Inferring Drosophila gap gene regulatory network: a parameter sensitivity and perturbation analysis

<p>Abstract</p> <p>Background</p> <p>Inverse modelling of gene regulatory networks (GRNs) capable of simulating continuous spatio-temporal biological processes requires accurate data and a good description of the system. If quantitative relations between genes cannot be extracted from direct measurements, an efficient method to estimate the unknown parameters is mandatory. A model that has been proposed to simulate spatio-temporal gene expression patterns is the connectionist model. This method describes the quantitative dynamics of a regulatory network in space. The model parameters are estimated by means of model-fitting algorithms. The gene interactions are identified without making any prior assumptions concerning the network connectivity. As a result, the inverse modelling might lead to multiple circuits showing the same quantitative behaviour and it is not possible to identify one optimal circuit. Consequently, it is important to address the quality of the circuits in terms of model robustness.</p> <p>Results</p> <p>Here we investigate the sensitivity and robustness of circuits obtained from reverse engineering a model capable of simulating measured gene expression patterns. As a case study we use the early gap gene segmentation mechanism in <it>Drosophila melanogaster</it>. We consider the limitations of the connectionist model used to describe GRN Inferred from spatio-temporal gene expression. We address the problem of circuit discrimination, where the selection criterion within the optimization technique is based of the least square minimization on the error between data and simulated results.</p> <p>Conclusion</p> <p>Parameter sensitivity analysis allows one to discriminate between circuits having significant parameter and qualitative differences but exhibiting the same quantitative pattern. Furthermore, we show that using a stochastic model derived from a deterministic solution, one can introduce fluctuations within the model to analyze the circuits' robustness. Ultimately, we show that there is a close relation between circuit sensitivity and robustness to fluctuation, and that circuit robustness is rather modular than global. The current study shows that reverse engineering of GRNs should not only focus on estimating parameters by minimizing the difference between observation and simulation but also on other model properties. Our study suggests that multi-objective optimization based on robustness and sensitivity analysis has to be considered.</p

Inferring Drosophila gap gene regulatory network: pattern analysis of simulated gene expression profiles and stability analysis

<p>Abstract</p> <p>Background</p> <p>Inference of gene regulatory networks (GRNs) requires accurate data, a method to simulate the expression patterns and an efficient optimization algorithm to estimate the unknown parameters. Using this approach it is possible to obtain alternative circuits without making any <it>a priori </it>assumptions about the interactions, which all simulate the observed patterns. It is important to analyze the properties of the circuits.</p> <p>Findings</p> <p>We have analyzed the simulated gene expression patterns of previously obtained circuits that describe gap gene dynamics during early <it>Drosophila melanogaster </it>embryogenesis. Using hierarchical clustering we show that amplitude variation and defects observed in the simulated gene expression patterns are linked to similar circuits, which can be grouped. Furthermore, analysis of the long-term dynamics revealed four main dynamical attractors comprising stable patterns and oscillatory patterns. In addition, we also performed a correlation analysis on the parameters showing an intricate correlation pattern.</p> <p>Conclusions</p> <p>The analysis demonstrates that the obtained gap gene circuits are not unique showing variable long-term dynamics and highly correlating scattered parameters. Furthermore, although the model can simulate the pattern up to gastrulation and confirms several of the known regulatory interactions, it does not reproduce the transient expression of all gap genes as observed experimentally. We suggest that the shortcomings of the model may be caused by overfitting, incomplete model description and/or missing data.</p

Impact of oxalate ligand in co-precipitation route on morphological properties and phase constitution of undoped and Rh-Doped BaTiO3 nanoparticles

In order to design and tailor materials for a specific application like gas sensors, the synthesis route is of great importance. Undoped and rhodium-doped barium titanate powders were successfully synthesized by two routes; oxalate route and classic route (a modified conventional route where solid-state reactions and thermal evaporation induced precipitation takes place). Both powders were calcined at different temperatures. X-ray diffraction (XRD), Raman spectroscopy, scanning electron microscopy (SEM), energy-dispersive x-ray spectroscopy (EDX) and Brunauer-Emmet-Teller (BET) analyses are employed to identify the phases and polymorphs, to determine the morphology, the chemical composition and the specific surface area of the synthesized materials, respectively. The so-called oxalate route yields pure BaTiO3 phase for undoped samples at 700?C and 900?C (containing both cubic and tetragonal structures), while the classic route-synthesized powder contains additional phases such as BaCO3, TiO2 and BaTi2O5. Samples of both synthesis routes prepared by the addition of Rh contain no metallic or oxide phase of rhodium. Instead, it was observed that Ti was substituted by Rh at temperatures 700 °C and 900 °C and there was some change in the composition of BaTiO3 polymorph (increase of tetragonal structure). Heat-treatments above these temperatures show that rhodium saturates out of the perovskite lattice at 1000 °C, yielding other secondary phases such as Ba3RhTi2O9 behind. Well-defined and less agglomerated spherical nanoparticles are obtained by the oxalic route, while the classic route yields particles with an undefined morphology forming very large block-like agglomerates. The surface area of the synthesized materials is higher with the oxalate route than with the classic route (4 times at 900 °C). The presence of the oxalate ligand with its steric hindrance that promotes the uniform distribution and the homogeneity of reactants could be responsible for the great difference observed between the powders prepared by two preparation routes

