Brownian motors: noisy transport far from equilibrium

A new in vitro assay using a feedback enhanced laser trap system allows direct measurement of force and displacement that results from the interaction of a single myosin molecule with a single suspended actin filament. Discrete stepwise movements averaging 11 nm were seen under conditions of low load, and single force transients averaging 3-4 pN were measured under isometric conditions. The magnitudes of the single forces and displacements are consistent with predictions of the conventional swinging-crossbridge model of muscle contraction.

Single myosin molecule mechanics: piconewton forces and nanometre steps

Muscle contraction consists of a cyclical interaction between myosin and actin driven by the concomitant hydrolysis of adenosine triphosphate (ATP). A model for the rigor complex of F actin and the myosin head was obtained by combining the molecular structures of the individual proteins with the low-resolution electron density maps of the complex derived by cryo-electron microscopy and image analysis. The spatial relation between the ATP binding pocket on myosin and the major contact area on actin suggests a working hypothesis for the crossbridge cycle that is consistent with previous independent structural and biochemical studies.

https://science.sciencemag.org/content/sci/261/5117/58.full.pdf

Structure of the actin-myosin complex and its implications for muscle contraction.

The microtubule-based kinesin motors and actin-based myosin motors generate motions associated with intracellular trafficking, cell division, and muscle contraction. Early studies suggested that these molecular motors work by very different mechanisms. Recently, however, it has become clear that kinesin and myosin share a common core structure and convert energy from adenosine triphosphate into protein motion using a similar conformational change strategy. Many different types of mechanical amplifiers have evolved that operate in conjunction with the conserved core. This modular design has given rise to a remarkable diversity of kinesin and myosin motors whose motile properties are optimized for performing distinct biological functions.

https://science.sciencemag.org/content/sci/288/5463/88.full.pdf

The Way Things Move: Looking Under the Hood of Molecular Motor Proteins

Kinesin, a mechanoenzyme that couples ATP hydrolysis to movement along microtubules, is thought to power vesicle transport and other forms of microtubule-based motility. Here, microscopic silica beads were precoated with carrier protein, exposed to low concentrations of kinesin, and individually manipulated with a single-beam gradient-force optical particle trap ('optical tweezers') directly onto microtubules. Optical tweezers greatly improved the efficiency of the bead assay, particularly at the lowest kinesin concentrations (corresponding to approximately 1 molecule per bead). Beads incubated with excess kinesin moved smoothly along a microtubule for many micrometres, but beads carrying from 0.17-3 kinesin molecules per bead, moved, on average, only about 1.4 microns and then spontaneously released from the microtubule. Application of the optical trap directly behind such moving beads often pulled them off the microtubule and back into the centre of the trap. This did not occur when a bead was bound by an AMP.PNP-induced rigor linkage, or when beads were propelled by several kinesin molecules. Our results are consistent with a model in which kinesin detaches briefly from the microtubule during a part of each mechanochemical cycle, rather than a model in which kinesin remains bound at all times.

Bead movement by single kinesin molecules studied with optical tweezers

Recordings of the change in tension in striated muscle after a sudden alteration of the length have made it possible to suggest how the force between the thick and thin muscle filaments may be generated.

Proposed Mechanism of Force Generation in Striated Muscle

THE control by calcium of the ATPase activities of myosin, actomyosin and myofibrils from molluscan muscles requires the presence of a particular ‘regulatory’ light chain of myosin1,2 In these muscles troponin is not found in stoichiometric amounts and does not function as a major regulatory component2,3 In scallop muscles one of the two regulatory light chains per myosin is readily and reversibly removed by reducing the divalent cation concentration with EDTA2,4, with the result that the preparations become ‘desensitised’ to calcium, that is, the ATPase activity is maximal whether or not calcium is present ‘Resensitising’ can be achieved by the recombination of regulatory light chains with myosin or myofibrils We have extended these studies to a scallop muscle preparation (chemically ‘skinned’ fibre bundles) in which the contractile machinery is intact, and we show here that the regulatory light chains can be removed and recombined, with a concomitant loss and recovery of calcium control over tension production

Reversible loss of calcium control of tension in scallop striated muscle associated with the removal of regulatory light chains

IN considering the energetics of an enzyme-catalysed reaction it is of interest to enquire into what constitutes the “drive”, in a thermodynamic sense, for the reaction, particularly when the enzyme is involved in an energy-coupled process. This often arises when speculations are made on the operation of a system on the basis of equilibrium constants for the reaction scheme determined on the system, or fragments of it, in vitro. In the case of active transport or muscular contraction the free energy for transport or contraction is derived from the hydrolysis of ATP and the overall drive arises because the chemical potential of ATP is greater than that of its products (ADP and Pi) at physiological concentrations. But to understand how the drive is expressed in the mechanism of such processes it is necessary to consider and define the relative free energy levels of the intermediates of the reaction. The free energy and standard free energy as normally defined as not sufficient for this purpose. They both, in general, refer to the system as a whole and are used in the context of free energy changes involving substrates, products and ligands. The drive of the system, in the sense used here, is to be sought in the relative disposition of the free energy levels of an individual (time-averaged) macromolecule and in the manner in which these levels favour (stochastically) a particular direction of the flux in what may be a complicated reaction scheme. We refer to these free energy levels of individual macromolecules as the “basic” free energy levels. To avoid confusion we have termed the overall free energy change of the whole system for a given transition as the “gross” free energy change. The definitions of and relationships between the standard, basic, and gross free energy levels for a system of macromolecules (either in free solution or immobilised) are given below, together with a simple example relevant to muscular contraction. A more mathematically detailed version of this work with more complicated examples for both muscle and active transport has been published elsewhere1,2.

Definitions of free energy levels in biochemical reactions

"Basic" and "gross" free energy levels are defined for the discrete states of a macromolecular biochemical kinetic system such as a free energy transducing enzyme (e.g., myosin or Na,K-ATPase). Basic free energy level differences are related to the first-order rate constants for transitions between states while gross free energy differences, along with the corresponding fluxes, determine the rate of entropy production in the system. In muscle contraction the analysis is complicated by the possibility of the system doing external mechanical work. The question of the sign of the flux or of the gross free energy level change in a given transition is examined for both single-cycle and multi-cycle models. More definite statements can be made in single-cycle cases. Some numerical examples are included. The more complicated cases are reserved for a subsequent paper.

Free energy levels and entropy production associated with biochemical kinetic diagrams

"Basic" and "gross" free energy levels of a macromolecule such as myosin or Na,K-ATPase, defined in a previous publication, are discussed here for two relatively complicated cases: a six-state kinetic diagram of the sort that could be used to describe the actin activation of myosin-ATPase in solution; and muscle contraction, where a similar kinetic diagram is needed for each value of a positional variable X.

R. M. Simmons

Papers

Proposed Mechanism of Force Generation in Striated Muscle

Reversible loss of calcium control of tension in scallop striated muscle associated with the removal of regulatory light chains

Definitions of free energy levels in biochemical reactions

Free energy levels and entropy production associated with biochemical kinetic diagrams

Free energy levels and entropy production in muscle contraction and in related solution systems.