Reshaping the epigenetic landscape during early flower development: induction of attractor transitions by relative differences in gene decay rates

Dissecting Mechanisms of Epigenetic Memory Through Computational Modeling

Understanding the mechanistic basis of epigenetic memory has proven to be a difficult task due to the underlying complexity of the systems involved in its establishment and maintenance. Here, we review the role of computational modeling in helping to unlock this complexity, allowing the dissection of intricate feedback dynamics. We focus on three forms of epigenetic memory encoded in gene regulatory networks, DNA methylation, and histone modifications and discuss the important advantages offered by plant systems in their dissection. We summarize the main modeling approaches involved and highlight the principal conceptual advances that the modeling has enabled through iterative cycles of predictive modeling and experiments. Lastly, we discuss remaining gaps in our understanding and how intertwined theory and experimental approaches might help in their resolution.

Inferring gene regulatory networks using transcriptional profiles as dynamical attractors

Genetic regulatory networks (GRNs) regulate the flow of genetic information from the genome to expressed messenger RNAs (mRNAs) and thus are critical to controlling the phenotypic characteristics of cells. Numerous methods exist for profiling mRNA transcript levels and identifying protein-DNA binding interactions at the genome-wide scale. These enable researchers to determine the structure and output of transcriptional regulatory networks, but uncovering the complete structure and regulatory logic of GRNs remains a challenge. The field of GRN inference aims to meet this challenge using computational modeling to derive the structure and logic of GRNs from experimental data and to encode this knowledge in Boolean networks, Bayesian networks, ordinary differential equation (ODE) models, or other modeling frameworks. However, most existing models do not incorporate dynamic transcriptional data since it has historically been less widely available in comparison to "static" transcriptional data. We report the development of an evolutionary algorithm-based ODE modeling approach (named EA) that integrates kinetic transcription data and the theory of attractor matching to infer GRN architecture and regulatory logic. Our method outperformed six leading GRN inference methods, none of which incorporate kinetic transcriptional data, in predicting regulatory connections among TFs when applied to a small-scale engineered synthetic GRN in Saccharomyces cerevisiae. Moreover, we demonstrate the potential of our method to predict unknown transcriptional profiles that would be produced upon genetic perturbation of the GRN governing a two-state cellular phenotypic switch in Candida albicans. We established an iterative refinement strategy to facilitate candidate selection for experimentation; the experimental results in turn provide validation or improvement for the model. In this way, our GRN inference approach can expedite the development of a sophisticated mathematical model that can accurately describe the structure and dynamics of the in vivo GRN.

Uncoding the interdependency of tumor microenvironment and macrophage polarization: insights from a continuous network approach

The balance between pro- and anti-inflammatory immune system responses is crucial to preventing complex diseases like cancer. Macrophages are essential immune cells that contribute to this balance constrained by the local signaling profile of the tumor microenvironment. To understand how pro- and anti-inflammatory unbalance emerges in cancer, we developed a theoretical analysis of macrophage differentiation that is derived from activated monocytes circulating in the blood. Once recruited to the site of inflammation, monocytes can be polarized based on the specific interleukins and chemokines in the microenvironment. To quantify this process, we used a previous regulatory network reconstructed by our group and transformed Boolean Network attractors of macrophage polarization to an ODE scheme, it enables us to quantify the activation of their genes in a continuous fashion. The transformation was developed using the interaction rules with a fuzzy logic approach. By implementing this approach, we analyzed different aspects that cannot be visualized in the Boolean setting. For example, this approach allows us to explore the dynamic behavior at different concentrations of cytokines and transcription factors in the microenvironment. One important aspect to assess is the evaluation of the transitions between phenotypes, some of them characterized by an abrupt or a gradual transition depending on specific concentrations of exogenous cytokines in the tumor microenvironment. For instance, IL-10 can induce a hybrid state that transits between an M2c and an M2b macrophage. Interferon- γ can induce a hybrid between M1 and M1a macrophage. We further demonstrated the plasticity of macrophages based on a combination of cytokines and the existence of hybrid phenotypes or partial polarization. This mathematical model allows us to unravel the patterns of macrophage differentiation based on the competition of expression of transcriptional factors. Finally, we survey how macrophages may respond to a continuously changing immunological response in a tumor microenvironment.

