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1.  To Lyse or Not to Lyse: Transient-Mediated Stochastic Fate Determination in Cells Infected by Bacteriophages 
PLoS Computational Biology  2011;7(3):e1002006.
Cell fate determination is usually described as the result of the stochastic dynamics of gene regulatory networks (GRNs) reaching one of multiple steady-states each of which corresponds to a specific decision. However, the fate of a cell is determined in finite time suggesting the importance of transient dynamics in cellular decision making. Here we consider cellular decision making as resulting from first passage processes of regulatory proteins and examine the effect of transient dynamics within the initial lysis-lysogeny switch of phage λ. Importantly, the fate of an infected cell depends, in part, on the number of coinfecting phages. Using a quantitative model of the phage λ GRN, we find that changes in the likelihood of lysis and lysogeny can be driven by changes in phage co-infection number regardless of whether or not there exists steady-state bistability within the GRN. Furthermore, two GRNs which yield qualitatively distinct steady state behaviors as a function of phage infection number can show similar transient responses, sufficient for alternative cell fate determination. We compare our model results to a recent experimental study of cell fate determination in single cell assays of multiply infected bacteria. Whereas the experimental study proposed a “quasi-independent” hypothesis for cell fate determination consistent with an observed data collapse, we demonstrate that observed cell fate results are compatible with an alternative form of data collapse consistent with a partial gene dosage compensation mechanism. We show that including partial gene dosage compensation at the mRNA level in our stochastic model of fate determination leads to the same data collapse observed in the single cell study. Our findings elucidate the importance of transient gene regulatory dynamics in fate determination, and present a novel alternative hypothesis to explain single-cell level heterogeneity within the phage λ lysis-lysogeny decision switch.
Author Summary
Multicellular organisms, single-celled organisms, and even viruses can exhibit alternative responses to various internal and environmental conditions. At the cellular level, alternative fate determination is usually described as the result of the inherent bistability of gene regulatory networks (GRNs). However, the fate of a cell is determined in finite time suggesting the importance of transient dynamics to cellular decision making. Here, we present a quantitative gene regulatory model of how bacteriophages determine the fate of an infected bacterium. We find that increasing the number of infecting phages increases the chance of quiescent (i.e., lysogeny) vs. productive (i.e. lysis) viral growth, in agreement with prior studies. However, unlike previous theoretical studies, the bias in cell fate is a result of the transient divergence of stochastic gene expression dynamics. We compare and contrast our theoretical model with recent observations of cell fate measured at the single-cell level within multiply-infected cells. Predicted heterogeneity in cell fate is shown to agree with data when including a previously unidentified gene dosage compensation mechanism, which represents an alternative hypothesis to how multiple phages interact in influencing cell fate. Together, our results suggest the importance of quantitative details of transient gene regulation in driving stochastic fate determination.
doi:10.1371/journal.pcbi.1002006
PMCID: PMC3053317  PMID: 21423715
2.  Interlinked nonlinear subnetworks underlie the formation of robust cellular patterns in Arabidopsis epidermis: a dynamic spatial model 
BMC Systems Biology  2008;2:98.
Background
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.
Results
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.
Conclusion
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.
doi:10.1186/1752-0509-2-98
PMCID: PMC2600786  PMID: 19014692
3.  Monte Carlo analysis of an ODE Model of the Sea Urchin Endomesoderm Network 
BMC Systems Biology  2009;3:83.
Background
Gene Regulatory Networks (GRNs) control the differentiation, specification and function of cells at the genomic level. The levels of interactions within large GRNs are of enormous depth and complexity. Details about many GRNs are emerging, but in most cases it is unknown to what extent they control a given process, i.e. the grade of completeness is uncertain. This uncertainty stems from limited experimental data, which is the main bottleneck for creating detailed dynamical models of cellular processes. Parameter estimation for each node is often infeasible for very large GRNs. We propose a method, based on random parameter estimations through Monte-Carlo simulations to measure completeness grades of GRNs.
Results
We developed a heuristic to assess the completeness of large GRNs, using ODE simulations under different conditions and randomly sampled parameter sets to detect parameter-invariant effects of perturbations. To test this heuristic, we constructed the first ODE model of the whole sea urchin endomesoderm GRN, one of the best studied large GRNs. We find that nearly 48% of the parameter-invariant effects correspond with experimental data, which is 65% of the expected optimal agreement obtained from a submodel for which kinetic parameters were estimated and used for simulations. Randomized versions of the model reproduce only 23.5% of the experimental data.
