Finding optimal control policy by using dynamic programming in conjunction with state reduction

In this paper we study the problem of finding optimal control policy for probabilistic Boolean networks (PBNs). Previous works have been done by using dynamic programming-based (DP) method. However, due to the high computational complexity of PBNs, DP method is computationally inefficient for large networks. Inspired by the state reduction strategies studied in [10], we consider using dynamic programming in conjunction with state reduction approach to reduce the computational cost of DP method. Numerical examples are given to demonstrate the efficiency of our proposed method. © 2011 IEEE.published_or_final_versionThe 2011 IEEE International Conference on Systems Biology (ISB), Zhuhai, China, 2-4 September 2011. In Proceedings of ISB, 2011, p. 274-27

Genomic Regulatory Networks, Reduction Mappings and Control

All high-level living organisms are made of small cell units, containing DNA, RNA, genes, proteins etc. Genes are important components of the cells and it is necessary to understand the inter-gene relations, in order to comprehend, predict and ultimately intervene in the cells’ dynamics. Genetic regulatory networks (GRN) represent the gene interactions that dictate the cell behavior. Translational genomics aims to mathematically model GRNs and one of the main goals is to alter the networks’ behavior away from undesirable phenotypes such as cancer. The mathematical framework that has been often used for modeling GRNs is the probabilistic Boolean network (PBN), which is a collection of constituent Boolean networks with perturbation, BNp. This dissertation uses BNps, to model gene regulatory networks with an intent of designing stationary control policies (CP) for the networks to shift their dynamics toward more desirable states. Markov Chains (MC) are used to represent the PBNs and stochastic control has been employed to find stationary control policies to affect steady-state distribution of the MC. However, as the number of genes increases, it becomes computationally burdensome, or even infeasible, to derive optimal or greedy intervention policies. This dissertation considers the problem of modeling and intervening in large GRNs. To overcome the computational challenges associated with large networks, two approaches are proposed: first, a reduction mapping that deletes genes from the network; and second, a greedy control policy that can be directly designed on large networks. Simulation results show that these methods achieve the goal of controlling large networks by shifting the steady-state distribution of the networks toward more desirable states. Furthermore, a new inference method is used to derive a large 17-gene Boolean network from microarray experiments on gastrointestinal cancer samples. The new algorithm has similarities to a previously developed well-known inference method, which uses seed genes to grow subnetworks, out of a large network; however, it has major differences with that algorithm. Most importantly, the objective of the new algorithm is to infer a network from a seed gene with an intention to derive the Gene Activity Profile toward more desirable phenotypes. The newly introduced reduction mappings approach is used to delete genes from the 17-gene GRN and when the network is small enough, an intervention policy is designed for the reduced network and induced back to the original network. In another experiment, the greedy control policy approach is used to directly design an intervention policy on the large 17-gene network to beneficially change the long-run behavior of the network. Finally, a novel algorithm is developed for selecting only non-isomorphic BNs, while generating synthetic networks, using a method that generates synthetic BNs, with a prescribed set of attractors. The goal of the new method described in this dissertation is to discard isomorphic networks

On optimal control policy for Probabilistic Boolean Network: a state reduction approach

BACKGROUND: Probabilistic Boolean Network (PBN) is a popular model for studying genetic regulatory networks. An important and practical problem is to find the optimal control policy for a PBN so as to avoid the network from entering into undesirable states. A number of research works have been done by using dynamic programming-based (DP) method. However, due to the high computational complexity of PBNs, DP method is computationally inefficient for a large size network. Therefore it is natural to seek for approximation methods. RESULTS: Inspired by the state reduction strategies, we consider using dynamic programming in conjunction with state reduction approach to reduce the computational cost of the DP method. Numerical examples are given to demonstrate both the effectiveness and the efficiency of our proposed method. CONCLUSIONS: Finding the optimal control policy for PBNs is meaningful. The proposed problem has been shown to be ∑ p 2 - hard . By taking state reduction approach into consideration, the proposed method can speed up the computational time in applying dynamic programming-based algorithm. In particular, the proposed method is effective for larger size networks.published_or_final_versio

