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

Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using $10$ reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's $Z$-parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states.

A predictive model for ethylene-mediated auxin and cytokinin patterning in the Arabidopsis root

The interaction between auxin and cytokinin is important in many aspects of plant development. Experimental measurements of both auxin and cytokinin concentration and reporter gene expression clearly show the coexistence of auxin and cytokinin concentration patterning in Arabidopsis root development. However, in the context of crosstalk among auxin, cytokinin, and ethylene, little is known about how auxin and cytokinin concentration patterns simultaneously emerge and how they regulate each other in the Arabidopsis root. This work utilizes a wide range of experimental observations to propose a mechanism for simultaneous patterning of auxin and cytokinin concentrations. In addition to revealing the regulatory relationships between auxin and cytokinin, this mechanism shows that ethylene signaling is an important factor in achieving simultaneous auxin and cytokinin patterning, while also predicting other experimental observations. Combining the mechanism with a realistic in silico root model reproduces experimental observations of both auxin and cytokinin patterning. Predictions made by the mechanism can be compared with a variety of experimental observations, including those obtained by our group and other independent experiments reported by other groups. Examples of these predictions include patterning of auxin biosynthesis rate, changes in PIN1 and PIN2 patterns in pin3,4,7 mutants, changes in cytokinin patterning in the pls mutant, PLS patterning, and various trends in different mutants. This research reveals a plausible mechanism for simultaneous patterning of auxin and cytokinin concentrations in Arabidopsis root development and suggests a key role for ethylene pattern integration.

DyCeModel: a tool for 1D simulation for distribution of plant hormones controlling tissue patterning

To study the mechanisms of growth and development, it is necessary to analyze the dynamics of the tissue patterning regulators in time and space and to take into account their effect on the cellular dynamics within a tissue. Plant hormones are the main regulators of the cell dynamics in plant tissues; they form gradients and maxima and control molecular processes in a concentration-dependent manner. Here, we present DyCeModel, a software tool implemented in MATLAB for one-dimensional simulation of tissue with a dynamic cellular ensemble, where changes in hormone (or other active substance) concentration in the cells are described by ordinary differential equations (ODEs). We applied DyCeModel to simulate cell dynamics in plant meristems with different cellular structures and demonstrated that DyCeModel helps to identify the relationships between hormone concentration and cellular behaviors. The tool visualizes the simulation progress and presents a video obtained during the calculation. Importantly, the tool is capable of automatically adjusting the parameters by fitting the distribution of the substance concentrations predicted in the model to experimental data taken from the microscopic images. Noteworthy, DyCeModel makes it possible to build models for distinct types of plant meristems with the same ODEs, recruiting specific input characteristics for each meristem. We demonstrate the tool's efficiency by simulation of the effect of auxin and cytokinin distributions on tissue patterning in two types of Arabidopsis thaliana stem cell niches: the root and shoot apical meristems. The resulting models represent a promising framework for further study of the role of hormone-controlled gene regulatory networks in cell dynamics.

Leveraging developmental landscapes for model selection in Boolean gene regulatory networks

Boolean models are a well-established framework to model developmental gene regulatory networks (DGRNs) for acquisition of cellular identities. During the reconstruction of Boolean DGRNs, even if the network structure is given, there is generally a large number of combinations of Boolean functions that will reproduce the different cell fates (biological attractors). Here we leverage the developmental landscape to enable model selection on such ensembles using the relative stability of the attractors. First we show that previously proposed measures of relative stability are strongly correlated and we stress the usefulness of the one that captures best the cell state transitions via the mean first passage time (MFPT) as it also allows the construction of a cellular lineage tree. A property of great computational importance is the insensitivity of the different stability measures to changes in noise intensities. That allows us to use stochastic approaches to estimate the MFPT and thereby scale up the computations to large networks. Given this methodology, we revisit different Boolean models of Arabidopsis thaliana root development, showing that a most recent one does not respect the biologically expected hierarchy of cell states based on relative stabilities. We therefore developed an iterative greedy algorithm that searches for models which satisfy the expected hierarchy of cell states and found that its application to the root development model yields many models that meet this expectation. Our methodology thus provides new tools that can enable reconstruction of more realistic and accurate Boolean models of DGRNs.

