Session D29: Molecular Machines and Motors

Processivity of helicase-induced DNA strand separation

Helicases are molecular motors which unwind double-stranded nucleic acids (dsNA) in cells. Many helicases move with directional bias on single-stranded nucleic acids (ssNA), and couple their directional translocation to strand separation. A simple model of the coupling between translocation and unwinding uses an interaction potential between the helicase and the ss-ds junction which can capture both `passive' and `active' mechanisms of NA unwinding. A passive helicase relies on fluctuations which open the dsNA base pairs to advance while its presence on the strand inhibits NA closing. An active helicase directly destabilizes dsNA base pairs where it is bound, thus accelerating the opening rate. Here, we take into account the effects of helicase detachment from the NA strand corresponding to a limited processivity. The average helicase attachment time then depends on the form of the interaction potential. For a passive helicase the mean attachment time does not change between ss translocation and ds unwinding, while for an active helicase in general a decrease in attachment time occurs during unwinding as compared to ss translocation.   

A nanojet: propulsion of a molecular machine by an asymmetric distribution of reaction--products

A simple model for the reaction-driven propulsion of a small device is proposed as a model for (part of) a molecular machine in aqueous media. Motion of the device is driven by an asymmetric distribution of reaction products. We calculate the propulsive velocity of the device as well as the scale of the velocity fluctuations. We also consider the effects of hydrodynamic flow as well as a number of different scenarios for the kinetics of the reaction.   

Twirling of Actin by Myosins II and V

A polarized total internal reflectance fluorescence microscope was used to measure the 3D orientation of single rhodamine molecules with 40 ms time resolution (Forkey et al., \textit{Nature} 422:399, 2003). We modified this setup by adding excitation polarizations at $\pm 45^\circ $ relative to the optical axis of the microscope, thus enabling us to uniquely monitor 1/4 of the probe's angular phase space (previously 1/8). Phase shifts in the optics were compensated with an adjustable waveplate. Using actin filaments sparsely labeled with tetramethylrhodamine at Cys-374, the increased range of discernable angles was used to determine the handedness of filament rotation about its axis in a gliding filament assay. During translocation by Myosin II or V, approximately half of the observed actin filaments exhibit a `twirling' helical path of rotation around the filament axis. Myosin II and V consistently induce a left-handed twirling motion (opposite to the long-pitch helix of actin) with pitch of $1.0\pm 0.2\,\mu \mbox{m}$ for myosin II and $1.5\pm 0.1\,\mu \mbox{m}$for myosin V. Several factors may be the cause of this twirling including: the direction of the force vector between actin and myosin, the distribution of myosin binding sites on actin, and cooperation between myosins translocating an individual actin filament. Supported by NIH grant AR26846 and NSF grant DMR04-25780.   

Synthetic Motors and Nanomachines.

A bistable and palindromically-constituted [3]rotaxane incorporating two mechanically-mobile rings interlocked around a linear dumbbell component, has been designed to operate like the sarcomeres of skeletal muscle. Contraction and extension occurs when the inter-ring distance of the two rings switch, ideally, between 4.2 and 1.4 nm upon redox stimulation either chemically or electrochemically in the solution phase. When the mobile rings of these artificial molecular muscles are bound onto the tops of gold-coated, micron-scale cantilever beams, their controllable nanometer motions have a chance to be amplified along the long axis of each cantilever. It turns out that $\sim $6 billion of the self-assembled [3]rotaxanes can bend the cantilevers in a bistable manner concomitant with the cycled addition of redox agents. The extent of bending is commensurate with 10's of pN of force per [3]rotaxane. Recent studies on a set of ``single-shot'' control [2]rotaxanes have provided additional evidence for the origins of the force generation as it arises from a molecule-based electrostatic repulsion energy of about 10 kcal/mol at 300 K. These findings will be presented in terms of the underlying thermodynamics and kinetics that have been utilized extensively to direct the design and synthesis of artificial molecular machines and which may also serve as a guide for the rational design of unidirectional molecular motors.   

