Nucleic acids questions

Like Flying Cookie said, no specific basis for gout has been found. However, to add a few details, the main culprit in gout is high level of uric acid. This can be caused either by under-excretion or over-production of uric acid. Purines, which are double ring nucleotides, ultimately catabolize to form uric acid in your body.
One proposed mechanism is that uric acid crystallizes to form monosodium urate crystals. In a case of hyperuricemia (increased levels of uric acid), the monodsodium urate crystals may get deposited in different places. One common site for deposition is joints. When this happens, there is some sort of complex signalling (which we can ignore for present) that causes inflammation. This is characterized by increased presence of macrophages and other phagocytic cells such as neutrophils. So uric acid deposition in joints leads to "gouty arthritis".
Sometimes, over a long period of time, monosodium urate crystals may get deposited in your soft tissues in the form of nodules which are also called tophi (you can skip this if you find it difficult). The form of gout that results is called chronic tophaceous gout.

SO, to return to your original case: excess nucleic acid increases production of uric acid, which crystallized as monosodium urate in joints and soft tissues, leading to an inflammatory response which is called gout.
If you have any questions, ask away!