ORESARA 15, a PLATZ transcription factor, controls root meristem size through auxin and cytokinin signalling-related pathways

An optimal size of post-embryonic root apical meristem (RAM) is achieved by a balance between cell division and differentiation. Despite extensive research, molecular mechanisms underlying the coordination of cell division and differentiation are still fragmentary. Here, we report that ORESARA 15 (ORE15), an Arabidopsis PLANT A/T-RICH SEQUENCE-AND ZINC-BINDING PROTEIN (PLATZ) transcription factor preferentially expressed in the RAM, determines RAM size. Primary root length, RAM size, cell division rate, and stem cell niche activity were reduced in an ore15 loss-of-function mutant but enhanced in an activation-tagged line overexpressing ORE15, compared with wild type. ORE15 forms mutually positive and negative feedback loops with auxin and cytokinin signalling, respectively. Collectively, our findings imply that ORE15 controls RAM size by mediating the antagonistic interaction between auxin and cytokinin signalling-related pathways.

Identification of dynamic driver sets controlling phenotypical landscapes

Controlling phenotypical landscapes is of vital interest to modern biology. This task becomes highly demanding because cellular decisions involve complex networks engaging in crosstalk interactions. Previous work on control theory indicates that small sets of compounds can control single phenotypes. However, a dynamic approach is missing to determine the drivers of the whole network dynamics. By analyzing 35 biologically motivated Boolean networks, we developed a method to identify small sets of compounds sufficient to decide on the entire phenotypical landscape. These compounds do not strictly prefer highly related compounds and show a smaller impact on the stability of the attractor landscape. The dynamic driver sets include many intervention targets and cellular reprogramming drivers in human networks. Finally, by using a new comprehensive model of colorectal cancer, we provide a complete workflow on how to implement our approach to shift from in silico to in vitro guided experiments.

Live Plant Cell Tracking: Fiji plugin to analyze cell proliferation dynamics and understand morphogenesis

Arabidopsis (Arabidopsis thaliana) primary and lateral roots (LRs) are well suited for 3D and 4D microscopy, and their development provides an ideal system for studying morphogenesis and cell proliferation dynamics. With fast-advancing microscopy techniques used for live-imaging, whole tissue data are increasingly available, yet present the great challenge of analyzing complex interactions within cell populations. We developed a plugin "Live Plant Cell Tracking" (LiPlaCeT) coupled to the publicly available ImageJ image analysis program and generated a pipeline that allows, with the aid of LiPlaCeT, 4D cell tracking and lineage analysis of populations of dividing and growing cells. The LiPlaCeT plugin contains ad hoc ergonomic curating tools, making it very simple to use for manual cell tracking, especially when the signal-to-noise ratio of images is low or variable in time or 3D space and when automated methods may fail. Performing time-lapse experiments and using cell-tracking data extracted with the assistance of LiPlaCeT, we accomplished deep analyses of cell proliferation and clonal relations in the whole developing LR primordia and constructed genealogical trees. We also used cell-tracking data for endodermis cells of the root apical meristem (RAM) and performed automated analyses of cell population dynamics using ParaView software (also publicly available). Using the RAM as an example, we also showed how LiPlaCeT can be used to generate information at the whole-tissue level regarding cell length, cell position, cell growth rate, cell displacement rate, and proliferation activity. The pipeline will be useful in live-imaging studies of roots and other plant organs to understand complex interactions within proliferating and growing cell populations. The plugin includes a step-by-step user manual and a dataset example that are available at https://www.ibt.unam.mx/documentos/diversos/LiPlaCeT.zip.

The hidden half comes into the spotlight: Peeking inside the black box of root developmental phases

Efficient use of natural resources (e.g., light, water, and nutrients) can be improved with a tailored developmental program that maximizes the lifetime and fitness of plants. In plant shoots, a developmental phase represents a time window in which the meristem triggers the development of unique morphological and physiological traits, leading to the emergence of leaves, flowers, and fruits. Whereas developmental phases in plant shoots have been shown to enhance food production in crops, this phenomenon has remained poorly investigated in roots. In light of recent advances, we suggest that root development occurs in three main phases: root apical meristem appearance, foraging, and senescence. We provide compelling evidence suggesting that these phases are regulated by at least four developmental pathways: autonomous, non-autonomous, hormonal, and periodic. Root developmental pathways differentially coordinate organ plasticity, promoting morphological alterations, tissue regeneration, and cell death regulation. Furthermore, we suggest how nutritional checkpoints may allow progression through the developmental phases, thus completing the root life cycle. These insights highlight novel and exciting advances in root biology that may help maximize the productivity of crops through more sustainable agriculture and the reduced use of chemical fertilizers.

