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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.

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.

The study of the concerted action of hormones and transcription factors is fundamental to understand cell differentiation and pattern formation during organ development. The root apical meristem of Arabidopsis thaliana is a useful model to address this. It has a stem cell niche near its tip conformed of a quiescent organizer and stem or initial cells around it, then a proliferation domain followed by a transition domain, where cells diminish division rate before transiting to the elongation zone; here, cells grow anisotropically prior to their final differentiation towards the plant base. A minimal model of the gene regulatory network that underlies cell-fate specification and patterning at the root stem cell niche was proposed before. In this study, we update and couple such network with both the auxin and cytokinin hormone signaling pathways to address how they collectively give rise to attractors that correspond to the genetic and hormonal activity profiles that are characteristic of different cell types along A. thaliana root apical meristem. We used a Boolean model of the genetic-hormonal regulatory network to integrate known and predicted regulatory interactions into alternative models. Our analyses show that, after adding some putative missing interactions, the model includes the necessary and sufficient components and regulatory interactions to recover attractors characteristic of the root cell types, including the auxin and cytokinin activity profiles that correlate with different cellular behaviors along the root apical meristem. Furthermore, the model predicts the existence of activity configurations that could correspond to the transition domain. The model also provides a possible explanation for apparently paradoxical cellular behaviors in the root meristem. For example, how auxin may induce and at the same time inhibit WOX5 expression. According to the model proposed here the hormonal regulation of WOX5 might depend on the cell type. Our results illustrate how non-linear multi-stable qualitative network models can aid at understanding how transcriptional regulators and hormonal signaling pathways are dynamically coupled and may underlie both the acquisition of cell fate and the emergence of hormonal activity profiles that arise during complex organ development.

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

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.

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.

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.

In his Editorial “Quo vadis, Mexican science?” (26 July, p. [301][1]), A. Lazcano expressed concern about cuts to the budget of the Mexican National Council of Science and Technology (CONACYT) and questioned my leadership of the organization. The data summarized here should allay Lazcano's concerns. In Mexico, the total budget for science, technology, and innovation (STI) in 2019 (77.3 billion MP) was the highest it has been in 7 years ([ 1 ][2]–[ 3 ][3]). Despite the 2.4 billion MP cut to CONACYT's funding in 2019, an efficient administration and coordination among federal sectors that receive STI resources have redirected other funds to support the scientific community more than ever ([ 1 ][2]–[ 3 ][3]). During previous years, there was limited or no support for basic science, and many high-quality proposals went unfunded. In 2019, 1.6 billion MP have been assigned to be transferred to fund high-rated peer-reviewed basic science projects ([ 3 ][3]). Calls for novel technological development and innovation approaches were recently announced. In addition, interdisciplinary projects geared toward the UN Sustainable Development Goals will be published soon; they address pressing challenges such as acute lymphoblastic leukemia, the most common cause of mortality in Mexican children ([ 4 ][4]–[ 6 ][5]). CONACYT allocated 5.65 billion MP to support Mexico's 27 public research centers in 2019 ([ 1 ][2]–[ 3 ][3]). By optimizing the use of such public resources, we are committed to improving conditions at these research centers. Additionally, all Mexican scientists are protected by the social health insurance system, and their private health insurance has been maintained in public universities. Lazcano worries that our changes could “extinguish international collaborations… and fuel a brain drain.” However, all students and scientists may continue to travel for scientific and educational goals as usual. Moreover, CONACYT has allocated more than 10 billion MP (41% of the total budget) to fund ongoing and new fellowships for Mexican graduate students and postgraduate researchers in national and international programs and to continue supporting international graduates and postgraduates to study in Mexico ([ 1 ][2]–[ 3 ][3]). Furthermore, 1.11 billion MP have been directed to support early career scientists. Finally, the National System of Researchers, administrated by CONACYT, complements the salary of over 30,000 colleagues at all levels of career development. This year, CONACYT has accepted over 3000 additional members through collegiate procedures ([ 1 ][2]–[ 3 ][3]). As a scientist, I would have never dared to ask for restrictions or, even worse, to exclude peer review or collegiate decisions, as Lazcano alleges. In contrast, we are proposing more rigorous evaluation mechanisms and regulations. These will be included in the new legal framework under discussion among scientists, students, technologists, entrepreneurs, and the public. Lazcano claims that I am opposed to “hegemonic rational Western science.” Proudly trained in Mexican and U.S. universities, I am convinced of the fundamental role of (Western) STI to face global challenges. However, in some cases where western development has fallen short, the diverse and deep cultures at the roots of our country could provide new approaches and valuable knowledge. 1. [↵][6]Presupuesto de Egresos de la Federacion para el Ejercicio Fiscal (PEF) 2018, Anexo 12 “Programa de Ciencia, Tecnologia e Innovacion”, Ramo 38 CONACYT (2018); [www.dof.gob.mx/nota_detalle.php?codigo=5506080&fecha=29/11/2017][7] [in Spanish]. 2. Presupuesto de Egresos de la Federacion para el Ejercicio Fiscal (PEF) 2019, Anexo 12 “Programa de Ciencia, Tecnologia e Innovacion”, Ramo 38 CONACYT (2019); [in Spanish]. 3. [↵][8]CONACYT, Transparencia focalizada: Avances del CONACYT 2013–2019 ([www.conacyt.gob.mx/index.php/transparencia/transparencia-focalizada][9]) [in Spanish]. 4. [↵][10]Centro Nacional para la Salud de la Infancia y Adolescencia. “Cancer infantil en Mexico” (2019); [www.gob.mx/salud%7Ccensia/articulos/cancer-infantil-en-mexico-130956][11] [in Spanish]. 5. 1. F. Bray , Cancer J. Clin. 68, 394 (2018). [OpenUrl][12] 6. [↵][13]Secretaria de Salud, “Cubos Dinamicos-poblacion: Proyecciones de la Poblacion municipal de Mexico 2010–2018” (CONAPO, 2019). 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Fuente TESIUNAM

Fuente TESIUNAM