Track Switching and Crossing by Microtubule Motors.

Cytoskeletal filaments in cells form a network of crossing tracks for motor proteins carrying vesicular and protein cargoes. The ability to pass through, switch, or dissociate at such intersections is relevant to the motor's ability to effectively navigate in the cell and deliver goods to the appropriate location. We have formed an \textit{in vitro} system of crossed microtubules to study the outcome of kinesin motors and dynein-dynactin complexes when they encounter an intersection. Microtubules were flowed into the sample chamber from two orthogonal directions and aligned with the flow direction when they attached to glass cover slips via biotin-streptavidin. The first flow direction defined the microtubules closest to the glass surface. Using total internal reflection fluorescence (TIRF) microscopy, we visualized single GFP-kinesin motors and dynein-dynactin-GFP complexes during processive motility at 1 mM ATP. Both dynein and kinesin can switch microtubules, pass by an intersection, or dissociate. Using optical trapping, we placed 1 $\mu $m polymer beads decorated with multiple motors to simulate a large cargo encountering an intersection at 1 mM ATP. Beads are more likely to pause at the intersection at high motor number and can pass and switch as the motor concentration is titrated down. The differences between kinesin and dynein could inform of the ability of these motors to navigate the cell, both separately and in coordination. Supported by NIH grant AR51174.   

Collective dynamics of molecular motors pulling on fluid membranes

The collective dynamics of $N$ weakly coupled processive molecular motors when an external force is exerted on the first one, are considered theoretically. We show, using a discrete lattice model, that the velocity-force curves strongly depend on the effective dynamic interactions between motors and differ significantly from the mean field prediction. They become essentially independent of $N$ when this number is large enough. For strongly biased motors such as kinesin, this may occur for $N$ as small as $5$. The study of a two-state model shows that the existence of internal states can induce effective interactions. Several analytical predictions are discussed and checked numerically both for the discrete lattice model and the two-state model with Langevin dynamics. Typically, motors cooperate constructively so that the collective stall force and the mean velocity are larger than the mean field expectations. The implications on the interpretation of previous experiments on membrane tubes pulled by collective motors and possible design of new experiments are discussed.   

Entropic pulling: how Hsp70 chaperones translocate proteins through membrane pores

Hsp70s are highly conserved ATPase molecular chaperones mediating the translocation of proteins across membranes and the active unfolding and disassembly of stress-induced protein aggregates. Here, we introduce a mechanism named \textit{entropic pulling}, based on entropy loss due to excluded volume effects, by which Hsp70 molecules can convert the energy of ATP hydrolysis into a force capable to drive the translocation of polypeptides into mitochondria. Entropic pulling represents a possible solution to the long-standing debate between the \textit{power-stroke} and the \textit{Brownian ratchet} models for Hsp70-mediated protein translocation across membranes. Moreover, in a very different context devoid of membrane and components of the import pore, the same physical principles apply to the forceful unfolding, solubilization and assisted native refolding of stable protein aggregates by individual Hsp70 molecules, thus providing a unifying mechanism for the different Hsp70 functions.   

Biological motors: Conventional and Unconventional Myosins

Molecular motors are smart, soft machines that regulate their dynamics and energy consumption for efficient tuning to their cell-biological role and mechanics of their cargo. The efficiency is derived partly from harnessing the chaotic thermal fluctuations nano-scale machines experience, rather than struggle against them. Reciprocal coupling between the enzymatic chemistry, structural changes, and mechanical steps is expected from the thermodynamics of an energy-transducing nano-machine. Strong evidence for this bidirectional coupling exists for muscle (conventional) myosin and unconventional myosins. The structural dynamics of myosin leading to translocation along actin are detectable by Optical Trap Mechanical Nanometry (OTNM), Single-Molecule Fluorescence Polarization Microscopy (SMFPM), Fluorescence Imaging at One Nanometer Accuracy (FIONA) and various combinations of these methods. We are in an Acronym Rich Environment (ARE). Progress and puzzles make this a lively research area.   

