Simulation study on effects of signaling network structure on the developmental increase in complexity

The developmental increase in structural complexity in multicellular lifeforms depends on local, often non-periodic differences in gene expression. These, in turn, depend on a network of gene-gene interactions coded within the organismal genome. To see what architectural features of a network (size, connectivity, etc.) affect the likelihood of patterns with multiple cell types (i.e. patterns where cells express > or = 3 different combinations of genes), developmental pattern formation was simulated in virtual blastoderm embryos with small artificial genomes. Several basic properties of these genomic signaling networks, such as the number of genes, the distributions of positive (inductive) and negative (repressive) interactions, and the strengths of gene-gene interactions were tested. The results show that the frequencies of complex and/or stable patterns depended not only on the existence of negative interactions, but also on the distribution of regulatory interactions: for example, coregulation of signals and their intracellular effectors increased the likelihood of pattern formation compared to differential regulation of signaling pathway components. Interestingly, neither quantitative differences in strengths of signaling interactions nor multiple response thresholds to different levels of signal concentration (as in morphogen gradients) were essential for formation of multiple, spatially unique "cell types". However, those combinations of architectural features that greatly increased the likelihood for pattern complexity tended to decrease the likelihoods for pattern stability and developmental robustness. Nevertheless, elements of complex patterns (e.g. genes, cell type order within the pattern) could differ in their developmental robustness, which may be important for the evolution of complexity. The results show that depending on the network structure, the same set of genes can produce patterns of different complexity, robustness and stability. Because of this, the evolution of metazoan complexity with a combinatorial code of gene regulation may have depended at least as much on selection for favorable distribution of connections between existing developmental regulatory genes as on the simple increase in numbers of regulatory genes.     

Genes under weaker stabilizing selection increase network evolvability and rapid regulatory adaptation to an environmental shift

Regulatory networks play a central role in the modulation of gene expression, the control of cellular differentiation, and the emergence of complex phenotypes. Regulatory networks could constrain or facilitate evolutionary adaptation in gene expression levels. Here, we model the adaptation of regulatory networks and gene expression levels to a shift in the environment that alters the optimal expression level of a single gene. Our analyses show signatures of natural selection on regulatory networks that both constrain and facilitate rapid evolution of gene expression level towards new optima. The analyses are interpreted from the standpoint of neutral expectations and illustrate the challenge to making inferences about network adaptation. Furthermore, we examine the consequence of variable stabilizing selection across genes on the strength and direction of interactions in regulatory networks and in their subsequent adaptation. We observe that directional selection on a highly constrained gene previously under strong stabilizing selection was more efficient when the gene was embedded within a network of partners under relaxed stabilizing selection pressure. The observation leads to the expectation that evolutionarily resilient regulatory networks will contain optimal ratios of genes whose expression is under weak and strong stabilizing selection. Altogether, our results suggest that the variable strengths of stabilizing selection across genes within regulatory networks might itself contribute to the long‐term adaptation of complex phenotypes.     

Discovering Implicit Entity Relation with the Gene-Citation-Gene Network

In this paper, we apply the entitymetrics model to our constructed Gene-Citation-Gene (GCG) network. Based on the premise there is a hidden, but plausible, relationship between an entity in one article and an entity in its citing article, we constructed a GCG network of gene pairs implicitly connected through citation. We compare the performance of this GCG network to a gene-gene (GG) network constructed over the same corpus but which uses gene pairs explicitly connected through traditional co-occurrence. Using 331,411 MEDLINE abstracts collected from 18,323 seed articles and their references, we identify 25 gene pairs. A comparison of these pairs with interactions found in BioGRID reveal that 96% of the gene pairs in the GCG network have known interactions. We measure network performance using degree, weighted degree, closeness, betweenness centrality and PageRank. Combining all measures, we find the GCG network has more gene pairs, but a lower matching rate than the GG network. However, combining top ranked genes in both networks produces a matching rate of 35.53%. By visualizing both the GG and GCG networks, we find that cancer is the most dominant disease associated with the genes in both networks. Overall, the study indicates that the GCG network can be useful for detecting gene interaction in an implicit manner.     

