Macromolecular physiology. One small step for myosin

Mechanical response analysis and power generation by single-cell stretching

To harvest useful information about cell response due to mechanical perturbations under physiological conditions, a cantilever-based technique was designed, which allowed precise application of arbitrary forces or deformation histories on a single cell in vitro. Essential requirements for these investigations are a mechanism for applying an automated cell force and an induced-deformation detection system based on fiber-optical force sensing and closed loop control. The required mechanical stability of the setup can persist for several hours since mechanical drifts due to thermal gradients can be eliminated sufficiently (these gradients are caused by local heating of the cell observation chamber to 37 degrees C). During mechanical characterization, the cell is visualized with an optical microscope, which enables the simultaneous observation of cell shape and intracellular morphological changes. Either the cell elongation is observed as a reaction against a constant load or the cell force is measured as a response to constant deformation. Passive viscoelastic deformation and active cell response can be discriminated. The active power generated during contraction is in the range of Pmax= 10(-16) Watts, which corresponds to 2500 ATP molecules s(-1) at 10 k(B)T/molecule. The ratio of contractive to dissipative power is estimated to be in the range of 10(-2). The highest forces supported by the cell suggest that about 10(4) molecular motors must be involved in contraction. This indicates an energy-conversion efficiency of approximately 0.5. Our findings propose that, in addition to the recruitment of cell-contractile elements upon mechanical stimulation, the cell cytoskeleton becomes increasingly crosslinked in response to a mechanical pull. Quantitative stress-strain data, such as those presented here, may be employed to test physical models that describe cellular responses to mechanical stimuli.

Myosin cross-bridge mechanics: geometrical determinants for continuous sliding

Advances in experimental techniques have provided new details on the molecular mechanisms governing the cross-bridge kinetics. Nevertheless, the issue of micromechanics of sliding is still debated. In particular, uncertainty exists regarding the myosin filament arrangement and structure and the mechanics of the myosin head with respect to the working stroke distance (WS) and the duty ratio (r), i.e. the fraction of the ATPase cycle time the myosin head is attached to the actin filament. The object of the present work is to provide a theoretical framework to correlate different features of cross-bridge mechanics; the main hypothesis is that the attachment between the actin filament and the surrounding myosin filaments has to be continuous through the sliding (continuous sliding hypothesis) in order to maximise the effect of the myosin head performance. A 3-D model of the sliding mechanism based on a geometrical approach is presented, which is able to identify the architectures that accomplish the continuous sliding under unloaded conditions. About 200 different configurations have been simulated by changing the myosin head binding range, i.e. its ability to reach an actin binding site from its rest position, WS, the myosin head orientation and the actin filament orientation. Only few configurations were consistent with the continuous sliding hypothesis. Depending on the parameter set adopted, the percentage of attached heads (%AH) calculated ranges between 4% and 28%, r between 0.08 and 0.02s(-1), and the sliding velocity between 0.7 and 10.6 microm/s. In all the cases, results were not affected by the WS value.

Probing the relation between force--lifetime--and chemistry in single molecular bonds

On laboratory time scales, the energy landscape of a weak bond along a dissociation pathway is fully explored through Brownian-thermal excitations, and energy barriers become encoded in a dissociation time that varies with applied force. Probed with ramps of force over an enormous range of rates (force/time), this kinetic profile is transformed into a dynamic spectrum of bond rupture force as a function of loading rate. On a logarithmic scale in loading rate, the force spectrum provides an easy-to-read map of the prominent energy barriers traversed along the force-driven pathway and exposes the differences in energy between barriers. In this way, the method of dynamic force spectroscopy (DFS) is being used to probe the complex relation between force-lifetime-and chemistry in single molecular bonds. Most important, DFS probes the inner world of molecular interactions to reveal barriers that are difficult or impossible to detect in assays of near equilibrium dissociation but that determine bond lifetime and strength under rapid detachment. To use an ultrasensitive force probe as a spectroscopic tool, we need to understand the physics of bond dissociation under force, the impact of experimental technique on the measurement of detachment force (bond strength), the consequences of complex interactions in macromolecular bonds, and effects of multiply-bonded attachments.

Femtonewton force spectroscopy of single extended DNA molecules

We studied the thermal fluctuations of single DNA molecules with a novel optical tweezer based force spectroscopy technique. This technique combines femtonewton sensitivity with millisecond time resolution, surpassing the sensitivity of previous force measurements in aqueous solution with comparable bandwidth by a hundredfold. Our data resolve long-standing questions concerning internal hydrodynamics of the polymer and anisotropy in the molecular relaxation times and friction coefficients. The dynamics at high extension show interesting nonlinear behavior.

