Megaphylls, present in the majority of vascular plants, show in many plant lineages an abaxial-adaxial polarity in their dorsoventral axis. This polarity commonly translates into different tissues developing on each side of the leaf blade. This is important because it promotes better photosynthetic efficiency as related to light absorption and gas exchange. Many researchers have studied the molecular bases of the emergence of leaf abaxial-adaxial polarity, showing that it is produced by the interaction and differential expression of particular genes and other molecules. However, until now, it is still unclear if the molecular components documented thus far are sufficient to explain the emergence of leaf polarity. In this work, we integrated the available experimental data to construct a graph of the Gene Regulatory Network (GRN) involved in the formation of abaxial-adaxial polarity in the leaf primordium of Arabidopsis thaliana. This graph consisted of 21 nodes and 47 regulations. We extracted the main components of the graph to obtain a Minimum Network consisting of six genes and 22 possible regulations. Then, we used the Boolean network (BN) formalism to describe the dynamics of this Minimum Network. We identified 1905 distinct BNs that comprised the regulations of the Minimum Network and exclusively generated the two attractors representing the abaxial and adaxial cell types. This highlights the fact that most graphs, including our network, can describe experimentally observed behaviors with many BN dynamics. By performing mutant simulations and robustness analysis, we found that two of the 1905 BNs better reproduce experimentally available information. To produce the expected attractors, both BNs predict the same missing regulations, which we propose should be experimentally analyzed to confirm their existence. Interestingly, these two BNs have low robustness to perturbations compared with previously analyzed GRNs. This was an unexpected result since abaxial-adaxial polarity is a robust biological trait, which suggests more components or regulations of the network are missing.

This paper leans on two similar areas so far detached from each other. On the one hand, Dung's pioneering contributions to abstract argumentation, almost thirty years ago, gave rise to a plethora of successors, including abstract dialectical frameworks (ADFs). On the other hand, Boolean networks (BNs), devised as models of gene regulation, have been successful for studying the behavior of molecular processes within cells. ADFs and BNs are similar to each other: both can be viewed as functions from vectors of bits to vectors of bits. As soon as similarities emerge between these two formalisms, however, differences appear. For example, conflict-freedom is prominent in argumentation (where we are interested in a self-consistent, i.e., conflict-free, set of beliefs) but absent in BNs. By contrast, asynchrony (where only one gene is updated at a time) is conspicuous in BNs and lacking in argumentation. Finally, while a monotonicity-based notion occurs in signed reasoning of both argumentation and gene regulation, a different, derivative-based notion only appears in the BN literature. To identify common mathematical structure between both formalisms, these differences need clarification. This contribution is a partial review of both these areas, where we cover enough ground to exhibit their more evident similarities, to then reconcile some of their apparent differences. We highlight a range of avenues of research resulting from ironing out discrepancies between these two fields. Unveiling their common concerns should enable these two areas to cross-fertilize so as to transfer ideas and results between each other.

Biological organisms have an immense diversity of forms. Some of them exhibit conspicuous and fascinating fractal structures that present self-similar patterns at all scales. How such structures are produced by biological processes is intriguing. In a recent publication, we used a multi-scale modelling approach to understand how gene activity can produce macroscopic cauliflower curds. Our work provides a plausible explanation for the appearance of fractal-like structures in plants, linking gene activity with development.

Double strand break (DSB) repair is critical to maintaining the integrity of the genome. DSB repair deficiency underlies multiple pathologies, including cancer, chromosome instability syndromes, and, potentially, neurodevelopmental defects. DSB repair is mainly handled by two pathways: highly accurate homologous recombination (HR), which requires a sister chromatid for template-based repair, limited to S/G2 phases of the cell cycle, and canonical non-homologous end joining (c-NHEJ), available throughout the cell cycle in which minimum homology is sufficient for highly efficient yet error-prone repair. Some circumstances, such as cancer, require alternative highly mutagenic DSB repair pathways like microhomology-mediated end-joining (MMEJ) and single-strand annealing (SSA), which are triggered to attend to DNA damage. These non-canonical repair alternatives are emerging as prominent drivers of resistance in drug-based tumor therapies. Multiple DSB repair options require tight inter-pathway regulation to prevent unscheduled activities. In addition to this complexity, epigenetic modifications of the histones surrounding the DSB region are emerging as critical regulators of the DSB repair pathway choice. Modeling approaches to understanding DSBs repair pathway choice are advantageous to perform simulations and generate predictions on previously uncharacterized aspects of DSBs response. In this work, we present a Boolean network model of the DSB repair pathway choice that incorporates the knowledge, into a dynamic system, of the inter-pathways regulation involved in DSB repair, i.e., HR, c-NHEJ, SSA, and MMEJ. Our model recapitulates the well-characterized HR activity observed in wild-type cells in response to DSBs. It also recovers clinically relevant behaviors of BRCA1/FANCS mutants, and their corresponding drug resistance mechanisms ascribed to DNA repair gain-of-function pathogenic variants. Since epigenetic modifiers are dynamic and possible druggable targets, we incorporated them into our model to better characterize their involvement in DSB repair. Our model predicted that loss of the TIP60 complex and its corresponding histone acetylation activity leads to activation of SSA in response to DSBs. Our experimental validation showed that TIP60 effectively prevents activation of RAD52, a key SSA executor, and confirms the suitable use of Boolean network modeling for understanding DNA DSB repair.

