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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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

Edgar Delgado-Eckert¹

¹Centre for Mathematical Sciences, Technische Universität München, Garching, Germany.

|March 20, 2009

Summary

Reverse engineering biochemical networks requires specific data sets. Even with optimized data and improved algorithms, accurately reconstructing these complex systems remains challenging due to data limitations.

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Area of Science:

Biochemistry
Systems Biology
Computational Biology

Background:

High-throughput profiling methods have increased interest in reverse engineering biochemical networks.
A recent algorithm by Laubenbacher and Stigler uses discrete dynamical systems for this purpose.
This algorithm's reliance on Gröbner-bases calculations necessitates a specific term order choice.

Purpose of the Study:

To identify minimal data set requirements for the reverse engineering algorithm.
To characterize optimal data sets for improved accuracy.
To develop a generalized algorithm independent of term order choice.

Main Methods:

Determining minimal data set requirements based on function terms.
Characterizing optimal data sets using the geometric property of "general position".
Developing a constructive method for generating optimal data sets under a codimensional condition.

Main Results:

Minimal data requirements were identified based on the number of terms in functions.
Optimal data sets were characterized by "general position".
A generalized algorithm was developed, removing the term order dependency.
A probability formula for model recovery was derived, showing rapid convergence to zero.

Conclusions:

The reverse engineering of biochemical networks is computationally challenging.
Even with optimal data sets and generalized algorithms, the problem remains largely unfeasible.
Prodigious amounts of data, currently experimentally unattainable, are required for success.