Leveraging developmental landscapes for model selection in Boolean gene regulatory networks

Boolean models are a well-established framework to model developmental gene regulatory networks (DGRNs) for acquisition of cellular identities. During the reconstruction of Boolean DGRNs, even if the network structure is given, there is generally a large number of combinations of Boolean functions that will reproduce the different cell fates (biological attractors). Here we leverage the developmental landscape to enable model selection on such ensembles using the relative stability of the attractors. First we show that previously proposed measures of relative stability are strongly correlated and we stress the usefulness of the one that captures best the cell state transitions via the mean first passage time (MFPT) as it also allows the construction of a cellular lineage tree. A property of great computational importance is the insensitivity of the different stability measures to changes in noise intensities. That allows us to use stochastic approaches to estimate the MFPT and thereby scale up the computations to large networks. Given this methodology, we revisit different Boolean models of Arabidopsis thaliana root development, showing that a most recent one does not respect the biologically expected hierarchy of cell states based on relative stabilities. We therefore developed an iterative greedy algorithm that searches for models which satisfy the expected hierarchy of cell states and found that its application to the root development model yields many models that meet this expectation. Our methodology thus provides new tools that can enable reconstruction of more realistic and accurate Boolean models of DGRNs.

Identification of dynamic driver sets controlling phenotypical landscapes

Controlling phenotypical landscapes is of vital interest to modern biology. This task becomes highly demanding because cellular decisions involve complex networks engaging in crosstalk interactions. Previous work on control theory indicates that small sets of compounds can control single phenotypes. However, a dynamic approach is missing to determine the drivers of the whole network dynamics. By analyzing 35 biologically motivated Boolean networks, we developed a method to identify small sets of compounds sufficient to decide on the entire phenotypical landscape. These compounds do not strictly prefer highly related compounds and show a smaller impact on the stability of the attractor landscape. The dynamic driver sets include many intervention targets and cellular reprogramming drivers in human networks. Finally, by using a new comprehensive model of colorectal cancer, we provide a complete workflow on how to implement our approach to shift from in silico to in vitro guided experiments.

The flowering transition pathways converge into a complex gene regulatory network that underlies the phase changes of the shoot apical meristem in Arabidopsis thaliana

Post-embryonic plant development is characterized by a period of vegetative growth during which a combination of intrinsic and extrinsic signals triggers the transition to the reproductive phase. To understand how different flowering inducing and repressing signals are associated with phase transitions of the Shoot Apical Meristem (SAM), we incorporated available data into a dynamic gene regulatory network model for Arabidopsis thaliana. This Flowering Transition Gene Regulatory Network (FT-GRN) formally constitutes a dynamic system-level mechanism based on more than three decades of experimental data on flowering. We provide novel experimental data on the regulatory interactions of one of its twenty-three components: a MADS-box transcription factor XAANTAL2 (XAL2). These data complement the information regarding flowering transition under short days and provides an example of the type of questions that can be addressed by the FT-GRN. The resulting FT-GRN is highly connected and integrates developmental, hormonal, and environmental signals that affect developmental transitions at the SAM. The FT-GRN is a dynamic multi-stable Boolean system, with 2²³ possible initial states, yet it converges into only 32 attractors. The latter are coherent with the expression profiles of the FT-GRN components that have been experimentally described for the developmental stages of the SAM. Furthermore, the attractors are also highly robust to initial states and to simulated perturbations of the interaction functions. The model recovered the meristem phenotypes of previously described single mutants. We also analyzed the attractors landscape that emerges from the postulated FT-GRN, uncovering which set of signals or components are critical for reproductive competence and the time-order transitions observed in the SAM. Finally, in the context of such GRN, the role of XAL2 under short-day conditions could be understood. Therefore, this model constitutes a robust biological module and the first multi-stable, dynamical systems biology mechanism that integrates the genetic flowering pathways to explain SAM phase transitions.

Using linkage logic theory to control dynamics of a gene regulatory network of a chordate embryo

Linkage logic theory provides a mathematical criterion to control network dynamics by manipulating activities of a subset of network nodes, which are collectively called a feedback vertex set (FVS). Because many biological functions emerge from dynamics of biological networks, this theory provides a promising tool for controlling biological functions. By manipulating the activity of FVS molecules identified in a gene regulatory network (GRN) for fate specification of seven tissues in ascidian embryos, we previously succeeded in reproducing six of the seven cell types. Simultaneously, we discovered that the experimentally reconstituted GRN lacked information sufficient to reproduce muscle cells. Here, we utilized linkage logic theory as a tool to find missing edges in the GRN. Then, we identified a FVS from an updated version of the GRN and confirmed that manipulating the activity of this FVS was sufficient to induce all seven cell types, even in a multi-cellular environment. Thus, linkage logic theory provides tools to find missing edges in experimentally reconstituted networks, to determine whether reconstituted networks contain sufficient information to fulfil expected functions, and to reprogram cell fate.

