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1.  Dynamic Network-Based Epistasis Analysis: Boolean Examples 
In this article we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the inference of gene regulatory networks. Here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson, epistasis is defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus (herein, classical epistasis). Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct inference of gene interaction topologies is hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our article complements previous accounts, not only by focusing on the implications of the hierarchical and single-path assumption, but also by demonstrating the importance of considering temporal dynamics, and specifically introducing the usefulness of Boolean network models and also reviewing some key properties of network approaches.
PMCID: PMC3355816  PMID: 22645556
epistasis; gene regulatory networks; Boolean networks; feedback loops; feed-forward loops; temporal dynamics; modeling; gene interactions
2.  ARACNe-based inference, using curated microarray data, of Arabidopsis thaliana root transcriptional regulatory networks 
BMC Plant Biology  2014;14:97.
Uncovering the complex transcriptional regulatory networks (TRNs) that underlie plant and animal development remains a challenge. However, a vast amount of data from public microarray experiments is available, which can be subject to inference algorithms in order to recover reliable TRN architectures.
In this study we present a simple bioinformatics methodology that uses public, carefully curated microarray data and the mutual information algorithm ARACNe in order to obtain a database of transcriptional interactions. We used data from Arabidopsis thaliana root samples to show that the transcriptional regulatory networks derived from this database successfully recover previously identified root transcriptional modules and to propose new transcription factors for the SHORT ROOT/SCARECROW and PLETHORA pathways. We further show that these networks are a powerful tool to integrate and analyze high-throughput expression data, as exemplified by our analysis of a SHORT ROOT induction time-course microarray dataset, and are a reliable source for the prediction of novel root gene functions. In particular, we used our database to predict novel genes involved in root secondary cell-wall synthesis and identified the MADS-box TF XAL1/AGL12 as an unexpected participant in this process.
This study demonstrates that network inference using carefully curated microarray data yields reliable TRN architectures. In contrast to previous efforts to obtain root TRNs, that have focused on particular functional modules or tissues, our root transcriptional interactions provide an overview of the transcriptional pathways present in Arabidopsis thaliana roots and will likely yield a plethora of novel hypotheses to be tested experimentally.
PMCID: PMC4021103  PMID: 24739361
Transcriptional regulatory networks; Root; Arabidopsis; Transcription factor; ARACNe
3.  Tetramer formation in Arabidopsis MADS domain proteins: analysis of a protein-protein interaction network 
MADS domain proteins are transcription factors that coordinate several important developmental processes in plants. These proteins interact with other MADS domain proteins to form dimers, and it has been proposed that they are able to associate as tetrameric complexes that regulate transcription of target genes. Whether the formation of functional tetramers is a widespread property of plant MADS domain proteins, or it is specific to few of these transcriptional regulators remains unclear.
We analyzed the structure of the network of physical interactions among MADS domain proteins in Arabidopsis thaliana. We determined the abundance of subgraphs that represent the connection pattern expected for a MADS domain protein heterotetramer. These subgraphs were significantly more abundant in the MADS domain protein interaction network than in randomized analogous networks. Importantly, these subgraphs are not significantly frequent in a protein interaction network of TCP plant transcription factors, when compared to expectation by chance. In addition, we found that MADS domain proteins in tetramer-like subgraphs are more likely to be expressed jointly than proteins in other subgraphs. This effect is mainly due to proteins in the monophyletic MIKC clade, as there is no association between tetramer-like subgraphs and co-expression for proteins outside this clade.
Our results support that the tendency to form functional tetramers is widespread in the MADS domain protein-protein interaction network. Our observations also suggest that this trend is prevalent, or perhaps exclusive, for proteins in the MIKC clade. Because it is possible to retrodict several experimental results from our analyses, our work can be an important aid to make new predictions and facilitates experimental research on plant MADS domain proteins.
PMCID: PMC3913338  PMID: 24468197
MADS domain proteins; Protein-protein interaction network; Transcription factors; Tetramers; Subgraph abundance; Arabidopsis thaliana
4.  Mechanical forces as information: an integrated approach to plant and animal development 
Mechanical forces such as tension and compression act throughout growth and development of multicellular organisms. These forces not only affect the size and shape of the cells and tissues but are capable of modifying the expression of genes and the localization of molecular components within the cell, in the plasma membrane, and in the plant cell wall. The magnitude and direction of these physical forces change with cellular and tissue properties such as elasticity. Thus, mechanical forces and the mesoscopic fields that emerge from their local action constitute important sources of positional information. Moreover, physical and biochemical processes interact in non-linear ways during tissue and organ growth in plants and animals. In this review we discuss how such mechanical forces are generated, transmitted, and sensed in these two lineages of multicellular organisms to yield long-range positional information. In order to do so we first outline a potentially common basis for studying patterning and mechanosensing that relies on the structural principle of tensegrity, and discuss how tensegral structures might arise in plants and animals. We then provide some examples of morphogenesis in which mechanical forces appear to act as positional information during development, offering a possible explanation for ubiquitous processes, such as the formation of periodic structures. Such examples, we argue, can be interpreted in terms of tensegral phenomena. Finally, we discuss the hypothesis of mechanically isotropic points as a potentially generic mechanism for the localization and maintenance of stem-cell niches in multicellular organisms. This comparative approach aims to help uncovering generic mechanisms of morphogenesis and thus reach a better understanding of the evolution and development of multicellular phenotypes, focusing on the role of physical forces in these processes.
