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175
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 199 (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
Robustness and fragility of boolean models for genetic regulatory networks
 J. Theoretical Biology
, 2005
"... Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or logical approaches. We propose a new modeling framework for gene ..."
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Cited by 70 (10 self)
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Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or logical approaches. We propose a new modeling framework for gene regulatory networks, that combines the intuitive appeal of a qualitative description of gene states with a high flexibility in incorporating stochasticity in the duration of cellular processes. We apply our methods to the regulatory network of the segment polarity genes, thus gaining novel insights into the development of gene expression patterns. For example, we show that very short synthesis and decay times can perturb the wild type pattern. On the other hand, separation of timescales between pre and posttranslational processes and a minimal prepattern ensure convergence to the wild type expression pattern regardless of fluctuations.
A computational algebra approach to the reverse engineering of gene regulatory networks
 Journal of Theoretical Biology
, 2004
"... This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is timediscrete deterministic dynamical systems, with a finite set of states for each of the variables. The simplest examples of such models are Boolean networks, in whi ..."
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Cited by 65 (9 self)
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This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is timediscrete deterministic dynamical systems, with a finite set of states for each of the variables. The simplest examples of such models are Boolean networks, in which variables have only two possible states. The use of a larger number of possible states allows a finer discretization of experimental data and more than one possible mode of action for the variables, depending on threshold values. Furthermore, with a suitable choice of state set, one can employ powerful tools from computational algebra, that underlie the reverseengineering algorithm, avoiding costly enumeration strategies. To perform well, the algorithm requires wildtype together with perturbation time courses. This makes it suitable for small to mesoscale networks rather than networks on a genomewide scale. An analysis of the complexity of the algorithm is performed. The algorithm is validated on a recently published Boolean network model of segment polarity development in Drosophila melanogaster.
A gene regulatory network model for cellfate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles
 Plant Cell
, 2004
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Graphic Requirements for Multistability and Attractive Cycles in a Boolean Dynamical Framework
, 2008
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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 (16 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 37 (9 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.
Reverseengineering of polynomial dynamical systems
 Advances in Applied Mathematics, 39:477–489
, 2007
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Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence
, 2007
"... The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs) from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation ..."
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Cited by 17 (6 self)
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The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs) from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation is that the characteristics of a single Boolean network without perturbation may be determined by its pairwise transitions. Because the network function is fixed and there are no perturbations, a given state will always be followed by a unique state at the succeeding time point. Thus, a transition counting matrix compiled over a data sequence will be sparse and contain only one entry per line. If the network also has perturbations, with small perturbation probability, then the transition counting matrix would have some insignificant nonzero entries replacing some (or all) of the zeros. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1) separate the data sequence into “pure ” subsequences corresponding to constituent Boolean networks; (2) given a subsequence, infer a Boolean network; and (3) infer the probabilities of perturbation, the probability of there being a switch between constituent Boolean networks, and the selection probabilities governing