Quantifying the landscape and kinetic paths for epithelial-mesenchymal transition from a core circuit

Energy Landscape Reveals the Underlying Mechanism of Cancer-Adipose Conversion in Gene Network Models

Cancer is a systemic heterogeneous disease involving complex molecular networks. Tumor formation involves an epithelial-mesenchymal transition (EMT), which promotes both metastasis and plasticity of cancer cells. Recent experiments have proposed that cancer cells can be transformed into adipocytes via a combination of drugs. However, the underlying mechanisms for how these drugs work, from a molecular network perspective, remain elusive. To reveal the mechanism of cancer-adipose conversion (CAC), this study adopts a systems biology approach by combing mathematical modeling and molecular experiments, based on underlying molecular regulatory networks. Four types of attractors are identified, corresponding to epithelial (E), mesenchymal (M), adipose (A) and partial/intermediate EMT (P) cell states on the CAC landscape. Landscape and transition path results illustrate that intermediate states play critical roles in the cancer to adipose transition. Through a landscape control approach, two new therapeutic strategies for drug combinations are identified, that promote CAC. These predictions are verified by molecular experiments in different cell lines. The combined computational and experimental approach provides a powerful tool to explore molecular mechanisms for cell fate transitions in cancer networks. The results reveal underlying mechanisms of intermediate cell states that govern the CAC, and identified new potential drug combinations to induce cancer adipogenesis.

Tipping points in epithelial-mesenchymal lineages from single-cell transcriptomics data

Understanding cell fate decision-making during complex biological processes is an open challenge that is now aided by high-resolution single-cell sequencing technologies. Specifically, it remains challenging to identify and characterize transition states corresponding to "tipping points" whereby cells commit to new cell states. Here, we present a computational method that takes advantage of single-cell transcriptomics data to infer the stability and gene regulatory networks (GRNs) along cell lineages. Our method uses the unspliced and spliced counts from single-cell RNA sequencing data and cell ordering along lineage trajectories to train an RNA splicing multivariate model, from which cell-state stability along the lineage is inferred based on spectral analysis of the model's Jacobian matrix. Moreover, the model infers the RNA cross-species interactions resulting in GRNs and their variation along the cell lineage. When applied to epithelial-mesenchymal transition in ovarian and lung cancer-derived cell lines, our model predicts a saddle-node transition between the epithelial and mesenchymal states passing through an unstable, intermediate cell state. Furthermore, we show that the underlying GRN controlling epithelial-mesenchymal transition rearranges during the transition, resulting in denser and less modular networks in the intermediate state. Overall, our method represents a flexible tool to study cell lineages with a combination of theory-driven modeling and single-cell transcriptomics data.

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional (8D) limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

Data- and theory-driven approaches for understanding paths of epithelial-mesenchymal transition

Reversible transitions between epithelial and mesenchymal cell states are a crucial form of epithelial plasticity for development and disease progression. Recent experimental data and mechanistic models showed multiple intermediate epithelial-mesenchymal transition (EMT) states as well as trajectories of EMT underpinned by complex gene regulatory networks. In this review, we summarize recent progress in quantifying EMT and characterizing EMT paths with computational methods and quantitative experiments including omics-level measurements. We provide perspectives on how these studies can help relating fundamental cell biology to physiological and pathological outcomes of EMT.

Quantifying cancer cell plasticity with gene regulatory networks and single-cell dynamics

Phenotypic plasticity of cancer cells can lead to complex cell state dynamics during tumor progression and acquired resistance. Highly plastic stem-like states may be inherently drug-resistant. Moreover, cell state dynamics in response to therapy allow a tumor to evade treatment. In both scenarios, quantifying plasticity is essential for identifying high-plasticity states or elucidating transition paths between states. Currently, methods to quantify plasticity tend to focus on 1) quantification of quasi-potential based on the underlying gene regulatory network dynamics of the system; or 2) inference of cell potency based on trajectory inference or lineage tracing in single-cell dynamics. Here, we explore both of these approaches and associated computational tools. We then discuss implications of each approach to plasticity metrics, and relevance to cancer treatment strategies.

Theoretical and computational tools to model multistable gene regulatory networks

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.

Theoretical and computational tools to model multistable gene regulatory networks

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.

Structure and function in artificial, zebrafish and human neural networks

Network science provides a set of tools for the characterization of the structure and functional behavior of complex systems. Yet a major problem is to quantify how the structural domain is related to the dynamical one. In other words, how the diversity of dynamical states of a system can be predicted from the static network structure? Or the reverse problem: starting from a set of signals derived from experimental recordings, how can one discover the network connections or the causal relations behind the observed dynamics? Despite the advances achieved over the last two decades, many challenges remain concerning the study of the structure-dynamics interplay of complex systems. In neuroscience, progress is typically constrained by the low spatio-temporal resolution of experiments and by the lack of a universal inferring framework for empirical systems. To address these issues, applications of network science and artificial intelligence to neural data have been rapidly growing. In this article, we review important recent applications of methods from those fields to the study of the interplay between structure and functional dynamics of human and zebrafish brain. We cover the selection of topological features for the characterization of brain networks, inference of functional connections, dynamical modeling, and close with applications to both the human and zebrafish brain. This review is intended to neuroscientists who want to become acquainted with techniques from network science, as well as to researchers from the latter field who are interested in exploring novel application scenarios in neuroscience.

