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Scalefree networks in cell biology
 JOURNAL OF CELL SCIENCE
"... A cell’s behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond to and adapt to an everchanging environ ..."
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Cited by 203 (6 self)
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A cell’s behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond to and adapt to an everchanging environment. The large number of components, the degree of interconnectivity and the complex control of cellular networks are becoming evident in the integrated genomic and proteomic analyses that are emerging. It is increasingly recognized that the understanding of properties that arise from wholecell function require integrated, theoretical descriptions of the relationships between different cellular components. Recent
R (2006) Methods of robustness analysis for boolean models of gene control networks
 IET Systems Biology
"... As a discrete approach to genetic regulatory networks, Boolean models provide an essential qualitative description of the structure of interactions among genes and proteins. Boolean models generally assume only two possible states (expressed or not expressed) for each gene or protein in the network ..."
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Cited by 47 (17 self)
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As a discrete approach to genetic regulatory networks, Boolean models provide an essential qualitative description of the structure of interactions among genes and proteins. Boolean models generally assume only two possible states (expressed or not expressed) for each gene or protein in the network as well as a high level of synchronization among the various regulatory processes. In this paper, we discuss and compare two possible methods of adapting qualitative models to incorporate the continuoustime character of regulatory networks. The first method consists of introducing asynchronous updates in the Boolean model. In the second method, we adopt the approach introduced by L. Glass to obtain a set of piecewise linear differential equations which continuously describe the states of each gene or protein in the network. We apply both methods to a particular example: a Boolean model of the segment polarity gene network of Drosophila melanogaster. We analyze the dynamics of the model, and provide a theoretical characterization of the model’s gene pattern prediction as a function of the timescales of the various processes. 1
Molecular systems biology and control
 EUR. J. CONTROL 11:396–435
, 2005
"... This paper, prepared for a tutorial at the 2005 IEEE Conference on Decision and Control, presents an introduction to molecular systems biology and some associated problems in control theory. It provides an introduction to basic biological concepts, describes several questions in dynamics and control ..."
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Cited by 41 (8 self)
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This paper, prepared for a tutorial at the 2005 IEEE Conference on Decision and Control, presents an introduction to molecular systems biology and some associated problems in control theory. It provides an introduction to basic biological concepts, describes several questions in dynamics and control that arise in the field, and argues that new theoretical problems arise naturally in this context. A final section focuses on the combined use of graphtheoretic, qualitative knowledge about monotone buildingblocks and steadystate step responses for components.
Uncovering operational interactions in genetic networks using asynchronous boolean dynamics
 in "J. Theor. Biol
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The Effect of Negative Feedback Loops on the Dynamics of Boolean Networks
, 2008
"... Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distancetopositivefeedback which, in essence, captures the number of independent negative feedback loops in the network, a ..."
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Cited by 15 (2 self)
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Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distancetopositivefeedback which, in essence, captures the number of independent negative feedback loops in the network, a property inherent in the network topology. Through a computational study using Boolean networks, it is shown that distancetopositivefeedback has a strong influence on network dynamics and correlates very well with the number and length of limit cycles in the phase space of the network. To be precise, it is shown that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact that certain natural biological networks exhibit generally regular behavior and have fewer negative feedback loops than randomized networks with the same number of nodes and same connectivity.
Controllability of Boolean control networks via the PerronFrobenius theory
 AUTOMATICA
, 2012
"... Boolean control networks (BCNs) are recently attracting considerable interest as computational models for genetic and cellular networks. Addressing controltheoretic problems in BCNs may lead to a better understanding of the intrinsic control in biological systems, as well as to developing suitable ..."
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Cited by 13 (3 self)
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Boolean control networks (BCNs) are recently attracting considerable interest as computational models for genetic and cellular networks. Addressing controltheoretic problems in BCNs may lead to a better understanding of the intrinsic control in biological systems, as well as to developing suitable protocols for manipulating biological systems using exogenous inputs. We introduce two definitions for controllability of a BCN, and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive, respectively. Our analysis is based on a result that may be of independent interest, namely, a simple algebraic formula for the number of different control sequences that steer a BCN between given initial and final states in a given number of time steps, while avoiding a set of forbidden states.
Discrete Dynamic Modeling of Cellular Signaling Networks
"... Provided for noncommercial research and educational use only. Not for reproduction, distribution or commercial use. This chapter was originally published in the book Methods in Enzymology, Vol. 467, published by Elsevier, and the attached copy is provided by Elsevier for the author's benefit a ..."
