Stochastic model of admixed basal and pulsatile hormone secretion as modulated by a deterministic oscillator

Neuroendocrine ensembles communicate with their remote and proximal target cells via an intermittent pattern of chemical signaling. The lack of a biomathematical formulation of the underlying burst-generating mechanics of such pulsatile secretory systems has greatly hampered quantitative analysis of the physiological, pharmacological, and pathological regulation of the amplitude and frequency components of seemingly randomly dispersed neuroendocrine signals. Here we present a stochastic differential equation model of episodic glandular signaling in which random, but structured, variations in burst amplitudes superimposed on basal hormone release are combined with a nonstationary Poisson process responsible for the timing of scattered secretory bursts. Burst timing and/or amplitude can be modulated by underlying deterministic trends, e.g., circadian variations in mean expected neurosecretory burst frequency or mass. We illustrate the diversity of output of this model and suggest its use in extracting underlying properties of irregular biological signals in relevant hormone time series. This representation of episodic secretory behavior combines stochastic and deterministic elements inherent in the intermittent activity of a neuroendocrine apparatus.