Role of noise and parametric variation in the dynamics of gene regulatory circuits

Dissecting reversible and irreversible single cell state transitions from gene regulatory networks

Understanding cell state transitions and their governing regulatory mechanisms remains one of the fundamental questions in biology. We develop a computational method, state transition inference using cross-cell correlations (STICCC), for predicting reversible and irreversible cell state transitions at single-cell resolution by using gene expression data and a set of gene regulatory interactions. The method is inspired by the fact that the gene expression time delays between regulators and targets can be exploited to infer past and future gene expression states. From applications to both simulated and experimental single-cell gene expression data, we show that STICCC-inferred vector fields capture basins of attraction and irreversible fluxes. By connecting regulatory information with systems' dynamical behaviors, STICCC reveals how network interactions influence reversible and irreversible state transitions. Compared to existing methods that infer pseudotime and RNA velocity, STICCC provides complementary insights into the gene regulation of cell state transitions.

Gene regulatory network topology governs resistance and treatment escape in glioma stem-like cells

Poor prognosis and drug resistance in glioblastoma (GBM) can result from cellular heterogeneity and treatment-induced shifts in phenotypic states of tumor cells, including dedifferentiation into glioma stem-like cells (GSCs). This rare tumorigenic cell subpopulation resists temozolomide, undergoes proneural-to-mesenchymal transition (PMT) to evade therapy, and drives recurrence. Through inference of transcriptional regulatory networks (TRNs) of patient-derived GSCs (PD-GSCs) at single-cell resolution, we demonstrate how the topology of transcription factor interaction networks drives distinct trajectories of cell-state transitions in PD-GSCs resistant or susceptible to cytotoxic drug treatment. By experimentally testing predictions based on TRN simulations, we show that drug treatment drives surviving PD-GSCs along a trajectory of intermediate states, exposing vulnerability to potentiated killing by siRNA or a second drug targeting treatment-induced transcriptional programs governing nongenetic cell plasticity. Our findings demonstrate an approach to uncover TRN topology and use it to rationally predict combinatorial treatments that disrupt acquired resistance in GBM.

Data-driven modeling of core gene regulatory network underlying leukemogenesis in IDH mutant AML

Acute myeloid leukemia (AML) is characterized by uncontrolled proliferation of poorly differentiated myeloid cells, with a heterogenous mutational landscape. Mutations in IDH1 and IDH2 are found in 20% of the AML cases. Although much effort has been made to identify genes associated with leukemogenesis, the regulatory mechanism of AML state transition is still not fully understood. To alleviate this issue, here we develop a new computational approach that integrates genomic data from diverse sources, including gene expression and ATAC-seq datasets, curated gene regulatory interaction databases, and mathematical modeling to establish models of context-specific core gene regulatory networks (GRNs) for a mechanistic understanding of tumorigenesis of AML with IDH mutations. The approach adopts a new optimization procedure to identify the top network according to its accuracy in capturing gene expression states and its flexibility to allow sufficient control of state transitions. From GRN modeling, we identify key regulators associated with the function of IDH mutations, such as DNA methyltransferase DNMT1, and network destabilizers, such as E2F1. The constructed core regulatory network and outcomes of in-silico network perturbations are supported by survival data from AML patients. We expect that the combined bioinformatics and systems-biology modeling approach will be generally applicable to elucidate the gene regulation of disease progression.

Increased heterogeneity in expression of genes associated with cancer progression and drug resistance

Fluctuations in the number of regulatory molecules and differences in timings of molecular events can generate variation in gene expression among genetically identical cells in the same environmental condition. This variation, termed as expression noise, can create differences in metabolic state and cellular functions, leading to phenotypic heterogeneity. Expression noise and phenotypic heterogeneity have been recognized as important contributors to intra-tumor heterogeneity, and have been associated with cancer growth, progression, and therapy resistance. However, how expression noise changes with cancer progression in actual cancer patients has remained poorly explored. Such an analysis, through identification of genes with increasing expression noise, can provide valuable insights into generation of intra-tumor heterogeneity, and could have important implications for understanding immune-suppression, drug tolerance and therapy resistance. In this work, we performed a genome-wide identification of changes in gene expression noise with cancer progression using single-cell RNA-seq data of lung adenocarcinoma patients at different stages of cancer. We identified 37 genes in epithelial cells that showed an increasing noise trend with cancer progression, many of which were also associated with cancer growth, EMT and therapy resistance. We found that expression of several of these genes was positively associated with expression of mitochondrial genes, suggesting an important role of mitochondria in generation of heterogeneity. In addition, we uncovered substantial differences in sample-specific noise profiles which could have implications for personalized prognosis and treatment.

