Cesium: A public database of evolved oscillatory reaction networks

Generating synthetic signaling networks for in silico modeling studies

Predictive models of signaling pathways have proven to be difficult to develop. Traditional approaches to developing mechanistic models rely on collecting experimental data and fitting a single model to that data. This approach works for simple systems but has proven unreliable for complex systems such as biological signaling networks. Thus, there is a need to develop new approaches to create predictive mechanistic models of complex systems. To meet this need, we developed a method for generating artificial signaling networks that were reasonably realistic and thus could be treated as ground truth models. These synthetic models could then be used to generate synthetic data for developing and testing algorithms designed to recover the underlying network topology and associated parameters. We defined the reaction degree and reaction distance to measure the topology of reaction networks, especially to consider enzymes. To determine whether our generated signaling networks displayed meaningful behavior, we compared them with signaling networks from the BioModels Database. This comparison indicated that our generated signaling networks had high topological similarities with BioModels signaling networks with respect to the reaction degree and distance distributions. In addition, our synthetic signaling networks had similar behavioral dynamics with respect to both steady states and oscillations, suggesting that our method generated synthetic signaling networks comparable with BioModels and thus could be useful for building network evaluation tools.

An oscillating reaction network with an exact closed form solution in the time domain

BACKGROUND

Oscillatory behavior is critical to many life sustaining processes such as cell cycles, circadian rhythms, and notch signaling. Important biological functions depend on the characteristics of these oscillations (hereafter, oscillation characteristics or OCs): frequency (e.g., event timings), amplitude (e.g., signal strength), and phase (e.g., event sequencing). Numerous oscillating reaction networks have been documented or proposed. Some investigators claim that oscillations in reaction networks require nonlinear dynamics in that at least one rate law is a nonlinear function of species concentrations. No one has shown that oscillations can be produced for a reaction network with linear dynamics. Further, no one has obtained closed form solutions for the frequency, amplitude and phase of any oscillating reaction network. Finally, no one has published an algorithm for constructing oscillating reaction networks with desired OCs.

RESULTS

This is a theoretical study that analyzes reaction networks in terms of their representation as systems of ordinary differential equations. Our contributions are: (a) construction of an oscillating, two species reaction network [two species harmonic oscillator (2SHO)] that has no nonlinearity; (b) obtaining closed form formulas that calculate frequency, amplitude, and phase in terms of the parameters of the 2SHO reaction network, something that has not been done for any published oscillating reaction network; and (c) development of an algorithm that parameterizes the 2SHO to achieve desired oscillation, a capability that has not been produced for any published oscillating reaction network.

CONCLUSIONS

Our 2SHO demonstrates the feasibility of creating an oscillating reaction network whose dynamics are described by a system of linear differential equations. Because it is a linear system, we can derive closed form expressions for the frequency, amplitude, and phase of oscillations, something that has not been done for other published reaction networks. With these formulas, we can design 2SHO reaction networks to have desired oscillation characteristics. Finally, our sensitivity analysis suggests an approach to constructing a 2SHO for a biochemical system.