SNAIL driven by a feed forward loop motif promotes TGFβinduced epithelial to mesenchymal transition

Epithelial to Mesenchymal Transition (EMT) plays an important role in tissue regeneration, embryonic development, and cancer metastasis. Several signaling pathways are known to regulate EMT, among which the modulation of TGFβ(Transforming Growth Factor-β) induced EMT is crucial in several cancer types. Several mathematical models were built to explore the role of core regulatory circuit of ZEB/miR-200, SNAIL/miR-34 double negative feedback loops in modulating TGFβinduced EMT. Different emergent behavior including tristability, irreversible switching, existence of hybrid EMT states were inferred though these models. Some studies have explored the role of TGFβreceptor activation, SMADs nucleocytoplasmic shuttling and complex formation. Recent experiments have revealed that MDM2 along with SMAD complex regulates SNAIL expression driven EMT. Encouraged by this, in the present study we developed a mathematical model for p53/MDM2 dependent TGFβinduced EMT regulation. Inclusion of p53 brings in an additional mechanistic perspective in exploring the EM transition. The network formulated comprises a C1FFL moderating SNAIL expression involving MDM2 and SMAD complex, which functions as a noise filter and persistent detector. The C1FFL was also observed to operate as a coincidence detector driving the SNAIL dependent downstream signaling into phenotypic switching decision. Systems modelling and analysis of the devised network, displayed interesting dynamic behavior, systems response to various inputs stimulus, providing a better understanding of p53/MDM2 dependent TGF-βinduced Epithelial to Mesenchymal Transition.

NRF2-dependent Epigenetic Regulation can Promote the Hybrid Epithelial/Mesenchymal Phenotype

The epithelial-mesenchymal transition (EMT) is a cellular process critical for wound healing, cancer metastasis and embryonic development. Recent efforts have identified the role of hybrid epithelial/mesenchymal states, having both epithelial and mesehncymal traits, in enabling cancer metastasis and resistance to various therapies. Also, previous work has suggested that NRF2 can act as phenotypic stability factor to help stablize such hybrid states. Here, we incorporate a phenomenological epigenetic feedback effect into our previous computational model for EMT signaling. We show that this type of feedback can stabilize the hybrid state as compared to the fully mesenchymal phenotype if NRF2 can influence SNAIL at an epigenetic level, as this link makes transitions out of hybrid state more difficult. However, epigenetic regulation on other NRF2-related links do not significantly change the EMT dynamics. Finally, we considered possible cell division effects in our epigenetic regulation model, and our results indicate that the degree of epigenetic inheritance does not appear to be a critical factor for the hybrid E/M state stabilizing behavior of NRF2.

Energy Landscape Analysis of the Epithelial-Mesenchymal Transition Network

The epithelial-mesenchymal transition (EMT) is a key developmental program that is often activated during the cancer invasion, metastasis, and drug resistance. However, it remains a critical question to elucidate the mechanisms of EMT. For example, how to quantify the global stability and stochastic transition dynamics of EMT under fluctuations is yet to be clarified. Here, we describe a framework and detailed steps for stochastic dynamics analysis of EMT. Starting from the underlying EMT gene regulatory network, we quantify the energy landscape of the EMT computationally. Multiple steady-state attractors are identified on the landscape surface, characterizing different cell phenotypes. The kinetic transition paths based on large deviation theory delineate the transition processes between different attractors quantitatively. The EMT or the reverse process, the mesenchymal-epithelial transition (MET), can be achieved by either a direct transition or a step-wise transition that goes through an intermediate state, depending on different extracellular environments. The landscape and transition paths presented in this chapter provide a new physical and quantitative picture to understand the underlying mechanisms of the EMT process. The approach for landscape and path analysis can be extended to other biological networks.

Systems-level network modeling deciphers the master regulators of phenotypic plasticity and heterogeneity in melanoma

Phenotypic (i.e. non-genetic) heterogeneity in melanoma drives dedifferentiation, recalcitrance to targeted therapy and immunotherapy, and consequent tumor relapse and metastasis. Various markers or regulators associated with distinct phenotypes in melanoma have been identified, but, how does a network of interactions among these regulators give rise to multiple "attractor" states and phenotypic switching remains elusive. Here, we inferred a network of transcription factors (TFs) that act as master regulators for gene signatures of diverse cell-states in melanoma. Dynamical simulations of this network predicted how this network can settle into different "attractors" (TF expression patterns), suggesting that TF network dynamics drives the emergence of phenotypic heterogeneity. These simulations can recapitulate major phenotypes observed in melanoma and explain de-differentiation trajectory observed upon BRAF inhibition. Our systems-level modeling framework offers a platform to understand trajectories of phenotypic transitions in the landscape of a regulatory TF network and identify novel therapeutic strategies targeting melanoma plasticity.

Landscape and kinetic path quantify critical transitions in epithelial-mesenchymal transition

Epithelial-mesenchymal transition (EMT), a basic developmental process that might promote cancer metastasis, has been studied from various perspectives. Recently, the early warning theory has been used to anticipate critical transitions in EMT from mathematical modeling. However, the underlying mechanisms of EMT involving complex molecular networks remain to be clarified. Especially, how to quantify the global stability and stochastic transition dynamics of EMT and what the underlying mechanism for early warning theory in EMT is remain to be fully clarified. To address these issues, we constructed a comprehensive gene regulatory network model for EMT and quantified the corresponding potential landscape. The landscape for EMT displays multiple stable attractors, which correspond to E, M, and some other intermediate states. Based on the path-integral approach, we identified the most probable transition paths of EMT, which are supported by experimental data. Correspondingly, the results of transition actions demonstrated that intermediate states can accelerate EMT, consistent with recent studies. By integrating the landscape and path with early warning concept, we identified the potential barrier height from the landscape as a global and more accurate measure for early warning signals to predict critical transitions in EMT. The landscape results also provide an intuitive and quantitative explanation for the early warning theory. Overall, the landscape and path results advance our mechanistic understanding of dynamical transitions and roles of intermediate states in EMT, and the potential barrier height provides a new, to our knowledge, measure for critical transitions and quantitative explanations for the early warning theory.

