Global robust power-rate stability of delayed genetic regulatory networks with noise perturbations

In this paper, by using the Lyapunov method, Itô’s differential formula and linear matrix inequality (LMI) approach, the global robust power-rate stability in mean square is discussed for genetic regulatory networks with unbounded time-varying delay, noise perturbations and parameter uncertainties. Sufficient conditions are given to ensure the robust power-rate stability (in mean square) of the genetic regulatory networks. Meanwhile, the criteria ensuring global power-rate stability in mean square are a byproduct of the criteria guaranteeing global robust power-rate stability in mean square. The obtained conditions are derived in terms of linear matrix inequalities (LMIs) which are easy to be verified via the LMI toolbox. An illustrative example is given to show the effectiveness of the obtained result.     

OptORF: Optimal metabolic and regulatory perturbations for metabolic engineering of microbial strains

Background  

Computational modeling and analysis of metabolic networks has been successful in metabolic engineering of microbial strains for valuable biochemical production. Limitations of currently available computational methods for metabolic engineering are that they are often based on reaction deletions rather than gene deletions and do not consider the regulatory networks that control metabolism. Due to the presence of multi-functional enzymes and isozymes, computational designs based on reaction deletions can sometimes result in strategies that are genetically complicated or infeasible. Additionally, strains might not be able to grow initially due to regulatory restrictions. To overcome these limitations, we have developed a new approach (OptORF) for identifying metabolic engineering strategies based on gene deletion and overexpression.     

Visualizing regulatory interactions in metabolic networks

Background  

Direct visualization of data sets in the context of biochemical network drawings is one of the most appealing approaches in the field of data evaluation within systems biology. One important type of information that is very helpful in interpreting and understanding metabolic networks has been overlooked so far. Here we focus on the representation of this type of information given by the strength of regulatory interactions between metabolite pools and reaction steps.     

A relative variation-based method to unraveling gene regulatory networks

Gene regulatory network (GRN) reconstruction is essential in understanding the functioning and pathology of a biological system. Extensive models and algorithms have been developed to unravel a GRN. The DREAM project aims to clarify both advantages and disadvantages of these methods from an application viewpoint. An interesting yet surprising observation is that compared with complicated methods like those based on nonlinear differential equations, etc., methods based on a simple statistics, such as the so-called Z-score, usually perform better. A fundamental problem with the Z-score, however, is that direct and indirect regulations can not be easily distinguished. To overcome this drawback, a relative expression level variation (RELV) based GRN inference algorithm is suggested in this paper, which consists of three major steps. Firstly, on the basis of wild type and single gene knockout/knockdown experimental data, the magnitude of RELV of a gene is estimated. Secondly, probability for the existence of a direct regulation from a perturbed gene to a measured gene is estimated, which is further utilized to estimate whether a gene can be regulated by other genes. Finally, the normalized RELVs are modified to make genes with an estimated zero in-degree have smaller RELVs in magnitude than the other genes, which is used afterwards in queuing possibilities of the existence of direct regulations among genes and therefore leads to an estimate on the GRN topology. This method can in principle avoid the so-called cascade errors under certain situations. Computational results with the Size 100 sub-challenges of DREAM3 and DREAM4 show that, compared with the Z-score based method, prediction performances can be substantially improved, especially the AUPR specification. Moreover, it can even outperform the best team of both DREAM3 and DREAM4. Furthermore, the high precision of the obtained most reliable predictions shows that the suggested algorithm may be very helpful in guiding biological experiment designs.     

Inference of dynamic biological networks based on responses to drug perturbations

Drugs that target specific proteins are a major paradigm in cancer research. In this article, we extend a modeling framework for drug sensitivity prediction and combination therapy design based on drug perturbation experiments. The recently proposed target inhibition map approach can infer stationary pathway models from drug perturbation experiments, but the method is limited to a steady-state snapshot of the underlying dynamical model. We consider the inverse problem of possible dynamic models that can generate the static target inhibition map model. From a deterministic viewpoint, we analyze the inference of Boolean networks that can generate the observed binarized sensitivities under different target inhibition scenarios. From a stochastic perspective, we investigate the generation of Markov chain models that satisfy the observed target inhibition sensitivities.     

