Optimal Intervention in Markovian Gene Regulatory Networks With Random-Length Therapeutic Response to Antitumor Drug

The most effective cancer treatments are the ones that prolong patients' lives while offering a reasonable quality of life during and after treatment. The treatments must also 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. Due to biological and microenvironmental variabilities within tumor cells, the action period of an administered drug can vary among a population of patients. In this paper, based on a recently proposed model for tumor growth inhibition, we first probabilistically characterize the variability of the length of drug action. Then, we present a methodology to devise optimal intervention strategies for any Markovian genetic regulatory network governing the tumor when the antitumor drug has a random-length duration of action.

[1]  Edward R. Dougherty,et al.  Steady-state probabilities for attractors in probabilistic Boolean networks , 2005, Signal Process..

[2]  M Rocchetti,et al.  A mathematical model to study the effects of drugs administration on tumor growth dynamics. , 2006, Mathematical biosciences.

[3]  Giuseppe De Nicolao,et al.  A Minimal Model of Tumor Growth Inhibition , 2008, IEEE Transactions on Biomedical Engineering.

[4]  Aniruddha Datta,et al.  Optimal Intervention Strategies for Cyclic Therapeutic Methods , 2009, IEEE Transactions on Biomedical Engineering.

[5]  Aniruddha Datta,et al.  Intervention in Context-Sensitive Probabilistic Boolean Networks Revisited , 2009, EURASIP J. Bioinform. Syst. Biol..

[6]  John J Tyson,et al.  A model for restriction point control of the mammalian cell cycle. , 2004, Journal of theoretical biology.

[7]  Edward R. Dougherty,et al.  Dynamics Preserving Size Reduction Mappings for Probabilistic Boolean Networks , 2007, IEEE Transactions on Signal Processing.

[8]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[9]  Edward R. Dougherty,et al.  CAN MARKOV CHAIN MODELS MIMIC BIOLOGICAL REGULATION , 2002 .

[10]  Edward R. Dougherty,et al.  Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks , 2002, Bioinform..

[11]  Aniruddha Datta,et al.  Intervention in context-sensitive probabilistic Boolean networks , 2005, Bioinform..

[12]  Aniruddha Datta,et al.  Optimal infinite horizon control for probabilistic Boolean networks , 2006, 2006 American Control Conference.

[13]  Aniruddha Datta,et al.  Optimal Intervention Strategies for Therapeutic Methods With Fixed-Length Duration of Drug Effectiveness , 2012, IEEE Transactions on Signal Processing.

[14]  D. J. White,et al.  Finite Dynamic Programming: An Approach to Finite Markov Decision Processes , 1978 .

[15]  Edward R. Dougherty,et al.  State reduction for network intervention in probabilistic Boolean networks , 2010, Bioinform..

[16]  Edward R. Dougherty,et al.  Selection Policy-Induced Reduction Mappings for Boolean Networks , 2010, IEEE Transactions on Signal Processing.

[17]  Edward R. Dougherty,et al.  Genomic Signal Processing (Princeton Series in Applied Mathematics) , 2007 .

[18]  Aurélien Naldi,et al.  Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle , 2006, ISMB.

[19]  Aniruddha Datta,et al.  Optimal Intervention in Asynchronous Genetic Regulatory Networks , 2008, IEEE Journal of Selected Topics in Signal Processing.

[20]  Edward R. Dougherty,et al.  A CoD-based reduction algorithm for designing stationary control policies on Boolean networks , 2010, Bioinform..