Properties of sparse penalties on inferring gene regulatory networks from time‐course gene expression data

Genes regulate each other and form a gene regulatory network (GRN) to realise biological functions. Elucidating GRN from experimental data remains a challenging problem in systems biology. Numerous techniques have been developed and sparse linear regression methods become a promising approach to infer accurate GRNs. However, most linear methods are either based on steady‐state gene expression data or their statistical properties are not analysed. Here, two sparse penalties, adaptive least absolute shrinkage and selection operator and smoothly clipped absolute deviation, are proposed to infer GRNs from time‐course gene expression data based on an auto‐regressive model and their Oracle properties are proved under mild conditions. The effectiveness of those methods is demonstrated by applications to in silico and real biological data.Inspec keywords: genetics, autoregressive processesOther keywords: sparse penalties, gene regulatory networks, time‐course gene expression data, GRN, biological functions, systems biology, sparse linear regression methods, steady‐state gene expression data, adaptive least absolute shrinkage, selection operator, smoothly clipped absolute deviation, autoregressive model, Oracle properties     

Adaptive modelling of gene regulatory network using Bayesian information criterion‐guided sparse regression approach

Inferring gene regulatory networks (GRNs) from microarray expression data are an important but challenging issue in systems biology. In this study, the authors propose a Bayesian information criterion (BIC)‐guided sparse regression approach for GRN reconstruction. This approach can adaptively model GRNs by optimising the l ₁ ‐norm regularisation of sparse regression based on a modified version of BIC. The use of the regularisation strategy ensures the inferred GRNs to be as sparse as natural, while the modified BIC allows incorporating prior knowledge on expression regulation and thus avoids the overestimation of expression regulators as usual. Especially, the proposed method provides a clear interpretation of combinatorial regulations of gene expression by optimally extracting regulation coordination for a given target gene. Experimental results on both simulation data and real‐world microarray data demonstrate the competent performance of discovering regulatory relationships in GRN reconstruction.Inspec keywords: genetics, Bayes methods, genomics, regression analysis, inference mechanisms, bioinformaticsOther keywords: adaptive modelling, gene regulatory network, Bayesian information criterion‐guided sparse regression approach, GRN, microarray expression data, systems biology, GRN reconstruction, optimisation, l₁ ‐norm regularisation     

Bifurcation analysis of bistable and oscillatory dynamics in biological networks using the root‐locus method

Most of the biological systems including gene regulatory networks can be described well by ordinary differential equation models with rational non‐linearities. These models are derived either based on the reaction kinetics or by curve fitting to experimental data. This study demonstrates the applicability of the root‐locus‐based bifurcation analysis method for studying the complex dynamics of such models. The effectiveness of the bifurcation analysis in determining the exact parameter regions in each of which the system shows a certain dynamical behaviour, such as bistability, oscillation, and asymptotically equilibrium dynamics is shown by considering two mostly studied gene regulatory networks, namely Gardner''s genetic toggle switch and p53 gene network possessing two‐phase (mono‐stable/oscillation) dynamics.Inspec keywords: oscillations, curve fitting, differential equations, bifurcation, genetics, nonlinear dynamical systemsOther keywords: nonlinearities, reaction kinetics, root‐locus‐based bifurcation analysis method, complex dynamics, exact parameter regions, dynamical behaviour, equilibrium dynamics, studied gene regulatory networks, p53 gene network, bistable dynamics, oscillatory dynamics, biological networks, root‐locus method, biological systems, ordinary differential equation models     

