Communication and complexity in a GRN-based multicellular system for graph colouring

Artificial Genetic Regulatory Networks (GRNs) are interesting control models through their simplicity and versatility. They can be easily implemented, evolved and modified, and their similarity to their biological counterparts makes them interesting for simulations of life-like systems as well. These aspects suggest they may be perfect control systems for distributed computing in diverse situations, but to be usable for such applications the computational power and evolvability of GRNs need to be studied. In this research we propose a simple distributed system implementing GRNs to solve the well known NP-complete graph colouring problem. Every node (cell) of the graph to be coloured is controlled by an instance of the same GRN. All the cells communicate directly with their immediate neighbours in the graph so as to set up a good colouring. The quality of this colouring directs the evolution of the GRNs using a genetic algorithm. We then observe the quality of the colouring for two different graphs according to different communication protocols and the number of different proteins in the cell (a measure for the possible complexity of a GRN). Those two points, being the main scalability issues that any computational paradigm raises, will then be discussed.     

Evolution of Gene Regulatory Networks by Fluctuating Selection and Intrinsic Constraints

Various characteristics of complex gene regulatory networks (GRNs) have been discovered during the last decade, e.g., redundancy, exponential indegree distributions, scale-free outdegree distributions, mutational robustness, and evolvability. Although progress has been made in this field, it is not well understood whether these characteristics are the direct products of selection or those of other evolutionary forces such as mutational biases and biophysical constraints. To elucidate the causal factors that promoted the evolution of complex GRNs, we examined the effect of fluctuating environmental selection and some intrinsic constraining factors on GRN evolution by using an individual-based model. We found that the evolution of complex GRNs is remarkably promoted by fixation of beneficial gene duplications under unpredictably fluctuating environmental conditions and that some internal factors inherent in organisms, such as mutational bias, gene expression costs, and constraints on expression dynamics, are also important for the evolution of GRNs. The results indicate that various biological properties observed in GRNs could evolve as a result of not only adaptation to unpredictable environmental changes but also non-adaptive processes owing to the properties of the organisms themselves. Our study emphasizes that evolutionary models considering such intrinsic constraining factors should be used as null models to analyze the effect of selection on GRN evolution.     

Stochastic Boolean networks: An efficient approach to modeling gene regulatory networks

ABSTRACT: BACKGROUND: Various computational models have been of interest due to their use in the modelling of gene regulatory networks (GRNs). As a logical model, probabilistic Boolean networks (PBNs) consider molecular and genetic noise, so the study of PBNs provides significant insights into the understanding of the dynamics of GRNs. This will ultimately lead to advances in developing therapeutic methods that intervene in the process of disease development and progression. The applications of PBNs, however, are hindered by the complexities involved in the computation of the state transition matrix and the steady-state distribution of a PBN. For a PBN with n genes and N Boolean networks, the complexity to compute the state transition matrix is O(nN22n) or O(nN2n) for a sparse matrix. RESULTS: This paper presents a novel implementation of PBNs based on the notions of stochastic logic and stochastic computation. This stochastic implementation of a PBN is referred to as a stochastic Boolean network (SBN). An SBN provides an accurate and efficient simulation of a PBN without and with random gene perturbation. The state transition matrix is computed in an SBN with a complexity of O(nL2n), where L is a factor related to the stochastic sequence length. Since the minimum sequence length required for obtaining an evaluation accuracy approximately increases in a polynomial order with the number of genes, n, and the number of Boolean networks, N, usually increases exponentially with n, L is typically smaller than N, especially in a network with a large number of genes. Hence, the computational complexity of an SBN is primarily limited by the number of genes, but not directly by the total possible number of Boolean networks. Furthermore, a time-frame expanded SBN enables an efficient analysis of the steady-state distribution of a PBN. These findings are supported by the simulation results of a simplified p53 network, several randomly generated networks and a network inferred from a T cell immune response dataset. An SBN can also implement the function of an asynchronous PBN and is potentially useful in a hybrid approach in combination with a continuous or single-molecule level stochastic model. CONCLUSIONS: Stochastic Boolean networks (SBNs) are proposed as an efficient approach to modelling gene regulatory networks (GRNs). The SBN approach is able to recover biologically-proven regulatory behaviours, such as the oscillatory dynamics of the p53-Mdm2 network and the dynamic attractors in a T cell immune response network. The proposed approach can further predict the network dynamics when the genes are under perturbation, thus providing biologically meaningful insights for a better understanding of the dynamics of GRNs. The algorithms and methods described in this paper have been implemented in Matlab packages, which are attached as Additional files.     

