Quantifying the Landscape for Development and Cancer from a Core Cancer Stem Cell Circuit

The impact of Helicobacter pylori on gastric cancer formation and early warning signal identification

Gastric cancer is highly prevalent in Asia and is characterized by poor prognosis post-surgery and a high recurrence rate within five years. Research has highlighted the role of Helicobacter pylori in initiating or accelerating gastric cancer development. However, quantitative analysis of its impact on gastric cancer carcinogenesis is still lacking. This study employs gene regulatory networks and landscape and flux theory, integrating genetic and epigenetic factors, to quantitatively elucidate how Helicobacter pylori influences gastric cancer progression. Varied Helicobacter pylori infection concentrations lead to significant shifts in system thermodynamic and dynamic driving forces, altering gene expression levels. Quantitative analysis of entropy production rate and mean-flux in the gastric cancer system reveals the global changes in thermodynamic and dynamic driving forces. Coupled with autocorrelation, cross correlation, and variance analysis, we pinpoint critical stages of Helicobacter pylori infection, serving as early warning signals for gastric cancer. This approach bridges theoretical and clinical realms, dynamically assessing Helicobacter pylori's impact on gastric cancer and identifying crucial early warning signals, with significant clinical and translational implications.

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.

Mitochondrial genetic variations in leukemia: a comprehensive overview

Leukemias are a group of heterogeneous hematological malignancies driven by diverse genetic variations, and the advent of genomic sequencing technologies facilitates the investigation of genetic abnormalities in leukemia. However, these sequencing-based studies mainly focus on nuclear DNAs. Increasing evidence indicates that mitochondrial dysfunction is an important mechanism of leukemia pathogenesis, which is closely related to the mitochondrial genome variations. Here, we provide an overview of current research progress concerning mitochondrial genetic variations in leukemia, encompassing gene mutations and copy number variations. We also summarize currently accessible mitochondrial DNA (mtDNA) sequencing methods. Notably, somatic mtDNA mutations may serve as natural genetic barcodes for lineage tracing and longitudinal assessment of clonal dynamics. Collectively, these findings enhance our understanding of leukemia pathogenesis and foster the identification of novel therapeutic targets and interventions.

The mathematical exploration for the mechanism of lung adenocarcinoma formation and progression

Lung adenocarcinoma, a prevalent subtype of lung cancer, represents one of the most lethal human malignancies. Despite substantial efforts to elucidate its biological underpinnings, the underlying mechanisms governing lung adenocarcinoma remain enigmatic. Modeling and comprehending the dynamics of gene regulatory networks are crucial for unraveling the fundamental mechanisms of lung adenocarcinoma. Conventionally, the cancer is modeled as an equilibrium process based on a time-invariant gene regulatory network to investigate stable cell states. However, the cancer is a nonequilibrium process and the gene regulatory network should be regarded as time-varying in actual. Therefore, a feasible framework was developed to explore the formation and progression of lung adenocarcinoma. On the one hand, to delve into the underlying mechanisms of lung adenocarcinoma formation, the time-invariant gene regulatory network for lung adenocarcinoma was initially undertaken, and the composition of stable cell states was elucidated based on landscape theory. Furthermore, the plasticity of different states was quantified using energy landscape decomposition theory by incorporating cell proliferation. And transition probabilities between different states were defined to elucidate the transition between stable cell states. Additionally, the global sensitivity analysis was performed and a total of three genes and three regulations were identified to be more critical for the formation lung adenocarcinoma, offering a novel strategy for designing network-based therapies for its treatment. On the other hand, the time-invariant gene regulatory network is extended as time-varying to delve into the underlying mechanisms of lung adenocarcinoma progression. The lung adenocarcinoma progression was characterized as four different disease stages based on the mixed states of cell population and the evolutionary direction. And the progressionary mechanism of transition between stages was expounded by evaluating their dynamical transport, with the dynamical transport cost between different stages quantified using Wasserstein metrics.

Unveiling the Dynamics behind Glioblastoma Multiforme Single-Cell Data Heterogeneity

Glioblastoma Multiforme is a brain tumor distinguished by its aggressiveness. We suggested that this aggressiveness leads single-cell RNA-sequence data (scRNA-seq) to span a representative portion of the cancer attractors domain. This conjecture allowed us to interpret the scRNA-seq heterogeneity as reflecting a representative trajectory within the attractor's domain. We considered factors such as genomic instability to characterize the cancer dynamics through stochastic fixed points. The fixed points were derived from centroids obtained through various clustering methods to verify our method sensitivity. This methodological foundation is based upon sample and time average equivalence, assigning an interpretative value to the data cluster centroids and supporting parameters estimation. We used stochastic simulations to reproduce the dynamics, and our results showed an alignment between experimental and simulated dataset centroids. We also computed the Waddington landscape, which provided a visual framework for validating the centroids and standard deviations as characterizations of cancer attractors. Additionally, we examined the stability and transitions between attractors and revealed a potential interplay between subtypes. These transitions might be related to cancer recurrence and progression, connecting the molecular mechanisms of cancer heterogeneity with statistical properties of gene expression dynamics. Our work advances the modeling of gene expression dynamics and paves the way for personalized therapeutic interventions.

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.

