We will discuss about “Frequency Spectra and the Color of Cellular Noise”, bioRxiv (2020).

The invention of the Fourier integral in the 19th century laid the foundation for 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 single-cell trajectories, owing to their distinctive noisy character forged by the underlying discrete stochastic dynamics of the living cell, typically modelled as a continuous-time Markov chain (CTMC). Here we draw on stochastic process theory to develop a spectral theory and computational methodologies tailored specifically to the computation and analysis of frequency spectra of noisy cellular networks. For linear 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 methods to obtain accurate Padé approximants 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.