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Though streptokinase, was obtained from streptococcus bacteria, it is not being done now similarly. The enzyme has been cloned and is prepared in tissue cultures in a strict and controlled environment.
Commercial preparation of streptokinase, are manufactured via tissue cultures, with Bacillus Subtilis strains, and they undergo multiple levels of purification and processing, before actual packaging for medical use.
Hence there is no reason to worry that, use of streptokinase can result in streptococcal infection.
Like all enzymes, streptokinase is a enzyme, and it will act only on a specific substrates. In this case the substrate for streptokinase is a clot formed by combination of fibrinogen, plasminogen, and thrombin.
Since normal tissues do not express the above substrates, streptokinase does not affect them.
In addition to use in thrombolytic therapy, Streptokinase is also used in the treatment of complicated parapneumonic effusions and empyema.
I hope this answers your doubts.