Brandilyn Stigler

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.

Parameter estimation for Boolean models of biological networks

Boolean networks have long been used as models of molecular networks, and they play an increasingly important role in systems biology. This paper describes a software package, Polynome, offered as a web service, that helps users construct Boolean network models based on experimental data and biological input. The key feature is a discrete analog of parameter estimation for continuous models. With only experimental data as input, the software can be used as a tool for reverse-engineering of Boolean network models from experimental time course data.

A Gröbner fan method for biochemical network modeling

Polynomial dynamical systems (PDSs) have been used successfully as a framework for the reconstruction, or reverse engineering of biochemical networks from experimental data. Within this modeling space, a particular PDS is chosen by way of a Gröbner basis, and using different monomial orders may result in different polynomial models. In this paper, we present a systematic method for selecting most likely polynomial models for a given data set, using the Gröbner fan of the ideal of the input data. We apply the method to reverse engineer two biochemical networks, a Boolean model of lactose metabolism in E. coli and a protein signal transduction network in S. cerevisiae and compare our results to those from two published network-reconstruction methods.

Reverse engineering of dynamic networks.

Abstract:u2002 We consider the problem of reverse‐engineering dynamic models of biochemical networks from experimental data using polynomial dynamic systems. In earlier work, we developed an algorithm to identify minimal wiring diagrams, that is, directed graphs that represent the causal relationships between network variables. Here we extend this algorithm to identify a most likely dynamic model from the set of all possible dynamic models that fit the data over a fixed wiring diagram. To illustrate its performance, the method is applied to simulated time‐course data from a published gene regulatory network in the fruitfly Drosophila melanogaster.

A regulatory network modeled from wild-type gene expression data guides functional predictions in Caenorhabditis elegans development

BackgroundComplex gene regulatory networks underlie many cellular and developmental processes. While a variety of experimental approaches can be used to discover how genes interact, few biological systems have been systematically evaluated to the extent required for an experimental definition of the underlying network. Therefore, the development of computational methods that can use limited experimental data to define and model a gene regulatory network would provide a useful tool to evaluate many important but incompletely understood biological processes. Such methods can assist in extracting all relevant information from data that are available, identify unexpected regulatory relationships and prioritize future experiments.ResultsTo facilitate the analysis of gene regulatory networks, we have developed a computational modeling pipeline method that complements traditional evaluation of experimental data. For a proof-of-concept example, we have focused on the gene regulatory network in the nematode C. elegans that mediates the developmental choice between mesodermal (muscle) and ectodermal (skin) cell fates in the embryonic C lineage. We have used gene expression data to build two models: a knowledge-driven model based on gene expression changes following gene perturbation experiments, and a data-driven mathematical model derived from time-course gene expression data recovered from wild-type animals. We show that both models can identify a rich set of network gene interactions. Importantly, the mathematical model built only from wild-type data can predict interactions demonstrated by the perturbation experiments better than chance, and better than an existing knowledge-driven model built from the same data set. The mathematical model also provides new biological insight, including a dissection of zygotic from maternal functions of a key transcriptional regulator, PAL-1, and identification of non-redundant activities of the T-box genes tbx-8 and tbx-9.ConclusionsThis work provides a strong example for a mathematical modeling approach that solely uses wild-type data to predict an underlying gene regulatory network. The modeling approach complements traditional methods of data analysis, suggesting non-intuitive network relationships and guiding future experiments.

Computing Gröbner bases of ideals of few points in high dimensions

A contemporary and exciting application of Gröbner bases is their use in computational biology, particularly in the reverse engineering of gene regulatory networks from experimental data. In this setting, the data are typically limited to tens of points, while the number of genes or variables is potentially in the thousands. As such data sets vastly underdetermine the biological network, many models may fit the same data and reverse engineering programs often require the use of methods for choosing parsimonious models. Gröbner bases have recently been employed as a selection tool for polynomial dynamical systems that are characterized by maps in a vector space over a finite field.n While there are numerous existing algorithms to compute Gröbner bases, to date none has been specifically designed to cope with large numbers of variables and few distinct data points. In this paper, we present an algorithm for computing Gröbner bases of zero-dimensional ideals that is optimized for the case when the number m of points is much smaller than the number n of indeterminates. The algorithm identifies those variables that are essential, that is, in the support of the standard monomials associated to a polynomial ideal, and computes the relations in the Gröbner basis in terms of these variables. When n is much larger than m, the complexity is dominated by nm3. The algorithm has been implemented and tested in the computer algebra system Macaulay 2. We provide a comparison of its performance to the Buchberger-Möller algorithm, as built into the system.

Algebraic and Geometric Methods in Statistics: Design of experiments and biochemical network inference

Design of experiments is a branch of statistics that aims to identify efficient procedures for planning experiments in order to optimize knowledge discovery. Network inference is a subfield of systems biology devoted to the identification of biochemical networks from experimental data. Common to both areas of research is their focus on the maximization of information gathered from experimentation. The goal of this paper is to establish a connection between these two areas coming from the common use of polynomial models and techniques from computational algebra.

System Identification for Discrete Polynomial Models of Gene Regulatory Networks

Abstract This paper gives a review of tools for the system identification of dynamic models for gene regulatory networks, using the modeling framework of polynomial dynamical systems over finite fields.

Data Identification for Improving Gene Network Inference using Computational Algebra

Identification of models of gene regulatory networks is sensitive to the amount of data used as input. Considering the substantial costs in conducting experiments, it is of value to have an estimate of the amount of data required to infer the network structure. To minimize wasted resources, it is also beneficial to know which data are necessary to identify the network. Knowledge of the data and knowledge of the terms in polynomial models are often required a priori in model identification. In applications, it is unlikely that the structure of a polynomial model will be known, which may force data sets to be unnecessarily large in order to identify a model. Furthermore, none of the known results provides any strategy for constructing data sets to uniquely identify a model. We provide a specialization of an existing criterion for deciding when a set of data points identifies a minimal polynomial model when its monomial terms have been specified. Then, we relax the requirement of the knowledge of the monomials and present results for model identification given only the data. Finally, we present a method for constructing data sets that identify minimal polynomial models.

Applications of the gröbner fan to gene network reconstruction (abstract only)

Gröbner fans have gained popularity in computational commutative algebra and algebraic geometry with applications ranging from Gröbner basis conversion to the emerging field of tropical mathematics. Recently Gröbner fans have been employed for the selection of minimal models that fit measurement data from gene regulatory networks. The model space is described as the sum of an interpolating polynomial function f and the set of all polynomials that vanish on the data, that is, the ideal of data points. A minimal model can be chosen by computing the reduction of f with respect to a fixed Gröbner basis, which is dependent on the choice of term order. As Gröbner fans partition the set of Gröbner bases into equivalence classes, they can be thought of as parametrizations of the model space. This characterization permits exploration of the model space and discovery of most likely models. In this poster we show how Gröbner fans are used to two reconstruct gene regulatory networks: lactose metabolism in the bacterium E. coli and tissue development in the roundworm C. elegans.