On the Contributions of Topological Features to Transcriptional Regulatory Network Robustness (original) (raw)
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Robustness Can Evolve Gradually in Complex Regulatory Gene Networks with Varying Topology
PLOS Computational Biology, 2007
The topology of cellular circuits (the who-interacts-with-whom) is key to understand their robustness to both mutations and noise. The reason is that many biochemical parameters driving circuit behavior vary extensively and are thus not fine-tuned. Existing work in this area asks to what extent the function of any one given circuit is robust. But is high robustness truly remarkable, or would it be expected for many circuits of similar topology? And how can high robustness come about through gradual Darwinian evolution that changes circuit topology gradually, one interaction at a time? We here ask these questions for a model of transcriptional regulation networks, in which we explore millions of different network topologies. Robustness to mutations and noise are correlated in these networks. They show a skewed distribution, with a very small number of networks being vastly more robust than the rest. All networks that attain a given gene expression state can be organized into a graph whose nodes are networks that differ in their topology. Remarkably, this graph is connected and can be easily traversed by gradual changes of network topologies. Thus, robustness is an evolvable property. This connectedness and evolvability of robust networks may be a general organizational principle of biological networks. In addition, it exists also for RNA and protein structures, and may thus be a general organizational principle of all biological systems. Citation: Ciliberti S, Martin OC, Wagner A (2007) Robustness can evolve gradually in complex regulatory gene networks with varying topology. PLoS Comput Biol 3(2): e15.
Optimal topology of gene-regulatory networks: role of the average shortest path
Proceedings of the 9th EAI International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS), 2016
Gene regulatory networks (GRNs) possess an important structural property; they are sparse and resilient, with a robust topology that affords protection against random "attacks" (e.g., gene deletions). However, such networks exhibit optimal or near-optimal topological features not present in other scale-free networks. This paper utilizes an integer linear program formulation to gauge the exact structural optimality of scale-free networks measured using the average shortest path between transcription factors and the regulated genes of a gene-regulatory network sampled from the Escherichia coli bacterium. While randomly generated versions of these networks show several cases for improvement, few subnetworks sampled from Escherichia coli's transcriptional network show optimized solutions that differ substantially from their original topology. We therefore conclude that sampled transcriptional subnetworks from Escherichia coli exhibit an "optimal" topology not present in alternative networks. Because these analyses do not consider the biology of expression dynamics and are based on topology alone, other communication systems, such as wireless networks, may benefit from a more detailed examination of the role in which the average shortest path affects system function, such as with noise or other signaling disruptions.
Topological effects of data incompleteness of gene regulatory networks
BMC Systems Biology, 2012
The topological analysis of biological networks has been a prolific topic in network science during the last decade. A persistent problem with this approach is the inherent uncertainty and noisy nature of the data. One of the cases in which this situation is more marked is that of transcriptional regulatory networks (TRNs) in bacteria. The datasets are incomplete because regulatory pathways associated to a relevant fraction of bacterial genes remain unknown. Furthermore, direction, strengths and signs of the links are sometimes unknown or simply overlooked. Finally, the experimental approaches to infer the regulations are highly heterogeneous, in a way that induces the appearance of systematic experimental-topological correlations. And yet, the quality of the available data increases constantly. In this work we capitalize on these advances to point out the influence of data (in)completeness and quality on some classical results on topological analysis of TRNs, specially regarding modularity at different levels. In doing so, we identify the most relevant factors affecting the validity of previous findings, highlighting important caveats to future prokaryotic TRNs topological analysis.
Interrogating the Topological Robustness of Gene Regulatory Circuits
2016
One of the most important roles of cells is performing their cellular tasks properly for survival. Cells usually achieve robust functionality, for example cell-fate decision-making and signal transduction, through multiple layers of regulation involving many genes. Despite the combinatorial complexity of gene regulation, its quantitative behavior has been typically studied on the basis of experimentally-verified core gene regulatory circuitry, composed of a small set of important elements. It is still unclear how such a core circuit operates in the presence of many other regulatory molecules and in a crowded and noisy cellular environment. Here we report a new computational method, named random circuit perturbation (RACIPE), for interrogating the robust dynamical behavior of a gene regulatory circuit even without accurate measurements of circuit kinetic parameters. RACIPE generates an ensemble of random kinetic models corresponding to a fixed circuit topology, and utilizes statistic...
On the basic computational structure of gene regulatory networks
Arxiv preprint arXiv: …, 2009
Gene regulatory networks constitute the first layer of the cellular computation for cell adaptation and surveillance. In these webs, a set of causal relations is built up from thousands of interactions between transcription factors and their target genes. The large size of these webs and their entangled nature make difficult to achieve a global view of their internal organisation. Here, this problem has been addressed through a comparative study for Escherichia coli, Bacillus subtilis and Saccharomyces cerevisiae gene regulatory networks. We extract the minimal core of causal relations, uncovering the hierarchical and modular organisation from a novel dynamical/causal perspective. Our results reveal a marked top-down hierarchy containing several small dynamical modules for E. coli and B. subtilis. Conversely, the yeast network displays a single but large dynamical module in the middle of a bow-tie structure. We found that these dynamical modules capture the relevant wiring among both common and organism-specific biological functions such as transcription initiation, metabolic control, signal transduction, response to stress, sporulation and cell cycle. Functional and topological results suggest that two fundamentally different forms of logic organisation may have evolved in bacteria and yeast.
