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Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics.

ABSTRACT: The nonsinusoidal waveform is emerging as an important feature of neuronal oscillations. However, the role of single-cycle shape dynamics in rapidly unfolding brain activity remains unclear. Here, we develop an analytical framework that isolates oscillatory signals from time series using masked empirical mode decomposition to quantify dynamical changes in the shape of individual cycles (along with amplitude, frequency, and phase) with instantaneous frequency. We show how phase-alignment, a process of projecting cycles into a regularly sampled phase grid space, makes it possible to compare cycles of different durations and shapes. "Normalized shapes" can then be constructed with high temporal detail while accounting for differences in both duration and amplitude. We find that the instantaneous frequency tracks nonsinusoidal shapes in both simulated and real data. Notably, in local field potential recordings of mouse hippocampal CA1, we find that theta oscillations have a stereotyped slow-descending slope in the cycle-wise average yet exhibit high variability on a cycle-by-cycle basis. We show how principal component analysis allows identification of motifs of theta cycle waveform that have distinct associations to cycle amplitude, cycle duration, and animal movement speed. By allowing investigation into oscillation shape at high temporal resolution, this analytical framework will open new lines of inquiry into how neuronal oscillations support moment-by-moment information processing and integration in brain networks.NEW & NOTEWORTHY We propose a novel analysis approach quantifying nonsinusoidal waveform shape. The approach isolates oscillations with empirical mode decomposition before waveform shape is quantified using phase-aligned instantaneous frequency. This characterizes the full shape profile of individual cycles while accounting for between-cycle differences in duration, amplitude, and timing. We validated in simulations before applying to identify a range of data-driven nonsinusoidal shape motifs in hippocampal theta oscillations.

SUBMITTER: Quinn AJ

PROVIDER: S-EPMC7611760 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BACKGROUND: Constructing predictive dynamic models of interacting signalling networks remains one of the great challenges facing systems biology. While detailed dynamical data exists about individual pathways, the task of combining such data without further lengthy experimentation is highly nontrivial. The communicating links between pathways, implicitly assumed to be unimportant and thus excluded, are precisely what become important in the larger system and must be reinstated. To maintain the delicate phase relationships between signals, signalling networks demand accurate dynamical parameters, but parameters optimised in isolation and under varying conditions are unlikely to remain optimal when combined. The computational burden of estimating parameters increases exponentially with increasing system size, so it is crucial to find precise and efficient ways of measuring the behaviour of systems, in order to re-use existing work. RESULTS: Motivated by the above, we present a new frequency domain-based systematic analysis technique that attempts to address the challenge of network assembly by defining a rigorous means to quantify the behaviour of stochastic systems. As our focus we construct a novel coupled oscillatory model of p53, NF-kB and the mammalian cell cycle, based on recent experimentally verified mathematical models. Informed by online databases of protein networks and interactions, we distilled their key elements into simplified models containing the most significant parts. Having coupled these systems, we constructed stochastic models for use in our frequency domain analysis. We used our new technique to investigate the crosstalk between the components of our model and measure the efficacy of certain network-based heuristic measures. CONCLUSIONS: We find that the interactions between the networks we study are highly complex and not intuitive: (i) points of maximum perturbation do not necessarily correspond to points of maximum proximity to influence; (ii) increased coupling strength does not necessarily increase perturbation; (iii) different perturbations do not necessarily sum and (iv) overall, susceptibility to perturbation is amplitude and frequency dependent and cannot easily be predicted by heuristic measures.Our methodology is particularly relevant for oscillatory systems, though not limited to these, and is most revealing when applied to the results of stochastic simulation. The technique is able to characterise precisely the distance in behaviour between different models, different systems and different parts within the same system. It can also measure the difference between different simulation algorithms used on the same system and can be used to inform the choice of dynamic parameters. By measuring crosstalk between subsystems it can also indicate mechanisms by which such systems may be controlled in experiments and therapeutics. We have thus found our technique of frequency domain analysis to be a valuable benchmark systems-biological tool.

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Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics.

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