An Engineering Approach Towards Personalized Cancer Therapy

Cells behave as complex systems with regulatory processes that make use of many elements such as switches based on thresholds, memory, feedback, error-checking, and other components commonly encountered in electrical engineering. It is therefore not surprising that these complex systems are amenable to study by engineering methods. A great deal of effort has been spent on observing how cells store, modify, and use information. Still, an understanding of how one uses this knowledge to exert control over cells within a living organism is unavailable. Our prime objective is "Personalized Cancer Therapy" which is based on characterizing the treatment for every individual cancer patient. Knowing how one can systematically alter the behavior of an abnormal cancerous cell will lead towards personalized cancer therapy. Towards this objective, it is required to construct a model for the regulation of the cell and utilize this model to devise effective treatment strategies. The proposed treatments will have to be validated experimentally, but selecting good treatment candidates is a monumental task by itself. It is also a process where an analytic approach to systems biology can provide significant breakthrough. In this dissertation, theoretical frameworks towards effective treatment strategies in the context of probabilistic Boolean networks, a class of gene regulatory networks, are addressed. These proposed analytical tools provide insight into the design of effective therapeutic interventions

Probabilistic reconstruction of the tumor progression process in gene regulatory networks in the presence of uncertainty

<p>Abstract</p> <p>Background</p> <p>Accumulation of gene mutations in cells is known to be responsible for tumor progression, driving it from benign states to malignant states. However, previous studies have shown that the detailed sequence of gene mutations, or the steps in tumor progression, may vary from tumor to tumor, making it difficult to infer the exact path that a given type of tumor may have taken.</p> <p>Results</p> <p>In this paper, we propose an effective probabilistic algorithm for reconstructing the tumor progression process based on partial knowledge of the underlying gene regulatory network and the steady state distribution of the gene expression values in a given tumor. We take the BNp (Boolean networks with pertubation) framework to model the gene regulatory networks. We assume that the true network is not exactly known but we are given an uncertainty class of networks that contains the true network. This network uncertainty class arises from our partial knowledge of the true network, typically represented as a set of local pathways that are embedded in the global network. Given the SSD of the cancerous network, we aim to simultaneously identify the true normal (healthy) network and the set of gene mutations that drove the network into the cancerous state. This is achieved by analyzing the effect of gene mutation on the SSD of a gene regulatory network. At each step, the proposed algorithm reduces the uncertainty class by keeping only those networks whose SSDs get close enough to the cancerous SSD as a result of additional gene mutation. These steps are repeated until we can find the best candidate for the true network and the most probable path of tumor progression.</p> <p>Conclusions</p> <p>Simulation results based on both synthetic networks and networks constructed from actual pathway knowledge show that the proposed algorithm can identify the normal network and the actual path of tumor progression with high probability. The algorithm is also robust to model mismatch and allows us to control the trade-off between efficiency and accuracy.</p

Efficient experimental design for uncertainty reduction in gene regulatory networks

BACKGROUND: An accurate understanding of interactions among genes plays a major role in developing therapeutic intervention methods. Gene regulatory networks often contain a significant amount of uncertainty. The process of prioritizing biological experiments to reduce the uncertainty of gene regulatory networks is called experimental design. Under such a strategy, the experiments with high priority are suggested to be conducted first. RESULTS: The authors have already proposed an optimal experimental design method based upon the objective for modeling gene regulatory networks, such as deriving therapeutic interventions. The experimental design method utilizes the concept of mean objective cost of uncertainty (MOCU). MOCU quantifies the expected increase of cost resulting from uncertainty. The optimal experiment to be conducted first is the one which leads to the minimum expected remaining MOCU subsequent to the experiment. In the process, one must find the optimal intervention for every gene regulatory network compatible with the prior knowledge, which can be prohibitively expensive when the size of the network is large. In this paper, we propose a computationally efficient experimental design method. This method incorporates a network reduction scheme by introducing a novel cost function that takes into account the disruption in the ranking of potential experiments. We then estimate the approximate expected remaining MOCU at a lower computational cost using the reduced networks. CONCLUSIONS: Simulation results based on synthetic and real gene regulatory networks show that the proposed approximate method has close performance to that of the optimal method but at lower computational cost. The proposed approximate method also outperforms the random selection policy significantly. A MATLAB software implementing the proposed experimental design method is available at http://gsp.tamu.edu/Publications/supplementary/roozbeh15a/