The study of biological tissues is extremely complicated, as they comprise mechanisms and properties at many different temporal and spatial scales. For this reason, modeling is becoming one of the most active and important research fields for the analysis and understanding of tissues. However, this is not a simple task, as it requires mathematical and computational skills, as well as the development of software tools for its implementation. Here, we provide an introduction covering some of the most important and basic issues for modeling tissues. In particular, we focus on both the chemical and cellular properties of a tissue. We explain how to represent and couple these properties within a virtual tissue. All our examples were done using Multicell, a Python library that simplifies their reproducibility, even by readers with little experience in biological modeling.

Throughout development, plant meristems regularly produce organs in defined spiral, opposite, or whorl patterns. Cauliflowers present an unusual organ arrangement with a multitude of spirals nested over a wide range of scales. How such a fractal, self-similar organization emerges from developmental mechanisms has remained elusive. Combining experimental analyses in an Arabidopsis thaliana cauliflower-like mutant with modeling, we found that curd self-similarity arises because the meristems fail to form flowers but keep the "memory" of their transient passage in a floral state. Additional mutations affecting meristem growth can induce the production of conical structures reminiscent of the conspicuous fractal Romanesco shape. This study reveals how fractal-like forms may emerge from the combination of key, defined perturbations of floral developmental programs and growth dynamics.

The arrangement of plant organs, called phyllotaxis, produce remarkable spiral or whorled patterns. Cauliflowers present a unique phyllotaxis with a multitude of spirals over a wide range of scales. How such a self-similar fractal organization emerges from developmental mechanisms has remained elusive. Combining experimental assays with modeling, we found that cauliflowers arise due to the hysteresis of the bistable floral network that generates inflorescences imprinted by a transient floral state. We further show how additional mutations affecting meristem growth dynamics can induce the production of conical phyllotactic structures reminiscent of the conspicuous fractal Romanesco shape. This study reveals how the spectacular morphological modification of the inflorescences in cauliflower and Romanesco shape arises from the hysteresis of the genetic programs controlling inflorescence development. One Sentence Summary The molecular making of cauliflowers

Gene expression noise is not just ubiquitous but also variable, and we still do not understand some of the most elementary factors that affect it. Among them is the residence time of a transcription factor (TF) on DNA, the mean time that a DNA-bound TF remains bound. Here, we use a stochastic model of transcriptional regulation to study how residence time affects the gene expression noise that arises when a TF induces gene expression. We find that the effect of residence time on gene expression noise depends on the TF's concentration and its affinity to DNA, which determine the level of induction of the gene. At high levels of induction, residence time has no effect on gene expression noise. However, as the level of induction decreases, short residence times reduce gene expression noise. The reason is that fast on-off TF binding dynamics prevent long periods where proteins are predominantly synthesized or degraded, which can cause excessive fluctuations in gene expression. As a consequence, short residence times can help a gene regulation system acquire information about the cellular environment it operates in. Our predictions are consistent with the observation that experimentally measured residence times are usually modest and lie between seconds to minutes.

All living systems acquire information about their environment. At the cellular level, they do so through signaling pathways, which rely on interactions between molecules that detect and transmit the presence of an extracellular cue or signal to the cell’s interior. Such interactions are inherently stochastic and thus noisy. In classical information theory, a noisy communication channel degrades the amount of transmissible information relative to a noise-free channel. For this reason, one would expect that the kinetic parameters that determine a pathway’s operation minimize noise. We show that this is not the case under a wide range of biologically sensible parameter values. Specifically, we perform computational simulations of simple signaling systems, which show that a noisy molecular interaction dynamics is a necessary condition for information acquisition. Moreover, we show that optimal information acquisition, where a system reacts most sensitively to changes in the environment, can be obtained close to the maximal attainable level of noise in the system. Our work highlights the positive role that noise can have in biological information processing. Author summary The acquisition of information is fundamental for living systems, because the decisions they take based on such information directly affect survival and reproduction. The molecular mechanisms used by cells to acquire information are signaling pathways. The molecular interactions of signaling pathways, such as the binding of a signal to a receptor, are by nature noisy. This is important, because noise disrupts information. Hence, to maximize the acquisition of information, signaling pathways should minimize the noise of their molecular interactions. Here we show that a noisy dynamic of the molecular interactions can improve the acquisition of information, and that the maximal capacity to acquire information can be obtained with a close-to-maximal level of noise in a signaling pathway. Thus, contrary to expectations, noise can improve the acquisition of information in living systems.

