Sphingosine-1-Phosphate Metabolism and Intestinal Tumorigenesis: Lipid Signaling Strikes Again

Superficially similar traits in phylogenetically unrelated species often result from adaptation to common selection pressures. Examples of convergent evolution are known at the levels of whole organisms, organ systems, gene networks and specific proteins. The phenotypic properties of living things, on the other hand, are determined in large part by complex networks of interacting proteins. Here we present a mathematical model of the network of proteins that controls DNA synthesis and cell division in the alpha-proteobacterium, Caulobacter crescentus. By comparing the protein regulatory circuits for cell reproduction in Caulobacter with that in budding yeast (Saccharomyces cerevisiae), we suggest that convergent evolution may have created similar molecular reaction networks in order to accomplish the same purpose of coordinating DNA synthesis to cell division. Although the genes and proteins involved in cell cycle regulation in prokaryotes and eukaryotes are very different and (apparently) phylogenetically unrelated, they seem to be wired together in similar regulatory networks, which coordinate cell cycle events by identical dynamical principles.     

Selection for distinct gene expression properties favours the evolution of mutational robustness in gene regulatory networks

Mutational robustness is a genotype's tendency to keep a phenotypic trait with little and few changes in the face of mutations. Mutational robustness is both ubiquitous and evolutionarily important as it affects in different ways the probability that new phenotypic variation arises. Understanding the origins of robustness is specially relevant for systems of development that are phylogenetically widespread and that construct phenotypic traits with a strong impact on fitness. Gene regulatory networks are examples of this class of systems. They comprise sets of genes that, through cross‐regulation, build the gene activity patterns that define cellular responses, different tissues or distinct cell types. Several empirical observations, such as a greater robustness of wild‐type phenotypes, suggest that stabilizing selection underlies the evolution of mutational robustness. However, the role of selection in the evolution of robustness is still under debate. Computer simulations of the dynamics and evolution of gene regulatory networks have shown that selection for any gene activity pattern that is steady and self‐sustaining is sufficient to promote the evolution of mutational robustness. Here, I generalize this scenario using a computational model to show that selection for different aspects of a gene activity phenotype increases mutational robustness. Mutational robustness evolves even when selection favours properties that conflict with the stationarity of a gene activity pattern. The results that I present support an important role for stabilizing selection in the evolution of robustness in gene regulatory networks.     

Elementary network reconstruction: A framework for the analysis of regulatory networks in biological systems

Complexity of regulatory networks arises from the high degree of interaction between network components such as DNA, RNA, proteins, and metabolites. We have developed a modeling tool, elementary network reconstruction (ENR), to characterize these networks. ENR is a knowledge-driven, steady state, deterministic, quantitative modeling approach based on linear perturbation theory. In ENR we demonstrate a novel means of expressing control mechanisms by way of dimensionless steady state gains relating input and output variables, which are purely in terms of species abundances (extensive variables). As a result of systematic enumeration of network species in n×n matrix, the two properties of linear perturbation are manifested in graphical representations: transitive property is evident in a special L-shape structure, and additive property is evident in multiple L-shape structures arriving at the same matrix cell. Upon imposing mechanistic (lowest-level) gains, network self-assembly through transitive and additive properties results in elucidation of inherent topology and explicit cataloging of higher level gains, which in turn can be used to predict perturbation results. Application of ENR to the regulatory network behind carbon catabolite repression in Escherichia coli is presented. Through incorporation of known molecular mechanisms governing transient and permanent repressions, the ENR model correctly predicts several key features of this regulatory network, including a 50% downshift in intracellular cAMP level upon exposure to glucose. Since functional genomics studies are mainly concerned with redistribution of species abundances in perturbed systems, ENR could be exploited in the system-level analysis of biological systems.     

The lens in focus: a comparison of lens development in Drosophila and vertebrates

The evolution of the eye has been a major subject of study dating back centuries. The advent of molecular genetics offered the surprising finding that morphologically distinct eyes rely on conserved regulatory gene networks for their formation. While many of these advances often stemmed from studies of the compound eye of the fruit fly, Drosophila melanogaster, and later translated to discoveries in vertebrate systems, studies on vertebrate lens development far outnumber those in Drosophila. This may be largely historical, since Spemann and Mangold's paradigm of tissue induction was discovered in the amphibian lens. Recent studies on lens development in Drosophila have begun to define molecular commonalities with the vertebrate lens. Here, we provide an overview of Drosophila lens development, discussing intrinsic and extrinsic factors controlling lens cell specification and differentiation. We then summarize key morphological and molecular events in vertebrate lens development, emphasizing regulatory factors and networks strongly associated with both systems. Finally, we provide a comparative analysis that highlights areas of research that would help further clarify the degree of conservation between the formation of dioptric systems in invertebrates and vertebrates.     

