Does David have a reasonable expectation of privacy in his DNA?

The Florida DNA Collection Act (FDCA) allows state and local law enforcement officers to collect DNA samples without a warrant from individuals who are arrested for a crime of violence or an attempted crime of violence. David the Defendant was arrested for aggravated battery. While under arrest, David’s DNA was collected and logged in Florida’s DNA database. That database matched David’s DNA to a DNA sample from an unsolved rape case. This sample was the only evidence linking David to the rape. Please explain in a 2-3 page paper what a warrant is and how the above fact pattern may or may not violate David’s Fourth Amendment rights. Does David have a reasonable expectation of privacy in his DNA? Does the government need a warrant to obtain David’s DNA?