In regards to cortisol, UA may help protect the brain from damage caused by high cortisol:
"The cytoprotective potential of UA against corticosterone-induced cytotoxicity and its ability to modulate intracellular signaling pathways involved in cell proliferation and survival suggest that UA may be a relevant strategy to manage stress-related disorders such as MDD."
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This is not about cortisol specifically but I thought it was interesting and in the spirit of the OP inquiry:
Ursolic acid is a pentacyclic triterpenoid found in several plants. Despite its initial use as a pharmacologically inactive emulsifier in pharmaceutical, cosmetic and food industries, several biological activities have been reported for this compound so far, including anti-tumoural, anti-diabetic, cardioprotective and hepatoprotective properties. The biological effects of ursolic acid have been evaluated in vitro, in different cell types and against several toxic insults (i.e. 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine, amyloid-β peptides, kainic acid and others); in animal models of brain-related disorders (Alzheimer disease, Parkinson disease, depression, traumatic brain injury) and ageing; and in clinical studies with cancer patients and for muscle atrophy. Most of the protective effects of ursolic acid are related to its ability to prevent oxidative damage and excessive inflammation, common mechanisms associated with multiple brain disorders. Additionally, ursolic acid is capable of modulating the monoaminergic system, an effect that might be involved in its ability to prevent mood and cognitive dysfunctions associated with neurodegenerative and psychiatric conditions. This review presents and discusses the available evidence of the possible beneficial effects of ursolic acid for the management of neurodegenerative and psychiatric disorders. We also discuss the chemical features, major sources and potential limitations of the use of ursolic acid as a pharmacological treatment for brain-related diseases.
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In regards to estrogen, UA probably won't lower your E2 levels on bloodwork but it may serve as an anti-estrogen at certain receptor sites:
"Furthermore, both mRNA and protein levels of ERα were reduced by treatment with UA or BA, suggesting that UA and BA inhibit estrogen signaling by suppressing the expression of ERα. Interestingly, both compounds enhanced Invalid Link Removed promoter activity. Collectively, these findings demonstrate that UA and BA are responsible for the antiestrogenic effects of P. vulgaris and suggest their potential use as therapeutic agents against estrogen-dependent tumors."
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