On the Relation Between Noise Spectra and the Distribution of Time Between Steps for Single Molecular Motors

Kinetic analysis methods applied to single motor protein trajectories

Molecular motors convert chemical or electrical energy into mechanical displacement, either linear or rotary. Under ideal circumstances, single-molecule measurements can spatially and temporally resolve individual steps of the motor, revealing important properties of the underlying mechanochemical process. Unfortunately, steps are often hard to resolve, as they are masked by thermal noise. In such cases, details of the mechanochemistry can nonetheless be recovered by analyzing the fluctuations in the recorded traces. Here, we expand upon existing statistical analysis methods, providing two new avenues to extract the motor step size, the effective number of rate-limiting chemical states per translocation step, and the compliance of the link between the motor and the probe particle. We first demonstrate the power and limitations of these methods using simulated molecular motor trajectories, and we then apply these methods to experimental data of kinesin, the bacterial flagellar motor, and F1-ATPase.

Kinesin-8 is a low-force motor protein with a weakly bound slip state

During the cell cycle, kinesin-8s control the length of microtubules by interacting with their plus ends. To reach these ends, the motors have to be able to take many steps without dissociating. However, the underlying mechanism for this high processivity and how stepping is affected by force are unclear. Here, we tracked the motion of yeast (Kip3) and human (Kif18A) kinesin-8s with high precision under varying loads using optical tweezers. Surprisingly, both kinesin-8 motors were much weaker compared with other kinesins. Furthermore, we discovered a force-induced stick-slip motion: the motor frequently slipped, recovered from this state, and then resumed normal stepping motility without detaching from the microtubule. The low forces are consistent with kinesin-8s being regulators of microtubule dynamics rather than cargo transporters. The weakly bound slip state, reminiscent of a molecular safety leash, may be an adaptation for high processivity.

Mechanistic constraints from the substrate concentration dependence of enzymatic fluctuations

The time it takes an enzyme to complete its reaction is a stochastic quantity governed by thermal fluctuations. With the advent of high-resolution methods of single-molecule manipulation and detection, it is now possible to observe directly this natural variation in the enzymatic cycle completion time and extract kinetic information from the statistics of its fluctuations. To this end, the inverse of the squared coefficient of variation, which we term n(min), is a useful measure of fluctuations because it places a strict lower limit on the number of kinetic states in the enzymatic mechanism. Here we show that there is a single general expression for the substrate dependence of n(min) for a wide range of kinetic models. This expression is governed by three kinetic parameters, which we term N(L), N(S), and alpha. These parameters have simple geometric interpretations and provide clear constraints on possible kinetic mechanisms. As a demonstration of this analysis, we fit the fluctuations in the dwell times of the packaging motor of the bacteriophage varphi29, revealing additional features of the nucleotide loading process in this motor. Because a diverse set of kinetic models display the same substrate dependence for their fluctuations, the expression for this general dependence may prove of use in the characterization and study of the dynamics of a wide range of enzymes.

Protein friction limits diffusive and directed movements of kinesin motors on microtubules

Friction limits the operation of macroscopic engines and is critical to the performance of micromechanical devices. We report measurements of friction in a biological nanomachine. Using optical tweezers, we characterized the frictional drag force of individual kinesin-8 motor proteins interacting with their microtubule tracks. At low speeds and with no energy source, the frictional drag was related to the diffusion coefficient by the Einstein relation. At higher speeds, the frictional drag force increased nonlinearly, consistent with the motor jumping 8 nanometers between adjacent tubulin dimers along the microtubule, and was asymmetric, reflecting the structural polarity of the microtubule. We argue that these frictional forces arise from breaking bonds between the motor domains and the microtubule, and they limit the speed and efficiency of kinesin.

Single molecule studies of homologous recombination

Single molecule methods offer an unprecedented opportunity to examine complex macromolecular reactions that are obfuscated by ensemble averaging. The application of single molecule techniques to study DNA processing enzymes has revealed new mechanistic details that are unobtainable from bulk biochemical studies. Homologous DNA recombination is a multi-step pathway that is facilitated by numerous enzymes that must precisely and rapidly manipulate diverse DNA substrates to repair potentially lethal breaks in the DNA duplex. In this review, we present an overview of single molecule assays that have been developed to study key aspects of homologous recombination and discuss the unique information gleaned from these experiments.

