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39
Quantitative characterization of a mitotic cyclin threshold regulating exit from mitosis
, 2005
"... Regulation of cyclin abundance is central to eukaryotic cell cycle control. Strong overexpression of mitotic cyclins is known to lock the system in mitosis, but the quantitative behavior of the control system as this threshold is approached has only been characterized in the in vitro Xenopus extract ..."
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Regulation of cyclin abundance is central to eukaryotic cell cycle control. Strong overexpression of mitotic cyclins is known to lock the system in mitosis, but the quantitative behavior of the control system as this threshold is approached has only been characterized in the in vitro Xenopus extract system. Here, we quantitate the threshold for mitotic block in budding yeast caused by constitutive overexpression of the mitotic cyclin Clb2. Near this threshold, the system displays marked loss of robustness, in that loss or even heterozygosity for some regulators becomes deleterious or lethal, even though complete loss of these regulators is tolerated at normal cyclin expression levels. Recently, we presented a quantitative kinetic model of the budding yeast cell cycle. Here, we use this model to generate biochemical predictions for Clb2 levels, asynchronous as well as through the cell cycle, as the Clb2 overexpression threshold is approached. The model predictions compare well with biochemical data, even though no data of this type were available during model generation. The loss of robustness of the Clb2 overexpressing system is also predicted by the model. These results provide strong confirmation of the model’s predictive ability. This article was published online ahead of print in MBC in Press
On differentiation and homeostatic behaviours of Boolean dynamical systems
 of Lecture Notes in Computer Science
, 2007
"... Abstract. We study rules proposed by the biologist R. Thomas relating the structure of a concurrent system of interacting genes (represented by a signed directed graph called a regulatory graph) with its dynamical properties. We prove that the results in [10] are stable under projection, and this en ..."
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Abstract. We study rules proposed by the biologist R. Thomas relating the structure of a concurrent system of interacting genes (represented by a signed directed graph called a regulatory graph) with its dynamical properties. We prove that the results in [10] are stable under projection, and this enables us to relax the assumptions under which they are valid. More precisely, we relate here the presence of a positive (resp. negative) circuit in a regulatory graph to a more general form of biological differentiation (resp. of homeostasis). 1
Intervention in Gene Regulatory Networks via Greedy
 Control Policies Based on LongRun Behavior,” BMC Systems Biology
"... Abstract—A salient purpose for studying gene regulatory networks is to derive intervention strategies to identify potential drug targets and design genebased therapeutic intervention. Optimal and approximate intervention strategies based on the transition probability matrix of the underlying Markov ..."
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Abstract—A salient purpose for studying gene regulatory networks is to derive intervention strategies to identify potential drug targets and design genebased therapeutic intervention. Optimal and approximate intervention strategies based on the transition probability matrix of the underlying Markov chain have been studied extensively for probabilistic Boolean networks. While the key goal of control is to reduce the steadystate probability mass of undesirable network states, in practice it is important to limit collateral damage and this constraint should be taken into account when designing intervention strategies with network models. In this paper, we propose two new phenotypically constrained stationary control policies by directly investigating the effects on the network longrun behavior. They are derived to reduce the risk of visiting undesirable states in conjunction with constraints on the shift of undesirable steadystate mass so that only limited collateral damage can be introduced. We have studied the performance of the new constrained control policies together with the previous greedy control policies to randomly generated probabilistic Boolean networks. A preliminary example for intervening in a metastatic melanoma network is also given to show their potential application in designing genetic therapeutics to reduce the risk of entering both aberrant phenotypes and other ambiguous states corresponding to complications or collateral damage. Experiments on both random network ensembles and the melanoma network demonstrate that, in general, the new proposed control policies exhibit the desired performance. As shown by intervening in the melanoma network, these control policies can potentially serve as future practical gene therapeutic intervention strategies. Index Terms—Gene regulatory networks, probabilistic Boolean networks, network intervention, Markov chain, stationary control policy, melanoma. Ç
Boolean Dynamics of Biological Networks with Multiple Coupled Feedback Loops
, 2007
"... Boolean networks have been frequently used to study the dynamics of biological networks. In particular, there have been various studies showing that the network connectivity and the update rule of logical functions affect the dynamics of Boolean networks. There has been, however, relatively little ..."