Data mining and mathematical models in cancer prognosis and prediction

Cancer is a fetal and complex disease. Individual differences of the same cancer type or the same patient at different stages of cancer development may require distinct treatments. Pathological differences are reflected in tissues, cells and gene levels etc. The interactions between the cancer cells and nearby microenvironments can also influence the cancer progression and metastasis. It is a huge challenge to understand all of these mechanistically and quantitatively. Researchers applied pattern recognition algorithms such as machine learning or data mining to predict cancer types or classifications. With the rapidly growing and available computing powers, researchers begin to integrate huge data sets, multi-dimensional data types and information. The cells are controlled by the gene expressions determined by the promoter sequences and transcription regulators. For example, the changes in the gene expression through these underlying mechanisms can modify cell progressing in the cell-cycle. Such molecular activities can be governed by the gene regulations through the underlying gene regulatory networks, which are essential for cancer study when the information and gene regulations are clear and available. In this review, we briefly introduce several machine learning methods of cancer prediction and classification which include Artificial Neural Networks (ANNs), Decision Trees (DTs), Support Vector Machine (SVM) and naive Bayes. Then we describe a few typical models for building up gene regulatory networks such as Correlation, Regression and Bayes methods based on available data. These methods can help on cancer diagnosis such as susceptibility, recurrence, survival etc. At last, we summarize and compare the modeling methods to analyze the development and progression of cancer through gene regulatory networks. These models can provide possible physical strategies to analyze cancer progression in a systematic and quantitative way.

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

Unraveling the stochastic transition mechanism between oscillation states by landscape and minimum action path theory

Cell fate transitions have been studied from various perspectives, such as the transition between stable states, or the transition between stable states and oscillation states. However, there is a lack...

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

Deciphering the molecular mechanism of the cancer formation by chromosome structural dynamics

Cancer reflects the dysregulation of the underlying gene network, which is strongly related to the 3D genome organization. Numerous efforts have been spent on experimental characterizations of the structural alterations in cancer genomes. However, there is still a lack of genomic structural-level understanding of the temporal dynamics for cancer initiation and progression. Here, we use a landscape-switching model to investigate the chromosome structural transition during the cancerization and reversion processes. We find that the chromosome undergoes a non-monotonic structural shape-changing pathway with initial expansion followed by compaction during both of these processes. Furthermore, our analysis reveals that the chromosome with a more expanding structure than those at both the normal and cancer cell during cancerization exhibits a sparse contact pattern, which shows significant structural similarity to the one at the embryonic stem cell in many aspects, including the trend of contact probability declining with the genomic distance, the global structural shape geometry and the spatial distribution of loci on the chromosome. In light of the intimate structure-function relationship at the chromosomal level, we further describe the cell state transition processes by the chromosome structural changes, suggesting an elevated cell stemness during the formation of the cancer cells. We show that cell cancerization and reversion are highly irreversible processes in terms of the chromosome structural transition pathways, spatial repositioning of chromosomal loci and hysteresis loop of contact evolution analysis. Our model draws a molecular-scale picture of cell cancerization from the chromosome structural perspective. The process contains initial reprogramming towards the stem cell followed by the differentiation towards the cancer cell, accompanied by an initial increase and subsequent decrease of the cell stemness.

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.

Computational quantification of global effects induced by mutations and drugs in signaling networks of colorectal cancer cells

Colorectal cancer (CRC) is one of the most deadly and commonly diagnosed tumors worldwide. Several genes are involved in its development and progression. The most frequent mutations concern APC, KRAS, SMAD4, and TP53 genes, suggesting that CRC relies on the concomitant alteration of the related pathways. However, with classic molecular approaches, it is not easy to simultaneously analyze the interconnections between these pathways. To overcome this limitation, recently these pathways have been included in a huge chemical reaction network (CRN) describing how information sensed from the environment by growth factors is processed by healthy colorectal cells. Starting from this CRN, we propose a computational model which simulates the effects induced by single or multiple concurrent mutations on the global signaling network. The model has been tested in three scenarios. First, we have quantified the changes induced on the concentration of the proteins of the network by a mutation in APC, KRAS, SMAD4, or TP53. Second, we have computed the changes in the concentration of p53 induced by up to two concurrent mutations affecting proteins upstreams in the network. Third, we have considered a mutated cell affected by a gain of function of KRAS, and we have simulated the action of Dabrafenib, showing that the proposed model can be used to determine the most effective amount of drug to be delivered to the cell. In general, the proposed approach displays several advantages, in that it allows to quantify the alteration in the concentration of the proteins resulting from a single or multiple given mutations. Moreover, simulations of the global signaling network of CRC may be used to identify new therapeutic targets, or to disclose unexpected interactions between the involved pathways.

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.

Resilience function uncovers the critical transitions in cancer initiation

Considerable evidence suggests that during the progression of cancer initiation, the state transition from wellness to disease is not necessarily smooth but manifests switch-like nonlinear behaviors, preventing the cancer prediction and early interventional therapy for patients. Understanding the mechanism of such wellness-to-disease transitions is a fundamental and challenging task. Despite the advances in flux theory of nonequilibrium dynamics and 'critical slowing down'-based system resilience theory, a system-level approach still lacks to fully describe this state transition. Here, we present a novel framework (called bioRFR) to quantify such wellness-to-disease transition during cancer initiation through uncovering the biological system's resilience function from gene expression data. We used bioRFR to reconstruct the biologically and dynamically significant resilience functions for cancer initiation processes (e.g. BRCA, LUSC and LUAD). The resilience functions display the similar resilience pattern with hysteresis feature but different numbers of tipping points, which implies that once the cell become cancerous, it is very difficult or even impossible to reverse to the normal state. More importantly, bioRFR can measure the severe degree of cancer patients and identify the personalized key genes that are associated with the individual system's state transition from normal to tumor in resilience perspective, indicating that bioRFR can contribute to personalized medicine and targeted cancer therapy.

