Motivated by the famous Waddington’s epigenetic landscape metaphor in developmental biology, biophysicists and applied mathematicians made different proposals to construct the landscape for multi-stable complex systems. We aim to summarize and elucidate the relationships among these theories from a mathematical point of view. We systematically investigate and compare three different but closely related realizations in the recent literature: the Wang’s potential landscape theory from steady state distribution of stochastic differential equations (SDEs), the Freidlin-Wentzell quasi-potential from the large deviation theory, and the construction through SDE decomposition and A-type integral. We revisit that the quasi-potential is the zero noise limit of the potential landscape, and the potential function in the third proposal coincides with the quasi-potential. We compare the difference between local and global quasi-potential through the viewpoint of exchange of limit order for time and noise amplitude. We argue that local quasi-potentials are responsible for getting transition rates between neighboring stable states, while the global quasi-potential mainly characterizes the residence time of the states as the system reaches stationarity. The difference between these two is prominent when the transitivity property is broken. The most probable transition path by minimizing the Onsager-Machlup or Freidlin-Wentzell action functional is also discussed. As a consequence of the established connections among different proposals, we arrive at the novel result which guarantees the existence of SDE decomposition while denies its uniqueness in general cases. It is, therefore, clarified that the A-type integral is more appropriate to be applied to the decomposed SDEs rather than its primitive form as believed by previous researchers. Our results contribute to a deeper understanding of landscape theories for biological systems.

Extracting dynamical information from single‐cell transcriptomics is a novel task with the promise to advance our understanding of cell state transition and interactions between genes. Yet, theory‐oriented, bottom‐up approaches that consider differences among cell states are largely lacking. Here, we present spliceJAC, a method to quantify the multivariate mRNA splicing from single‐cell RNA sequencing (scRNA‐seq). spliceJAC utilizes the unspliced and spliced mRNA count matrices to constructs cell state‐specific gene–gene regulatory interactions and applies stability analysis to predict putative driver genes critical to the transitions between cell states. By applying spliceJAC to biological systems including pancreas endothelium development and epithelial–mesenchymal transition (EMT) in A549 lung cancer cells, we predict genes that serve specific signaling roles in different cell states, recover important differentially expressed genes in agreement with pre‐existing analysis, and predict new transition genes that are either exclusive or shared between different cell state transitions.

Spatial transcriptomics and messenger RNA splicing encode extensive spatiotemporal information for cell states and transitions. The current lineage-inference methods either lack spatial dynamics for state transition or cannot capture different dynamics associated with multiple cell states and transition paths. Here we present spatial transition tensor (STT), a method that uses messenger RNA splicing and spatial transcriptomes through a multiscale dynamical model to characterize multistability in space. By learning a four-dimensional transition tensor and spatial-constrained random walk, STT reconstructs cell-state-specific dynamics and spatial state transitions via both short-time local tensor streamlines between cells and long-time transition paths among attractors. Benchmarking and applications of STT on several transcriptome datasets via multiple technologies on epithelial–mesenchymal transitions, blood development, spatially resolved mouse brain and chicken heart development, indicate STT’s capability in recovering cell-state-specific dynamics and their associated genes not seen using existing methods. Overall, STT provides a consistent multiscale description of single-cell transcriptome data across multiple spatiotemporal scales.

Rosacea is a chronic inflammatory skin disorder, whose underlying cellular and molecular mechanisms remain obscure. Here, we generate a single-cell atlas of facial skin from female rosacea patients and healthy individuals. Among keratinocytes, a subpopulation characterized by IFNγ-mediated barrier function damage is found to be unique to rosacea lesions. Blocking IFNγ signaling alleviates rosacea-like phenotypes and skin barrier damage in mice. The papulopustular rosacea is featured by expansion of pro-inflammatory fibroblasts, Schwann, endothelial and macrophage/dendritic cells. The frequencies of type 1/17 and skin-resident memory T cells are increased, and vascular mural cells are characterized by activation of inflammatory pathways and impaired muscle contraction function in rosacea. Most importantly, fibroblasts are identified as the leading cell type producing pro-inflammatory and vasodilative signals in rosacea. Depletion of fibroblasts or knockdown of PTGDS, a gene specifically upregulated in fibroblasts, blocks rosacea development in mice. Our study provides a comprehensive understanding of the aberrant alterations of skin-resident cell populations and identifies fibroblasts as a key determinant in rosacea development.

Cervical cancer is a leading cause of gynecological tumor related deaths worldwide. The applications of conventional approaches such as chemoradiotherapy and surgery are restricted due to their side effects and drug resistances. Although immune checkpoint inhibitors (ICIs) have emerged as novel choices, their clinical response rates are rather limited. To date there is a lack of effective treatment regimens for patients with metastatic or recurrent cervical cancer. Recently nanomaterials like liposomes, dendrimers, and polymers are considered as promising delivery carriers with advantages of tumor‐specific administration, reduced toxicity, and improved biocompatibility. Here, we review the applications of nanoparticles in the fields of drug delivery, CRISPR based genome‐editing and therapeutic vaccines in cervical cancer treatment.This article is categorized under: Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease

Epithelial-to-mesenchymal transition (EMT) plays an important role in many biological processes during development and cancer. The advent of single-cell transcriptome sequencing techniques allows the dissection of dynamical details underlying EMT with unprecedented resolution. Despite several single-cell data analysis on EMT, how cell communicates and regulates dynamics along the EMT trajectory remains elusive. Using single-cell transcriptomic datasets, here we infer the cell–cell communications and the multilayer gene–gene regulation networks to analyze and visualize the complex cellular crosstalk and the underlying gene regulatory dynamics along EMT. Combining with trajectory analysis, our approach reveals the existence of multiple intermediate cell states (ICSs) with hybrid epithelial and mesenchymal features. Analyses on the time-series datasets from cancer cell lines with different inducing factors show that the induced EMTs are context-specific: the EMT induced by transforming growth factor B1 (TGFB1) is synchronous, whereas the EMTs induced by epidermal growth factor and tumor necrosis factor are asynchronous, and the responses of TGF-β pathway in terms of gene expression regulations are heterogeneous under different treatments or among various cell states. Meanwhile, network topology analysis suggests that the ICSs during EMT serve as the signaling in cellular communication under different conditions. Interestingly, our analysis of a mouse skin squamous cell carcinoma dataset also suggests regardless of the significant discrepancy in concrete genes between in vitro and in vivo EMT systems, the ICSs play dominant role in the TGF-β signaling crosstalk. Overall, our approach reveals the multiscale mechanisms coupling cell–cell communications and gene–gene regulations responsible for complex cell-state transitions.