This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is time-discrete deterministic dynamical systems, with a finite set of states for each of the variables. The simplest examples of such models are Boolean networks, in which variables have only two possible states. The use of a larger number of possible states allows a finer discretization of experimental data and more than one possible mode of action for the variables, depending on threshold values. Furthermore, with a suitable choice of state set, one can employ powerful tools from computational algebra, that underlie the reverse-engineering algorithm, avoiding costly enumeration strategies. To perform well, the algorithm requires wildtype together with perturbation time courses. This makes it suitable for small to meso-scale networks rather than networks on a genome-wide scale. An analysis of the complexity of the algorithm is performed. The algorithm is validated on a recently published Boolean network model of segment polarity development in Drosophila melanogaster. r

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This paper lays the foundations of a combinatorial homotopy theory, called A-theory, for simplicial complexes, which reflects their connectivity properties. A collection of bigraded groups is constructed, and methods for computation are given. A Seifert-Van Kampen type theorem and a long exact sequence of relative A-groups are derived. A related theory for graphs is constructed as well. This theory provides a general framework encompassing homotopy methods used to prove connectivity results about buildings, graphs, and matroids.

This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory networks. In the same context, polynomial functions over finite fields have been used to develop network inference methods for gene regulatory networks. Finally, unate cascade functions have been studied in the design of logic circuits and binary decision diagrams. This paper shows that the class of nested canalyzing functions is equal to that of unate cascade functions. Furthermore, it provides a description of nested canalyzing functions as a certain type of Boolean polynomial function. Using the polynomial framework one can show that the class of nested canalyzing functions, or, equivalently, the class of unate cascade functions, forms an algebraic variety which makes their analysis amenable to the use of techniques from algebraic geometry and computational algebra. As a corollary of the functional equivalence derived here, a formula in the literature for the number of unate cascade functions provides such a formula for the number of nested canalyzing functions.

Iron is critical to the survival of almost all living organisms. However, inappropriately low or high levels of iron are detrimental and contribute to a wide range of diseases. Recent advances in the study of iron metabolism have revealed multiple intricate pathways that are essential to the maintenance of iron homeostasis. Further, iron regulation involves processes at several scales, ranging from the subcellular to the organismal. This complexity makes a systems biology approach crucial, with its enabling technology of computational models based on a mathematical description of regulatory systems. Systems biology may represent a new strategy for understanding imbalances in iron metabolism and their underlying causes.

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It is well known that significant metabolic change take place as cells are transformed from normal to malignant. This review focuses on the use of different bioinformatics tools in cancer metabolomics studies. The article begins by describing different metabolomics technologies and data generation techniques. Overview of the data pre-processing techniques is provided and multivariate data analysis techniques are discussed and illustrated with case studies, including principal component analysis, clustering techniques, self-organizing maps, partial least squares, and discriminant function analysis. Also included is a discussion of available software packages.

Iron is required for survival of mammalian cells. Recently, understanding of iron metabolism and trafficking has increased dramatically, revealing a complex, interacting network largely unknown just a few years ago. This provides an excellent model for systems biology development and analysis. The first step in such an analysis is the construction of a structural network of iron metabolism, which we present here. This network was created using CellDesigner version 3.5.2 and includes reactions occurring in mammalian cells of numerous tissue types. The iron metabolic network contains 151 chemical species and 107 reactions and transport steps. Starting from this general model, we construct iron networks for specific tissues and cells that are fundamental to maintaining body iron homeostasis. We include subnetworks for cells of the intestine and liver, tissues important in iron uptake and storage, respectively; as well as the reticulocyte and macrophage, key cells in iron utilization and recycling. The addition of kinetic information to our structural network will permit the simulation of iron metabolism in different tissues as well as in health and disease.