A global and physical mechanism of gastric cancer formation and progression

Gastric cancer is regarded as a major health issue for human being nowadays. The Helicobacter pylori (H. pylori) infection has been found to accelerate the development of gastritis and gastric cancer. Significant efforts have been made towards the understanding of the biology of gastric cancer on both genetic and epigenetic levels. However the physical mechanism behind the gastric cancer formation is still elusive. In this study, we constructed a model for investigating gastric cancer formation by explored the gastric cancer landscape and the flow flux. We uncovered three stable state attractors on the landscape: normal, gastritis and gastric cancer. The definition of each attractor is based on the biological function and gene expression levels. The global stabilities and the switching processes were quantified through the barrier heights and dominant kinetic paths. To investigate the underlying mechanism of the process from normal through the gastritis to the gastric cancer caused by genetic or epigenetic factors, we simulate the oncogenesis of gastric cancer through changes of several gene regulation strengths and H. pylori infection. The simulated results can illustrate the developmental and metastasis process of gastric cancer. Different H. pylori infection degrees accelerating the process from gastritis to gastric cancer can be quantified. Then we applied global sensitivity analysis, one key gene and four key regulations were found. These results are consist with the experimental results and can be used to design the polygenic anti-cancer agents through multiple key genes or regulations. The landscape approach provides a physical and simple strategy for analyzing gastric cancer in a systematic and quantitative way. It also offers new insight into treatment strategy for gastric cancer by adjusting relevant polygenic genes and regulations.

A Monte Carlo method for in silico modeling and visualization of Waddington's epigenetic landscape with intermediate details

Waddington's epigenetic landscape is a classic metaphor for describing the cellular dynamics during the development modulated by gene regulation. Quantifying Waddington's epigenetic landscape by mathematical modeling would be useful for understanding the mechanisms of cell fate determination. A few computational methods have been proposed for quantitative modeling of landscape; however, to model and visualize the landscape of a high dimensional gene regulatory system with realistic details is still challenging. Here, we propose a Monte Carlo method for modeling the Waddington's epigenetic landscape of a gene regulatory network (GRN). The method estimates the probability distribution of cellular states by collecting a large number of time-course simulations with random initial conditions. By projecting all the trajectories into a 2-dimensional plane of dimensions i and j, we can approximately calculate the quasi-potential U(x_i,x_j,∗)=-ln P(x_i,x_j,∗), where P(x_i,x_j,∗) is the estimated probability of an equilibrium steady state or a non-equilibrium state. Compared to the state-of-the-art methods, our Monte Carlo method can quantify the global potential landscape (or emergence behavior) of GRN for a high dimensional system. The potential landscapes show that not only attractors represent stability, but the paths between attractors are also part of the stability or robustness of biological systems. We demonstrate the novelty and reliability of our method by plotting the potential landscapes of a few published models of GRN.

A single-cell survey of cellular hierarchy in acute myeloid leukemia

Background

Acute myeloid leukemia (AML) is a fatal hematopoietic malignancy and has a prognosis that varies with its genetic complexity. However, there has been no appropriate integrative analysis on the hierarchy of different AML subtypes.

Methods

Using Microwell-seq, a high-throughput single-cell mRNA sequencing platform, we analyzed the cellular hierarchy of bone marrow samples from 40 patients and 3 healthy donors. We also used single-cell single-molecule real-time (SMRT) sequencing to investigate the clonal heterogeneity of AML cells.

Results

From the integrative analysis of 191727 AML cells, we established a single-cell AML landscape and identified an AML progenitor cell cluster with novel AML markers. Patients with ribosomal protein high progenitor cells had a low remission rate. We deduced two types of AML with diverse clinical outcomes. We traced mitochondrial mutations in the AML landscape by combining Microwell-seq with SMRT sequencing. We propose the existence of a phenotypic “cancer attractor” that might help to define a common phenotype for AML progenitor cells. Finally, we explored the potential drug targets by making comparisons between the AML landscape and the Human Cell Landscape.

Conclusions

We identified a key AML progenitor cell cluster. A high ribosomal protein gene level indicates the poor prognosis. We deduced two types of AML and explored the potential drug targets. Our results suggest the existence of a cancer attractor.

Uncovering the Underlying Mechanisms of Cancer Metabolism through the Landscapes and Probability Flux Quantifications

Cancer metabolism is critical for understanding the mechanism of tumorigenesis, yet the understanding is still challenging. We studied gene-metabolism regulatory interactions and quantified the global driving forces for cancer-metabolism dynamics as the underlying landscape and probability flux. We uncovered four steady-state attractors: a normal state attractor, a cancer OXPHOS state attractor, a cancer glycolysis state attractor, and an intermediate cancer state attractor. We identified the key regulatory interactions through global sensitivity analysis based on the landscape topography. Different landscape topographies of glycolysis switch between normal cells and cancer cells were identified. We uncovered that the normal state to cancer state transformation is associated with the peaks of the probability flux and the thermodynamic dissipation, giving dynamical and thermodynamic origin of cancer formation. We found that cancer metabolism oscillations consume more energy to support cancer malignancy. This study provides a quantitative understanding of cancer metabolism and suggests a metabolic therapeutic strategy.