Gene regulatory network topology governs resistance and treatment escape in glioma stem-like cells

Poor prognosis and drug resistance in glioblastoma (GBM) can result from cellular heterogeneity and treatment-induced shifts in phenotypic states of tumor cells, including dedifferentiation into glioma stem-like cells (GSCs). This rare tumorigenic cell subpopulation resists temozolomide, undergoes proneural-to-mesenchymal transition (PMT) to evade therapy, and drives recurrence. Through inference of transcriptional regulatory networks (TRNs) of patient-derived GSCs (PD-GSCs) at single-cell resolution, we demonstrate how the topology of transcription factor interaction networks drives distinct trajectories of cell state transitions in PD-GSCs resistant or susceptible to cytotoxic drug treatment. By experimentally testing predictions based on TRN simulations, we show that drug treatment drives surviving PD-GSCs along a trajectory of intermediate states, exposing vulnerability to potentiated killing by siRNA or a second drug targeting treatment-induced transcriptional programs governing non-genetic cell plasticity. Our findings demonstrate an approach to uncover TRN topology and use it to rationally predict combinatorial treatments that disrupts acquired resistance in GBM.

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.

Critical transition and reversion of tumorigenesis

Cancer is caused by the accumulation of genetic alterations and therefore has been historically considered to be irreversible. Intriguingly, several studies have reported that cancer cells can be reversed to be normal cells under certain circumstances. Despite these experimental observations, conceptual and theoretical frameworks that explain these phenomena and enable their exploration in a systematic way are lacking. In this review, we provide an overview of cancer reversion studies and describe recent advancements in systems biological approaches based on attractor landscape analysis. We suggest that the critical transition in tumorigenesis is an important clue for achieving cancer reversion. During tumorigenesis, a critical transition may occur at a tipping point, where cells undergo abrupt changes and reach a new equilibrium state that is determined by complex intracellular regulatory events. We introduce a conceptual framework based on attractor landscapes through which we can investigate the critical transition in tumorigenesis and induce its reversion by combining intracellular molecular perturbation and extracellular signaling controls. Finally, we present a cancer reversion therapy approach that may be a paradigm-changing alternative to current cancer cell-killing therapies.

A quantitative evaluation of topological motifs and their coupling in gene circuit state distributions

One of the major challenges in biology is to understand how gene interactions collaborate to determine overall functions of biological systems. Here, we present a new computational framework that enables systematic, high-throughput, and quantitative evaluation of how small transcriptional regulatory circuit motifs, and their coupling, contribute to functions of a dynamical biological system. We illustrate how this approach can be applied to identify four-node gene circuits, circuit motifs, and motif coupling responsible for various gene expression state distributions, including those derived from single-cell RNA sequencing data. We also identify seven major classes of four-node circuits from clustering analysis of state distributions. The method is applied to establish phenomenological models of gene circuits driving human neuron differentiation, revealing important biologically relevant regulatory interactions. Our study will shed light on a better understanding of gene regulatory mechanisms in creating and maintaining cellular states.

A data-driven optimization method for coarse-graining gene regulatory networks

One major challenge in systems biology is to understand how various genes in a gene regulatory network (GRN) collectively perform their functions and control network dynamics. This task becomes extremely hard to tackle in the case of large networks with hundreds of genes and edges, many of which have redundant regulatory roles and functions. The existing methods for model reduction usually require the detailed mathematical description of dynamical systems and their corresponding kinetic parameters, which are often not available. Here, we present a data-driven method for coarse-graining large GRNs, named SacoGraci, using ensemble-based mathematical modeling, dimensionality reduction, and gene circuit optimization by Markov Chain Monte Carlo methods. SacoGraci requires network topology as the only input and is robust against errors in GRNs. We benchmark and demonstrate its usage with synthetic, literature-based, and bioinformatics-derived GRNs. We hope SacoGraci will enhance our ability to model the gene regulation of complex biological systems.

