We explore quantization of the response of a molecular motor to periodic modulation of control parameters. We formulate the pumping-quantization theorem (PQT) that identifies the conditions for robust integer quantized behavior of a periodically driven molecular machine. Implication of PQT on experiments with catenane molecules are discussed. ACKNOWLEDGMENTS We are grateful to M. Chertkov, J. R. Klein, and J. Horowitz for useful discussions. This material is based upon work supported by NSF under Grant Nos. CHE-0808910 and ECCS-0925618.
Chernyak VY, Sinitsyn NA. (2009). Robust quantization of a molecular motor motion in a stochastic environment. J. Chem. Phys. 131, 181101 doi:10.1063/1.3263821