Modeling Basins of Attraction for Breast Cancer Using Hopfield Networks

Cancer is a genetic disease for which traditional treatments cause harmful side effects. After two decades of genomics technological breakthroughs, personalized medicine is being used to improve treatment outcomes and mitigate side effects. In mathematical modeling, it has been proposed that cancer matches an attractor in Waddington's epigenetic landscape. The use of Hopfield networks is an attractive modeling approach because it requires neither previous biological knowledge about protein-protein interactions nor kinetic parameters. In this report, Hopfield network modeling was used to analyze bulk RNA-Seq data of paired breast tumor and control samples from 70 patients. We characterized the control and tumor attractors with respect to their size and potential energy and correlated the Euclidean distances between the tumor samples and the control attractor with their corresponding clinical data. In addition, we developed a protocol that outlines the key genes involved in tumor state stability. We found that the tumor basin of attraction is larger than that of the control and that tumor samples are associated with a more substantial negative energy than control samples, which is in agreement with previous reports. Moreover, we found a negative correlation between the Euclidean distances from tumor samples to the control attractor and patient overall survival. The ascending order of each node's density in the weight matrix and the descending order of the number of patients that have the target active only in the tumor sample were the parameters that withdrew more tumor samples from the tumor basin of attraction with fewer gene inhibitions. The combinations of therapeutic targets were specific to each patient. We performed an initial validation through simulation of trastuzumab treatment effects in HER2+ breast cancer samples. For that, we built an energy landscape composed of single-cell and bulk RNA-Seq data from trastuzumab-treated and non-treated HER2+ samples. The trajectory from the non-treated bulk sample toward the treated bulk sample was inferred through the perturbation of differentially expressed genes between these samples. Among them, we characterized key genes involved in the trastuzumab response according to the literature.

Quantification of the Underlying Mechanisms and Relationships Among Cancer, Metastasis, and Differentiation and Development

Recurrence and metastasis have been regarded as two of the greatest obstacles to cancer therapy. Cancer stem cells (CSCs) contribute to cancer development, with the distinctive features of recurrence and resistance to popular treatments such as drugs and chemotherapy. In addition, recent discoveries suggest that the epithelial mesenchymal transition (EMT) is an essential process in normal embryogenesis and tissue repair, as well as being a required step in cancer metastasis. Although there are many indications of the connections between metastasis and stem cells, these have often been studied separately or at most bi-laterally, not in an integrated way. In this study, we aimed to explore the global mechanisms and interrelationships among cancer, development, and metastasis, which are currently poorly understood. First, we constructed a core gene regulatory network containing specific genes and microRNAs of CSCs, EMT, and cancer. We uncovered seven distinct states emerging from the underlying landscape, denoted normal, premalignant, cancer, stem cell, CSC, lesion, and hyperplasia. Given the biological definition of each state, we also discuss the metastasis ability of each state. We show how and which types of cells can be transformed to a cancer state, and the connections among cancer, CSCs, and EMT. The barrier height and flux of the kinetic paths are explored to quantify how and which cells switch stochastically between the states. Our landscape model provides a quantitative approach to reveal the global mechanisms of cancer, development, and metastasis.

Revealing Dynamic Mechanisms of Cell Fate Decisions From Single-Cell Transcriptomic Data

Cell fate decisions play a pivotal role in development, but technologies for dissecting them are limited. We developed a multifunction new method, Topographer, to construct a "quantitative" Waddington's landscape of single-cell transcriptomic data. This method is able to identify complex cell-state transition trajectories and to estimate complex cell-type dynamics characterized by fate and transition probabilities. It also infers both marker gene networks and their dynamic changes as well as dynamic characteristics of transcriptional bursting along the cell-state transition trajectories. Applying this method to single-cell RNA-seq data on the differentiation of primary human myoblasts, we not only identified three known cell types, but also estimated both their fate probabilities and transition probabilities among them. We found that the percent of genes expressed in a bursty manner is significantly higher at (or near) the branch point (~97%) than before or after branch (below 80%), and that both gene-gene and cell-cell correlation degrees are apparently lower near the branch point than away from the branching. Topographer allows revealing of cell fate mechanisms in a coherent way at three scales: cell lineage (macroscopic), gene network (mesoscopic), and gene expression (microscopic).

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.

Landscape perspectives of tumor, EMT, and development

A tumor is rarely fatal until becoming metastatic. Recent discoveries suggest that epithelial mesenchymal transition(EMT) is an important process which contributes to not only cancer metastasis but also increased stemness. Cancer cells with stem cell characteristics are called cancer stem cells (CSCs). We review recent efforts to quantify and delineate the relationship among EMT, CSC and tumor development. When the gene regulatory network is tightly regulated through the effectively fast regulatory binding, Cancer, Premalignant, Normal, CSC, stem cell (SC), Lesion and Hyperplasia states emerged. The corresponding landscape topography for all of these states can be quantified to a global way for uncovering the relationship among the tumor, metastasis, and development. On the other hand, phenotypic and functional heterogeneity is regarded as one of the greatest challenge in cancer treatment. Cancer and CSCs are heterogeneous and give rise to tumorigenic and non-tumorigenic cells during self-renewal, differentiation and epigenetic diversification. Further, if the gene regulatory network is weakly regulated through the effective slow regulatory binding (by DNA methylation or histone modification etc), multiple meta-stable states can emerge. This model can provide an epigenetic and physical rather than genetic and fixed origin of heterogeneity. Elucidating the origin of and dynamic nature of tumor cells will likely help better understand the cellular basis of therapeutic response, resistance, and relapse.

