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      Robustness Can Evolve Gradually in Complex Regulatory Gene Networks with Varying Topology

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          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          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.

          Author Summary

          Living things are astonishingly complex, yet unlike houses of cards they are also highly robust. That is, they have persisted for billions of years, despite being exposed to an endless stream of environmental stressors and random mutations. Is this robustness an evolvable property? Do different biological systems vary in their robustness? Has natural selection shaped this robustness? These questions are very difficult to answer experimentally for most systems, be they proteins or large gene networks. Here we address these questions with a model of the transcription regulation networks that regulate both cellular functions and embryonic development in many organisms. We examine millions of such networks that differ in the topology or architecture of their regulatory interactions, that is, in the “who interacts with whom” of a network. We find that radically different network architectures can show the same gene expression pattern. The networks' robustness to both mutations and gene expression noise shows a broad distribution: some network architectures are highly robust, whereas others are quite fragile. Importantly, the entire space of network architectures can be traversed through small changes of individual regulatory interactions, without changing a network's gene expression pattern. This means that high robustness in gene expression can evolve through gradual and neutral evolution in the space of network architectures. Our results show that the robustness of transcriptional regulation networks is an evolvable trait that natural selection can change like any other trait.

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          Most cited references59

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          Waddington's canalization revisited: developmental stability and evolution.

          Most species maintain abundant genetic variation and experience a range of environmental conditions, yet phenotypic variation is low. That is, development is robust to changes in genotype and environment. It has been claimed that this robustness, termed canalization, evolves because of long-term natural selection for optimal phenotypes. We show that the developmental process, here modeled as a network of interacting transcriptional regulators, constrains the genetic system to produce canalization, even without selection toward an optimum. The extent of canalization, measured as the insensitivity to mutation of a network's equilibrium state, depends on the complexity of the network, such that more highly connected networks evolve to be more canalized. We argue that canalization may be an inevitable consequence of complex developmental-genetic processes and thus requires no explanation in terms of evolution to suppress phenotypic variation.
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            Evolutionary capacitance as a general feature of complex gene networks.

            An evolutionary capacitor buffers genotypic variation under normal conditions, thereby promoting the accumulation of hidden polymorphism. But it occasionally fails, thereby revealing this variation phenotypically. The principal example of an evolutionary capacitor is Hsp90, a molecular chaperone that targets an important set of signal transduction proteins. Experiments in Drosophila and Arabidopsis have demonstrated three key properties of Hsp90: (1) it suppresses phenotypic variation under normal conditions and releases this variation when functionally compromised; (2) its function is overwhelmed by environmental stress; and (3) it exerts pleiotropic effects on key developmental processes. But whether these properties necessarily make Hsp90 a significant and unique facilitator of adaptation is unclear. Here we use numerical simulations of complex gene networks, as well as genome-scale expression data from yeast single-gene deletion strains, to present a mechanism that extends the scope of evolutionary capacitance beyond the action of Hsp90 alone. We illustrate that most, and perhaps all, genes reveal phenotypic variation when functionally compromised, and that the availability of loss-of-function mutations accelerates adaptation to a new optimum phenotype. However, this effect does not require the mutations to be conditional on the environment. Thus, there might exist a large class of evolutionary capacitors whose effects on phenotypic variation complement the systemic, environment-induced effects of Hsp90.
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              The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster.

              Expression of the Drosophila segment polarity genes is initiated by a pre-pattern of pair-rule gene products and maintained by a network of regulatory interactions throughout several stages of embryonic development. Analysis of a model of gene interactions based on differential equations showed that wild-type expression patterns of these genes can be obtained for a wide range of kinetic parameters, which suggests that the steady states are determined by the topology of the network and the type of regulatory interactions between components, not the detailed form of the rate laws. To investigate this, we propose and analyse a Boolean model of this network which is based on a binary ON/OFF representation of mRNA and protein levels, and in which the interactions are formulated as logical functions. In this model the spatial and temporal patterns of gene expression are determined by the topology of the network and whether components are present or absent, rather than the absolute levels of the mRNAs and proteins and the functional details of their interactions. The model is able to reproduce the wild-type gene expression patterns, as well as the ectopic expression patterns observed in overexpression experiments and various mutants. Furthermore, we compute explicitly all steady states of the network and identify the basin of attraction of each steady state. The model gives important insights into the functioning of the segment polarity gene network, such as the crucial role of the wingless and sloppy paired genes, and the network's ability to correct errors in the pre-pattern.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                pcbi
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                February 2007
                2 February 2007
                : 3
                : 2
                : e15
                Affiliations
                [1 ] Laboratoire de Physique Théoique et Modèles Statistiques, Universite Paris-Sud, Orsay, France
                [2 ] Centre National de la Recherche Scientifique, Universite Paris-Sud, Orsay, France
                [3 ] Laboratoire de Genetique Vegetale du Moulon, Universite Paris-Sud, Gif-sur-Yvette, France
                [4 ] L'Institut National de la Recherche Agronomique, Universite Paris-Sud, Gif-sur-Yvette
                [5 ] Centre National de la Recherche Scientifique, Universite Paris-Sud, Gif-sur-Yvette, France
                [6 ] Department of Biochemistry, University of Zurich, Switzerland
                Harvard University, United States of America
                Author notes
                * To whom correspondence should be addressed. E-mail: wagnera@ 123456unm.edu
                Article
                06-PLCB-RA-0158R3 plcb-03-02-03
                10.1371/journal.pcbi.0030015
                1794322
                17274682
                855a5ef3-c362-49c7-8a66-e4cb5cb55a4c
                Copyright: © 2007 Ciliberti et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
                History
                : 27 April 2006
                : 18 December 2006
                Page count
                Pages: 10
                Categories
                Research Article
                Evolutionary Biology
                None
                Custom metadata
                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. doi: 10.1371/journal.pcbi.0030015

                Quantitative & Systems biology
                Quantitative & Systems biology

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