The flowering transition pathways converge into a complex gene regulatory network that underlies the phase changes of the shoot apical meristem in Arabidopsis thaliana

Post-embryonic plant development is characterized by a period of vegetative growth during which a combination of intrinsic and extrinsic signals triggers the transition to the reproductive phase. To understand how different flowering inducing and repressing signals are associated with phase transitions of the Shoot Apical Meristem (SAM), we incorporated available data into a dynamic gene regulatory network model for Arabidopsis thaliana. This Flowering Transition Gene Regulatory Network (FT-GRN) formally constitutes a dynamic system-level mechanism based on more than three decades of experimental data on flowering. We provide novel experimental data on the regulatory interactions of one of its twenty-three components: a MADS-box transcription factor XAANTAL2 (XAL2). These data complement the information regarding flowering transition under short days and provides an example of the type of questions that can be addressed by the FT-GRN. The resulting FT-GRN is highly connected and integrates developmental, hormonal, and environmental signals that affect developmental transitions at the SAM. The FT-GRN is a dynamic multi-stable Boolean system, with 2²³ possible initial states, yet it converges into only 32 attractors. The latter are coherent with the expression profiles of the FT-GRN components that have been experimentally described for the developmental stages of the SAM. Furthermore, the attractors are also highly robust to initial states and to simulated perturbations of the interaction functions. The model recovered the meristem phenotypes of previously described single mutants. We also analyzed the attractors landscape that emerges from the postulated FT-GRN, uncovering which set of signals or components are critical for reproductive competence and the time-order transitions observed in the SAM. Finally, in the context of such GRN, the role of XAL2 under short-day conditions could be understood. Therefore, this model constitutes a robust biological module and the first multi-stable, dynamical systems biology mechanism that integrates the genetic flowering pathways to explain SAM phase transitions.

Hormonal orchestration of root apical meristem formation and maintenance in Arabidopsis

Plant hormones are key regulators of a number of developmental and adaptive responses in plants, integrating the control of intrinsic developmental regulatory circuits with environmental inputs. Here we provide an overview of the molecular mechanisms underlying hormonal regulation of root development. We focus on key events during both embryonic and post-embryonic development, including specification of the hypophysis as a future organizer of the root apical meristem (RAM), hypophysis asymmetric division, specification of the quiescent centre (QC) and the stem cell niche (SCN), RAM maturation and maintenance of QC/SCN activity, and RAM size. We address both well-established and newly proposed concepts, highlight potential ambiguities in recent terminology and classification criteria of longitudinal root zonation, and point to contrasting results and alternative scenarios for recent models. In the concluding remarks, we summarize the common principles of hormonal control during root development and the mechanisms potentially explaining often antagonistic outputs of hormone action, and propose possible future research directions on hormones in the root.

Integrating the Roles for Cytokinin and Auxin in De Novo Shoot Organogenesis: From Hormone Uptake to Signaling Outputs

De novo shoot organogenesis (DNSO) is a procedure commonly used for the in vitro regeneration of shoots from a variety of plant tissues. Shoot regeneration occurs on nutrient media supplemented with the plant hormones cytokinin (CK) and auxin, which play essential roles in this process, and genes involved in their signaling cascades act as master regulators of the different phases of shoot regeneration. In the last 20 years, the genetic regulation of DNSO has been characterized in detail. However, as of today, the CK and auxin signaling events associated with shoot regeneration are often interpreted as a consequence of these hormones simply being present in the regeneration media, whereas the roles for their prior uptake and transport into the cultivated plant tissues are generally overlooked. Additionally, sucrose, commonly added to the regeneration media as a carbon source, plays a signaling role and has been recently shown to interact with CK and auxin and to affect the efficiency of shoot regeneration. In this review, we provide an integrative interpretation of the roles for CK and auxin in the process of DNSO, adding emphasis on their uptake from the regeneration media and their interaction with sucrose present in the media to their complex signaling outputs that mediate shoot regeneration.

