Optimal constrained stationary intervention in gene regulatory networks

Abstract

A key objective of gene network modeling is to develop intervention strategies to alter regulatory dynamics in such a way as to reduce the likelihood of undesirable phenotypes. Optimal stationary intervention policies have been developed for gene regulation in the framework of probabilistic Boolean networks in a number of settings. To mitigate the possibility of detrimental side effects, for instance, in the treatment of cancer, it may be desirable to limit the expected number of treatments beneath some bound. This paper formulates a general constraint approach for optimal therapeutic intervention by suitably adapting the reward function and then applies this formulation to bound the expected number of treatments. A mutated mammalian cell cycle is considered as a case study.

Figure 1

The steady-state probability of gene-activity profile of the PBN associated with the mammalian cell-cycle network before intervention. The vertical line separates the undesirable gene-activity profiles from the desirable ones.

Figure 2

The steady-state probability of gene-activity profile of the PBN associated with the mammalian cell-cycle network after intervention using Rb as the control gene, when the frequency of applying control is unconstrained, . The vertical line separates the undesirable gene-activity profiles from the desirable ones.

Figure 3

The steady-state probability of gene-activity profile of the PBN associated with the mammalian cell-cycle network after intervention using Rb as the control gene, when the frequency of applying control is upper bounded by . The vertical line separates the undesirable gene-activity profiles from the desirable ones.

Figure 4

The steady-state probability of gene-activity profile of the PBN associated with the mammalian cell-cycle network after intervention using EF as the control gene, when the frequency of applying control is is unconstrained, . The vertical line separates the undesirable gene-activity profiles from the desirable ones.

Figure 5

The steady-state probability of gene-activity profile of the PBN associated with the mammalian cell-cycle network after intervention using EF as the control gene, when the frequency of applying control upper bounded by . The vertical line separates the undesirable gene-activity profiles from the desirable ones.