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Uncovering operational interactions in genetic networks using asynchronous boolean dynamics
 in "J. Theor. Biol
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Robust intervention in probabilistic Boolean networks
 IEEE Trans
, 2008
"... Abstract—Probabilistic Boolean networks (PBNs) have been recently introduced as a paradigm for modeling genetic regulatory networks. One of the objectives of PBN modeling is to use the network for the design and analysis of intervention strategies aimed at moving the network out of undesirable state ..."
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Abstract—Probabilistic Boolean networks (PBNs) have been recently introduced as a paradigm for modeling genetic regulatory networks. One of the objectives of PBN modeling is to use the network for the design and analysis of intervention strategies aimed at moving the network out of undesirable states, such as those associated with disease, and into desirable ones. To date, a number of intervention strategies have been proposed in the context of PBNs. However, all these techniques assume perfect knowledge of the transition probability matrix of the PBN. Such an assumption cannot be satisfied in practice since the presence of noise and the availability of limited number of samples will prevent the transition probabilities from being accurately determined. Moreover, even if the exact transition probabilities could be estimated from the data, mismatch between the PBN model and the actual genetic regulatory network will invariably be present. Thus, it is important to study the effect of modeling errors on the final outcome of an intervention strategy and one of the goals of this paper is to do precisely that when the uncertainties are in the entries of the transition probability matrix. In addition, the paper develops a robust intervention strategy that is obtained by minimizing the worstcase cost over the uncertainty set. Index Terms—Control of biological networks, estimation errors, robust dynamic programming, robust minimax control, perturbation bounds. I.
Effect of Function Perturbation on the Steadystate Distribution of Genetic regulatory Networks
 Optimal Structural Intervention’, IEEE Transactions and Signal Processing
, 2008
"... Abstract—The dynamics of a rulebased gene regulatory network are determined by the regulatory functions in conjunction with whatever probability distributions are involved in network transitions. In the case of Boolean networks (BNs) and, more generally, probabilistic Boolean networks (PBNs), the ..."
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Abstract—The dynamics of a rulebased gene regulatory network are determined by the regulatory functions in conjunction with whatever probability distributions are involved in network transitions. In the case of Boolean networks (BNs) and, more generally, probabilistic Boolean networks (PBNs), there has been a significant amount of investigation into the effect of perturbing gene states, in particular, the design of intervention strategies based on finite or infinitehorizon control polices. This paper considers the less investigated issue of function perturbations. A single function perturbation affects network dynamics and alters the longrun distribution, whereas any individual gene perturbation has only transient effects and does not change the longrun distribution. We derive analytic results for changes in the steadystate distributions of PBNs resulting from modifications to the underlying regulatory rules and apply the derived results to find optimal structural interventions to avoid undesirable states. The results are applied to a WNT5A network and a mammalian cell cycle related network, respectively, to achieve more favorable steadystate distributions and reduce the risk of getting into aberrant phenotypes. Index Terms—Boolean networks (BNs), genetic regulatory networks, Markov chains, metastasis, optimal structural intervention, probabilistic Boolean networks (PBNs), steadystate distribution. I.
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.
Recent advances in intervention in markovian regulatory networks
 Curr Genomics
, 2009
"... Abstract: Markovian regulatory networks constitute a class of discrete statespace models used to study gene regulatory dynamics and discover methods that beneficially alter those dynamics. Thereby, this class of models provides a framework to discover effective drug targets and design potent therap ..."
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Abstract: Markovian regulatory networks constitute a class of discrete statespace models used to study gene regulatory dynamics and discover methods that beneficially alter those dynamics. Thereby, this class of models provides a framework to discover effective drug targets and design potent therapeutic strategies. The salient translational goal is to design therapeutic strategies that desirably modify network dynamics via external signals that vary the expressions of a control gene. The objective of an intervention strategy is to reduce the likelihood of the pathological cellular function related to a disease. The task of finding an effective intervention strategy can be formulated as a sequential decision making problem for a predefined cost of intervention and a costperstage function that discriminates the geneactivity profiles. An effective intervention strategy prescribes the actions associated with an external signal that result in the minimum expected cost. This strategy in turn can be used as a treatment that reduces the longrun likelihood of gene expressions favorable to the disease. In this tutorial, we briefly summarize the first method proposed to design such therapeutic interventions, and then move on to some of the recent refinements that have been proposed. Each of these recent intervention methods is motivated by practical or analytical considerations. The presentation of the key ideas is facilitated with the help of two case studies.
Quantifying the Objective Cost of Uncertainty in Complex Dynamical Systems
, 2013
"... Realworld problems often involve complex systems that cannot be perfectly modeled or identified, and many engineering applications aim to design operators that can perform reliably in the presence of such uncertainty. In this paper, we propose a novel Bayesian framework for objectivebased uncertai ..."
