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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.
Integrating Data Clustering and Visualization for the Analysis of 3D Gene Expression Data
 IEEE Transactions on Computational Biology and Bioinformatics
, 2010
"... Copyright Notice: ©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of thi ..."
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Cited by 14 (3 self)
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Copyright Notice: ©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the
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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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.
Symbolic approaches to finding control strategies in boolean networks
 Proceedings of The Sixth AsiaPacific Bioinformatics Conference, (APBC
, 2008
"... We present an exact algorithm, based on techniques from the field of Model Checking, for finding control policies for Boolean networks (BN) with control nodes. Given a BN, a set of starting states, I, a set of goal states, F, and a target time, t, our algorithm automatically finds a sequence of cont ..."
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We present an exact algorithm, based on techniques from the field of Model Checking, for finding control policies for Boolean networks (BN) with control nodes. Given a BN, a set of starting states, I, a set of goal states, F, and a target time, t, our algorithm automatically finds a sequence of control signals that deterministically drives the BN from I to F at, or before time t, or else guarantees that no such policy exists. Despite recent hardnessresults for finding control policies for BNs, we show that, in practice, our algorithm runs in seconds to minutes on over 13,400 BNs of varying sizes and topologies, including a BN model of embryogenesis in D. melanogaster with 15,360 Boolean variables. We then extend our method to automatically identify a set of Boolean transfer functions that reproduce the qualitative behavior of gene regulatory networks. Specifically, we automatically (re)learn a BN model of D. melanogaster embryogenesis in 5.3 seconds, from a Computational cellular and systems modeling is playing an increasingly important role in biology, bioengineering, and medicine. The promise of computer modeling is that it becomes a conduit through which reductionist data can be translated into scientific discoveries, clinical practice, and the design of new technologies. The reality of modeling is that there are still a number of unmet
Monomial dynamical systems over finite fields
 COMPLEX SYSTEMS
, 2006
"... An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over an arbitrary finite field. For systems that can be described by monomials, one can obtain information about t ..."
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Cited by 12 (4 self)
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An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over an arbitrary finite field. For systems that can be described by monomials, one can obtain information about the limit cycle structure from the structure of the monomials. In particular, the paper contains a sufficient condition for a monomial system to have only fixed points as limit cycles. The condition is derived by reducing the problem to the study of a Boolean monomial system and a linear system over a finite ring.
Dynamic patterns of gene regulation I: Simple twogene systems
 Journal of Theoretical Biology
, 2007
"... SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peerreviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for pap ..."
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SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peerreviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu
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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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,
SA: Adaptive walks in a gene network model of morphogenesis: insights into the Cambrian explosion
 Int J Dev Biol
"... SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peerreviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for pap ..."
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Cited by 11 (1 self)
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SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peerreviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu SANTA FE INSTITUTE Adaptive walks in a gene network model of morphogenesis: insights into the Cambrian explosion
On the detection of gene network interconnections using directed mutual information
 in ITA, SanDeigo
, 2007
"... Abstract — In this paper, we suggest and validate a systematic method for inferring biological gene networks. So far, the identification of even a small portion of gene networks has been achieved by consensus over multiple cellular biology labs. A gene refers to the sequence of DNA that encodes a si ..."
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Abstract — In this paper, we suggest and validate a systematic method for inferring biological gene networks. So far, the identification of even a small portion of gene networks has been achieved by consensus over multiple cellular biology labs. A gene refers to the sequence of DNA that encodes a single protein. Proteins encoded by a gene can regulate other genes in the living cell, forming a complex network that determines cell growth, health, and disease. We view gene networks as dynamic systems, in discretetime, formed by the interconnection among genes, which are abstracted as nodes whose state takes values in the range [1, 1]. The state of each node is a function of the past values of the state of other nodes in the network. The edges of the gene network and their directions indicate functional dependence among the nodes state and their causality relationships, respectively. New engineering developments, such as quantum dot sensors, will allow measurement of gene dynamics inside living cells. From gene timecourse data, we show how each edge in a gene network can be inferred using the concept of directed mutual information. We validated our method using small networks generated randomly, as well as for the known network for flagella biosynthesis in E.Coli, which we used to generate gene timecourse data (with noise) in simulations. For acyclic graphs with 7 (or fewer) genes with summation operations only, we were able to infer all edges perfectly. We also present a heuristic method to deal with Boolean operations. I.
From minimal signed circuits to the dynamics of Boolean regulatory networks
, 2008
"... It is acknowledged that the presence of positive or negative circuits in regulatory networks such as genetic networks is linked to the emergence of significant dynamical properties such as multistability (involved in differentiation) and periodic oscillations (involved in homeostasis). Rules propose ..."
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Cited by 10 (5 self)
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It is acknowledged that the presence of positive or negative circuits in regulatory networks such as genetic networks is linked to the emergence of significant dynamical properties such as multistability (involved in differentiation) and periodic oscillations (involved in homeostasis). Rules proposed by the biologist R. Thomas assert that these circuits are necessary for such dynamical properties. These rules have been studied by several authors. Their obvious interest is that they relate the rather simple information contained in the structure of the network (signed circuits) to its much more complex dynamical behaviour. We prove in this article a nontrivial converse of these rules, namely that certain positive or negative circuits in a regulatory graph are actually sufficient for the observation of a restricted form of the corresponding dynamical property, differentiation or homeostasis. More precisely, the crucial property that we require is that the circuit be globally minimal. We then apply these results to the vertebrate immune system, and show that the 2 minimal functional positive circuits of the model indeed behave as modules which combine to explain the presence of the 3 stable states corresponding to the Th0, Th1 and Th2 cells.