Pablo Padilla-Longoria

A Gene Regulatory Network Model for Cell-Fate Determination during Arabidopsis thaliana Flower Development That Is Robust and Recovers Experimental Gene Expression Profiles

Flowers are icons in developmental studies of complex structures. The vast majority of 250,000 angiosperm plant species have flowers with a conserved organ plan bearing sepals, petals, stamens, and carpels in the center. The combinatorial model for the activity of the so-called ABC homeotic floral genes has guided extensive experimental studies in Arabidopsis thaliana and many other plant species. However, a mechanistic and dynamical explanation for the ABC model and prevalence among flowering plants is lacking. Here, we put forward a simple discrete model that postulates logical rules that formally summarize published ABC and non-ABC gene interaction data for Arabidopsis floral organ cell fate determination and integrates this data into a dynamic network model. This model shows that all possible initial conditions converge to few steady gene activity states that match gene expression profiles observed experimentally in primordial floral organ cells of wild-type and mutant plants. Therefore, the network proposed here provides a dynamical explanation for the ABC model and shows that precise signaling pathways are not required to restrain cell types to those found in Arabidopsis, but these are rather determined by the overall gene network dynamics. Furthermore, we performed robustness analyses that clearly show that the cell types recovered depend on the network architecture rather than on specific values of the models gene interaction parameters. These results support the hypothesis that such a network constitutes a developmental module, and hence provide a possible explanation for the overall conservation of the ABC model and overall floral plan among angiosperms. In addition, we have been able to predict the effects of differences in network architecture between Arabidopsis and Petunia hybrida.

Floral Morphogenesis: Stochastic Explorations of a Gene Network Epigenetic Landscape

In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical temporal pattern in gene expression during flower development. We modeled the regulatory network of organ identity genes in the Arabidopsis thaliana flower as a stochastic system. This network has previously been shown to converge to ten fixed-point attractors, each with gene expression arrays that characterize inflorescence cells and primordial cells of sepals, petals, stamens, and carpels. The network used is binary, and the logical rules that govern its dynamics are grounded in experimental evidence. We introduced different levels of uncertainty in the updating rules of the network. Interestingly, for a level of noise of around 0.5–10%, the system exhibited a sequence of transitions among attractors that mimics the sequence of gene activation configurations observed in real flowers. We also implemented the gene regulatory network as a continuous system using the Glass model of differential equations, that can be considered as a first approximation of kinetic-reaction equations, but which are not necessarily equivalent to the Boolean model. Interestingly, the Glass dynamics recover a temporal sequence of attractors, that is qualitatively similar, although not identical, to that obtained using the Boolean model. Thus, time ordering in the emergence of cell-fate patterns is not an artifact of synchronous updating in the Boolean model. Therefore, our model provides a novel explanation for the emergence and robustness of the ubiquitous temporal pattern of floral organ specification. It also constitutes a new approach to understanding morphogenesis, providing predictions on the population dynamics of cells with different genetic configurations during development.

Single-Cell Profiling of Epigenetic Modifiers Identifies PRDM14 as an Inducer of Cell Fate in the Mammalian Embryo

Cell plasticity or potency is necessary for the formation of multiple cell types. The mechanisms underlying this plasticity are largely unknown. Preimplantation mouse embryos undergo drastic changes in cellular potency, starting with the totipotent zygote through to the formation of the pluripotent inner cell mass (ICM) and differentiated trophectoderm in the blastocyst. Here, we set out to identify and functionally characterize chromatin modifiers that define the transitions of potency and cell fate in the mouse embryo. Using a quantitative microfluidics approach in single cells, we show that developmental transitions are marked by distinctive combinatorial profiles of epigenetic modifiers. Pluripotent cells of the ICM are distinct from their differentiated trophectoderm counterparts. We show that PRDM14 is heterogeneously expressed in 4-cell-stage embryos. Forced expression of PRDM14 at the 2-cell stage leads to increased H3R26me2 and can induce a pluripotent ICM fate. Our results shed light on the epigenetic networks that govern cellular potency and identity in vivo.

