Linear and Nonlinear Modes and Data Signatures in Dynamic Systems Biology Models

The particulars of stimulus-response experiments performed on dynamic biosystems clearly limit what one can learn and validate about their structural interconnectivity (topology), even when collected kinetic output data are perfect (noise-free). As always, available access ports and other data limitations rule. For linear systems, exponential modes, visible and hidden, play an important role in understanding data limitations, embodied in what we call dynamical signatures in the data. We show here how to circumscribe and analyze modal response data in compartmentalizing model structures-so that modal analysis can be used constructively in systems biology mechanistic model building-for some nonlinear (NL) as well as linear biosystems. We do this by developing and exploiting the modal basis for dynamical signatures in hypothetical (perfect) input-output (I-O) data associated with a (mechanistic) structural model-one that includes inputs and outputs explicitly. The methodology establishes model dimensionality (size and complexity) from particular I-O datasets; helps select among multiple candidate models (model distinguishability); helps in designing new I-O experiments to extract "hidden" structure; and helps to simplify (reduce) models to their essentials. These modal analysis tools are introduced to NL enzyme-regulated and protein-protein interaction biosystems via nonlinear normal mode (NNM) and quasi-steady state approximation (QSSA) analyses and unified with linear models on invariant 2-dimensional manifolds in phase space, with properties similarly informative about their dominant dynamical properties. Some automation of these highly technical aspects of biomodeling is also introduced.