Related Articles

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Background

Identifying gene regulatory network (GRN) from time course gene expression data has attracted more and more attentions. Due to the computational complexity, most approaches for GRN reconstruction are limited on a small number of genes and low connectivity of the underlying networks. These approaches can only identify a single network for a given set of genes. However, for a large-scale gene network, there might exist multiple potential sub-networks, in which genes are only functionally related to others in the sub-networks.

Results

We propose the network and community identification (NCI) method for identifying multiple subnetworks from gene expression data by incorporating community structure information into GRN inference. The proposed algorithm iteratively solves two optimization problems, and can promisingly be applied to large-scale GRNs. Furthermore, we present the efficient Block PCA method for searching communities in GRNs.

Conclusions

The NCI method is effective in identifying multiple subnetworks in a large-scale GRN. With the splitting algorithm, the Block PCA method shows a promosing attempt for exploring communities in a large-scale GRN.

Background

Biological networks are constantly subjected to random perturbations, and efficient feedback and compensatory mechanisms exist to maintain their stability. There is an increased interest in building gene regulatory networks (GRNs) from temporal gene expression data because of their numerous applications in life sciences. However, because of the limited number of time points at which gene expressions can be gathered in practice, computational techniques of building GRN often lead to inaccuracies and instabilities. This paper investigates the stability of sparse auto-regressive models of building GRN from gene expression data.

Results

Criteria for evaluating the stability of estimating GRN structure are proposed. Thereby, stability of multivariate vector autoregressive (MVAR) methods - ridge, lasso, and elastic-net - of building GRN were studied by simulating temporal gene expression datasets on scale-free topologies as well as on real data gathered over Hela cell-cycle. Effects of the number of time points on the stability of constructing GRN are investigated. When the number of time points are relatively low compared to the size of network, both accuracy and stability are adversely affected. At least, the number of time points equal to the number of genes in the network are needed to achieve decent accuracy and stability of the networks. Our results on synthetic data indicate that the stability of lasso and elastic-net MVAR methods are comparable, and their accuracies are much higher than the ridge MVAR. As the size of the network grows, the number of time points required to achieve acceptable accuracy and stability are much less relative to the number of genes in the network. The effects of false negatives are easier to improve by increasing the number time points than those due to false positives. Application to HeLa cell-cycle gene expression dataset shows that biologically stable GRN can be obtained by introducing perturbations to the data.

Conclusions

Accuracy and stability of building GRN are crucial for investigation of gene regulations. Sparse MVAR techniques such as lasso and elastic-net provide accurate and stable methods for building even GRN of small size. The effect of false negatives is corrected much easier with the increased number of time points than those due to false positives. With real data, we demonstrate how stable networks can be derived by introducing random perturbation to data.

The large influx of data from high-throughput genomic and proteomic technologies has encouraged the researchers to seek approaches for understanding the structure of gene regulatory networks and proteomic networks. This work reviews some of the most important statistical methods used for modeling of gene regulatory networks (GRNs) and protein-protein interaction (PPI) networks. The paper focuses on the recent advances in the statistical graphical modeling techniques, state-space representation models, and information theoretic methods that were proposed for inferring the topology of GRNs. It appears that the problem of inferring the structure of PPI networks is quite different from that of GRNs. Clustering and probabilistic graphical modeling techniques are of prime importance in the statistical inference of PPI networks, and some of the recent approaches using these techniques are also reviewed in this paper. Performance evaluation criteria for the approaches used for modeling GRNs and PPI networks are also discussed.

Understanding how metabolic reactions, cell signaling, and developmental pathways translate the genome of an organism into its phenotype is a grand challenge in biology. Genome-wide association studies (GWAS) statistically connect genotypes to phenotypes, without any recourse to known molecular interactions, whereas a molecular biology approach directly ties gene function to phenotype through gene regulatory networks (GRNs). Using natural variation in allele-specific expression, GWAS and GRN approaches can be merged into a single framework via structural equation modeling (SEM). This approach leverages the myriad of polymorphisms in natural populations to elucidate and quantitate the molecular pathways that underlie phenotypic variation. The SEM framework can be used to quantitate a GRN, evaluate its consistency across environments or sexes, identify the differences in GRNs between species, and annotate GRNs de novo in non-model organisms.

Systems biology aims for building quantitative models to address unresolved issues in molecular biology. In order to describe the behavior of biological cells adequately, gene regulatory networks (GRNs) are intensively investigated. As the validity of models built for GRNs depends crucially on the kinetic rates, various methods have been developed to estimate these parameters from experimental data. For this purpose, it is favorable to choose the experimental conditions yielding maximal information. However, existing experimental design principles often rely on unfulfilled mathematical assumptions or become computationally demanding with growing model complexity. To solve this problem, we combined advanced methods for parameter and uncertainty estimation with experimental design considerations. As a showcase, we optimized three simulated GRNs in one of the challenges from the Dialogue for Reverse Engineering Assessment and Methods (DREAM). This article presents our approach, which was awarded the best performing procedure at the DREAM6 Estimation of Model Parameters challenge. For fast and reliable parameter estimation, local deterministic optimization of the likelihood was applied. We analyzed identifiability and precision of the estimates by calculating the profile likelihood. Furthermore, the profiles provided a way to uncover a selection of most informative experiments, from which the optimal one was chosen using additional criteria at every step of the design process. In conclusion, we provide a strategy for optimal experimental design and show its successful application on three highly nonlinear dynamic models. Although presented in the context of the GRNs to be inferred for the DREAM6 challenge, the approach is generic and applicable to most types of quantitative models in systems biology and other disciplines.