Noise distorts the epigenetic landscape and shapes cell-fate decisions

The Waddington epigenetic landscape has become an iconic representation of the cellular differentiation process. Recent single-cell transcriptomic data provide new opportunities for quantifying this originally conceptual tool, offering insight into the gene regulatory networks underlying cellular development. While many methods for constructing the landscape have been proposed, by far the most commonly employed approach is based on computing the landscape as the negative logarithm of the steady-state probability distribution. Here, we use simple models to highlight the complexities and limitations that arise when reconstructing the potential landscape in the presence of stochastic fluctuations. We consider how the landscape changes in accordance with different stochastic systems and show that it is the subtle interplay between the deterministic and stochastic components of the system that ultimately shapes the landscape. We further discuss how the presence of noise has important implications for the identifiability of the regulatory dynamics from experimental data. A record of this paper's transparent peer review process is included in the supplemental information.

Cell Plasticity and Prostate Cancer: The Role of Epithelial-Mesenchymal Transition in Tumor Progression, Invasion, Metastasis and Cancer Therapy Resistance

Simple Summary

Although epithelial-to-mesenchymal transition (EMT) is a well-known cellular process involved during normal embryogenesis and wound healing, it also has a dark side; it is a complex process that provides tumor cells with a more aggressive phenotype, facilitating tumor metastasis and even resistance to therapy. This review focuses on the key pathways of EMT in the pathogenesis of prostate cancer and the development of metastases and evasion of currently available treatments.

Abstract

Prostate cancer, the second most common malignancy in men, is characterized by high heterogeneity that poses several therapeutic challenges. Epithelial–mesenchymal transition (EMT) is a dynamic, reversible cellular process which is essential in normal embryonic morphogenesis and wound healing. However, the cellular changes that are induced by EMT suggest that it may also play a central role in tumor progression, invasion, metastasis, and resistance to current therapeutic options. These changes include enhanced motility and loss of cell–cell adhesion that form a more aggressive cellular phenotype. Moreover, the reverse process (MET) is a necessary element of the metastatic tumor process. It is highly probable that this cell plasticity reflects a hybrid state between epithelial and mesenchymal status. In this review, we describe the underlying key mechanisms of the EMT-induced phenotype modulation that contribute to prostate tumor aggressiveness and cancer therapy resistance, in an effort to provide a framework of this complex cellular process.

Computational systems-biology approaches for modeling gene networks driving epithelial-mesenchymal transitions

Epithelial-mesenchymal transition (EMT) is an important biological process through which epithelial cells undergo phenotypic transitions to mesenchymal cells by losing cell-cell adhesion and gaining migratory properties that cells use in embryogenesis, wound healing, and cancer metastasis. An important research topic is to identify the underlying gene regulatory networks (GRNs) governing the decision making of EMT and develop predictive models based on the GRNs. The advent of recent genomic technology, such as single-cell RNA sequencing, has opened new opportunities to improve our understanding about the dynamical controls of EMT. In this article, we review three major types of computational and mathematical approaches and methods for inferring and modeling GRNs driving EMT. We emphasize (1) the bottom-up approaches, where GRNs are constructed through literature search; (2) the top-down approaches, where GRNs are derived from genome-wide sequencing data; (3) the combined top-down and bottom-up approaches, where EMT GRNs are constructed and simulated by integrating bioinformatics and mathematical modeling. We discuss the methodologies and applications of each approach and the available resources for these studies.

Epigenetic Regulation of Epithelial to Mesenchymal Transition in the Cancer Metastatic Cascade: Implications for Cancer Therapy

Metastasis is the end stage of cancer progression and the direct cause of most cancer-related deaths. The spreading of cancer cells from the primary site to distant organs is a multistep process known as the metastatic cascade, including local invasion, intravasation, survival in the circulation, extravasation, and colonization. Each of these steps is driven by the acquisition of genetic and/or epigenetic alterations within cancer cells, leading to subsequent transformation of metastatic cells. Epithelial–mesenchymal transition (EMT), a cellular process mediating the conversion of cell from epithelial to mesenchymal phenotype, and its reverse transformation, termed mesenchymal–epithelial transition (MET), together endow metastatic cells with traits needed to generate overt metastases in different scenarios. The dynamic shift between these two phenotypes and their transitional state, termed partial EMT, emphasizes the plasticity of EMT. Recent advances attributed this plasticity to epigenetic regulation, which has implications for the therapeutic targeting of cancer metastasis. In this review, we will discuss the association between epigenetic events and the multifaceted nature of EMT, which may provide insights into the steps of the cancer metastatic cascade.

Inference of Intercellular Communications and Multilayer Gene-Regulations of Epithelial-Mesenchymal Transition From Single-Cell Transcriptomic Data

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.

Quantifying the Landscape and Transition Paths for Proliferation-Quiescence Fate Decisions

The cell cycle, essential for biological functions, experiences delicate spatiotemporal regulation. The transition between G1 and S phase, which is called the proliferation–quiescence decision, is critical to the cell cycle. However, the stability and underlying stochastic dynamical mechanisms of the proliferation–quiescence decision have not been fully understood. To quantify the process of the proliferation–quiescence decision, we constructed its underlying landscape based on the relevant gene regulatory network. We identified three attractors on the landscape corresponding to the G0, G1, and S phases, individually, which are supported by single-cell data. By calculating the transition path, which quantifies the potential barrier, we built expression profiles in temporal order for key regulators in different transitions. We propose that the two saddle points on the landscape characterize restriction point (RP) and G1/S checkpoint, respectively, which provides quantitative and physical explanations for the mechanisms of Rb governing the RP while p21 controlling the G1/S checkpoint. We found that Emi1 inhibits the transition from G0 to G1, while Emi1 in a suitable range facilitates the transition from G1 to S. These results are partially consistent with previous studies, which also suggested new roles of Emi1 in the cell cycle. By global sensitivity analysis, we identified some critical regulatory factors influencing the proliferation–quiescence decision. Our work provides a global view of the stochasticity and dynamics in the proliferation–quiescence decision of the cell cycle.