Rational design of complex phenotype via network models

We demonstrate a modeling and computational framework that allows for rapid screening of thousands of potential network designs for particular dynamic behavior. To illustrate this capability we consider the problem of hysteresis, a prerequisite for construction of robust bistable switches and hence a cornerstone for construction of more complex synthetic circuits. We evaluate and rank most three node networks according to their ability to robustly exhibit hysteresis where robustness is measured with respect to parameters over multiple dynamic phenotypes. Focusing on the highest ranked networks, we demonstrate how additional robustness and design constraints can be applied. We compare our results to more traditional methods based on specific parameterization of ordinary differential equation models and demonstrate a strong qualitative match at a small fraction of the computational cost.

A major challenge in the domains of systems and synthetic biology is an inability to efficiently predict function(s) of complex networks. This work demonstrates a modeling and computational framework that allows for a mathematically justifiable rigorous screening of thousands of potential network designs for a wide variety of dynamical behavior. We screen all 3-node genetic networks and rank them based on their ability to act as an inducible bistable switch. Our results are summarized in a searchable database that can be used to construct robust switches. The ability to quickly screen thousands of designs significantly reduces the set of viable designs and allows synthetic biologists to focus their experimental and more traditional modeling tools to this much smaller set.

Osmotic stress-induced somatic embryo maturation of coffee Coffea arabica L., shoot and root apical meristems development and robustness

Somatic embryogenesis (SE) is the most important plant biotechnology process for plant regeneration, propagation, genetic transformation and genome editing of coffee, Coffea arabica L. Somatic embryo (SEs) conversion to plantlets is the principal bottleneck for basic and applied use of this process. In this study we focus on the maturation of SEs of C. arabica var. Typica. SEs conversion to plantlet up to 95.9% was achieved under osmotic stress, using 9 g/L gelrite, as compared with only 39.34% in non-osmotic stress. Mature SEs induced in osmotic stress developed shoot and root apical meristems, while untreated SEs were unable to do it. C. arabica regenerated plants from osmotic stress were robust, with higher leaf and root area and internode length. To understand a possible regulatory mechanism, gene expression of key genes of C. arabica, homologous to sequences in the Arabidopsis thaliana genome, were analyzed. A set of two component system and cytokinin signaling-related coding genes (AHK1, AHK3, AHP4 and ARR1) which interact with WUSCHEL and WOX5 homedomains and morphogenic genes, BABY-BOOM, LEC1, FUS3 and AGL15, underwent significant changes during maturation of SEs of C. arabica var. Typica. This protocol is currently being applied in genetic transformation with high rate of success.

Hormonal Regulation of Stem Cell Proliferation at the Arabidopsis thaliana Root Stem Cell Niche

The root stem cell niche (SCN) of Arabidopsis thaliana consists of the quiescent center (QC) cells and the surrounding initial stem cells that produce progeny to replenish all the tissues of the root. The QC cells divide rather slowly relative to the initials, yet most root tissues can be formed from these cells, depending on the requirements of the plant. Hormones are fundamental cues that link such needs with the cell proliferation and differentiation dynamics at the root SCN. Nonetheless, the crosstalk between hormone signaling and the mechanisms that regulate developmental adjustments is still not fully understood. Developmental transcriptional regulatory networks modulate hormone biosynthesis, metabolism, and signaling, and conversely, hormonal responses can affect the expression of transcription factors involved in the spatiotemporal patterning at the root SCN. Hence, a complex genetic-hormonal regulatory network underlies root patterning, growth, and plasticity in response to changing environmental conditions. In this review, we summarize the scientific literature regarding the role of hormones in the regulation of QC cell proliferation and discuss how hormonal signaling pathways may be integrated with the gene regulatory network that underlies cell fate in the root SCN. The conceptual framework we present aims to contribute to the understanding of the mechanisms by which hormonal pathways act as integrators of environmental cues to impact on SCN activity.

