Open Access Open Badges Research article

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

Franziska Hinkelmann12, Madison Brandon3, Bonny Guang4, Rustin McNeill5, Grigoriy Blekherman1, Alan Veliz-Cuba12 and Reinhard Laubenbacher12*

Author Affiliations

1 Virginia Bioinformatics Institute, Virginia Tech, Washington Street, MC 0477, Blacksburg, VA 24061, USA

2 Department of Mathematics, Virginia Tech, 460 McBryde, Blacksburg, VA 24061-0123, USA

3 Department of Mathematics, The University of Tennessee, 227 Ayres Hall, 1403 Circle Drive, Knoxville, TN 37996-1320, USA

4 Department of Mathematics, Harvey Mudd College, 301 Platt Boulevard, Claremont, CA 91711-5901, USA

5 Department of Mathematics and Statistics, University of North Carolina - Greensboro, 116 Petty Building, Greensboro, NC 27402-6170, USA

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BMC Bioinformatics 2011, 12:295  doi:10.1186/1471-2105-12-295

Published: 20 July 2011



Many 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.


We 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.


Discrete 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.