What if you engineer a completely novel protein, with novel regulatory sequences, for a novel function? Should you be unable to patent such an invention?
Sequence space is very large. There are only a total of 8 million US patents. There are 16 million 12-base-pair nucleotide sequences. To patent the sequence space of a functional product and regulatory region would require more patents than there are molecules in the universe.
Also to patent something you have to show use.
If a group of people synthesize and test many synthetic DNA sequences and then patent the useful ones, that seems fine to me. You might even call them "synthetic biologists". They have invented new things, which are not found in nature, by the process of their own skills, knowledge, and labor, and which are useful to other people. It seems perfectly reasonable that those inventions should be protected by the patent system.
It's not the synthesis method that is at stake here, it is the engineered biological system itself (system referring to a gene, regulatory sequence, genetic pathway, or organism). The kind of innovation involved in this kind of engineering is precisely what the patent system is designed to protect, so that it can be monetized while also disseminated. Without patents these innovations will remain trade secrets and hold back the progress of synthetic biology. Without patents private companies may not be able to justify investment required for innovation. Without patents inability to monetize inventions reduces the overall economic impact (return on investment) for public financing of life sciences, which in turn removes a powerful incentive for government financing of research.
For instance, a company finds a compound that fights cancer. The company invents a way to synthesize or purify this compound and sell it. The patent protects the inventor and allows them to recoup the investment. This is widely accepted. Now consider that company engineers an organism that can produce the compound in large bio-reactors. The modified organism - and in particular the engineered DNA sequences - are completely analogous to the chemical manufacturing process, and should be similarly protected.
Moreover, consider that the second process may remove a need to use the organic carbon precursors necessary for chemical synthesis (fossil fuels), or eliminates a toxic by-product of chemical synthesis, or is much cheaper and therefore reduces the cost of the compound, benefiting the public. These are real world consequences of synthetic biology protected by the patent system. They don't seem so scary to me.
That being said, I think that even if you take a natural gene and modify it meaningfully - that should be patent-able. For instance, if you take an enzyme and engineer a version that doesn't degrade as readily, or has much better activity, that should be patent-able, don't you think?
EDIT: There's a good deal of prior art regarding numbers. As for patenting molecules, we allow that all the time... drugs, compounds, etc. Because they are discovered as I describe above.