Understanding the Principles of Pattern Formation Driven by Notch Signaling by Integrating Experiments and Theoretical Models

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 that 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, including the effect 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.

Epigenetic feedback and stochastic partitioning during cell division can drive resistance to EMT

Epithelial-mesenchymal transition (EMT) and its reverse process mesenchymal-epithelial transition (MET) are central to metastatic aggressiveness and therapy resistance in solid tumors. While molecular determinants of both processes have been extensively characterized, the heterogeneity in the response of tumor cells to EMT and MET inducers has come into focus recently, and has been implicated in the failure of anti-cancer therapies. Recent experimental studies have shown that some cells can undergo an irreversible EMT depending on the duration of exposure to EMT-inducing signals. While the irreversibility of MET, or equivalently, resistance to EMT, has not been studied in as much detail, evidence supporting such behavior is slowly emerging. Here, we identify two possible mechanisms that can underlie resistance of cells to undergo EMT: epigenetic feedback in ZEB1/GRHL2 feedback loop and stochastic partitioning of biomolecules during cell division. Identifying the ZEB1/GRHL2 axis as a key determinant of epithelial-mesenchymal plasticity across many cancer types, we use mechanistic mathematical models to show how GRHL2 can be involved in both the abovementioned processes, thus driving an irreversible MET. Our study highlights how an isogenic population may contain subpopulation with varying degrees of susceptibility or resistance to EMT, and proposes a next set of questions for detailed experimental studies characterizing the irreversibility of MET/resistance to EMT.

SMAD7 and SERPINE1 as novel dynamic network biomarkers detect and regulate the tipping point of TGF-beta induced EMT

Epithelial-mesenchymal transition (EMT) is a complex nonlinear biological process that plays essential roles in fundamental biological processes such as embryogenesis, wounding healing, tissue regeneration, and cancer metastasis. A hallmark of EMT is the switch-like behavior during state transition, which is characteristic of phase transitions. Hence, detecting the tipping point just before mesenchymal state transition is critical for understanding molecular mechanism of EMT. Through dynamic network biomarkers (DNB) model, a DNB group with 37 genes was identified which can provide the early-warning signals of EMT. Particularly, we found that two DNB genes, i.e., SMAD7 and SERPINE1 promoted EMT by switching their regulatory network which was further validated by biological experiments. Survival analyses revealed that SMAD7 and SERPINE1 as DNB genes further acted as prognostic biomarkers for lung adenocarcinoma.

Chemical Langevin equation: A path-integral view of Gillespie's derivation

In 2000, Gillespie rehabilitated the chemical Langevin equation (CLE) by describing two conditions that must be satisfied for it to yield a valid approximation of the chemical master equation (CME). In this work, we construct an original path-integral description of the CME and show how applying Gillespie's two conditions to it directly leads to a path-integral equivalent to the CLE. We compare this approach to the path-integral equivalent of a large system size derivation and show that they are qualitatively different. In particular, both approaches involve converting many sums into many integrals, and the difference between the two methods is essentially the difference between using the Euler-Maclaurin formula and using Riemann sums. Our results shed light on how path integrals can be used to conceptualize coarse-graining biochemical systems and are readily generalizable.

Computational models to explore the complexity of the epithelial to mesenchymal transition in cancer

Epithelial to mesenchymal transition (EMT) is a complex biological process that plays a key role in cancer progression and metastasis formation. Its activation results in epithelial cells losing adhesion and polarity and becoming capable of migrating from their site of origin. At this step the disease is generally considered incurable. As EMT execution involves several individual molecular components, connected by nontrivial relations, in vitro techniques are often inadequate to capture its complexity. Computational models can be used to complement experiments and provide additional knowledge difficult to build up in a wetlab. Indeed in silico analysis gives the user total control on the system, allowing to identify the contribution of each independent element. In the following, two kinds of approaches to the computational study of EMT will be presented. The first relies on signal transduction networks description and details how changes in gene expression could influence this process, both focusing on specific aspects of the EMT and providing a general frame for this phenomenon easily comparable with experimental data. The second integrates single cell and population level descriptions in a multiscale model that can be considered a more accurate representation of the EMT. The advantages and disadvantages of each approach will be highlighted, together with the importance of coupling computational and experimental results. Finally, the main challenges that need to be addressed to improve our knowledge of the role of EMT in the neoplastic disease and the scientific and translational value of computational models in this respect will be presented. This article is categorized under: Analytical and Computational Methods > Computational Methods.

A Computational Model of the Endothelial to Mesenchymal Transition

Endothelial cells (ECs) form the lining of lymph and blood vessels. Changes in tissue requirements or wounds may cause ECs to behave as tip or stalk cells. Alternatively, they may differentiate into mesenchymal cells (MCs). These processes are known as EC activation and endothelial-to-mesenchymal transition (EndMT), respectively. EndMT, Tip, and Stalk EC behaviors all require SNAI1, SNAI2, and Matrix metallopeptidase (MMP) function. However, only EndMT inhibits the expression of VE-cadherin, PECAM1, and VEGFR2, and also leads to EC detachment. Physiologically, EndMT is involved in heart valve development, while a defective EndMT regulation is involved in the physiopathology of cardiovascular malformations, congenital heart disease, systemic and organ fibrosis, pulmonary arterial hypertension, and atherosclerosis. Therefore, the control of EndMT has many promising potential applications in regenerative medicine. Despite the fact that many molecular components involved in EC activation and EndMT have been characterized, the system-level molecular mechanisms involved in this process have not been elucidated. Toward this end, hereby we present Boolean network model of the molecular involved in the regulation of EC activation and EndMT. The simulated dynamic behavior of our model reaches fixed and cyclic patterns of activation that correspond to the expected EC and MC cell types and behaviors, recovering most of the specific effects of simple gain and loss-of-function mutations as well as the conditions associated with the progression of several diseases. Therefore, our model constitutes a theoretical framework that can be used to generate hypotheses and guide experimental inquiry to comprehend the regulatory mechanisms behind EndMT. Our main findings include that both the extracellular microevironment and the pattern of molecular activity within the cell regulate EndMT. EndMT requires a lack of VEGFA and sufficient oxygen in the extracellular microenvironment as well as no FLI1 and GATA2 activity within the cell. Additionally Tip cells cannot undergo EndMT directly. Furthermore, the specific conditions that are sufficient to trigger EndMT depend on the specific pattern of molecular activation within the cell.

