A Markovian engine for a biological energy transducer: the catalytic wheel

The molecular machines in biological cells are made of proteins, DNAs and other classes of molecules. The structures of these molecules are characteristically "soft", highly flexible, and yet their interactions with other molecules or ions are specific and selective. This chapter discusses a prevalent form, the catalytic wheel, or the energy transducer of cells, examines its mechanism of action, and extracts from it a set of simple but general rules for understanding the energetics of the biomolecular devices. These rules should also benefit design of manmade nanometer scale machines such as rotary motors or track-guided linear transporters. We will focus on an electric work that, by matching system dynamics and then enhancing the conformational fluctuation of one or several driver proteins, converts stochastic input of energy into rotation or locomotion of a receptor protein. The spatial (or barrier) and temporal symmetry breakings required for selected driver/receptor combinations are examined. This electric ratchet consists of a core engine that follows the Markovian dynamic, alleviates difficulties encountered in rigid mechanical model, and tailors to the soft-matter characteristics of the biomolecules.