Mayo argues that the patent impermissibly tries to claim laws of nature, and that the claims are so broad and preempt natural phenomena such that there is no room for competition. According to Mayo's reading of the patent, a doctor drawing blood from a patient and simply thinking about an appropriate range of drug to apply amounts to infringement, and that this is far too broad for patent protection to extend.
On the other hand, the patent owner, Prometheus, emphasized that their patent protects the application of a law of nature, which is patentable, rather than the law of nature itself. They highlighted that they use specific drugs (thiopurines) to treat specific diseases (certain autoimmune diseases) by a particular process that involves certain claimed levels of metabolites "indicating a need" to increase or decrease the dosage of the administered drug. They maintain that this is therefore a process based in the physical world and that it does not preemt follow-on innovation.
A common theme running throughout the arguments, and the Supreme Court Justices' questions, was falling back to a discussion of novelty and obviousness under 35 U.S.C. 102 and 103 rather than addressing the threshold inquiry of patent eligibility under 35 U.S.C. 101, which was the reason for challenging the patent and the topic of the question before the Court. This may be a result of the law being more settled with regard to novelty and obviousness than for patent eligibility. This may, however, as the United States as amicus curiae argued, be because novelty and/or obviousness is a more appropriate challenge for this patent than patent eligibility.
The Court acknowledged that laws of nature are not patentable, but that applications of laws of nature are patentable. They seemed most concerned with delineating where the line between the two is - in other words, how much does an inventor have to add to a law of nature to get patent eligible subject matter? The Justice's inquiries from the parties on this line failed to provide clear examples. Hopefully, the Supreme Court will be able to provide concrete guidance on this point when they issue their opinion in the coming months.
For those interested, a copy of the transcript can be found here.