Conclusion
The method described in this paper enables an evaluation of network topologies of GRNs without requiring any parameter values. The benefit of this method is exemplified in the first mathematical analysis of the complete Endomesoderm Network Model. The predictions we provide deliver candidate nodes in the network that are likely to be erroneous or miss unknown connections, which may need additional experiments to improve the network topology. This mathematical model can serve as a scaffold for detailed and more realistic models. We propose that our method can be used to assess a completeness grade of any GRN. This could be especially useful for GRNs involved in human diseases, where often the amount of connectivity is unknown and/or many genes/interactions are missing.
doi:10.1186/1752-0509-3-83
PMCID: PMC2739852  PMID: 19698179
4.  GeStoDifferent: a Cytoscape plugin for the generation and the identification of gene regulatory networks describing a stochastic cell differentiation process 
Bioinformatics  2013;29(4):513-514.
Summary: The characterization of the complex phenomenon of cell differentiation is a key goal of both systems and computational biology. GeStoDifferent is a Cytoscape plugin aimed at the generation and the identification of gene regulatory networks (GRNs) describing an arbitrary stochastic cell differentiation process. The (dynamical) model adopted to describe general GRNs is that of noisy random Boolean networks (NRBNs), with a specific focus on their emergent dynamical behavior. GeStoDifferent explores the space of GRNs by filtering the NRBN instances inconsistent with a stochastic lineage differentiation tree representing the cell lineages that can be obtained by following the fate of a stem cell descendant. Matched networks can then be analyzed by Cytoscape network analysis algorithms or, for instance, used to define (multiscale) models of cellular dynamics.
Availability: Freely available at http://bimib.disco.unimib.it/index.php/Retronet#GESTODifferent or at the Cytoscape App Store http://apps.cytoscape.org/.
Contact: marco.antoniotti@unimib.it
doi:10.1093/bioinformatics/bts726
PMCID: PMC3888149  PMID: 23292740
5.  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.
doi:10.1199/tab.0127
PMCID: PMC3244948  PMID: 22303253
6.  A Kalman-Filter Based Approach to Identification of Time-Varying Gene Regulatory Networks 
PLoS ONE  2013;8(10):e74571.
Motivation
Conventional identification methods for gene regulatory networks (GRNs) have overwhelmingly adopted static topology models, which remains unchanged over time to represent the underlying molecular interactions of a biological system. However, GRNs are dynamic in response to physiological and environmental changes. Although there is a rich literature in modeling static or temporally invariant networks, how to systematically recover these temporally changing networks remains a major and significant pressing challenge. The purpose of this study is to suggest a two-step strategy that recovers time-varying GRNs.
Results
It is suggested in this paper to utilize a switching auto-regressive model to describe the dynamics of time-varying GRNs, and a two-step strategy is proposed to recover the structure of time-varying GRNs. In the first step, the change points are detected by a Kalman-filter based method. The observed time series are divided into several segments using these detection results; and each time series segment belonging to two successive demarcating change points is associated with an individual static regulatory network. In the second step, conditional network structure identification methods are used to reconstruct the topology for each time interval. This two-step strategy efficiently decouples the change point detection problem and the topology inference problem. Simulation results show that the proposed strategy can detect the change points precisely and recover each individual topology structure effectively. Moreover, computation results with the developmental data of Drosophila Melanogaster show that the proposed change point detection procedure is also able to work effectively in real world applications and the change point estimation accuracy exceeds other existing approaches, which means the suggested strategy may also be helpful in solving actual GRN reconstruction problem.
doi:10.1371/journal.pone.0074571
PMCID: PMC3792119  PMID: 24116005
7.  Network component analysis provides quantitative insights on an Arabidopsis transcription factor-gene regulatory network 
BMC Systems Biology  2013;7:126.
Background
Gene regulatory networks (GRNs) are models of molecule-gene interactions instrumental in the coordination of gene expression. Transcription factor (TF)-GRNs are an important subset of GRNs that characterize gene expression as the effect of TFs acting on their target genes. Although such networks can qualitatively summarize TF-gene interactions, it is highly desirable to quantitatively determine the strengths of the interactions in a TF-GRN as well as the magnitudes of TF activities. To our knowledge, such analysis is rare in plant biology. A computational methodology developed for this purpose is network component analysis (NCA), which has been used for studying large-scale microbial TF-GRNs to obtain nontrivial, mechanistic insights. In this work, we employed NCA to quantitatively analyze a plant TF-GRN important in floral development using available regulatory information from AGRIS, by processing previously reported gene expression data from four shoot apical meristem cell types.
