This paper is dedicated to the R package FMM which implements a novel approach to describe rhythmic patterns in oscillatory signals. The frequency modulated Möbius (FMM) model is defined as a parametric signal plus a Gaussian noise, where the signal can be described as a single or a sum of waves. The FMM approach is flexible enough to describe a great variety of rhythmic patterns. The FMM package includes all required functions to fit and explore single and multi-wave FMM models, as well as a restricted version that allows equality constraints between parameters representing a priori knowledge about the shape to be included. Moreover, the FMM package can generate synthetic data and visualize the results of the fitting process. The potential of this methodology is illustrated with examples of such biological oscillations as the circadian rhythm in gene expression, the electrical activity of the heartbeat and the neuronal activity.
The Hodgkin-Huxley model, decades after its first presentation, is still a reference model in neuroscience as it has successfully reproduced the electrophysiological activity of many organisms. The primary signal in the model represents the membrane potential of a neuron. A parametric and simple representation of this signal is presented in this paper.The new proposal is an adapted Frequency Modulated Möbius multicomponent model defined as a flexible decomposition in waves that describe the signal morphology. A specific feature of the new model is that the parameters are subject to interpretable restrictions.A broad simulation experiment is conducted to show the new model accurately represents the simulated Hodgkin-Huxley signal. Moreover, the model potential to predict the neuron’s relevant characteristics, described with parameters of the Hodgkin Huxley model, is shown using different Machine Learning methods. The proposed model is also validated with real data from Squid Giant Axons. The comparison of the parameter configuration between the simulated and real data demonstrated the flexibility of the model as well as interesting differences.Author summaryAlejandro Rodríguez-Collado. I received the double degree in Statistics and Computer Engineering and the Master’s degree in Business Intelligence and Big Data from the Universidad de Valladolid in 2019 and 2020, respectively. I work as researcher and Professor for the Department of Statistics and Operational Research at the Universidad de Valladolid. My main research interests include oscillatory signal processing, neuroscience, multivariate data analysis and supervised learning.Cristina Rueda. I received the BS degree in mathematics from the Universidad de Valladolid in 1987 and the PhD degree in statistical science from the Universidad de Valladolid in 1989. I am currently Professor in the Department of Statistics and Operational Research at the Universidad de Valladolid. My main research interests include statistical inference methods under restrictions, circular data, computational biology, and statistical methods for signal analysis.
The complete understanding of the mammalian brain requires exact knowledge of the function of each neuron subpopulation composing its parts. To achieve this goal, an exhaustive, precise, reproducible, and robust neuronal taxonomy should be defined. In this paper, a new circular taxonomy based on transcriptomic features and novel electrophysiological features is proposed. The approach is validated by analysing more than 1850 electrophysiological signals of different mouse visual cortex neurons proceeding from the Allen Cell Types database. The study is conducted on two different levels: neurons and their cell-type aggregation into Cre lines. At the neuronal level, electrophysiological features have been extracted with a promising model that has already proved its worth in neuronal dynamics. At the Cre line level, electrophysiological and transcriptomic features are joined on cell types with available genetic information. A taxonomy with a circular order is revealed by a simple transformation of the first two principal components that allow the characterization of the different Cre lines. Moreover, the proposed methodology locates other Cre lines in the taxonomy that do not have transcriptomic features available. Finally, the taxonomy is validated by Machine Learning methods which are able to discriminate the different neuron types with the proposed electrophysiological features.
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