Local and global responses in complex gene regulation networks (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.
The tissues of metazoans appear, as for their gene expression profile, as one of the most striking manifestations of order and organization in nature: more than twenty thousand genes display a tissue specific average expression rate, with a four order of magnitude span from the least to the most expressed element. These profiles are strictly invariant so that samples coming from the same kind of tissue of two different individuals are correlated with values near to unity. This organization as an origin resembling classical statistical mechanics principles that allow us to assume a different view point on biological regulation.
PLoS Computational Biology, 2013
Gene regulatory networks show robustness to perturbations. Previous works identified robustness as an emergent property of gene network evolution but the underlying molecular mechanisms are poorly understood. We used a multi-tier modeling approach that integrates molecular sequence and structure information with network architecture and population dynamics. Structural models of transcription factor-DNA complexes are used to estimate relative binding specificities. In this model, mutations in the DNA cause changes on two levels: (a) at the sequence level in individual binding sites (modulating binding specificity), and (b) at the network level (creating and destroying binding sites). We used this model to dissect the underlying mechanisms responsible for the evolution of robustness in gene regulatory networks. Results suggest that in sparse architectures (represented by short promoters), a mixture of local-sequence and network-architecture level changes are exploited. At the local-sequence level, robustness evolves by decreasing the probabilities of both the destruction of existent and generation of new binding sites. Meanwhile, in highly interconnected architectures (represented by long promoters), robustness evolves almost entirely via network level changes, deleting and creating binding sites that modify the network architecture.
Cooperative Adaptive Responses in Gene Regulatory Networks with Many Degrees of Freedom
PLoS Computational Biology, 2013
Cells generally adapt to environmental changes by first exhibiting an immediate response and then gradually returning to their original state to achieve homeostasis. Although simple network motifs consisting of a few genes have been shown to exhibit such adaptive dynamics, they do not reflect the complexity of real cells, where the expression of a large number of genes activates or represses other genes, permitting adaptive behaviors. Here, we investigated the responses of gene regulatory networks containing many genes that have undergone numerical evolution to achieve high fitness due to the adaptive response of only a single target gene; this single target gene responds to changes in external inputs and later returns to basal levels. Despite setting a single target, most genes showed adaptive responses after evolution. Such adaptive dynamics were not due to common motifs within a few genes; even without such motifs, almost all genes showed adaptation, albeit sometimes partial adaptation, in the sense that expression levels did not always return to original levels. The genes split into two groups: genes in the first group exhibited an initial increase in expression and then returned to basal levels, while genes in the second group exhibited the opposite changes in expression. From this model, genes in the first group received positive input from other genes within the first group, but negative input from genes in the second group, and vice versa. Thus, the adaptation dynamics of genes from both groups were consolidated. This cooperative adaptive behavior was commonly observed if the number of genes involved was larger than the order of ten. These results have implications in the collective responses of gene expression networks in microarray measurements of yeast Saccharomyces cerevisiae and the significance to the biological homeostasis of systems with many components.
Universal attenuators and their interactions with feedback loops in gene regulatory networks
Nucleic acids research, 2017
Using a combination of mathematical modelling, statistical simulation and large-scale data analysis we study the properties of linear regulatory chains (LRCs) within gene regulatory networks (GRNs). Our modelling indicates that downstream genes embedded within LRCs are highly insulated from the variation in expression of upstream genes, and thus LRCs act as attenuators. This observation implies a progressively weaker functionality of LRCs as their length increases. When analyzing the preponderance of LRCs in the GRNs of Escherichia coli K12 and several other organisms, we find that very long LRCs are essentially absent. In both E. coli and M. tuberculosis we find that four-gene LRCs are intimately linked to identical feedback loops that are involved in potentially chaotic stress response, indicating that the dynamics of these potentially destabilising motifs are strongly restrained under homeostatic conditions. The same relationship is observed in a human cancer cell line (K562), an...
Gene Regulatory Networks: A Primer in Biological Processes and Statistical Modelling
Methods in Molecular Biology, 2018
Modelling gene regulatory networks not only requires a thorough understanding of the biological system depicted but also the ability to accurately represent this system from a mathematical perspective. Throughout this chapter, we aim to familiarise the reader with the biological processes and molecular factors at play in the process of gene expression regulation. We first describe the different interactions controlling each step of the expression process, from transcription to mRNA and protein decay. In the second section, we provide statistical tools to accurately represent this biological complexity in the form of mathematical models. Amongst other considerations, we discuss the topological properties of biological networks, the application of deterministic and stochastic frameworks and the quantitative modelling of regulation. We particularly focus on the use of such models for the simulation of expression data that can serve as a benchmark for the testing of network inference algorithms.
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.
Memory functions reveal structural properties of gene regulatory networks
PLoS computational biology, 2018
Gene regulatory networks (GRNs) control cellular function and decision making during tissue development and homeostasis. Mathematical tools based on dynamical systems theory are often used to model these networks, but the size and complexity of these models mean that their behaviour is not always intuitive and the underlying mechanisms can be difficult to decipher. For this reason, methods that simplify and aid exploration of complex networks are necessary. To this end we develop a broadly applicable form of the Zwanzig-Mori projection. By first converting a thermodynamic state ensemble model of gene regulation into mass action reactions we derive a general method that produces a set of time evolution equations for a subset of components of a network. The influence of the rest of the network, the bulk, is captured by memory functions that describe how the subnetwork reacts to its own past state via components in the bulk. These memory functions provide probes of near-steady state dy...
Information processing in the transcriptional regulatory network of yeast: Functional robustness
BMC Systems Biology, 2009
Background: Gene networks are considered to represent various aspects of molecular biological systems meaningfully because they naturally provide a systems perspective of molecular interactions. In this respect, the functional understanding of the transcriptional regulatory network is considered as key to elucidate the functional organization of an organism.