Multi-level gene regulatory network models to understand complex mechanisms underlying plant development

Patterning in plant development is the emergent outcome of the feedback-based interplay between tissue-coupled intracellular regulatory networks and physicochemical fields. This interplay gives rise to dynamics that evolve on a wide spectrum of spatiotemporal scales. This imposes important challenges for computational approaches to model the dynamics of plant development. These challenges are being tackled in recent times by computational and mathematical advances that have made progress in the modelling of regulatory networks, as well as in approaches to couple the latter to physicochemical fields. Efforts in this direction are fundamental to identify the dynamical constraints that emerge from non-cellular autonomous activity in cell-fate decisions and patterning, and requires an understanding of how multi-level and multi-scale processes are coupled. Here, we discuss the use of multi-level modeling and simulation tools for the study of multicellular systems, with emphasis on plants. As illustrative examples, we discuss recent works elucidating the mechanisms that underlie patterning in the root meristem of Arabidopsis thaliana, and in plant responses to environmental conditions.

Type 2 diabetes progression: A regulatory network approach

In order to elucidate central elements underlying type 2 diabetes, we constructed a regulatory network model involving 37 components (molecules, receptors, processes, etc.) associated to signaling pathways of pancreatic beta-cells. In a first approximation, the network topology was described by Boolean rules whose interacting dynamics predicted stationary patterns broadly classified as health, metabolic syndrome, and diabetes stages. A subsequent approximation based on a continuous logic analysis allowed us to characterize the progression of the disease as transitions between these states associated to alterations of cell homeostasis due to exhaustion or exacerbation of specific regulatory signals. The method allowed the identification of key transcription factors involved in metabolic stress as essential for the progression of the disease. Integration of the present analysis with existent mathematical models designed to yield accurate account of experimental data in human or animal essays leads to reliable predictions for beta-cell mass, insulinemia, glycemia, and glycosylated hemoglobin in diabetic fatty rats.

A system-level mechanistic explanation for asymmetric stem cell fates: Arabidopsis thaliana root niche as a study system

Asymmetric divisions maintain long-term stem cell populations while producing new cells that proliferate and then differentiate. Recent reports in animal systems show that divisions of stem cells can be uncoupled from their progeny differentiation, and the outcome of a division could be influenced by microenvironmental signals. But the underlying system-level mechanisms, and whether this dynamics also occur in plant stem cell niches (SCN), remain elusive. This article presents a cell fate regulatory network model that contributes to understanding such mechanism and identify critical cues for cell fate transitions in the root SCN. Novel computational and experimental results show that the transcriptional regulator SHR is critical for the most frequent asymmetric division previously described for quiescent centre stem cells. A multi-scale model of the root tip that simulated each cell's intracellular regulatory network, and the dynamics of SHR intercellular transport as a cell-cell coupling mechanism, was developed. It revealed that quiescent centre cell divisions produce two identical cells, that may acquire different fates depending on the feedback between SHR's availability and the state of the regulatory network. Novel experimental data presented here validates our model, which in turn, constitutes the first proposed systemic mechanism for uncoupled SCN cell division and differentiation.

Quantitative Modelling of the Waddington Epigenetic Landscape

C.H. Waddington introduced the epigenetic landscape as a metaphor to represent cellular decision-making during development. Like a population of balls rolling down a rough hillside, developing cells follow specific trajectories (valleys) and eventually come to rest in one or another low-energy state that represents a mature cell type. Waddington depicted the topography of this landscape as determined by interactions among gene products, thereby connecting genotype to phenotype. In modern terms, each point on the landscape represents a state of the underlying genetic regulatory network, which in turn is described by a gene expression profile. In this chapter we demonstrate how the mathematical formalism of Hopfield networks can be used to model this epigenetic landscape. Hopfield networks are auto-associative artificial neural networks; input patterns are stored as attractors of the network and can be recalled from noisy or incomplete inputs. The resulting models capture the temporal dynamics of a gene regulatory network, yielding quantitative insight into cellular development and phenotype.

Medical Systems Biology

The aim of this volume is to encourage the use of systems-level methodologies to contribute to the improvement of human-health . We intend to motivate biomedical researchers to complement their current theoretical and empirical practice with up-to-date systems biology conceptual approaches. Our perspective is based on the deep understanding of the key biomolecular regulatory mechanisms that underlie health, as well as the emergence and progression of human-disease . We strongly believe that the contemporary systems biology perspective opens the door to the effective development of novel methodologies to the improvement of prevention . This requires a deeper and integrative understanding of the involved underlying systems-level mechanisms. In order to explain our proposal in a simple way, in this chapter we privilege the conceptual exposition of our chosen framework over formal considerations. The formal exposition of our proposal will be expanded and discussed later in the next chapters.

