Modeling the Flowering Activation Motif during Vernalization in Legumes: A Case Study of M. trancatula.

In many plant species, flowering is promoted by the cold treatment or vernalization. The mechanism of vernalization-induced flowering has been extensively studied in Arabidopsis but remains largely unknown in legumes. The orthologs of the FLC gene, a major regulator of vernalization response in Arabidopsis, are absent or non-functional in the vernalization-sensitive legume species. Nevertheless, the legume integrator genes FT and SOC1 are involved in the transition of the vernalization signal to meristem identity genes, including PIM (AP1 ortholog). However, the regulatory contribution of these genes to PIM activation in legumes remains elusive. Here, we presented the theoretical and data-driven analyses of a feed-forward regulatory motif that includes a vernalization-responsive FT gene and several SOC1 genes, which independently activate PIM and thereby mediate floral transition. Our theoretical model showed that the multiple regulatory branches in this regulatory motif facilitated the elimination of no-sense signals and amplified useful signals from the upstream regulator. We further developed and analyzed four data-driven models of PIM activation in Medicago trancatula in vernalized and non-vernalized conditions in wild-type and fta1-1 mutants. The model with FTa1 providing both direct activation and indirect activation via three intermediate activators, SOC1a, SOC1b, and SOC1c, resulted in the most relevant PIM dynamics. In this model, the difference between regulatory inputs of SOC1 genes was nonessential. As a result, in the M. trancatula model, the cumulative action of SOC1a, SOC1b, and SOC1c was favored. Overall, in this study, we first presented the in silico analysis of vernalization-induced flowering in legumes. The considered vernalization network motif can be supplemented with additional regulatory branches as new experimental data become available.

Prognostic Analysis of Human Pluripotent Stem Cells Based on Their Morphological Portrait and Expression of Pluripotent Markers.

The ability of human pluripotent stem cells for unlimited proliferation and self-renewal promotes their application in the fields of regenerative medicine. The morphological assessment of growing colonies and cells, as a non-invasive method, allows the best clones for further clinical applications to be safely selected. For this purpose, we analyzed seven morphological parameters of both colonies and cells extracted from the phase-contrast images of human embryonic stem cell line H9, control human induced pluripotent stem cell (hiPSC) line AD3, and hiPSC line HPCASRi002-A (CaSR) in various passages during their growth for 120 h. The morphological phenotype of each colony was classified using a visual analysis and associated with its potential for pluripotency and clonality maintenance, thus defining the colony phenotype as the control parameter. Using the analysis of variance for the morphological parameters of each line, we showed that selected parameters carried information about different cell lines and different phenotypes within each line. We demonstrated that a model of classification of colonies and cells by phenotype, built on the selected parameters as predictors, recognized the phenotype with an accuracy of 70-75%. In addition, we performed a qRT-PCR analysis of eleven pluripotency markers genes. By analyzing the variance of their expression in samples from different lines and with different phenotypes, we identified group-specific sets of genes that could be used as the most informative ones for the separation of the best clones. Our results indicated the fundamental possibility of constructing a morphological portrait of a colony informative for the automatic identification of the phenotype and for linking this portrait to the expression of pluripotency markers.

Stochastic Effects in Retrotransposon Dynamics Revealed by Modeling under Competition for Cellular Resources.

Transposons are genomic elements that can relocate within a host genome using a 'cut'- or 'copy-and-paste' mechanism. They make up a significant part of many genomes, serve as a driving force for genome evolution, and are linked with Mendelian diseases and cancers. Interactions between two specific retrotransposon types, autonomous (e.g., LINE1/L1) and nonautonomous (e.g., Alu), may lead to fluctuations in the number of these transposons in the genome over multiple cell generations. We developed and examined a simple model of retrotransposon dynamics under conditions where transposon replication machinery competed for cellular resources: namely, free ribosomes and available energy (i.e., ATP molecules). Such competition is likely to occur in stress conditions that a malfunctioning cell may experience as a result of a malignant transformation. The modeling revealed that the number of actively replicating LINE1 and Alu elements in a cell decreases with the increasing competition for resources; however, stochastic effects interfere with this simple trend. We stochastically simulated the transposon dynamics in a cell population and showed that the population splits into pools with drastically different transposon behaviors. The early extinction of active Alu elements resulted in a larger number of LINE1 copies occurring in the first pool, as there was no competition between the two types of transposons in this pool. In the other pool, the competition process remained and the number of L1 copies was kept small. As the level of available resources reached a critical value, both types of dynamics demonstrated an increase in noise levels, and both the period and the amplitude of predator-prey oscillations rose in one of the cell pools. We hypothesized that the presented dynamical effects associated with the impact of the competition for cellular resources inflicted on the dynamics of retrotransposable elements could be used as a characteristic feature to assess a cell state, or to control the transposon activity.