Results
The NCA model satisfactorily accounted for gene expression measurements in a TF-GRN of seven TFs (LFY, AG, SEPALLATA3 [SEP3], AP2, AGL15, HY5 and AP3/PI) and 55 genes. NCA found strong interactions between certain TF-gene pairs including LFY → MYB17, AG → CRC, AP2 → RD20, AGL15 → RAV2 and HY5 → HLH1, and the direction of the interaction (activation or repression) for some AGL15 targets for which this information was not previously available. The activity trends of four TFs - LFY, AG, HY5 and AP3/PI as deduced by NCA correlated well with the changes in expression levels of the genes encoding these TFs across all four cell types; such a correlation was not observed for SEP3, AP2 and AGL15.
Conclusions
For the first time, we have reported the use of NCA to quantitatively analyze a plant TF-GRN important in floral development for obtaining nontrivial information about connectivity strengths between TFs and their target genes as well as TF activity. However, since NCA relies on documented connectivity information about the underlying TF-GRN, it is currently limited in its application to larger plant networks because of the lack of documented connectivities. In the future, the identification of interactions between plant TFs and their target genes on a genome scale would allow the use of NCA to provide quantitative regulatory information about plant TF-GRNs, leading to improved insights on cellular regulatory programs.
doi:10.1186/1752-0509-7-126
PMCID: PMC3843564  PMID: 24228871
8.  The endoderm gene regulatory network in sea urchin embryos up to mid-blastula stage☆ 
Developmental biology  2009;340(2):188-199.
As the result of early specification processes, sea urchin embryos eventually form various mesodermal cell lineages and a gut consisting of fore-, mid- and hindgut. The progression of specification as well as the overall spatial organization of the organism is encoded in its gene regulatory networks (GRNs). We have analyzed the GRN driving endoderm specification up to the onset of gastrulation and present in this paper the mechanisms which determine this process up to mid-blastula stage. At this stage, the embryo consists of two separate lineages of endoderm precursor cells with distinct regulatory states. One of these lineages, the veg2 cell lineage, gives rise to endoderm and mesoderm cell types. The separation of these cell fates is initiated by the spatially confined activation of the mesoderm GRN superimposed on a generally activated endoderm GRN within veg2 descendants. Here we integrate the architecture of regulatory interactions with the spatial restriction of regulatory gene expression to model the logic control of endoderm development.
doi:10.1016/j.ydbio.2009.10.037
PMCID: PMC3981691  PMID: 19895806
Gene regulatory network; Endoderm; Mesoderm; Embryonic specification
9.  Use of transcriptome sequencing to understand the pistillate flowering in hickory (Carya cathayensis Sarg.) 
BMC Genomics  2013;14:691.
Background
Different from herbaceous plants, the woody plants undergo a long-period vegetative stage to achieve floral transition. They then turn into seasonal plants, flowering annually. In this study, a preliminary model of gene regulations for seasonal pistillate flowering in hickory (Carya cathayensis) was proposed. The genome-wide dynamic transcriptome was characterized via the joint-approach of RNA sequencing and microarray analysis.
Results
Differential transcript abundance analysis uncovered the dynamic transcript abundance patterns of flowering correlated genes and their major functions based on Gene Ontology (GO) analysis. To explore pistillate flowering mechanism in hickory, a comprehensive flowering gene regulatory network based on Arabidopsis thaliana was constructed by additional literature mining. A total of 114 putative flowering or floral genes including 31 with differential transcript abundance were identified in hickory. The locations, functions and dynamic transcript abundances were analyzed in the gene regulatory networks. A genome-wide co-expression network for the putative flowering or floral genes shows three flowering regulatory modules corresponding to response to light abiotic stimulus, cold stress, and reproductive development process, respectively. Totally 27 potential flowering or floral genes were recruited which are meaningful to understand the hickory specific seasonal flowering mechanism better.