Topology of Mammalian Transcription Networks
2005
We present a first attempt to evaluate the generic topological principles underlying the mammalian transcriptional regulatory networks. Transcription networks, TN, studied here are represented as graphs where vertices are genes coding for transcription factors and edges are causal links between the genes, each edge combining both gene expression and trans-regulation events. Two transcription networks were retrieved from the TRANSPATH ® database: The first one, TN_RN, is a 'complete' transcription network referred to as a reference network. The second one, TN_p53, displays a particular transcriptional sub-network centered at p53 gene. We found these networks to be fundamentally non-random and inhomogeneous. Their topology follows a power-law degree distribution and is best described by the scale-free model. Shortest-path-length distribution and the average clustering coefficient indicate a small-world feature of these networks. The networks show the dependence of the clustering coefficient on the degree of a vertex, thereby indicating the presence of hierarchical modularity. Clear positive correlation between the values of betweenness and the degree of vertices has been observed in both networks. The top list of genes displaying high degree and high betweennes, such as p53, c-fos, c-jun and c-myc, is enriched with genes that are known as having tumorsuppressor or proto-oncogene properties, which supports the biological significance of the identified key topological elements.
Journal of Mathematical Biology, 2009
The concept of robustness of regulatory networks has been closely related to the nature of the interactions among genes, and the capability of pattern maintenance or reproducibility. Defining this robustness property is a challenging task, but mathematical models have often associated it to the volume of the space of admissible parameters. Not only the volume of the space but also its topology and geometry contain information on essential aspects of the network, including feasible pathways, switching between two parallel pathways or distinct/disconnected active regions of parameters. A method is presented here to characterize the space of admissible parameters, by writing it as a semi-algebraic set, and then theoretically analyzing its topology and geometry, as well as volume. This method provides a more objective and complete measure of the robustness of a developmental module. As a detailed case study, the segment polarity gene network is analyzed.
Three topological features of regulatory networks control life-essential and specialized subsystems
Scientific Reports, 2021
Gene regulatory networks (GRNs) play key roles in development, phenotype plasticity, and evolution. Although graph theory has been used to explore GRNs, associations amongst topological features, transcription factors (TFs), and systems essentiality are poorly understood. Here we sought the relationship amongst the main GRN topological features that influence the control of essential and specific subsystems. We found that the Knn, page rank, and degree are the most relevant GRN features: the ones are conserved along the evolution and are also relevant in pluripotent cells. Interestingly, life-essential subsystems are governed mainly by TFs with intermediary Knn and high page rank or degree, whereas specialized subsystems are mainly regulated by TFs with low Knn. Hence, we suggest that the high probability of TFs be toured by a random signal, and the high probability of the signal propagation to target genes ensures the life-essential subsystems’ robustness. Gene/genome duplication i...
Versatility and Connectivity Efficiency of Bipartite Transcription Networks
Biophysical Journal, 2006
The modulation of promoter activity by DNA-binding transcription regulators forms a bipartite network between the regulators and genes, in which a smaller number of regulators control a much lager number of genes. To facilitate representation of gene expression data with the simplest possible network structure, we have characterized the ability of bipartite networks to describe data. This has led to the classification of two types of bipartite networks, versatile and nonversatile. Versatile networks can describe any data of the same rank, and are indistinguishable from one another. Nonversatile networks require constraints to be present in data they describe, which may be used to distinguish between different network topologies. By quantifying the ability of bipartite networks to represent data we were able to define connectivity efficiency, which is a measure of how economic the use of connections is within a network with respect to data representation and generation. We postulated that it may be desirable for an organism to maximize its gene expression range per network edge, since development of a regulatory connection may have some evolutionary cost. We found that the transcriptional regulatory networks of both Saccharomyces cerevisiae and Escherichia coli lie close to their respective connectivity efficiency maxima, suggesting that connectivity efficiency may have some evolutionary influence.
Generic properties of random gene regulatory networks
Quantitative Biology, 2013
Modeling gene regulatory networks (GRNs) is an important topic in systems biology. Although there has been much work focusing on various specific systems, the generic behavior of GRNs with continuous variables is still elusive. In particular, it is not clear typically how attractors partition among the three types of orbits: steady state, periodic and chaotic, and how the dynamical properties change with network's topological characteristics. In this work, we first investigated these questions in random GRNs with different network sizes, connectivity, fraction of inhibitory links and transcription regulation rules. Then we searched for the core motifs that govern the dynamic behavior of large GRNs. We show that the stability of a random GRN is typically governed by a few embedding motifs of small sizes, and therefore can in general be understood in the context of these short motifs. Our results provide insights for the study and design of genetic networks.