### Comparative identification of differential interactions from trajectories of dynamic biological networks

*Z. Ouyang*

*and M. Song*

#### Abstract

It is often challenging to reconstruct accurately a complete dynamic biological network due to the scarcity of data collected in cost-effective experiments. This paper addresses the possibility of comparatively identifying qualitative interaction shifts between two dynamical networks from comparative time course data. An innovative approach is developed to achieve differential interaction detection by statistically comparing the trajectories, instead of numerically comparing the reconstructed interactions. The core of this approach is a statistical heterogeneity test that compares two multiple linear regression equations for the derivatives in nonlinear ordinary differential equations, statistically instead of numerically. In detecting any shift of an interaction, the uncertainty in estimated regression coefficients is taken into account by this test, while it is ignored by the reconstruction-based numerical comparison. The heterogeneity test is accomplished by assessing the gain in goodnessof-fit from using a single common interaction to using a pair of differential interactions. Compared with previous numerical comparison methods, the proposed statistical comparison always achieves higher statistical power. As sample size decreases or noise increases in a certain range, the improvement becomes substantial. The advantage is illustrated by a simulation study on the statistical power as functions of the noise level, the sample size, and the interaction complexity. This method is also capable of detecting interaction shifts in the oscillated and excitable domains of a dynamical system model describing cdc2-cyclin interactions during cell division cycle. Generally, the described approach is applicable to comparing dynamical systems of additive nonlinear ordinary differential equations.

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