Autoosc

Autoosc analyzes time-series oscillatory signals by extracting information from Fourier spectra to identify and parameterize candidate first-order differential equation models of biological and chemical systems.

Key Features:

• Implementation: Implemented as a Mathematica package for computational analysis of oscillatory signals.
• Fourier spectral analysis: Extracts meaningful information from the Fourier spectra of time-series signals.
• Automated model matching: Automatically matches observed signal shapes to a wide array of pre-defined model structures.
• Model class: Uses models based on first-order differential equations representing potential oscillation-generating mechanisms.
• Parameter estimation: Computes parameter values for each candidate model via mode decomposition of the signals.
• Algebraic formulation: Formulates the matching process as systems of simultaneous polynomial equations.
• Model enumeration: Enumerates and returns lists of models consistent with the observed data, including alternative equations that can yield excellent fits.

Scientific Applications:

• Model validation: Identifies model structures consistent with observed oscillatory data for validation of theoretical models.
• Interaction discovery and classification: Discovers and classifies types of interactions that can generate observed oscillations.
• Experimental design optimization: Informs and supports optimization of experimental designs by narrowing candidate model sets.
• Circadian rhythm analysis: Applied to mouse microarray time-series to identify candidate model structures describing gene regulatory interactions in circadian rhythms.

Methodology:

Matches observed signal shapes to pre-defined model structures based on first-order differential equations, uses Fourier spectral analysis and mode decomposition to compute parameter values, and formulates the matching as systems of simultaneous polynomial equations.