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Boolean networks have been frequently used to study the dynamics of biological networks. In particular, there have been various studies showing that the network connectivity and the update rule of logical functions affect the dynamics of Boolean networks. There has been, however, relatively little attention paid to the dynamical role of a feedback loop, which is a circular chain of interactions between Boolean variables. We note that such feedback loops are ubiquitously found in various biological systems as multiple coupled structures and they are often the primary cause of complex dynamics. In this article, we investigate the relationship between the multiple coupled feedback loops and the dynamics of Boolean networks. We show that networks have a larger proportion of basins corresponding to fixedpoint attractors as they have more coupled positive feedback loops, and a larger proportion of basins for limitcycle attractors as they have more coupled negative feedback loops.
Shaping Robust System through Evolution
, 807
"... Biological functions are generated as a result of developmental dynamics that form phenotypes governed by genotypes. The dynamical system for development is shaped through genetic evolution following natural selection based on the fitness of the phenotype. Here we study how this dynamical system is ..."
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Biological functions are generated as a result of developmental dynamics that form phenotypes governed by genotypes. The dynamical system for development is shaped through genetic evolution following natural selection based on the fitness of the phenotype. Here we study how this dynamical system is robust to noise during development and to genetic change by mutation. We adopt a simplified transcription regulation network model to govern gene expression, which gives a fitness function. Through simulations of the network that undergoes mutation and selection, we show that a certain level of noise in gene expression is required for the network to acquire both types of robustness. The results reveal how the noise that cells encounter during development shapes any network’s robustness, not only to noise but also to mutations. We also establish a relationship between developmental and mutational robustness through phenotypic variances caused by genetic variation and epigenetic noise. A universal relationship between the two variances is
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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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.
Mechanistic insights into metabolic disturbance during type2 diabetes and obesity using qualitative networks
 T. Comp. Sys. Biology
"... Abstract. In many complex biological processes quantitative data is scarce, which makes it problematic to create accurate quantitative models of the system under study. In this work, we suggest that the Qualitative Networks (QNs) framework is an appropriate approach for modeling biological networks ..."
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Abstract. In many complex biological processes quantitative data is scarce, which makes it problematic to create accurate quantitative models of the system under study. In this work, we suggest that the Qualitative Networks (QNs) framework is an appropriate approach for modeling biological networks when only little quantitative data is available. Using QNs we model a metabolic network related to fat metabolism, which plays an important role in type2 diabetes and obesity. The model is based on gene expression data of the regulatory network of a key transcription factor Mlxipl. Our model reproduces the experimental data and allows insilico testing of new hypotheses. Specifically, the QN framework allows to predict new modes of interactions between components within the network. Furthermore, we demonstrate the value of the QNs approach in directing future experiments and its potential to facilitate our understanding of the modeled system.
Parameter estimation for Boolean models of biological networks
, 2009
"... Boolean networks have long been used as models of molecular networks and play an increasingly important role in systems biology. This paper describes a software package, Polynome, offered as a web service, that helps users construct Boolean network models based on experimental data and biological in ..."
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Boolean networks have long been used as models of molecular networks and play an increasingly important role in systems biology. This paper describes a software package, Polynome, offered as a web service, that helps users construct Boolean network models based on experimental data and biological input. The key feature is a discrete analog of parameter estimation for continuous models. With only experimental data as input, the software can be used as a tool for reverseengineering of Boolean network models from experimental time course data.
Observability of Boolean Networks: A GraphTheoretic Approach
, 2013
"... Boolean networks (BNs) are discretetime dynamical systems with Boolean statevariables and outputs. BNs are recently attracting considerable interest as computational models for genetic and cellular networks. We consider the observability of BNs, that is, the possibility of uniquely determining the ..."
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Boolean networks (BNs) are discretetime dynamical systems with Boolean statevariables and outputs. BNs are recently attracting considerable interest as computational models for genetic and cellular networks. We consider the observability of BNs, that is, the possibility of uniquely determining the initial state given a time sequence of outputs. Our main result is that determining whether a BN is observable is NPhard. This holds for both synchronous and asynchronous BNs. Thus, unless P=NP, there does not exist an algorithm with polynomial time complexity that solves the observability problem. We also give two simple algorithms, with exponential complexity, that solve this problem. Our results are based on combining the algebraic representation of BNs derived by D. Cheng with a graphtheoretic approach. Some of the theoretical results are applied to study the observability of a BN model of the mammalian cell cycle.
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.