Conclusions
Flowering event of pistillate flower bud in hickory is triggered by several pathways synchronously including the photoperiod, autonomous, vernalization, gibberellin, and sucrose pathway. Totally 27 potential flowering or floral genes were recruited from the genome-wide co-expression network function module analysis. Moreover, the analysis provides a potential FLC-like gene based vernalization pathway and an 'AC’ model for pistillate flower development in hickory. This work provides an available framework for pistillate flower development in hickory, which is significant for insight into regulation of flowering and floral development of woody plants.
doi:10.1186/1471-2164-14-691
PMCID: PMC3853572  PMID: 24106755
Co-expression network; Carya cathayensis Sarg; Floral development; Seasonal flowering; Hickory; High-throughput data analysis
10.  myGRN: a database and visualisation system for the storage and analysis of developmental genetic regulatory networks 
Background
Biological processes are regulated by complex interactions between transcription factors and signalling molecules, collectively described as Genetic Regulatory Networks (GRNs). The characterisation of these networks to reveal regulatory mechanisms is a long-term goal of many laboratories. However compiling, visualising and interacting with such networks is non-trivial. Current tools and databases typically focus on GRNs within simple, single celled organisms. However, data is available within the literature describing regulatory interactions in multi-cellular organisms, although not in any systematic form. This is particularly true within the field of developmental biology, where regulatory interactions should also be tagged with information about the time and anatomical location of development in which they occur.
Description
We have developed myGRN (), a web application for storing and interrogating interaction data, with an emphasis on developmental processes. Users can submit interaction and gene expression data, either curated from published sources or derived from their own unpublished data. All interactions associated with publications are publicly visible, and unpublished interactions can only be shared between collaborating labs prior to publication. Users can group interactions into discrete networks based on specific biological processes. Various filters allow dynamic production of network diagrams based on a range of information including tissue location, developmental stage or basic topology. Individual networks can be viewed using myGRV, a tool focused on displaying developmental networks, or exported in a range of formats compatible with third party tools. Networks can also be analysed for the presence of common network motifs. We demonstrate the capabilities of myGRN using a network of zebrafish interactions integrated with expression data from the zebrafish database, ZFIN.
Conclusion
Here we are launching myGRN as a community-based repository for interaction networks, with a specific focus on developmental networks. We plan to extend its functionality, as well as use it to study networks involved in embryonic development in the future.
doi:10.1186/1471-213X-9-33
PMCID: PMC2702357  PMID: 19500400
11.  Anomaly detection in gene expression via stochastic models of gene regulatory networks 
BMC Genomics  2009;10(Suppl 3):S26.
Background
The steady-state behaviour of gene regulatory networks (GRNs) can provide crucial evidence for detecting disease-causing genes. However, monitoring the dynamics of GRNs is particularly difficult because biological data only reflects a snapshot of the dynamical behaviour of the living organism. Also most GRN data and methods are used to provide limited structural inferences.
Results
In this study, the theory of stochastic GRNs, derived from G-Networks, is applied to GRNs in order to monitor their steady-state behaviours. This approach is applied to a simulation dataset which is generated by using the stochastic gene expression model, and observe that the G-Network properly detects the abnormally expressed genes in the simulation study. In the analysis of real data concerning the cell cycle microarray of budding yeast, our approach finds that the steady-state probability of CLB2 is lower than that of other agents, while most of the genes have similar steady-state probabilities. These results lead to the conclusion that the key regulatory genes of the cell cycle can be expressed in the absence of CLB type cyclines, which was also the conclusion of the original microarray experiment study.
Conclusion
G-networks provide an efficient way to monitor steady-state of GRNs. Our method produces more reliable results then the conventional t-test in detecting differentially expressed genes. Also G-networks are successfully applied to the yeast GRNs. This study will be the base of further GRN dynamics studies cooperated with conventional GRN inference algorithms.
doi:10.1186/1471-2164-10-S3-S26
PMCID: PMC2788379  PMID: 19958490
12.  Short-term information processing, long-term responses: Insights by mathematical modeling of signal transduction 
Bioessays  2012;34(7):542-550.
How do cells interpret information from their environment and translate it into specific cell fate decisions? We propose that cell fate is already encoded in early signaling events and thus can be predicted from defined signal properties. Specifically, we hypothesize that the time integral of activated key signaling molecules can be correlated to cellular behavior such as proliferation or differentiation. The identification of these decisive key signal mediators and their connection to cell fate is facilitated by mathematical modeling. A possible mechanistic linkage between signaling dynamics and cellular function is the directed control of gene regulatory networks by defined signals. Targeted experiments in combination with mathematical modeling can increase our understanding of how cells process information and realize distinct cell fates.
doi:10.1002/bies.201100172
PMCID: PMC3440590  PMID: 22528856
cell fate decision; gene regulatory network; integrated response; mathematical model; signaling dynamics
13.  Perturbation analysis analyzed - Mathematical modeling of intact and perturbed gene regulatory circuits for animal development 
Developmental biology  2010;344(2):1110-1118.