The effect of Cissus quadrangularis (CQR-300) and a Cissus formulation (CORE) on obesity and obesity-induced oxidative stress

AIM: Obesity is generally linked to complications in lipid metabolism and oxidative stress. The aim of this study was to compare the effect of a proprietary extract of Cissus quadrangularis (CQR-300) to that of a proprietary formulation containing CQR-300 (CORE) on weight, blood lipids, and oxidative stress in overweight and obese people. METHODS: The first part of the study investigated the in vitro antioxidant properties of CQR-300 and CORE using 3 different methods, while the second part of the study was a double-blind placebo controlled design, involving initially 168 overweight and obese persons (38.7% males; 61.3% females; ages 19–54), of whom 153 completed the study. All participants received two daily doses of CQR-300, CORE, or placebo and were encouraged to maintain their normal levels of physical activity. Anthropometric measurements and blood sampling were done at the beginning and end of the study period. RESULTS: CQR-300 as well as CORE exhibited antioxidant properties in vitro. They also acted as in vivo antioxidants, bringing about significant (p < 0.001) reductions in plasma TBARS and carbonyls. Both CQR-300 and CORE also brought about significant reductions in weight, body fat, total cholesterol, LDL-cholesterol, triglycerides, and fasting blood glucose levels over the respective study periods. These changes were accompanied by a significant increase in HDL-cholesterol levels, plasma 5-HT, and creatinine. CONCLUSION: CQR-300 (300 mg daily) and CORE (1028 mg daily) brought about significant reductions in weight and blood glucose levels, while decreasing serum lipids thus improving cardiovascular risk factors. The increase in plasma 5-HT and creatinine for both groups hypothesizes a mechanism of controlling appetite and promoting the increase of lean muscle mass by Cissus quadrangularis, thereby supporting the clinical data for weight loss and improving cardiovascular health

Oxidative stress and blood lipid profile in Cameroonian obese subjects

The relationship between obesity, blood lipids and oxidative stress was investigated in 200 participants. The Body Mass Index of the subjects were positively correlated with the percentage body fat, the systolic and diastolic blood pressure, the fasting blood glucose level, the oxidation of proteins and lipids as well as the concentrations of total and LDL cholesterol. On the other hand, the Body Mass Index was negatively correlated to sulhydryl and protein levels. Obese subjects also had significantly higher body fat (p<.001), waist circumference (p<.001), fasting blood glucose (p<.01) as well as systolic blood pressure (p<.05). Obesity, therefore, can be said to increase the oxidation of plasma proteins and lipids while reducing the antioxidant status as observed by the inverse relation between plasma sulfhydryl groups and the percentage body fat. This increase in oxidative stress can predispose obese people to illnesses such as cardiovascular diseases and diabetes mellitus

The Role of Regulated mRNA Stability in Establishing Bicoid Morphogen Gradient in Drosophila Embryonic Development

The Bicoid morphogen is amongst the earliest triggers of differential spatial pattern of gene expression and subsequent cell fate determination in the embryonic development of Drosophila. This maternally deposited morphogen is thought to diffuse in the embryo, establishing a concentration gradient which is sensed by downstream genes. In most model based analyses of this process, the translation of the bicoid mRNA is thought to take place at a fixed rate from the anterior pole of the embryo and a supply of the resulting protein at a constant rate is assumed. Is this process of morphogen generation a passive one as assumed in the modelling literature so far, or would available data support an alternate hypothesis that the stability of the mRNA is regulated by active processes? We introduce a model in which the stability of the maternal mRNA is regulated by being held constant for a length of time, followed by rapid degradation. With this more realistic model of the source, we have analysed three computational models of spatial morphogen propagation along the anterior-posterior axis: (a) passive diffusion modelled as a deterministic differential equation, (b) diffusion enhanced by a cytoplasmic flow term; and (c) diffusion modelled by stochastic simulation of the corresponding chemical reactions. Parameter estimation on these models by matching to publicly available data on spatio-temporal Bicoid profiles suggests strong support for regulated stability over either a constant supply rate or one where the maternal mRNA is permitted to degrade in a passive manner

A Software Tool to Model Genetic Regulatory Networks. Applications to the Modeling of Threshold Phenomena and of Spatial Patterning in Drosophila

