Boolean networks with biologically relevant rules show ordered behavior

Nikolajewa, Swetlana; Friedel, Maik; Wilhelm, Thomas

doi:10.1016/j.biosystems.2006.06.007

Cited by 51 publications

(56 citation statements)

References 25 publications

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“…It is usually the case that additional information on the likely structure of the model is available. For illustration purposes, we follow the work of [32] and references therein, showing that a large part of the known gene activation rules fall in a subclass of hierarchically (or nested) canalizing functions [33]. Note that hierarchically canalizing functions are a proper subset of unate functions.…”

Section: Exploiting a Priori Knowledgementioning

confidence: 99%

Structural identification of unate-like genetic network models from time-lapse protein concentration measurements

Porreca

Cinquemani

Lygeros

et al. 2010

49th IEEE Conference on Decision and Control (CDC)

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We consider the problem of learning dynamical models of genetic regulatory networks from time-lapse measurements of gene expression. In our previous work [1], we described a method for the structural and parametric identification of ODE models that makes use of concurrent measurements of concentrations and synthesis rates of the gene products, and requires the knowledge of the noise statistics. In this paper we assume all these pieces of information are not simultaneously available. In particular we propose extensions of [1] that make the method applicable to protein concentration measurements only. We discuss the performance of the method on experimental data from the network IRMA, a benchmark synthetic network engineered in yeast Saccharomices cerevisiae. Abstract-We consider the problem of learning dynamical models of genetic regulatory networks from time-lapse measurements of gene expression. In our previous work [1], we described a method for the structural and parametric identification of ODE models that makes use of concurrent measurements of concentrations and synthesis rates of the gene products, and requires the knowledge of the noise statistics. In this paper we assume all these pieces of information are not simultaneously available. In particular we propose extensions of [1] that make the method applicable to protein concentration measurements only. We discuss the performance of the method on experimental data from the network IRMA, a benchmark synthetic network engineered in yeast Saccharomices cerevisiae.

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Section: Exploiting a Priori Knowledgementioning

confidence: 99%

Structural identification of unate-like genetic network models from time-lapse protein concentration measurements

Porreca

Cinquemani

Lygeros

et al. 2010

49th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

“…HCFs received much attention since it was observed that the vast majority of the known regulatory interactions between genes can be written in terms of HFC-type rules, see [5], [4], [6]. In particular, two specific subfamilies of HCFs, termed S 0 and S 1 , appear to explain most of the known interactions.…”

Section: Boolean Rules: Hierarchically Canalizing Functionsmentioning

confidence: 99%

“…. , , exists, see [4], but we do not need it here.) In order to express canalizing rules by algebraic relationships, for any x j ∈ {0, 1}, let us overload the notation by defining σ + (x j ) = x j and σ − (x j ) = 1 − x j .…”

Section: Boolean Rules: Hierarchically Canalizing Functionsmentioning

confidence: 99%

“…The key observation is that, out of all possible dynamical interactions among genes, it is likely that a restricted family of interaction patterns is found in the actual biological systems. In the context of Boolean networks, it was observed in the literature that most of the known gene activation rules fall in a specific class of Boolean functions, namely the Hierarchically Canalizing Functions (HCF) [4], [5], [6]. When translated into a kinetic modelling framework, this means that a restricted set of nonlinearities should be considered for the modelling and identification.…”

Section: Introductionmentioning

confidence: 99%

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Canalizing structure of genetic network dynamics: modelling and identification via mixed-integer programming

Cinquemani

Porreca

Lygeros

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-We discuss the identification of genetic networks based on a class of boolean gene activation rules known as hierarchically canalizing functions. We introduce a class of kinetic models for the concentration of the proteins in the network built on a family of canalizing functions that has been shown to capture the vast majority of the known interaction networks. The simultaneous identification of the structure and of the parameters of the model from experimental data is addressed based on a mixed integer parametrization of the model class. The resulting regression problem is solved numerically via standard branch-and-bound techniques. The performance of the method is tested on simulated data generated by a simple model of Escherichia coli nutrient stress response.

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“…Because from a historical perspective the expression of genes has often been thought of in terms of ON/OFF (e.g., expressed or not expressed), the employment of Boolean models seemed quite natural. It is then no surprise that many subsequent Boolean models of gene networks and their analysis have been developed [14][15][16][17][18][19]. However, what about the modeling of the even more complex modern networks that make up the cellular interactome?…”

Section: Introductionmentioning

confidence: 99%

Boolean Modeling of Biochemical Networks

Helikar¹,

Kochi

Konvalina

et al. 2011

TOBIOIJ

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Abstract:The use of modeling to observe and analyze the mechanisms of complex biochemical network function is becoming an important methodological tool in the systems biology era. Number of different approaches to model these networks have been utilized--they range from analysis of static connection graphs to dynamical models based on kinetic interaction data. Dynamical models have a distinct appeal in that they make it possible to observe these networks in action, but they also pose a distinct challenge in that they require detailed information describing how the individual components of these networks interact in living cells. Because this level of detail is generally not known, dynamic modeling requires simplifying assumptions in order to make it practical. In this review Boolean modeling will be discussed, a modeling method that depends on the simplifying assumption that all elements of a network exist only in one of two states.Keywords: Systems biology, dynamical modeling, signal transduction, boolean networks.The modern era of cellular biochemistry has been characterized by the discovery of large interaction networks that are notable for their highly nonlinear connection structures. Such structures complicate study since they are often quite difficult to reduce into linear subsets that function in isolation from the embedding network [1,2]. It is for this reason that the concept of "systems biology" has been developed and is now being applied to these complicated biochemical networks [1,3,4].One of the first steps taken toward applying a systems approach to understanding biochemical networks was to begin organizing the connection information determined in the laboratory by creating connection maps (wiring diagrams) that could then be analyzed using graph theory concepts. While these studies have been highly successful [5], the fact that cells are dynamical systems means the next major step in the study of these systems involves the creation of models that take into account how they move and function in time. Thus we are now in a new era of creating large-scale dynamical models of biochemical systems.An obvious choice for the modeling of dynamical systems is to describe the system with a system of differential equations, and this approach has been used extensively to study protein and/or gene interactions in a variety of relatively small models (for examples, see [6][7][8][9]). One of the advantages of continuous modeling via differential equations is that one can potentially describe molecular interactions with high precision and in quantitative terms that correspond to realistic laboratory measurements. However, that precision tends to make them computationally unwieldy for the large scale models necessary for the systems approach. There *Address correspondence to this author at the Department of Mathematics, University of Nebraska at Omaha, 6001 Dodge Street, Omaha, NE 68182, USA; Tel: 402 554-3110: Fax: 402 554-2975; E-mail: jrogers@unmc.edu is currently a great deal of work being done in order to simpl...

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Boolean networks with biologically relevant rules show ordered behavior

Cited by 51 publications

References 25 publications

Structural identification of unate-like genetic network models from time-lapse protein concentration measurements

Structural identification of unate-like genetic network models from time-lapse protein concentration measurements

Canalizing structure of genetic network dynamics: modelling and identification via mixed-integer programming

Boolean Modeling of Biochemical Networks

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