Integrative Transcriptomic Analysis Reveals a Multiphasic Epithelial-Mesenchymal Spectrum in Cancer and Non-tumorigenic Cells

Epithelial-mesenchymal transition (EMT), the conversion between rigid epithelial cells and motile mesenchymal cells, is a reversible cellular process involved in tumorigenesis, metastasis, and chemoresistance. Numerous studies have found that several types of tumor cells show a high degree of cell-to-cell heterogeneity in terms of their gene expression signatures and cellular phenotypes related to EMT. Recently, the prevalence and importance of partial or intermediate EMT states have been reported. It is unclear, however, whether there is a general pattern of cancer cell distribution in terms of the overall expression of epithelial-related genes and mesenchymal-related genes, and how this distribution is related to EMT process in normal cells. In this study, we performed integrative transcriptomic analysis that combines cancer cell transcriptomes, time course data of EMT in non-tumorigenic epithelial cells, and epithelial cells with perturbations of key EMT factors. Our statistical analysis shows that cancer cells are widely distributed in the EMT spectrum, and the majority of these cells can be described by an EMT path that connects the epithelial and the mesenchymal states via a hybrid expression region in which both epithelial genes and mesenchymal genes are highly expressed overall. We found that key patterns of this EMT path are observed in EMT progression in non-tumorigenic cells and that transcription factor ZEB1 plays a key role in defining this EMT path via diverse gene regulatory circuits connecting to epithelial genes. We performed Gene Set Variation Analysis to show that the cancer cells at hybrid EMT states also possess hybrid cellular phenotypes with both high migratory and high proliferative potentials. Our results reveal critical patterns of cancer cells in the EMT spectrum and their relationship to the EMT process in normal cells, and provide insights into the mechanistic basis of cancer cell heterogeneity and plasticity.

Exposing the Underlying Relationship of Cancer Metastasis to Metabolism and Epithelial-Mesenchymal Transitions

Cancer is a disease governed by the underlying gene regulatory networks. The hallmarks of cancer have been proposed to characterize the cancerization, e.g., abnormal metabolism, epithelial to mesenchymal transition (EMT), and cancer metastasis. We constructed a metabolism-EMT-metastasis regulatory network and quantified its underlying landscape. We identified four attractors, characterizing epithelial, abnormal metabolic, mesenchymal, and metastatic cell states, respectively. Importantly, we identified an abnormal metabolic state. Based on the transition path theory, we quantified the kinetic transition paths among these different cell states. Our results for landscape and paths indicate that metastasis is a sequential process: cells tend to first change their metabolism, then activate the EMT and eventually reach the metastatic state. This demonstrates the importance of the temporal order for different gene circuits switching on or off during metastatic progression of cancer cells and underlines the cascading regulation of metastasis through an abnormal metabolic intermediate state.

Morphological State Transition Dynamics in EGF-Induced Epithelial to Mesenchymal Transition

Epithelial to Mesenchymal Transition (EMT) is a multi-state process. Here, we investigated phenotypic state transition dynamics of Epidermal Growth Factor (EGF)-induced EMT in a breast cancer cell line MDA-MB-468. We have defined phenotypic states of these cells in terms of their morphologies and have shown that these cells have three distinct morphological states-cobble, spindle, and circular. The spindle and circular states are the migratory phenotypes. Using quantitative image analysis and mathematical modeling, we have deciphered state transition trajectories in different experimental conditions. This analysis shows that the phenotypic state transition during EGF-induced EMT in these cells is reversible, and depends upon the dose of EGF and level of phosphorylation of the EGF receptor (EGFR). The dominant reversible state transition trajectory in this system was cobble to circular to spindle to cobble. We have observed that there exists an ultrasensitive on/off switch involving phospho-EGFR that decides the transition of cells in and out of the circular state. In general, our observations can be explained by the conventional quasi-potential landscape model for phenotypic state transition. As an alternative to this model, we have proposed a simpler discretized energy-level model to explain the observed state transition dynamics.

Quantifying Cancer Epithelial-Mesenchymal Plasticity and its Association with Stemness and Immune Response

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.

Stability and mean residence times for hybrid epithelial/mesenchymal phenotype

Cancer metastasis and drug resistance remain unsolved clinical challenges. A phenotypic transition that is often implicated in both these processes is epithelial-mesenchymal transition (EMT) during which epithelial cells weaken their cell-cell adhesion and gain traits of migration and invasion, typical of mesenchymal cells. However, recent studies indicate that apart from these two states, cells can also exist in one or more hybrid E/M state(s), which plays an aggressive role in progression of the disease. Furthermore, computational and experimental studies have identified a variety of phenotypic stability factors (PSFs) that stabilize the hybrid E/M state(s) and can increase disease aggressiveness. In this work, we study EMT regulatory networks, in the presence of different PSFs, as dynamical systems subjected to random fluctuations. The cells thus explore different stable E, M, E/M states in the potential landscape and our aim is to quantify the residence time in each of these states. Our stochastic simulations indicate an universal feature that the mean residence time (MRT) in the hybrid E/M state is enhanced in the presence of PSFs. We demonstrate that the feature is consistent for a variety of PSFs, namely, GRHL2, OVOL, ΔNp63α, miR-145/OCT4, participating in the core EMT regulatory network. Our results reveal potential targets for pushing cells out of a hybrid E/M state and thus halting metastatic progression.

