Abstract Background The dynamics of gene regulation play a crucial role in a cellular control: allowing the cell to express the right proteins to meet changing needs. Some needs, such as correctly anticipating the day-night cycle, require complicated oscillatory features. In the analysis of gene regulatory networks, mathematical models are frequently used to understand how a network’s structure enables it to respond appropriately to external inputs. These models typically consist of a set of ordinary differential equations, describing a network of biochemical reactions, and unknown kinetic parameters, chosen such that the model best captures experimental data. However, since a model’s parameter values are uncertain, and since dynamic responses to inputs are highly parameter-dependent, it is difficult to assess the confidence associated with these in silico predictions. In particular, models with complex dynamics - such as oscillations - must be fit with computationally expensive global optimization routines, and cannot take advantage of existing measures of identifiability. Despite their difficulty to model mathematically, limit cycle oscillations play a key role in many biological processes, including cell cycling, metabolism, neuron firing, and circadian rhythms. Results In this study, we employ an efficient parameter estimation technique to enable a bootstrap uncertainty analysis for limit cycle models. Since the primary role of systems biology models is the insight they provide on responses to rate perturbations, we extend our uncertainty analysis to include first order sensitivity coefficients. Using a literature model of circadian rhythms, we show how predictive precision is degraded with decreasing sample points and increasing relative error. Additionally, we show how this method can be used for model discrimination by comparing the output identifiability of two candidate model structures to published literature data. Conclusions Our method permits modellers of oscillatory systems to confidently show that a model’s dynamic characteristics follow directly from experimental data and model structure, relaxing assumptions on the particular parameters chosen. Ultimately, this work highlights the importance of continued collection of high-resolution data on gene and protein activity levels, as they allow the development of predictive mathematical models.

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data from individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure.