Narrow Results

Oscillations exist at all levels of biological systems and are often crucial for their proper functioning. Among the various types of oscillations, limit cycles have received particular attention for more than one hundred years. Specifically, theorems have been established that characterize whether a system might have the capability of exhibiting limit cycles. However, the practical application of these theorems is usually cumbersome and there are hardly any guidelines for devising de novo models that exhibit limit cycles of a desired form. In this paper, we propose a simple method for constructing and customizing stable limit cycles in two-dimensional systems according to desired features, including frequency, amplitude, and phase shift between system variables. The method is based on "inverting" a criterion proposed by Lewis for characterizing oscillations in two-dimensional S-system models. First, we execute comprehensive simulations that result in a set of over 2000 prototype limit cycles. Second, we show with examples how these prototypes can be further customized to adhere to predetermined specifications. This two-step process is fast and efficacious, especially when one considers the paucity of alternative methods. Finally, we illustrate how one may create systems with more complex dynamics by modulating the prototypes with external input signals.

Novel high-throughput measurement techniques in vivo are beginning to produce dense high-quality time series which can be used to investigate the structure and regulation of biochemical networks. We propose an automated information extraction procedure which takes advantage of the unique S-system structure and supports model building from time traces, curve fitting, model selection, and structure identification based on parameter estimation. The procedure comprises of three modules: model Generation, parameter estimation or model Fitting, and model Selection (GFS algorithm).The GFS algorithm has been implemented in MATLAB and returns a list of candidate S-systems which adequately explain the data and guides the search to the most plausible model for the time series under study. By combining two strategies (namely decoupling and limiting connectivity) with methods of data smoothing, the proposed algorithm is scalable up to realistic situations of moderate size. We illustrate the proposed methodology with a didactic example.

Many biological systems are genuinely hybrids consisting of interacting discrete and continuous components and processes that often operate at different time scales. It is therefore desirable to create modeling frameworks capable of combining differently structured processes and permitting their analysis over multiple time horizons. During the past 40 years, Biochemical Systems Theory (BST) has been a very successful approach to elucidating metabolic, gene regulatory, and signaling systems. However, its foundation in ordinary differential equations has precluded BST from directly addressing problems containing switches, delays, and stochastic effects. In this study, we extend BST to hybrid modeling within the framework of Hybrid Functional Petri Nets (HFPN). First, we show how the canonical GMA and S-system models in BST can be directly implemented in a standard Petri Net framework. In a second step we demonstrate how to account for different types of time delays as well as for discrete, stochastic, and switching effects. Using representative test cases, we validate the hybrid modeling approach through comparative analyses and simulations with other approaches and highlight the feasibility, quality, and efficiency of the hybrid method.