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Phenotypic heterogeneity along the epithelial-mesenchymal (E-M) axis contributes to cancer metastasis and drug resistance. Recent experimental efforts have collated detailed time-course data on the emergence and dynamics of E-M heterogeneity in a cell population. However, it remains unclear how different possible processes interplay in shaping the dynamics of E-M heterogeneity: a) intracellular regulatory interaction among biomolecules, b) cell division and death, and c) stochastic cell-state transition (biochemical reaction noise and asymmetric cell division). Here, we propose a Cell Population Balance (Partial Differential Equation (PDE)) based model that captures the dynamics of cell population density along the E-M phenotypic axis due to abovementioned multi-scale cellular processes. We demonstrate how population distribution resulting from intracellular regulatory networks driving cell-state transition gets impacted by stochastic fluctuations in E-M regulatory biomolecules, differences in growth rates among cell subpopulations, and initial population distribution. Further, we reveal that a linear dependence of the cell growth rate on the population heterogeneity is sufficient to recapitulate the faster in vivo growth of orthotopic injected heterogeneous E-M subclones reported before experimentally. Overall, our model contributes to the combined understanding of intracellular and cell-population levels dynamics in the emergence of E-M heterogeneity in a cell population.

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. It also includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and 'classical' systems typically studied in non-equilibrium statistical and quantum mechanics., Comment: 81 pages, 13 figures

Consensus decision-making in social groups strongly depends on communication links that determine to whom individuals send, and from whom they receive, information. Here, we ask how consensus decisions are affected by strategic updating of links and how this effect varies with the direction of communication. We quantified the co-evolution of link and opinion dynamics in a large population with binary opinions using mean-field numerical simulations of two voter-like models of opinion dynamics: an Incoming model (where individuals choose who to receive opinions from) and an Outgoing model (where individuals choose who to send opinions to). We show that individuals can bias group-level outcomes in their favor by breaking disagreeing links while receiving opinions (Incoming Model) and retaining disagreeing links while sending opinions (Outgoing Model). Importantly, these biases can help the population avoid stalemates and achieve consensus. However, the role of disagreement avoidance is diluted in the presence of strong preferences - highly stubborn individuals can shape decisions to favor their preferences, giving rise to non-consensus outcomes. We conclude that collectively changing communication structures can bias consensus decisions, as a function of the strength of preferences and the direction of communication.

Cancer cells have the plasticity to adjust their metabolic phenotypes for survival and metastasis. During metastasis, a developmental program known as the epithelial-mesenchymal transition (EMT) plays a critical role. There is extensive cross-talk between metabolism and EMT, but how this leads to coordinated physiological changes is still uncertain. The elusive connection between metabolism and EMT compromises the efficacy of metabolic therapies targeting metastasis. In this review, we aim for clarifying causation between metabolism and EMT based on recent experimental studies and propose integrated theoretical-experimental efforts to better understand the coupled decision-making of metabolism and EMT., Comment: 31 pages, 3 figures

Notch signaling is an evolutionary conserved cell-cell communication pathway. Besides regulating cell-fate decisions at an individual cell level, Notch signaling coordinates the emergent spatiotemporal patterning in a tissue through ligand-receptor interactions among transmembrane molecules of neighboring cells, as seen in embryonic development, angiogenesis, or wound healing. Due to its ubiquitous nature, Notch signaling is also implicated in several aspects of cancer progression, including tumor angiogenesis, stemness of cancer cells and cellular invasion. Here, we review experimental and computational models to help understand the operating principles of cell patterning driven by Notch signaling. First, we discuss the basic mechanisms of spatial patterning via canonical lateral inhibition and lateral induction mechanisms, including examples from angiogenesis, inner ear development and cancer metastasis. Next, we analyze additional layers of complexity in the Notch pathway such as the effects of varying cell sizes and shapes, ligand-receptor binding within the same cell, variable binding affinity of different ligand/receptor subtypes, and filopodia. Finally, we discuss some recent evidence of mechanosensitivity in the Notch pathway in driving collective epithelial cell migration and cardiovascular morphogenesis.

Epithelial-Mesenchymal Transition (EMT), and the corresponding reverse process, Mesenchymal-Epithelial Transition (MET), are dynamic and reversible cellular programs orchestrated by many changes at biochemical and morphological levels. A recent surge in identifying the molecular mechanisms underlying EMT/MET has led to the development of various mathematical models that have contributed to our improved understanding of dynamics at single-cell and population levels: a) multi-stability (how many phenotypes can cells attain en route EMT/MET?), b) reversibility/irreversibility (what time and/or concentration of an EMT inducer marks the 'tipping point' when cells induced to undergo EMT cannot revert?), c) symmetry in EMT/MET (do cells take the same path while reverting as they took during the induction of EMT?), and d) non-cell autonomous mechanisms (how does a cell undergoing EMT alter the tendency of its neighbors to undergo EMT?). These dynamical traits may facilitate a heterogeneous response within a cell population undergoing EMT/MET. Here, we present a few examples of designing different mathematical models that can contribute to decoding EMT/MET dynamics.