Gene regulatory networks for animal development are the underlying mechanisms controlling cell fate specification and differentiation. The architecture of gene regulatory circuits determines their information processing properties and their developmental function. It is a major task to derive realistic network models from exceedingly advanced high throughput experimental data. Here we use mathematical modeling to study the dynamics of gene regulatory circuits to advance the ability to infer regulatory connections and logic function from experimental data. This study is guided by experimental methodologies that are commonly used to study gene regulatory networks that control cell fate specification. We study the effect of a perturbation of an input on the level of its downstream genes and compare between the cis-regulatory execution of OR and AND logics. Circuits that initiate gene activation and circuits that lock on the expression of genes are analyzed. The model improves our ability to analyze experimental data and construct from it the network topology. The model also illuminates information processing properties of gene regulatory circuits for animal development.
doi:10.1016/j.ydbio.2010.06.020
PMCID: PMC2920143  PMID: 20599898
Gene regulatory networks; Perturbation analysis; Mathematical modeling
14.  Inferring robust gene networks from expression data by a sensitivity-based incremental evolution method 
BMC Bioinformatics  2012;13(Suppl 7):S8.
Background
Reconstructing gene regulatory networks (GRNs) from expression data is one of the most important challenges in systems biology research. Many computational models and methods have been proposed to automate the process of network reconstruction. Inferring robust networks with desired behaviours remains challenging, however. This problem is related to network dynamics but has yet to be investigated using network modeling.
Results
We propose an incremental evolution approach for inferring GRNs that takes network robustness into consideration and can deal with a large number of network parameters. Our approach includes a sensitivity analysis procedure to iteratively select the most influential network parameters, and it uses a swarm intelligence procedure to perform parameter optimization. We have conducted a series of experiments to evaluate the external behaviors and internal robustness of the networks inferred by the proposed approach. The results and analyses have verified the effectiveness of our approach.
Conclusions
Sensitivity analysis is crucial to identifying the most sensitive parameters that govern the network dynamics. It can further be used to derive constraints for network parameters in the network reconstruction process. The experimental results show that the proposed approach can successfully infer robust GRNs with desired system behaviors.
doi:10.1186/1471-2105-13-S7-S8
PMCID: PMC3348052  PMID: 22595005
15.  Vasohibin-1 is identified as a master-regulator of endothelial cell apoptosis using gene network analysis 
BMC Genomics  2013;14:23.
Background
Apoptosis is a critical process in endothelial cell (EC) biology and pathology, which has been extensively studied at protein level. Numerous gene expression studies of EC apoptosis have also been performed, however few attempts have been made to use gene expression data to identify the molecular relationships and master regulators that underlie EC apoptosis. Therefore, we sought to understand these relationships by generating a Bayesian gene regulatory network (GRN) model.
Results
ECs were induced to undergo apoptosis using serum withdrawal and followed over a time course in triplicate, using microarrays. When generating the GRN, this EC time course data was supplemented by a library of microarray data from EC treated with siRNAs targeting over 350 signalling molecules.
The GRN model proposed Vasohibin-1 (VASH1) as one of the candidate master-regulators of EC apoptosis with numerous downstream mRNAs. To evaluate the role played by VASH1 in EC, we used siRNA to reduce the expression of VASH1. Of 10 mRNAs downstream of VASH1 in the GRN that were examined, 7 were significantly up- or down-regulated in the direction predicted by the GRN.Further supporting an important biological role of VASH1 in EC, targeted reduction of VASH1 mRNA abundance conferred resistance to serum withdrawal-induced EC death.
Conclusion
We have utilised Bayesian GRN modelling to identify a novel candidate master regulator of EC apoptosis. This study demonstrates how GRN technology can complement traditional methods to hypothesise the regulatory relationships that underlie important biological processes.
doi:10.1186/1471-2164-14-23
PMCID: PMC3570387  PMID: 23324451
Vasohibin; HUVEC; Bayesian; Gene regulatory network
16.  Floral Morphogenesis: Stochastic Explorations of a Gene Network Epigenetic Landscape 
PLoS ONE  2008;3(11):e3626.
