Force generation by cellular motors

Cell motility processes in non-muscle cells depend on the activity of motor proteins that bind to either microtubules or actin filaments. From presently available data it must be concluded that the driving force is generated by transient interaction of the respective motors with microtubules or actin filaments which then activates the binding and hydrolysis of ATP. This reaction results in an abrupt discharge of the motor molecule, the direction of which is determined by the spatial orientation of its binding to the helical and polar vehicle. The latter is thereby propelled in its length direction and simultaneously undergoes an axial rotation, while the expelled motor exerts an oppositely directed current in the surrounding fluid, comparable to jet propulsion. Force production, propulsion velocities and energy requirements known from in vitro studies comply with those derived from the theory. The theory opens new ways for the understanding of cellular activities such as particle transport, mitosis and morphodynamics.     

Force and motion generation of myosin motors: muscle contraction

Brownian ratchet theory refers to the phenomenon that non-equilibrium fluctuations in an isothermal medium and anisotropic system can induce mechanical force and motion. This concept of noise-induced transport has motivated an abundance of theoretical and applied research. One of the exciting applications of the ratchet theory lies in the possible explanation of the operating mode of biological molecular motors. Biomolecular motors are proteins able of converting chemical reactions into mechanical motion and force. Operating at energy levels only a few times greater than the energy levels of thermal baths, their operating mode has to be stochastic in nature. Here, we review the theoretical concepts of the Brownian ratchet theory and its possible link to the operation of the myosin II motors involved in muscle contraction.     

Mechanochemical coupling of the motion of molecular motors to ATP hydrolysis.

The typical biochemical paradigm for coupling between hydrolysis of ATP and the performance of chemical or mechanical work involves a well-defined sequence of events (a kinetic mechanism) with a fixed stoichiometry between the number of ATP molecules hydrolyzed and the turnover of the output reaction. Recent experiments show, however, that such a deterministic picture of coupling may not be adequate to explain observed behavior of molecular motor proteins in the presence of applied forces. Here we present a general model in which the binding of ATP and release of ADP serve to modulate the binding energy of a motor protein as it travels along a biopolymer backbone. The mechanism is loosely coupled--the average number of ATPs hydrolyzed to cause a single step from one binding site to the next depends strongly on the magnitude of an applied force and on the effective viscous drag force. The statistical mechanical perspective described here offers insight into how local anisotrophy along the "track" for a molecular motor, combined with an energy-releasing chemical reaction to provide a source of nonequilibrium fluctuations, can lead to macroscopic motion.     

The role of thermal activation in motion and force generation by molecular motors

The currently accepted mechanism for ATP-driven motion of kinesin is called the hand-over-hand model, where some chemical transition during the ATP hydrolysis cycle stretches a spring, and motion and force production result from the subsequent relaxation. It is essential in this mechanism for the moving head of kinesin to dissociate, while the other head remains firmly attached to the microtubule. Here we propose an alternative Brownian motor model where the action of ATP modulates the interaction potential between kinesin and the microtubule rather than a spring internal to the kinesin molecule alone. In this model neither head need dissociate (which predicts that under some circumstances a single-headed kinesin can display processive motion) and the transitions by which the motor moves are best described as thermally activated steps. This model is consistent with a wide range of experimental data on the force-velocity curves, the one ATP to one-step stoichiometry observed at small load, and the stochastic properties of the stepping.     

Force generation and work production by covalently cross-linked actin-myosin cross-bridges in rabbit muscle fibers.

To separate a fraction of the myosin cross-bridges that are attached to the thin filaments and that participate in the mechanical responses, muscle fibers were cross-linked with 1-(3-dimethylaminopropyl)-3-ethylcarbodiimide and then immersed in high-salt relaxing solution (HSRS) of 0.6 M ionic strength for detaching the unlinked myosin heads. The mechanical properties and force-generating ability of the cross-linked cross-bridges were tested with step length changes (L-steps) and temperature jumps (T-jumps) from 6-10 degrees C to 30-40 degrees C. After partial cross-linking, when instantaneous stiffness in HSRS was 25-40% of that in rigor, the mechanical behavior of the fibers was similar to that during active contraction. The kinetics of the T-jump-induced tension transients as well as the rate of the fast phase of tension recovery after length steps were close to those in unlinked fibers during activation. Under feedback force control, the T-jump initiated fiber shortening by up to 4 nm/half-sarcomere. Work produced by a cross-linked myosin head after the T-jump was up to 30 x 10(-21) J. When the extent of cross-linking was increased and fiber stiffness in HSRS approached that in rigor, the fibers lost their viscoelastic properties and ability to generate force with a rise in temperature.     

