Early effects of gene duplication on the robustness and phenotypic variability of gene regulatory networks.

BACKGROUND: Research on gene duplication is abundant and comes from a wide range of approaches, from high-throughput analyses and experimental evolution to bioinformatics and theoretical models. Notwithstanding, a consensus is still lacking regarding evolutionary mechanisms involved in evolution through gene duplication as well as the conditions that affect them. We argue that a better understanding of evolution through gene duplication requires considering explicitly that genes do not act in isolation. It demands studying how the perturbation that gene duplication implies percolates through the web of gene interactions. Due to evolution's contingent nature, the paths that lead to the final fate of duplicates must depend strongly on the early stages of gene duplication, before gene copies have accumulated distinctive changes. METHODS: Here we use a widely-known model of gene regulatory networks to study how gene duplication affects network behavior in early stages. Such networks comprise sets of genes that cross-regulate. They organize gene activity creating the gene expression patterns that give cells their phenotypic properties. We focus on how duplication affects two evolutionarily relevant properties of gene regulatory networks: mitigation of the effect of new mutations and access to new phenotypic variants through mutation. RESULTS: Among other observations, we find that those networks that are better at maintaining the original phenotype after duplication are usually also better at buffering the effect of single interaction mutations and that duplication tends to enhance further this ability. Moreover, the effect of mutations after duplication depends on both the kind of mutation and genes involved in it. We also found that those phenotypes that had easier access through mutation before duplication had higher chances of remaining accessible through new mutations after duplication. CONCLUSION: Our results support that gene duplication often mitigates the impact of new mutations and that this effect is not merely due to changes in the number of genes. The work that we put forward helps to identify conditions under which gene duplication may enhance evolvability and robustness to mutations.

Recombination facilitates genetic assimilation of new traits in gene regulatory networks.

A new phenotypic variant may appear first in organisms through plasticity, that is, as a response to an environmental signal or other nongenetic perturbation. If such trait is beneficial, selection may increase the frequency of alleles that enable and facilitate its development. Thus, genes may take control of such traits, decreasing dependence on nongenetic disturbances, in a process called genetic assimilation. Despite an increasing amount of empirical studies supporting genetic assimilation, its significance is still controversial. Whether genetic assimilation is widespread depends, to a great extent, on how easily mutation and recombination reduce the trait's dependence on nongenetic perturbations. Previous research suggests that this is the case for mutations. Here we use simulations of gene regulatory network dynamics to address this issue with respect to recombination. We find that recombinant offspring of parents that produce a new phenotype through plasticity are more likely to produce the same phenotype without requiring any perturbation. They are also prone to preserve the ability to produce that phenotype after genetic and nongenetic perturbations. Our work also suggests that ancestral plasticity can play an important role for setting the course that evolution takes. In sum, our results indicate that the manner in which phenotypic variation maps unto genetic variation facilitates evolution through genetic assimilation in gene regulatory networks. Thus, we contend that the importance of this evolutionary mechanism should not be easily neglected.

MADS-box genes underground becoming mainstream: plant root developmental mechanisms.

Plant growth is largely post-embryonic and depends on meristems that are active throughout the lifespan of an individual. Developmental patterns rely on the coordinated spatio-temporal expression of different genes, and the activity of transcription factors is particularly important during most morphogenetic processes. MADS-box genes constitute a transcription factor family in eukaryotes. In Arabidopsis, their proteins participate in all major aspects of shoot development, but their role in root development is still not well characterized. In this review we synthetize current knowledge pertaining to the function of MADS-box genes highly expressed in roots: XAL1, XAL2, ANR1 and AGL21, as well as available data for other MADS-box genes expressed in this organ. The role of Trithorax group and Polycomb group complexes on MADS-box genes' epigenetic regulation is also discussed. We argue that understanding the role of MADS-box genes in root development of species with contrasting architectures is still a challenge. Finally, we propose that MADS-box genes are key components of the gene regulatory networks that underlie various gene expression patterns, each one associated with the distinct developmental fates observed in the root. In the case of XAL1 and XAL2, their role within these networks could be mediated by regulatory feedbacks with auxin.

On the role of sparseness in the evolution of modularity in gene regulatory networks.

Modularity is a widespread property in biological systems. It implies that interactions occur mainly within groups of system elements. A modular arrangement facilitates adjustment of one module without perturbing the rest of the system. Therefore, modularity of developmental mechanisms is a major factor for evolvability, the potential to produce beneficial variation from random genetic change. Understanding how modularity evolves in gene regulatory networks, that create the distinct gene activity patterns that characterize different parts of an organism, is key to developmental and evolutionary biology. One hypothesis for the evolution of modules suggests that interactions between some sets of genes become maladaptive when selection favours additional gene activity patterns. The removal of such interactions by selection would result in the formation of modules. A second hypothesis suggests that modularity evolves in response to sparseness, the scarcity of interactions within a system. Here I simulate the evolution of gene regulatory networks and analyse diverse experimentally sustained networks to study the relationship between sparseness and modularity. My results suggest that sparseness alone is neither sufficient nor necessary to explain modularity in gene regulatory networks. However, sparseness amplifies the effects of forms of selection that, like selection for additional gene activity patterns, already produce an increase in modularity. That evolution of new gene activity patterns is frequent across evolution also supports that it is a major factor in the evolution of modularity. That sparseness is widespread across gene regulatory networks indicates that it may have facilitated the evolution of modules in a wide variety of cases.

