Frequent Regulatory Rules in Molecular Interaction Networks

David Murrugarra (June 27, 2019)

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Abstract

Understanding the regulatory mechanisms in molecular interaction networks is an important goal in systems biology. This talk will focus on processes at the molecular level that determine the state of an individual cell, involving signaling or cell regulation. The mathematical framework to be used is that of Boolean networks and their multi-state generalization. These models represent the interactions of different molecular species as logical rules that describe how these species combine to regulate others. Regulatory rules that appear in published models tend to have special features such as the property of being nested canalizing, a concept inspired by the concept of canalization in evolutionary biology. This talk will survey a set of results about nested canalizing rules and how these constrain network dynamics. It has been shown that networks comprised of nested canalizing functions have dynamic properties that make them suitable for modeling gene regulatory networks, namely small number of attractors and short limit cycles. In this talk, I will discuss a normal form as polynomial function that applies to any Boolean or multi-state function. This description provides a partition of the inputs of any Boolean function or multi-state function into canalizing and non-canalizing variables and, within the canalizing ones, we can categorize the input variables into layers of canalization. I will also describe the structure of the non-canalizing variables. Applications for how to use this normal form and some other properties of these functions will be given at the end of the talk.