Modeling Procedures

Being concerned by the understanding of the mechanism underlying chronic degenerative diseases , we presented in the previous chapter the medical systems biology conceptual framework that we present for that purpose in this volume. More specifically, we argued there the clear advantages offered by a state-space perspective when applied to the systems-level description of the biomolecular machinery that regulates complex degenerative diseases. We also discussed the importance of the dynamical interplay between the risk factors and the network of interdependencies that characterizes the biochemical, cellular, and tissue-level biomolecular reactions that underlie the physiological processes in health and disease. As we pointed out in the previous chapter, the understanding of this interplay (articulated around cellular phenotypic plasticity properties, regulated by specific kinds of gene regulatory networks) is necessary if prevention is chosen as the human-health improvement strategy (potentially involving the modulation of the patient's lifestyle). In this chapter we provide the medical systems biology mathematical and computational modeling tools required for this task.

Role of Cytokine Combinations on CD4+ T Cell Differentiation, Partial Polarization, and Plasticity: Continuous Network Modeling Approach

Purpose: We put forward a theoretical and dynamical approach for the semi-quantitative analysis of CD4+ T cell differentiation, the process by which cells with different functions are derived from activated CD4+ T naïve lymphocytes in the presence of particular cytokine microenvironments. We explore the system-level mechanisms that underlie CD4+ T plasticity-the conversion of polarized cells to phenotypes different from those originally induced. Methods: In this paper, we extend a previous study based on a Boolean network to a continuous framework. The network includes transcription factors, signaling pathways, as well as autocrine and exogenous cytokines, with interaction rules derived using fuzzy logic. Results: This approach allows us to assess the effect of relative differences in the concentrations and combinations of exogenous and endogenous cytokines, as well as of the expression levels of diverse transcription factors. We found either abrupt or gradual differentiation patterns between observed phenotypes depending on critical concentrations of single or multiple environmental cytokines. Plastic changes induced by environmental cytokines were observed in conditions of partial phenotype polarization in the T helper 1 to T helper 2 transition. On the other hand, the T helper 17 to induced regulatory T-cells transition was highly dependent on cytokine concentrations, with TGFβ playing a prime role. Conclusion: The present approach is useful to further understand the system-level mechanisms underlying observed patterns of CD4+ T differentiation and response to changing immunological challenges.

NetLand: quantitative modeling and visualization of Waddington's epigenetic landscape using probabilistic potential

Summary

Waddington’s epigenetic landscape is a powerful metaphor for cellular dynamics driven by gene regulatory networks (GRNs). Its quantitative modeling and visualization, however, remains a challenge, especially when there are more than two genes in the network. A software tool for Waddington’s landscape has not been available in the literature. We present NetLand, an open-source software tool for modeling and simulating the kinetic dynamics of GRNs, and visualizing the corresponding Waddington’s epigenetic landscape in three dimensions without restriction on the number of genes in a GRN. With an interactive and graphical user interface, NetLand can facilitate the knowledge discovery and experimental design in the study of cell fate regulation (e.g. stem cell differentiation and reprogramming).

Availability and Implementation

NetLand can run under operating systems including Windows, Linux and OS X. The executive files and source code of NetLand as well as a user manual, example models etc. can be downloaded from http://netland-ntu.github.io/NetLand/.

Supplementary information

Supplementary data are available at Bioinformatics online.

Modeling the Epigenetic Landscape in Plant Development

Computational mechanistic models enable a systems-level understanding of plant development by integrating available molecular experimental data and simulating their collective dynamical behavior. Boolean gene regulatory network dynamical models have been extensively used as a qualitative modeling framework for such purpose. More recently, network modeling protocols have been extended to model the epigenetic landscape associated with gene regulatory networks. In addition to understanding the concerted action of interconnected genes, epigenetic landscape models aim to uncover the patterns of cell state transition events that emerge under diverse genetic and environmental background conditions. In this chapter we present simple protocols that naturally extend gene regulatory network modeling and demonstrate their use in modeling plant developmental processes under the epigenetic landscape framework. We focus on conceptual clarity and practical implementation, providing directions to the corresponding technical literature. The protocols presented here can be applied to any well-characterized gene regulatory network in plants, animals, or human disease.

The CD4+ T cell regulatory network mediates inflammatory responses during acute hyperinsulinemia: a simulation study

Background

Obesity is frequently linked to insulin resistance, high insulin levels, chronic inflammation, and alterations in the behaviour of CD4+ T cells. Despite the biomedical importance of this condition, the system-level mechanisms that alter CD4+ T cell differentiation and plasticity are not well understood.