A single polymer Brownian motor

We study a polymer chain in a flashing ratchet potential to determine how the mechanism of this Brownian motor system is affected by the presence of internal degrees of freedom. Each monomer is acted upon by a 1D asymmetric, piecewise linear potential of spatial period $L$ comparable to the radius of gyration of the polymer. We characterize the average motor velocity as a function of $L$, $T_{\mathrm{off}}$, and $N$ to determine optimal parameter ranges, and we evaluate motor performance in terms of finite dispersion, Peclet number, rectification efficiency, stall-force, and transportation of a load against a viscous drag. We find that the polymer motor performs qualitatively better than a single particle in a flashing ratchet: with increasing $N$, the polymer loses velocity much more slowly than expected in the absence of internal degrees of freedom, and the motor stall force increases linearly with $N$. To understand these cooperative aspects of motor operation, we analyze relevant Rouse modes. The experimental feasibility is analyzed and the parameters of the model are scaled to those of $\lambda$-DNA. Finally, in the context of experimental realization, we present initial modeling results for a 2D flashing ratchet constructed using an electrode array.   

Imaging and Manipulation of Nanocars by STM

The nanocar molecule - four fullerene wheels connected by rotating alkyne axles to a central chassis - is the first molecule designed and fabricated specifically for nanoscale manipulation. We have investigated the imaging and manipulation of the nanocar molecule on Au(111) by variable-temperature STM. From the observed movement of the nanocars, we can show that their motion is due to rolling, not sliding, across the gold surface. Additionally, we have begun to explore the conditions for nanoscale rolling in a number of other molecules built from our set of ``molecular tinker toys'' with an eye towards remote manipulation and increased system complexity.   

Physical mechanism of the nuclear pore transport.

Functioning of eukaryotic cells depends on precise regulation of the transport of proteins in and out of the nucleus. All the transport in an out of the nucleus proceeds through the nuclear pore complex (NPC). NPC is an efficient transport device, which transports proteins between the nucleus and the cytoplasm in milliseconds time. NPC is highly selective, only allowing efficient passage of the molecules bound to the transporter proteins. Although, one GTP is used per transported cargo, the process of translocation through the pore is passive and does not involve active energy consumption. The key component in the NPC function is the attractive interaction between the transporter proteins, and the flexible filaments, lining the internal surface of the pore. We model the transport through the NPC as diffusion in an effective potential due to attachments to the flexible filaments. Using analytical theory and computer simulations, we explain known functional features of the NPC, in terms of its basic physical properties.   

Vectorial Loading of Processive Motor Proteins: Microtubule buckling experiment revisited

Experiments on the motor protein kinesin by Howard and coworkers (1996) observed the buckling of partially clamped microtubules caused by bound motors responding to the induced parallel, $F_x$, and perpendicular, $F_z$, load components. To analyze such results, we have applied simple mechanochemical models for vectorial loads $\boldmath{F=(F_x,F_y,F_z)}$ by implementing a three-dimensional free-energy landscape formulation. An expression for the velocity, $V(F_x,F_z;\textit{[ATP]})$, is obtained by fitting to the velocity and randomness data of Block and coworkers (2003) who imposed both resisting $(F_x < 0 )$ and assisting $(F_x > 0)$ loads. While our results agree qualitatively with the buckling experiments, the analysis predicts that the velocity {\em decreases} under perpendicular loading $(F_z > 0 )$ contrary to the conclusion of Howard and coworkers. This suggests the possibility that the geometry of stressed microtubules might influence the motility of kinesin motors.\\ \noindent [1] Y. C. Kim and M. E. Fisher, J. Phys.: Condens. Matter {\bf 17}, S3821 (2005).