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

"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

Single-cell approaches for understanding morphogenesis using Computational Morphodynamics

In multicellular organisms cells grow, divide and adopt different fates, resulting in tissues and organs with specific functions. In recent years, a number of studies have brought quantitative knowledge about how these processes are orchestrated, shed-ding new light on cells as active and central players in morphogenesis. We explore recent advances in understanding plant morphogenesis from a quantitative perspective, defining the re-search field of Computational Morphodynamics. The focus is on studies combining theoretical and experimental approaches integrating hypotheses of how molecular and mechanical regulation at the cellular level lead to tissue behaviour. Finally, we dis-cuss some of the main challenges for future work

An introduction to modelling flower primordium initiation

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

Role of transcriptional regulation in the evolution of plant phenotype: A dynamic systems approach

© 2015 Wiley Periodicals, Inc. A growing body of evidence suggests that alterations in transcriptional regulation of genes involved in modulating development are an important part of phenotypic evolution, and this can be documented among species and within populations. While the effects of differential transcriptional regulation in organismal development have been preferentially studied in animal systems, this phenomenon has also been addressed in plants. In this review, we summarize evidence for cis-regulatory mutations, trans-regulatory changes and epigenetic modifications as molecular events underlying important phenotypic alterations, and thus shaping the evolution of plant development. We postulate that a mechanistic understanding of why such molecular alterations have a key role in development, morphology and evolution will have to rely on dynamic models of complex regulatory networks that consider the concerted action of genetic and nongenetic components, and that also incorporate the restrictions underlying the genotype to phenotype mapping process.CONACyT 180098, 180380, 167705, 152649 and PAPIIT UNAM IN203214-3, IN203113-3, IN203814-3. BFU2012–34821 (MINECO) to C.G. and an institutional grant from Fundación Ramón Aceres to CBMSOPeer Reviewe

Evolving Sensitivity Balances Boolean Networks

We investigate the sensitivity of Boolean Networks (BNs) to mutations. We are interested in Boolean Networks as a model of Gene Regulatory Networks (GRNs). We adopt Ribeiro and Kauffman’s Ergodic Set and use it to study the long term dynamics of a BN. We define the sensitivity of a BN to be the mean change in its Ergodic Set structure under all possible loss of interaction mutations. Insilico experiments were used to selectively evolve BNs for sensitivity to losing interactions. We find that maximum sensitivity was often achievable and resulted in the BNs becoming topologically balanced, i.e. they evolve towards network structures in which they have a similar number of inhibitory and excitatory interactions. In terms of the dynamics, the dominant sensitivity strategy that evolved was to build BNs with Ergodic Sets dominated by a single long limit cycle which is easily destabilised by mutations. We discuss the relevance of our findings in the context of Stem Cell Differentiation and propose a relationship between pluripotent stem cells and our evolved sensitive networks