Stochastic modelling of tyrosine kinase inhibitor rotation therapy in chronic myeloid leukaemia

Background

Resistance towards targeted cancer treatments caused by single nucleotide variations is a major issue in many malignancies. Currently, there are a number of available drugs for chronic myeloid leukaemia (CML), which are overcome by different sets of mutations. The main aim of this study was to explore if it can be possible to exploit this and create a treatment protocol that outperforms each drug on its own.

Methods

We present a computer program to test different treatment protocols against CML, based on available resistance mutation growth data. The evolution of a relatively stable pool of cancer stem cells is modelled as a stochastic process, with the growth of cells expressing a tumourigenic protein (here, Abl1) and any emerging mutants determined principally by the drugs used in the therapy.

Results

There can be some benefit to Bosutinib-Ponatinib rotation therapy even if the mutation status is unknown, whereas Imatinib-Nilotinib rotation is unlikely to improve the outcomes. Furthermore, an interplay between growth inhibition and selection effects generates a non-linear relationship between drug doses and the risk of developing resistance.

Conclusions

Drug rotation therapy might be able to delay the onset of resistance in CML patients without costly ongoing observation of mutation status. Moreover, the simulations give credence to the suggestion that lower drug concentrations may achieve better results following major molecular response in CML.

Electronic supplementary material

The online version of this article (10.1186/s12885-019-5690-5) contains supplementary material, which is available to authorized users.

An enriched network motif family regulates multistep cell fate transitions with restricted reversibility

Multistep cell fate transitions with stepwise changes of transcriptional profiles are common to many developmental, regenerative and pathological processes. The multiple intermediate cell lineage states can serve as differentiation checkpoints or branching points for channeling cells to more than one lineages. However, mechanisms underlying these transitions remain elusive. Here, we explored gene regulatory circuits that can generate multiple intermediate cellular states with stepwise modulations of transcription factors. With unbiased searching in the network topology space, we found a motif family containing a large set of networks can give rise to four attractors with the stepwise regulations of transcription factors, which limit the reversibility of three consecutive steps of the lineage transition. We found that there is an enrichment of these motifs in a transcriptional network controlling the early T cell development, and a mathematical model based on this network recapitulates multistep transitions in the early T cell lineage commitment. By calculating the energy landscape and minimum action paths for the T cell model, we quantified the stochastic dynamics of the critical factors in response to the differentiation signal with fluctuations. These results are in good agreement with experimental observations and they suggest the stable characteristics of the intermediate states in the T cell differentiation. These dynamical features may help to direct the cells to correct lineages during development. Our findings provide general design principles for multistep cell linage transitions and new insights into the early T cell development. The network motifs containing a large family of topologies can be useful for analyzing diverse biological systems with multistep transitions.

The functions of cells are dynamically controlled in many biological processes including development, regeneration and disease progression. Cell fate transition, or the switch of cellular functions, often involves multiple steps. The intermediate stages of the transition provide the biological systems with the opportunities to regulate the transitions in a precise manner. These transitions are controlled by key regulatory genes of which the expression shows stepwise patterns, but how the interactions of these genes can determine the multistep processes was unclear. Here, we present a comprehensive analysis on the design principles of gene circuits that govern multistep cell fate transition. We found a large network family with common structural features that can generate systems with the ability to control three consecutive steps of the transition. We found that this type of networks is enriched in a gene circuit controlling the development of T lymphocyte, a crucial type of immune cells. We performed mathematical modeling using this gene circuit and we recapitulated the stepwise and irreversible loss of stem cell properties of the developing T lymphocytes. Our findings can be useful to analyze a wide range of gene regulatory networks controlling multistep cell fate transitions.

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.

MTA3-SOX2 Module Regulates Cancer Stemness and Contributes to Clinical Outcomes of Tongue Carcinoma

Cancer cell plasticity plays critical roles in both tumorigenesis and tumor progression. Metastasis-associated protein 3 (MTA3), a component of the nucleosome remodeling and histone deacetylase (NuRD) complex and multi-effect coregulator, can serve as a tumor suppressor in many cancer types. However, the role of MTA3 in tongue squamous cell cancer (TSCC) remains unclear although it is the most prevalent head and neck cancer and often with poor prognosis. By analyzing both published datasets and clinical specimens, we found that the level of MTA3 was lower in TSCC compared to normal tongue tissues. Data from gene set enrichment analysis (GSEA) also indicated that MTA3 was inversely correlated with cancer stemness. In addition, the levels of MTA3 in both samples from TSCC patients and TSCC cell lines were negatively correlated with SOX2, a key regulator of the plasticity of cancer stem cells (CSCs). We also found that SOX2 played an indispensable role in MTA3-mediated CSC repression. Using the mouse model mimicking human TSCC we demonstrated that the levels of MTA3 and SOX2 decreased and increased, respectively, during the process of tumorigenesis and progression. Finally, we showed that the patients in the MTA3^low/SOX2^high group had the worst prognosis suggesting that MTA3^low/SOX2^high can serve as an independent prognostic factor for TSCC patients. Altogether, our data suggest that MTA3 is capable of repressing TSCC CSC properties and tumor growth through downregulating SOX2 and MTA3^low/SOX2^high might be a potential prognostic factor for TSCC patients.

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.