Application of Domain- and Genotype-Specific Models to Infer Post-Transcriptional Regulation of Segmentation Gene Expression in Drosophila.

Unlike transcriptional regulation, the post-transcriptional mechanisms underlying zygotic segmentation gene expression in early Drosophila embryo have been insufficiently investigated. Condition-specific post-transcriptional regulation plays an important role in the development of many organisms. Our recent study revealed the domain- and genotype-specific differences between mRNA and the protein expression of Drosophila hb, gt, and eve genes in cleavage cycle 14A. Here, we use this dataset and the dynamic mathematical model to recapitulate protein expression from the corresponding mRNA patterns. The condition-specific nonuniformity in parameter values is further interpreted in terms of possible post-transcriptional modifications. For hb expression in wild-type embryos, our results predict the position-specific differences in protein production. The protein synthesis rate parameter is significantly higher in hb anterior domain compared to the posterior domain. The parameter sets describing Gt protein dynamics in wild-type embryos and Kr mutants are genotype-specific. The spatial discrepancy between gt mRNA and protein posterior expression in Kr mutants is well reproduced by the whole axis model, thus rejecting the involvement of post-transcriptional mechanisms. Our models fail to describe the full dynamics of eve expression, presumably due to its complex shape and the variable time delays between mRNA and protein patterns, which likely require a more complex model. Overall, our modeling approach enables the prediction of regulatory scenarios underlying the condition-specific differences between mRNA and protein expression in early embryo.

Dynamical Modeling of the Core Gene Network Controlling Transition to Flowering in Pisum sativum.

Transition to flowering is an important stage of plant development. Many regulatory modules that control floral transition are conservative across plants. This process is best studied for the model plant Arabidopsis thaliana. The homologues of Arabidopsis genes responsible for the flowering initiation in legumes have been identified, and available data on their expression provide a good basis for gene network modeling. In this study, we developed several dynamical models of a gene network controlling transition to flowering in pea (Pisum sativum) using two different approaches. We used differential equations for modeling a previously proposed gene regulation scheme of floral initiation in pea and tested possible alternative hypothesis about some regulations. As the second approach, we applied neural networks to infer interactions between genes in the network directly from gene expression data. All models were verified on previously published experimental data on the dynamic expression of the main genes in the wild type and in three mutant genotypes. Based on modeling results, we made conclusions about the functionality of the previously proposed interactions in the gene network and about the influence of different growing conditions on the network architecture. It was shown that regulation of the PIM, FTa1, and FTc genes in pea does not correspond to the previously proposed hypotheses. The modeling suggests that short- and long-day growing conditions are characterized by different gene network architectures. Overall, the results obtained can be used to plan new experiments and create more accurate models to study the flowering initiation in pea and, in a broader context, in legumes.

Dynamical Modeling of the Core Gene Network Controlling Flowering Suggests Cumulative Activation From the FLOWERING LOCUS T Gene Homologs in Chickpea.