PMCID: PMC4051191  PMID: 24959170
mechanical forces; tensegrity; positional information; multicellular development; stem-cell niches
5.  An efficient flat-surface collar-free grafting method for Arabidopsis thaliana seedlings 
Plant Methods  2013;9:14.
Grafting procedures are an excellent tool to study long range signalling processes within a plant. In the last decade, suitable flat-surface grafting procedures for young Arabidopsis seedlings using a collar to support the graft have been developed, allowing the study of long-range signals from a molecular perspective.
In the modification presented here, scion and stock are put together on the medium without supporting elements, while cotyledons are removed from the scion, resulting in increased grafting success that can reach up to 100%. At the same time, the protocol enables to process as many as 36 seedlings per hour, which combined with the high success percentage represents increased efficiency per time unit.
Growing cotyledons usually push the scion and the rootstock away in the absence of a supporting element. Removing them at the grafting step greatly improved success rate and reduced post-grafting manipulations.
PMCID: PMC3668283  PMID: 23641687
6.  New Genes in Traditional Seed Systems: Diffusion, Detectability and Persistence of Transgenes in a Maize Metapopulation 
PLoS ONE  2012;7(10):e46123.
Gene flow of transgenes into non-target populations is an important biosafety concern. The case of genetically modified (GM) maize in Mexico has been of particular interest because of the country’s status as center of origin and landrace diversity. In contrast to maize in the U.S. and Europe, Mexican landraces form part of an evolving metapopulation in which new genes are subject to evolutionary processes of drift, gene flow and selection. Although these processes are affected by seed management and particularly seed flow, there has been little study into the population genetics of transgenes under traditional seed management. Here, we combine recently compiled data on seed management practices with a spatially explicit population genetic model to evaluate the importance of seed flow as a determinant of the long-term fate of transgenes in traditional seed systems. Seed flow between farmers leads to a much wider diffusion of transgenes than expected by pollen movement alone, but a predominance of seed replacement over seed mixing lowers the probability of detection due to a relative lack of homogenization in spatial frequencies. We find that in spite of the spatial complexities of the modeled system, persistence probabilities under positive selection are estimated quite well by existing theory. Our results have important implications concerning the feasibility of long term transgene monitoring and control in traditional seed systems.
PMCID: PMC3463572  PMID: 23056246
7.  "Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis 
BMC Bioinformatics  2011;12:490.
In Thomas' formalism for modeling gene regulatory networks (GRNs), branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a) asynchrony, (b) incompletely specified behavior, and (c) interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulators, because infinitely many paths may appear, limiting ordinary simulators to statistical conclusions. Model checkers for branching time, by contrast, are able to prove properties in the presence of infinitely many paths.
We have developed Antelope ("Analysis of Networks through TEmporal-LOgic sPEcifications",, a model checker for analyzing and constructing Boolean GRNs. Currently, software systems for Boolean GRNs use branching time almost exclusively for asynchrony. Antelope, by contrast, also uses branching time for incompletely specified behavior and environment interaction. We show the usefulness of modeling these two phenomena in the development of a Boolean GRN of the Arabidopsis thaliana root stem cell niche.
There are two obstacles to a direct approach when applying model checking to Boolean GRN analysis. First, ordinary model checkers normally only verify whether or not a given set of model states has a given property. In comparison, a model checker for Boolean GRNs is preferable if it reports the set of states having a desired property. Second, for efficiency, the expressiveness of many model checkers is limited, resulting in the inability to express some interesting properties of Boolean GRNs.
Antelope tries to overcome these two drawbacks: Apart from reporting the set of all states having a given property, our model checker can express, at the expense of efficiency, some properties that ordinary model checkers (e.g., NuSMV) cannot. This additional expressiveness is achieved by employing a logic extending the standard Computation-Tree Logic (CTL) with hybrid-logic operators.
We illustrate the advantages of Antelope when (a) modeling incomplete networks and environment interaction, (b) exhibiting the set of all states having a given property, and (c) representing Boolean GRN properties with hybrid CTL.
