On Classes of One-dimensional Self-assembling Automata
Kazuhiro Saitou
Department of Mechanical Engineering and Applied Mechanics,
University of Michigan, Ann Arbor, MI
Mark J. Jakiela
Hunter Associate Professor of Mechanical Design,
Department of Mechanical Engineering,
Washington University, St. Louis, MO
Abstract
An abstract model of self-assembling systems is presented where assembly instructions are written as conformational switches---local rules that specify conformational changes of a component. The self-assembling automaton model is defined as a sequential rule-based machine that operates on one-dimensional strings of symbols. An algorithm is provided for constructing a self-assembling automaton that self-assembles an one-dimensional string of distinct symbols in a given particular subassembly sequence. Classes of self-assembling automata are then defined based on classes of subassembly sequences in which the components self-assemble. For each class of subassembly sequence, the minimum number of conformations is provided which is necessary to encode subassembly sequences in the class. It is shown that three conformations for each component are enough to encode any subassembly sequences of a string with arbitrary length.