NetAct: a computational platform to construct core transcription factor regulatory networks using gene activity

A major question in systems biology is how to identify the core gene regulatory circuit that governs the decision-making of a biological process. Here, we develop a computational platform, named NetAct, for constructing core transcription factor regulatory networks using both transcriptomics data and literature-based transcription factor-target databases. NetAct robustly infers regulators' activity using target expression, constructs networks based on transcriptional activity, and integrates mathematical modeling for validation. Our in silico benchmark test shows that NetAct outperforms existing algorithms in inferring transcriptional activity and gene networks. We illustrate the application of NetAct to model networks driving TGF-β-induced epithelial-mesenchymal transition and macrophage polarization.

What Makes a Functional Gene Regulatory Network? A Circuit Motif Analysis

One of the key questions in systems biology is to understand the roles of gene regulatory circuits in determining cellular states and their functions. In previous studies, some researchers have inferred large gene networks from genome wide genomics/transcriptomics data using the top-down approach, while others have modeled core gene circuits of small sizes using the bottom-up approach. Despite many existing systems biology studies, there is still no general rule on what sizes of gene networks and what types of circuit motifs a system would need to achieve robust biological functions. Here, we adopt a gene circuit motif analysis to discover four-node circuits responsible for multiplicity (rich in dynamical behavior), flexibility (versatile to alter gene expression), or both. We identify the most reoccurring two-node circuit motifs and the co-occurring motif pairs. Furthermore, we investigate the contributing factors of multiplicity and flexibility for large gene networks of different types and sizes. We find that gene networks of intermediate sizes tend to have combined high levels of multiplicity and flexibility. Our study will contribute to a better understanding of the dynamical mechanisms of gene regulatory circuits and provide insights into rational designs of robust gene circuits in synthetic and systems biology.

Dynamics of hepatocyte-cholangiocyte cell-fate decisions during liver development and regeneration

The immense regenerative potential of the liver is attributed to the ability of its two key cell types – hepatocytes and cholangiocytes – to trans-differentiate to one another either directly or through intermediate progenitor states. However, the dynamic features of decision-making between these cell-fates during liver development and regeneration remains elusive. Here, we identify a core gene regulatory network comprising c/EBPα, TGFBR2, and SOX9 which is multistable in nature, enabling three distinct cell states – hepatocytes, cholangiocytes, and liver progenitor cells (hepatoblasts/oval cells) – and stochastic switching among them. Predicted expression signature for these three states are validated through multiple bulk and single-cell transcriptomic datasets collected across developmental stages and injury-induced liver repair. This network can also explain the experimentally observed spatial organization of phenotypes in liver parenchyma and predict strategies for efficient cellular reprogramming. Our analysis elucidates how the emergent dynamics of underlying regulatory networks drive diverse cell-fate decisions in liver development and regeneration.

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Identified minimal regulatory network to model liver development and regeneration

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Changes in phenotypic landscapes by in-silico perturbations of regulatory networks

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Ability to explain physiological spatial patterning of liver cell types

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Decoded strategies for efficient reprogramming among liver cell phenotypes

Stochastic fluctuations promote ordered pattern formation of cells in the Notch-Delta signaling pathway

The Notch-Delta signaling pathway mediates cell differentiation implicated in many regulatory processes including spatiotemporal patterning in tissues by promoting alternate cell fates between neighboring cells. At the multicellular level, this "lateral inhibition” principle leads to checkerboard patterns with alternation of Sender and Receiver cells. While it is well known that stochasticity modulates cell fate specification, little is known about how stochastic fluctuations at the cellular level propagate during multicell pattern formation. Here, we model stochastic fluctuations in the Notch-Delta pathway in the presence of two different noise types–shot and white–for a multicell system. Our results show that intermediate fluctuations reduce disorder and guide the multicell lattice toward checkerboard-like patterns. By further analyzing cell fate transition events, we demonstrate that intermediate noise amplitudes provide enough perturbation to facilitate “proofreading” of disordered patterns and cause cells to switch to the correct ordered state (Sender surrounded by Receivers, and vice versa). Conversely, high noise can override environmental signals coming from neighboring cells and lead to switching between ordered and disordered patterns. Therefore, in analogy with spin glass systems, intermediate noise levels allow the multicell Notch system to escape frustrated patterns and relax towards the lower energy checkerboard pattern while at large noise levels the system is unable to find this ordered base of attraction.