Initiation of flowering moves plants from vegetative to reproductive development. The time when this transition happens (flowering time), an important indicator of productivity, depends on both endogenous and environmental factors. The core genetic regulatory network canalizing the flowering signals to the decision to flower has been studied extensively in the model plant Arabidopsis thaliana and has been shown to preserve its main regulatory blocks in other species. It integrates activation from the FLOWERING LOCUS T (FT) gene or its homologs to the flowering decision expressed as high expression of the meristem identity genes, including AP1. We elaborated a dynamical model of this flowering gene regulatory network and applied it to the previously published expression data from two cultivars of domesticated chickpea (Cicer arietinum), obtained for two photoperiod durations. Due to a large number of free parameters in the model, we used an ensemble approach analyzing the model solutions at many parameter sets that provide equally good fit to data. Testing several alternative hypotheses about regulatory roles of the five FT homologs present in chickpea revealed no preference in segregating individual FT copies as singled-out activators with their own regulatory parameters, thus favoring the hypothesis that the five genes possess similar regulatory properties and provide cumulative activation in the network. The analysis reveals that different levels of activation from AP1 can explain a small difference observed in the expression of the two homologs of the repressor gene TFL1. Finally, the model predicts highly reduced activation between LFY and AP1, thus suggesting that this regulatory block is not conserved in chickpea and needs other mechanisms. Overall, this study provides the first attempt to quantitatively test the flowering time gene network in chickpea based on data-driven modeling.

Translating natural genetic variation to gene expression in a computational model of the Drosophila gap gene regulatory network.

Annotating the genotype-phenotype relationship, and developing a proper quantitative description of the relationship, requires understanding the impact of natural genomic variation on gene expression. We apply a sequence-level model of gap gene expression in the early development of Drosophila to analyze single nucleotide polymorphisms (SNPs) in a panel of natural sequenced D. melanogaster lines. Using a thermodynamic modeling framework, we provide both analytical and computational descriptions of how single-nucleotide variants affect gene expression. The analysis reveals that the sequence variants increase (decrease) gene expression if located within binding sites of repressors (activators). We show that the sign of SNP influence (activation or repression) may change in time and space and elucidate the origin of this change in specific examples. The thermodynamic modeling approach predicts non-local and non-linear effects arising from SNPs, and combinations of SNPs, in individual fly genotypes. Simulation of individual fly genotypes using our model reveals that this non-linearity reduces to almost additive inputs from multiple SNPs. Further, we see signatures of the action of purifying selection in the gap gene regulatory regions. To infer the specific targets of purifying selection, we analyze the patterns of polymorphism in the data at two phenotypic levels: the strengths of binding and expression. We find that combinations of SNPs show evidence of being under selective pressure, while individual SNPs do not. The model predicts that SNPs appear to accumulate in the genotypes of the natural population in a way biased towards small increases in activating action on the expression pattern. Taken together, these results provide a systems-level view of how genetic variation translates to the level of gene regulatory networks via combinatorial SNP effects.

In silico evolution of the Drosophila gap gene regulatory sequence under elevated mutational pressure.

BACKGROUND: Cis-regulatory sequences are often composed of many low-affinity transcription factor binding sites (TFBSs). Determining the evolutionary and functional importance of regulatory sequence composition is impeded without a detailed knowledge of the genotype-phenotype map. RESULTS: We simulate the evolution of regulatory sequences involved in Drosophila melanogaster embryo segmentation during early development. Natural selection evaluates gene expression dynamics produced by a computational model of the developmental network. We observe a dramatic decrease in the total number of transcription factor binding sites through the course of evolution. Despite a decrease in average sequence binding energies through time, the regulatory sequences tend towards organisations containing increased high affinity transcription factor binding sites. Additionally, the binding energies of separate sequence segments demonstrate ubiquitous mutual correlations through time. Fewer than 10% of initial TFBSs are maintained throughout the entire simulation, deemed 'core' sites. These sites have increased functional importance as assessed under wild-type conditions and their binding energy distributions are highly conserved. Furthermore, TFBSs within close proximity of core sites exhibit increased longevity, reflecting functional regulatory interactions with core sites. CONCLUSION: In response to elevated mutational pressure, evolution tends to sample regulatory sequence organisations with fewer, albeit on average, stronger functional transcription factor binding sites. These organisations are also shaped by the regulatory interactions among core binding sites with sites in their local vicinity.

Analysis of functional importance of binding sites in the Drosophila gap gene network model.

