Modelling approaches to molecular computation

Molecular computing is a nascent field aiming to study the use of molecules as a substrate for computation. Motivations for this range from developing massively parallel computer systems that begin to approach the Bremermann limit, the limit on computational speed imposed by the uncertainty principle, to the idea of a 'Doctor in a cell', capable of automatic diagnosis and treatment of medical conditions on near-atomic scales. The natural choice is to use biological systems for their self-assembly and far-from-equilibrium properties, but current approaches fall short of the original motivations. This project proposes an alternative approach to address these shortcomings. Many computational systems rely on single tapes or strings to represent programs, with computational evolution implemented by symbol transformations. A seemingly ideal set of systems to emulate include the lambda and pi calculi, their favourable properties including self-containment of individual programs (making parallelisation trivial), and the coding efficiency with which higher level languages such as LISP can be reduced to lambda expressions. It is not possible to engineer these models with current molecular methods. Rather, the aim is to consider and model the properties of more general contextual rule-based replacement systems, but limited to static rulesets. This class of systems includes 1D cellular automata (CA), which will be implemented as a proof of concept with the additional bonus that some elementary CAs are in fact Turing-complete - capable of universal
computation. Rule application will be implemented via short oligomers, complementary to their targets and conjugated to their replacements, and computation by iterative assembly of generations of ssDNA molecules. Accounting for noise will be a particular challenge.