Intermediate cell states in epithelial-to-mesenchymal transition

The transition of epithelial cells into a mesenchymal state (epithelial-to-mesenchymal transition or EMT) is a highly dynamic process implicated in various biological processes. During EMT, cells do not necessarily exist in 'pure' epithelial or mesenchymal states. There are cells with mixed (or hybrid) features of the two, which are termed as the intermediate cell states (ICSs). While the exact functions of ICS remain elusive, together with EMT it appears to play important roles in embryogenesis, tissue development, and pathological processes such as cancer metastasis. Recent single cell experiments and advanced mathematical modeling have improved our capability in identifying ICS and provided a better understanding of ICS in development and disease. Here, we review the recent findings related to the ICS in/or EMT and highlight the challenges in the identification and functional characterization of ICS.

Landscape of gene networks for random parameter perturbation

Landscape approaches have been exploited to study the stochastic dynamics of gene networks. However, how to calculate the landscape with a wide range of parameter variations and how to investigate the influence of the network topology on the global properties of gene networks remain to be elucidated. Here, I developed an approach for the landscape of random parameter perturbation (LRPP) to address this issue. Based on a self-consistent approximation approach, by making perturbations to parameters in a given range, I obtained the landscape for gene network systems. I applied this approach to two biological models, one for the mutual repression model and the other for the embryonic stem (ES) cell differentiation network. For the mutual repression model, my results confirm quantitatively that positive feedback promotes the robustness of multistability. For the ES cell differentiation model, I identify three cell states, representing the ES cell, the differentiation cell, and the intermediate state cell, respectively. I propose that the intermediate states and the wide range of parameter values coming from inhomogeneous cellular environments provide possible explanations for the heterogeneity observed in single cell experiments. I also offer a counterintuitive result that noise could reduce heterogeneity and promote the stability of cell states. These results support that the network topology determines the operating principles of the genetic networks, reflected by the representative landscapes from LRPP. This work provides a new route to obtain the potential landscape for a gene network system given a wide range of parameter values and study the influences of the network topology on the global properties of the system.

Transition state characteristics during cell differentiation

Models describing the process of stem-cell differentiation are plentiful, and may offer insights into the underlying mechanisms and experimentally observed behaviour. Waddington's epigenetic landscape has been providing a conceptual framework for differentiation processes since its inception. It also allows, however, for detailed mathematical and quantitative analyses, as the landscape can, at least in principle, be related to mathematical models of dynamical systems. Here we focus on a set of dynamical systems features that are intimately linked to cell differentiation, by considering exemplar dynamical models that capture important aspects of stem cell differentiation dynamics. These models allow us to map the paths that cells take through gene expression space as they move from one fate to another, e.g. from a stem-cell to a more specialized cell type. Our analysis highlights the role of the transition state (TS) that separates distinct cell fates, and how the nature of the TS changes as the underlying landscape changes-change that can be induced by e.g. cellular signaling. We demonstrate that models for stem cell differentiation may be interpreted in terms of either a static or transitory landscape. For the static case the TS represents a particular transcriptional profile that all cells approach during differentiation. Alternatively, the TS may refer to the commonly observed period of heterogeneity as cells undergo stochastic transitions.

Interconnected feedback loops among ESRP1, HAS2, and CD44 regulate epithelial-mesenchymal plasticity in cancer

Aberrant activation of epithelial-mesenchymal transition (EMT) in carcinoma cells contributes to increased migration and invasion, metastasis, drug resistance, and tumor-initiating capacity. EMT is not always a binary process; rather, cells may exhibit a hybrid epithelial/mesenchymal (E/M) phenotype. ZEB1-a key transcription factor driving EMT-can both induce and maintain a mesenchymal phenotype. Recent studies have identified two novel autocrine feedback loops utilizing epithelial splicing regulatory protein 1 (ESRP1), hyaluronic acid synthase 2 (HAS2), and CD44 which maintain high levels of ZEB1. However, how the crosstalk between these feedback loops alters the dynamics of epithelial-hybrid-mesenchymal transition remains elusive. Here, using an integrated theoretical-experimental framework, we identify that these feedback loops can enable cells to stably maintain a hybrid E/M phenotype. Moreover, computational analysis identifies the regulation of ESRP1 as a crucial node, a prediction that is validated by experiments showing that knockdown of ESRP1 in stable hybrid E/M H1975 cells drives EMT. Finally, in multiple breast cancer datasets, high levels of ESRP1, ESRP1/HAS2, and ESRP1/ZEB1 correlate with poor prognosis, supporting the relevance of ZEB1/ESRP1 and ZEB1/HAS2 axes in tumor progression. Together, our results unravel how these interconnected feedback loops act in concert to regulate ZEB1 levels and to drive the dynamics of epithelial-hybrid-mesenchymal transition.

A landscape view on the interplay between EMT and cancer metastasis

The epithelial-mesenchymal transition (EMT) is a basic developmental process that converts epithelial cells to mesenchymal cells. Although EMT might promote cancer metastasis, the molecular mechanisms for it remain to be fully clarified. To address this issue, we constructed an EMT-metastasis gene regulatory network model and quantified the potential landscape of cancer metastasis-promoting system computationally. We identified four steady-state attractors on the landscape, which separately characterize anti-metastatic (A), metastatic (M), and two other intermediate (I1 and I2) cell states. The tetrastable landscape and the existence of intermediate states are consistent with recent single-cell measurements. We identified one of the two intermediate states I1 as the EMT state. From a MAP approach, we found that for metastatic progression cells need to first undergo EMT (enter the I1 state), and then become metastatic (switch from the I1 state to the M state). Specifically, for metastatic progression, EMT genes (such as ZEB) should be activated before metastasis genes (such as BACH1). This suggests that temporal order is important for the activation of cellular programs in biological systems, and provides a possible mechanism of EMT-promoting cancer metastasis. To identify possible therapeutic targets from this landscape view, we performed sensitivity analysis for individual molecular factors, and identified optimal interventions for landscape control. We found that minimizing transition actions more effectively identifies optimal combinations of targets that induce transitions between attractors than single-factor sensitivity analysis. Overall, the landscape view not only suggests that intermediate states increase plasticity during cell fate decisions, providing a possible source for tumor heterogeneity that is critically important in metastatic progress, but also provides a way to identify therapeutic targets for preventing cancer progression.