[This corrects the article DOI: 10.1371/journal.pcbi.1005488.].

DNA damage adaptation (DDA) allows the division of cells with unrepaired DNA damage. DNA repair deficient cells might take advantage of DDA to survive. The Fanconi anemia (FA) pathway repairs DNA interstrand crosslinks (ICLs), and deficiencies in this pathway cause a fraction of breast and ovarian cancers as well as FA, a chromosome instability syndrome characterized by bone marrow failure and cancer predisposition. FA cells are hypersensitive to ICLs; however, DDA might promote their survival. We present the FA-CHKREC Boolean Network Model, which explores how FA cells might use DDA. The model integrates the FA pathway with the G2 checkpoint and the checkpoint recovery (CHKREC) processes. The G2 checkpoint mediates cell-cycle arrest (CCA) and the CHKREC activates cell-cycle progression (CCP) after resolution of DNA damage. Analysis of the FA-CHKREC network indicates that CHKREC drives DDA in FA cells, ignoring the presence of unrepaired DNA damage and allowing their division. Experimental inhibition of WIP1, a CHKREC component, in FA lymphoblast and cancer cell lines prevented division of FA cells, in agreement with the prediction of the model.

Boolean networks are important models of biochemical systems, located at the high end of the abstraction spectrum. A number of Boolean gene networks have been inferred following essentially the same method. Such a method first considers experimental data for a typically underdetermined “regulation” graph. Next, Boolean networks are inferred by using biological constraints to narrow the search space, such as a desired set of (fixed-point or cyclic) attractors. We describe Griffin, a computer tool enhancing this method. Griffin incorporates a number of well-established algorithms, such as Dubrova and Teslenko's algorithm for finding attractors in synchronous Boolean networks. In addition, a formal definition of regulation allows Griffin to employ “symbolic” techniques, able to represent both large sets of network states and Boolean constraints. We observe that when the set of attractors is required to be an exact set, prohibiting additional attractors, a naive Boolean coding of this constraint may be unfeasible. Such cases may be intractable even with symbolic methods, as the number of Boolean constraints may be astronomically large. To overcome this problem, we employ an Artificial Intelligence technique known as “clause learning” considerably increasing Griffin's scalability. Without clause learning only toy examples prohibiting additional attractors are solvable: only one out of seven queries reported here is answered. With clause learning, by contrast, all seven queries are answered. We illustrate Griffin with three case studies drawn from the Arabidopsis thaliana literature. Griffin is available at: http://turing.iimas.unam.mx/griffin.

Molecular regulation was initially assumed to follow both a unidirectional and a hierarchical organization forming pathways. Regulatory processes, however, form highly interlinked networks with non-hierarchical and non-unidirectional structures that contain statistically overrepresented circuits or motifs. Here, we analyze the behavior of pathways containing non-unidirectional (i.e. bidirectional) and non-hierarchical interactions that create motifs. In comparison with unidirectional and hierarchical pathways, our pathways have a high diversity of behaviors, characterized by the size and number of attractors. Motifs have been studied individually showing that feedback circuit motifs regulate the number and size of attractors. It is less clear what happens in molecular networks that usually contain multiple feedbacks. Here, we find that the way feedback circuits couple to each other (i.e., the combination of the functionalities of feedback circuits) regulate both the number and size of the attractors. We show that the different expected results of epistasis analysis (a method to infer regulatory interactions) are produced by many non-hierarchical and non-unidirectional structures. Thus, these structures cannot be correctly inferred by epistasis analysis. Finally, we show that the combinations of functionalities, combined with other network properties, allow for a better characterization of regulatory structures.

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.

This chapter presents models of the processes involved in floral initiation and development. It begins by briefy presenting models of hormonal transport. The focus is on two key aspects of floral development, namely floral initiation, due to the periodic local accumulation of auxin (a plant hormone) near the plant apex, and the genetic regulation of floral development. The main assumptions about auxin transport that have been proposed and tested in the literature are described, and it is shown how the use of models makes it possible to test assumptions expressed in terms of local cell-cell interaction rules and to check if they lead to patterning in the growing tissue that is consistent with observation. The gene regulatory networks (GRNs) that control the initial steps of floral development and differentiation are investigated. In a simplified form, this network contains dozens of components that interact with each other in space and time. The understanding of such a complex system also requires a modeling approach in order to quantify these interactions and analyze their properties. There are two main formalisms that are used to model GRN: the Boolean and the ODE formalisms. Both these are illustrated on a submodule of the floral GRN and their main advantages and drawbacks are discussed. It is shown how manipulations of the network models can be used to make predictions corresponding to possible biological manipulations of the GRN (e.g., loss-of-function mutants). Throughout, specific mathematical topics of particular interest for the development of these ideas are detailed in separate boxes which can be read relatively independently of the main text.