Muscle contraction as a Markov process. I: Energetics of the process

Force generation during muscle contraction can be understood in terms of cyclical length changes in segments of actin thin filaments moving through the three-dimensional lattice of myosin thick filaments. Recent anomalies discovered in connection with analysis of myosin step sizes in in vitro motility assays and with skinned fibres can be rationalized by assuming that ATP hydrolysis on actin accompanies these length changes. The paradoxically rapid regeneration of tension in quick release experiments, as well as classical energetic relationships, such as Hill's force-velocity curve, the Fenn effect, and the unexplained enthalpy of shortening, can be given mutually self-consistent explanations with this model. When muscle is viewed as a Markov process, the vectorial process of chemomechanical transduction can be understood in terms of lattice dependent transitions, wherein the phosphate release steps of the myosin and actin ATPases depend only on occurrence of allosteric changes in neighbouring molecules. Tropomyosin has a central role in coordinating the steady progression of these cooperative transitions along actin filaments and in gearing up the system in response to higher imposed loads.

Modelling and simulation of motility in actomyosin systems

We present a model mechanism for simulating the diffusive motion and fluctuations inherent in myofibrillar sarcomere and its subunits at the molecular level. The model couples Langevin dynamics with Huxley kinetics to reproduce the transient patterns of momentum transfer, force generation and resulting motility due to the interactive activities of actin and myosin crossbridges. When myosin is detached from actin, our model predicts Brownian displacements centered at 0 +/- 8 nm (mean +/- SD, n = 265,308) and it is broadly distributed due to the Brownian noise. Attachment events produced displacements with step sizes of approximately 8 +/- 6 nm (mean +/- SD, n = 34,693), which is in agreement with some recent optical-tweezers transducer experimental results. The proposed model could form the basis for a complete qualitative and quantitative description of the evolving complex interactions of the molecular proteins--actin and myosin--in the overall framework of muscular contraction studies.

Molecular motors: structural adaptations to cellular functions

Molecular motors are protein machines whose directed movement along cytoskeletal filaments is driven by ATP hydrolysis. Eukaryotic cells contain motors that help to transport organelles to their correct cellular locations and to establish and alter cellular morphology during cell locomotion and division. The best-studied motors, myosin from skeletal muscle and conventional kinesin from brain, are remarkably similar in structure, yet have very different functions. These differences can be understood in terms of the 'duty ratio', the fraction of the time that a motor is attached to its filament. Differences in duty ratio can explain the diversity of structures, speeds and oligomerization states of members of the large kinesin, myosin and dynein families of motors.

Smooth muscle and skeletal muscle myosins produce similar unitary forces and displacements in the laser trap

Purified smooth muscle myosin in the in vitro motility assay propels actin filaments at 1/10 the velocity, yet produces 3-4 times more force than skeletal muscle myosin. At the level of a single myosin molecule, these differences in force and actin filament velocity may be reflected in the size and duration of single motion and force-generating events, or in the kinetics of the cross-bridge cycle. Specifically, an increase in either unitary force or duty cycle may explain the enhanced force-generating capacity of smooth muscle myosin. Similarly, an increase in attached time or decrease in unitary displacement may explain the reduced actin filament velocity of smooth muscle myosin. To discriminate between these possibilities, we used a laser trap to measure unitary forces and displacements from single smooth and skeletal muscle myosin molecules. We analyzed our data using mean-variance analysis, which does not rely on scoring individual events by eye, and emphasizes periods in the data with constant properties. Both myosins demonstrated multiple but similar event populations with discrete peaks at approximately +11 and -11 nm in displacement, and 1.5 and 3.5 pN in force. Mean attached times for smooth muscle myosin were longer than for skeletal-muscle myosin. These results explain much of the difference in actin filament velocity between these myosins, and suggest that an increased duty cycle is responsible for the enhanced force-generating capacity of smooth over skeletal-muscle myosin.

Actin filament mechanics in the laser trap

Numerous biological processes, including muscular contraction, depend upon the mechanical properties of actin filaments. One such property is resistance to bending (flexural rigidity, EI). To estimate EI, we attached the ends of fluorescently labelled actin filaments to two microsphere 'handles' captured in independent laser traps. The positions of the traps were manipulated to apply a range of tensions (0-8 pN) to the filaments via the microsphere handles. With increasing filament tension, the displacement of the microspheres was inconsistent with a microsphere-filament system that is rigid. We maintain that this inconsistency is due to the microspheres rotating in the trap and the filaments bending near either attachments to accommodate this rotation. Fitting the experimental data to a simple model of this phenomena, we estimate actin's EI to be approximately 15 x 10(3) pNnm2, a value within the range of previously reported results, albeit using a novel method. These results both: support the idea that actin filaments are more compliant than historically assumed; and, indicate that without appropriately pretensioning the actin filament in similar laser traps, measurements of unitary molecular events (e.g. myosin displacement) may be significantly underestimated.