Kinetic theory of ATP-driven translocases on one-dimensional polymer lattices

A theory is presented to describe the coupling of the directional movement of ATPase-containing translocases (such as helicases) along polymeric lattices to the steady-state kinetic parameters of the ATPase activity that drives this movement. This theory was developed to explain the results of an experimental investigation of one such enzyme, the bacteriophage T4 gene 41 protein helicase. The salient feature of the theory is that it correctly predicts the dependence of the rate of ATP hydrolysis by ATP-driven translocases on the length of polymer lattices along which they move. In the steady-state rate equation: [formula: see text] either Vmax, or K(act), or both, may depend on the lattice length. Two translocation models are considered. The first is a simple mechanism of the type E<-->E-Lat-->E, where the E-Lat-->E step represents the sum of the translocation steps of the enzyme along, and enzyme release from, the lattice. In the second model this mechanism is expanded to add an additional kinetic step, either before or after the translocation process. Variants of this second model can be used to represent the most simple translocase mechanisms. Another method of measuring the lattice length dependence of an ATP-driven translocase, which is applicable particularly to ATPases moving along DNA lattices, involves the use of lattice-binding proteins (such as single-stranded DNA binding proteins) that can block the movement of the translocases and therefore simulate lattice ends. In this protocol the dependence of the ATPase kinetics of the translocase on lattice length can be studied by experiments on long lattices complexed with lattice-binding proteins to various binding densities. This method is not always as unambiguous as direct measurement of ATPase activity on lattices of defined length, but can help to discriminate between mechanisms. The significance of the steady-state kinetic parameters obtained in such experiments is discussed in terms of the mechanistic rate constants that define the models we have investigated.