Structural Properties of Gene Regulatory Networks: Definitions and Connections

The study of gene regulatory networks is a significant problem in systems biology. Of particular interest is the problem of determining the unknown or hidden higher level regulatory signals by using gene expression data from DNA microarray experiments. Several studies in this area have demonstrated the critical aspect of the network structure in tackling the network modelling problem. Structural analysis of systems has proved useful in a number of contexts, viz., observability, controllability, fault diagnosis, sparse matrix computations etc. In this contribution, we formally define structural properties that are relevant to Gene Regulatory Networks. We explore the structural implications of certain quantitative methods and explain completely the connections between the identifiability conditions and structural criteria of observability and distinguishability. We illustrate these concepts in case studies using representative biologically motivated network examples. The present work bridges the quantitative modelling methods with those based on the structural analysis.     

Hierarchical evolution of animal body plans

An open question in animal evolution is why the phylum- and superphylum-level body plans have changed so little, while the class- and family-level body plans have changed so greatly since the early Cambrian. Davidson and Erwin (Davidson and Erwin, 2006; Erwin and Davidson, 2009) proposed that the hierarchical structure of gene regulatory networks leads to different observed evolutionary rates for terminal properties of the body plan versus major aspects of body plan morphology. Here, we calculated the speed of evolution of genes in these gene regulatory networks. We found that the genes which determine the phylum and superphylum characters evolve slowly, while those genes which determine the classes, families, and speciation evolve more rapidly. This result furnishes genetic support to the hypothesis that the hierarchical structure of developmental regulatory networks provides an organizing structure which guides the evolution of aspects of the body plan.     

Modeling and simulation of genetic regulatory systems: a literature review.

In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.     

A publish-subscribe model of genetic networks

We present a simple model of genetic regulatory networks in which regulatory connections among genes are mediated by a limited number of signaling molecules. Each gene in our model produces (publishes) a single gene product, which regulates the expression of other genes by binding to regulatory regions that correspond (subscribe) to that product. We explore the consequences of this publish-subscribe model of regulation for the properties of single networks and for the evolution of populations of networks. Degree distributions of randomly constructed networks, particularly multimodal in-degree distributions, which depend on the length of the regulatory sequences and the number of possible gene products, differed from simpler Boolean NK models. In simulated evolution of populations of networks, single mutations in regulatory or coding regions resulted in multiple changes in regulatory connections among genes, or alternatively in neutral change that had no effect on phenotype. This resulted in remarkable evolvability in both number and length of attractors, leading to evolved networks far beyond the expectation of these measures based on random distributions. Surprisingly, this rapid evolution was not accompanied by changes in degree distribution; degree distribution in the evolved networks was not substantially different from that of randomly generated networks. The publish-subscribe model also allows exogenous gene products to create an environment, which may be noisy or stable, in which dynamic behavior occurs. In simulations, networks were able to evolve moderate levels of both mutational and environmental robustness.     

De Novo Evolution of Complex, Global and Hierarchical Gene Regulatory Mechanisms

Gene regulatory networks exhibit complex, hierarchical features such as global regulation and network motifs. There is much debate about whether the evolutionary origins of such features are the results of adaptation, or the by-products of non-adaptive processes of DNA replication. The lack of availability of gene regulatory networks of ancestor species on evolutionary timescales makes this a particularly difficult problem to resolve. Digital organisms, however, can be used to provide a complete evolutionary record of lineages. We use a biologically realistic evolutionary model that includes gene expression, regulation, metabolism and biosynthesis, to investigate the evolution of complex function in gene regulatory networks. We discover that: (i) network architecture and complexity evolve in response to environmental complexity, (ii) global gene regulation is selected for in complex environments, (iii) complex, inter-connected, hierarchical structures evolve in stages, with energy regulation preceding stress responses, and stress responses preceding growth rate adaptations and (iv) robustness of evolved models to mutations depends on hierarchical level: energy regulation and stress responses tend not to be robust to mutations, whereas growth rate adaptations are more robust and non-lethal when mutated. These results highlight the adaptive and incremental evolution of complex biological networks, and the value and potential of studying realistic in silico evolutionary systems as a way of understanding living systems.     

