Gene expression model (in)validation by Fourier analysis

The determination of the right model structure describing a gene regulation network and the identification of its parameters are major goals in systems biology. The task is often hampered by the lack of relevant experimental data with sufficiently low noise level, but the subset of genes whose concentration levels exhibit an oscillatory behavior in time can readily be analyzed on the basis of their Fourier spectrum, known to turn complex signals into few relatively noise-free parameters. Such genes therefore offer opportunities of understanding gene regulation quantitatively.

Fourier analysis is applied to data on gene expression levels in mouse liver cells that oscillate according to the circadian rhythm. Several model structures in the form of linear and nonlinear differential equations are matched to the data and it is shown that although the considered models can reproduce many features of the oscillatory patterns, some can be excluded on the basis of Fourier analysis without appeal to prior knowledge of regulatory pathways. A systematic method for testing models is also proposed based on measuring the effects of variations in gene copy-number on the expression levels of coupled genes.

Fourier analysis is a technique that is well-adapted to the study of biological oscillators and can be used instead or in addition to conventional modeling techniques. Its usefulness will increase as more high-resolution data become available.