Recent innovations in microfluidics make it possible to quantitatively measure single-cell dynamics for long periods of time over multiple generations 3, 4, 5. The rapid pace of development in imaging technology coupled with advanced image processing techniques has made it viable to obtain high-resolution time-lapse live-cell data for a multitude of cell-types and biological processes. Modern microscopy and the advent of a wide array of fluorescent proteins 1 have afforded scientists the unprecedented ability to monitor the dynamics of living biological cells 2. Several examples are presented to illustrate how our results provide frequency-based methods for the design and analysis of noisy intracellular networks. Specifically, we develop a method to compute the frequency spectrum for general nonlinear networks, and for linear networks we present a decomposition that expresses the frequency spectrum in terms of its sources. Here we develop a spectral theory and computational methodologies tailored specifically to the computation and analysis of frequency spectra of noisy intracellular networks. While this idea has precipitated several scientific and technological advances, its impact has been fairly limited in cell biology, largely due to the difficulties in connecting the underlying noisy intracellular networks to the frequency content of observed single-cell trajectories. This integral decomposes a temporal signal into its frequency components, providing deep insights into its generating process. The invention of the Fourier integral in the 19th century laid the foundation for modern spectral analysis methods.

Spectra s2 parts