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The failure of cancer treatments, including immunotherapy, continues to be a major obstacle in preventing durable remission. This failure often results from tumor evolution, both genotypic and phenotypic, away from sensitive cell states. Here, we propose a mathematical framework for studying the dynamics of adaptive immune evasion that tracks the number of tumor-associated antigens available for immune targeting. We solve for the unique optimal cancer evasion strategy using stochastic dynamic programming and demonstrate that this policy results in increased cancer evasion rates compared to a passive, fixed strategy. Our foundational model relates the likelihood and temporal dynamics of cancer evasion to features of the immune microenvironment, where tumor immunogenicity reflects a balance between cancer adaptation and host recognition. In contrast with a passive strategy, optimally adaptive evaders navigating varying selective environments result in substantially heterogeneous post-escape tumor antigenicity, giving rise to immunogenically hot and cold tumors.

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.

Epithelial–mesenchymal transition (EMT) and its reverse mesenchymal–epithelial transition (MET) are critical during embryonic development, wound healing and cancer metastasis. While phenotypic changes during short-term EMT induction are reversible, long-term EMT induction has been often associated with irreversibility. Here, we show that phenotypic changes seen in MCF10A cells upon long-term EMT induction by TGF β need not be irreversible, but have relatively longer time scales of reversibility than those seen in short-term induction. Next, using a phenomenological mathematical model to account for the chromatin-mediated epigenetic silencing of the miR-200 family by ZEB family, we highlight how the epigenetic memory gained during long-term EMT induction can slow the recovery to the epithelial state post-TGF β withdrawal. Our results suggest that epigenetic modifiers can govern the extent and time scale of EMT reversibility and advise caution against labelling phenotypic changes seen in long-term EMT induction as ‘irreversible’.

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.