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.

Rare-event sampling of epigenetic landscapes and phenotype transitions

Stochastic simulation has been a powerful tool for studying the dynamics of gene regulatory networks, particularly in terms of understanding how cell-phenotype stability and fate-transitions are impacted by noisy gene expression. However, gene networks often have dynamics characterized by multiple attractors. Stochastic simulation is often inefficient for such systems, because most of the simulation time is spent waiting for rare, barrier-crossing events to occur. We present a rare-event simulation-based method for computing epigenetic landscapes and phenotype-transitions in metastable gene networks. Our computational pipeline was inspired by studies of metastability and barrier-crossing in protein folding, and provides an automated means of computing and visualizing essential stationary and dynamic information that is generally inaccessible to conventional simulation. Applied to a network model of pluripotency in Embryonic Stem Cells, our simulations revealed rare phenotypes and approximately Markovian transitions among phenotype-states, occurring with a broad range of timescales. The relative probabilities of phenotypes and the transition paths linking pluripotency and differentiation are sensitive to global kinetic parameters governing transcription factor-DNA binding kinetics. Our approach significantly expands the capability of stochastic simulation to investigate gene regulatory network dynamics, which may help guide rational cell reprogramming strategies. Our approach is also generalizable to other types of molecular networks and stochastic dynamics frameworks.

RACIPE: a computational tool for modeling gene regulatory circuits using randomization

Background

One of the major challenges in traditional mathematical modeling of gene regulatory circuits is the insufficient knowledge of kinetic parameters. These parameters are often inferred from existing experimental data and/or educated guesses, which can be time-consuming and error-prone, especially for large networks.

Results

We present a user-friendly computational tool for the community to use our newly developed method named random circuit perturbation (RACIPE), to explore the robust dynamical features of gene regulatory circuits without the requirement of detailed kinetic parameters. Taking the network topology as the only input, RACIPE generates an ensemble of circuit models with distinct randomized parameters and uniquely identifies robust dynamical properties by statistical analysis. Here, we discuss the implementation of the software and the statistical analysis methods of RACIPE-generated data to identify robust gene expression patterns and the functions of genes and regulatory links. Finally, we apply the tool on coupled toggle-switch circuits and a published circuit of B-lymphopoiesis.

Conclusions

We expect our new computational tool to contribute to a more comprehensive and unbiased understanding of mechanisms underlying gene regulatory networks. RACIPE is a free open source software distributed under (Apache 2.0) license and can be downloaded from GitHub (https://github.com/simonhb1990/RACIPE-1.0).

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0594-6) contains supplementary material, which is available to authorized users.

Landscape reveals critical network structures for sharpening gene expression boundaries

Background

Spatial pattern formation is a critical issue in developmental biology. Gene expression boundary sharpening has been observed from both experiments and modeling simulations. However, the mechanism to determine the sharpness of the boundary is not fully elucidated.

Results

We investigated the boundary sharpening resulted by three biological motifs, interacting with morphogens, and uncovered their probabilistic landscapes. The landscape view, along with calculated average switching time between attractors, provides a natural explanation for the boundary sharpening behavior relying on the noise induced gene state switchings. To possess boundary sharpening potential, a gene network needs to generate an asymmetric bistable state, i.e. one of the two stable states is less stable than the other. We found that the mutual repressed self-activation model displays more robust boundary sharpening ability against parameter perturbation, compared to the mutual repression or the self-activation model. This is supported by the results of switching time calculated from the landscape, which indicate that the mutual repressed self-activation model has shortest switching time, among three models. Additionally, introducing cross gradients of morphogens provides a more stable mechanism for the boundary sharpening of gene expression, due to a two-way switching mechanism.

Conclusions

Our results reveal the underlying principle for the gene expression boundary sharpening, and pave the way for the mechanistic understanding of cell fate decisions in the pattern formation processes of development.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0595-5) contains supplementary material, which is available to authorized users.

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.

Dynamical analysis of cellular ageing by modeling of gene regulatory network based attractor landscape

Ageing is a natural phenomenon that is inherently complex and remains a mystery. Conceptual model of cellular ageing landscape was proposed for computational studies of ageing. However, there is a lack of quantitative model of cellular ageing landscape. This study aims to investigate the mechanism of cellular ageing in a theoretical model using the framework of Waddington's epigenetic landscape. We construct an ageing gene regulatory network (GRN) consisting of the core cell cycle regulatory genes (including p53). A model parameter (activation rate) is used as a measure of the accumulation of DNA damage. Using the bifurcation diagrams to estimate the parameter values that lead to multi-stability, we obtained a conceptual model for capturing three distinct stable steady states (or attractors) corresponding to homeostasis, cell cycle arrest, and senescence or apoptosis. In addition, we applied a Monte Carlo computational method to quantify the potential landscape, which displays: I) one homeostasis attractor for low accumulation of DNA damage; II) two attractors for cell cycle arrest and senescence (or apoptosis) in response to high accumulation of DNA damage. Using the Waddington's epigenetic landscape framework, the process of ageing can be characterized by state transitions from landscape I to II. By in silico perturbations, we identified the potential landscape of a perturbed network (inactivation of p53), and thereby demonstrated the emergence of a cancer attractor. The simulated dynamics of the perturbed network displays a landscape with four basins of attraction: homeostasis, cell cycle arrest, senescence (or apoptosis) and cancer. Our analysis also showed that for the same perturbed network with low DNA damage, the landscape displays only the homeostasis attractor. The mechanistic model offers theoretical insights that can facilitate discovery of potential strategies for network medicine of ageing-related diseases such as cancer.