Directionality and processivity of molecular motors.

Analysis of a mutant with altered directionality has led to new insights into motor directionality. The prediction from current models for processivity of a two-heads-bound state has been confirmed by electron microscopy for myosin V and by unbinding experiments for kinesin. Evidence is emerging that non-processive motors bind their filament with one head, hydrolyze ATP and then release, requiring binding by a second motor to complete a step.     

Force generation in RNA polymerase.

RNA polymerase (RNAP) is a processive molecular motor capable of generating forces of 25-30 pN, far in excess of any other known ATPase. This force derives from the hydrolysis free energy of nucleotides as they are incorporated into the growing RNA chain. The velocity of procession is limited by the rate of pyrophosphate release. Here we demonstrate how nucleotide triphosphate binding free energy can rectify the diffusion of RNAP, and show that this is sufficient to account for the quantitative features of the measured load-velocity curve. Predictions are made for the effect of changing pyrophosphate and nucleotide concentrations and for the statistical behavior of the system.     

Fluctuations, responses and energetics of molecular motors

A novel equality relating the rate of energy dissipation to a degree of violation of the fluctuation-response relation (FRR) in non-equilibrium Langevin systems is described. The FRR is a relation between the correlation function of the fluctuations and the response function of macroscopic variables. Although it has been established that the FRR holds in equilibrium, physical significance of violation of the FRR in non-equilibrium systems has been under debate. Recently, the authors have found that an extent of the FRR violation is related in a simple equality to the rate of energy dissipation into the environment in non-equilibrium Langevin systems. In this paper, we fully explain the FRR, the FRR violation, and the new equality with regard to a Langevin model termed a Brownian motor model, which is considered as a simple model of a biological molecular motor. Furthermore, applications of our result to experimental studies of molecular motors are discussed, and, as an illustration, we predict the value of a new time constant regarding the motion of a KIF1A, which is a kind of single-headed kinesin.     

Linking molecular motors to Alzheimer's disease.

It is currently thought that Alzheimer's disease develops due to aberrant generation of amyloid-beta peptides. However, the mechanisms underlying the aberrant generation of amyloid-beta peptides remain unknown. An emerging concept suggests that impaired axonal transport may play a pivotal role in the aberrant generation of amyloid-beta peptides. Here we review and discuss advances in understanding AD with the primary focus on the possible role of molecular motors and axonal transport in its pathogenesis.     

Organelle transport and molecular motors in fungi

Polarized growth, secretion of exoenzymes, organelle inheritance, and organelle positioning require vectorial transport along cytoskeletal elements. The discovery of molecular motors and intensive studies on their biological function during the past 3 years confirmed a central role of these mechanoenzymes in morphogenesis and development of yeasts and filamentous fungi. Saccharomyces cerevisiae proved to be an excellent model system, in which the complete set of molecular motors is presumed to be known. Genetic studies combined with cell biological methods revealed unexpected functional relationships between these motors and has greatly improved our understanding of nuclear migration, exocytosis, and endocytosis in yeasts. Tip growth of elongated hyphae, compared to budding, however, does require vectorial transport over long distances. The identification of ubiquitous motors that are not present in yeast indicates that studies on filamentous fungi might be helpful to elucidate the role of motors in long-distance organelle transport within higher eukaryotic cells. Copyright 1998 Academic Press.     

Single molecule measurements and molecular motors

Single molecule imaging and manipulation are powerful tools in describing the operations of molecular machines like molecular motors. The single molecule measurements allow a dynamic behaviour of individual biomolecules to be measured. In this paper, we describe how we have developed single molecule measurements to understand the mechanism of molecular motors. The step movement of molecular motors associated with a single cycle of ATP hydrolysis has been identified. The single molecule measurements that have sensitivity to monitor thermal fluctuation have revealed that thermal Brownian motion is involved in the step movement of molecular motors. Several mechanisms have been suggested in different motors to bias random thermal motion to directional movement.     

Microtubule dynamics and the role of molecular motors in Neurospora crassa.

Live-cell imaging methods were used to study microtubule dynamics in the apical regions of leading hyphae and germ tubes of Neurospora crassa expressing beta-tubulin-GFP. Microtubule polymerization rates in hyphae of N. crassa were much faster than those previously reported in any other eukaryotic organism. In order to address the roles of motor proteins in microtubule dynamic instability in N. crassa, the microtubule-motor mutant strains, Deltankin and ro-1, were examined. Polymerization and depolymerization rates in leading hyphae of these strains were reduced by one half relative to the wild type. Furthermore, microtubules in germ tubes of wild type and microtubule-motor mutants exhibited similar dynamic characteristics as those in hyphae of mutant strains. Small microtubule fragments exhibiting anterograde and retrograde motility were present in leading hyphae of all strains and germ tubes of wild-type strains. Our data suggest that microtubule motors play important roles in regulating microtubule dynamic instability in leading hyphae but not in germ tubes.     

