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

TL;DR

This paper investigates the minimal data requirements and optimal data set properties for reverse engineering biochemical networks using discrete dynamical systems, revealing fundamental limitations in data sufficiency.

Contribution

It characterizes minimal and optimal data sets for a top-down reverse engineering algorithm and introduces a generalized method with a probability formula for correct model identification.

Findings

Optimal data sets are characterized by a geometric 'general position' property.

The probability of correctly identifying the model decreases exponentially with the number of variables.

Even with optimal data, reverse engineering remains infeasible without enormous data quantities.

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. 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 r^(q^n), where q is a natural number and 0<r<1. 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.