Marked Point Process Secretory Events Statistically Characterize Leptin Pulsatile Dynamics

Abstract

Recent studies have highlighted leptin, a key hormone that regulates energy intake and induces satiety, due to the worldwide prevalence of obesity. In this study, we analyzed plasma leptin measurements from 18 women with premenopausal obesity before and after bromocriptine treatment. By using underlying pulses recovered through deconvolution, we modeled the leptin secretory pulses as marked point processes and applied statistical distributions to evaluate the dynamics of leptin, including the interpulse intervals and amplitudes of the secretion. We fit the generalized inverse Gaussian and lognormal distributions to the intervals and the Gaussian, lognormal, and gamma distributions to the amplitudes of pulses. We evaluated the models' goodness of fit using statistical metrics including Akaike's information criterion, Kolmogorov-Smirnov plots, and quantile-quantile plots. Our evaluation results revealed the effectiveness of these statistical distributions in modeling leptin secretion. Although the lognormal and gamma distributions performed the best based on the metrics, we found all distributions capable of accurately modeling the timing of secretory events, leading us to a better understanding of the physiology of leptin secretion and providing a basis for leptin monitoring. In terms of pulse amplitude, the evaluation metrics indicated the gamma distribution as the most accurate statistical representation. We found no statistically significant effect of bromocriptine intake on the model parameters except for one distribution model.

Keywords: Akaike's information criterion; Kolmogorov-Smirnov plot; bromocriptine; generalized inverse Gaussian; leptin; quantile-quantile plot; statistical signal processing.

Figure 1.

Examples of the generalized inverse Gaussian (GIG) and lognormal models with different parameter values. The GIG model and lognormal model can have similar shapes with certain parameter values.

Figure 2.

Example plasma leptin concentration level (line plot) and the extracted pulses (stem plot). An increase in plasma leptin level can be observed in both figures immediately following each pulse, especially ones with large amplitudes.

Figure 3.

Example distribution of interpulse intervals with the estimated models and the corresponding Kolmogorov-Smirnov (KS) plots. The closeness between the estimated distribution models and the empirical histogram can be observed directly and is also indicated by the closeness between the KS plots and the line from (0, 0) to (1, 1). The upper and lower dashed lines are the boundaries of the 95% CI.

Figure 4.

Demonstration of effects of parameters in the diffusion generalized inverse Gaussian (GIG) model. The graphs show the effects of a changing λ or a changing concentration parameter. In both graphs, the scale parameter $\sqrt{\chi /\psi }=1$, and a concentration shift to the right is present. “Con” stands for the concentration parameter $\sqrt{\psi \chi }$.

Figure 5.

Example Q-Q plot of pulse amplitudes vs models. The models are Gaussian, lognormal, and gamma distributions. The dashed line in the middle is the reference line indicating the ideal case in which the two distributions are the same. The upper and lower dashed lines are the boundaries of the 95% CI.