Construction of quasipotentials for stochastic dynamical systems: An optimization approach

The construction of effective and informative landscapes for stochastic dynamical systems has proven a long-standing and complex problem. In many situations, the dynamics may be described by a Langevin equation while constructing a landscape comes down to obtaining the quasipotential, a scalar function that quantifies the likelihood of reaching each point in the state space. In this work we provide a novel method for constructing such landscapes by extending a tool from control theory: the sum-of-squares method for generating Lyapunov functions. Applicable to any system described by polynomials, this method provides an analytical polynomial expression for the potential landscape, in which the coefficients of the polynomial are obtained via a convex optimization problem. The resulting landscapes are based on a decomposition of the deterministic dynamics of the original system, formed in terms of the gradient of the potential and a remaining "curl" component. By satisfying the condition that the inner product of the gradient of the potential and the remaining dynamics is everywhere negative, our derived landscapes provide both upper and lower bounds on the true quasipotential; these bounds becoming tight if the decomposition is orthogonal. The method is demonstrated to correctly compute the quasipotential for high-dimensional linear systems and also for a number of nonlinear examples.

scEpath: energy landscape-based inference of transition probabilities and cellular trajectories from single-cell transcriptomic data

Motivation

Single-cell RNA-sequencing (scRNA-seq) offers unprecedented resolution for studying cellular decision-making processes. Robust inference of cell state transition paths and probabilities is an important yet challenging step in the analysis of these data.

Results

Here we present scEpath, an algorithm that calculates energy landscapes and probabilistic directed graphs in order to reconstruct developmental trajectories. We quantify the energy landscape using 'single-cell energy' and distance-based measures, and find that the combination of these enables robust inference of the transition probabilities and lineage relationships between cell states. We also identify marker genes and gene expression patterns associated with cell state transitions. Our approach produces pseudotemporal orderings that are-in combination-more robust and accurate than current methods, and offers higher resolution dynamics of the cell state transitions, leading to new insight into key transition events during differentiation and development. Moreover, scEpath is robust to variation in the size of the input gene set, and is broadly unsupervised, requiring few parameters to be set by the user. Applications of scEpath led to the identification of a cell-cell communication network implicated in early human embryo development, and novel transcription factors important for myoblast differentiation. scEpath allows us to identify common and specific temporal dynamics and transcriptional factor programs along branched lineages, as well as the transition probabilities that control cell fates.

Availability and implementation

A MATLAB package of scEpath is available at https://github.com/sqjin/scEpath.

Supplementary information

Supplementary data are available at Bioinformatics online.

Exploring intermediate cell states through the lens of single cells

As our catalog of cell states expands, appropriate characterization of these states and the transitions between them is crucial. Here we discuss the roles of intermediate cell states (ICSs) in this growing collection. We begin with definitions and discuss evidence for the existence of ICSs and their relevance in various tissues. We then provide a list of possible functions for ICSs with examples. Finally, we describe means by which ICSs and their functional roles can be identified from single-cell data or predicted from models.

Identifying the optimal anticancer targets from the landscape of a cancer-immunity interaction network

Cancer immunotherapy, an approach of targeting immune cells to attack tumor cells, has been suggested to be a promising way for cancer treatment recently. However, the successful application of this approach warrants a deeper understanding of the intricate interplay between cancer cells and the immune system. Especially, the mechanisms of immunotherapy remain elusive. In this work, we constructed a cancer-immunity interplay network by incorporating interactions among cancer cells and some representative immune cells, and uncovered the potential landscape of the cancer-immunity network. Three attractors emerge on the landscape, representing the cancer state, the immune state, and the hybrid state, which can correspond to escape, elimination, and equilibrium phases in the immunoediting theory, respectively. We quantified the transition processes between the cancer state and the immune state by calculating transition actions and identifying the corresponding minimum action paths (MAPs) between these two attractors. The transition actions, directly calculated from the high dimensional system, are correlated with the barrier heights from the landscape, but provide a more precise description of the dynamics of a system. By optimizing the transition actions from the cancer state to the immune state, we identified some optimal combinations of anticancer targets. Our combined approach of the landscape and optimization of transition actions offers a framework to study the stochastic dynamics and identify the optimal combination of targets for the cancer-immunity interplay, and can be applied to other cell communication networks or gene regulatory networks.

Complex Determinants of Epithelial: Mesenchymal Phenotypic Plasticity in Ovarian Cancer

Unlike most epithelial malignancies which metastasize hematogenously, metastasis of epithelial ovarian cancer (EOC) occurs primarily via transcoelomic dissemination, characterized by exfoliation of cells from the primary tumor, avoidance of detachment-induced cell death (anoikis), movement throughout the peritoneal cavity as individual cells and multi-cellular aggregates (MCAs), adhesion to and disruption of the mesothelial lining of the peritoneum, and submesothelial matrix anchoring and proliferation to generate widely disseminated metastases. This exceptional microenvironment is highly permissive for phenotypic plasticity, enabling mesenchymal-to-epithelial (MET) and epithelial-to-mesenchymal (EMT) transitions. In this review, we summarize current knowledge on EOC heterogeneity in an EMT context, outline major regulators of EMT in ovarian cancer, address controversies in EMT and EOC chemoresistance, and highlight computational modeling approaches toward understanding EMT/MET in EOC.