Evolving modular genetic regulatory networks with a recursive,top-down approach

Being able to design genetic regulatory networks (GRNs) to achieve a desired cellular function is one of the main goals of synthetic biology. However, determining minimal GRNs that produce desired time-series behaviors is non-trivial. In this paper, we propose a ‘top-down’ approach to evolving small GRNs and then use these to recursively boot-strap the identification of larger, more complex, modular GRNs. We start with relatively dense GRNs and then use differential evolution (DE) to evolve interaction coefficients. When the target dynamical behavior is found embedded in a dense GRN, we narrow the focus of the search and begin aggressively pruning out excess interactions at the end of each generation. We first show that the method can quickly rediscover known small GRNs for a toggle switch and an oscillatory circuit. Next we include these GRNs as non-evolvable subnetworks in the subsequent evolution of more complex, modular GRNs. Successful solutions found in canonical DE where we truncated small interactions to zero, with or without an interaction penalty term, invariably contained many excess interactions. In contrast, by incorporating aggressive pruning and the penalty term, the DE was able to find minimal or nearly minimal GRNs in all test problems.     

On multistability of delayed genetic regulatory networks with multivariable regulation functions

Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and multivariable regulation functions are usually inevitable in such GRNs. In this paper, multistability of GRNs is analyzed by applying the control theory and mathematical tools. This study is to provide a theoretical tool to facilitate the design of synthetic gene circuit with multistability in the perspective of control theory. By transforming such GRNs into a new and uniform mathematical formulation, we put forward a general sector-like regulation function that is capable of quantifying the regulation effects in a more precise way. By resorting to up-to-date techniques, a novel Lyapunov-Krasovskii functional (LKF) is introduced for achieving delay dependence to ensure less conservatism. New conditions are then proposed to ensure the multistability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the delays. Our multistability conditions are applicable to several frequently used regulation functions especially the multivariable ones. Two examples are employed to illustrate the applicability and usefulness of the developed theoretical results.     

Conditional mutual inclusive information enables accurate quantification of associations in gene regulatory networks

Mutual information (MI), a quantity describing the nonlinear dependence between two random variables, has been widely used to construct gene regulatory networks (GRNs). Despite its good performance, MI cannot separate the direct regulations from indirect ones among genes. Although the conditional mutual information (CMI) is able to identify the direct regulations, it generally underestimates the regulation strength, i.e. it may result in false negatives when inferring gene regulations. In this work, to overcome the problems, we propose a novel concept, namely conditional mutual inclusive information (CMI2), to describe the regulations between genes. Furthermore, with CMI2, we develop a new approach, namely CMI2NI (CMI2-based network inference), for reverse-engineering GRNs. In CMI2NI, CMI2 is used to quantify the mutual information between two genes given a third one through calculating the Kullback–Leibler divergence between the postulated distributions of including and excluding the edge between the two genes. The benchmark results on the GRNs from DREAM challenge as well as the SOS DNA repair network in Escherichia coli demonstrate the superior performance of CMI2NI. Specifically, even for gene expression data with small sample size, CMI2NI can not only infer the correct topology of the regulation networks but also accurately quantify the regulation strength between genes. As a case study, CMI2NI was also used to reconstruct cancer-specific GRNs using gene expression data from The Cancer Genome Atlas (TCGA). CMI2NI is freely accessible at http://www.comp-sysbio.org/cmi2ni.     

