Perturbation analysis analyzed—mathematical modeling of intact and perturbed gene regulatory circuits for animal development

Gene regulatory networks for animal development are the underlying mechanisms controlling cell fate specification and differentiation. The architecture of gene regulatory circuits determines their information processing properties and their developmental function. It is a major task to derive realistic network models from exceedingly advanced high throughput experimental data. Here we use mathematical modeling to study the dynamics of gene regulatory circuits to advance the ability to infer regulatory connections and logic function from experimental data. This study is guided by experimental methodologies that are commonly used to study gene regulatory networks that control cell fate specification. We study the effect of a perturbation of an input on the level of its downstream genes and compare between the cis-regulatory execution of OR and AND logics. Circuits that initiate gene activation and circuits that lock on the expression of genes are analyzed. The model improves our ability to analyze experimental data and construct from it the network topology. The model also illuminates information processing properties of gene regulatory circuits for animal development

Gradient Descent Optimization in Gene Regulatory Pathways

BACKGROUND: Gene Regulatory Networks (GRNs) have become a major focus of interest in recent years. Elucidating the architecture and dynamics of large scale gene regulatory networks is an important goal in systems biology. The knowledge of the gene regulatory networks further gives insights about gene regulatory pathways. This information leads to many potential applications in medicine and molecular biology, examples of which are identification of metabolic pathways, complex genetic diseases, drug discovery and toxicology analysis. High-throughput technologies allow studying various aspects of gene regulatory networks on a genome-wide scale and we will discuss recent advances as well as limitations and future challenges for gene network modeling. Novel approaches are needed to both infer the causal genes and generate hypothesis on the underlying regulatory mechanisms. METHODOLOGY: In the present article, we introduce a new method for identifying a set of optimal gene regulatory pathways by using structural equations as a tool for modeling gene regulatory networks. The method, first of all, generates data on reaction flows in a pathway. A set of constraints is formulated incorporating weighting coefficients. Finally the gene regulatory pathways are obtained through optimization of an objective function with respect to these weighting coefficients. The effectiveness of the present method is successfully tested on ten gene regulatory networks existing in the literature. A comparative study with the existing extreme pathway analysis also forms a part of this investigation. The results compare favorably with earlier experimental results. The validated pathways point to a combination of previously documented and novel findings. CONCLUSIONS: We show that our method can correctly identify the causal genes and effectively output experimentally verified pathways. The present method has been successful in deriving the optimal regulatory pathways for all the regulatory networks considered. The biological significance and applicability of the optimal pathways has also been discussed. Finally the usefulness of the present method on genetic engineering is depicted with an example

A service-oriented architecture for integrating the modeling and formal verification of genetic regulatory networks

<p>Abstract</p> <p>Background</p> <p>The study of biological networks has led to the development of increasingly large and detailed models. Computer tools are essential for the simulation of the dynamical behavior of the networks from the model. However, as the size of the models grows, it becomes infeasible to manually verify the predictions against experimental data or identify interesting features in a large number of simulation traces. Formal verification based on temporal logic and model checking provides promising methods to automate and scale the analysis of the models. However, a framework that tightly integrates modeling and simulation tools with model checkers is currently missing, on both the conceptual and the implementational level.</p> <p>Results</p> <p>We have developed a generic and modular web service, based on a service-oriented architecture, for integrating the modeling and formal verification of genetic regulatory networks. The architecture has been implemented in the context of the qualitative modeling and simulation tool G<smcaps>NA</smcaps> and the model checkers N<smcaps>U</smcaps>SMV and C<smcaps>ADP</smcaps>. G<smcaps>NA</smcaps> has been extended with a verification module for the specification and checking of biological properties. The verification module also allows the display and visual inspection of the verification results.</p> <p>Conclusions</p> <p>The practical use of the proposed web service is illustrated by means of a scenario involving the analysis of a qualitative model of the carbon starvation response in <it>E. coli</it>. The service-oriented architecture allows modelers to define the model and proceed with the specification and formal verification of the biological properties by means of a unified graphical user interface. This guarantees a transparent access to formal verification technology for modelers of genetic regulatory networks.</p