Phenotypic Plasticity and Cell Fate Decisions in Cancer: Insights from Dynamical Systems Theory

Waddington's epigenetic landscape, a famous metaphor in developmental biology, depicts how a stem cell progresses from an undifferentiated phenotype to a differentiated one. The concept of "landscape" in the context of dynamical systems theory represents a high-dimensional space, in which each cell phenotype is considered as an "attractor" that is determined by interactions between multiple molecular players, and is buffered against environmental fluctuations. In addition, biological noise is thought to play an important role during these cell-fate decisions and in fact controls transitions between different phenotypes. Here, we discuss the phenotypic transitions in cancer from a dynamical systems perspective and invoke the concept of "cancer attractors"-hidden stable states of the underlying regulatory network that are not occupied by normal cells. Phenotypic transitions in cancer occur at varying levels depending on the context. Using epithelial-to-mesenchymal transition (EMT), cancer stem-like properties, metabolic reprogramming and the emergence of therapy resistance as examples, we illustrate how phenotypic plasticity in cancer cells enables them to acquire hybrid phenotypes (such as hybrid epithelial/mesenchymal and hybrid metabolic phenotypes) that tend to be more aggressive and notoriously resilient to therapies such as chemotherapy and androgen-deprivation therapy. Furthermore, we highlight multiple factors that may give rise to phenotypic plasticity in cancer cells, such as (a) multi-stability or oscillatory behaviors governed by underlying regulatory networks involved in cell-fate decisions in cancer cells, and (b) network rewiring due to conformational dynamics of intrinsically disordered proteins (IDPs) that are highly enriched in cancer cells. We conclude by discussing why a therapeutic approach that promotes "recanalization", i.e., the exit from "cancer attractors" and re-entry into "normal attractors", is more likely to succeed rather than a conventional approach that targets individual molecules/pathways.

Epithelial/mesenchymal plasticity: how have quantitative mathematical models helped improve our understanding?

Phenotypic plasticity, the ability of cells to reversibly alter their phenotypes in response to signals, presents a significant clinical challenge to treating solid tumors. Tumor cells utilize phenotypic plasticity to evade therapies, metastasize, and colonize distant organs. As a result, phenotypic plasticity can accelerate tumor progression. A well‐studied example of phenotypic plasticity is the bidirectional conversions among epithelial, mesenchymal, and hybrid epithelial/mesenchymal (E/M) phenotype(s). These conversions can alter a repertoire of cellular traits associated with multiple hallmarks of cancer, such as metabolism, immune evasion, invasion, and metastasis. To tackle the complexity and heterogeneity of these transitions, mathematical models have been developed that seek to capture the experimentally verified molecular mechanisms and act as ‘hypothesis‐generating machines’. Here, we discuss how these quantitative mathematical models have helped us explain existing experimental data, guided further experiments, and provided an improved conceptual framework for understanding how multiple intracellular and extracellular signals can drive E/M plasticity at both the single‐cell and population levels. We also discuss the implications of this plasticity in driving multiple aggressive facets of tumor progression.

EMT and MET: necessary or permissive for metastasis?

Epithelial‐to‐mesenchymal transition (EMT) and its reverse mesenchymal‐to‐epithelial transition (MET) have been suggested to play crucial roles in metastatic dissemination of carcinomas. These phenotypic transitions between states are not binary. Instead, carcinoma cells often exhibit a spectrum of epithelial/mesenchymal phenotype(s). While epithelial/mesenchymal plasticity has been observed preclinically and clinically, whether any of these phenotypic transitions are indispensable for metastatic outgrowth remains an unanswered question. Here, we focus on epithelial/mesenchymal plasticity in metastatic dissemination and propose alternative mechanisms for successful dissemination and metastases beyond the traditional EMT/MET view. We highlight multiple hypotheses that can help reconcile conflicting observations, and outline the next set of key questions that can offer valuable insights into mechanisms of metastasis in multiple tumor models.

Decoding early myelopoiesis from dynamics of core endogenous network

A decade ago mainstream molecular biologists regarded it impossible or biologically ill-motivated to understand the dynamics of complex biological phenomena, such as cancer genesis and progression, from a network perspective. Indeed, there are numerical difficulties even for those who were determined to explore along this direction. Undeterred, seven years ago a group of Chinese scientists started a program aiming to obtain quantitative connections between tumors and network dynamics. Many interesting results have been obtained. In this paper we wish to test such idea from a different angle: the connection between a normal biological process and the network dynamics. We have taken early myelopoiesis as our biological model. A standard roadmap for the cell-fate diversification during hematopoiesis has already been well established experimentally, yet little was known for its underpinning dynamical mechanisms. Compounding this difficulty there were additional experimental challenges, such as the seemingly conflicting hematopoietic roadmaps and the cell-fate inter-conversion events. With early myeloid cell-fate determination in mind, we constructed a core molecular endogenous network from well-documented gene regulation and signal transduction knowledge. Turning the network into a set of dynamical equations, we found computationally several structurally robust states. Those states nicely correspond to known cell phenotypes. We also found the states connecting those stable states. They reveal the developmental routes-how one stable state would most likely turn into another stable state. Such interconnected network among stable states enabled a natural organization of cell-fates into a multi-stable state landscape. Accordingly, both the myeloid cell phenotypes and the standard roadmap were explained mechanistically in a straightforward manner. Furthermore, recent challenging observations were also explained naturally. Moreover, the landscape visually enables a prediction of a pool of additional cell states and developmental routes, including the non-sequential and cross-branch transitions, which are testable by future experiments. In summary, the endogenous network dynamics provide an integrated quantitative framework to understand the heterogeneity and lineage commitment in myeloid progenitors.