Optimization of regulatory architectures in metabolic reaction networks

Successful biotechnological applications, such as amino acid production, have demonstrated significant improvement in bioprocess performance by genetic modifications of metabolic control architectures and enzyme expression levels. However, the stoichiometric complexity of metabolic pathways, along with their strongly nonlinear nature and regulatory coupling, necessitates the use of structured kinetic models to direct experimental applications and aid in quantitative understanding of cellular bioprocesses. A novel optimization problem is introduced here, the objective of which is to identify changes in the regulatory characteristics of pertinent enzymes and in their cellular content which should be implemented to optimize a particular metabolic process. The mathematical representation of the metabolic reaction networks used is the S-system representation, which at steady state is characterized by linear equations. Exploiting the linearity of the representation, we formulated the optimization problem as a mixed-integer linear programming (MILP) problem. This formulation allows the consideration of a regulatory superstructure that contains all alternative regulatory structures that can be considered for a given pathway. The proposed approach is developed and illustrated using a simple linear pathway. Application of the framework on a complicated pathway-namely, the xanthine monophosphate (XMP) and guanosine monophosphate (GMP) synthesis pathway-identified the modification of the regulatory architecture that, along with changes in enzyme expression levels, can increase the XMP and GMP concentration by over 114 times the reference value, which is 50 times more than could be achieved by changes in enzyme expression levels only. (c) 1996 John Wiley & Sons, Inc.     

A joint model of regulatory and metabolic networks

Background  

Gene regulation and metabolic reactions are two primary activities of life. Although many works have been dedicated to study each system, the coupling between them is less well understood. To bridge this gap, we propose a joint model of gene regulation and metabolic reactions.     

Gene regulatory networks from multifactorial perturbations using Graphical Lasso: application to the DREAM4 challenge

A major challenge in the field of systems biology consists of predicting gene regulatory networks based on different training data. Within the DREAM4 initiative, we took part in the multifactorial sub-challenge that aimed to predict gene regulatory networks of size 100 from training data consisting of steady-state levels obtained after applying multifactorial perturbations to the original in silico network. Due to the static character of the challenge data, we tackled the problem via a sparse Gaussian Markov Random Field, which relates network topology with the covariance inverse generated by the gene measurements. As for the computations, we used the Graphical Lasso algorithm which provided a large range of candidate network topologies. The main task was to select the optimal network topology and for that, different model selection criteria were explored. The selected networks were compared with the golden standards and the results ranked using the scoring metrics applied in the challenge, giving a better insight in our submission and the way to improve it.Our approach provides an easy statistical and computational framework to infer gene regulatory networks that is suitable for large networks, even if the number of the observations (perturbations) is greater than the number of variables (genes).     

Periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbations

In this paper, we derive new criteria for evaluating the global stability of periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbation, which appear in many biological systems at biomolecular or cellular levels due to the weak coupling and signal diffusion (or transport) process. Our results rely on the Lipschtiz conditions of Hill function, topology of gene networks and delay kernels. In particular, Our method based on the proposed model transforms the original network into matrix analysis problem, thereby not only significantly reducing the computational complexity but also making analysis of periodic oscillation tractable for even large-scale nonlinear networks.     

Chaotic gene regulatory networks can be robust against mutations and noise

Robustness to mutations and noise has been shown to evolve through stabilizing selection for optimal phenotypes in model gene regulatory networks. The ability to evolve robust mutants is known to depend on the network architecture. How do the dynamical properties and state-space structures of networks with high and low robustness differ? Does selection operate on the global dynamical behavior of the networks? What kind of state-space structures are favored by selection? We provide damage propagation analysis and an extensive statistical analysis of state spaces of these model networks to show that the change in their dynamical properties due to stabilizing selection for optimal phenotypes is minor. Most notably, the networks that are most robust to both mutations and noise are highly chaotic. Certain properties of chaotic networks, such as being able to produce large attractor basins, can be useful for maintaining a stable gene-expression pattern. Our findings indicate that conventional measures of stability, such as damage propagation, do not provide much information about robustness to mutations or noise in model gene regulatory networks.     

Orthogonal filtered recoupled-STOCSY to extract metabolic networks associated with minor perturbations from NMR spectroscopy

Supervised multivariate statistical analyses of NMR spectroscopic data sets are often required to identify metabolic differences between sample classes, and the use of orthogonal filters has proven to be highly efficient even when dealing with weak perturbations. In this note, we associate orthogonal filters to the recently reported recoupled-statistical total correlation spectroscopy (RSTOCSY). An initial supervised deflation of the spectral matrix is applied to remove all information orthogonal to the effect of interest and is followed by an RSTOCSY analysis to extract a list of pairs of metabolites that experience correlated perturbations. This list can then be used to find possibilities for the perturbed metabolic network. This supervised RSTOCSY approach, dubbed OR-STOCSY, yields metabolites related to perturbations of biological interest, even if they make a minor contribution to the global variance of a complex data set compared to other (possibly confounding) effects under study. The method is demonstrated with the application to genetic phenotypes in Caenorhabditis elegans.