Optimal Intervention in Markovian Genetic Regulatory Networks for Cancer Therapy

Abstract

A basic issue for translational genomics is to model gene interactions via gene regulatory networks (GRNs) and thereby provide an informatics environment to derive and study effective interventions eradicating the tumor. In this dissertation, we present two different approaches to intervention methods in cancer-related GRNs.

Decisions regarding possible interventions are assumed to be made at every state transition of the network. To account for dosing constraints, a model for the sequence of treatment windows is considered, where treatments are allowed only at the beginning of each treatment cycle followed by a recovery phase. Due to biological variabilities within tumor cells, the action period of an antitumor drug can vary among a population of patients. That is, a treatment typically has a random duration of action. We propose a unified approach to such intervention models for any Markovian GRN governing the tumor. To accomplish this, we place the problem in the general framework of partially controlled decision intervals with infinite horizon discounting cost. We present a methodology to devise optimal intervention policies for synthetically generated gene regulatory networks as well as a mutated mammalian cell-cycle network.

As a different approach, we view the phenotype as a characterization of the long- run behavior of the Markovian GRN and desire interventions that optimally move the probability mass from undesirable to desirable states. We employ a linear programming approach to formulate the maximal shift problem, that is, optimization is directly based on the amount of shift. Moreover, the same basic linear programming structure is used for a constrained optimization, where there is a limit on the amount of mass that may be shifted to states that are not directly undesirable relative to the pathology of interest, but which bear some perceived risk. We demonstrate the performance of optimal policies on synthetic networks as well as two real GRNs derived from the metastatic melanoma and mammalian cell cycle.

These methods, as any effective cancer treatment must, aim to carry out their actions rapidly and with high efficiency such that a very large percentage of tumor cells die or shift into a state where they stop proliferating.