Towards a general theory of adaptive walks on rugged landscapes

Adaptive evolution, to a large extent, is a complex combinatorial optimization process. In this article we take beginning steps towards developing a general theory of adaptive "walks" via fitter variants in such optimization processes. We introduce the basic idea of a space of entities, each a 1-mutant neighbor of many other entities in the space, and the idea of a fitness ascribed to each entity. Adaptive walks proceed from an initial entity, via fitter neighbors, to locally or globally optimal entities that are fitter than their neighbors. We develop a general theory for the number of local optima, lengths of adaptive walks, and the number of alternative local optima accessible from any given initial entity, for the baseline case of an uncorrelated fitness landscape. Most fitness landscapes are correlated, however. Therefore we develop parts of a universal theory of adaptation on correlated landscapes by adaptive processes that have sufficient numbers of mutations per individual to "jump beyond" the correlation lengths in the underlying landscape. In addition, we explore the statistical character of adaptive walks in two independent complex combinatorial optimization problems, that of evolving a specific cell type in model genetic networks, and that of finding good solutions to the traveling salesman problem. Surprisingly, both show similar statistical features, encouraging the hope that a general theory for adaptive walks on correlated and uncorrelated landscapes can be found. In the final section we explore two limits to the efficacy of selection. The first is new, and surprising: for a wide class of systems, as the complexity of the entities under selection increases, the local optima that are attainable fall progressively closer to the mean properties of the underlying space of entities. This may imply that complex biological systems, such as genetic regulatory systems, are "close" to the mean properties of the ensemble of genomic regulatory systems explored by evolution. The second limit shows that with increasing complexity and a fixed mutation rate, selection often becomes unable to pull an adapting population to those local optima to which connected adaptive walks via fitter variants exist. These beginning steps in theory development are applied to maturation of the immune response, and to the problem of radiation and stasis. Despite the limitations of the adaptive landscape metaphor, we believe that further development along the lines begun here will prove useful.     

Synthetic circuits reveal how mechanisms of gene regulatory networks constrain evolution

Phenotypic variation is the raw material of adaptive Darwinian evolution. The phenotypic variation found in organismal development is biased towards certain phenotypes, but the molecular mechanisms behind such biases are still poorly understood. Gene regulatory networks have been proposed as one cause of constrained phenotypic variation. However, most pertinent evidence is theoretical rather than experimental. Here, we study evolutionary biases in two synthetic gene regulatory circuits expressed in Escherichia coli that produce a gene expression stripe—a pivotal pattern in embryonic development. The two parental circuits produce the same phenotype, but create it through different regulatory mechanisms. We show that mutations cause distinct novel phenotypes in the two networks and use a combination of experimental measurements, mathematical modelling and DNA sequencing to understand why mutations bring forth only some but not other novel gene expression phenotypes. Our results reveal that the regulatory mechanisms of networks restrict the possible phenotypic variation upon mutation. Consequently, seemingly equivalent networks can indeed be distinct in how they constrain the outcome of further evolution.     

Patterning the dorsal–ventral axis of the wasp Nasonia vitripennis

Regulatory networks composed of interacting genes are responsible for pattern formation and cell type specification in a wide variety of developmental contexts. Evolution must act on these regulatory networks in order to change the proportions, distribution, and characteristics of specified cells. Thus, understanding how these networks operate in homologous systems across multiple levels of phylogenetic divergence is critical for understanding the evolution of developmental systems. Among the most thoroughly characterized regulatory networks is the dorsal–ventral patterning system of the fly Drosophila melanogaster. Due to the thorough understanding of this system, it is an ideal starting point for comparative analyses. Here we report an analysis of the DV patterning system of the wasp, Nasonia vitripennis. This wasp undergoes a mode of long germ embryogenesis that is superficially nearly identical to that of Drosophila, but one that was likely independently derived. We have found that while the expression of genes just prior to the onset of gastrulation is almost identical in Nasonia and Drosophila, both the upstream network responsible for generating this pattern, and the downstream morphogenetic movements that it sets in motion, are significantly diverged. From this we conclude that many network structures are available to evolution to achieve particular developmental ends.     

Influence of metabolic network structure and function on enzyme evolution

Background  

Most studies of molecular evolution are focused on individual genes and proteins. However, understanding the design principles and evolutionary properties of molecular networks requires a system-wide perspective. In the present work we connect molecular evolution on the gene level with system properties of a cellular metabolic network. In contrast to protein interaction networks, where several previous studies investigated the molecular evolution of proteins, metabolic networks have a relatively well-defined global function. The ability to consider fluxes in a metabolic network allows us to relate the functional role of each enzyme in a network to its rate of evolution.