Dynamical approaches to modeling developmental gene regulatory networks

The network of interacting regulatory signals within a cell comprises one of the most complex and powerful computational systems in biology. Gene regulatory networks (GRNs) play a key role in transforming the information encoded in a genome into morphological form. To achieve this feat, GRNs must respond to and integrate environmental signals with their internal dynamics in a robust and coordinated fashion. The highly dynamic nature of this process lends itself to interpretation and analysis in the language of dynamical models. Modeling provides a means of systematically untangling the complicated structure of GRNs, a framework within which to simulate the behavior of reconstructed systems and, in some cases, suites of analytic tools for exploring that behavior and its implications. This review provides a general background to the idea of treating a regulatory network as a dynamical system, and describes a variety of different approaches that have been taken to the dynamical modeling of GRNs. Birth Defects Research (Part C) 87:131–142, 2009. © 2009 Wiley‐Liss, Inc.     

Computational approaches for modeling human intestinal absorption and permeability

Human intestinal absorption (HIA) is an important roadblock in the formulation of new drug substances. Computational models are needed for the rapid estimation of this property. The measurements are determined via in vivo experiments or in vitro permeability studies. We present several computational models that are able to predict the absorption of drugs by the human intestine and the permeability through human Caco-2 cells. The training and prediction sets were derived from literature sources and carefully examined to eliminate compounds that are actively transported. We compare our results to models derived by other methods and find that the statistical quality is similar. We believe that models derived from both sources of experimental data would provide greater consistency in predictions. The performance of several QSPR models that we investigated to predict outside the training set for either experimental property clearly indicates that caution should be exercised while applying any of the models for quantitative predictions. However, we are able to show that the qualitative predictions can be obtained with close to a 70% success rate.Electronic Supplementary Material Supplementary material is available for this article at .Dedicated to Professor Dr. Paul von Ragué Schleyer on the occasion of his 75th birthday.     

Computational identification of cellular networks and pathways

In this article we highlight recent developments in computational functional genomics to identify networks of functionally related genes and proteins based on diverse sources of genomic data. Our specific focus is on statistical methods to identify genetic networks. We discuss integrated analysis of microarray datasets, methods to combine heterogeneous data sources, the analysis of high-dimensional phenotyping screens and describe efforts to establish a reliable and unbiased gold standard for method comparison and evaluation.     

Biological networks 101: Computational modeling for molecular biologists

Computational modeling of biological networks permits the comprehensive analysis of cells and tissues to define molecular phenotypes and novel hypotheses. Although a large number of software tools have been developed, the versatility of these tools is limited by mathematical complexities that prevent their broad adoption and effective use by molecular biologists. This study clarifies the basic aspects of molecular modeling, how to convert data into useful input, as well as the number of time points and molecular parameters that should be considered for molecular regulatory models with both explanatory and predictive potential. We illustrate the necessary experimental preconditions for converting data into a computational model of network dynamics. This model requires neither a thorough background in mathematics nor precise data on intracellular concentrations, binding affinities or reaction kinetics. Finally, we show how an interactive model of crosstalk between signal transduction pathways in primary human articular chondrocytes allows insight into processes that regulate gene expression.     

Comparing different ODE modelling approaches for gene regulatory networks

A fundamental step in synthetic biology and systems biology is to derive appropriate mathematical models for the purposes of analysis and design. For example, to synthesize a gene regulatory network, the derivation of a mathematical model is important in order to carry out in silico investigations of the network dynamics and to investigate parameter variations and robustness issues. Different mathematical frameworks have been proposed to derive such models. In particular, the use of sets of nonlinear ordinary differential equations (ODEs) has been proposed to model the dynamics of the concentrations of mRNAs and proteins. These models are usually characterized by the presence of highly nonlinear Hill function terms. A typical simplification is to reduce the number of equations by means of a quasi-steady-state assumption on the mRNA concentrations. This yields a class of simplified ODE models. A radically different approach is to replace the Hill functions by piecewise-linear approximations [Casey, R., de Jong, H., Gouz, J.-L., 2006. Piecewise-linear models of genetic regulatory networks: equilibria and their stability. J. Math. Biol. 52 (1), 27-56]. A further modelling approach is the use of discrete-time maps [Coutinho, R., Fernandez, B., Lima, R., Meyroneinc, A., 2006. Discrete time piecewise affine models of genetic regulatory networks. J. Math. Biol. 52, 524-570] where the evolution of the system is modelled in discrete, rather than continuous, time. The aim of this paper is to discuss and compare these different modelling approaches, using a representative gene regulatory network. We will show that different models often lead to conflicting conclusions concerning the existence and stability of equilibria and stable oscillatory behaviours. Moreover, we shall discuss, where possible, the viability of making certain modelling approximations (e.g. quasi-steady-state mRNA dynamics or piecewise-linear approximations of Hill functions) and their effects on the overall system dynamics.     

