Design of two-tooth unidirectional rotary-ratchet molecular machines driven by linearly polarized ac fields

An artificial molecular rotor system mounted in a biological membrane, which can unidirectionally rotate in response to weak pumping from a linearly polarized ac field, is modeled. The dynamics of the rotor unit are described by the Langevin equation for a particle in a two-dimensional bistable potential with a two-tooth ratchet structure. This model reveals effects due to the two-dimensionality of the ratchet and the polarization of the applied field. First, we demonstrate that a unidirectional rotation appears with stochastic resonance exhibiting a bell-shaped peak for noise intensity in the mean angular momentum (MAM) of the rotor. An analytical expression for the MAM, (L), is obtained on the basis of a four-state Markov approximation. Second, a significant effect due to torsional nonlinearity (representing the ratchet-like structure) in the potential geometry is quantified: in the absence of torsion, the MAM depends on the polarization angle φ of the applied field as (L) sin(2φ), whereas in the presence of torsion, an additional bias appears in the MAM as (L)(bias + sin(2φ)). It is found that this effect can be used to make the rotor system robustly maintain rotation in a single direction independent of the mounting conditions. Possible designs for an artificial molecular rotor system using the torsion effect are discussed.