Background

The regulation of gene expression is achieved through gene regulatory networks (GRNs) in which collections of genes interact with one another and other substances in a cell. In order to understand the underlying function of organisms, it is necessary to study the behavior of genes in a gene regulatory network context. Several computational approaches are available for modeling gene regulatory networks with different datasets. In order to optimize modeling of GRN, these approaches must be compared and evaluated in terms of accuracy and efficiency.

Results

In this paper, two important computational approaches for modeling gene regulatory networks, probabilistic Boolean network methods and dynamic Bayesian network methods, are compared using a biological time-series dataset from the Drosophila Interaction Database to construct a Drosophila gene network. A subset of time points and gene samples from the whole dataset is used to evaluate the performance of these two approaches.

Conclusion

The comparison indicates that both approaches had good performance in modeling the gene regulatory networks. The accuracy in terms of recall and precision can be improved if a smaller subset of genes is selected for inferring GRNs. The accuracy of both approaches is dependent upon the number of selected genes and time points of gene samples. In all tested cases, DBN identified more gene interactions and gave better recall than PBN.

In flowering plants, the egg and sperm cells form within haploid gametophytes. The female gametophyte of Arabidopsis consists of two gametic cells, the egg cell and the central cell, which are flanked by five accessory cells. Both gametic and accessory cells are vital for fertilization; however, the mechanisms that underlie the formation of accessory versus gametic cell fate are unknown. In a screen for regulators of egg cell fate, we isolated the lachesis (lis) mutant which forms supernumerary egg cells. In lis mutants, accessory cells differentiate gametic cell fate, indicating that LIS is involved in a mechanism that prevents accessory cells from adopting gametic cell fate. The temporal and spatial pattern of LIS expression suggests that this mechanism is generated in gametic cells. LIS is homologous to the yeast splicing factor PRP4, indicating that components of the splice apparatus participate in cell fate decisions.

Author Summary

The selection and specification of the egg cell determine the number of eggs produced by an animal or plant, which in turn dictates how many offspring that organism can produce. In most higher plants, the egg cell forms in a specialized structure consisting of four different cell types. Two cells, the egg cell and the central cell, are fertilized by sperm cells and develop into the embryo proper and the nutritive tissue (endosperm), respectively. These two gametic cells are flanked by accessory cells; but why do some cells become gametic while others differentiate into accessory cells? To answer this question, we looked for mutants in which this process is disturbed. In the lachesis mutant, accessory cells become extra egg cells. Interestingly, it seems that the misspecification of these accessory cells results from defects in the gametic cells. This suggests that accessory cells monitor the state of the gametic cells to act as a backup if required, ensuring the formation of the key reproductive cells.

In plant egg cells, gametophytes differentiate into both gametic and accessory cells; here the authors characterize a mutant that turns accessory cells into gametic cells.

Various characteristics of complex gene regulatory networks (GRNs) have been discovered during the last decade, e.g., redundancy, exponential indegree distributions, scale-free outdegree distributions, mutational robustness, and evolvability. Although progress has been made in this field, it is not well understood whether these characteristics are the direct products of selection or those of other evolutionary forces such as mutational biases and biophysical constraints. To elucidate the causal factors that promoted the evolution of complex GRNs, we examined the effect of fluctuating environmental selection and some intrinsic constraining factors on GRN evolution by using an individual-based model. We found that the evolution of complex GRNs is remarkably promoted by fixation of beneficial gene duplications under unpredictably fluctuating environmental conditions and that some internal factors inherent in organisms, such as mutational bias, gene expression costs, and constraints on expression dynamics, are also important for the evolution of GRNs. The results indicate that various biological properties observed in GRNs could evolve as a result of not only adaptation to unpredictable environmental changes but also non-adaptive processes owing to the properties of the organisms themselves. Our study emphasizes that evolutionary models considering such intrinsic constraining factors should be used as null models to analyze the effect of selection on GRN evolution.

Author Summary

Various organismal traits, including the morphology of multicellular species and metabolism in unicellular species, are determined by the amount and combinations of proteins in the cell. The complex regulatory network plays an important role in controlling the protein profiles in a cell. Recent studies have revealed that gene regulatory networks have many interesting structural and mutational features such as their scale-free structure, mutational robustness, and evolvability. However, why and how these features have emerged from evolution is unknown. In this paper, we constructed an evolutionary model of gene regulatory networks and simulated its evolution under various environmental conditions. The results show that most features of known gene regulatory networks evolve as a result of adaptation to unpredictable environmental fluctuations. In addition, some internal organismal factors, such as mutational bias, gene expression costs, and constraints on expression dynamics, are also important for GRN evolution observed in real organisms. Thus, these GRN features appear to evolve as a result of not only adaptation to unpredictable environmental changes but also non-adaptive processes owing to the properties of the organisms themselves.

