DNA Linear Self-Assembly And The Theory Of Its Equilibrium

Over the last few decades, much of the emphasis in computer sciences has been on building computers that are more complex and correspondingly more powerful. Recently, however, there has been an increasing awareness of the need for alternative model of computation, quantum computation and DNA computing being two notable examples. The latter necessitates the development of a theory of self-assembly. Despite its importance, self-assembly is poorly understood. Winfree proved that self-assembling tile systems in a plane are capable of doing universal computation, and when restricted to a line are exactly as powerful as discrete finite automa.The mathematical theory of Linear Self-assembly was mainly developed by Adleman. He presented a mathematical formal model of Linear Self-assembly and studied the character of dynamics of the model-time-complexity and equilibrium. His works only consider the uniform case. In this paper, I develop his theory and study the non-uniform case focusing on equilibrium. I prove that the Linear Self-assembly ultimately reach equilibrium in this case. I also show that if the fraction of association-rates to dissociation-rates is uniform, the equilibrium value of each tile is the same.