Hopping and stalling of processive molecular motors

When a two-headed molecular motor such as kinesin is attached to its track by just a single head in the presence of an applied load, thermally activated head detachment followed by rapid re-attachment at another binding site can cause the motor to ‘hop’ backwards. Such hopping, on its own, would produce a linear force-velocity relation. However, for kinesin, we must incorporate hopping into the motor's alternating-head scheme, where we expect it to be most important for the state prior to neck-linker docking. We show that hopping can account for the backward steps, run length and stalling of conventional kinesin. In particular, although hopping does not hydrolyse ATP, we find that the hopping rate obeys the same Michaelis-Menten relation as the ATP hydrolysis rate. Hopping can also account for the reduced processivity observed in kinesins with mutations in their tubulin-binding loop. Indeed, it may provide a general mechanism for the breakdown of perfect processivity in two-headed molecular motors.     

Coiled coils and SAH domains in cytoskeletal molecular motors

Cytoskeletal motors include myosins, kinesins and dyneins. Myosins move along tracks of actin filaments, whereas kinesins and dyneins move along microtubules. Many of these motors are involved in trafficking cargo in cells. However, myosins are mostly monomeric, whereas kinesins are mostly dimeric, owing to the presence of a coiled coil. Some myosins (myosins 6, 7 and 10) contain an SAH (single α-helical) domain, which was originally thought to be a coiled coil. These myosins are now known to be monomers, not dimers. The differences between SAH domains and coiled coils are described and the potential roles of SAH domains in molecular motors are discussed.     

Interactions and regulation of molecular motors in Xenopus melanophores

Many cellular components are transported using a combination of the actin- and microtubule-based transport systems. However, how these two systems work together to allow well-regulated transport is not clearly understood. We investigate this question in the Xenopus melanophore model system, where three motors, kinesin II, cytoplasmic dynein, and myosin V, drive aggregation or dispersion of pigment organelles called melanosomes. During dispersion, myosin V functions as a "molecular ratchet" to increase outward transport by selectively terminating dynein-driven minus end runs. We show that there is a continual tug-of-war between the actin and microtubule transport systems, but the microtubule motors kinesin II and dynein are likely coordinated. Finally, we find that the transition from dispersion to aggregation increases dynein-mediated motion, decreases myosin V--mediated motion, and does not change kinesin II--dependent motion. Down-regulation of myosin V contributes to aggregation by impairing its ability to effectively compete with movement along microtubules.     

Dwell time symmetry in random walks and molecular motors

The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result, theoretical results for cycle completion in enzyme kinetics do not apply to stepping data. To allow correct parameter estimation, and to guide data analysis and experiment design, a theoretical treatment is needed that takes this observation into account. In this article, we model the distribution of dwell times and number of forward and backward steps using first passage processes, based on the assumption that forward and backward steps correspond to different directions of the same transition. We extend recent results for systems with a single cycle and consider the full dwell time distributions as well as models with multiple pathways, detectable substeps, and detachments. Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle. We demonstrate our results by analyzing recent stepping data for a bacterial flagellar motor, and discuss the implications for the efficiency and reversibility of the force-generating subunits.     

Force generation and temperature-jump and length-jump tension transients in muscle fibers.

Muscle tension rises with increasing temperature. The kinetics that govern the tension rise of maximally Ca(2+)-activated, skinned rabbit psoas fibers over a temperature range of 0-30 degrees C was characterized in laser temperature-jump experiments. The kinetic response is simple and can be readily interpreted in terms of a basic three-step mechanism of contraction, which includes a temperature-sensitive rapid preequilibrium(a) linked to a temperature-insensitive rate-limiting step and followed by a temperature-sensitive tension-generating step. These data and mechanism are compared and contrasted with the more complex length-jump Huxley-Simmons phases in which all states that generate tension or bear tension are perturbed. The rate of the Huxley-Simmons phase 4 is temperature sensitive at low temperatures but plateaus at high temperatures, indicating a change in rate-limiting step from a temperature-sensitive (phase 4a) to a temperature-insensitive reaction (phase 4b); the latter appears to correlate with the slow, temperature-insensitive temperature-jump relaxation. Phase 3 is absent in the temperature-jump, which excludes it from tension generation. We confirm that de novo tension generation occurs as an order-disorder transition during phase 2slow and the equivalent, temperature-sensitive temperature-jump relaxation.