Impulsive model of endocrine regulation with a local continuous feedback

Whereas development of mathematical models describing the endocrine system as a whole remains a challenging problem, visible progress has been demonstrated in modeling its subsystems, or axes. Models of hormonal axes portray only the most essential interactions between the hormones and can be described by low-order systems of differential equations. This paper analyzes the properties of a novel model of a hypothalamic-pituitary axis, portraying the interactions in a chain of a release hormone (secreted by the hypothalamus), a tropic hormone (produced by the pituitary gland) and an effector hormone (secreted by a target gland). This model, unlike previously published ones, captures two prominent features of neurohormonal regulation systems, namely, the pulsatile (episodic) production of the release hormone and a complex non-cyclic feedback mechanism that maintains the involved hormone concentrations within certain biological limits. At the same time, the discussed model is analytically tractable; in particular, the existence of a so-called 1-cycle featured by a single pulse over one period is proven mathematically

TSPO: kaleidoscopic 18-kDa amid biochemical pharmacology, control and targeting of mitochondria

The 18-kDa translocator protein (TSPO) localizes in the outer mitochondrial membrane (OMM) of cells and is readily up-regulated under various pathological conditions such as cancer, inflammation, mechanical lesions and neurological diseases. Able to bind with high affinity synthetic and endogenous ligands, its core biochemical function resides in the translocation of cholesterol into the mitochondria influencing the subsequent steps of (neuro-)steroid synthesis and systemic endocrine regulation. Over the years, however, TSPO has also been linked to core cellular processes such as apoptosis and autophagy. It interacts and forms complexes with other mitochondrial proteins such as the voltage-dependent anion channel (VDAC) via which signalling and regulatory transduction of these core cellular events may be influenced. Despite nearly 40 years of study, the precise functional role of TSPO beyond cholesterol trafficking remains elusive even though the recent breakthroughs on its high-resolution crystal structure and contribution to quality-control signalling of mitochondria. All this along with a captivating pharmacological profile provides novel opportunities to investigate and understand the significance of this highly conserved protein as well as contribute the development of specific therapeutics as presented and discussed in the present review

Impulsive Goodwin’s Oscillator Model of Endocrine Regulation: Local Feedback Leads to Multistability

The impulsive Goodwin’s oscillator (IGO) is a hybrid model that captures complex dynamics arising in continuous systems controlled by pulse-modulated (event-based) feedback. Being conceived to describe pulsatile endocrine regulation, it has also found applications in e.g. pharmacokinetics. The original version of the IGO assumes the continuous part of the model to be a chain of first-order blocks. This paper explores the nonlinear phenomena arising due to the introduction of a local continuous feedback as suggested by the endocrine applications. The effects caused by a nonlinear feedback law parameterized by a Hill function are compared to those arising due to a simpler and previously treated case of affine feedback law. The hybrid dynamics of the IGO are reduced to a (discrete) Poincaré map governing the propagation of the model’s continuous states through the firing instants of the impulsive feedback. Bifurcation analysis of the map reveals in particular that both the local Hill function and affine feedback can lead to multistability, which phenomenon has not been observed in the usual IGO model

The "Ram Effect": A "Non-Classical" Mechanism for Inducing LH Surges in Sheep

During spring sheep do not normally ovulate but exposure to a ram can induce ovulation. In some ewes an LH surge is induced immediately after exposure to a ram thus raising questions about the control of this precocious LH surge. Our first aim was to determine the plasma concentrations of oestradiol (E2) E2 in anoestrous ewes before and after the "ram effect" in ewes that had a "precocious" LH surge (starting within 6 hours), a "normal" surge (between 6 and 28h) and "late» surge (not detected by 56h). In another experiment we tested if a small increase in circulating E2 could induce an LH surge in anoestrus ewes. The concentration of E2 significantly was not different at the time of ram introduction among ewes with the three types of LH surge. "Precocious" LH surges were not preceded by a large increase in E2 unlike "normal" surges and small elevations of circulating E2 alone were unable to induce LH surges. These results show that the "precocious" LH surge was not the result of E2 positive feedback. Our second aim was to test if noradrenaline (NA) is involved in the LH response to the "ram effect". Using double labelling for Fos and tyrosine hydroxylase (TH) we showed that exposure of anoestrous ewes to a ram induced a higher density of cells positive for both in the A1 nucleus and the Locus Coeruleus complex compared to unstimulated controls. Finally, the administration by retrodialysis into the preoptic area, of NA increased the proportion of ewes with an LH response to ram odor whereas treatment with the α1 antagonist Prazosin decreased the LH pulse frequency and amplitude induced by a sexually active ram. Collectively these results suggest that in anoestrous ewes NA is involved in ram-induced LH secretion as observed in other induced ovulators