Inference, analysis, and control of Boolean network models

Elena Dimitrova

California Polytechinc State University, San Luis Obispo (Mathematics)

"A unified approach to reverse engineering and data selection for unique network identification"

Due to cost concerns, it is optimal to gain insight into the connectivity of biological and other networks using as few experiments as possible. Data selection for unique network connectivity identification has been an open problem since the introduction of algebraic methods for reverse engineering for almost two decades. In this talk we determine what data sets uniquely identify the unsigned wiring diagram corresponding to a system that is discrete in time and space. Furthermore, we answer the question of uniqueness for signed wiring diagrams for Boolean networks. Computationally, unsigned and signed wiring diagrams have been studied separately, and in this talk we also show that there exists a polynomial ideal capable of encoding both unsigned and signed information. This provides a unified approach to studying reverse engineering that also gives significant computational benefits.

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Brandilyn Stigler

Southern Methodist University (Mathematics)

"Computational Algebraic Methods for Boolean Network Modeling"

Biological data science is a field replete with many substantial data sets from laboratory experiments and myriad diverse methods for modeling, simulation, and analysis. As a data set can have a large number of associated models, model selection is often required as a post-processing step. In parallel experimental design can be utilized as a preprocessing step to minimize the number of resulting models, many of which may be biologically irrelevant. In this talk we focus on the problem of inferring Boolean models of biological networks from data. We will outline theoretical results and computational algorithms related to model construction and model selection. This work draws from algebraic geometry and algebraic combinatorics, and has been used to model a variety of biological processes including tissue development and tumor progression.

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Claus Kadelka

Iowa State University (Department of Mathematics)

"A modular design of gene regulatory networks emerges naturally in response to an evolutionary multi-objective optimization problem"

Building complicated structures from simpler building blocks is a widely observed principle in both natural and engineered systems. In molecular systems biology, it is also widely accepted, even though there has not emerged a clear definition of what constitutes a simple building block, or module. For a Boolean network, we recently proposed to define its modules as the strongly connected components of its wiring diagram. This structure-based definition of modularity implies a decomposition of the dynamics of a Boolean network. In this talk, I show through simulation studies that modularity allows Boolean networks to maximize both their phenotypical robustness and their dynamical complexity. The former is biologically desirable as gene regulatory networks need to robustly maintain a phenotype in the presence of perturbations. At the same time, meaningful biological networks must harbor multiple phenotypes (corresponding to attractors of the Boolean network), allowing the network to dynamically shift from one phenotype to another based on its current need. These findings provide evidence that modularity, defined using the graph-theoretical concept of strong connectedness, is evolutionarily advantageous.

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Daniel R. Plaugher

University of Kentucky (Department of Toxicology and Cancer Biology)

"Phenotype control techniques for gene regulatory networks"

Modeling cell signal transduction pathways with Boolean networks (BNs) has become an established method for analyzing intracellular communications over the last few decades. What's more, BNs provide a course-grained approach, not only to understanding molecular communications, but also for targeting pathway components that alter the long-term outcomes of the system. This has come to be known as phenotype control theory. In this presentation we discuss the interplay of various approaches for controlling gene regulatory networks. We will also explore comparisons between the methods on a specific cancer model, and highlight some challenges facing each technique.

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