The Notch pathway is involved in many biological processes and is known to form precise spatial patterns alternating Sender and Receiver cell states. Quantifying the implications of stochastic fluctuations provided insight that patterns formed in Notch-mediated pathways must follow a predetermined path towards checkerboard or exist in a noisy environment which promotes order through error correction.

We model Notch pattern formation stochastically and analyze the spatiotemporal dynamics. Our results show multicellular systems equilibrate towards ordered systems, but mistakes in the initial lattice propagate causing the systems to relax into frustrated systems. Only through existing in a noisy environment are the systems able to relax into the checkerboard pattern. Analyzing the temporal dynamics confirms, in environments with intermediate noise, the “incorrect” cells (Sender in a Sender environment, and vice versa) can be flipped to the correct state (Sender in a Receiver environment, and vice versa). Comparing with the spin glass energy landscape, we suggest the multicellular model follows a rugged landscape to form patterns with stochastic fluctuations required to enforce order throughout the system.

Bronchial epithelium epithelial-mesenchymal plasticity forms aberrant basaloid-like cells in vitro

Although epithelial-mesenchymal transition (EMT) is a common feature of fibrotic lung disease, its role in fibrogenesis is controversial. Recently, aberrant basaloid cells were identified in fibrotic lung tissue as a novel epithelial cell type displaying a partial EMT phenotype. The developmental origin of these cells remains unknown. To elucidate the role of EMT in the development of aberrant basaloid cells from the bronchial epithelium, we mapped EMT-induced transcriptional changes at the population and single-cell levels. Human bronchial epithelial cells grown as submerged or air-liquid interface (ALI) cultures with or without EMT induction were analyzed by bulk and single-cell RNA-Sequencing. Comparison of submerged and ALI cultures revealed differential expression of 8,247 protein coding (PC) and 1,621 long noncoding RNA (lncRNA) genes and revealed epithelial cell-type-specific lncRNAs. Similarly, EMT induction in ALI cultures resulted in robust transcriptional reprogramming of 6,020 PC and 907 lncRNA genes. Although there was no evidence for fibroblast/myofibroblast conversion following EMT induction, cells displayed a partial EMT gene signature and an aberrant basaloid-like cell phenotype. The substantial transcriptional differences between submerged and ALI cultures highlight that care must be taken when interpreting data from submerged cultures. This work supports that lung epithelial EMT does not generate fibroblasts/myofibroblasts and confirms ALI cultures provide a physiologically relevant system to study aberrant basaloid-like cells and mechanisms of EMT. We provide a catalog of PC and lncRNA genes and an interactive browser (https://bronc-epi-in-vitro.cells.ucsc.edu/) of single-cell RNA-Seq data for further exploration of potential roles in the lung epithelium in health and lung disease.

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.

Emergent dynamics of a three-node regulatory network explain phenotypic switching and heterogeneity: a case study of Th1/Th2/Th17 cell differentiation

Naïve helper (CD4+) T-cells can differentiate into distinct functional subsets including Th1, Th2, and Th17 phenotypes. Each of these phenotypes has a 'master regulator' - T-bet (Th1), GATA3 (Th2) and RORγT (Th17) - that inhibits the other two master regulators. Such mutual repression among them at a transcriptional level can enable multistability, giving rise to six experimentally observed phenotypes - Th1, Th2, Th17, hybrid Th/Th2, hybrid Th2/Th17 and hybrid Th1/Th17. However, the dynamics of switching among these phenotypes, particularly in the case of epigenetic influence, remains unclear. Here, through mathematical modeling, we investigated the coupled transcription-epigenetic dynamics in a three-node mutually repressing network to elucidate how epigenetic changes mediated by any 'master regulator' can influence the transition rates among different cellular phenotypes. We show that the degree of plasticity exhibited by one phenotype depends on relative strength and duration of mutual epigenetic repression mediated among the master regulators in a three-node network. Further, our model predictions can offer putative mechanisms underlying relatively higher plasticity of Th17 phenotype as observed in vitro and in vivo. Together, our modeling framework characterizes phenotypic plasticity and heterogeneity as an outcome of emergent dynamics of a three-node regulatory network, such as the one mediated by T-bet/GATA3/RORγT.

