Issues in Design and Simulation of Oligonucleotide Mixtures  

To help us in working out the detailed design of oligo mixtures that will implement particular machines, we have constructed a computer simulation of the relevant chemical processes. The simulator follows the evolution of a typical line of descendants of an initial DNA strand over a sequence of PCR cycles (PCR is a standard technique for replicating DNA). During each PCR cycle, the temperature of the reaction mixture is brought down from an initial high level (e.g., 98 C) at which all DNA is single-stranded, to a desired lower level (typically 30-55 C) at which the mutagenic oligos will stick to the long template molecules, after which they can be extended by polymerase. This temperature change is simulated to occur in about one minute (PCR machines can do this). The mixture is held at the low "annealing" temperature long enough for the oligos to bind and for polymerase to begin extending them, and then the temperature is raised to an intermediate temperature, to complete the polymerization quickly and allow ligase to join all the fragments, and then the temperature is raised back to 100 and the whole cycle is repeated. At each tick of the simulation, we use known thermodynamic parameters of base-pairing, and known rates of DNA reassociation to compute the probability that each oligonucleotide will associate with each unoccupied site on the template strand, or disassociate if it is already bound at that site. The outcome is determined randomly, based on these calculated probabilities. At the end of the annealing phase, we look at which oligos are bound, construct a new strand containing them, and proceed to the next cycle using the new strand as the template.

In the process of creating the simulator, we found a number of imporant quantitative relations affecting the design of oligo mixtures:

• To a first approximation, the odds of binding (assuming no competitors) are determined by the temperature, oligo concentration, oligo length, and the number of mismatches.
• The odds of binding are proportional to the concentration, and more or less exponential in all the other factors. Therefore, those other factors must be balanced against each other carefully.
• The rate of oligo association/dissociation is more or less proportional to the oligo concentration, and inversely proportional to the square root of the oligo length.