The orchestration of mammalian tissue morphogenesis through a series of coherent feed-forward loops

Tissue morphogenesis requires intricate temporal and spatial control of gene expression that is executed through specific gene regulatory networks (GRNs). GRNs are comprised from individual subcircuits of different levels of complexity. An important question is to elucidate the mutual relationship between those genes encoding DNA-binding factors that trigger the subcircuit with those that play major "later" roles during terminal differentiation via expression of specific genes that constitute the phenotype of individual tissues. The ocular lens is a classical model system to study tissue morphogenesis. Pax6 is essential for both lens placode formation and subsequent stages of lens morphogenesis, whereas c-Maf controls terminal differentiation of lens fibers, including regulation of crystallins, key lens structural proteins required for its transparency and refraction. Here, we show that Pax6 directly regulates c-Maf expression during lens development. A 1.3-kb c-Maf promoter with a 1.6-kb upstream enhancer (CR1) recapitulated the endogenous c-Maf expression pattern in lens and retinal pigmented epithelium. ChIP assays revealed binding of Pax6 and c-Maf to multiple regions of the c-Maf locus in lens chromatin. To predict functional Pax6-binding sites, nine novel variants of Pax6 DNA-binding motifs were identified and characterized. Two of these motifs predicted a pair of Pax6-binding sites in the CR1. Mutagenesis of these Pax6-binding sites inactivated transgenic expression in the lens but not in retinal pigmented epithelium. These data establish a novel regulatory role for Pax6 during lens development, link together the Pax6/c-Maf/crystallin regulatory network, and suggest a novel type of GRN subcircuit that controls a major part of embryonic lens development.     

Comparison of evolutionary algorithms in gene regulatory network model inference

Background  

The evolution of high throughput technologies that measure gene expression levels has created a data base for inferring GRNs (a process also known as reverse engineering of GRNs). However, the nature of these data has made this process very difficult. At the moment, several methods of discovering qualitative causal relationships between genes with high accuracy from microarray data exist, but large scale quantitative analysis on real biological datasets cannot be performed, to date, as existing approaches are not suitable for real microarray data which are noisy and insufficient.     

Developmental evolution in social insects: regulatory networks from genes to societies

The evolution and development of complex phenotypes in social insect colonies, such as queen-worker dimorphism or division of labor, can, in our opinion, only be fully understood within an expanded mechanistic framework of Developmental Evolution. Conversely, social insects offer a fertile research area in which fundamental questions of Developmental Evolution can be addressed empirically. We review the concept of gene regulatory networks (GRNs) that aims to fully describe the battery of interacting genomic modules that are differentially expressed during the development of individual organisms. We discuss how distinct types of network models have been used to study different levels of biological organization in social insects, from GRNs to social networks. We propose that these hierarchical networks spanning different organizational levels from genes to societies should be integrated and incorporated into full GRN models to elucidate the evolutionary and developmental mechanisms underlying social insect phenotypes. Finally, we discuss prospects and approaches to achieve such an integration.     

On the role of periodism in the origin of proteins

Two different views have been proposed for origins of genes (or proteins). One is that primordial genes evolved from random sequences. This view underlies the concept of modern in vitro evolution experiments that functional molecules (even proteins) evolved from random sequence-libraries. On the contrary, the second view reminds that "random sequences" would be an unusual state in which to find RNA or DNA, because it is their inherent nature to yield periodic structures during the course of semi-conservative replication. In this second view, the periodicity of DNA (or RNA) is responsible for emergence of primordial genes. Although recent reports on the variety of periodicities present in proteins, genes and genomes are consistent with the second view, it has yet to be experimentally tested. We assessed the significance of periodicities of DNA in the origin of genes by constructing such periodic DNAs. The results showed that periodic DNA produced ordered proteins at very high rates, which is in contrast to the fact that proteins with random sequences lack secondary structures. We concluded that periodicity played a pivotal role in the origin of many genes. The observation should pave the way for new experimental evolution systems for proteins.