Fibonacci Ensemble and High Fidelity DNA Codes

Anthony J. Macula

ABSTRACT: DNA nanotechnology often requires collections of oligonucleotides called DNA free energy gap codes that do not produce erroneous crosshybridizations in a competitive muliplexing environment. This talk addresses the question of how to design these codes to accomplish a desired amount of work within an acceptable error rate. Using a statistical thermodynamic and probabilistic model of DNA code fidelity, mathematical random coding theory methods and a connection to the Fibonacci numbers, theoretical lower bounds on the size of DNA codes are given. More importantly, DNA code design parameters, e.g., strand number, strand length and sequence composition, needed to achieve experimental goals are identified.