BACKGROUND: The statistical thermodynamics based approach provides a promising framework for construction of the genotype-phenotype map in many biological systems. Among important aspects of a good model connecting the DNA sequence information with that of a molecular phenotype (gene expression) is the selection of regulatory interactions and relevant transcription factor bindings sites. As the model may predict different levels of the functional importance of specific binding sites in different genomic and regulatory contexts, it is essential to formulate and study such models under different modeling assumptions. RESULTS: We elaborate a two-layer model for the Drosophila gap gene network and include in the model a combined set of transcription factor binding sites and concentration dependent regulatory interaction between gap genes hunchback and Kruppel. We show that the new variants of the model are more consistent in terms of gene expression predictions for various genetic constructs in comparison to previous work. We quantify the functional importance of binding sites by calculating their impact on gene expression in the model and calculate how these impacts correlate across all sites under different modeling assumptions. CONCLUSIONS: The assumption about the dual interaction between hb and Kr leads to the most consistent modeling results, but, on the other hand, may obscure existence of indirect interactions between binding sites in regulatory regions of distinct genes. The analysis confirms the previously formulated regulation concept of many weak binding sites working in concert. The model predicts a more or less uniform distribution of functionally important binding sites over the sets of experimentally characterized regulatory modules and other open chromatin domains.

A new stochastic model for subgenomic hepatitis C virus replication considers drug resistant mutants.

As an RNA virus, hepatitis C virus (HCV) is able to rapidly acquire drug resistance, and for this reason the design of effective anti-HCV drugs is a real challenge. The HCV subgenomic replicon-containing cells are widely used for experimental studies of the HCV genome replication mechanisms, for drug testing in vitro and in studies of HCV drug resistance. The NS3/4A protease is essential for virus replication and, therefore, it is one of the most attractive targets for developing specific antiviral agents against HCV. We have developed a stochastic model of subgenomic HCV replicon replication, in which the emergence and selection of drug resistant mutant viral RNAs in replicon cells is taken into account. Incorporation into the model of key NS3 protease mutations leading to resistance to BILN-2061 (A156T, D168V, R155Q), VX-950 (A156S, A156T, T54A) and SCH 503034 (A156T, A156S, T54A) inhibitors allows us to describe the long term dynamics of the viral RNA suppression for various inhibitor concentrations. We theoretically showed that the observable difference between the viral RNA kinetics for different inhibitor concentrations can be explained by differences in the replication rate and inhibitor sensitivity of the mutant RNAs. The pre-existing mutants of the NS3 protease contribute more significantly to appearance of new resistant mutants during treatment with inhibitors than wild-type replicon. The model can be used to interpret the results of anti-HCV drug testing on replicon systems, as well as to estimate the efficacy of potential drugs and predict optimal schemes of their usage.

Mechanisms of developmental robustness.

We present a review of noise buffering mechanisms responsible for developmental robustness. We focus on functions of chaperone Hsp90, miRNA, and cross-regulation of gap genes in Drosophila. The noise buffering mechanisms associated with these functions represent specific examples of the developmental canalization, reducing the phenotypical variability in presence of either genetic or environmental perturbations. We demonstrate that robustness often appears as a function of a network of interacting elements and that the system level approach is needed to understand the mechanisms of noise filtering.

Mechanisms of gap gene expression canalization in the Drosophila blastoderm.

BACKGROUND: Extensive variation in early gap gene expression in the Drosophila blastoderm is reduced over time because of gap gene cross regulation. This phenomenon is a manifestation of canalization, the ability of an organism to produce a consistent phenotype despite variations in genotype or environment. The canalization of gap gene expression can be understood as arising from the actions of attractors in the gap gene dynamical system. RESULTS: In order to better understand the processes of developmental robustness and canalization in the early Drosophila embryo, we investigated the dynamical effects of varying spatial profiles of Bicoid protein concentration on the formation of the expression border of the gap gene hunchback. At several positions on the anterior-posterior axis of the embryo, we analyzed attractors and their basins of attraction in a dynamical model describing expression of four gap genes with the Bicoid concentration profile accounted as a given input in the model equations. This model was tested against a family of Bicoid gradients obtained from individual embryos. These gradients were normalized by two independent methods, which are based on distinct biological hypotheses and provide different magnitudes for Bicoid spatial variability. We showed how the border formation is dictated by the biological initial conditions (the concentration gradient of maternal Hunchback protein) being attracted to specific attracting sets in a local vicinity of the border. Different types of these attracting sets (point attractors or one dimensional attracting manifolds) define several possible mechanisms of border formation. The hunchback border formation is associated with intersection of the spatial gradient of the maternal Hunchback protein and a boundary between the attraction basins of two different point attractors. We demonstrated how the positional variability for hunchback is related to the corresponding variability of the basin boundaries. The observed reduction in variability of the hunchback gene expression can be accounted for by specific geometrical properties of the basin boundaries. CONCLUSION: We clarified the mechanisms of gap gene expression canalization in early Drosophila embryos. These mechanisms were specified in the case of hunchback in well defined terms of the dynamical system theory.