We present a general methodology in order to build mathematical models of genetic regulatory networks. This approach is based on the mass action law and on the Jacob and Monod operon model. The mathematical models are built symbolically by the Mathematica software package GeneticNetworks. This package accepts as input the interaction graphs of the transcriptional activators and repressors of a biological process and, as output, gives the mathematical model in the form of a system of ordinary differential equations. All the relevant biological parameters are chosen automatically by the software. Within this framework, we show that concentration dependent threshold effects in biology emerge from the catalytic properties of genes and its associated conservation laws. We apply this methodology to the segment patterning in Drosophila early development and we calibrate the genetic transcriptional network responsible for the patterning of the gap gene proteins Hunchback and Knirps, along the antero-posterior axis of the Drosophila embryo. In this approach, the zygotically produced proteins Hunchback and Knirps do not diffuse along the antero-posterior axis of the embryo of Drosophila, developing a spatial pattern due to concentration dependent thresholds. This shows that patterning at the gap genes stage can be explained by the concentration gradients along the embryo of the transcriptional regulators

An Extended Gene Protein/Products Boolean Network Model Including Post-Transcriptional Regulation

Background: Networks Biology allows the study of complex interactions between biological systems using formal, well structured, and computationally friendly models. Several different network models can be created, depending on the type of interactions that need to be investigated. Gene Regulatory Networks (GRN) are an effective model commonly used to study the complex regulatory mechanisms of a cell. Unfortunately, given their intrinsic complexity and non discrete nature, the computational study of realistic-sized complex GRNs requires some abstractions. Boolean Networks (BNs), for example, are a reliable model that can be used to represent networks where the possible state of a node is a boolean value (0 or 1). Despite this strong simplification, BNs have been used to study both structural and dynamic properties of real as well as randomly generated GRNs. Results: In this paper we show how it is possible to include the post-transcriptional regulation mechanism (a key process mediated by small non-coding RNA molecules like the miRNAs) into the BN model of a GRN. The enhanced BN model is implemented in a software toolkit (EBNT) that allows to analyze boolean GRNs from both a structural and a dynamic point of view. The open-source toolkit is compatible with available visualization tools like Cytoscape and allows to run detailed analysis of the network topology as well as of its attractors, trajectories, and state-space. In the paper, a small GRN built around the mTOR gene is used to demonstrate the main capabilities of the toolkit. Conclusions: The extended model proposed in this paper opens new opportunities in the study of gene regulation. Several of the successful researches done with the support of BN to understand high-level characteristics of regulatory networks, can now be improved to better understand the role of post-transcriptional regulation for example as a network-wide noise-reduction or stabilization mechanism

Inferring robust gene networks from expression data by a sensitivity-based incremental evolution method

<p>Abstract</p> <p>Background</p> <p>Reconstructing gene regulatory networks (GRNs) from expression data is one of the most important challenges in systems biology research. Many computational models and methods have been proposed to automate the process of network reconstruction. Inferring robust networks with desired behaviours remains challenging, however. This problem is related to network dynamics but has yet to be investigated using network modeling.</p> <p>Results</p> <p>We propose an incremental evolution approach for inferring GRNs that takes network robustness into consideration and can deal with a large number of network parameters. Our approach includes a sensitivity analysis procedure to iteratively select the most influential network parameters, and it uses a swarm intelligence procedure to perform parameter optimization. We have conducted a series of experiments to evaluate the external behaviors and internal robustness of the networks inferred by the proposed approach. The results and analyses have verified the effectiveness of our approach.</p> <p>Conclusions</p> <p>Sensitivity analysis is crucial to identifying the most sensitive parameters that govern the network dynamics. It can further be used to derive constraints for network parameters in the network reconstruction process. The experimental results show that the proposed approach can successfully infer robust GRNs with desired system behaviors.</p

Gene Circuit Analysis of the Terminal Gap Gene huckebein

The early embryo of Drosophila melanogaster provides a powerful model system to study the role of genes in pattern formation. The gap gene network constitutes the first zygotic regulatory tier in the hierarchy of the segmentation genes involved in specifying the position of body segments. Here, we use an integrative, systems-level approach to investigate the regulatory effect of the terminal gap gene huckebein (hkb) on gap gene expression. We present quantitative expression data for the Hkb protein, which enable us to include hkb in gap gene circuit models. Gap gene circuits are mathematical models of gene networks used as computational tools to extract regulatory information from spatial expression data. This is achieved by fitting the model to gap gene expression patterns, in order to obtain estimates for regulatory parameters which predict a specific network topology. We show how considering variability in the data combined with analysis of parameter determinability significantly improves the biological relevance and consistency of the approach. Our models are in agreement with earlier results, which they extend in two important respects: First, we show that Hkb is involved in the regulation of the posterior hunchback (hb) domain, but does not have any other essential function. Specifically, Hkb is required for the anterior shift in the posterior border of this domain, which is now reproduced correctly in our models. Second, gap gene circuits presented here are able to reproduce mutants of terminal gap genes, while previously published models were unable to reproduce any null mutants correctly. As a consequence, our models now capture the expression dynamics of all posterior gap genes and some variational properties of the system correctly. This is an important step towards a better, quantitative understanding of the developmental and evolutionary dynamics of the gap gene network