A Boolean network model of the double-strand break repair pathway choice.

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.

Cauliflowers or how the perseverance of a plant to make flowers produces an amazing fractal structure.

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.

Les organismes biologiques possèdent une immense diversité de formes. Certains d'entre eux arborent des structures fractales remarquables et fascinantes présentant des motifs similaires à toutes les échelles. La manière dont ces structures sont produites par des processus biologiques est intrigante. Dans une publication récente, nous avons utilisé une approche de modélisation multi-échelle pour comprendre comment l'activité de certains gènes peut engendrer des pommes de chou-fleur macroscopiques. Notre travail fournit une explication plausible quant à l'apparition de structures de type fractal chez les plantes, en reliant l'activité des gènes au développement.

Introduction to Computational Modeling of Multicellular Tissues.

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.

Cauliflower fractal forms arise from perturbations of floral gene networks.

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.

Signaling pathways have an inherent need for noise to acquire information.

BACKGROUND: All living systems acquire information about their environment. At the cellular level, they do so through signaling pathways. Such pathways rely on reversible binding interactions between molecules that detect and transmit the presence of an extracellular cue or signal to the cell's interior. These interactions are inherently stochastic and thus noisy. On the one hand, noise can cause a signaling pathway to produce the same response for different stimuli, which reduces the amount of information a pathway acquires. On the other hand, in processes such as stochastic resonance, noise can improve the detection of weak stimuli and thus the acquisition of information. It is not clear whether the kinetic parameters that determine a pathway's operation cause noise to reduce or increase the acquisition of information. RESULTS: We analyze how the kinetic properties of the reversible binding interactions used by signaling pathways affect the relationship between noise, the response to a signal, and information acquisition. Our results show that, under a wide range of biologically sensible parameter values, a noisy dynamic of reversible binding interactions is necessary to produce distinct responses to different stimuli. As a consequence, noise is indispensable for the acquisition of information in signaling pathways. CONCLUSIONS: Our observations go beyond previous work by showing that noise plays a positive role in signaling pathways, demonstrating that noise is essential when such pathways acquire information.

Short Residence Times of DNA-Bound Transcription Factors Can Reduce Gene Expression Noise and Increase the Transmission of Information in a Gene Regulation System.

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.

WIP1 Contributes to the Adaptation of Fanconi Anemia Cells to DNA Damage as Determined by the Regulatory Network of the Fanconi Anemia and Checkpoint Recovery Pathways.

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.

Griffin: A Tool for Symbolic Inference of Synchronous Boolean Molecular Networks.

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.

A dynamic genetic-hormonal regulatory network model explains multiple cellular behaviors of the root apical meristem of Arabidopsis thaliana.

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 combination of the functionalities of feedback circuits is determinant for the attractors' number and size in pathway-like Boolean networks.

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.

A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle.

Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes.

Fanconi anemia cells with unrepaired DNA damage activate components of the checkpoint recovery process.

BACKGROUND: The FA/BRCA pathway repairs DNA interstrand crosslinks. Mutations in this pathway cause Fanconi anemia (FA), a chromosome instability syndrome with bone marrow failure and cancer predisposition. Upon DNA damage, normal and FA cells inhibit the cell cycle progression, until the G2/M checkpoint is turned off by the checkpoint recovery, which becomes activated when the DNA damage has been repaired. Interestingly, highly damaged FA cells seem to override the G2/M checkpoint. In this study we explored with a Boolean network model and key experiments whether checkpoint recovery activation occurs in FA cells with extensive unrepaired DNA damage. METHODS: We performed synchronous/asynchronous simulations of the FA/BRCA pathway Boolean network model. FA-A and normal lymphoblastoid cell lines were used to study checkpoint and checkpoint recovery activation after DNA damage induction. The experimental approach included flow cytometry cell cycle analysis, cell division tracking, chromosome aberration analysis and gene expression analysis through qRT-PCR and western blot. RESULTS: Computational simulations suggested that in FA mutants checkpoint recovery activity inhibits the checkpoint components despite unrepaired DNA damage, a behavior that we did not observed in wild-type simulations. This result implies that FA cells would eventually reenter the cell cycle after a DNA damage induced G2/M checkpoint arrest, but before the damage has been fixed. We observed that FA-A cells activate the G2/M checkpoint and arrest in G2 phase, but eventually reach mitosis and divide with unrepaired DNA damage, thus resolving the initial checkpoint arrest. Based on our model result we look for ectopic activity of checkpoint recovery components. We found that checkpoint recovery components, such as PLK1, are expressed to a similar extent as normal undamaged cells do, even though FA-A cells harbor highly damaged DNA. CONCLUSIONS: Our results show that FA cells, despite extensive DNA damage, do not loss the capacity to express the transcriptional and protein components of checkpoint recovery that might eventually allow their division with unrepaired DNA damage. This might allow cell survival but increases the genomic instability inherent to FA individuals and promotes cancer.

Development of cell differentiation in the transition to multicellularity: a dynamical modeling approach.

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.

XAANTAL2 (AGL14) Is an Important Component of the Complex Gene Regulatory Network that Underlies Arabidopsis Shoot Apical Meristem Transitions.

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.

Gene regulatory network models for floral organ determination.