Immunosuppressive Traits of the Hybrid Epithelial/Mesenchymal Phenotype

Recent preclinical and clinical data suggests enhanced metastatic fitness of hybrid epithelial/mesenchymal (E/M) phenotypes, but mechanistic details regarding their survival strategies during metastasis remain unclear. Here, we investigate immune-evasive strategies of hybrid E/M states. We construct and simulate the dynamics of a minimalistic regulatory network encompassing the known associations among regulators of EMT (epithelial-mesenchymal transition) and PD-L1, an established immune-suppressor. Our simulations for the network consisting of SLUG, ZEB1, miR-200, CDH1 and PD-L1, integrated with single-cell and bulk RNA-seq data analysis, elucidate that hybrid E/M cells can have high levels of PD-L1, similar to those seen in cells with a full EMT phenotype, thus obviating the need for cancer cells to undergo a full EMT to be immune-evasive. Specifically, in breast cancer, we show the co-existence of hybrid E/M phenotypes, enhanced resistance to anti-estrogen therapy and increased PD-L1 levels. Our results underscore how the emergent dynamics of interconnected regulatory networks can coordinate different axes of cellular fitness during metastasis.

Noise-induced quasiperiod and period switching

We employ a typical genetic circuit model to explore how noise can influence dynamic structure. With the increase of a key interactive parameter, the model will deterministically go through two bifurcations and three dynamic structure regions. We find that a quasiperiodic component, which is not allowed by deterministic dynamics, will be generated by noise inducing in the first two regions, and this quasiperiod will be more and more stable along with the increase in noise. In particular, in the second region the quasiperiod will compete with a stable limit cycle and perform a new transient rhythm. Furthermore, we ascertain the entropy production rate and the heat dissipation rate, and discover a minimal value with theoretical elucidation. In the end, we unveil the mechanism of the formation of quasiperiods, and show a practical biological example. We expect this work to be helpful in solving some biological or ecological problems, such as the genetic origin of periodical cicadas and population dynamics with fluctuation.

Metacode: One code to rule them all

The code of codes or metacode is a microcosm where biological layers, as well as their codes, interact together allowing the continuity of information flow in organisms by increasing biological entities' complexity. Through this novel organic code, biological systems scale towards niches with higher informatic freedom building structures that increase the entropy in the universe. Code biology has developed a novel informational framework where biological entities strive themselves through the information flow carried out through organic codes consisting of two molecular or functional landscapes intertwined through arbitrary linkages via an adaptor whose nature is autonomous from molecular determinism. Here we will integrate genomic and epigenomic codes according to the evidence released in ENCODE (phase 3), psychENCODE and GTEx project, outlining the principles of the metacode, to address the continuous nature of biological systems and their inter-layered information flow. This novel complex metacode maps from very constrained sets of elements (i.e., regulation sites modulating gene expression) to new ones with greater freedom of decoding (i.e., a continuous cell phenotypic space). This leads to a new domain in code biology where biological systems are informatic attractors that navigate an energy metaspace through a complexity-noise balance, stalling in emergent niches where organic codes take meaning.

Gene Circuit Explorer (GeneEx): an interactive web-app for visualizing, simulating and analyzing gene regulatory circuits

SUMMARY

GeneEx is an interactive web-app that uses an ODE-based mathematical modeling approach to simulate, visualize and analyze gene regulatory circuits (GRCs) for an explicit kinetic parameter set or for a large ensemble of random parameter sets. GeneEx offers users the freedom to modify many aspects of the simulation such as the parameter ranges, the levels of gene expression noise and the GRC network topology itself. This degree of flexibility allows users to explore a variety of hypotheses by providing insight into the number and stability of attractors for a given GRC. Moreover, users have the option to upload, and subsequently compare, experimental gene expression data to simulated data generated from the analysis of a built or uploaded custom circuit. Finally, GeneEx offers a curated database that contains circuit motifs and known biological GRCs to facilitate further inquiry into these. Overall, GeneEx enables users to investigate the effects of parameter variation, stochasticity and/or topological changes on gene expression for GRCs using a systems-biology approach.