A computational analysis of protein interactions in metabolic networks reveals novel enzyme pairs potentially involved in metabolic channeling

Protein-protein interactions are operative at almost every level of cell structure and function as, for example, formation of sub-cellular organelles, packaging of chromatin, muscle contraction, signal transduction, and regulation of gene expression. Public databases of reported protein-protein interactions comprise hundreds of thousands interactions, and this number is steadily growing. Elucidating the implications of protein-protein interactions for the regulation of the underlying cellular or extra-cellular reaction network remains a great challenge for computational biochemistry. In this work, we have undertaken a systematic and comprehensive computational analysis of reported enzyme-enzyme interactions in the metabolic networks of the model organisms Escherichia coli and Saccharomyces cerevisiae. We grouped all enzyme pairs according to the topological distance that the catalyzed reactions have in the metabolic network and performed a statistical analysis of reported enzyme-enzyme interactions within these groups. We found a higher frequency of reported enzyme-enzyme interactions within the group of enzymes catalyzing reactions that are adjacent in the network, i.e. sharing at least one metabolite. As some of these interacting enzymes have already been implicated in metabolic channeling our analysis may provide a useful screening for candidates of this phenomenon. To check for a possible regulatory role of interactions between enzymes catalyzing non-neighboring reactions, we determined potentially regulatory enzymes using connectivity in the network and absolute change of Gibbs free energy. Indeed a higher portion of reported interactions pertain to such potentially regulatory enzymes.     

Inference of gene regulatory networks and compound mode of action from time course gene expression profiles

MOTIVATION: Time series expression experiments are an increasingly popular method for studying a wide range of biological systems. Here we developed an algorithm that can infer the local network of gene-gene interactions surrounding a gene of interest. This is achieved by a perturbation of the gene of interest and subsequently measuring the gene expression profiles at multiple time points. We applied this algorithm to computer simulated data and to experimental data on a nine gene network in Escherichia coli. RESULTS: In this paper we show that it is possible to recover the gene regulatory network from a time series data of gene expression following a perturbation to the cell. We show this both on simulated data and on a nine gene subnetwork part of the DNA-damage response pathway (SOS pathway) in the bacteria E. coli. CONTACT: dibernardo@tigem.it SUPLEMENTARY INFORMATION: Supplementary data are available at http://dibernado.tigem.it     

Algebraic connectivity may explain the evolution of gene regulatory networks

Gene expression is a result of the interplay between the structure, type, kinetics, and specificity of gene regulatory interactions, whose diversity gives rise to the variety of life forms. As the dynamic behavior of gene regulatory networks depends on their structure, here we attempt to determine structural reasons which, despite the similarities in global network properties, may explain the large differences in organismal complexity. We demonstrate that the algebraic connectivity, the smallest non-trivial eigenvalue of the Laplacian, of the directed gene regulatory networks decreases with the increase of organismal complexity, and may therefore explain the difference between the variety of analyzed regulatory networks. In addition, our results point out that, for the species considered in this study, evolution favours decreasing concentration of strategically positioned feed forward loops, so that the network as a whole can increase the specificity towards changing environments. Moreover, contrary to the existing results, we show that the average degree, the length of the longest cascade, and the average cascade length of gene regulatory networks cannot recover the evolutionary relationships between organisms. Whereas the dynamical properties of special subnetworks are relatively well understood, there is still limited knowledge about the evolutionary reasons for the already identified design principles pertaining to these special subnetworks, underlying the global quantitative features of gene regulatory networks of different organisms. The behavior of the algebraic connectivity, which we show valid on gene regulatory networks extracted from curated databases, can serve as an additional evolutionary principle of organism-specific regulatory networks.     