Towards a dynamic view of genetic networks: A Kalman filtering framework for recovering temporally-rewiring stable networks from undersampled data

It is widely accepted that cellular requirements and environmental conditions dictate the architecture of genetic regulatory networks. Nonetheless, the status quo in regulatory network modeling and analysis assumes an invariant network topology over time. We refocus on a dynamic perspective of genetic networks, one that can uncover substantial topological changes in network structure during biological processes such as developmental growth and cancer progression. We propose a novel outlook on the inference of time-varying genetic networks, from a limited number of noisy observations, by formulating the networks estimation as a target tracking problem. Assuming linear dynamics, we formulate a constrained Kalman ltering framework, which recursively computes the minimum mean-square, sparse and stable estimate of the network connectivity at each time point. The sparsity constraint is enforced using the weighted l1-norm; and the stability constraint is incorporated using the Lyapounov stability condition. The proposed constrained Kalman lter is formulated to preserve the convex nature of the problem. The algorithm is applied to estimate the time-varying networks during the life cycle of the Drosophila Melanogaster (fruit fly)

Assessing regulatory information in developmental gene regulatory networks

Gene regulatory networks (GRNs) provide a transformation function between the static genomic sequence and the primary spatial specification processes operating development. The regulatory information encompassed in developmental GRNs thus goes far beyond the control of individual genes. We here address regulatory information at different levels of network organization, from single node to subcircuit to large-scale GRNs and discuss how regulatory design features such as network architecture, hierarchical organization, and cis-regulatory logic contribute to the developmental function of network circuits. Using specific subcircuits from the sea urchin endomesoderm GRN, for which both circuit design and biological function have been described, we evaluate by Boolean modeling and in silico perturbations the import of given circuit features on developmental function. The examples include subcircuits encoding positive feedback, mutual repression, and coherent feedforward, as well as signaling interaction circuitry. Within the hierarchy of the endomesoderm GRN, these subcircuits are organized in an intertwined and overlapping manner. Thus, we begin to see how regulatory information encoded at individual nodes is integrated at all levels of network organization to control developmental process

Implications of Rewiring Bacterial Quorum Sensing

Bacteria employ quorum sensing, a form of cell-cell communication, to sense changes in population density and regulate gene expression accordingly. This work investigated the rewiring of one quorum-sensing module, the lux circuit from the marine bacterium Vibrio fischeri. Steady-state experiments demonstrate that rewiring the network architecture of this module can yield graded, threshold, and bistable gene expression as predicted by a mathematical model. The experiments also show that the native lux operon is most consistent with a threshold, as opposed to a bistable, response. Each of the rewired networks yielded functional population sensors at biologically relevant conditions, suggesting that this operon is particularly robust. These findings (i) permit prediction of the behaviors of quorum-sensing operons in bacterial pathogens and (ii) facilitate forward engineering of synthetic gene circuits

Formal methods for Hopfield-like networks.

International audienceBuilding a meaningful model of biological regulatory network is usually done by specifying the components (e.g. the genes) and their interactions, by guessing the values of parameters, by comparing the predicted behaviors to the observed ones, and by modifying in a trial-error process both architecture and parameters in order to reach an optimal fitness. We propose here a different approach to construct and analyze biological models avoiding the trial-error part, where structure and dynamics are represented as formal constraints. We apply the method to Hopfield-like networks, a formalism often used in both neural and regulatory networks modeling. The aim is to characterize automatically the set of all models consistent with all the available knowledge (about structure and behavior). The available knowledge is formalized into formal constraints. The latter are compiled into Boolean formula in conjunctive normal form and then submitted to a Boolean satisfiability solver. This approach allows to formulate a wide range of queries, expressed in a high level language, and possibly integrating formalized intuitions. In order to explore its potential, we use it to find cycles for 3-nodes networks and to determine the flower morphogenesis regulatory network of Arabidopsis thaliana. Applications of this technique are numerous and concern the building of models from data as well as the design of biological networks possessing specified behaviors