A Boolean Model of the Gene Regulatory Network Underlying Mammalian Cortical Area Development

The cerebral cortex is divided into many functionally distinct areas. The emergence of these areas during neural development is dependent on the expression patterns of several genes. Along the anterior-posterior axis, gradients of Fgf8, Emx2, Pax6, Coup-tfi, and Sp8 play a particularly strong role in specifying areal identity. However, our understanding of the regulatory interactions between these genes that lead to their confinement to particular spatial patterns is currently qualitative and incomplete. We therefore used a computational model of the interactions between these five genes to determine which interactions, and combinations of interactions, occur in networks that reproduce the anterior-posterior expression patterns observed experimentally. The model treats expression levels as Boolean, reflecting the qualitative nature of the expression data currently available. We simulated gene expression patterns created by all possible networks containing the five genes of interest. We found that only of these networks were able to reproduce the experimentally observed expression patterns. These networks all lacked certain interactions and combinations of interactions including auto-regulation and inductive loops. Many higher order combinations of interactions also never appeared in networks that satisfied our criteria for good performance. While there was remarkable diversity in the structure of the networks that perform well, an analysis of the probability of each interaction gave an indication of which interactions are most likely to be present in the gene network regulating cortical area development. We found that in general, repressive interactions are much more likely than inductive ones, but that mutually repressive loops are not critical for correct network functioning. Overall, our model illuminates the design principles of the gene network regulating cortical area development, and makes novel predictions that can be tested experimentally.     

Specialization Can Drive the Evolution of Modularity

Organismal development and many cell biological processes are organized in a modular fashion, where regulatory molecules form groups with many interactions within a group and few interactions between groups. Thus, the activity of elements within a module depends little on elements outside of it. Modularity facilitates the production of heritable variation and of evolutionary innovations. There is no consensus on how modularity might evolve, especially for modules in development. We show that modularity can increase in gene regulatory networks as a byproduct of specialization in gene activity. Such specialization occurs after gene regulatory networks are selected to produce new gene activity patterns that appear in a specific body structure or under a specific environmental condition. Modules that arise after specialization in gene activity comprise genes that show concerted changes in gene activities. This and other observations suggest that modularity evolves because it decreases interference between different groups of genes. Our work can explain the appearance and maintenance of modularity through a mechanism that is not contingent on environmental change. We also show how modularity can facilitate co-option, the utilization of existing gene activity to build new gene activity patterns, a frequent feature of evolutionary innovations.     

Modeling genetic regulatory dynamics in neural development.

We model genetic regulatory networks in the framework of continuous-time recurrent networks. The network parameters are determined from gene expression level time series data using genetic algorithms. We have applied the method to expression data from the development of rat central nervous system, where the active genes cluster into four groups, within which the temporal expression patterns are similar. The data permit us to identify approximately the interactions between these groups of genes. We find that generally a single time series is of limited value in determining the interactions in the network, but multiple time series collected in related tissues or under treatment with different drugs can fix their values much more precisely.     

A model-based optimization framework for the inference on gene regulatory networks from DNA array data

MOTIVATION: Identification of the regulatory structures in genetic networks and the formulation of mechanistic models in the form of wiring diagrams is one of the significant objectives of expression profiling using DNA microarray technologies and it requires the development and application of identification frameworks. RESULTS: We have developed a novel optimization framework for identifying regulation in a genetic network using the S-system modeling formalism. We show that balance equations on both mRNA and protein species led to a formulation suitable for analyzing DNA-microarray data whereby protein concentrations have been eliminated and only mRNA relative concentrations are retained. Using this formulation, we examined if it is possible to infer a set of possible genetic regulatory networks consistent with observed mRNA expression patterns. Two origins of changes in mRNA expression patterns were considered. One derives from changes in the biophysical properties of the system that alter the molecular-interaction kinetics and/or message stability. The second is due to gene knock-outs. We reduced the identification problem to an optimization problem (of the so-called mixed-integer non-linear programming class) and we developed an algorithmic procedure for solving this optimization problem. Using simulated data generated by our mathematical model, we show that our method can actually find the regulatory network from which the data were generated. We also show that the number of possible alternate genetic regulatory networks depends on the size of the dataset (i.e. number of experiments), but this dependence is different for each of the two types of problems considered, and that a unique solution requires fewer datasets than previously estimated in the literature. This is the first method that also allows the identification of every possible regulatory network that could explain the data, when the number of experiments does not allow identification of unique regulatory structure.     

