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

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.