Cancer cells can acquire a spectrum of stable hybrid epithelial/mesenchymal (E/M) states during epithelial-mesenchymal transition (EMT). Cells in these hybrid E/M phenotypes often combine epithelial and mesenchymal features and tend to migrate collectively commonly as small clusters. Such collectively migrating cancer cells play a pivotal role in seeding metastases and their presence in cancer patients indicates an adverse prognostic factor. Moreover, cancer cells in hybrid E/M phenotypes tend to be more associated with stemness which endows them with tumor-initiation ability and therapy resistance. Most recently, cells undergoing EMT have been shown to promote immune suppression for better survival. A systematic understanding of the emergence of hybrid E/M phenotypes and the connection of EMT with stemness and immune suppression would contribute to more effective therapeutic strategies. In this review, we first discuss recent efforts combining theoretical and experimental approaches to elucidate mechanisms underlying EMT multi-stability (i.e. the existence of multiple stable phenotypes during EMT) and the properties of hybrid E/M phenotypes. Following we discuss non-cell-autonomous regulation of EMT by cell cooperation and extracellular matrix. Afterwards, we discuss various metrics that can be used to quantify EMT spectrum. We further describe possible mechanisms underlying the formation of clusters of circulating tumor cells. Last but not least, we summarize recent systems biology analysis of the role of EMT in the acquisition of stemness and immune suppression., Comment: 50 pages, 6 figures

Purpose of review: The epithelial-Mesenchymal Transition (EMT) and the generation of Cancer Stem Cells (CSC) are two fundamental aspects contributing to tumor growth, acquisition of resistance to therapy, formation of metastases, and tumor relapse. Recent experimental data identifying the circuits regulating EMT and CSCs have driven the development of computational models capturing the dynamics of these circuits and consequently various aspects of tumor progression. Recent findings: We review the contribution made by these models in a) recapitulating experimentally observed behavior, b) making experimentally testable predictions, and c) driving emerging notions in the field, including the emphasis on the aggressive potential of hybrid epithelial/mesenchymal (E/M) phenotype(s). We discuss dynamical and statistical models at intracellular and population level relating to dynamics of EMT and CSCs, and those focusing on interconnections between these two processes. Summary: These models highlight the insights gained via mathematical modeling approaches, and emphasizes that the connections between hybrid E/M phenotype(s) and stemness can be explained by analyzing underlying regulatory circuits. Such experimentally curated models have the potential of serving as platforms for better therapeutic design strategies.

Clusters of circulating tumor cells (CTCs), although rare, may account for more than 95% of metastases. Inflammatory breast cancer (IBC) is a highly aggressive subtype that chiefly metastasizes via CTC clusters. Theory suggests that physical systems with hierarchical organization tend to be more adaptable due to their ability to efficiently span the set of available states. We used the cophenetic correlation coefficient (CCC) to quantify the hierarchical organization in the expression of collective dissemination associated and IBC associated genes, and found that the CCC of both gene sets was higher in (a) epithelial cell lines as compared to mesenchymal cell lines and (b) IBC tumor samples as compared to non-IBC breast cancer samples. A higher CCC of both networks was also correlated with a higher rate of metastatic relapse in breast cancer patients. Gene set enrichment analysis could not provide similar insights, indicating that the CCC provides additional information regarding the organizational complexity of gene expression. These results suggest that retention of epithelial traits in disseminating tumor cells as IBC progresses promotes successful metastasis and the CCC may be a prognostic factor for IBC., Comment: 38 pages, 13 figures

Background: The Epithelial-Mesenchymal Transition (EMT) endows epithelial-looking cells with enhanced migratory ability during embryonic development and tissue repair. EMT can also be co-opted by cancer cells to acquire metastatic potential and drug-resistance. Recent research has argued that epithelial (E) cells can undergo either a partial EMT to attain a hybrid epithelial/mesenchymal (E/M) phenotype that typically displays collective migration, or a complete EMT to adopt a mesenchymal (M) phenotype that shows individual migration. The core EMT regulatory network - miR-34/SNAIL/miR-200/ZEB1 - has been identified by various studies, but how this network regulates the transitions among the E, E/M, and M phenotypes remains controversial. Two major mathematical models - ternary chimera switch (TCS) and cascading bistable switches (CBS) - that both focus on the miR-34/SNAIL/miR-200/ZEB1 network, have been proposed to elucidate the EMT dynamics, but a detailed analysis of how well either or both of these two models can capture recent experimental observations about EMT dynamics remains to be done. Results: Here, via an integrated experimental and theoretical approach, we first show that both these two models can be used to understand the two-step transition of EMT - E-E/M-M, the different responses of SNAIL and ZEB1 to exogenous TGF-b and the irreversibility of complete EMT. Next, we present new experimental results that tend to discriminate between these two models. We show that ZEB1 is present at intermediate levels in the hybrid E/M H1975 cells, and that in HMLE cells, overexpression of SNAIL is not sufficient to initiate EMT in the absence of ZEB1 and FOXC2. Conclusions: These experimental results argue in favor of the TCS model proposing that miR-200/ZEB1 behaves as a three-way decision-making switch enabling transitions among the E, hybrid E/M and M phenotypes.