Molecular Computing by Signaling Pathways

Summary

To reduce the computing cost (i.e., the molecular number and time) of molecular computers by using DNA, RNA, and other biomolecules is an important task for enhancing their computing performance with parallelism obtained by biological implementation. For this purpose, we propose a new molecular computing method, namely, computing with Rho family GTPases, which differs from the Adleman-Lipton paradigm of DNA computing [1,9] and surfaced-based techniques [2]. This method employs the signaling pathways (the pathways of Rho family GTPases) of in situ cells that are formalized as a special kind of hypergraph rewriting, thus forming “conceptualized pathway objects” that systematically guarantee the rigorousness of massive parallel computing processes.

The 3-SAT problem is used as a benchmark for testing the algorithm of our method. The initial values, the given clauses of the 3-SAT problem, are encoded as signaling molecules and treated as cell input by means of inter-cell communication. Then, after being transmitted by the sender molecules of the cells’ skeleton, these molecules are accepted by the receptor molecules within the cells. Consequently, the pathways of the cells are activated to generate candidate solutions in the reactant molecules’ form in parallel. The process of making these molecules interact in a stepwise manner is carried out recursively based on the implicit constraints within the problem solving itself. Depending on the complexity of the biological mechanism of the molecules for biochemical reactions in the cells, a high degree of autonomy, both in computation theory and in biological faithfulness, is obtained by the entire computing process. By applying our method to solve 3-SAT problems, we have obtained a space complexity of O(m x n)and a time complexity of O(m), where m is the number of clauses and n is the number of variables.

The experimental results obtained from a corresponding software simulator (impleme ntation) of our method show that the algorithm that we have obtained is efficient from the viewpoint of computing costs and that it also has reasonable biological faithfulness with a strong potential for further biological implementation by cells in situ.