Motor step size and ATP coupling efficiency of the dsDNA translocase EcoR124I

The Type I restriction-modification enzyme EcoR124I is an archetypical helicase-based dsDNA translocase that moves unidirectionally along the 3′–5′ strand of intact duplex DNA. Using a combination of ensemble and single-molecule measurements, we provide estimates of two physicochemical constants that are fundamental to a full description of motor protein activity—the ATP coupling efficiency (the number of ATP consumed per base pair) and the step size (the number of base pairs transported per motor step). Our data indicate that EcoR124I makes small steps along the DNA of 1 bp in length with 1 ATP consumed per step, but with some uncoupling of the ATPase and translocase cycles occurring so that the average number of ATP consumed per base pair slightly exceeds unity. Our observations form a framework for understanding energy coupling in a great many other motors that translocate along dsDNA rather than ssDNA.

DNA mechanics as a tool to probe helicase and translocase activity

Helicases and translocases are proteins that use the energy derived from ATP hydrolysis to move along or pump nucleic acid substrates. Single molecule manipulation has proved to be a powerful tool to investigate the mechanochemistry of these motors. Here we first describe the basic mechanical properties of DNA unraveled by single molecule manipulation techniques. Then we demonstrate how the knowledge of these properties has been used to design single molecule assays to address the enzymatic mechanisms of different translocases. We report on four single molecule manipulation systems addressing the mechanism of different helicases using specifically designed DNA substrates: UvrD enzyme activity detection on a stretched nicked DNA molecule, HCV NS3 helicase unwinding of a RNA hairpin under tension, the observation of RecBCD helicase/nuclease forward and backward motion, and T7 gp4 helicase mediated opening of a synthetic DNA replication fork. We then discuss experiments on two dsDNA translocases: the RuvAB motor studied on its natural substrate, the Holliday junction, and the chromosome-segregation motor FtsK, showing its unusual coupling to DNA supercoiling.

Single-Molecule Manipulation Measurements of DNA Transport Proteins

Single-molecule measurements of the manipulation of three different DNA motor proteins are reviewed. Despite some differences in the structure and mechanisms of the proteins, there are consistent phenomenological themes that relate them. Each of the experiments described represents a significant advance in the understanding of the mechanisms of DNA transport.

Single-molecule assay reveals strand switching and enhanced processivity of UvrD

DNA helicases are enzymes capable of unwinding double-stranded DNA (dsDNA) to provide the single-stranded DNA template required in many biological processes. Among these, UvrD, an essential DNA repair enzyme, has been shown to unwind dsDNA while moving 3'-5' on one strand. Here, we use a single-molecule manipulation technique to monitor real-time changes in extension of a single, stretched, nicked dsDNA substrate as it is unwound by a single enzyme. This technique offers a means for measuring the rate, lifetime, and processivity of the enzymatic complex as a function of ATP, and for estimating the helicase step size. Strikingly, we observe a feature not seen in bulk assays: unwinding is preferentially followed by a slow, enzyme-translocation-limited rezipping of the separated strands rather than by dissociation of the enzymatic complex followed by quick rehybridization of the DNA strands. We address the mechanism underlying this phenomenon and propose a fully characterized model in which UvrD switches strands and translocates backwards on the other strand, allowing the DNA to reanneal in its wake.

The mechanism of type IA topoisomerases

The topology of cellular DNA is carefully controlled by enzymes called topoisomerases. By using single-molecule techniques, we monitored the activity of two type IA topoisomerases in real time under conditions in which single relaxation events were detected. The strict one-at-a-time removal of supercoils we observed establishes that these enzymes use an enzyme-bridged strand-passage mechanism that is well suited to their physiological roles and demonstrates a mechanistic unity with type II topoisomerases.