  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.

Mesoscale and Nanoscale Physics;Statistical Mechanics;Combinatorics;Cellular Automata and Lattice Gases;Quantitative Methods