Mathematical Modeling of Leptin Dynamics and Some Insights into Biomathematics (paper review)

Source: Vander et al.: Human Physiology: The Mechanism of Body Function, Eighth Edition. 

it is  developed a physiologically-based mathematical model for leptin. Leptin is a master hormone in the body that controls hunger and feelings of satiety, however it is a key hormone for controlling metabolism regarding energy expenditure. Leptin is secreted mainly by adipose (fat) tissue, white tissues, so the more overweight a person is, typically, the higher his leptin levels. Leptin does not change just with fat mass, other factors can influence.

In the following scheme we can see the interplay between adipocytes, brain (mainly hypothalamus), and the central nervous system. In essence, the higher the fat tissue mass, the more it is produced leptin, the central nervous system is activated meaning that we have energy on board. This loop might seem unstable, but it can reach equilibrium from two perspectives: when eating balance energy expenditure or when other hormones interferes such as insulin or ghrelin.   

The hormonal control system created by leptin.
Source: Youtube, 2014. 

Source: Youtube, 2014.

Energy Homeostasis, or energy balance, is an aspect of bioenergetics concerning the energy flow through living systems; metabolic regulation in human terms covers the means by which we take in nutrients in discrete meals, and deliver energy as required, varying from moment to moment and from tissue to tissue, in a pattern which may have no relationship at all to the pattern of intake, by metabolism Frayn (2010). Energy homeostasis involves the human body using chemical and neural signals to adjust the amount of energy flows; and to regulate caloric intake by signaling the brain to regulate the sensation of hunger.

"This controversy underscores the fact that, despite the impressive progress made over the past few decades in unraveling many of the molecular pathways involved in energy regulation, we still have a rather murky understanding of how all the pieces fit together to function as an integrated system. Most previous mathematical models of metabolic energy regulation have not explicitly modeled the neuroendocrine feedback system that maintains energy homeostasis. In order to address this deficiency, we have developed a mathematical model that simulates the physiological system that regulates energy metabolism."

Simulation deficient-leptin mouse against a normal one.
Source: own work.

Simulation of a food-control. 
Source: own work.

Paper reviewed:

Tam, J.; Fukumura, D.;  Jain, R. K.; A mathematical model of murine metabolic regulation by leptin: energy balance and defense of a stable body weight. Cell Metab. 2009 January 7; 9(1): 52–63. doi:10.1016/j.cmet.2008.11.005.

Further

Uluseker, C.; Mathematical Model for Leptin Dynamics. Master of Science Thesis, MathMods Erasmus Mundus M.Sc. Programme, Mathematical Models in Life and Social Sciences. Department of Information Engineering, Computer Science and Mathematics. University of L'Aquila: Italy: 2014. 

Carla Eduarda Machado Romero; Angelina Zanesco. O papel dos hormônios leptina e grelina na gênese da obesidade. Rev. Nutr. vol.19 no.1 Campinas Jan./Feb. 2006. 

References mentioned

Keith N. Frayn, Metabolic Regulation A Human Perspective. Third Edition. wiley-blackwell, 2010.