Uncovering the underlying mechanism of cancer tumorigenesis and development under an immune microenvironment from global quantification of the landscape

The study of the cancer-immune system is important for understanding tumorigenesis and the development of cancer and immunotherapy. In this work, we build a comprehensive cancer-immune model including both cells and cytokines to uncover the underlying mechanism of cancer immunity based on landscape topography. We quantify three steady-state attractors, normal state, low cancer state and high cancer state, for the innate immunity and adaptive immunity of cancer. We also illustrate the cardinal inhibiting cancer immunity interactions and promoting cancer immunity interactions through global sensitivity analysis. We simulate tumorigenesis and the development of cancer and classify these into six stages. The characteristics of the six stages can be classified further into three groups. These correspond to the escape, elimination and equilibrium phases in immunoediting, respectively. Under specific cell-cell interactions strength oscillations emerge. We found that tumorigenesis and cancer recovery processes may need to go through cancer-immune oscillation, which consumes more energy. Based on the cancer-immune landscape, we predict three types of cells and two types of cytokines for cancer immunotherapy as well as combination immunotherapy. This landscape framework provides a quantitative way to understand the underlying mechanisms of the interplay between cancer and the immune system for cancer tumorigenesis and development.

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.

Mesenchymal stem cells over-expressing cxcl12 enhance the radioresistance of the small intestine

The chemokine C-X-C motif chemokine 12 (CXCL12) greatly impacts various biological processes in mammals, including cell survival, growth and migration. Mesenchymal stem cells (MSCs) are promising tools for carrying foreign genes to treat radiation-induced injuries in the intestinal epithelium. In this study, human adipose-derived MSCs were constructed to over-express the mouse cxcl12 gene to treat such injuries. In vitro, because of the high levels of mouse CXCL12 in conditioned medium produced by mouse cxcl12 gene-modified cells, phosphorylation of Akt at Ser473 and Erk1/2 at Thr202/Thr204 was increased within crypt cells of irradiated organoids compared with unmodified controls. Moreover, intracellular stabilization of β-catenin was achieved after treatment of mouse cxcl12 gene-modified cells with conditioned medium. As a result, survival of crypt cells was maintained and their proliferation was promoted. When delivering mouse cxcl12 gene-modified cells into irradiated BALB/c nude mice, mice were rescued despite the clearance of cells from the host within 1 week. Irradiated mice that received mouse cxcl12 gene-modified MSCs exhibited reduced serum levels of interleukin-1α (IL-1α) and IL-6 as well as elevated levels of CXCL12. Additionally, epithelial recovery from radiation stress was accelerated compared with the irradiated-alone controls. Moreover, mouse cxcl12 gene-modified MSCs were superior to unmodified cells at strengthening host repair responses to radiation stress as well as presenting increased serum CXCL12 levels and decreased serum IL-1α levels. Furthermore, the number of crypt cells that were positive for phosphorylated Akt at Ser473 and phosphorylated Erk1/2 at Thr202/Thr204 increased following treatment with mouse cxcl12 gene-modified MSCs. Thus, cxcl12 gene-modified MSCs confer radioresistance to the intestinal epithelium.

Distinguishing mechanisms underlying EMT tristability

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-β 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.

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.

Modeling the response of a tumor-suppressive network to mitogenic and oncogenic signals

Intrinsic tumor-suppressive mechanisms protect normal cells against aberrant proliferation. Although cellular signaling pathways engaged in tumor repression have been largely identified, how they are orchestrated to fulfill their function still remains elusive. Here, we built a tumor-suppressive network model composed of three modules responsible for the regulation of cell proliferation, activation of p53, and induction of apoptosis. Numerical simulations show a rich repertoire of network dynamics when normal cells are subject to serum stimulation and adenovirus E1A overexpression. We showed that oncogenic signaling induces ARF and that ARF further promotes p53 activation to inhibit proliferation. Mitogenic signaling activates E2F activators and promotes Akt activation. p53 and E2F1 cooperate to induce apoptosis, whereas Akt phosphorylates p21 to repress caspase activation. These prosurvival and proapoptotic signals compete to dictate the cell fate of proliferation, cell-cycle arrest, or apoptosis. The cellular outcome is also impacted by the kinetic mode (ultrasensitivity or bistability) of p53. When cells are exposed to serum deprivation and recovery under fixed E1A, the shortest starvation time required for apoptosis induction depends on the terminal serum concentration, which was interpreted in terms of the dynamics of caspase-3 activation and cytochrome c release. We discovered that caspase-3 can be maintained active at high serum concentrations and that E1A overexpression sensitizes serum-starved cells to apoptosis. This work elucidates the roles of tumor repressors and prosurvival factors in tumor repression based on a dynamic network analysis and provides a framework for quantitatively exploring tumor-suppressive mechanisms.

