Cyclone: open-source package for simulation and analysis of finite dynamical systems.

MOTIVATION: While there are software packages that analyze Boolean, ternary, or other multi-state models, none compute the complete state space of function-based models over any finite set. Results: We propose Cyclone, a simple light-weight software package which simulates the complete state space for a finite dynamical system over any finite set. AVAILABILITY AND IMPLEMENTATION: Source code is freely available at https://github.com/discretedynamics/cyclone under the Apache-2.0 license.

Geometric Characterization of Data Sets with Unique Reduced Gröbner Bases.

Model selection based on experimental data is an important challenge in biological data science. Particularly when collecting data is expensive or time-consuming, as it is often the case with clinical trial and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models. We identify geometric properties of input data that result in an unique algebraic model, and we show that if the data form a staircase, or a so-called linear shift of a staircase, the ideal of the points has a unique reduced Gröbner basis and thus corresponds to a unique model. We use linear shifts to partition data into equivalence classes with the same basis. We demonstrate the utility of the results by applying them to a Boolean model of the well-studied lac operon in E. coli.

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.

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

BACKGROUND: Complex 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. RESULTS: To 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. CONCLUSIONS: This 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.

Boolean models can explain bistability in the lac operon.

The lac operon in Escherichia coli has been studied extensively and is one of the earliest gene systems found to undergo both positive and negative control. The lac operon is known to exhibit bistability, in the sense that the operon is either induced or uninduced. Many dynamical models have been proposed to capture this phenomenon. While most are based on complex mathematical formulations, it has been suggested that for other gene systems network topology is sufficient to produce the desired dynamical behavior. We present a Boolean network as a discrete model for the lac operon. Our model includes the two main glucose control mechanisms of catabolite repression and inducer exclusion. We show that this Boolean model is capable of predicting the ON and OFF steady states and bistability. Further, we present a reduced model which shows that lac mRNA and lactose form the core of the lac operon, and that this reduced model exhibits the same dynamics. This work suggests that the key to model qualitative dynamics of gene systems is the topology of the network and Boolean models are well suited for this purpose.

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.