In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical temporal pattern in gene expression during flower development. We modeled the regulatory network of organ identity genes in the Arabidopsis thaliana flower as a stochastic system. This network has previously been shown to converge to ten fixed-point attractors, each with gene expression arrays that characterize inflorescence cells and primordial cells of sepals, petals, stamens, and carpels. The network used is binary, and the logical rules that govern its dynamics are grounded in experimental evidence. We introduced different levels of uncertainty in the updating rules of the network. Interestingly, for a level of noise of around 0.5–10%, the system exhibited a sequence of transitions among attractors that mimics the sequence of gene activation configurations observed in real flowers. We also implemented the gene regulatory network as a continuous system using the Glass model of differential equations, that can be considered as a first approximation of kinetic-reaction equations, but which are not necessarily equivalent to the Boolean model. Interestingly, the Glass dynamics recover a temporal sequence of attractors, that is qualitatively similar, although not identical, to that obtained using the Boolean model. Thus, time ordering in the emergence of cell-fate patterns is not an artifact of synchronous updating in the Boolean model. Therefore, our model provides a novel explanation for the emergence and robustness of the ubiquitous temporal pattern of floral organ specification. It also constitutes a new approach to understanding morphogenesis, providing predictions on the population dynamics of cells with different genetic configurations during development.
doi:10.1371/journal.pone.0003626
PMCID: PMC2572848  PMID: 18978941
17.  Oscillatory Protein Expression Dynamics Endows Stem Cells with Robust Differentiation Potential 
PLoS ONE  2011;6(11):e27232.
The lack of understanding of stem cell differentiation and proliferation is a fundamental problem in developmental biology. Although gene regulatory networks (GRNs) for stem cell differentiation have been partially identified, the nature of differentiation dynamics and their regulation leading to robust development remain unclear. Herein, using a dynamical system modeling cell approach, we performed simulations of the developmental process using all possible GRNs with a few genes, and screened GRNs that could generate cell type diversity through cell-cell interactions. We found that model stem cells that both proliferated and differentiated always exhibited oscillatory expression dynamics, and the differentiation frequency of such stem cells was regulated, resulting in a robust number distribution. Moreover, we uncovered the common regulatory motifs for stem cell differentiation, in which a combination of regulatory motifs that generated oscillatory expression dynamics and stabilized distinct cellular states played an essential role. These findings may explain the recently observed heterogeneity and dynamic equilibrium in cellular states of stem cells, and can be used to predict regulatory networks responsible for differentiation in stem cell systems.
doi:10.1371/journal.pone.0027232
PMCID: PMC3207845  PMID: 22073296
18.  Understanding the Dynamic Behavior of Genetic Regulatory Networks by Functional Decomposition 
Current genomics  2006;7(6):333-341.
A number of mechanistic and predictive genetic regulatory networks (GRNs) comprising dozens of genes have already been characterized at the level of cis-regulatory interactions. Reconstructions of networks of 100’s to 1000’s of genes and their interactions are currently underway. Understanding the organizational and functional principles underlying these networks is probably the single greatest challenge facing genomics today. We review the current approaches to deciphering large-scale GRNs and discuss some of their limitations. We then propose a bottom-up approach in which large-scale GRNs are first organized in terms of functionally distinct GRN building blocks of one or a few genes. Biological processes may then be viewed as the outcome of functional interactions among these simple, well-characterized functional building blocks. We describe several putative GRN functional building blocks and show that they can be located within GRNs on the basis of their interaction topology and additional, simple and experimentally testable constraints.
doi:10.2174/138920206778948718
PMCID: PMC2134916  PMID: 18079985
Genetic regulatory networks; systems biology; transcriptional regulation; visualization
19.  The Quest to Understand the Basis and Mechanisms that Control Expression of Introduced Transgenes in Crop Plants 
Plant Signaling & Behavior  2006;1(4):185-195.
We discuss mechanisms and factors that influence levels and stability of expressed heterologous proteins in crop plants. We have seen substantial progress in this field over the past two decades in model experimental organisms such as Arabidopsis and tobacco. There is no question such studies have resulted in furthering our understanding of key processes in the plant cell and the elaboration of sophisticated models to explain underlying mechanisms that might influence the fate, levels and stability of expression of recombinant heterologous proteins in plants. However, very often, such information is not applicable outside these laboratory experimental models. In order to generate a knowledge basis that can be used to achieve high levels and stability of heterologous proteins in relevant crop plants it is imperative to perform such studies on the target crops. With this in mind, we discuss key elements of the process at the DNA, RNA and protein levels. We believe it is essential to discuss recombinant protein production in crops in a holistic manner in order to develop a comprehensive knowledge base that will in turn serve plant biotechnology applications well.
