algorithm to paired single-cell multi-omics data, such as 10X Multiome, SHARE-seq, and CITE-seq. We showed that it achieves superior performance compared to state-of-the-art methods for ground-truth label retrieval, with high specificity and distinct biological interpretability.

The human brain is a complex interconnected structure controlling all elementary and high-level cognitive tasks. It is composed of many regions that exhibit specific distributions of cell types and distinct patterns of functional connections. This complexity is rooted in differential transcription. The constituent cell types of different brain regions express distinctive combinations of genes as they develop and mature, ultimately shaping their functional state in adulthood. How precisely the genetic information of anatomical structures is connected to their underlying biological functions remains an open question in modern neuroscience. A major challenge is the identification of “universal patterns”, which do not depend on the particular individual, but are instead basic structural properties shared by all brains. Despite the vast amount of gene expression data available at both the bulk and single-cell levels, this task remains challenging, mainly due to the lack of suitable data mining tools. In this paper, we propose an approach to address this issue based on a hierarchical version of Stochastic Block Modeling. Thanks to its specific choice of priors, the method is particularly effective in identifying these universal features. We use as a laboratory to test our algorithm a dataset obtained from six independent human brains from the Allen Human Brain Atlas. We show that the proposed method is indeed able to identify universal patterns much better than more traditional algorithms such as Latent Dirichlet Allocation or Weighted Correlation Network Analysis. The probabilistic association between genes and samples that we find well represents the known anatomical and functional brain organization. Moreover, leveraging the peculiar “fuzzy” structure of the gene sets obtained with our method, we identify examples of transcriptional and post-transcriptional pathways associated with specific brain regions, highlighting the potential of our approach.

The availability of high-dimensional transcriptomic datasets is increasing at a tremendous pace, together with the need for suitable computational tools. Clustering and dimensionality reduction methods are popular go-to methods to identify basic structures in these datasets. At the same time, different topic modeling techniques have been developed to organize the deluge of available data of natural language using their latent topical structure. This paper leverages the statistical analogies between text and transcriptomic datasets to compare different topic modeling methods when applied to gene expression data. Specifically, we test their accuracy in the specific task of discovering and reconstructing the tissue structure of the human transcriptome and distinguishing healthy from cancerous tissues. We examine the properties of the latent space recovered by different methods, highlight their differences, and their pros and cons across different tasks. We focus in particular on how different statistical priors can affect the results and their interpretability. Finally, we show that the latent topic space can be a useful low-dimensional embedding space, where a basic neural network classifier can annotate transcriptomic profiles with high accuracy.

Waddington's epigenetic landscape has long served as a conceptual framework for understanding cell fate decisions. The landscape's geometry encodes the molecular mechanisms that guide the gene expression profiles of uncommitted cells toward terminally differentiated cell types. In this study, we demonstrate that applying the concept of intrinsic dimension to single-cell transcriptomic data can effectively capture trends in expression trajectories, supporting this framework. This approach allows us to define a robust cell potency score without relying on prior biological information. By analyzing an extensive collection of datasets from various species, experimental protocols, and differentiation processes, we validate our method and successfully reproduce established hierarchies of cell type potency. Our work provides a direct link between geometric properties of single-cell expression profiles and the level of differentiation of a cell population.

To achieve near-zero training error in a classification problem, the layers of a feed-forward network have to disentangle the manifolds of data points with different labels to facilitate the discrimination. However, excessive class separation can lead to overfitting because good generalization requires learning invariant features, which involve some level of entanglement. We report on numerical experiments showing how the optimization dynamics finds representations that balance these opposing tendencies with a non-monotonic trend. After a fast segregation phase, a slower rearrangement (conserved across datasets and architectures) increases the class entanglement. The training error at the inversion is stable under subsampling and across network initializations and optimizers, which characterizes it as a property solely of the data structure and (very weakly) of the architecture. The inversion is the manifestation of tradeoffs elicited by well-defined and maximally stable elements of the training set called 'stragglers', which are particularly influential for generalization. Feed-forward neural networks have become powerful tools in machine learning, but their behaviour during optimization is still not well understood. Ciceri and colleagues find that during optimization, class representations first separate and then rejoin, prompted by specific elements of the training set.