Using Individual Factor Information in Fractional Factorial Designs

While literature on constructing efficient experimental designs has been plentiful, how best to incorporate prior information when assigning factors to the columns of a nonregular design has received little attention. Following Li, Zhou, and Zhang (2015 Li, W., Zhou, Q., and Zhang, R. C. (2015), “Effective Designs Based on Individual Word Length Patterns,” Journal of Statistical Planning and Inference, 163, 43–47.[Crossref], [Web of Science ®] , [Google Scholar]), we propose the individual generalized word length pattern (iGWLP) for ranking columns of a nonregular design. Taking examples from the literature of recommended orthogonal arrays, we illustrate how iGWLP helps to identify important differences in the aliasing that is likely otherwise missed. Given the complexity of characterizing partial aliasing for nonregular designs, iGWLP will help practitioners make more informed assignment of factors to columns when using nonregular fractions. We provide theoretical justification of the proposed iGWLP. A theorem is given to relate the proposed iGWLP criterion to the expected bias caused by model misspecifications. We also show that the proposed criterion may lead to designs having better projection properties in the factors considered most likely to be important. Furthermore, we discuss how iGWLP can be used for design selection. We propose a criterion for choosing best designs when the focus is on a small set of important factors, for which the aliasing of effects involving these factors is minimized.     

CFD-DEM study on the mixing characteristics of binary particle systems in a fluidized bed of refuse-derived fuel

The fluidization of quartz in the fluidized bed has great influence on the combustion and gasification of refuse-derived fuel (RDF). The combined computational fluid dynamics (CFD) and discrete element method (DEM) approach was used to explore the gas-solid hydrodynamics and mixing characteristics in a three-dimensional fluidized bed. All numerical analyses were performed referring to the experiments (Goldschmidt, Beetstra, and Kuipers 2004 Goldschmidt, M. J. V., R. Beetstra, and J. A. M. Kuipers. 2004. Hydrodynamic modelling of dense gas-fluidised beds: Comparison and validation of 3D discrete particle and continuum models. Powder Technology 142 (1):23–47. doi:10.1016/j.powtec.2004.02.020[Crossref], [Web of Science ®] , [Google Scholar]). The simulation results indicated that the quartz volume fraction agrees well with the experimental data. Furthermore, the cylinder-shaped RDF particles can mix well with the quartz particles as they were added from upside. For binary systems, it is necessary to investigate solid flow characteristics as well as pressure drops and examine the influence of superficial gas velocity on the solid mixing. Two main parameters are discussed: mixing degree and the time required to reach the steady state. It is also found that inlet gas velocity and particle properties (particle density ratio, shape and size) are significant factors on particle mixing in a fluidized bed.     

Hierarchical parameter estimation of GRN based on topological analysis

Reverse engineering of gene regulatory network (GRN) is an important and challenging task in systems biology. Existing parameter estimation approaches that compute model parameters with the same importance are usually computationally expensive or infeasible, especially in dealing with complex biological networks.In order to improve the efficiency of computational modeling, the paper applies a hierarchical estimation methodology in computational modeling of GRN based on topological analysis. This paper divides nodes in a network into various priority levels using the graph‐based measure and genetic algorithm. The nodes in the first level, that correspond to root strongly connected components(SCC) in the digraph of GRN, are given top priority in parameter estimation. The estimated parameters of vertices in the previous priority level ARE used to infer the parameters for nodes in the next priority level. The proposed hierarchical estimation methodology obtains lower error indexes while consuming less computational resources compared with single estimation methodology. Experimental outcomes with insilico networks and a realistic network show that gene networks are decomposed into no more than four levels, which is consistent with the properties of inherent modularity for GRN. In addition, the proposed hierarchical parameter estimation achieves a balance between computational efficiency and accuracy.Inspec keywords: biology computing, network theory (graphs), reverse engineering, graph theory, genetics, genetic algorithms, directed graphs, parameter estimationOther keywords: hierarchical parameter estimation, GRN, topological analysis, gene regulatory network, important task, computational systems biology, compute model parameters, complex biological networks, efficient information, model quality, parameter reliability, computational modelling, study divides nodes, priority levels, graph‐based measure, previous priority level, hierarchical estimation methodology obtains, computational resources, single time estimation, insilico network, realistic network show, computational efficiency