PMCID: PMC2634025  PMID: 19521484
transgene expression; protein trafficking; silencing mechanisms; chromatin remodeling; crop plants
20.  GeNESiS: gene network evolution simulation software 
BMC Bioinformatics  2008;9:541.
Background
There has been a lot of interest in recent years focusing on the modeling and simulation of Gene Regulatory Networks (GRNs). However, the evolutionary mechanisms that give rise to GRNs in the first place are still largely unknown. In an earlier work, we developed a framework to analyze the effect of objective functions, input types and starting populations on the evolution of GRNs with a specific emphasis on the robustness of evolved GRNs.
Results
In this work, we present a parallel software package, GeNESiS for the modeling and simulation of the evolution of gene regulatory networks (GRNs). The software models the process of gene regulation through a combination of finite-state and stochastic models. The evolution of GRNs is then simulated by means of a genetic algorithm with the network connections represented as binary strings. The software allows users to simulate the evolution under varying selective pressures and starting conditions. We believe that the software provides a way for researchers to understand the evolutionary behavior of populations of GRNs.
Conclusion
We believe that GeNESiS will serve as a useful tool for scientists interested in understanding the evolution of gene regulatory networks under a range of different conditions and selective pressures. Such modeling efforts can lead to a greater understanding of the network characteristics of GRNs.
doi:10.1186/1471-2105-9-541
PMCID: PMC2640387  PMID: 19087333
21.  Inferring Nonlinear Gene Regulatory Networks from Gene Expression Data Based on Distance Correlation 
PLoS ONE  2014;9(2):e87446.
Nonlinear dependence is general in regulation mechanism of gene regulatory networks (GRNs). It is vital to properly measure or test nonlinear dependence from real data for reconstructing GRNs and understanding the complex regulatory mechanisms within the cellular system. A recently developed measurement called the distance correlation (DC) has been shown powerful and computationally effective in nonlinear dependence for many situations. In this work, we incorporate the DC into inferring GRNs from the gene expression data without any underling distribution assumptions. We propose three DC-based GRNs inference algorithms: CLR-DC, MRNET-DC and REL-DC, and then compare them with the mutual information (MI)-based algorithms by analyzing two simulated data: benchmark GRNs from the DREAM challenge and GRNs generated by SynTReN network generator, and an experimentally determined SOS DNA repair network in Escherichia coli. According to both the receiver operator characteristic (ROC) curve and the precision-recall (PR) curve, our proposed algorithms significantly outperform the MI-based algorithms in GRNs inference.
doi:10.1371/journal.pone.0087446
PMCID: PMC3925093  PMID: 24551058
22.  B-cell lymphoma gene regulatory networks: biological consistency among inference methods 
Frontiers in Genetics  2013;4:281.
Despite the development of numerous gene regulatory network (GRN) inference methods in the last years, their application, usage and the biological significance of the resulting GRN remains unclear for our general understanding of large-scale gene expression data in routine practice. In our study, we conduct a structural and a functional analysis of B-cell lymphoma GRNs that were inferred using 3 mutual information-based GRN inference methods: C3Net, BC3Net and Aracne. From a comparative analysis on the global level, we find that the inferred B-cell lymphoma GRNs show major differences. However, on the edge-level and the functional-level—that are more important for our biological understanding—the B-cell lymphoma GRNs were highly similar among each other. Also, the ranks of the degree centrality values and major hub genes in the inferred networks are highly conserved as well. Interestingly, the major hub genes of all GRNs are associated with the G-protein-coupled receptor pathway, cell-cell signaling and cell cycle. This implies that hub genes of the GRNs can be highly consistently inferred with C3Net, BC3Net, and Aracne, representing prominent targets for signaling pathways. Finally, we describe the functional and structural relationship between C3Net, BC3Net and Aracne gene regulatory networks. Our study shows that these GRNs that are inferred from large-scale gene expression data are promising for the identification of novel candidate interactions and pathways that play a key role in the underlying mechanisms driving cancer hallmarks. Overall, our comparative analysis reveals that these GRNs inferred with considerably different inference methods contain large amounts of consistent, method independent, biological information.
doi:10.3389/fgene.2013.00281
PMCID: PMC3864360  PMID: 24379827
gene regulatory network; C3Net; BC3Net; Aracne; GPEA; statistical inference
23.  The gene regulatory network basis of the “community effect,” and analysis of a sea urchin embryo example 
Developmental biology  2009;340(2):170-178.
