I do not know whether the attached article could be of help.

Best regards

Robert

You mean that whether the degree of adipocyte differentiation is correlated with autophagy activation. Under the hypo-nutrient conditions (starvation), the differentiated adipocytes highly expressing PPAR-gamma down-regulate p62 and increase the ratio of LC3-II/ LC3-I by the LC-3 conversion (lipidation with PE). By contrast, mature adipocytes which accumulate TG are expected not to activate autophagy.  

Article Autophagy regulates adipose mass and differentiation in mice

 In 3T3-L1 cells, autophagic function was required for these cells to differentiate into white adipocytes. In the more complex in vivo situation of the mouse model with an inhibition of autophagy in adipose tissue, 2 striking changes occurred in WAT. First, WAT mass decreased dramatically, indicating that a loss of autophagy led to a reduction in adipocyte size and/or cell number. The 4-fold increase in the number of cells per tissue area, along with the marked reduction in LD size, indicates that the predominant effect was a decrease in cell size. Decreased cell size presumably resulted from the marked reduction in stored lipid in these cells, as the intracellular space of a mature white adipocyte is composed almost entirely of a single large LD. In addition to the decrease in mass, the second effect in WAT in the Atg7-knockout mice was the presence of features of brown fat, as indicated by characteristic histology, increased number of mitochondria, and elevated levels of molecular markers of brown adipocytes such as UCP-1, PGC-1α, and mitochondrial enzymes. Thus, 2 possible mechanisms exist for the decrease in lipid storage in WAT. First, a block in white adipocyte differentiation may have led to a failure of these cells to accumulate lipid, without which they remained small in size. Alternatively, the increase in fatty acid β-oxidation and uncoupled respiration that occurred with the conversion of WAT to brown adipocytes, together with the increase in BAT mass, may have decreased the amount of lipid available for storage in WAT. The absence of any increase in serum fatty acids and the failure to accumulate excess lipid in nonadipose organs such as liver and heart that would occur if WAT lipid storage was simply blocked without any increase in energy usage suggest that increased energy expenditure was the main mechanism for the decrease in WAT mass.