Integrative Roles of Phytohormones on Cell Proliferation, Elongation and Differentiation in the Arabidopsis thaliana Primary Root

The growth of multicellular organisms relies on cell proliferation, elongation and differentiation that are tightly regulated throughout development by internal and external stimuli. The plasticity of a growth response largely depends on the capacity of the organism to adjust the ratio between cell proliferation and cell differentiation. The primary root of Arabidopsis thaliana offers many advantages toward understanding growth homeostasis as root cells are continuously produced and move from cell proliferation to elongation and differentiation that are processes spatially separated and could be studied along the longitudinal axis. Hormones fine tune plant growth responses and a huge amount of information has been recently generated on the role of these compounds in Arabidopsis primary root development. In this review, we summarized the participation of nine hormones in the regulation of the different zones and domains of the Arabidopsis primary root. In some cases, we found synergism between hormones that function either positively or negatively in proliferation, elongation or differentiation. Intriguingly, there are other cases where the interaction between hormones exhibits unexpected results. Future analysis on the molecular mechanisms underlying crosstalk hormone action in specific zones and domains will unravel their coordination over PR development.

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.

A system-level mechanistic explanation for asymmetric stem cell fates: Arabidopsis thaliana root niche as a study system

Asymmetric divisions maintain long-term stem cell populations while producing new cells that proliferate and then differentiate. Recent reports in animal systems show that divisions of stem cells can be uncoupled from their progeny differentiation, and the outcome of a division could be influenced by microenvironmental signals. But the underlying system-level mechanisms, and whether this dynamics also occur in plant stem cell niches (SCN), remain elusive. This article presents a cell fate regulatory network model that contributes to understanding such mechanism and identify critical cues for cell fate transitions in the root SCN. Novel computational and experimental results show that the transcriptional regulator SHR is critical for the most frequent asymmetric division previously described for quiescent centre stem cells. A multi-scale model of the root tip that simulated each cell's intracellular regulatory network, and the dynamics of SHR intercellular transport as a cell-cell coupling mechanism, was developed. It revealed that quiescent centre cell divisions produce two identical cells, that may acquire different fates depending on the feedback between SHR's availability and the state of the regulatory network. Novel experimental data presented here validates our model, which in turn, constitutes the first proposed systemic mechanism for uncoupled SCN cell division and differentiation.

Plant-Associated Microbes Alter Root Growth by Modulating Root Apical Meristem

Rhizobacteria are known to produce a variety of signal molecules which may modify plant growth by interfering with phytohormone balance. Among the microbial signals are phytohormones, known to contribute to plant endogenous pool of phytohormones. The current chapter describes different methods to study the regulation of gene expression in root apical meristem in response to rhizobacterial inoculation. We describe protocol for the detection of in planta modulation of CKs and IAA by rhizobacteria and their impact on root growth, dissecting the underlying plant signaling pathway by RNA sequencing.

PlantSimLab - a modeling and simulation web tool for plant biologists

BACKGROUND

At the molecular level, nonlinear networks of heterogeneous molecules control many biological processes, so that systems biology provides a valuable approach in this field, building on the integration of experimental biology with mathematical modeling. One of the biggest challenges to making this integration a reality is that many life scientists do not possess the mathematical expertise needed to build and manipulate mathematical models well enough to use them as tools for hypothesis generation. Available modeling software packages often assume some modeling expertise. There is a need for software tools that are easy to use and intuitive for experimentalists.

RESULTS

This paper introduces PlantSimLab, a web-based application developed to allow plant biologists to construct dynamic mathematical models of molecular networks, interrogate them in a manner similar to what is done in the laboratory, and use them as a tool for biological hypothesis generation. It is designed to be used by experimentalists, without direct assistance from mathematical modelers.

CONCLUSIONS

Mathematical modeling techniques are a useful tool for analyzing complex biological systems, and there is a need for accessible, efficient analysis tools within the biological community. PlantSimLab enables users to build, validate, and use intuitive qualitative dynamic computer models, with a graphical user interface that does not require mathematical modeling expertise. It makes analysis of complex models accessible to a larger community, as it is platform-independent and does not require extensive mathematical expertise.

Plant Networks as Traits and Hypotheses: Moving Beyond Description

Biology relies on the central thesis that the genes in an organism encode molecular mechanisms that combine with stimuli and raw materials from the environment to create a final phenotypic expression representative of the genomic programming. While conceptually simple, the genotype-to-phenotype linkage in a eukaryotic organism relies on the interactions of thousands of genes and an environment with a potentially unknowable level of complexity. Modern biology has moved to the use of networks in systems biology to try to simplify this complexity to decode how an organism's genome works. Previously, biological networks were basic ways to organize, simplify, and analyze data. However, recent advances are allowing networks to move beyond description and become phenotypes or hypotheses in their own right. This review discusses these efforts, like mapping responses across biological scales, including relationships among cellular entities, and the direct use of networks as traits or hypotheses.

