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

Single-cell and coupled GRN models of cell patterning in the Arabidopsis thaliana root stem cell niche

<p>Abstract</p> <p>Background</p> <p>Recent experimental work has uncovered some of the genetic components required to maintain the <it>Arabidopsis thaliana </it>root stem cell niche (SCN) and its structure. Two main pathways are involved. One pathway depends on the genes <it>SHORTROOT </it>and <it>SCARECROW </it>and the other depends on the <it>PLETHORA </it>genes, which have been proposed to constitute the auxin readouts. Recent evidence suggests that a regulatory circuit, composed of <it>WOX5 </it>and <it>CLE40</it>, 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.</p> <p>Results</p> <p>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.</p> <p>Conclusions</p> <p>These models are the first published approximations for a dynamic mechanism of the <it>A. thaliana </it>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.</p

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

<p>Abstract</p> <p>Background</p> <p>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 <it>Arabidopsis</it>. 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.</p> <p>Results</p> <p>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.</p> <p>Conclusion</p> <p>The spatial meta-GRN model integrates available experimental data and contributes to further understanding of the <it>Arabidopsis </it>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 <it>versus </it>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.</p

Dispersal of transgenes through maize seed systems in Mexico.

ObjectivesCurrent 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.MethodsWe 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.ResultsRecombinant 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.ConclusionsUnderstanding 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

"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis

<p>Abstract</p> <p>Background</p> <p>In Thomas' formalism for modeling gene regulatory networks (GRNs), <it>branching time</it>, where a state can have <it>more than one possible future</it>, 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 <it>infinitely many </it>paths may appear, limiting ordinary simulators to statistical conclusions. <it>Model checkers </it>for branching time, by contrast, are able to prove properties in the presence of infinitely many paths.</p> <p>Results</p> <p>We have developed <it>Antelope </it>("Analysis of Networks through TEmporal-LOgic sPEcifications", <url>http://turing.iimas.unam.mx:8080/AntelopeWEB/</url>), a model checker for analyzing and constructing Boolean GRNs. Currently, software systems for Boolean GRNs use branching time almost exclusively for asynchrony. <it>Antelope</it>, 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 <it>Arabidopsis thaliana </it>root stem cell niche.</p> <p>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 <it>given </it>set of model states has a given property. In comparison, a model checker for Boolean GRNs is preferable if it <it>reports </it>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.</p> <p><it>Antelope </it>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.</p> <p>Conclusions</p> <p>We illustrate the advantages of <it>Antelope </it>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.</p

Origins and Proliferative States of Human Oligodendrocyte Precursor Cells.

Human cerebral cortex size and complexity has increased greatly during evolution. While increased progenitor diversity and enhanced proliferative potential play important roles in human neurogenesis and gray matter expansion, the mechanisms of human oligodendrogenesis and white matter expansion remain largely unknown. Here, we identify EGFR-expressing "Pre-OPCs" that originate from outer radial glial cells (oRGs) and undergo mitotic somal translocation (MST) during division. oRG-derived Pre-OPCs provide an additional source of human cortical oligodendrocyte precursor cells (OPCs) and define a lineage trajectory. We further show that human OPCs undergo consecutive symmetric divisions to exponentially increase the progenitor pool size. Additionally, we find that the OPC-enriched gene, PCDH15, mediates daughter cell repulsion and facilitates proliferation. These findings indicate properties of OPC derivation, proliferation, and dispersion important for human white matter expansion and myelination