We consider DNA codes based on the nearest-neighbor (stem) similarity model which adequately reflects the “hybridization potential” of two DNA sequences. Our aim is to present a survey of bounds on the rate of DNA codes with respect to a thermodynamically motivated similarity measure called an additive stem similarity. These results yield a method to analyze and compare known samples of the nearest neighbor “thermo-dynamic weights” associated to stacked pairs that occurred in DNA secondary structures.

We consider DNA codes based on the concept of a weighted 2-stem similarity measure which reflects the ldquohybridization potentialrdquo of two DNA sequences. A random coding bound on the rate of DNA codes with respect to a thermodynamic motivated similarity measure is proved. Ensembles of DNA strands whose sequence composition is restricted in a manner similar to the restrictions in binary Fibonacci sequences are introduced to obtain the bound.

For q-ary n-sequences, we develop the concept of similarity functions that can be used (for q = 4) to model a thermodynamic similarity on DNA sequences. A similarity function is identified by the length of a longest common subsequence between two q-ary n-sequences. Codes based on similarity functions are called DNA codes. DNA codes are important components in biomolecular computing and other biotechnical applications that employ DNA hybridization assays. We present our unpublished results connected with the conventional deletion similarity function used in the theory of error-correcting codes. The main aim of this paper - to obtain lower bounds on the rate of optimal DNA codes for a biologically motivated similarity function called a similarity of blocks. We also present constructions of suboptimal DNA codes based on the parity-check code detecting one error in the Hamming metric

Kautz-Singleton (1964) suggested a class of binary superimposed codes which are based on the q-ary Reed-Solomon codes (RS codes). Applying a concatenation of the binary constant-weight error-correcting codes and the shortened RS codes, we obtain new constructions of superimposed codes. Tables of their parameters are given. From the tables it follows that the rate of obtained codes exceeds the corresponding random coding bound.