Understanding how genotypes map unto phenotypes implies an integrative understanding of the processes regulating cell differentiation and morphogenesis, which comprise development. Such a task requires the use of theoretical and computational approaches to integrate and follow the concerted action of multiple genetic and nongenetic components that hold highly nonlinear interactions. Gene regulatory network (GRN) models have been proposed to approach such task. GRN models have become very useful to understand how such types of interactions restrict the multi-gene expression patterns that characterize different cell-fates. More recently, such temporal single-cell models have been extended to recover the temporal and spatial components of morphogenesis. Since the complete genomic GRN is still unknown and intractable for any organism, and some clear developmental modules have been identified, we focus here on the analysis of well-curated and experimentally grounded small GRN modules. One of the first experimentally grounded GRN that was proposed and validated corresponds to the regulatory module involved in floral organ determination. In this chapter we use this GRN as an example of the methodologies involved in: (1) formalizing and integrating molecular genetic data into the logical functions (Boolean functions) that rule gene interactions and dynamics in a Boolean GRN; (2) the algorithms and computational approaches used to recover the steady-states that correspond to each cell type, as well as the set of initial GRN configurations that lead to each one of such states (i.e., basins of attraction); (3) the approaches used to validate a GRN model using wild type and mutant or overexpression data, or to test the robustness of the GRN being proposed; (4) some of the methods that have been used to incorporate random fluctuations in the GRN Boolean functions and enable stochastic GRN models to address the temporal sequence with which gene configurations and cell fates are attained; (5) the methodologies used to approximate discrete Boolean GRN to continuous systems and their use in further dynamic analyses. The methodologies explained for the GRN of floral organ determination developed here in detail can be applied to any other functional developmental module.

Cell patterns emerge from coupled chemical and physical fields with cell proliferation dynamics: the Arabidopsis thaliana root as a study system.

A central issue in developmental biology is to uncover the mechanisms by which stem cells maintain their capacity to regenerate, yet at the same time produce daughter cells that differentiate and attain their ultimate fate as a functional part of a tissue or an organ. In this paper we propose that, during development, cells within growing organs obtain positional information from a macroscopic physical field that is produced in space while cells are proliferating. This dynamical interaction triggers and responds to chemical and genetic processes that are specific to each biological system. We chose the root apical meristem of Arabidopsis thaliana to develop our dynamical model because this system is well studied at the molecular, genetic and cellular levels and has the key traits of multicellular stem-cell niches. We built a dynamical model that couples fundamental molecular mechanisms of the cell cycle to a tension physical field and to auxin dynamics, both of which are known to play a role in root development. We perform extensive numerical calculations that allow for quantitative comparison with experimental measurements that consider the cellular patterns at the root tip. Our model recovers, as an emergent pattern, the transition from proliferative to transition and elongation domains, characteristic of stem-cell niches in multicellular organisms. In addition, we successfully predict altered cellular patterns that are expected under various applied auxin treatments or modified physical growth conditions. Our modeling platform may be extended to explicitly consider gene regulatory networks or to treat other developmental systems.

Finding Missing Interactions of the Arabidopsis thaliana Root Stem Cell Niche Gene Regulatory Network.

Over the last few decades, the Arabidopsis thaliana root stem cell niche (RSCN) has become a model system for the study of plant development and stem cell niche dynamics. Currently, many of the molecular mechanisms involved in RSCN maintenance and development have been described. A few years ago, we published a gene regulatory network (GRN) model integrating this information. This model suggested that there were missing components or interactions. Upon updating the model, the observed stable gene configurations of the RSCN could not be recovered, indicating that there are additional missing components or interactions in the model. In fact, due to the lack of experimental data, GRNs inferred from published data are usually incomplete. However, predicting the location and nature of the missing data is a not trivial task. Here, we propose a set of procedures for detecting and predicting missing interactions in Boolean networks. We used these procedures to predict putative missing interactions in the A. thaliana RSCN network model. Using our approach, we identified three necessary interactions to recover the reported gene activation configurations that have been experimentally uncovered for the different cell types within the RSCN: (1) a regulation of PHABULOSA to restrict its expression domain to the vascular cells, (2) a self-regulation of WOX5, possibly by an indirect mechanism through the auxin signaling pathway, and (3) a positive regulation of JACKDAW by MAGPIE. The procedures proposed here greatly reduce the number of possible Boolean functions that are biologically meaningful and experimentally testable and that do not contradict previous data. We believe that these procedures can be used on any Boolean network. However, because the procedures were designed for the specific case of the RSCN, formal demonstrations of the procedures should be shown in future efforts.

Dynamic models of epidermal patterning as an approach to plant eco-evo-devo.

Epidermal patterning in Arabidopsis thaliana leaves and root has become a model system for experimental and theoretical developmental studies, yielding well-characterized regulatory networks. We succinctly review the dynamic models proposed for this system and then argue that it provides an excellent instance to integrate and further study the role of non-genetic factors in plant development and evolution. Then, we set up to review the role of phytohormones and environmental stimuli in the regulation of cell-fate determination and patterning in this system. We conclude that dynamic modeling of complex regulatory networks can help understand the plasticity and variability of cellular patterns, and hence, such modeling approaches can be expanded to advance in the consolidation of plant Evolutionary and Ecological Developmental Biology (eco-evo-devo).

Hormone symphony during root growth and development.

Hormones regulate plant growth and development in response to external environmental stimuli via complex signal transduction pathways, which in turn form complex networks of interaction. Several classes of hormones have been reported, and their activity depends on their biosynthesis, transport, conjugation, accumulation in the vacuole, and degradation. However, the activity of a given hormone is also dependent on its interaction with other hormones. Indeed, there is a complex crosstalk between hormones that regulates their biosynthesis, transport, and/or signaling functionality, although some hormones have overlapping or opposite functions. The plant root is a particularly useful system in which to study the complex role of plant hormones in the plastic control of plant development. Physiological, cellular, and molecular genetic approaches have been used to study the role of plant hormones in root meristem homeostasis. In this review, we discuss recent findings on the synthesis, signaling, transport of hormones and role during root development and examine the role of hormone crosstalk in maintaining homeostasis in the apical root meristem.