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Realworld problems often involve complex systems that cannot be perfectly modeled or identified, and many engineering applications aim to design operators that can perform reliably in the presence of such uncertainty. In this paper, we propose a novel Bayesian framework for objectivebased uncertainty quantification (UQ), which quantifies the uncertainty in a given system based on the expected increase of the operational cost that it induces. This measure of uncertainty, called MOCU (mean objective cost of uncertainty), provides a practical way of quantifying the effect of various types of system uncertainties on the operation of interest. Furthermore, the proposed UQ framework provides a general mathematical basis for designing robust operators, and it can be applied to diverse applications, including robust filtering, classification, and control. We demonstrate the utility and effectiveness of the proposed framework by applying it to the problem of robust structural intervention of gene regulatory networks, an important application in translational genomics. Index Terms Mean objective cost of uncertainty (MOCU), objectivebased uncertainty quantification (UQ), robust operator design, robust network intervention.
Epistemology and the Role of Mathematics in Translational Science
"... The terminology “translational science ” has recently become very popular; however, there has been little effort to give it an epistemological characterization and thereby give it meaning as a scientific enterprise. This paper takes a step in that direction by recognizing that translational science ..."
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The terminology “translational science ” has recently become very popular; however, there has been little effort to give it an epistemological characterization and thereby give it meaning as a scientific enterprise. This paper takes a step in that direction by recognizing that translational science must begin with the epistemology of science and, rooted in the scientific epistemology, extend that epistemology to encompass human actions in the physical world. The road taken here is to consider the classical understanding of operators on random processes in terms of analysis and synthesis, and to delineate their epistemological domains. The main focus of the paper is on synthesis as translational science, in which synthesis is characterized via operator optimization as opposed to being left to trial and error. Three translational settings are used as illustrations, the unity of these theories within the context of translational science being emphasized: (1) the WienerKolmogorov founding paradigm of optimal linear filters in the context of canonical signal representation, (2) the analogous optimal nonlinear filter theory for images in the context of granulometric spectral representation, and (3) the determination of optimal therapeutic strategies based on structural intervention in gene regulatory networks. The paper closes with some comments on the demands imposed by an epistemologically rigorous approach to translational science. 1
On the Limitations of Biological Knowledge
"... Abstract: Scientific knowledge is grounded in a particular epistemology and, owing to the requirements of that epistemology, possesses limitations. Some limitations are intrinsic, in the sense that they depend inherently on the nature of scientific knowledge; others are contingent, depending on the ..."
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Abstract: Scientific knowledge is grounded in a particular epistemology and, owing to the requirements of that epistemology, possesses limitations. Some limitations are intrinsic, in the sense that they depend inherently on the nature of scientific knowledge; others are contingent, depending on the present state of knowledge, including technology. Understanding limitations facilitates scientific research because one can then recognize when one is confronted by a limitation, as opposed to simply being unable to solve a problem within the existing bounds of possibility. In the hope that the role of limiting factors can be brought more clearly into focus and discussed, we consider several sources of limitation as they apply to biological knowledge: mathematical complexity, experimental constraints, validation, knowledge discovery, and human intellectual capacity.
Genomic Signal Processing Digital Object Identifier 10.1109/MSP.2012.2185868
, 2012
"... Signal processing has played a major auxiliary role in medicine via the array of technologies available to physicians. Only a rapidly diminishing proportion of the population can recall medicine without computer tomography, magnetic resonance imaging, and ultrasound. In this capacity, signal process ..."
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Signal processing has played a major auxiliary role in medicine via the array of technologies available to physicians. Only a rapidly diminishing proportion of the population can recall medicine without computer tomography, magnetic resonance imaging, and ultrasound. In this capacity, signal processing serves only a supporting function. The future will be different. Like a factory, regulatory logic defines the cell as an operational system [1]: “The roles of regulatory logic in the factory (or complex machine) and the cell are congruent because the key to the characterization of this logic lies in communication (between components) and control (of components)—that is, in systems theory, which therefore determines the epistemology of the cell. ” Ipso facto, the mathematical foundations of biology, and therefore its translational partner, medicine, reside in the mathematics of systems theory. Hence, the roles of signal processing and the closely related theories of communication, control, and information will play constitutive functions as medicine evolves into a translational science resting on a theoretical framework. This article illustrates these basicscience roles with diagnostic and therapeutic models involving logical circuits for combinatorial drug analysis, Karnaugh maps in the construction of gene regulatory networks, Markov chain perturbation theory for determining therapeutic action, queuing theory in analyzing the effects of gene copy number alterations (CNAs) on gene expression, and the use of minimummeansquareerror estimation in the design of biomarkers for disease. My aim is simple: attract engineers into theoretical medicine, where their expertise can improve the human condition. Recognition of the fundamental role of systems theory for the life sciences is not a
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.