From ABC genes to regulatory networks, epigenetic landscapes and flower morphogenesis: making biological sense of theoretical approaches.

The ABC model postulates that expression combinations of three classes of genes (A, B and C) specify the four floral organs at early stages of flower development. This classic model provides a solid framework to study flower development and has been the foundation for multiple studies in different plant species, as well as for new evolutionary hypotheses. Nevertheless, it has been shown that in spite of being necessary, these three gene classes are not sufficient for flower organ specification. Rather, flower organ specification depends on complex interactions of several genes, and probably other non-genetic factors. Being useful to study systems of complex interactions, mathematical and computational models have enlightened the origin of the A, B and C stereotyped and robust expression patterns and the process of early flower morphogenesis. Here, we present a brief introduction to basic modeling concepts and techniques and review the results that these models have rendered for the particular case of the Arabidopsis thaliana flower organ specification. One of the main results is the uncovering of a robust functional module that is sufficient to recover the gene configurations characterizing flower organ primordia. Another key result is that the temporal sequence with which such gene configurations are attained may be recovered only by modeling the aforementioned functional module as a noisy or stochastic system. Finally, modeling approaches enable testable predictions regarding the role of non-genetic factors (noise, mechano-elastic forces, etc.) in development. These predictions, along with some perspectives for future work, are also reviewed and discussed.

Interlinked nonlinear subnetworks underlie the formation of robust cellular patterns in Arabidopsis epidermis: a dynamic spatial model

BackgroundDynamical models are instrumental for exploring the way information required to generate robust developmental patterns arises from complex interactions among genetic and non-genetic factors. We address this fundamental issue of developmental biology studying the leaf and root epidermis of Arabidopsis. We propose an experimentally-grounded model of gene regulatory networks (GRNs) that are coupled by protein diffusion and comprise a meta-GRN implemented on cellularised domains.ResultsSteady states of the meta-GRN model correspond to gene expression profiles typical of hair and non-hair epidermal cells. The simulations also render spatial patterns that match the cellular arrangements observed in root and leaf epidermis. As in actual plants, such patterns are robust in the face of diverse perturbations. We validated the model by checking that it also reproduced the patterns of reported mutants. The meta-GRN model shows that interlinked sub-networks contribute redundantly to the formation of robust hair patterns and permits to advance novel and testable predictions regarding the effect of cell shape, signalling pathways and additional gene interactions affecting spatial cell-patterning.ConclusionThe spatial meta-GRN model integrates available experimental data and contributes to further understanding of the Arabidopsis epidermal system. It also provides a systems biology framework to explore the interplay among sub-networks of a GRN, cell-to-cell communication, cell shape and domain traits, which could help understanding of general aspects of patterning processes. For instance, our model suggests that the information needed for cell fate determination emerges from dynamic processes that depend upon molecular components inside and outside differentiating cells, suggesting that the classical distinction of lineage versus positional cell differentiation may be instrumental but rather artificial. It also suggests that interlinkage of nonlinear and redundant sub-networks in larger networks is important for pattern robustness. Pursuing dynamic analyses of larger (genomic) coupled networks is still not possible. A repertoire of well-characterised regulatory modules, like the one presented here, will, however, help to uncover general principles of the patterning-associated networks, as well as the peculiarities that originate diversity.

Dynamic Network-Based Epistasis Analysis: Boolean Examples

In this article we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the inference of gene regulatory networks. Here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson, epistasis is defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus (herein, classical epistasis). Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct inference of gene interaction topologies is hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our article complements previous accounts, not only by focusing on the implications of the hierarchical and single-path assumption, but also by demonstrating the importance of considering temporal dynamics, and specifically introducing the usefulness of Boolean network models and also reviewing some key properties of network approaches.

