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I am interested in the relationship between blood leptin concentration and fat mass. It is well known that as fat mass increases, leptin increases.

Have there been studies that look into whether the relationship is linear, or perhaps as fat mass increases, the level of leptin increases at a decreasing rate (e.g. logarithmic relationship) or an increasing rate (exponential) etc.

Furthermore, for two individuals with identical fat mass, is there a high variance of leptin concentration?

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The obese gene (OB gene) secretes a protein that functions in the signaling pathway of adipose tissue and adipocytes (fat cells) produce the hormone leptin (reference).

When the amount of fat in the body increases, the amount of leptin released into the blood also increases and signals to the brain that the body has enough to eat (reference). Inversely, studies in rodents suggest that a reduction in leptin level during weight loss signals to the brain to increase feeding and decrease energy expenditure (reference).

Other molecules have a role to play in the ratio of BMI to leptin like the ghrelin hormone (reference). The genetic and environmental factors other than overall adiposity may also regulate leptin concentrations (reference) which is why individuals with the same weight may have different leptin concentrations.

A study has reported finding a strong exponential relationship for leptin levels with body mass index (BMI) (reference). Hope that answers both your questions.

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The over-simplified answer to the question: "Have studies examined the linearity or non-linearity of leptin concentrations in the blood and body fat?" - is "yes".

Leptin (the product of the ob gene - that is, the obese gene) is typically thought of as being secreted in proportion to the amount of adipose (fat) tissue that an organism (mice, rats, primates, humans) has overall. Like most things in biology, though, it's likely not a perfect linear relationship across species or across a wide range of individual body weights within a particular species.

Even the plasma concentrations across individuals within a particular species with the exact (or very close) body weight is still different. In my own experience, when trying to "normalize" or "adjust" the estimated fat mass based on the leptin concentration there's still a good amount of variability between individuals. The leptin concentrations for a number of individuals at one specific body fat percentage are not identical - which could be due to some error in the measurement, but also due to biologic variability from other sources (for a example of this variability in animals matched for body weight see here). This is probably because there are a lot of other modifying factors or variables within the body that can affect leptin concentrations in the plasma (like other hormones or nutrients from the gastrointestinal tract). So yes, these other hormonal and/or nutrient signals probably contribute to the high variance of plasma leptin concentration for individuals with the same fat mass for all of the reasons listed above (I don't have any references that examine this specific question, though).

To my knowledge there are no studies that have examined leptin concentrations across multiple species or even within a large cohort of one species. Even though this might be interesting from a scientific perspective, it's not really necessary to be able to predict fat mass from leptin concentrations (or vice versa) for medical purposes, because we have 'good enough' methods for accurately determining fat mass in patients or animals.

Overall leptin is an adipose tissue hormone thought to be involved in control of body weight over long-term (weeks to months) time courses. For a good review of the long-term actions of leptin and other hormones controlling body weight see a great review on CNS control of body weight that discusses leptin and other factors that modify leptin and body weight regulation.

Additionally, Dr. Jeffrey Flier in Boston is a senior physician-scientist at Harvard Univeristy and has studied leptin biology and has some very nice articles on leptin including this review on leptin in energy balance and long term control of fat mass.

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