Apparently, the operations supported by DNA can serve as a biological computer.  Excerpts below.
www.newscientist.com/article/2391747-dna-based-computer-can-run-100-billion-different-programs/ 

John
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DNA-based computer can run 100 billion different programs

Mixing and matching various strands of DNA can create versatile biological computer circuits that can take the square roots of numbers or solve quadratic equations.A liquid computer can use strands of DNA to run over 100 billion different simple programs. It could eventually be used for diagnosing diseases within living cells.

Fei Wang at Shanghai Jiao Tong University in China and his colleagues set out to make circuits similar to those on a computer chip, except with DNA molecules acting as wires and instructing the wires to configure in certain ways.When you enter a command on a conventional computer, it instructs electrons to flow through a specific path on a silicon chip. These circuit configurations each correspond to different mathematical operations – adding functions to chips means adding such paths.

To replace the wiring with DNA, Wang and his team modelled how to combine short segments of DNA into larger structures that could serve as circuit components, like wires, or function to direct those wires to form different configurations. They put this into practice by filling tubes with DNA strands and a buffer fluid and letting them attach to each other, combining into larger molecules through chemical reactions. The researchers also equipped all the molecules with fluorescence markers so they could keep track of what the circuit was doing based on how its parts were glowing....