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Transcription has a mechanical component, as the translocation of the transcription machinery or RNA polymerase (RNAP) on DNA or chromatin is dynamically coupled to the chromatin torsion. This posits chromatin mechanics as a possible regulator of eukaryotic transcription, however, the modes and mechanisms of this regulation are elusive. Here, we first take a statistical mechanics approach to model the torsional response of topology-constrained chromatin. Our model recapitulates the experimentally observed weaker torsional stiffness of chromatin compared to bare DNA and proposes structural transitions of nucleosomes into chirally distinct states as the driver of the contrasting torsional mechanics. Coupling chromatin mechanics with RNAP translocation in stochastic simulations, we reveal a complex interplay of DNA supercoiling and nucleosome dynamics in governing RNAP velocity. Nucleosomes play a dual role in controlling the transcription dynamics. The steric barrier aspect of nucleosomes in the gene body counteracts transcription via hindering RNAP motion, whereas the chiral transitions facilitate RNAP motion via driving a low restoring torque upon twisting the DNA. While nucleosomes with low dissociation rates are typically transcriptionally repressive, highly dynamic nucleosomes offer less of a steric barrier and enhance the transcription elongation dynamics of weakly transcribed genes via buffering DNA twist. We use the model to predict transcription-dependent levels of DNA supercoiling in segments of the budding yeast genome that are in accord with available experimental data. The model unveils a paradigm of DNA supercoiling-mediated interaction between genes and makes testable predictions that will guide experimental design. 

Exploring the complexity of the epithelial-to-mesenchymal transition (EMT) unveils a diversity of potential cell fates; however, the exact timing and mechanisms by which early cell states diverge into distinct EMT trajectories remain unclear. Studying these EMT trajectories through single-cell RNA sequencing is challenging due to the necessity of sacrificing cells for each measurement. In this study, we employed optimal-transport analysis to reconstruct the past trajectories of different cell fates during TGF-beta-induced EMT in the MCF10A cell line. Our analysis revealed three distinct trajectories leading to low EMT, partial EMT, and high EMT states. Cells along the partial EMT trajectory showed substantial variations in the EMT signature and exhibited pronounced stemness. Throughout this EMT trajectory, we observed a consistent downregulation of theEEDandEZH2genes. This finding was validated by recent inhibitor screens of EMT regulators and CRISPR screen studies. Moreover, we applied our analysis of early-phase differential gene expression to gene sets associated with stemness and proliferation, pinpointingITGB4,LAMA3, andLAMB3as genes differentially expressed in the initial stages of the partial versus high EMT trajectories. We also found thatCENPF,CKS1B, andMKI67showed significant upregulation in the high EMT trajectory. While the first group of genes aligns with findings from previous studies, our work uniquely pinpoints the precise timing of these upregulations. Finally, the identification of the latter group of genes sheds light on potential cell cycle targets for modulating EMT trajectories. 

Regulatory networks as large and complex as those implicated in cell-fate choice are expected to exhibit intricate, very high-dimensional dynamics. Cell-fate choice, however, is a macroscopically simple process. Additionally, regulatory network models are almost always incomplete and/or inexact, and do not incorporate all the regulators and interactions that may be involved in cell-fate regulation. In spite of these issues, regulatory network models have proven to be incredibly effective tools for understanding cell-fate choice across contexts and for making useful predictions. Here, we show that minimal frustration—a feature of biological networks across contexts but not of random networks—can compel simple, low-dimensional steady-state behavior even in large and complex networks. Moreover, the steady-state behavior of minimally frustrated networks can be recapitulated by simpler networks such as those lacking many of the nodes and edges and those that treat multiple regulators as one. The present study provides a theoretical explanation for the success of network models in biology and for the challenges in network inference. 

The emergence of and transitions between distinct phenotypes in isogenic cells can be attributed to the intricate interplay of epigenetic marks, external signals, and gene-regulatory elements. These elements include chromatin remodelers, histone modifiers, transcription factors, and regulatory RNAs. Mathematical models known as gene-regulatory networks (GRNs) are an increasingly important tool to unravel the workings of such complex networks. In such models, epigenetic factors are usually proposed to act on the chromatin regions directly involved in the expression of relevant genes. However, it has been well-established that these factors operate globally and compete with each other for targets genome-wide. Therefore, a perturbation of the activity of a regulator can redistribute epigenetic marks across the genome and modulate the levels of competing regulators. In this paper, we propose a conceptual and mathematical modeling framework that incorporates both local and global competition effects between antagonistic epigenetic regulators, in addition to local transcription factors, and show the counterintuitive consequences of such interactions. We apply our approach to recent experimental findings on the epithelial–mesenchymal transition (EMT). We show that it can explain the puzzling experimental data, as well as provide verifiable predictions. 

While aerobic glycolysis, or the Warburg effect, has for a long time been considered a hallmark of tumor metabolism, recent studies have revealed a far more complex picture. Tumor cells exhibit widespread metabolic heterogeneity, not only in their presentation of the Warburg effect but also in the nutrients and the metabolic pathways they are dependent on. Moreover, tumor cells can switch between different metabolic phenotypes in response to environmental cues and therapeutic interventions. A framework to analyze the observed metabolic heterogeneity and plasticity is, however, lacking. Using a mechanistic model that includes the key metabolic pathways active in tumor cells, we show that the inhibition of phosphofructokinase by excess ATP in the cytoplasm can drive a preference for aerobic glycolysis in fast-proliferating tumor cells. The differing rates of ATP utilization by tumor cells can therefore drive heterogeneity with respect to the presentation of the Warburg effect. Building upon this idea, we couple the metabolic phenotype of tumor cells to their migratory phenotype, and show that our model predictions are in agreement with previous experiments. Next, we report that the reliance of proliferating cells on different anaplerotic pathways depends on the relative availability of glucose and glutamine, and can further drive metabolic heterogeneity. Finally, using treatment of melanoma cells with a BRAF inhibitor as an example, we show that our model can be used to predict the metabolic and gene expression changes in cancer cells in response to drug treatment. By making predictions that are far more generalizable and interpretable as compared to previous tumor metabolism modeling approaches, our framework identifies key principles that govern tumor cell metabolism, and the reported heterogeneity and plasticity. These principles could be key to targeting the metabolic vulnerabilities of cancer. 

The epithelial–mesenchymal transition (EMT) is a process by which cells lose epithelial traits, such as cell–cell adhesion and apico-basal polarity, and acquire migratory and invasive traits. EMT is crucial to embryonic development and wound healing. Misregulated EMT has been implicated in processes associated with cancer aggressiveness, including metastasis. Recent experimental advances such as single-cell analysis and temporal phenotypic characterization have established that EMT is a multistable process wherein cells exhibit and switch among multiple phenotypic states. This is in contrast to the classical perception of EMT as leading to a binary choice. Mathematical modeling has been at the forefront of this transformation for the field, not only providing a conceptual framework to integrate and analyze experimental data, but also making testable predictions. In this article, we review the key features and characteristics of EMT dynamics, with a focus on the mathematical modeling approaches that have been instrumental to obtaining various useful insights.