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Here is the short version of what they do in the skin: So it is not just soothing for the sake of soothing

Decreases incidence of chronic conditions like diabetes, arthritis, cancer, etc., and also helps in fighting against autoimmune conditions

The recommended daily intake is 2.3 mg for men and 1.8 mg for women ( Manganese deficiency can present with skin and hair alterations (such as dermatitis, impaired growth of hair and nails, and color changes in hair and beard), nausea and vomiting, ataxia and loss of equilibrium, altered carbohydrate and lipid metabolism, skeletal changes with defects and poor bone formation, impaired reproductive function, and reduced concentrations of clotting proteins (354)

The differential equations are then solved to determine the steady-state values of the concentrations of all the variables and the steady state rates of all the reactions