Figure 5.

A minimal mathematical model for human leptin variation

(A) Quadratic relation between leptin and fat in a human population, adapted from Considine et al., 1996.²⁴ Best fit in full lines, with standard deviation of parameters estimation.

(B) The diet and appetite curves form a minimal model of leptin action suggest that intake is inverse to fat, and locks to its maximal level when fat drops below a critical level.

(C) Leptin resistance increases the steady state fat level, as long as fat is above the critical level $F_c$. The latter rises with leptin resistance.

(D) In this regime, variation between individuals in leptin resistance accounts for the main difference in fat between individuals.

(E) In severe leptin resistance, food intake hits a ceiling equal to the satiety food intake level $u_{\mathit{max}}$.

(F) In this regime, variations between individuals in the satiety food intake level $u_{\mathit{max}}$ mainly account for differences in fat.