The specific activity of an enzyme is another common unit. This is the activity of an enzyme per milligram of total protein (expressed in μmol min−1mg−1). Specific activity gives a measurement of enzyme purity in the mixture. It is the moles of product formed by an enzyme in a given amount of time (minutes) under given conditions per milligram of total proteins. Specific activity is equal to the rate of reaction multiplied by the volume of reaction divided by the mass of total protein. The SI unit is katal kg−1, but a more practical unit is μmol mg−1 min−1. Specific activity is a measure of enzyme processivity, at a specific (usually saturating) substrate concentration, and is usually constant for a pure enzyme. For elimination of errors arising from differences in cultivation batches and/or misfolded enzyme etc. an active site titration needs to be done. This is a measure of the amount of active enzyme, calculated by e.g. titrating the amount of active sites present by employing an irreversible inhibitor. The specific activity should then be expressed as μmol min−1mg−1 active enzyme. If the molecular weight of the enzyme is known, the turnover number, or μmol product per second per μmol of active enzyme, can be calculated from the specific activity. The turnover number can be visualized as the number of times each enzyme molecule carries out its catalytic cycle per second.
Relative activity of enzyme:
Is the activity of a certain enzyme compared to other enzymes included in its family.
For example in your case: Laccases (monophenol, dihydroxyphenylalanine: oxygen oxidoreductase, EC 1.14.18.1) are members ofthe multicupper oxidase
family of enzymes that catalyze the oxidation of a variety of aromatic substances to less hazardous compounds.
Relative activity of your enzyme = activity of your enzyme/activity of the most active (potent) enzyme in its class.