Phosphoproteomic approaches to elucidate cellular signaling networks

Protein phosphorylation is crucial in the regulation of signaling pathways that control various biological responses. Recent progress in diverse methodologies to investigate protein phosphorylation in complex biological samples has resulted in more rapid, detailed and quantitative analyses of signaling networks. In particular, advances in mass spectrometry (MS) have enabled the identification and quantification of thousands of both known and novel phosphorylation sites. Initial MS-based information can be complemented with a variety of recently developed and improved phosphoproteomic techniques. These include multiplexed microbead or kinase activity assays, flow cytometry based single-cell analysis, protein microarrays and interaction studies. The combination of multiple approaches, coupled with phenotypic response measurements, computational modeling and biochemical manipulations, will ultimately reveal the mechanistic regulation of signaling networks.     

Modular response analysis of cellular regulatory networks

The sheer complexity of intracellular regulatory networks, which involve signal transducing, metabolic, and genetic circuits, hampers our ability to carry out a quantitative analysis of their functions. Here, we describe an approach that greatly simplifies this type of analysis by capitalizing on the modular organization of such networks. Steady-state responses of the network as a whole are accounted for in terms of intermodular interactions between the modules alone; processes operating solely within modules need not be considered when analysing signal transfer through the entire network. The intermodular interactions are quantified through (local) response coefficients which populate an interaction map (matrix). This matrix can be derived from a biochemical or molecular biological analysis of (macro) molecular interactions that constitute the regulatory network. The approach is illustrated by two examples: (i) mitogenic signalling through the mitogen-activated protein kinase cascade in the epidermal growth factor receptor network and (ii) regulation of ammonium assimilation in Escherichia coli.     

Computational approaches for systems metabolomics

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Stochastic Boolean networks: An efficient approach to modeling gene regulatory networks

ABSTRACT: BACKGROUND: Various computational models have been of interest due to their use in the modelling of gene regulatory networks (GRNs). As a logical model, probabilistic Boolean networks (PBNs) consider molecular and genetic noise, so the study of PBNs provides significant insights into the understanding of the dynamics of GRNs. This will ultimately lead to advances in developing therapeutic methods that intervene in the process of disease development and progression. The applications of PBNs, however, are hindered by the complexities involved in the computation of the state transition matrix and the steady-state distribution of a PBN. For a PBN with n genes and N Boolean networks, the complexity to compute the state transition matrix is O(nN22n) or O(nN2n) for a sparse matrix. RESULTS: This paper presents a novel implementation of PBNs based on the notions of stochastic logic and stochastic computation. This stochastic implementation of a PBN is referred to as a stochastic Boolean network (SBN). An SBN provides an accurate and efficient simulation of a PBN without and with random gene perturbation. The state transition matrix is computed in an SBN with a complexity of O(nL2n), where L is a factor related to the stochastic sequence length. Since the minimum sequence length required for obtaining an evaluation accuracy approximately increases in a polynomial order with the number of genes, n, and the number of Boolean networks, N, usually increases exponentially with n, L is typically smaller than N, especially in a network with a large number of genes. Hence, the computational complexity of an SBN is primarily limited by the number of genes, but not directly by the total possible number of Boolean networks. Furthermore, a time-frame expanded SBN enables an efficient analysis of the steady-state distribution of a PBN. These findings are supported by the simulation results of a simplified p53 network, several randomly generated networks and a network inferred from a T cell immune response dataset. An SBN can also implement the function of an asynchronous PBN and is potentially useful in a hybrid approach in combination with a continuous or single-molecule level stochastic model. CONCLUSIONS: Stochastic Boolean networks (SBNs) are proposed as an efficient approach to modelling gene regulatory networks (GRNs). The SBN approach is able to recover biologically-proven regulatory behaviours, such as the oscillatory dynamics of the p53-Mdm2 network and the dynamic attractors in a T cell immune response network. The proposed approach can further predict the network dynamics when the genes are under perturbation, thus providing biologically meaningful insights for a better understanding of the dynamics of GRNs. The algorithms and methods described in this paper have been implemented in Matlab packages, which are attached as Additional files.     

Experimental and mathematical approaches to modeling plant metabolic networks

To support their sessile and autotrophic lifestyle higher plants have evolved elaborate networks of metabolic pathways. Dynamic changes in these metabolic networks are among the developmental forces underlying the functional differentiation of organs, tissues and specialized cell types. They are also important in the various interactions of a plant with its environment. Further complexity is added by the extensive compartmentation of the various interconnected metabolic pathways in plants. Thus, although being used widely for assessing the control of metabolic flux in microbes, mathematical modeling approaches that require steady-state approximations are of limited utility for understanding complex plant metabolic networks. However, considerable progress has been made when manageable metabolic subsystems were studied. In this article, we will explain in general terms and using simple examples the concepts underlying stoichiometric modeling (metabolic flux analysis and metabolic pathway analysis) and kinetic approaches to modeling (including metabolic control analysis as a special case). Selected studies demonstrating the prospects of these approaches, or combinations of them, for understanding the control of flux through particular plant pathways are discussed. We argue that iterative cycles of (dry) mathematical modeling and (wet) laboratory testing will become increasingly important for simulating the distribution of flux in plant metabolic networks and deriving rational experimental designs for metabolic engineering efforts.