Background

A number of models and algorithms have been proposed in the past for gene regulatory network (GRN) inference; however, none of them address the effects of the size of time-series microarray expression data in terms of the number of time-points. In this paper, we study this problem by analyzing the behaviour of three algorithms based on information theory and dynamic Bayesian network (DBN) models. These algorithms were implemented on different sizes of data generated by synthetic networks. Experiments show that the inference accuracy of these algorithms reaches a saturation point after a specific data size brought about by a saturation in the pair-wise mutual information (MI) metric; hence there is a theoretical limit on the inference accuracy of information theory based schemes that depends on the number of time points of micro-array data used to infer GRNs. This illustrates the fact that MI might not be the best metric to use for GRN inference algorithms. To circumvent the limitations of the MI metric, we introduce a new method of computing time lags between any pair of genes and present the pair-wise time lagged Mutual Information (TLMI) and time lagged Conditional Mutual Information (TLCMI) metrics. Next we use these new metrics to propose novel GRN inference schemes which provides higher inference accuracy based on the precision and recall parameters.

Results

It was observed that beyond a certain number of time-points (i.e., a specific size) of micro-array data, the performance of the algorithms measured in terms of the recall-to-precision ratio saturated due to the saturation in the calculated pair-wise MI metric with increasing data size. The proposed algorithms were compared to existing approaches on four different biological networks. The resulting networks were evaluated based on the benchmark precision and recall metrics and the results favour our approach.

Conclusions

To alleviate the effects of data size on information theory based GRN inference algorithms, novel time lag based information theoretic approaches to infer gene regulatory networks have been proposed. The results show that the time lags of regulatory effects between any pair of genes play an important role in GRN inference schemes.

Gene regulatory networks for development underlie cell fate specification and differentiation. Network topology, logic and dynamics can be obtained by thorough experimental analysis. Our understanding of the gene regulatory network controlling endomesoderm specification in the sea urchin embryo has attained an advanced level such that it explains developmental phenomenology. Here we review how the network explains the mechanisms utilized in development to control the formation of dynamic expression patterns of transcription factors and signaling molecules. The network represents the genomic program controlling timely activation of specification and differentiation genes in the correct embryonic lineages. It can also be used to study evolution of body plans. We demonstrate how comparing the sea urchin gene regulatory network to that of the sea star and to that of later developmental stages in the sea urchin, reveals mechanisms underlying the origin of evolutionary novelty. The experimentally based gene regulatory network for endomesoderm specification in the sea urchin embryo provides unique insights into the system level properties of cell fate specification and its evolution.

Background

Gene Regulatory Networks (GRNs) have become a major focus of interest in recent years. Elucidating the architecture and dynamics of large scale gene regulatory networks is an important goal in systems biology. The knowledge of the gene regulatory networks further gives insights about gene regulatory pathways. This information leads to many potential applications in medicine and molecular biology, examples of which are identification of metabolic pathways, complex genetic diseases, drug discovery and toxicology analysis. High-throughput technologies allow studying various aspects of gene regulatory networks on a genome-wide scale and we will discuss recent advances as well as limitations and future challenges for gene network modeling. Novel approaches are needed to both infer the causal genes and generate hypothesis on the underlying regulatory mechanisms.

Methodology

In the present article, we introduce a new method for identifying a set of optimal gene regulatory pathways by using structural equations as a tool for modeling gene regulatory networks. The method, first of all, generates data on reaction flows in a pathway. A set of constraints is formulated incorporating weighting coefficients. Finally the gene regulatory pathways are obtained through optimization of an objective function with respect to these weighting coefficients. The effectiveness of the present method is successfully tested on ten gene regulatory networks existing in the literature. A comparative study with the existing extreme pathway analysis also forms a part of this investigation. The results compare favorably with earlier experimental results. The validated pathways point to a combination of previously documented and novel findings.

Conclusions

We show that our method can correctly identify the causal genes and effectively output experimentally verified pathways. The present method has been successful in deriving the optimal regulatory pathways for all the regulatory networks considered. The biological significance and applicability of the optimal pathways has also been discussed. Finally the usefulness of the present method on genetic engineering is depicted with an example.

In this Perspective, we synthesize past and present observations in the field of epigenetics to propose a model in which the epigenome can modulate cellular plasticity in development and disease by regulating the effects of noise. In this model, the epigenome facilitates phase transitions in development and mediates robustness during cell fate commitment. After grounding our argument in a discussion of stochastic noise and non-genetic heterogeneity, we explore the hypothesis that distinct chromatin domains, which are known to be dysregulated in disease and remodeled during development, might underlie cellular plasticity more generally. We then present a modern portrayal of Waddington's epigenetic landscape through a mathematical formalism. We speculate that this new framework might impact how we approach the unraveling of disease mechanisms. In particular, it may help to explain the observation that the variability of DNA methylation and gene expression are increased in cancer, which leads to tumor cell heterogeneity.