Biomathematical modeling of pulsatile hormone secretion: a historical perspective

Abstract

Shortly after the recognition of the profound physiological significance of the pulsatile nature of hormone secretion, computer-based modeling techniques were introduced for the identification and characterization of such pulses. Whereas these earlier approaches defined perturbations in hormone concentration-time series, deconvolution procedures were subsequently employed to separate such pulses into their secretion event and clearance components. Stochastic differential equation modeling was also used to define basal and pulsatile hormone secretion. To assess the regulation of individual components within a hormone network, a method that quantitated approximate entropy within hormone concentration-times series was described. To define relationships within coupled hormone systems, methods including cross-correlation and cross-approximate entropy were utilized. To address some of the inherent limitations of these methods, modeling techniques with which to appraise the strength of feedback signaling between and among hormone-secreting components of a network have been developed. Techniques such as dynamic modeling have been utilized to reconstruct dose-response interactions between hormones within coupled systems. A logical extension of these advances will require the development of mathematical methods with which to approximate endocrine networks exhibiting multiple feedback interactions and subsequently reconstruct their parameters based on experimental data for the purpose of testing regulatory hypotheses and estimating alterations in hormone release control mechanisms.

Figure 14.1

Control of pituitary hormone synthesis and secretion by the hypothalamus as hypothesized by Green and Harris (1947). Chemical messengers secreted by nerve cells within the hypothalamus were proposed to travel through the hypothalamic-hypophyseal portal circulation to the anterior pituitary gland where they would stimulate, inhibit, orotherwise modulatethe synthesis and release of hormones.

Figure 14.2

Luteinizing hormone (LH) secretion in Rhesus monkeys with (A) intact hypothalamic function, (B) after ablation of the medial basal hypothalamus, (C) in response to a continuous GnRH infusion after hypothalamic ablation, and (D) in response to pulsatile GnRH infusion after ablation of the hypothalamus. These studies (Knobil, 1980) were the first to demonstrate the profound importance of the pulsatile versus nonvarying nature of GnRH secretion with regard to LH and FSH secretion.

Figure 14.3

Number of LH pulses identified in concentration-time series obtained over a 24-h period of time during the midluteal phase of the menstrual cycle of normal women. The same data sets were analyzed with independent pulse detection algorithms, including Santen & Bardin (S & B), Pulsar, Cycle Detector (Cycle), and Ultra. Note the considerable difference in number of pulses detected as a function of the pulse analysis program used for the analysis (Evans et al., 1992).

Figure 14.4

(Top) A serum LH concentration-time series constructed from samples obtained from a normalwoman in the early follicular phase of her menstrual cycle. Samples were collected at 10-min intervals over a 24-h period of time. (Bottom) LH secretory bursts resolved from this concentration-time series using the deconvolution procedure Deconv (Veldhuis, Carlson and Johnson, 1987).

Figure 14.5

Deconvolution-resolved number of secretory bursts (/24 h; top), burst mass (IU/liter; middle), and half-life (minutes; bottom) in LH concentration-time series obtained from normalwomen in the early follicular (EF), late follicular (LF), and midlu-teal (ML) phases of the menstrual cycle and in postmenopausal (PM) women. For each group, values identified with different superscripts differ significantly (p <0.05)(Booth et al.,1996; Sollenberger et al.,1990).

Figure 14.6

A synthetic endocrine network (left) and estimate of the level of feedback control (LFC) for the A-to-B negative coupling (table on right) corresponding to the gradual increase in the feedback strength and simultaneous decrease of the independent factor (Farhy et al., 2006).

Figure 14.7

Modeling of pituitary LH stimulation by hypothalamic GnRH in a representative ewe treated with naloxone (solid bar). (Top) Model fit (solid line) and observed (errorbars) LH (80% of the variance of LH is accounted for). (Bottom) GnRHconcentration. (Inset) Reconstructed dose^response interaction between GnRH concentration and LH secretion over the range ofobserved GnRH.

Figure 14.8

Examples of endocrine networks with multiple delayed feedback loops.

Figure 14.9

Computer-generated output (concentration of B vs time) of the core system shown in Fig. 14.8, middle left.