PMCID: PMC3316443  PMID: 22192526
8.  Single-cell and coupled GRN models of cell patterning in the Arabidopsis thaliana root stem cell niche 
BMC Systems Biology  2010;4:134.
Recent experimental work has uncovered some of the genetic components required to maintain the Arabidopsis thaliana root stem cell niche (SCN) and its structure. Two main pathways are involved. One pathway depends on the genes SHORTROOT and SCARECROW and the other depends on the PLETHORA genes, which have been proposed to constitute the auxin readouts. Recent evidence suggests that a regulatory circuit, composed of WOX5 and CLE40, also contributes to the SCN maintenance. Yet, we still do not understand how the niche is dynamically maintained and patterned or if the uncovered molecular components are sufficient to recover the observed gene expression configurations that characterize the cell types within the root SCN. Mathematical and computational tools have proven useful in understanding the dynamics of cell differentiation. Hence, to further explore root SCN patterning, we integrated available experimental data into dynamic Gene Regulatory Network (GRN) models and addressed if these are sufficient to attain observed gene expression configurations in the root SCN in a robust and autonomous manner.
We found that an SCN GRN model based only on experimental data did not reproduce the configurations observed within the root SCN. We developed several alternative GRN models that recover these expected stable gene configurations. Such models incorporate a few additional components and interactions in addition to those that have been uncovered. The recovered configurations are stable to perturbations, and the models are able to recover the observed gene expression profiles of almost all the mutants described so far. However, the robustness of the postulated GRNs is not as high as that of other previously studied networks.
These models are the first published approximations for a dynamic mechanism of the A. thaliana root SCN cellular pattering. Our model is useful to formally show that the data now available are not sufficient to fully reproduce root SCN organization and genetic profiles. We then highlight some experimental holes that remain to be studied and postulate some novel gene interactions. Finally, we suggest the existence of a generic dynamical motif that can be involved in both plant and animal SCN maintenance.
PMCID: PMC2972269  PMID: 20920363
9.  Flower Development 
Flowers are the most complex structures of plants. Studies of Arabidopsis thaliana, which has typical eudicot flowers, have been fundamental in advancing the structural and molecular understanding of flower development. The main processes and stages of Arabidopsis flower development are summarized to provide a framework in which to interpret the detailed molecular genetic studies of genes assigned functions during flower development and is extended to recent genomics studies uncovering the key regulatory modules involved. Computational models have been used to study the concerted action and dynamics of the gene regulatory module that underlies patterning of the Arabidopsis inflorescence meristem and specification of the primordial cell types during early stages of flower development. This includes the gene combinations that specify sepal, petal, stamen and carpel identity, and genes that interact with them. As a dynamic gene regulatory network this module has been shown to converge to stable multigenic profiles that depend upon the overall network topology and are thus robust, which can explain the canalization of flower organ determination and the overall conservation of the basic flower plan among eudicots. Comparative and evolutionary approaches derived from Arabidopsis studies pave the way to studying the molecular basis of diverse floral morphologies.
PMCID: PMC3244948  PMID: 22303253
10.  Dispersal of Transgenes through Maize Seed Systems in Mexico 
PLoS ONE  2009;4(5):e5734.
Current models of transgene dispersal focus on gene flow via pollen while neglecting seed, a vital vehicle for gene flow in centers of crop origin and diversity. We analyze the dispersal of maize transgenes via seeds in Mexico, the crop's cradle.
We use immunoassays (ELISA) to screen for the activity of recombinant proteins in a nationwide sample of farmer seed stocks. We estimate critical parameters of seed population dynamics using household survey data and combine these estimates with analytical results to examine presumed sources and mechanisms of dispersal.
Recombinant proteins Cry1Ab/Ac and CP4/EPSPS were found in 3.1% and 1.8% of samples, respectively. They are most abundant in southeast Mexico but also present in the west-central region. Diffusion of seed and grain imported from the United States might explain the frequency and distribution of transgenes in west-central Mexico but not in the southeast.
Understanding the potential for transgene survival and dispersal should help design methods to regulate the diffusion of germplasm into local seed stocks. Further research is needed on the interactions between formal and informal seed systems and grain markets in centers of crop origin and diversification.
PMCID: PMC2685455  PMID: 19503610
11.  Information flow during gene activation by signaling molecules: ethylene transduction in Arabidopsis cells as a study system 
BMC Systems Biology  2009;3:48.
We study root cells from the model plant Arabidopsis thaliana and the communication channel conformed by the ethylene signal transduction pathway. A basic equation taken from our previous work relates the probability of expression of the gene ERF1 to the concentration of ethylene.