The protein-protein interaction landscape of transcription factors during gynoecium development in Arabidopsis.

Flowers are composed of organs whose identity is defined by the combinatorial activity of transcription factors (TFs). The interactions between MADS-box TFs and protein complex formation have been schematized in the floral quartet model of flower development. The gynoecium is the flower's female reproductive part, crucial for fruit and seed production and, hence, for reproductive success. After the establishment of carpel identity, many tissues arise to form a mature gynoecium. TFs have been described as regulators of gynoecium development, and some interactions and complexes have been identified. However, broad knowledge about the interactions among these TFs and their participation during development remains scarce. In this study, we used a systems biology approach to understand the formation of a complex reproductive unit-as the gynoecium-by mapping binary interactions between well-characterized TFs. We analyzed almost 4500 combinations and detected more than 250 protein-protein interactions (PPIs), resulting in a process-specific interaction map. Topological analyses suggest hidden functions and novel roles for many TFs. In addition, we observed a close relationship between TFs involved in auxin and cytokinin-signaling pathways and other TFs. Furthermore, we analyzed the network by combining PPI data, expression, and genetic data, which helped us to dissect it into several dynamic spatio-temporal subnetworks related to gynoecium development processes. Finally, we generated an extended PPI network that predicts new players in gynoecium development. Taken together, all these results serve as a valuable resource for the plant community.

Phenotypic plasticity can facilitate adaptive evolution in gene regulatory circuits.

BACKGROUND: Many important evolutionary adaptations originate in the modification of gene regulatory circuits to produce new gene activity phenotypes. How do evolving populations sift through an astronomical number of circuits to find circuits with new adaptive phenotypes? The answer may often involve phenotypic plasticity. Phenotypic plasticity allows a genotype to produce different - alternative - phenotypes after non-genetic perturbations that include gene expression noise, environmental change, or epigenetic modification. RESULTS: We here analyze a well-studied model of gene regulatory circuits. A circuit's genotype encodes the regulatory interactions among circuit genes, and its phenotype corresponds to a stable gene activity pattern the circuit forms. For this model, we study how genotypes are arranged in genotype space, where the distance between two genotypes reflects the number of regulatory mutations that set those genotypes apart. Specifically, we address whether this arrangement favors adaptive evolution mediated by plasticity. We find that plasticity facilitates the origin of genotypes that produce a new phenotype in response to non-genetic perturbations. We also find that selection can then stabilize the new phenotype genetically, allowing it to become a circuit's dominant gene expression phenotype. These are generic properties of the circuits we study here. CONCLUSIONS: Taken together, our observations suggest that phenotypic plasticity frequently facilitates the evolution of novel beneficial gene activity patterns in gene regulatory circuits.

Specialization can drive the evolution of modularity.

Organismal development and many cell biological processes are organized in a modular fashion, where regulatory molecules form groups with many interactions within a group and few interactions between groups. Thus, the activity of elements within a module depends little on elements outside of it. Modularity facilitates the production of heritable variation and of evolutionary innovations. There is no consensus on how modularity might evolve, especially for modules in development. We show that modularity can increase in gene regulatory networks as a byproduct of specialization in gene activity. Such specialization occurs after gene regulatory networks are selected to produce new gene activity patterns that appear in a specific body structure or under a specific environmental condition. Modules that arise after specialization in gene activity comprise genes that show concerted changes in gene activities. This and other observations suggest that modularity evolves because it decreases interference between different groups of genes. Our work can explain the appearance and maintenance of modularity through a mechanism that is not contingent on environmental change. We also show how modularity can facilitate co-option, the utilization of existing gene activity to build new gene activity patterns, a frequent feature of evolutionary innovations.

Gene regulatory network models for plant development.

Accumulated genetic data are stimulating the use of mathematical and computational tools for studying the concerted action of genes during cell differentiation and morphogenetic processes. At the same time, network theory has flourished, enabling analyses of complex systems that have multiple elements and interactions. Reverse engineering methods that use genomic data or detailed experiments on gene interactions have been used to propose gene network architectures. Experiments on gene interactions incorporate enough detail for relatively small developmental modules and thus allow dynamical analyses that have direct functional interpretations. Generalities are beginning to emerge. For example, biological genetic networks are robust to environmental and genetic perturbations. Such dynamical studies also enable novel predictions that can lead to further experimental tests, which might then feedback to the theoretical analyses. This interplay is proving productive for understanding plant development. Finally, both experiments on gene interactions and theoretical analyses allow the identification of frequent or fixed evolutionary solutions to developmental problems, and thus are contributing to an understanding of the genetic basis of the evolution of development and body plan.

