Mechanical components of motor enzyme function

Enzyme Catalysis To Power Micro/Nanomachines

Enzymes play a crucial role in many biological processes which require harnessing and converting free chemical energy into kinetic forces in order to accomplish tasks. Enzymes are considered to be molecular machines, not only because of their capability of energy conversion in biological systems but also because enzymatic catalysis can result in enhanced diffusion of enzymes at a molecular level. Enlightened by nature's design of biological machinery, researchers have investigated various types of synthetic micro/nanomachines by using enzymatic reactions to achieve self-propulsion of micro/nanoarchitectures. Yet, the mechanism of motion is still under debate in current literature. Versatile proof-of-concept applications of these enzyme-powered micro/nanodevices have been recently demonstrated. In this review, we focus on discussing enzymes not only as stochastic swimmers but also as nanoengines to power self-propelled synthetic motors. We present an overview on different enzyme-powered micro/nanomachines, the current debate on their motion mechanism, methods to provide motion and speed control, and an outlook of the future potentials of this multidisciplinary field.

Exact solution of a linear molecular motor model driven by two-step fluctuations and subject to protein friction

We investigate by analytical means the stochastic equations of motion of a linear molecular motor model based on the concept of protein friction. Solving the coupled Langevin equations originally proposed by Mogilner et al. [Phys. Lett. A 237, 297 (1998)], and averaging over both the two-step internal conformational fluctuations and the thermal noise, we present explicit, analytical expressions for the average motion and the velocity-force relationship. Our results allow for a direct interpretation of details of this motor model which are not readily accessible from numerical solutions. In particular, we find that the model is able to predict physiologically reasonable values for the load-free motor velocity and the motor mobility.

Entropy and information in flagellar axoneme cybernetics: a radial spokes integrative function

Radial spokes and the consequences of their relationships with the central apparatus seem to play a very important role in the regulation of axonemal activity. We modeled their behavior and observed that it appears to differ in the cilium and the flagellum with respect to the development of bending as a function of time. Specifically, our calculation raises the question of the real function of the radial spokes in the regulation of the axoneme, because a given curvature of the flagellar axoneme may correspond to two opposite of their tilts. The stable nil/low amplitude shear points that we had characterized along the flagellum allowed us to describe their axoneme as a series of modules [Cibert, 2002: Cell Motil. Cytoskeleton 51:89-111]. We observed that a nil/low shearing point moves along each module during beating when a new bend is created at the base of the flagellum [Cibert, 2001: Cell Motil. Cytoskeleton 49:161-175]. We propose that the structural gradients of isoforms of tubulin could be basic verniers that act as structural references for the axonemal machinery during the beating. This allowed us to interpret the axonemal organization as a segmented structure, that could be analyzed according to the complexion(1) theory and Shannon's information theory, which associate entropy and probability in the creation of information. The important consequence of this interpretation is that regulation of the axonemal machinery appears to be due to the upstream and downstream cross-talk between the axonemal segments that do not involve any dedicated integrative structure but depend on the energy level of the entire length of each module.

Protein-protein ratchets: stochastic simulation and application to processive enzymes

Interaction between a protein and a series of binding sites on a cytoskeletal substrate can create a resistance, or "protein friction," as the protein is moved along the substrate. If attachment and detachment rates are specified asymmetrically, this resistance can depend on the direction of movement, and the binding interaction acts as a ratchet. Stochastic computer simulations have been used to examine this type of protein-protein interaction. The performance of a protein-protein ratchet in the piconewton and nanometer range is significantly limited by thermal fluctuations, which in experimental measurements with single molecules are evident as Brownian motion. Simulations with a two-component model combining a conventional motor enzyme model with a protein-protein ratchet confirm previous suggestions that the processive movement of a single motor enzyme molecule against a load, as seen in experiments with inner arm dynein molecules, might be made possible by an accessory protein interaction that prevents backward slippage. When this accessory protein interaction is defined so that it acts as a ratchet, backward slippage can be prevented with minimal interference with forward progression.

Computer simulation of flagellar movement: VII. Conventional but functionally different cross-bridge models for inner and outer arm dyneins can explain the effects of outer arm dynein removal

Outer arm dynein removal from flagella by genetic or chemical methods causes decreased frequency and power, but little change in bending pattern. These results suggest that outer arm dynein operates within bends to increase the speed of bend propagation, but does not produce forces that alter the bending pattern established by inner arm dyneins. A flagellar model incorporating different cross-bridge models for inner and outer arm dyneins has been examined. The inner arm dynein model has a hyperbolic force-velocity curve, with a maximum average force at 0 sliding velocity of about 14 pN for each 96 nm group of inner arm dyneins. The outer arm dynein model has a very different force-velocity curve, with a maximum force at about 10-15% of V(max). The outer arm dynein model is adjusted so that the unloaded sliding velocity for a realistic mixture of inner and outer arm dyneins is twice the unloaded sliding velocity for the inner arm dynein model alone. With these cross-bridge models, a flagellar model can be obtained that reduces its sliding velocity and frequency by approximately 50% when outer arm dyneins are removed, with little change in bending pattern. The addition of outer arm dyneins, therefore, gives an approximately 4-fold increase in power output against viscous resistances, and outer arm dyneins may generate 90% or more of the power output. Cell Motil.

A protein friction model of the actin sliding movement generated by myosin in mixtures of MgATP and MgGTP in vitro

The sliding movement of an actin filament generated by myosin heads with MgGTP bound is much slower than that by those with MgATP bound. Nonetheless, there is a report that the actin sliding velocity at low (11-21 microM) MgATP concentrations is increased by the addition of MgGTP in a range of 1-3 mM, although the actin sliding velocity at these MgATP concentrations is larger than the maximum sliding velocity attained in the presence of MgGTP alone. The convex rise in the velocity was called "mutual sensitization of MgATP and MgGTP" in the report. Here we propose a theoretical model to account for the mutual sensitization of MgATP and MgGTP. The model is an extension of a protein friction model, accommodating the presence of two different substrates and assuming the presence of motile and non-motile myosins. This new model is in accord with the characteristics of the actin/myosin sliding movement experimentally observed in mixtures of MgATP and MgGTP. Comparison of the model with the experimental results implies that the non-motile and motile myosins are those with the "converse and correct" orientations of their heads with respect to the direction of the actin sliding movement in vitro.

Computer simulation of flagellar movement: VII. Conventional but functionally different cross-bridge models for inner and outer arm dyneins can explain the effects of outer arm dynein removal

Outer arm dynein removal from flagella by genetic or chemical methods causes decreased frequency and power, but little change in bending pattern. These results suggest that outer arm dynein operates within bends to increase the speed of bend propagation, but does not produce forces that alter the bending pattern established by inner arm dyneins. A flagellar model incorporating different cross-bridge models for inner and outer arm dyneins has been examined. The inner arm dynein model has a hyperbolic force-velocity curve, with a maximum average force at 0 sliding velocity of about 14 pN for each 96 nm group of inner arm dyneins. The outer arm dynein model has a very different force-velocity curve, with a maximum force at about 10-15% of V(max). The outer arm dynein model is adjusted so that the unloaded sliding velocity for a realistic mixture of inner and outer arm dyneins is twice the unloaded sliding velocity for the inner arm dynein model alone. With these cross-bridge models, a flagellar model can be obtained that reduces its sliding velocity and frequency by approximately 50% when outer arm dyneins are removed, with little change in bending pattern. The addition of outer arm dyneins, therefore, gives an approximately 4-fold increase in power output against viscous resistances, and outer arm dyneins may generate 90% or more of the power output. Cell Motil.