Inference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy

One of the fundamental problems of cell biology is the understanding of complex regulatory networks. Such networks are ubiquitous in cells and knowledge of their properties is essential for the understanding of cellular behavior. In earlier work (Kholodenko et al. (PNAS 99: 12841), it was shown how the structure of biological networks can be quantified from experimental measurements of steady-state concentrations of key intermediates as a result of perturbations using a simple algorithm called "unravelling". Here, we study the effect of experimental uncertainty on the accuracy of the inferred structure (i.e. whether interactions are excitatory or inhibitory) of the networks determined using the unravelling algorithm. We show that the accuracy of the network structure depends not only on the noise level but on the strength of the interactions within the network. In particular, both very small and very large values of the connection strengths lead to large uncertainty in the inferred network. We describe a powerful geometric tool for the intuitive understanding of the effect of experimental error on the qualitative accuracy of the inferred network. In addition, we show that the use of additional data beyond that needed to minimally constrain the network not only improves the accuracy of the inferred network, but also may allow the detection of situations in which the initial assumptions of unravelling with respect to the network and the perturbations have been violated. Our ideas are illustrated using the mitogen-activated protein kinase (MAPK) signaling network as an example.     

An integer optimization algorithm for robust identification of non-linear gene regulatory networks

ABSTRACT: BACKGROUND: Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. RESULTS: We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in-silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data. CONCLUSIONS: Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any biological system.     

Construction and analysis of gene-gene dynamics influence networks based on a Boolean model

Background

Identification of novel gene-gene relations is a crucial issue to understand system-level biological phenomena. To this end, many methods based on a correlation analysis of gene expressions or structural analysis of molecular interaction networks have been proposed. They have a limitation in identifying more complicated gene-gene dynamical relations, though.

Results

To overcome this limitation, we proposed a measure to quantify a gene-gene dynamical influence (GDI) using a Boolean network model and constructed a GDI network to indicate existence of a dynamical influence for every ordered pair of genes. It represents how much a state trajectory of a target gene is changed by a knockout mutation subject to a source gene in a gene-gene molecular interaction (GMI) network. Through a topological comparison between GDI and GMI networks, we observed that the former network is denser than the latter network, which implies that there exist many gene pairs of dynamically influencing but molecularly non-interacting relations. In addition, a larger number of hub genes were generated in the GDI network. On the other hand, there was a correlation between these networks such that the degree value of a node was positively correlated to each other. We further investigated the relationships of the GDI value with structural properties and found that there are negative and positive correlations with the length of a shortest path and the number of paths, respectively. In addition, a GDI network could predict a set of genes whose steady-state expression is affected in E. coli gene-knockout experiments. More interestingly, we found that the drug-targets with side-effects have a larger number of outgoing links than the other genes in the GDI network, which implies that they are more likely to influence the dynamics of other genes. Finally, we found biological evidences showing that the gene pairs which are not molecularly interacting but dynamically influential can be considered for novel gene-gene relationships.

Conclusion

Taken together, construction and analysis of the GDI network can be a useful approach to identify novel gene-gene relationships in terms of the dynamical influence.

     

Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability

Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype) while allowing for switching between multiple phenotypes (network states) as occurs in development and in response to environmental change. However, the mechanisms through which genetic networks evolve such critical behavior have remained elusive. Here we present an evolutionary model in which criticality naturally emerges from the need to balance between the two essential components of evolvability: phenotype conservation and phenotype innovation under mutations. We simulated the Darwinian evolution of random Boolean networks that mutate gene regulatory interactions and grow by gene duplication. The mutating networks were subjected to selection for networks that both (i) preserve all the already acquired phenotypes (dynamical attractor states) and (ii) generate new ones. Our results show that this interplay between extending the phenotypic landscape (innovation) while conserving the existing phenotypes (conservation) suffices to cause the evolution of all the networks in a population towards criticality. Furthermore, the networks produced by this evolutionary process exhibit structures with hubs (global regulators) similar to the observed topology of real gene regulatory networks. Thus, dynamical criticality and certain elementary topological properties of gene regulatory networks can emerge as a byproduct of the evolvability of the phenotypic landscape.