PT - JOURNAL ARTICLE AU - Ankit Gupta AU - Mustafa Khammash TI - Frequency Spectra and the Color of Cellular Noise AID - 10.1101/2020.09.15.292664 DP - 2020 Jan 01 TA - bioRxiv PG - 2020.09.15.292664 4099 - http://biorxiv.org/content/early/2020/09/16/2020.09.15.292664.short 4100 - http://biorxiv.org/content/early/2020/09/16/2020.09.15.292664.full AB - The invention of the Fourier integral in the 19th century laid the foundation for today’s modern spectral analysis methods. By decomposing a (time) signal into its essential frequency components, these methods uncovered deep insights into the signal and its generating process, precipitating tremendous inventions and discoveries in many fields of engineering, technology, and physical science. In systems and synthetic biology, however, the impact of frequency methods has been far more limited despite their huge promise. This is in large part due to the difficulty of gleaning spectral information from singlecell trajectories, owing to their distinctive noisy character forged by the underlying discrete stochastic dynamics of the living cell. Here we develop new theory and methodologies tailored specifically to the computation and analysis of frequency spectra of noisy cellular networks. We draw on stochastic process theory to develop a spectral theory and computational methods for continuous-time Markov chains (CTMC), which are widely used models for discrete stochastic dynamics of biochemical reactions. For linear cellular networks we present exact expressions for the frequency spectrum and use them to decompose the variability of a signal into its sources. For nonlinear networks, we develop a method to obtain an accurate Padé approximant of the spectrum from a single Monte Carlo trajectory simulation. Our results provide new conceptual and practical methods for the analysis and design of noisy cellular networks based on their output frequency spectra. We illustrate this through diverse case studies in which we show that the single-cell frequency spectrum enables topology discrimination, synthetic oscillator optimization, cybergenetic controller design, and systematic investigation of stochastic entrainment.Competing Interest StatementThe authors have declared no competing interest.