Topic modeling is a popular technique in machine learning and natural language processing, where a corpus of text documents is classified into themes or topics using word frequency analysis. This approach has proven successful in various biological data analysis applications, such as predicting cancer subtypes with high accuracy and identifying genes, enhancers, and stable cell types simultaneously from sparse single-cell epigenomics data. The advantage of using a topic model is that it not only serves as a clustering algorithm, but it can also explain clustering results by providing word probability distributions over topics. Our study proposes a novel topic modeling approach for clustering single cells and detecting topics (gene signatures) in single-cell datasets that measure multiple omics simultaneously. We applied this approach to examine the transcriptional heterogeneity of luminal and triple-negative breast cancer cells using patient-derived xenograft models with acquired resistance to chemotherapy and targeted therapy. Through this approach, we identified protein-coding genes and long non-coding RNAs (lncRNAs) that group thousands of cells into biologically similar clusters, accurately distinguishing drug-sensitive and -resistant breast cancer types. In comparison to standard state-of-the-art clustering analyses, our approach offers an optimal partitioning of genes into topics and cells into clusters simultaneously, producing easily interpretable clustering outcomes. Additionally, we demonstrate that an integrative clustering approach, which combines the information from mRNAs and lncRNAs treated as disjoint omics layers, enhances the accuracy of cell classification.

Large-scale data on single-cell gene expression have the potential to unravel the specific transcriptional programs of different cell types. The structure of these expression datasets suggests a similarity with several other complex systems that can be analogously described through the statistics of their basic building blocks. Transcriptomes of single cells are collections of messenger RNA abundances transcribed from a common set of genes just as books are different collections of words from a shared vocabulary, genomes of different species are specific compositions of genes belonging to evolutionary families, and ecological niches can be described by their species abundances. Following this analogy, we identify several emergent statistical laws in single-cell transcriptomic data closely similar to regularities found in linguistics, ecology, or genomics. A simple mathematical framework can be used to analyze the relations between different laws and the possible mechanisms behind their ubiquity. Importantly, treatable statistical models can be useful tools in transcriptomics to disentangle the actual biological variability from general statistical effects present in most component systems and from the consequences of the sampling process inherent to the experimental technique.

Single-cell RNA sequencing is a powerful tool to explore cancer heterogeneity. However, the expression of lncRNAs in single cells is still to be studied extensively and methods to deal with the sparsity of this type of data are lacking. Here, we propose a topic modeling approach to investigate the transcriptional heterogeneity of luminal and triple negative breast cancer cells using patient-derived xenograft models of acquired resistance to chemotherapy and targeted therapy. We show that using an integrative clustering that combines the information coming from mRNAs and lncRNAs treated as disjoint omic layers greatly improves the accuracy of cell classification. Topics associated with specific breast cancer subpopulations show a clear enrichment for pathways involved in subtyping and progression of breast cancer and to sets of lncRNA encoded in the open chromatin regions of breast cancer cell lines. We identified lncRNAs strongly associated with cell clusters already well known in the literature, such as MALAT1 and NEAT1, and highlighted some others that may be clinically relevant. A larger scale study based on Smart-seq-total technology (8) has assayed a broad spectrum of mRNAs and lncRNAs from single cells and showed that the lncRNA content of cells significantly differs across cell types and dynamically changes throughout cellular processes such as cell cycle and cell differentiation. Another large-scale study, combining bulk tissue RNA-seq and scRNA-seq to deeply profile lncRNA expression during neocortical development, found that many lncRNAs are specific to distinct cell types and abundantly expressed in individual cells (9), thus supporting that cell type-specific expression of lncRNAs contributes to the low levels of lncRNAs observed in tissues.