Gene Regulatory Models for Plant Development and Evolution

We argue for the need of mathematical models as integrative tools for understanding processes of cell differentiation and morphogenesis, involving the concerted action of multiple components at different spatiotemporal scales during plant development. We propose dynamical models of gene regulatory networks (GRNs) as the basis for such means. Such models enable the identification of specific steady-state gene expression patterns (attractors), which correspond to different cell types. A comparison between discrete and continuous models is then presented, and we propose that the dynamical structure of a GRN subject to noise conceptually corresponds to Waddingtons “epigenetic landscape”. In the third section, we review methods to infer GRN topology from microarray experiments. These include reverse engineering techniques such as Bayesian networks, mutual information, and continuous analysis models. We discuss the application of these approaches to plant cases. However, detailed molecular biology experiments have been very successful in deciphering the structure of underlying small networks. Therefore, we then focus our attention on GRN models of such small modules for various processes of plant development. The first example corresponds to a single-cell GRN for primordial cell specification during early stages of Arabidopsis thaliana flower development. Then, some examples of coupled GRN dynamics in spatiotemporal domains are recalled: cell differentiation in A. thaliana leaf and root epidermis, and the spatiotemporal pattern of genes responsible for the apical shoot meristem behavior. Furthermore, we consider models on auxin transport mechanisms that are sufficient to generate observed morphogenetic shoot and root patterns. We also present several approaches to model signal transduction pathways that consider crosstalk among several biochemical pathways, as well as the influence of environmental factors. In Section 1.5 we consider the constructive role of noise in pattern formation in complex systems. We finally conclude that studies on GRN structure and dynamics aid at understanding evolutionary morphological patterns.

Spatial dynamics of floral organ formation

Understanding the emergence of biological structures and their changes is a complex problem. On a biochemical level, it is based on gene regulatory networks (GRN) consisting on interactions between the genes responsible for cell differentiation and coupled in a greater scale with external factors. In this work we provide a systematic methodological framework to construct Waddingtons epigenetic landscape of the GRN involved in cellular determination during the early stages of development of angiosperms. As a specific example we consider the flower of the plant Arabidopsis thaliana. Our model, which is based on experimental data, recovers accurately the spatial configuration of the flower during cell fate determination, not only for the wild type, but for its homeotic mutants as well. The method developed in this project is general enough to be used in the study of the relationship between genotype-phenotype in other living organisms.

Ultradian Rhythms Underlying the Dynamics of the Circadian Pacemaker

Before discussing rhythms and pacemakers, we would like to begin this chapter by quoting Albert Einstein (Einstein, 1934): “Our experience hitherto justifies us in trusting that nature is the realization of the simplest that is mathematically conceivable. I am convinced that purely mathematical construction enables us to find those concepts and those lawlike connections between them that provide the key to the understanding of natural phenomena”. Indeed, it seems that nature can be described and understood in mathematical terms. In the context of physical phenomena nobody can deny the usefulness, applicability and relevance of mathematical models. However, as strange and paradoxical as it might appear, the importance of mathematics in biology is still questioned. In the case of biological systems it is particularly important to discuss whether this confidence is based on facts. Among life scientists it is a widespread opinion that mathematical models just put in very complicated terms what they already knew. On the other hand this is in sharp contrast with what Darwin expresses in a letter, regretting not having deepened in some basic mathematical principles (Nowak, 2006). Mathematical models incorporate experimental information, both, quantitative and qualitative. Models have to mimic the observed behavior, but this is not enough. They have to allow for the understanding of the mechanisms underlying the studied phenomenon and also have to be able to make predictions (again, both qualitative and quantitative). The construction of a mathematical model is not an unidirectional process. The feedback at the different stages of the process is one of the most important and useful characteristics (see Figure 1). A mathematical model provides the necessary elements to compare and even discard different hypotheses, and, in many cases, to propose new experiments (FuentesPardo et al., 2005). Just to provide a few examples in which the construction of a mathematical model has been essential in the understanding of a biological process we mention the work by Hodgkin and Huxley in the early fifties, on the existence of selective ion channels on the membrane of a neuron. Their model not only enabled them to test this hypothesis, namely, but also to deduce qualitative properties of the transmission of electrical impulses, leading to the notion of action potential (Hodkgin et al., 1952a; Hodgkin & Huxley, 1952b, 1952c, 1952d, 1952e). In