Identifying Targets for Intervention by Analyzing Basins of Attraction

Abstract

Motivation:A grand challenge in the modeling of biological systems is the identification of key variables which can act as targets for intervention. Good intervention targets are the "key players" in a system and have significant influence over other variables; in other words, in the context of diseases such as cancer, targeting these variables with treatments and interventions will provide the greatest effects because of their direct and indirect control over other parts of the system. Boolean networks are among the simplest of models, yet they have been shown to adequately model many of the complex dynamics of biological systems. Often ignored in the Boolean network model, however, are the so called basins of attraction. As the attractor states alone have been shown to correspond to cellular phenotypes, it is logical to ask which variables are most responsible for triggering a path through a basin to a particular attractor.Results: This work claims that logic minimization (i.e. classical circuit design) of the collections of states in Boolean network basins of attraction reveals key players in the network. Furthermore, we claim that the key players identified by this method are often excellent targets for intervention given a network modeling a biological system, and more importantly, that the key players identified are not apparent from the attractor states alone, from existing Boolean network measures, or from other network measurements. We demonstrate these claims with a well-studied yeast cell cycle network and with a WNT5A network for melanoma, computationally predicted from gene expression data.

A Qualitative Model of the Differentiation Network in Chondrocyte Maturation: A Holistic View of Chondrocyte Hypertrophy

“…the robustness of canalisation and the robustness to perturbation. Other structural measures, such as the simple path measure [96], or topological features, such as betweenness [61], could also be employed [97]. However, we focused on robustness of canalisation and to perturbation as they take into account the dynamical behaviour of the network, such as the effect of changes on stable states.…”

“…A first measure is the size of the attractor basin [61]. Due to the exponential growth of the state space with the size of the network, it is not feasible to investigate a significant fraction of the state space in larger networks.…”

Template-based intervention in Boolean network models of biological systems

“…Despite its simplicity, the Boolean network model has proven to be quite viable at approximating certain aspects of biological processes [ 1 ]. For example, it has been used to simulate the yeast cell cycle [ 4 ], which we looked at closely in our work [ 5 ]. It has also been used to simulate the expression pattern of segment polarity genes in Drosophila melanogaster [ 6 ], as well as the vocal communication system of the songbird brain [ 7 ],[ 8 ].…”

“…An intervention, in the context of a Boolean network, is defined as a modification (set/reset) to one or more variables in an attractor state of a source basin with the intention that network rules will transition to any state in a given goal basin (thus eventually reaching the attractor of the goal basin). In our recent work [ 5 ], we employed a logic reduction algorithm to reduce the Boolean states comprising the basins of attraction to minimal representations, and from those minimizations, we identified high-quality intervention targets comprised of single variables. However, as the number of variables in a biological network increases, the more likely it is that a successful intervention target will require the combined efforts of multiple variables.…”

“…Here, we briefly describe pertinent points of our previous work [ 5 ] upon which the current methods and results build.…”