AVAILABILITY AND IMPLEMENTATION

GeneEx is available at https://geneex.jax.org. This web-app is released under the MIT license and is free and open to all users and there is no mandatory login requirement.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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.

Operating principles of circular toggle polygons

Decoding the dynamics of cellular decision-making and cell differentiation is a central question in cell and developmental biology. A common network motif involved in many cell-fate decisions is a mutually inhibitory feedback loop between two self-activating 'master regulators' A and B, also called as toggle switch. Typically, it can allow for three stable states-(high A, low B), (low A, high B) and (medium A, medium B). A toggle triad-three mutually repressing regulators A, B and C, i.e. three toggle switches arranged circularly (between A and B, between B and C, and between A and C)-can allow for six stable states: three 'single positive' and three 'double positive' ones. However, the operating principles of larger toggle polygons, i.e. toggle switches arranged circularly to form a polygon, remain unclear. Here, we simulate using both discrete and continuous methods the dynamics of different sized toggle polygons. We observed a pattern in their steady state frequency depending on whether the polygon was an even or odd numbered one. The even-numbered toggle polygons result in two dominant states with consecutive components of the network expressing alternating high and low levels. The odd-numbered toggle polygons, on the other hand, enable more number of states, usually twice the number of components with the states that follow 'circular permutation' patterns in their composition. Incorporating self-activations preserved these trends while increasing the frequency of multistability in the corresponding network. Our results offer insights into design principles of circular arrangement of regulatory units involved in cell-fate decision making, and can offer design strategies for synthesizing genetic circuits.

Modeling the activity of the dopamine signaling pathway by combination of analog electrical circuit and mathematical approaches

This paper demonstrates the application of the system biology principles on the example of the dopamine signaling pathway in neurons. Presented model is based on two approaches - cytomorphic electronic circuits and mathematical modeling. Transcription and phosphorylation of DARPP-32 was modeled by analog circuit, based on well-known approaches presented in [1]. It was shown that application of circuit helps to receive signal oscillations that close to described ones in real biological systems. This combination on the one hand gives possibility to simplify calculations, on another to show this signaling pathway dynamics. The expected effect of changes in the functioning of calcium channels is considered, and the mathematical model of the interaction of system components is proposed. The average frequency of calcium current oscillations due to the presence of dopamine was 30 Hz in presented model, that is consistent with the literature, where the frequency of such oscillations is up to several tens of Hz. All presented results shows good correlation with known data, which already published today.

Multi-stability in cellular differentiation enabled by a network of three mutually repressing master regulators

Identifying the design principles of complex regulatory networks driving cellular decision-making remains essential to decode embryonic development as well as enhance cellular reprogramming. A well-studied network motif involved in cellular decision-making is a toggle switch-a set of two opposing transcription factors A and B, each of which is a master regulator of a specific cell fate and can inhibit the activity of the other. A toggle switch can lead to two possible states-(high A, low B) and (low A, high B)-and drives the 'either-or' choice between these two cell fates for a common progenitor cell. However, the principles of coupled toggle switches remain unclear. Here, we investigate the dynamics of three master regulators A, B and C inhibiting each other, thus forming three-coupled toggle switches to form a toggle triad. Our simulations show that this toggle triad can lead to co-existence of cells into three differentiated 'single positive' phenotypes-(high A, low B, low C), (low A, high B, low C) and (low A, low B, high C). Moreover, the hybrid or 'double positive' phenotypes-(high A, high B, low C), (low A, high B, high C) and (high A, low B, high C)-can coexist together with 'single positive' phenotypes. Including self-activation loops on A, B and C can increase the frequency of 'double positive' states. Finally, we apply our results to understand cellular decision-making in terms of differentiation of naive CD4⁺ T cells into Th1, Th2 and Th17 states, where hybrid Th1/Th2 and hybrid Th1/Th17 cells have been reported in addition to the Th1, Th2 and Th17 ones. Our results offer novel insights into the design principles of a multi-stable network topology and provide a framework for synthetic biology to design tristable systems.

