Parameter estimation for Boolean models of biological networks

📝 Abstract

Boolean networks have long been used as models of molecular networks and 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.

💡 Analysis

Boolean networks have long been used as models of molecular networks and 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.

📄 Content

arXiv:0908.3037v1 [q-bio.MN] 21 Aug 2009 Parameter estimation for Boolean models of biological networks Elena Dimitrovaa, Luis David Garc´ıa-Puenteb,h, Franziska Hinkelmannc,d, Abdul S. Jarrahc,d, Reinhard Laubenbacher∗,c,d,h, Brandilyn Stiglere,h, Michael Stillmang, Paola Vera-Liconaf aDepartment of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA bDepartment of Mathematics and Statistics, Sam Houston State University, Huntsville, TX 77341-2206, USA cDepartment of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA dVirginia Bioinformatics Institute, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0477, USA eMathematics Department, Southern Methodist University, Dallas, TX 75275-0156, USA fDIMACS Center, Rutgers University, Piscataway, NJ 08854-8018, USA gMathematics Department, Cornell University, Ithaca, NY 14853-4201, USA hStatistical and Applied Mathematical Sciences Institute, Research Triangle Park, NC 27709-4006, USA Abstract Boolean networks have long been used as models of molecular networks and play an in- creasingly 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. Key words: 2000 MSC: Primary 92-08, 92B05; Secondary 13P10

1. Introduction During the last decade finite dynamical systems, that is, discrete dynamical systems with a finite phase space, have been used increasingly in systems biology to model a va- riety of biochemical networks, such as metabolic, gene regulatory, and signal transduction networks. In many cases, the available data quantity and quality is not sufficient to build ∗Corresponding author Email addresses: edimit@clemson.edu (Elena Dimitrova), lgarcia@shsu.edu (Luis David Garc´ıa-Puente), fhinkel@vt.edu (Franziska Hinkelmann), ajarrah@vbi.vt.edu (Abdul S. Jarrah), reinhard@vbi.vt.edu (Reinhard Laubenbacher), bstigler@smu.edu (Brandilyn Stigler), mike@math.cornell.edu (Michael Stillman), mveralic@math.rutgers.edu (Paola Vera-Licona) 1Partially supported by SAMSI New Researcher Fellowship. Preprint submitted to Theoretical Computer Science March 12, 2018 detailed quantitative models such as systems of ordinary differential equations, which re- quire many parameters that are frequently unknown. In addition, discrete models tend to be more intuitive and more easily accessible to life scientists. Boolean networks and the more general so-called logical models are the main types of finite dynamical systems that have been used successfully in modeling biological networks. Discrete dynamical models of biological networks were first introduced by Kauffman who used Boolean networks to study the dynamics of gene regulatory networks (Kauffman, 1969b,a, 1993). A gene is assumed to be in one of two states, expressed (1) or not expressed (0). The next state of a gene is determined by a Boolean function in terms of the current states of the gene and its immediate neighbors in the network. The state of a network in n variables is then a binary vector of length n, representing the state of each node of the network. Thus, there are 2n possible states. The dynamics of the network is represented by a directed graph on the 2n states, where each state has out-degree one, that is, each state is mapped to exactly one other state (possibly itself). Boolean models of biological systems are abundant, including gene regulatory networks such as the segment polarity network in the fruit fly (Albert and Othmer, 2003), the cell cycle in mammalian cells (Faure et al., 2006), in budding yeast (Li et al., 2004), and fission yeast (Davidich and Bornholdt, 2007), and metabolic networks in E. coli (Samal and Jain, 2008; Barrett et al., 2005) and in S. cerevisiae (Herrgard et al., 2006). Also, Boolean network models of signaling networks have recently been used to gain insight into different mechanisms such as the molecular neurotransmitter signaling pathway (Gupta et al., 2007), the T cell receptor signaling pathway (Saez-Rodriguez et al., 2007), the signaling network for the long-term survival of cytotoxic T lymphocytes in humans (Li et al., 2006), and the abscisic acid signaling pathway (Zhang et al., 2008). Boolean models require less detailed information about the system to be modeled, so they can be used in cases where quantitative information is missing. They are also useful if qualitative predictions from the model are desired, such as whether a T cell becomes pro- or anti-inflammatory. Finally, Boolean models are very intuitive compared to models based on differential equations or other more sophisticated formalisms. It is also eas

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