Robustness under Functional Constraint: The Genetic Network for Temporal Expression in Drosophila Neurogenesis

Precise temporal coordination of gene expression is crucial for many developmental processes. One central question in developmental biology is how such coordinated expression patterns are robustly controlled. During embryonic development of the Drosophila central nervous system, neural stem cells called neuroblasts express a group of genes in a definite order, which leads to the diversity of cell types. We produced all possible regulatory networks of these genes and examined their expression dynamics numerically. From the analysis, we identified requisite regulations and predicted an unknown factor to reproduce known expression profiles caused by loss-of-function or overexpression of the genes in vivo, as well as in the wild type. Following this, we evaluated the stability of the actual Drosophila network for sequential expression. This network shows the highest robustness against parameter variations and gene expression fluctuations among the possible networks that reproduce the expression profiles. We propose a regulatory module composed of three types of regulations that is responsible for precise sequential expression. This study suggests that the Drosophila network for sequential expression has evolved to generate the robust temporal expression for neuronal specification.     

Efficient reverse-engineering of a developmental gene regulatory network

Understanding the complex regulatory networks underlying development and evolution of multi-cellular organisms is a major problem in biology. Computational models can be used as tools to extract the regulatory structure and dynamics of such networks from gene expression data. This approach is called reverse engineering. It has been successfully applied to many gene networks in various biological systems. However, to reconstitute the structure and non-linear dynamics of a developmental gene network in its spatial context remains a considerable challenge. Here, we address this challenge using a case study: the gap gene network involved in segment determination during early development of Drosophila melanogaster. A major problem for reverse-engineering pattern-forming networks is the significant amount of time and effort required to acquire and quantify spatial gene expression data. We have developed a simplified data processing pipeline that considerably increases the throughput of the method, but results in data of reduced accuracy compared to those previously used for gap gene network inference. We demonstrate that we can infer the correct network structure using our reduced data set, and investigate minimal data requirements for successful reverse engineering. Our results show that timing and position of expression domain boundaries are the crucial features for determining regulatory network structure from data, while it is less important to precisely measure expression levels. Based on this, we define minimal data requirements for gap gene network inference. Our results demonstrate the feasibility of reverse-engineering with much reduced experimental effort. This enables more widespread use of the method in different developmental contexts and organisms. Such systematic application of data-driven models to real-world networks has enormous potential. Only the quantitative investigation of a large number of developmental gene regulatory networks will allow us to discover whether there are rules or regularities governing development and evolution of complex multi-cellular organisms.     

Inference of the Xenopus tropicalis embryonic regulatory network and spatial gene expression patterns

Background

During embryogenesis, signaling molecules produced by one cell population direct gene regulatory changes in neighboring cells and influence their developmental fates and spatial organization. One of the earliest events in the development of the vertebrate embryo is the establishment of three germ layers, consisting of the ectoderm, mesoderm and endoderm. Attempts to measure gene expression in vivo in different germ layers and cell types are typically complicated by the heterogeneity of cell types within biological samples (i.e., embryos), as the responses of individual cell types are intermingled into an aggregate observation of heterogeneous cell types. Here, we propose a novel method to elucidate gene regulatory circuits from these aggregate measurements in embryos of the frog Xenopus tropicalis using gene network inference algorithms and then test the ability of the inferred networks to predict spatial gene expression patterns.

Results

We use two inference models with different underlying assumptions that incorporate existing network information, an ODE model for steady-state data and a Markov model for time series data, and contrast the performance of the two models. We apply our method to both control and knockdown embryos at multiple time points to reconstruct the core mesoderm and endoderm regulatory circuits. Those inferred networks are then used in combination with known dorsal-ventral spatial expression patterns of a subset of genes to predict spatial expression patterns for other genes. Both models are able to predict spatial expression patterns for some of the core mesoderm and endoderm genes, but interestingly of different gene subsets, suggesting that neither model is sufficient to recapitulate all of the spatial patterns, yet they are complementary for the patterns that they do capture.

Conclusion

The presented methodology of gene network inference combined with spatial pattern prediction provides an additional layer of validation to elucidate the regulatory circuits controlling the spatial-temporal dynamics in embryonic development.     

Global gene expression profiling in Escherichia coli K12. The effects of oxygen availability and FNR

The work presented here is a first step toward a long term goal of systems biology, the complete elucidation of the gene regulatory networks of a living organism. To this end, we have employed DNA microarray technology to identify genes involved in the regulatory networks that facilitate the transition of Escherichia coli cells from an aerobic to an anaerobic growth state. We also report the identification of a subset of these genes that are regulated by a global regulatory protein for anaerobic metabolism, FNR. Analysis of these data demonstrated that the expression of over one-third of the genes expressed during growth under aerobic conditions are altered when E. coli cells transition to an anaerobic growth state, and that the expression of 712 (49%) of these genes are either directly or indirectly modulated by FNR. The results presented here also suggest interactions between the FNR and the leucine-responsive regulatory protein (Lrp) regulatory networks. Because computational methods to analyze and interpret high dimensional DNA microarray data are still at an early stage, and because basic issues of data analysis are still being sorted out, much of the emphasis of this work is directed toward the development of methods to identify differentially expressed genes with a high level of confidence. In particular, we describe an approach for identifying gene expression patterns (clusters) obtained from multiple perturbation experiments based on a subset of genes that exhibit high probability for differential expression values.