MADS-box genes underground becoming mainstream: plant root developmental mechanisms

Plant growth is largely post-embryonic and depends on meristems that are active throughout the lifespan of an individual. Developmental patterns rely on the coordinated spatio-temporal expression of different genes, and the activity of transcription factors is particularly important during most morphogenetic processes. MADS-box genes constitute a transcription factor family in eukaryotes. In Arabidopsis, their proteins participate in all major aspects of shoot development, but their role in root development is still not well characterized. In this review we synthetize current knowledge pertaining to the function of MADS-box genes highly expressed in roots: XAL1, XAL2, ANR1 and AGL21, as well as available data for other MADS-box genes expressed in this organ. The role of Trithorax group and Polycomb group complexes on MADS-box genes' epigenetic regulation is also discussed. We argue that understanding the role of MADS-box genes in root development of species with contrasting architectures is still a challenge. Finally, we propose that MADS-box genes are key components of the gene regulatory networks that underlie various gene expression patterns, each one associated with the distinct developmental fates observed in the root. In the case of XAL1 and XAL2, their role within these networks could be mediated by regulatory feedbacks with auxin.

PLOS Computational Biology Staff. Correction: A dynamic genetic-hormonal regulatory network model explains multiple cellular behaviors of the root apical meristem of Arabidopsis thaliana

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

How do Plants Keep their Functional Integrity?

Unlike animals, plants possess a non-strict and sometimes very fuzzy morphology. Mutual proportions of plant parts can vary to a much greater extent than in animals, changing according to the environmental conditions and the plant needs of nutrients, water and light. Despite the existence of this fundamental difference between plants and animals, it passes almost non-reflected in most studies on plants. In this review we make a preliminary attempt to gather together the mechanisms by which plants preserve their integrity, not loosing at the same time the physiological (and morphological) flexibility which allows them adapting to the different environments they can populate.

Analysis Tools for Interconnected Boolean Networks With Biological Applications

Boolean networks with asynchronous updates are a class of logical models particularly well adapted to describe the dynamics of biological networks with uncertain measures. The state space of these models can be described by an asynchronous state transition graph, which represents all the possible exits from every single state, and gives a global image of all the possible trajectories of the system. In addition, the asynchronous state transition graph can be associated with an absorbing Markov chain, further providing a semi-quantitative framework where it becomes possible to compute probabilities for the different trajectories. For large networks, however, such direct analyses become computationally untractable, given the exponential dimension of the graph. Exploiting the general modularity of biological systems, we have introduced the novel concept of asymptotic graph, computed as an interconnection of several asynchronous transition graphs and recovering all asymptotic behaviors of a large interconnected system from the behavior of its smaller modules. From a modeling point of view, the interconnection of networks is very useful to address for instance the interplay between known biological modules and to test different hypotheses on the nature of their mutual regulatory links. This paper develops two new features of this general methodology: a quantitative dimension is added to the asymptotic graph, through the computation of relative probabilities for each final attractor and a companion cross-graph is introduced to complement the method on a theoretical point of view.

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.

Stability of Signaling Pathways during Aging-A Boolean Network Approach

Biological pathways are thought to be robust against a variety of internal and external perturbations. Fail-safe mechanisms allow for compensation of perturbations to maintain the characteristic function of a pathway. Pathways can undergo changes during aging, which may lead to changes in their stability. Less stable or less robust pathways may be consequential to or increase the susceptibility of the development of diseases. Among others, NF- κ B signaling is a crucial pathway in the process of aging. The NF- κ B system is involved in the immune response and dealing with various internal and external stresses. Boolean networks as models of biological pathways allow for simulation of signaling behavior. They can help to identify which proposed mechanisms are biologically representative and which ones function but do not mirror physical processes-for instance, changes of signaling pathways during the aging process. Boolean networks can be inferred from time-series of gene expression data. This allows us to get insights into the changes of behavior of pathways such as NF- κ B signaling in aged organisms in comparison to young ones.