Statistical kinetics of processive molecular motors

We describe new theoretical and experimental tools for studying biological motor proteins at the single molecule scale. These tools enable measurements of molecular fuel economies, thereby providing insight into the pathways for conversion of biochemical energy into mechanical work.; Kinesin is an ATP-dependent motor that moves processively along microtubules in discrete steps of 8 nm. How many molecules of ATP are hydrolysed per step? To determine this coupling ratio, we develop a fluctuation analysis, which relates the variance in records of mechanical displacement to the number of rate-limiting biochemical transitions in the engine cycle. Using fluctuation analysis and optical trapping interferometry, we determine that near zero load, single molecules of kinesin hydrolyse one ATP nucleotide per 8-nm step.; To study kinesin behavior under load, we use a molecular force clamp, capable of maintaining constant loads on single kinesin motors moving processively. Analysis of records of motion under variable ATP concentrations and loads reveals that kinesin is a ‘tightly-coupled’ motor, maintaining the 1:1 coupling ratio up to loads of $\sim$5 pN. Moreover, a Michaelis-Menten analysis of velocity shows that the kinesin cycle contains at least two load-dependent transitions. The rate of one of these transitions affects ATP affinity, while the other does not. Therefore, the kinesin stall force must depend on the ATP concentration, as is demonstrated experimentally. These findings rule out existing theoretical models of kinesin motility.; We develop a simple theoretical formalism describing a tightly-coupled mechanism for movement. This ‘energy-landscape’ formalism quantitatively accounts for motile properties of RNA polymerase (RNAP), the enzyme that transcribes DNA into RNA. The shapes of RNAP force-velocity curves indicate that biochemical steps limiting transcription rates at low loads do not generate movement. Modeling suggests that high loads may halt RNAP by promoting a structural change which moves all or part of the enzyme backwards along the DNA through a distance of 5–10 base pairs. Using the energy landscape formalism, we also propose a model for kinesin. The model incorporates both the ATP-dependent and the ATP-independent mechanical transitions in the motor cycle and explains experimental measurements of kinesin velocity.