In this chapter we present models of processes involved in the initiation and development of a flower. In the first section, we briefly present models of hormonal transport. We focus on two key aspects of flower development, namely the initiation, due to the periodic local accumulation of auxin (a plant hormone) near at the plant apex, and the genetic regulation of its development. In the first section, we described the main assumptions about auxin transport that have been proposed and tested in the literature. We show how the use of models make it possible to test assumptions expressed in terms of local cell-to-cell interaction rules and to check if they lead to patterning in the growing tissue consistent with observation. Then, we investigated gene regulatory networks that controls the initial steps of flower development and differentiation. In a simplified form, this network contains a dozen of actors interacting with each other in space and time. The understanding of such a complex system here also requires a modeling approach in order to quantify these interactions and analyze their properties. We briefly present the two main formalisms that are used to model GRN: the Boolean and the ODE formalisms. We illustrate on a sub-module of the flower GRN both types of models and discuss their main advantages and drawbacks. We show how manipulations of the network models can be used to make predictions corresponding to possible biological manipulations of the GRN (e.g. loss-of-function mutants). Throughout the chapter, we highlight specific mathematical topics of particular interest to the development of the ideas developed in the different sections in separated boxes (called Math-boxes). The reading of these boxes is relatively independent of the main text.

Multicellularity has emerged and continues to emerge in a variety of lineages and under diverse environmental conditions. In order to attain individuality and integration, multicellular organisms must exhibit spatial cell differentiation, which in turn allows cell aggregates to robustly generate traits and behaviors at the multicellular level. Nevertheless, the mechanisms that may lead to the development of cellular differentiation and patterning in emerging multicellular organisms remain unclear. We briefly review two conceptual frameworks that have addressed this issue: the cooperation-defection framework and the dynamical patterning modules (DPMs) framework. Then, situating ourselves in the DPM formalism first put forward by S. A. Newman and collaborators, we state a hypothesis for cell differentiation and arrangement in cellular masses of emerging multicellular organisms. Our hypothesis is based on the role of the generic cell-to-cell communication and adhesion patterning mechanisms, which are two fundamental mechanisms for the evolution of multicellularity, and whose molecules seem to be well-conserved in extant multicellular organisms and their unicellular relatives. We review some fundamental ideas underlying this hypothesis and contrast them with empirical and theoretical evidence currently available. Next, we use a mathematical model to illustrate how the mechanisms and assumptions considered in the hypothesis we postulate may render stereotypical arrangements of differentiated cells in an emerging cellular aggregate and may contribute to the variation and recreation of multicellular phenotypes. Finally, we discuss the potential implications of our approach and compare them to those entailed by the cooperation-defection framework in the study of cell differentiation in the transition to multicellularity.

This work was designed to study the effect of loops in small networks with biological properties at the structural and dynamical level. Our results show the high impact that loops produce in these networks, which can be used to obtain better interpretation of experimental results.

In Arabidopsis thaliana, multiple genes involved in shoot apical meristem (SAM) transitions have been characterized, but the mechanisms required for the dynamic attainment of vegetative, inflorescence, and floral meristem (VM, IM, FM) cell fates during SAM transitions are not well understood. Here we show that a MADS-box gene, XAANTAL2 (XAL2/AGL14), is necessary and sufficient to induce flowering, and its regulation is important in FM maintenance and determinacy. xal2 mutants are late flowering, particularly under short-day (SD) condition, while XAL2 overexpressing plants are early flowering, but their flowers have vegetative traits. Interestingly, inflorescences of the latter plants have higher expression levels of LFY, AP1, and TFL1 than wild-type plants. In addition we found that XAL2 is able to bind the TFL1 regulatory regions. On the other hand, the basipetal carpels of the 35S::XAL2 lines lose determinacy and maintain high levels of WUS expression under SD condition. To provide a mechanistic explanation for the complex roles of XAL2 in SAM transitions and the apparently paradoxical phenotypes of XAL2 and other MADS-box (SOC1, AGL24) overexpressors, we conducted dynamic gene regulatory network (GRN) and epigenetic landscape modeling. We uncovered a GRN module that underlies VM, IM, and FM gene configurations and transition patterns in wild-type plants as well as loss and gain of function lines characterized here and previously. Our approach thus provides a novel mechanistic framework for understanding the complex basis of SAM development.