Predicting Ancestral Segmentation Phenotypes from Drosophila to Anopheles Using In Silico Evolution

Molecular evolution is an established technique for inferring gene homology but regulatory DNA turns over so rapidly that inference of ancestral networks is often impossible. In silico evolution is used to compute the most parsimonious path in regulatory space for anterior-posterior patterning linking two Dipterian species. The expression pattern of gap genes has evolved between Drosophila (fly) and Anopheles (mosquito), yet one of their targets, eve, has remained invariant. Our model predicts that stripe 5 in fly disappears and a new posterior stripe is created in mosquito, thus eve stripe modules 3+7 and 4+6 in fly are homologous to 3+6 and 4+5 in mosquito. We can place Clogmia on this evolutionary pathway and it shares the mosquito homologies. To account for the evolution of the other pair-rule genes in the posterior we have to assume that the ancestral Dipterian utilized a dynamic method to phase those genes in relation to eve.     

Stabilizing patterning in the Drosophila segment polarity network by selecting models in silico

The segmentation of Drosophila is a prime model to study spatial patterning during embryogenesis. The spatial expression of segment polarity genes results from a complex network of interacting proteins whose expression products are maintained after successful segmentation. This prompted us to investigate the stability and robustness of this process using a dynamical model for the segmentation network based on Boolean states. The model consists of intra-cellular as well as inter-cellular interactions between adjacent cells in one spatial dimension. We quantify the robustness of the dynamical segmentation process by a systematic analysis of mutations. Our starting point consists in a previous Boolean model for Drosophila segmentation. We define mathematically the notion of dynamical robustness and show that the proposed model exhibits limited robustness in gene expression under perturbations. We applied in silico evolution (mutation and selection) and discover two classes of modified gene networks that have a more robust spatial expression pattern. We verified that the enhanced robustness of the two new models is maintained in differential equations models. By comparing the predicted model with experiments on mutated flies, we then discuss the two types of enhanced models. Drosophila patterning can be explained by modelling the underlying network of interacting genes. Here we demonstrate that simple dynamical considerations and in silico evolution can enhance the model to robustly express the expected pattern, helping to elucidate the role of further interactions.     

Optimal In Silico Target Gene Deletion through Nonlinear Programming for Genetic Engineering

Background

Optimal selection of multiple regulatory genes, known as targets, for deletion to enhance or suppress the activities of downstream genes or metabolites is an important problem in genetic engineering. Such problems become more feasible to address in silico due to the availability of more realistic dynamical system models of gene regulatory and metabolic networks. The goal of the computational problem is to search for a subset of genes to knock out so that the activity of a downstream gene or a metabolite is optimized.

Methodology/Principal Findings

Based on discrete dynamical system modeling of gene regulatory networks, an integer programming problem is formulated for the optimal in silico target gene deletion problem. In the first result, the integer programming problem is proved to be NP-hard and equivalent to a nonlinear programming problem. In the second result, a heuristic algorithm, called GKONP, is designed to approximate the optimal solution, involving an approach to prune insignificant terms in the objective function, and the parallel differential evolution algorithm. In the third result, the effectiveness of the GKONP algorithm is demonstrated by applying it to a discrete dynamical system model of the yeast pheromone pathways. The empirical accuracy and time efficiency are assessed in comparison to an optimal, but exhaustive search strategy.

Significance

Although the in silico target gene deletion problem has enormous potential applications in genetic engineering, one must overcome the computational challenge due to its NP-hardness. The presented solution, which has been demonstrated to approximate the optimal solution in a practical amount of time, is among the few that address the computational challenge. In the experiment on the yeast pheromone pathways, the identified best subset of genes for deletion showed advantage over genes that were selected empirically. Once validated in vivo, the optimal target genes are expected to achieve higher genetic engineering effectiveness than a trial-and-error procedure.     

Emergence of robust regulatory motifs from in silico evolution of sustained oscillation

The relationship between robustness and evolvability (easiness to evolve), and the evolutionary emergence of robust genetic circuits in biology have attracted much attention in systems biology. This paper investigates in silico the influence of the cis-regulation logic and the coupling of feedback loops on the evolvability and robustness of gene regulatory motifs that can generate sustained oscillation. Our simulation results indicate that both evolvability and robustness of the considered regulatory motifs depend on the cis-regulation logic and the way in which positive and negative feedback loops are coupled. Most interestingly, our findings suggest that robust regulatory motifs can emerge from evolution without an explicit selection pressure on robustness and adding noise in the parameters during the evolution is likely to promote the evolution of sustained oscillation.     

BioJazz: in silico evolution of cellular networks with unbounded complexity using rule-based modeling

Systems biologists aim to decipher the structure and dynamics of signaling and regulatory networks underpinning cellular responses; synthetic biologists can use this insight to alter existing networks or engineer de novo ones. Both tasks will benefit from an understanding of which structural and dynamic features of networks can emerge from evolutionary processes, through which intermediary steps these arise, and whether they embody general design principles. As natural evolution at the level of network dynamics is difficult to study, in silico evolution of network models can provide important insights. However, current tools used for in silico evolution of network dynamics are limited to ad hoc computer simulations and models. Here we introduce BioJazz, an extendable, user-friendly tool for simulating the evolution of dynamic biochemical networks. Unlike previous tools for in silico evolution, BioJazz allows for the evolution of cellular networks with unbounded complexity by combining rule-based modeling with an encoding of networks that is akin to a genome. We show that BioJazz can be used to implement biologically realistic selective pressures and allows exploration of the space of network architectures and dynamics that implement prescribed physiological functions. BioJazz is provided as an open-source tool to facilitate its further development and use. Source code and user manuals are available at: http://oss-lab.github.io/biojazz and http://osslab.lifesci.warwick.ac.uk/BioJazz.aspx.     

Bistability in feedback circuits as a byproduct of evolution of evolvability

Noisy bistable dynamics in gene regulation can underlie stochastic switching and is demonstrated to be beneficial under fluctuating environments. It is not known, however, if fluctuating selection alone can result in bistable dynamics. Using a stochastic model of simple feedback networks, we apply fluctuating selection on gene expression and run in silico evolutionary simulations. We find that independent of the specific nature of the environment–fitness relationship, the main outcome of fluctuating selection is the evolution of increased evolvability in the network; system parameters evolve toward a nonlinear regime where phenotypic diversity is increased and small changes in genotype cause large changes in expression level. In the presence of noise, the evolution of increased nonlinearity results in the emergence and maintenance of bistability. Our results provide the first direct evidence that bistability and stochastic switching in a gene regulatory network can emerge as a mechanism to cope with fluctuating environments. They strongly suggest that such emergence occurs as a byproduct of evolution of evolvability and exploitation of noise by evolution.