The “Community Effect” denotes intra-territorial signaling amongst cells which constitute a particular tissue or embryonic progenitor field. The cells of the territory express the same transcriptional regulatory state, and the intra-territorial signaling is essential to maintenance of this specific regulatory state. The structure of the underlying gene regulatory network (GRN) subcircuitry explains the genomically wired mechanism by which community effect signaling is linked to the continuing transcriptional generation of the territorial regulatory state. A clear example is afforded by the oral ectoderm GRN of the sea urchin embryo where cis-regulatory evidence, experimental embryology, and network analysis combine to provide a complete picture. We review this example and consider less well known but similar cases in other developing systems where the same subcircuit GRN topology is present. To resolve mechanistic issues that arise in considering how community effect signaling could operate to produce its observed effects, we construct and analyze the behavior of a quantitative model of community effect signaling in the sea urchin embryo oral ectoderm. Community effect network topology could constitute part of the genomic regulatory code that defines transcriptional function in multicellular tissues composed of cells in contact, and hence may have arisen as a metazoan developmental strategy.
doi:10.1016/j.ydbio.2009.06.007
PMCID: PMC2854306  PMID: 19523466
Community effect; Intradomain signaling; sea urchin embryo; nodal gene regulation
24.  Inferring Gene Regulatory Networks by Singular Value Decomposition and Gravitation Field Algorithm 
PLoS ONE  2012;7(12):e51141.
Reconstruction of gene regulatory networks (GRNs) is of utmost interest and has become a challenge computational problem in system biology. However, every existing inference algorithm from gene expression profiles has its own advantages and disadvantages. In particular, the effectiveness and efficiency of every previous algorithm is not high enough. In this work, we proposed a novel inference algorithm from gene expression data based on differential equation model. In this algorithm, two methods were included for inferring GRNs. Before reconstructing GRNs, singular value decomposition method was used to decompose gene expression data, determine the algorithm solution space, and get all candidate solutions of GRNs. In these generated family of candidate solutions, gravitation field algorithm was modified to infer GRNs, used to optimize the criteria of differential equation model, and search the best network structure result. The proposed algorithm is validated on both the simulated scale-free network and real benchmark gene regulatory network in networks database. Both the Bayesian method and the traditional differential equation model were also used to infer GRNs, and the results were used to compare with the proposed algorithm in our work. And genetic algorithm and simulated annealing were also used to evaluate gravitation field algorithm. The cross-validation results confirmed the effectiveness of our algorithm, which outperforms significantly other previous algorithms.
doi:10.1371/journal.pone.0051141
PMCID: PMC3514269  PMID: 23226565
25.  Inference of gene regulatory networks from time series by Tsallis entropy 
BMC Systems Biology  2011;5:61.
Background
The inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays. Many techniques and models have been proposed for this task. However, it is not generally possible to recover the original topology with great accuracy, mainly due to the short time series data in face of the high complexity of the networks and the intrinsic noise of the expression measurements. In order to improve the accuracy of GRNs inference methods based on entropy (mutual information), a new criterion function is here proposed.
Results
In this paper we introduce the use of generalized entropy proposed by Tsallis, for the inference of GRNs from time series expression profiles. The inference process is based on a feature selection approach and the conditional entropy is applied as criterion function. In order to assess the proposed methodology, the algorithm is applied to recover the network topology from temporal expressions generated by an artificial gene network (AGN) model as well as from the DREAM challenge. The adopted AGN is based on theoretical models of complex networks and its gene transference function is obtained from random drawing on the set of possible Boolean functions, thus creating its dynamics. On the other hand, DREAM time series data presents variation of network size and its topologies are based on real networks. The dynamics are generated by continuous differential equations with noise and perturbation. By adopting both data sources, it is possible to estimate the average quality of the inference with respect to different network topologies, transfer functions and network sizes.
Conclusions
A remarkable improvement of accuracy was observed in the experimental results by reducing the number of false connections in the inferred topology by the non-Shannon entropy. The obtained best free parameter of the Tsallis entropy was on average in the range 2.5 ≤ q ≤ 3.5 (hence, subextensive entropy), which opens new perspectives for GRNs inference methods based on information theory and for investigation of the nonextensivity of such networks. The inference algorithm and criterion function proposed here were implemented and included in the DimReduction software, which is freely available at http://sourceforge.net/projects/dimreduction and http://code.google.com/p/dimreduction/.
doi:10.1186/1752-0509-5-61
PMCID: PMC3117729  PMID: 21545720

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