Identification of control targets in Boolean molecular network models via computational algebra.

David Murrugarra,Boris Aguilar,Reinhard Laubenbacher,Alan Veliz-Cuba

doi:10.1186/s12918-016-0332-x

Abstract

BackgroundMany problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system.ResultsThis paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg.ConclusionsThis paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0332-x) contains supplementary material, which is available to authorized users.

Highlights

Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment
In a Boolean networks (BN), the genes of a gene regulatory networks (GRNs) are represented by a set of nodes that can take on only two possible states (ON or OFF)
In the first example we focus on control with edge deletions while for the second we use control with node deletions and constant expressions

Summary

Introduction

Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. There is a rich theory for the control of continuous models such as systems of differential equations, [17,18,19,20] Discrete models such as Boolean networks (BN) have been proposed to study GRNs. In a BN, the genes of a GRN are represented by a set of nodes that can take on only two possible states (ON or OFF). Control methods for discrete models are still in their infancy, compared to the theory for continuous models

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