Canalization of gene expression in the Drosophila blastoderm by gap gene cross regulation.

Developing embryos exhibit a robust capability to reduce phenotypic variations that occur naturally or as a result of experimental manipulation. This reduction in variation occurs by an epigenetic mechanism called canalization, a phenomenon which has resisted understanding because of a lack of necessary molecular data and of appropriate gene regulation models. In recent years, quantitative gene expression data have become available for the segment determination process in the Drosophila blastoderm, revealing a specific instance of canalization. These data show that the variation of the zygotic segmentation gene expression patterns is markedly reduced compared to earlier levels by the time gastrulation begins, and this variation is significantly lower than the variation of the maternal protein gradient Bicoid. We used a predictive dynamical model of gene regulation to study the effect of Bicoid variation on the downstream gap genes. The model correctly predicts the reduced variation of the gap gene expression patterns and allows the characterization of the canalizing mechanism. We show that the canalization is the result of specific regulatory interactions among the zygotic gap genes. We demonstrate the validity of this explanation by showing that variation is increased in embryos mutant for two gap genes, Krüppel and knirps, disproving competing proposals that canalization is due to an undiscovered morphogen, or that it does not take place at all. In an accompanying article in PLoS Computational Biology (doi:10.1371/journal.pcbi.1000303), we show that cross regulation between the gap genes causes their expression to approach dynamical attractors, reducing initial variation and providing a robust output. These results demonstrate that the Bicoid gradient is not sufficient to produce gap gene borders having the low variance observed, and instead this low variance is generated by gap gene cross regulation. More generally, we show that the complex multigenic phenomenon of canalization can be understood at a quantitative and predictive level by the application of a precise dynamical model.

Canalization of gene expression and domain shifts in the Drosophila blastoderm by dynamical attractors.

The variation in the expression patterns of the gap genes in the blastoderm of the fruit fly Drosophila melanogaster reduces over time as a result of cross regulation between these genes, a fact that we have demonstrated in an accompanying article in PLoS Biology (see Manu et al., doi:10.1371/journal.pbio.1000049). This biologically essential process is an example of the phenomenon known as canalization. It has been suggested that the developmental trajectory of a wild-type organism is inherently stable, and that canalization is a manifestation of this property. Although the role of gap genes in the canalization process was established by correctly predicting the response of the system to particular perturbations, the stability of the developmental trajectory remains to be investigated. For many years, it has been speculated that stability against perturbations during development can be described by dynamical systems having attracting sets that drive reductions of volume in phase space. In this paper, we show that both the reduction in variability of gap gene expression as well as shifts in the position of posterior gap gene domains are the result of the actions of attractors in the gap gene dynamical system. Two biologically distinct dynamical regions exist in the early embryo, separated by a bifurcation at 53% egg length. In the anterior region, reduction in variation occurs because of stability induced by point attractors, while in the posterior, the stability of the developmental trajectory arises from a one-dimensional attracting manifold. This manifold also controls a previously characterized anterior shift of posterior region gap domains. Our analysis shows that the complex phenomena of canalization and pattern formation in the Drosophila blastoderm can be understood in terms of the qualitative features of the dynamical system. The result confirms the idea that attractors are important for developmental stability and shows a richer variety of dynamical attractors in developmental systems than has been previously recognized.

How gap genes make their domains: An analytical study based on data driven approximations.

We consider a mathematical formulation of the problem of protein production during segment determination in the Drosophila blastoderm, together with some preliminary results of its analytical study. We reformulate the spatial difference equations as a set of nonlinear partial differential equations and obtain their dimensionless form in the continuum limit. Using previous results obtained by the gene circuit method, we find an asymptotic statement of the problem with a small parameter. Some results of the comparison method applied to the model are obtained, and exact stationary upper solutions are derived. They exhibit distinctive features of localized bell-shaped structures. (c) 2001 American Institute of Physics.