The integration of transcriptional data with other layers of information, such as the post-transcriptional regulation mediated by microRNAs, can be crucial to identify the driver genes and the subtypes of complex and heterogeneous diseases such as cancer. This paper presents an approach based on topic modeling to accomplish this integration task. More specifically, we show how an algorithm based on a hierarchical version of stochastic block modeling can be naturally extended to integrate any combination of 'omics data. We test this approach on breast cancer samples from the TCGA database, integrating data on messenger RNA, microRNAs, and copy number variations. We show that the inclusion of the microRNA layer significantly improves the accuracy of subtype classification. Moreover, some of the hidden structures or "topics" that the algorithm extracts actually correspond to genes and microRNAs involved in breast cancer development and are associated to the survival probability.

The sense of smell helps us navigate the environment, but its molecular architecture and underlying logic remain understudied. The spatial location of odorant receptor genes (Olfrs) in the nose is thought to be independent of the structural diversity of the odorants they detect. Using spatial transcriptomics, we create a genome-wide 3D atlas of the mouse olfactory mucosa (OM). Topographic maps of genes differentially expressed in space reveal that both Olfrs and non-Olfrs are distributed in a continuous and overlapping fashion over at least five broad zones in the OM. The spatial locations of Olfrs correlate with the mucus solubility of the odorants they recognize, providing direct evidence for the chromatographic theory of olfaction. This resource resolves the molecular architecture of the mouse OM and will inform future studies on mechanisms underlying Olfr gene choice, axonal pathfinding, patterning of the nervous system, and basic logic for the peripheral representation of smell.

ABSTRACT The sense of smell helps us navigate the environment, but its molecular architecture and underlying logic remain unknown. The spatial location of odorant receptor genes ( Olfrs ) in the nose is widely thought to be independent of the structural diversity of the odorants they detect. Using spatial transcriptomics, we created a genome-wide 3D atlas of the mouse olfactory mucosa (OM). Topographic maps of genes differentially expressed in space reveal that both Olfrs and non- Olfrs are distributed in a continuous and overlapping fashion over five broad zones in the OM. The spatial locations of Olfrs correlate with the mucus solubility of the odorants they recognize, providing direct evidence for the chromatographic theory of olfaction. This resource resolved the molecular architecture of the mouse OM, and will inform future studies on mechanisms underlying Olfr gene choice, axonal pathfinding, patterning of the nervous system, and basic logic for the peripheral representation of smell.

Topic modelling is a widely used technique to extract relevant information from large arrays of data. The problem of finding a topic structure in a dataset was recently recognized to be analogous to the community detection problem in network theory. Leveraging on this analogy, a new class of topic modelling strategies has been introduced to overcome some of the limitations of classical methods. This paper applies these recent ideas to TCGA transcriptomic data on Breast and Lung cancer. The established cancer subtype organization is well reconstructed in the inferred latent topic structure. Moreover, we identify specific topics that are enriched in genes known to play a role in the corresponding disease and are strongly related to the survival probability of patients. Finally, we show that a simple neural network classifier operating in the low dimensional topic space is able to predict with high accuracy the cancer subtype of a test expression sample.

Topic modeling is a widely used technique to extract relevant information from large arrays of data. The problem of finding a topic structure in a dataset was recently recognized to be analogous to the community detection problem in network theory. Leveraging on this analogy, a new class of topic modeling strategies has been introduced to overcome some of the limitations of classical methods. This paper applies these recent ideas to TCGA transcriptomic data on breast and lung cancer. The established cancer subtype organization is well reconstructed in the inferred latent topic structure. Moreover, we identify specific topics that are enriched in genes known to play a role in the corresponding disease and are strongly related to the survival probability of patients. Finally, we show that a simple neural network classifier operating in the low dimensional topic space is able to predict with high accuracy the cancer subtype of a test expression sample.