Gene Regulatory Network Dynamical Logical Models for Plant Development.

Mathematical and computational approaches that integrate and model the concerted action of multiple genetic and nongenetic components holding highly nonlinear interactions are fundamental for the study of developmental processes. Among these, gene regulatory network (GRN) dynamical models are very useful to understand how diverse types of regulatory constraints restrict the multigene expression patterns that characterize different cell fates. In this chapter we present a hands-on approach to model GRN dynamics, taking as a working example a well-curated and experimentally grounded GRN developmental module proposed by our group: the flower organ specification gene regulatory network (FOS-GRN). We demonstrate how to build and analyze a GRN model according to the following steps: (1) integration of molecular genetic data and formulation of logical rules specifying the dynamic behavior of each gene; (2) determination of steady states (attractors) corresponding to each cell type; (3) validation of the GRN model; and (4) extension of the deterministic model with the inclusion of stochasticity in order to model cell-state transitions dependent on noise due to fluctuations of the involved gen products. The methodologies explained here in detail can be applied to any other developmental module.

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.

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.

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.

Case Studies.

The aim of this chapter is to illustrate the modeling procedures discussed in the previous chapter via three well-chosen examples.

Boolean Dynamic Modeling Approaches to Study Plant Gene Regulatory Networks: Integration, Validation, and Prediction.

Mathematical models based on dynamical systems theory are well-suited tools for the integration of available molecular experimental data into coherent frameworks in order to propose hypotheses about the cooperative regulatory mechanisms driving developmental processes. Computational analysis of the proposed models using well-established methods enables testing the hypotheses by contrasting predictions with observations. Within such framework, Boolean gene regulatory network dynamical models have been extensively used in modeling plant development. Boolean models are simple and intuitively appealing, ideal tools for collaborative efforts between theorists and experimentalists. In this chapter we present protocols used in our group for the study of diverse plant developmental processes. We focus on conceptual clarity and practical implementation, providing directions to the corresponding technical literature.

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.

Retroactivity effects dependency on the transcription factors binding mechanisms.

Downstream connection effects on transcription are caused by retroactivity. When biomolecular dynamical systems interconnect retroactivity is a property that becomes important. The biological functional meaning of these effects is increasingly becoming an area of interest. Downstream targets, which are operator binding sites in transcriptional networks, may induce behaviors such as ultrasensitive responses or even represent an undesired issue in regulation. To the best of our knowledge, the role of the binding mechanisms of transcription factors in relation to minimizing - or enhancing - retroactivity effects has not been previously addressed. Our aim is to evaluate retroactivity effects considering how the binding mechanism impacts the number of free functional transcription factor (FFTF) molecules using a simple model via deterministic and stochastic simulations. We study four transcription factor binding mechanisms (BM): simple monomer binding (SMB), dimer binding (DB), cooperative sequential binding (CSB) and cooperative sequential binding with dimerization (CSB_D). We consider weak and strong binding regimes for each mechanism, where we contrast the cases when the FFTF is bound or unbound to the downstream loads. Upon interconnection, the number of FFTF molecules changed less for the SMB mechanism while for DB they changed the most. Our results show that for the chosen mechanisms (in terms of the corresponding described dynamics), retroactivity effects depend on transcription binding mechanisms. This contributes to the understanding of how the transcription factor regulatory function-such as decision making-and its dynamic needs for the response, may determine the nature of the selected binding mechanism.

Retroactivity in the Context of Modularly Structured Biomolecular Systems.

Synthetic biology has intensively promoted the technical implementation of modular strategies in the fabrication of biological devices. Modules are considered as networks of reactions. The behavior displayed by biomolecular systems results from the information processes carried out by the interconnection of the involved modules. However, in natural systems, module wiring is not a free-of-charge process; as a consequence of interconnection, a reactive phenomenon called retroactivity emerges. This phenomenon is characterized by signals that propagate from downstream modules (the modules that receive the incoming signals upon interconnection) to upstream ones (the modules that send the signals upon interconnection). Such retroactivity signals, depending of their strength, may change and sometimes even disrupt the behavior of modular biomolecular systems. Thus, analysis of retroactivity effects in natural biological and biosynthetic systems is crucial to achieve a deeper understanding of how this interconnection between functionally characterized modules takes place and how it impacts the overall behavior of the involved cell. By discussing the modules interconnection in natural and synthetic biomolecular systems, we propose that such systems should be considered as quasi-modular.