Cancer as robust intrinsic state shaped by evolution: a key issues review

Cancer is a complex disease: its pathology cannot be properly understood in terms of independent players-genes, proteins, molecular pathways, or their simple combinations. This is similar to many-body physics of a condensed phase that many important properties are not determined by a single atom or molecule. The rapidly accumulating large 'omics' data also require a new mechanistic and global underpinning to organize for rationalizing cancer complexity. A unifying and quantitative theory was proposed by some of the present authors that cancer is a robust state formed by the endogenous molecular-cellular network, which is evolutionarily built for the developmental processes and physiological functions. Cancer state is not optimized for the whole organism. The discovery of crucial players in cancer, together with their developmental and physiological roles, in turn, suggests the existence of a hierarchical structure within molecular biology systems. Such a structure enables a decision network to be constructed from experimental knowledge. By examining the nonlinear stochastic dynamics of the network, robust states corresponding to normal physiological and abnormal pathological phenotypes, including cancer, emerge naturally. The nonlinear dynamical model of the network leads to a more encompassing understanding than the prevailing linear-additive thinking in cancer research. So far, this theory has been applied to prostate, hepatocellular, gastric cancers and acute promyelocytic leukemia with initial success. It may offer an example of carrying physics inquiring spirit beyond its traditional domain: while quantitative approaches can address individual cases, however there must be general rules/laws to be discovered in biology and medicine.

Modeling the Genetic Regulation of Cancer Metabolism: Interplay between Glycolysis and Oxidative Phosphorylation

Abnormal metabolism is a hallmark of cancer, yet its regulation remains poorly understood. Cancer cells were considered to utilize primarily glycolysis for ATP production, referred to as the Warburg effect. However, recent evidence suggests that oxidative phosphorylation (OXPHOS) plays a crucial role during cancer progression. Here we utilized a systems biology approach to decipher the regulatory principle of glycolysis and OXPHOS. Integrating information from literature, we constructed a regulatory network of genes and metabolites, from which we extracted a core circuit containing HIF-1, AMPK, and ROS. Our circuit analysis showed that while normal cells have an oxidative state and a glycolytic state, cancer cells can access a hybrid state with both metabolic modes coexisting. This was due to higher ROS production and/or oncogene activation, such as RAS, MYC, and c-SRC. Guided by the model, we developed two signatures consisting of AMPK and HIF-1 downstream genes, respectively, to quantify the activity of glycolysis and OXPHOS. By applying the AMPK and HIF-1 signatures to The Cancer Genome Atlas patient transcriptomics data of multiple cancer types and single-cell RNA-seq data of lung adenocarcinoma, we confirmed an anticorrelation between AMPK and HIF-1 activities and the association of metabolic states with oncogenes. We propose that the hybrid phenotype contributes to metabolic plasticity, allowing cancer cells to adapt to various microenvironments. Using model simulations, our theoretical framework of metabolism can serve as a platform to decode cancer metabolic plasticity and design cancer therapies targeting metabolism. Cancer Res; 77(7); 1564-74. ©2017 AACR.

A Physical Mechanism and Global Quantification of Breast Cancer

Initiation and progression of cancer depend on many factors. Those on the genetic level are often considered crucial. To gain insight into the physical mechanisms of breast cancer, we construct a gene regulatory network (GRN) which reflects both genetic and environmental aspects of breast cancer. The construction of the GRN is based on available experimental data. Three basins of attraction, representing the normal, premalignant and cancer states respectively, were found on the phenotypic landscape. The progression of breast cancer can be seen as switching transitions between different state basins. We quantified the stabilities and kinetic paths of the three state basins to uncover the biological process of breast cancer formation. The gene expression levels at each state were obtained, which can be tested directly in experiments. Furthermore, by performing global sensitivity analysis on the landscape topography, six key genes (HER2, MDM2, TP53, BRCA1, ATM, CDK2) and four regulations (HER2⊣TP53, CDK2⊣BRCA1, ATM→MDM2, TP53→ATM) were identified as being critical for breast cancer. Interestingly, HER2 and MDM2 are the most popular targets for treating breast cancer. BRCA1 and TP53 are the most important oncogene of breast cancer and tumor suppressor gene, respectively. This further validates the feasibility of our model and the reliability of our prediction results. The regulation ATM→MDM2 has been extensive studied on DNA damage but not on breast cancer. We notice the importance of ATM→MDM2 on breast cancer. Previous studies of breast cancer have often focused on individual genes and the anti-cancer drugs are mainly used to target the individual genes. Our results show that the network-based strategy is more effective on treating breast cancer. The landscape approach serves as a new strategy for analyzing breast cancer on both the genetic and epigenetic levels and can help on designing network based medicine for breast cancer.

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

Epithelial-mesenchymal transition (EMT), as a crucial process in embryonic development and cancer metastasis, has been investigated extensively. However, how to quantify the global stability and transition dynamics for EMT under fluctuations remains to be elucidated. Starting from a core EMT genetic circuit composed of three key proteins or microRNAs (microRNA-200, ZEB and SNAIL), we uncovered the potential landscape for the EMT process. Three attractors emerge from the landscape, which correspond to epithelial, mesenchymal and partial EMT states respectively. Based on the landscape, we analyzed two important quantities of the EMT system: the barrier heights between different basins of attraction that describe the degree of difficulty for EMT or backward transition, and the mean first passage time (MFPT) that characterizes the kinetic transition rate. These quantities can be harnessed as measurements for the stability of cell types and the degree of difficulty of transitions between different cell types. We also calculated the minimum action paths (MAPs) by path integral approaches. The MAP delineates the transition processes between different cell types quantitatively. We propose two different EMT processes: a direct EMT from E to P, and a step-wise EMT going through an intermediate state, depending on different extracellular environments. The landscape and kinetic paths we acquired offer a new physical and quantitative way for understanding the mechanisms of EMT processes, and indicate the possible roles for the intermediate states.