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Intervention in Gene Regulatory Networks via Greedy
 Control Policies Based on LongRun Behavior,” BMC Systems Biology
"... Abstract—A salient purpose for studying gene regulatory networks is to derive intervention strategies to identify potential drug targets and design genebased therapeutic intervention. Optimal and approximate intervention strategies based on the transition probability matrix of the underlying Markov ..."
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Abstract—A salient purpose for studying gene regulatory networks is to derive intervention strategies to identify potential drug targets and design genebased therapeutic intervention. Optimal and approximate intervention strategies based on the transition probability matrix of the underlying Markov chain have been studied extensively for probabilistic Boolean networks. While the key goal of control is to reduce the steadystate probability mass of undesirable network states, in practice it is important to limit collateral damage and this constraint should be taken into account when designing intervention strategies with network models. In this paper, we propose two new phenotypically constrained stationary control policies by directly investigating the effects on the network longrun behavior. They are derived to reduce the risk of visiting undesirable states in conjunction with constraints on the shift of undesirable steadystate mass so that only limited collateral damage can be introduced. We have studied the performance of the new constrained control policies together with the previous greedy control policies to randomly generated probabilistic Boolean networks. A preliminary example for intervening in a metastatic melanoma network is also given to show their potential application in designing genetic therapeutics to reduce the risk of entering both aberrant phenotypes and other ambiguous states corresponding to complications or collateral damage. Experiments on both random network ensembles and the melanoma network demonstrate that, in general, the new proposed control policies exhibit the desired performance. As shown by intervening in the melanoma network, these control policies can potentially serve as future practical gene therapeutic intervention strategies. Index Terms—Gene regulatory networks, probabilistic Boolean networks, network intervention, Markov chain, stationary control policy, melanoma. Ç
Optimal Intervention Strategies for Therapeutic Methods With FixedLength Duration of Drug Effectiveness
"... Abstract—Intervention in gene regulatory networks in the context of Markov decision processes has usually involved finding an optimal onetransition policy, where a decision is made at every transition whether or not to apply treatment. In an effort to model dosing constraint, a cyclic approach to i ..."
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Abstract—Intervention in gene regulatory networks in the context of Markov decision processes has usually involved finding an optimal onetransition policy, where a decision is made at every transition whether or not to apply treatment. In an effort to model dosing constraint, a cyclic approach to intervention has previously been proposed in which there is a sequence of treatment windows and treatment is allowed only at the beginning of each window. This protocol ignores two practical aspects of therapy. First, a treatment typically has some duration of action: adrugwillbeeffectiveforsomeperiod, after which there can be a recovery phase. This, too, might involve a cyclic protocol; however, in practice, a physician might monitor a patient at every stage and decide whether to apply treatment, and if treatment is applied, then the patient will be under the influence of the drug for some duration, followed by a recovery period. This results in an acyclic protocol. In this paper we take a unified approach to both cyclic and acyclic control with duration of effectiveness by placing the problem in the general framework of multiperiod decision epochs with infinite horizon discounting cost. The time interval between successive decision epochs can have multiple time units, where given the current state and the action taken, there is a joint probability distribution defined for the next state and the time when the next decision epoch will be called. Optimal control policies are derived, synthetic networks are used to investigate the properties of both cyclic and acyclic interventions with fixedduration of effectiveness, and the methodology is applied to a mutated mammalian cellcycle network. Index Terms—Acyclic intervention, cyclic intervention, drug scheduling, gene regulatory network, genomic signal processing, optimal control. I.
Cancer Informatics
"... This is an open access article. Unrestricted noncommercial use is permitted provided the original work is properly cited. Open Access Full open access to this and thousands of other papers at ..."
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This is an open access article. Unrestricted noncommercial use is permitted provided the original work is properly cited. Open Access Full open access to this and thousands of other papers at
Finitestate discretetime Markov chain models of gene regulatory networks
, 2014
"... In this study Markov chain models of gene regulatory networks (GRN) are developed. These models gives the ability to apply the well known theory and tools of Markov chains to GRN analysis. We introduce a new kind of the finite graph of the interactions called the combinatorial net that formally repr ..."
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In this study Markov chain models of gene regulatory networks (GRN) are developed. These models gives the ability to apply the well known theory and tools of Markov chains to GRN analysis. We introduce a new kind of the finite graph of the interactions called the combinatorial net that formally represent a GRN and the transition graphs constructed from interaction graphs. System dynamics are defined as a random walk on the transition graph that is some Markovian chain. A novel concurrent updating scheme (evolution rule) is developed to determine transitions in a transition graph. Our scheme is based on the firing of a random set of nonsteady state vertices of a combinatorial net. We demonstrate that this novel scheme gives an advance in the modeling of the asynchronicity. Also we proof the theorem that the combinatorial nets with this updating scheme can asynchronously compute a maximal independent sets of graphs. As proof of concept, we present here a number of simple combinatorial models: a discrete model of autorepression, a bistable switch, the Elowitz repressilator, a selfactivation and show that this models exhibit well known properties. 1
Optimal Intervention in Markovian Gene Regulatory Networks With RandomLength Therapeutic Response to Antitumor Drug
"... Abstract—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 s ..."
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Abstract—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 randomlength duration of action. Index Terms—Cancer therapy, gene regulatory networks (GRNs), optimal intervention, probabilistic Boolean networks (PBNs), tumor growth inhibition (TGI) model. I.