Reinhard C. Laubenbacher

A computational algebra approach to the reverse engineering of gene regulatory networks

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.

Bioinformatics tools for cancer metabolomics

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.

A systems biology view of cancer.

In order to understand how a cancer cell is functionally different from a normal cell it is necessary to assess the complex network of pathways involving gene regulation, signaling, and cell metabolism, and the alterations in its dynamics caused by the several different types of mutations leading to malignancy. Since the network is typically complex, with multiple connections between pathways and important feedback loops, it is crucial to represent it in the form of a computational model that can be used for a rigorous analysis. This is the approach of systems biology, made possible by new -omics data generation technologies. The goal of this review is to illustrate this approach and its utility for our understanding of cancer. After a discussion of recent progress using a network-centric approach, three case studies related to diagnostics, therapy, and drug development are presented in detail. They focus on breast cancer, B-cell lymphomas, and colorectal cancer. The discussion is centered on key mathematical and computational tools common to a systems biology approach.

Polynomial algebra of discrete models in systems biology

MOTIVATION An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. RESULTS This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. CONTACT alanavc@vt.edu SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

The Dynamics of Conjunctive and Disjunctive Boolean Network Models

For many biological networks, the topology of the network constrains its dynamics. In particular, feedback loops play a crucial role. The results in this paper quantify the constraints that (unsigned) feedback loops exert on the dynamics of a class of discrete models for gene regulatory networks. Conjunctive (resp. disjunctive) Boolean networks, obtained by using only the AND (resp. OR) operator, comprise a subclass of networks that consist of canalyzing functions, used to describe many published gene regulation mechanisms. For the study of feedback loops, it is common to decompose the wiring diagram into linked components each of which is strongly connected. It is shown that for conjunctive Boolean networks with strongly connected wiring diagram, the feedback loop structure completely determines the long-term dynamics of the network. A formula is established for the precise number of limit cycles of a given length, and it is determined which limit cycle lengths can appear. For general wiring diagrams, the situation is much more complicated, as feedback loops in one strongly connected component can influence the feedback loops in other components. This paper provides a sharp lower bound and an upper bound on the number of limit cycles of a given length, in terms of properties of the partially ordered set of strongly connected components.

Discretization of Time Series Data

An increasing number of algorithms for biochemical network inference from experimental data require discrete data as input. For example, dynamic Bayesian network methods and methods that use the framework of finite dynamical systems, such as Boolean networks, all take discrete input. Experimental data, however, are typically continuous and represented by computer floating point numbers. The translation from continuous to discrete data is crucial in preserving the variable dependencies and thus has a significant impact on the performance of the network inference algorithms. We compare the performance of two such algorithms that use discrete data using several different discretization algorithms. One of the inference methods uses a dynamic Bayesian network framework, the other-a time-and state-discrete dynamical system framework. The discretization algorithms are quantile, interval discretization, and a new algorithm introduced in this article, SSD. SSD is especially designed for short time series data and is capable of determining the optimal number of discretization states. The experiments show that both inference methods perform better with SSD than with the other methods. In addition, SSD is demonstrated to preserve the dynamic features of the time series, as well as to be robust to noise in the experimental data. A C++ implementation of SSD is available from the authors at http://polymath.vbi.vt.edu/discretization .

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

BackgroundMany biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed.ResultsWe propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second.ConclusionsDiscrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

A general map of iron metabolism and tissue-specific subnetworks.

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.

Simulating Epstein-Barr virus infection with C-ImmSim

MOTIVATION Epstein-Barr virus (EBV) infects greater than 90% of humans benignly for life but can be associated with tumors. It is a uniquely human pathogen that is amenable to quantitative analysis; however, there is no applicable animal model. Computer models may provide a virtual environment to perform experiments not possible in human volunteers. RESULTS We report the application of a relatively simple stochastic cellular automaton (C-ImmSim) to the modeling of EBV infection. Infected B-cell dynamics in the acute and chronic phases of infection correspond well to clinical data including the establishment of a long term persistent infection (up to 10 years) that is absolutely dependent on access of latently infected B cells to the peripheral pool where they are not subject to immunosurveillance. In the absence of this compartment the infection is cleared. AVAILABILITY The latest version 6 of C-ImmSim is available under the GNU General Public License and is downloadable from www.iac.cnr.it/~filippo/cimmsim.html

The Effect of Negative Feedback Loops on the Dynamics of Boolean Networks

Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distance-to-positive-feedback which, in essence, captures the number of independent negative feedback loops in the network, a property inherent in the network topology. Through a computational study using Boolean networks, it is shown that distance-to-positive-feedback has a strong influence on network dynamics and correlates very well with the number and length of limit cycles in the phase space of the network. To be precise, it is shown that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact that certain natural biological networks exhibit generally regular behavior and have fewer negative feedback loops than randomized networks with the same number of nodes and same connectivity.