The above equation is used to compute the Shannon entropy (H) or degree of uncertainty that the genetic machinery has during the decoding of the message encoded by the ethylene specific receptors embedded in the endoplasmic reticulum membrane and transmitted into the nucleus by the ethylene signaling pathway. We show that the amount of information associated with the expression of the master gene ERF1 (Ethylene Response Factor 1) can be computed. Then we examine the system response to sinusoidal input signals with varying frequencies to determine if the cell can distinguish between different regimes of information flow from the environment. Our results demonstrate that the amount of information managed by the root cell can be correlated with the frequency of the input signal.
The ethylene signaling pathway cuts off very low and very high frequencies, allowing a window of frequency response in which the nucleus reads the incoming message as a sinusoidal input. Out of this window the nucleus reads the input message as an approximately non-varying one. From this frequency response analysis we estimate: a) the gain of the system during the synthesis of the protein ERF1 (~-5.6 dB); b) the rate of information transfer (0.003 bits) during the transport of each new ERF1 molecule into the nucleus and c) the time of synthesis of each new ERF1 molecule (~21.3 s). Finally, we demonstrate that in the case of the system of a single master gene (ERF1) and a single slave gene (HLS1), the total Shannon entropy is completely determined by the uncertainty associated with the expression of the master gene. A second proposition shows that the Shannon entropy associated with the expression of the HLS1 gene determines the information content of the system that is related to the interaction of the antagonistic genes ARF1, 2 and HLS1.
PMCID: PMC2688479  PMID: 19416539
12.  Interlinked nonlinear subnetworks underlie the formation of robust cellular patterns in Arabidopsis epidermis: a dynamic spatial model 
BMC Systems Biology  2008;2:98.
Dynamical models are instrumental for exploring the way information required to generate robust developmental patterns arises from complex interactions among genetic and non-genetic factors. We address this fundamental issue of developmental biology studying the leaf and root epidermis of Arabidopsis. We propose an experimentally-grounded model of gene regulatory networks (GRNs) that are coupled by protein diffusion and comprise a meta-GRN implemented on cellularised domains.
Steady states of the meta-GRN model correspond to gene expression profiles typical of hair and non-hair epidermal cells. The simulations also render spatial patterns that match the cellular arrangements observed in root and leaf epidermis. As in actual plants, such patterns are robust in the face of diverse perturbations. We validated the model by checking that it also reproduced the patterns of reported mutants. The meta-GRN model shows that interlinked sub-networks contribute redundantly to the formation of robust hair patterns and permits to advance novel and testable predictions regarding the effect of cell shape, signalling pathways and additional gene interactions affecting spatial cell-patterning.
The spatial meta-GRN model integrates available experimental data and contributes to further understanding of the Arabidopsis epidermal system. It also provides a systems biology framework to explore the interplay among sub-networks of a GRN, cell-to-cell communication, cell shape and domain traits, which could help understanding of general aspects of patterning processes. For instance, our model suggests that the information needed for cell fate determination emerges from dynamic processes that depend upon molecular components inside and outside differentiating cells, suggesting that the classical distinction of lineage versus positional cell differentiation may be instrumental but rather artificial. It also suggests that interlinkage of nonlinear and redundant sub-networks in larger networks is important for pattern robustness. Pursuing dynamic analyses of larger (genomic) coupled networks is still not possible. A repertoire of well-characterised regulatory modules, like the one presented here, will, however, help to uncover general principles of the patterning-associated networks, as well as the peculiarities that originate diversity.
PMCID: PMC2600786  PMID: 19014692
13.  Critical Dynamics in Genetic Regulatory Networks: Examples from Four Kingdoms 
PLoS ONE  2008;3(6):e2456.
The coordinated expression of the different genes in an organism is essential to sustain functionality under the random external perturbations to which the organism might be subjected. To cope with such external variability, the global dynamics of the genetic network must possess two central properties. (a) It must be robust enough as to guarantee stability under a broad range of external conditions, and (b) it must be flexible enough to recognize and integrate specific external signals that may help the organism to change and adapt to different environments. This compromise between robustness and adaptability has been observed in dynamical systems operating at the brink of a phase transition between order and chaos. Such systems are termed critical. Thus, criticality, a precise, measurable, and well characterized property of dynamical systems, makes it possible for robustness and adaptability to coexist in living organisms. In this work we investigate the dynamical properties of the gene transcription networks reported for S. cerevisiae, E. coli, and B. subtilis, as well as the network of segment polarity genes of D. melanogaster, and the network of flower development of A. thaliana. We use hundreds of microarray experiments to infer the nature of the regulatory interactions among genes, and implement these data into the Boolean models of the genetic networks. Our results show that, to the best of the current experimental data available, the five networks under study indeed operate close to criticality. The generality of this result suggests that criticality at the genetic level might constitute a fundamental evolutionary mechanism that generates the great diversity of dynamically robust living forms that we observe around us.
PMCID: PMC2423472  PMID: 18560561

Results 1-13 (13)