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Reverse engineering time discrete finite dynamical systems: a feasible undertaking?

Delgado-Eckert E - PLoS ONE (2009)

Bottom Line: We found minimal requirements on a data set based on how many terms the functions to be reverse engineered display.Unfortunately, this formula converges to zero as fast as , where and .Such large data sets are experimentally impossible to generate with today's technologies.

View Article: PubMed Central - PubMed

Affiliation: Centre for Mathematical Sciences, Technische Universität München, Garching, Germany.

ABSTRACT
With the advent of high-throughput profiling methods, interest in reverse engineering the structure and dynamics of biochemical networks is high. Recently an algorithm for reverse engineering of biochemical networks was developed by Laubenbacher and Stigler. It is a top-down approach using time discrete dynamical systems. One of its key steps includes the choice of a term order, a technicality imposed by the use of Gröbner-bases calculations. The aim of this paper is to identify minimal requirements on data sets to be used with this algorithm and to characterize optimal data sets. We found minimal requirements on a data set based on how many terms the functions to be reverse engineered display. Furthermore, we identified optimal data sets, which we characterized using a geometric property called "general position". Moreover, we developed a constructive method to generate optimal data sets, provided a codimensional condition is fulfilled. In addition, we present a generalization of their algorithm that does not depend on the choice of a term order. For this method we derived a formula for the probability of finding the correct model, provided the data set used is optimal. We analyzed the asymptotic behavior of the probability formula for a growing number of variables n (i.e. interacting chemicals). Unfortunately, this formula converges to zero as fast as , where and . Therefore, even if an optimal data set is used and the restrictions in using term orders are overcome, the reverse engineering problem remains unfeasible, unless prodigious amounts of data are available. Such large data sets are experimentally impossible to generate with today's technologies.

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Related in: MedlinePlus

The notion of general position.A two-dimensional representation of the space of functions . Within this space, two one-dimensional subspaces are depicted. One subspace (green) is in general position, while the other one (red) is not.
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pone-0004939-g002: The notion of general position.A two-dimensional representation of the space of functions . Within this space, two one-dimensional subspaces are depicted. One subspace (green) is in general position, while the other one (red) is not.

Mentions: Figure 2 shows two one-dimensional subspaces. The red subspace is not in general position since its basis cannot be extended to a basis of the entire space (2 dimensions) by adjoining the first canonical unit vector (horizontal black arrow) to it.


Reverse engineering time discrete finite dynamical systems: a feasible undertaking?

Delgado-Eckert E - PLoS ONE (2009)

The notion of general position.A two-dimensional representation of the space of functions . Within this space, two one-dimensional subspaces are depicted. One subspace (green) is in general position, while the other one (red) is not.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2654658&req=5

pone-0004939-g002: The notion of general position.A two-dimensional representation of the space of functions . Within this space, two one-dimensional subspaces are depicted. One subspace (green) is in general position, while the other one (red) is not.
Mentions: Figure 2 shows two one-dimensional subspaces. The red subspace is not in general position since its basis cannot be extended to a basis of the entire space (2 dimensions) by adjoining the first canonical unit vector (horizontal black arrow) to it.

Bottom Line: We found minimal requirements on a data set based on how many terms the functions to be reverse engineered display.Unfortunately, this formula converges to zero as fast as , where and .Such large data sets are experimentally impossible to generate with today's technologies.

View Article: PubMed Central - PubMed

Affiliation: Centre for Mathematical Sciences, Technische Universität München, Garching, Germany.

ABSTRACT
With the advent of high-throughput profiling methods, interest in reverse engineering the structure and dynamics of biochemical networks is high. Recently an algorithm for reverse engineering of biochemical networks was developed by Laubenbacher and Stigler. It is a top-down approach using time discrete dynamical systems. One of its key steps includes the choice of a term order, a technicality imposed by the use of Gröbner-bases calculations. The aim of this paper is to identify minimal requirements on data sets to be used with this algorithm and to characterize optimal data sets. We found minimal requirements on a data set based on how many terms the functions to be reverse engineered display. Furthermore, we identified optimal data sets, which we characterized using a geometric property called "general position". Moreover, we developed a constructive method to generate optimal data sets, provided a codimensional condition is fulfilled. In addition, we present a generalization of their algorithm that does not depend on the choice of a term order. For this method we derived a formula for the probability of finding the correct model, provided the data set used is optimal. We analyzed the asymptotic behavior of the probability formula for a growing number of variables n (i.e. interacting chemicals). Unfortunately, this formula converges to zero as fast as , where and . Therefore, even if an optimal data set is used and the restrictions in using term orders are overcome, the reverse engineering problem remains unfeasible, unless prodigious amounts of data are available. Such large data sets are experimentally impossible to generate with today's technologies.

Show MeSH
Related in: MedlinePlus