Equivalent genetic regulatory networks in different contexts recover contrasting spatial cell patterns that resemble those in Arabidopsis root and leaf epidermis: a dynamic model.

In Arabidopsis thaliana, leaf and root epidermis hairs exhibit contrasting spatial arrangements even though the genetic networks regulating their respective cell-fate determination have very similar structures and components. We integrated available experimental data for leaf and root hair patterning in dynamic network models which may be reduced to activator-inhibitor models. This integration yielded expected results for these kinds of dynamic models, including striped and dotted cell patterns which are characteristic of root and leaf epidermis, respectively. However, these formal tools have led us to novel insights on current data and to put forward precise hypotheses which can be addressed experimentally. In particular, despite subtle differences in the root and leaf networks, these have equivalent dynamical behaviors. Our simulations also suggest that only when a biasing signal positively affects an activator in the network, the system recovers striped cellular patterns similar to those of root epidermis. We also postulate that cell shape may affect pattern stability in the root. Our results thus support the idea that in this and other cases, contrasting spatial cell patterns and other evolutionary morphogenetic novelties originate from conserved genetic network modules subject to divergent contextual traits.

Tetramer formation in Arabidopsis MADS domain proteins: analysis of a protein-protein interaction network.

BACKGROUND: MADS domain proteins are transcription factors that coordinate several important developmental processes in plants. These proteins interact with other MADS domain proteins to form dimers, and it has been proposed that they are able to associate as tetrameric complexes that regulate transcription of target genes. Whether the formation of functional tetramers is a widespread property of plant MADS domain proteins, or it is specific to few of these transcriptional regulators remains unclear. RESULTS: We analyzed the structure of the network of physical interactions among MADS domain proteins in Arabidopsis thaliana. We determined the abundance of subgraphs that represent the connection pattern expected for a MADS domain protein heterotetramer. These subgraphs were significantly more abundant in the MADS domain protein interaction network than in randomized analogous networks. Importantly, these subgraphs are not significantly frequent in a protein interaction network of TCP plant transcription factors, when compared to expectation by chance. In addition, we found that MADS domain proteins in tetramer-like subgraphs are more likely to be expressed jointly than proteins in other subgraphs. This effect is mainly due to proteins in the monophyletic MIKC clade, as there is no association between tetramer-like subgraphs and co-expression for proteins outside this clade. CONCLUSIONS: Our results support that the tendency to form functional tetramers is widespread in the MADS domain protein-protein interaction network. Our observations also suggest that this trend is prevalent, or perhaps exclusive, for proteins in the MIKC clade. Because it is possible to retrodict several experimental results from our analyses, our work can be an important aid to make new predictions and facilitates experimental research on plant MADS domain proteins.

Dynamic network-based epistasis analysis: boolean examples.

In this article we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the inference of gene regulatory networks. Here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson, epistasis is defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus (herein, classical epistasis). Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct inference of gene interaction topologies is hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our article complements previous accounts, not only by focusing on the implications of the hierarchical and single-path assumption, but also by demonstrating the importance of considering temporal dynamics, and specifically introducing the usefulness of Boolean network models and also reviewing some key properties of network approaches.

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

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.

Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape.

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.

A gene regulatory network model for cell-fate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles.

Flowers are icons in developmental studies of complex structures. The vast majority of 250,000 angiosperm plant species have flowers with a conserved organ plan bearing sepals, petals, stamens, and carpels in the center. The combinatorial model for the activity of the so-called ABC homeotic floral genes has guided extensive experimental studies in Arabidopsis thaliana and many other plant species. However, a mechanistic and dynamical explanation for the ABC model and prevalence among flowering plants is lacking. Here, we put forward a simple discrete model that postulates logical rules that formally summarize published ABC and non-ABC gene interaction data for Arabidopsis floral organ cell fate determination and integrates this data into a dynamic network model. This model shows that all possible initial conditions converge to few steady gene activity states that match gene expression profiles observed experimentally in primordial floral organ cells of wild-type and mutant plants. Therefore, the network proposed here provides a dynamical explanation for the ABC model and shows that precise signaling pathways are not required to restrain cell types to those found in Arabidopsis, but these are rather determined by the overall gene network dynamics. Furthermore, we performed robustness analyses that clearly show that the cell types recovered depend on the network architecture rather than on specific values of the model's gene interaction parameters. These results support the hypothesis that such a network constitutes a developmental module, and hence provide a possible explanation for the overall conservation of the ABC model and overall floral plan among angiosperms. In addition, we have been able to predict the effects of differences in network architecture between Arabidopsis and Petunia hybrida.