How gap genes make their domains: An analytical study based on data driven approximations

Learning Structures of Conceptual Models from Observed Dynamics Using Evolutionary Echo State Networks

Conceptual or explanatory models are a key element in the process of complex system modelling. They not only provide an intuitive way for modellers to comprehend and scope the complex phenomena under investigation through an abstract representation but also pave the way for the later development of detailed and higher-resolution simulation models. An evolutionary echo state network-based method for supporting the development of such models, which can help to expedite the generation of alternative models for explaining the underlying phenomena and potentially reduce the manual effort required, is proposed. It relies on a customised echo state neural network for learning sparse conceptual model representations from the observed data. In this paper, three evolutionary algorithms, a genetic algorithm, differential evolution and particle swarm optimisation are applied to optimize the network design in order to improve model learning. The proposed methodology is tested on four examples of problems that represent complex system models in the economic, ecological and physical domains. The empirical analysis shows that the proposed technique can learn models which are both sparse and effective for generating the output that matches the observed behaviour.

Coherent organization in gene regulation: a study on six networks

Structural and dynamical fingerprints of evolutionary optimization in biological networks are still unclear. Here we analyze the dynamics of genetic regulatory networks responsible for the regulation of cell cycle and cell differentiation in three organisms or cell types each, and show that they follow a version of Hebb's rule which we have termed coherence. More precisely, we find that simultaneously expressed genes with a common target are less likely to act antagonistically at the attractors of the regulatory dynamics. We then investigate the dependence of coherence on structural parameters, such as the mean number of inputs per node and the activatory/repressory interaction ratio, as well as on dynamically determined quantities, such as the basin size and the number of expressed genes.

Stochastic Spatio-Temporal Dynamic Model for Gene/Protein Interaction Network in Early Drosophila Development

In order to investigate the possible mechanisms for eve stripe formation of Drosophila embryo, a spatio-temporal gene/protein interaction network model is proposed to mimic dynamic behaviors of protein synthesis, protein decay, mRNA decay, protein diffusion, transcription regulations and autoregulation to analyze the interplay of genes and proteins at different compartments in early embryogenesis. In this study, we use the maximum likelihood (ML) method to identify the stochastic 3-D Embryo Space-Time (3-DEST) dynamic model for gene/protein interaction network via 3-D mRNA and protein expression data and then use the Akaike Information Criterion (AIC) to prune the gene/protein interaction network. The identified gene/protein interaction network allows us not only to analyze the dynamic interplay of genes and proteins on the border of eve stripes but also to infer that eve stripes are established and maintained by network motifs built by the cooperation between transcription regulations and diffusion mechanisms in early embryogenesis. Literature reference with the wet experiments of gene mutations provides a clue for validating the identified network. The proposed spatio-temporal dynamic model can be extended to gene/protein network construction of different biological phenotypes, which depend on compartments, e.g. postnatal stem/progenitor cell differentiation.

Modeling segmental patterning in Drosophila: Maternal and gap genes

We propose a new mathematical model describing the establishment of maternal and gap proteins segmental patterning along the antero-posterior axis of the Drosophila early embryo. This model is based on experimental data and, without recurring to pre-defined activation thresholds, predicts qualitatively and quantitatively the expression patterns of the maternal and gap proteins, as well as the expression patterns of proteins resulting from mRNA ectopic expression and from some loss-of-function mutations. We conclude that the gap genes segmental patterning and consequent spatial organization of the embryo is determined by three main factors: (1) the initial positioning of the maternal bicoid and torso mRNA inside the egg, and subsequent diffusion of the corresponding proteins; (2) the structure of the genetic regulatory network; (3) the role of conservation laws in the establishment of steady and non-uniform spatial distributions of non-diffusing proteins.

Robustness and fragility of Boolean models for genetic regulatory networks

Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or logical approaches. We propose a new modeling framework for gene regulatory networks, that combines the intuitive appeal of a qualitative description of gene states with a high flexibility in incorporating stochasticity in the duration of cellular processes. We apply our methods to the regulatory network of the segment polarity genes, thus gaining novel insights into the development of gene expression patterns. For example, we show that very short synthesis and decay times can perturb the wild-type pattern. On the other hand, separation of time-scales between pre- and post-translational processes and a minimal prepattern ensure convergence to the wild-type expression pattern regardless of fluctuations.

The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster

Expression of the Drosophila segment polarity genes is initiated by a pre-pattern of pair-rule gene products and maintained by a network of regulatory interactions throughout several stages of embryonic development. Analysis of a model of gene interactions based on differential equations showed that wild-type expression patterns of these genes can be obtained for a wide range of kinetic parameters, which suggests that the steady states are determined by the topology of the network and the type of regulatory interactions between components, not the detailed form of the rate laws. To investigate this, we propose and analyse a Boolean model of this network which is based on a binary ON/OFF representation of mRNA and protein levels, and in which the interactions are formulated as logical functions. In this model the spatial and temporal patterns of gene expression are determined by the topology of the network and whether components are present or absent, rather than the absolute levels of the mRNAs and proteins and the functional details of their interactions. The model is able to reproduce the wild-type gene expression patterns, as well as the ectopic expression patterns observed in overexpression experiments and various mutants. Furthermore, we compute explicitly all steady states of the network and identify the basin of attraction of each steady state. The model gives important insights into the functioning of the segment polarity gene network, such as the crucial role of the wingless and sloppy paired genes, and the network's ability to correct errors in the pre-pattern.