Results

We model how hyperinsulinemia alters the dynamics of the CD4+ T regulatory network, and this, in turn, modulates cell differentiation and plasticity. Different polarizing microenvironments are simulated under basal and high levels of insulin to assess impacts on cell-fate attainment and robustness in response to transient perturbations. In the presence of high levels of insulin Th1 and Th17 become more stable to transient perturbations, and their basin sizes are augmented, Tr1 cells become less stable or disappear, while TGFβ producing cells remain unaltered. Hence, the model provides a dynamic system-level framework and explanation to further understand the documented and apparently paradoxical role of TGFβ in both inflammation and regulation of immune responses, as well as the emergence of the adipose Treg phenotype. Furthermore, our simulations provide new predictions on the impact of the microenvironment in the coexistence of the different cell types, suggesting that in pro-Th1, pro-Th2 and pro-Th17 environments effector and regulatory cells can coexist, but that high levels of insulin severely diminish regulatory cells, especially in a pro-Th17 environment.

Conclusions

This work provides a first step towards a system-level formal and dynamic framework to integrate further experimental data in the study of complex inflammatory diseases.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0436-y) contains supplementary material, which is available to authorized users.

Gene regulatory network underlying the immortalization of epithelial cells

BACKGROUND

Tumorigenic transformation of human epithelial cells in vitro has been described experimentally as the potential result of spontaneous immortalization. This process is characterized by a series of cell-state transitions, in which normal epithelial cells acquire first a senescent state which is later surpassed to attain a mesenchymal stem-like phenotype with a potentially tumorigenic behavior. In this paper we aim to provide a system-level mechanistic explanation to the emergence of these cell types, and to the time-ordered transition patterns that are common to neoplasias of epithelial origin. To this end, we first integrate published functional and well-curated molecular data of the components and interactions that have been found to be involved in such cell states and transitions into a network of 41 molecular components. We then reduce this initial network by removing simple mediators (i.e., linear pathways), and formalize the resulting regulatory core into logical rules that govern the dynamics of each of the network components as a function of the states of its regulators.

RESULTS

Computational dynamic analysis shows that our proposed Gene Regulatory Network model recovers exactly three attractors, each of them defined by a specific gene expression profile that corresponds to the epithelial, senescent, and mesenchymal stem-like cellular phenotypes, respectively. We show that although a mesenchymal stem-like state can be attained even under unperturbed physiological conditions, the likelihood of converging to this state is increased when pro-inflammatory conditions are simulated, providing a systems-level mechanistic explanation for the carcinogenic role of chronic inflammatory conditions observed in the clinic. We also found that the regulatory core yields an epigenetic landscape that restricts temporal patterns of progression between the steady states, such that recovered patterns resemble the time-ordered transitions observed during the spontaneous immortalization of epithelial cells, both in vivo and in vitro.

CONCLUSION

Our study strongly suggests that the in vitro tumorigenic transformation of epithelial cells, which strongly correlates with the patterns observed during the pathological progression of epithelial carcinogenesis in vivo, emerges from underlying regulatory networks involved in epithelial trans-differentiation during development.

Dynamic network modelling to understand flowering transition and floral patterning

Differentiation and morphogenetic processes during plant development are particularly robust. At the cellular level, however, plants also show great plasticity in response to environmental conditions, and can even reverse apparently terminal differentiated states with remarkable ease. Can we understand and predict both robust and plastic systemic responses as a general consequence of the non-trivial interplay between intracellular regulatory networks, extrinsic environmental signalling, and tissue-level mechanical constraints? Flower development has become an ideal model system to study these general questions of developmental biology, which are especially relevant to understanding stem cell patterning in plants, animals, and human disease. Decades of detailed study of molecular developmental genetics, as well as novel experimental techniques for in vivo assays in both wild-type and mutant plants, enable the postulation and testing of experimentally grounded mathematical and computational network dynamical models. Research in our group aims to explain the emergence of robust transitions that occur at the shoot apical meristem, as well as flower development, as the result of the collective action of key molecular components in regulatory networks subjected to intra-organismal signalling and extracellular constraints. Here we present a brief overview of recent work from our group, and that of others, focusing on the use of simple dynamical models to address cell-fate specification and cell-state stochastic dynamics during flowering transition and cell-state transitions at the shoot apical meristem of Arabidopsis thaliana. We also focus on how our work fits within the general field of plant developmental modelling, which is being developed by many others.