Dear Mojtaba,
Research on depression with inflammatory markers has grown considerably in the last 25 years. Leptin is only one of several important markers. I would also examine c-reactive protein, a correlate of crp, because it is now used as for clinical diagnoses in many countries. Like leptin, crp is related to obesity, depression, plaques in the brain ( dementia) and certainly diabetes. It may be difficult to research leptin without considering crp or even insulin, which is related to anger and depression.
I currently have an undergraduate honors student who is completing his thesis. It shows that psychological distress (depression, anxiety) mediates increases in exercise in persons caring for a spouse with Alzheimer's disease, but not in matched older adults who are not caregivers.
Please be encouraged to pursue this research as it has great clinical meaning.
Here is an example with many good references.
Med Sci Sports Exerc. 2011 Jun;43(6):1002-9. doi: 10.1249/MSS.0b013e3182059eda.
Sixteen weeks of exercise reduces C-reactive protein levels in young women.
Arikawa AY1, Thomas W, Schmitz KH, Kurzer MS.
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