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Cited by 12 (1 self)
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Provided for noncommercial research and educational use only. Not for reproduction, distribution or commercial use. This chapter was originally published in the book Methods in Enzymology, Vol. 467, published by Elsevier, and the attached copy is provided by Elsevier for the author's benefit and for the benefit of the author's institution, for noncommercial research and educational use including without limitation use in instruction at your institution, sending it to specific colleagues who know you, and providing a copy to your institution’s administrator. All other uses, reproduction and distribution, including without limitation commercial reprints, selling or licensing copies or access, or posting on open internet sites, your personal or institution’s website or repository, are prohibited. For exceptions,
2008b) Quantitative analysis of robustness and fragility in biological networks based on feedback dynamics
 Bioinformatics
"... Motivation: It has been widely reported that biological networks are robust against perturbations such as mutations. On the contrary, it has also been known that biological networks are often fragile against unexpected mutations. There is a growing interest in these intriguing observations and the u ..."
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Cited by 11 (2 self)
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Motivation: It has been widely reported that biological networks are robust against perturbations such as mutations. On the contrary, it has also been known that biological networks are often fragile against unexpected mutations. There is a growing interest in these intriguing observations and the underlying design principle that causes such robust but fragile characteristics of biological networks. For relatively small networks, a feedback loop has been considered as an important motif for realizing the robustness. It is still however not clear how a number of coupled feedback loops actually affect the robustness of large complex biological networks. In particular, the relationship between fragility and feedback loops has not yet been investigated till now. Results: Through extensive computational experiments, we found that networks with a larger number of positive feedback loops and a smaller number of negative feedback loops are likely to be more robust against perturbations. Moreover, we found that the nodes of a robust network subject to perturbations are mostly involved with a smaller number of feedback loops compared with the other nodes not usually subject to perturbations. This topological characteristic eventually makes the robust network fragile against unexpected mutations at the nodes not previously exposed to perturbations. Contact:
Optimal intervention in asynchronous genetic regulatory networks
 IEEE J. Sel. Topics Signal Process
"... Abstract—There is an ongoing effort to design optimal intervention strategies for discrete statespace synchronous genetic regulatory networks in the context of probabilistic Boolean networks; however, to date, there has been no corresponding effort for asynchronous networks. This paper addresses ..."
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Cited by 11 (9 self)
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Abstract—There is an ongoing effort to design optimal intervention strategies for discrete statespace synchronous genetic regulatory networks in the context of probabilistic Boolean networks; however, to date, there has been no corresponding effort for asynchronous networks. This paper addresses this issue by postulating two asynchronous extensions of probabilistic Boolean networks and developing control policies for both. The first extension introduces deterministic genelevel asynchronism into the constituent Boolean networks of the probabilistic Boolean network, thereby providing the ability to cope with temporal context sensitivity. The second extension introduces asynchronism at the level of the gene activity profiles. Whereas control policies for both standard probabilistic Boolean networks and the first proposed extension are characterized within the framework of Markov decision processes, asynchronism at the profile level results in control being treated in the framework of semiMarkov decision processes. The advantage of the second model is the ability to obtain the necessary timing information from sequences of geneactivity profile measurements. Results from the theory of stochastic control are leveraged to determine optimal intervention strategies for each class of proposed asynchronous regulatory networks, the objective being to reduce the time duration that the system spends in undesirable states. Index Terms—Asynchronous genetic regulatory networks, optimal stochastic control, semiMarkov decision processes, translational genomics. I.
A Pontryagin Maximum Principle for Multi–Input Boolean Control Networks
"... A Boolean network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean networks have been studied extensively as models for simple artificial neural networks. Recently, Boolean networks gained considerable interest as models for biological syst ..."
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Cited by 9 (3 self)
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A Boolean network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean networks have been studied extensively as models for simple artificial neural networks. Recently, Boolean networks gained considerable interest as models for biological systems composed of elements that can be in one of two possible states. Examples include genetic regulation networks, where the ON (OFF) state corresponds to the transcribed (quiescent) state of a gene, and cellular networks where the two possible logic states may represent the open/closed state of an ion channel, basal/high activity of an enzyme, two possible conformational states of a protein, etc. Daizhan Cheng developed an algebraic statespace representation for Boolean control networks using the semi–tensor product of matrices. This representation proved quite useful for studying Boolean control networks in a controltheoretic framework. Using this representation, we consider a Mayertype optimal control problem for Boolean control networks. Our main result is a necessary condition for optimality. This provides a parallel of Pontryagin’s maximum principle to Boolean control networks.