Decoding the mechanisms underlying cell-fate decision-making during stem cell differentiation by random circuit perturbation

Stem cells can precisely and robustly undergo cellular differentiation and lineage commitment, referred to as stemness. However, how the gene network underlying stemness regulation reliably specifies cell fates is not well understood. To address this question, we applied a recently developed computational method, random circuit perturbation (RACIPE), to a nine-component gene regulatory network (GRN) governing stemness, from which we identified robust gene states. Among them, four out of the five most probable gene states exhibit gene expression patterns observed in single mouse embryonic cells at 32-cell and 64-cell stages. These gene states can be robustly predicted by the stemness GRN but not by randomized versions of the stemness GRN. Strikingly, we found a hierarchical structure of the GRN with the Oct4/Cdx2 motif functioning as the first decision-making module followed by Gata6/Nanog. We propose that stem cell populations, instead of being viewed as all having a specific cellular state, can be regarded as a heterogeneous mixture including cells in various states. Upon perturbations by external signals, stem cells lose the capacity to access certain cellular states, thereby becoming differentiated. The new gene states and key parameters regulating transitions among gene states proposed by RACIPE can be used to guide experimental strategies to better understand differentiation and design reprogramming. The findings demonstrate that the functions of the stemness GRN is mainly determined by its well-evolved network topology rather than by detailed kinetic parameters.

Random Parametric Perturbations of Gene Regulatory Circuit Uncover State Transitions in Cell Cycle

Many biological processes involve precise cellular state transitions controlled by complex gene regulation. Here, we use budding yeast cell cycle as a model system and explore how a gene regulatory circuit encodes essential information of state transitions. We present a generalized random circuit perturbation method for circuits containing heterogeneous regulation types and its usage to analyze both steady and oscillatory states from an ensemble of circuit models with random kinetic parameters. The stable steady states form robust clusters with a circular structure that are associated with cell cycle phases. This circular structure in the clusters is consistent with single-cell RNA sequencing data. The oscillatory states specify the irreversible state transitions along cell cycle progression. Furthermore, we identify possible mechanisms to understand the irreversible state transitions from the steady states. We expect this approach to be robust and generally applicable to unbiasedly predict dynamical transitions of a gene regulatory circuit.

Toward Modeling Context-Specific EMT Regulatory Networks Using Temporal Single Cell RNA-Seq Data

Epithelial-mesenchymal transition (EMT) is well established as playing a crucial role in cancer progression and being a potential therapeutic target. To elucidate the gene regulation that drives the decision making of EMT, many previous studies have been conducted to model EMT gene regulatory circuits (GRCs) using interactions from the literature. While this approach can depict the generic regulatory interactions, it falls short of capturing context-specific features. Here, we explore the effectiveness of a combined bioinformatics and mathematical modeling approach to construct context-specific EMT GRCs directly from transcriptomics data. Using time-series single cell RNA-sequencing data from four different cancer cell lines treated with three EMT-inducing signals, we identify context-specific activity dynamics of common EMT transcription factors. In particular, we observe distinct paths during the forward and backward transitions, as is evident from the dynamics of major regulators such as NF-KB (e.g., NFKB2 and RELB) and AP-1 (e.g., FOSL1 and JUNB). For each experimental condition, we systematically sample a large set of network models and identify the optimal GRC capturing context-specific EMT states using a mathematical modeling method named Random Circuit Perturbation (RACIPE). The results demonstrate that the approach can build high quality GRCs in certain cases, but not others and, meanwhile, elucidate the role of common bioinformatics parameters and properties of network structures in determining the quality of GRCs. We expect the integration of top-down bioinformatics and bottom-up systems biology modeling to be a powerful and generally applicable approach to elucidate gene regulatory mechanisms of cellular state transitions.

Computational study of parameter sensitivity in DevR regulated gene expression

The DevRS two-component system plays a pivotal role in signal transmission and downstream gene regulation in Mycobacterium tuberculosis. Under the hypoxic condition, phosphorylated DevR interacts with multiple binding sites at the promoter region of the target genes. In the present work, we carried out a detailed computational analysis to figure out the sensitivity of the kinetic parameters. The set of kinetic parameters takes care of the interaction among phosphorylated DevR and the binding sites, transcription and translation processes. We employ the method of stochastic optimization to quantitate the relevant kinetic parameter set necessary for DevR regulated gene expression. Measures of different correlation coefficients provide the relative ordering of kinetic parameters involved in gene regulation. Results obtained from correlation coefficients are further corroborated by sensitivity amplification.

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.

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.

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.