Nested Canalizing Functions

Motivation

Understanding the design principles of molecular interaction networks is an important goal of molecular systems biology. Part of my research has focused on the identification of patterns in the mechanisms that govern network dynamics. I have studied a class of logical rules that generalizes the concept of nested canalizing functions in the Boolean context to the multistate setting. In [1], it is shown that networks that employ this type of multivalued logic exhibit more robust dynamics than random networks, with few attractors and short limit cycles. It is also shown that the majority of regulatory functions in many published models of gene regulatory and signaling networks are nested canalizing. In a subsequent work, I described the class of nested canalizing functions as an algebraic variety and used this description to obtain a recursive formula to count the number of nested canalizing functions for a given number of inputs and states, see [2]. Then, I have used this formula to obtain asymptotic properties of this class of functions and shown that the ratio between the number of nested canalizing functions and the number of all possible functions tend to zero. This means that this class of regulatory rules is a small subset of the set of all regulatory rules. The later is important for the purpose of reverse engineering of networks that are controlled by a relevant class of functions. More recently, we have also obtained a finer categorization of the class nested canalizing rules into subclasses of functions. This categorization takes into account the level of influence of individual inputs of a nested canalizing function, see [3], and this is reflected in the dynamics of networks controlled by these subclasses of functions.

References:

  1. Regulatory Patterns in Molecular Interaction Networks. David Murrugarra and Reinhard Laubenbacher. Journal of Theoretical Biology, 288, 66-72, 2011. http://www.sciencedirect.com/science/article/pii/S0022519311004103.
  2. The Number of Multistate Nested Canalyzing Functions. David Murrugarra and Reinhard Laubenbacher. Physica D: Nonlinear Phenomena, 241, 929-938, 2012. http://dx.doi.org/10.1016/j.physd.2012.02.011.
  3. Boolean nested canalizing functions: a comprehensive analysis. Yuan Li, John O. Adeyeye, David Murrugarra, Boris Aguilar, Reinhard Laubenbacher. Theoretical Computer Science, 481, 24-36, 2013. http://dx.doi.org/10.1016/j.tcs.2013.02.020.