Molecular motors

A paradigm shift in modern biological physics began in the early 1990s, from methods that observed huge numbers of molecules in bulk to single-molecule methods capable of observing biological molecules working, one at a time, in real time. These advances in nanometry have allowed the observation of individual biological molecular machines and led to an understanding of their mechanisms in previously unimaginable detail. Slide 1 shows a movie of kinesin that illustrates the quality of information now obtainable. Modern measurement techniques have allowed the observation of individual biological molecular machines working, one at a time, in real time, leading to an understanding of their mechanisms in previously unimaginable detail.

Slide 1

Single-molecule biology is a large and fast-growing field, far too large to be covered in a single lecture. Instead, this lecture will focus on some key methods that have been applied to molecular motors. There are many reasons why single-molecule experiments are better than bulk methods (Slide 2). Perhaps most important is the fact that bulk experiments average away many of the interesting details of a molecular mechanism. There are two types of averaging that are avoided by single-molecule methods: time averaging (hiding variations in the behaviour or state of each with time) and ensemble averaging (hiding variations between molecules, even nominally identical molecules).

Single molecule experiments allow us to:

  • observe heterogeneity:
     – static (differences between molecules);
     – dynamic (history of a single molecule);
  • observe single molecules in vitro and in vivo, in real time;
  • measure positions with nanometre precision;
  • measure separations with subnanometre (ångström) precision.
  • Further advantages, compared with bulk measurements, include:

  • no need to synchronise population to observe dynamic behaviour;
  • ability to study transient events;
  • ability to apply force to molecules;
  • very small sample sizes.
  • 3.1 Optical microscopy

    3.1.1 Particle tracking

    Molecular machines are typically protein complexes of the order of 10 nm linear dimension. This is too small to see with light microscopy. High-resolution methods, such as electron microscopy or X-ray diffraction, require frozen, crystallised or otherwise inactive samples and/or are destructive. For non-invasive observation with optical microscopy, single-molecule methods frequently rely on particle tracking – that is, the attachment of visible labels to the molecule of interest. Molecular motion can be visualised by attaching micron-sized beads or gold nanoparticles to scatter light, or fluorescent labels such as organic fluorophores or quantum dots. Beads allow manipulation by optical traps. Labels are attached via antibodies or chemical modifications of the proteins in the molecular machine. Similar modifications can also be used to attach molecular motors specifically to a glass surface or the tip of an atomic force microscope.

    In the experiment shown in Slide 3, F1 (part of F1FO ATP synthase, see ‘Biological Energy’ Lecture 2) is disconnected from F0 and is running ‘backwards’, powered by ATP hydrolysis. The 40 nm gold bead scatters light very efficiently and the position of its centroid in a dark-field image can be fitted with nanometre resolution, even with frame rates close to 10 kHz. This small label exerts much less drag than the fluorescently labelled actin filaments (microns long) that were first used to prove that F1-ATPase is a rotary machine (see ‘Biological Energy’ Lecture 2). Combined with the fast video rates, this permits measurements with submillisecond time resolution that reveal substeps in the rotation of the stalk (rotor).

    The graph (Slide 3, top right) shows angle versus time traces for a single bead attached to F1 at an ATP concentration where the arrival of an ATP molecule typically takes a similar time to the rest of the mechanochemical cycle. F1 takes alternating long and short steps. A 90° step is associated with ATP binding (evidence: the average time before 90° steps is inversely proportional to the ATP concentration) and a subsequent 30° step is associated with hydrolysis and product release (the average time is independent of the ATP concentration). (Note that subsequent work revised these step sizes to 80° and 40°.) Also see the lecture ‘ATP Synthase’.

    3.1.2 Fluorescence microscopy

    Fluorescence localisation involves attaching a fluorescent molecule (a ‘label’ or ‘tag’) to a molecule of interest so that it can be made visible against a large background of non-fluorescent molecules (Slide 4).

    Labels may be small organic molecules (dyes), often coupled to purified proteins by chemical crosslinkers. A chosen protein can be genetically engineered such that it is expressed as a fusion with GFP (green rluorescent protein), providing a ready-made fluorescent label inside a living cell.

    There is a range of synthetic fluorophores (and engineered GFP variants) covering the visible and near-infrared spectrum. Fluorescent molecules absorb photons and re-emit longer wavelength photons with a delay (lifetime) that is typically of the order of nanoseconds. Fluorescence microscopes use filters to discriminate between excitation and emission wavelengths. The sensitivity of detectors (typically CCD cameras closely related to consumer digital cameras) is such that single fluorescent molecules can be detected if the background (light from other sources, particularly other fluorescent molecules) is reduced sufficiently.

    Slide 4 shows the chemical structure and absorption and emission spectra of the organic dye cy3.

    In total enternal reflection fluorescence (TIRF) microscopy (Slide 5) the sample is illuminated by an evanescent optical field near a glass–water (or glass–cell membrane) interface. The exciting laser radiation (bright, highly collimated) is incident above the critical angle so is totally internally reflected. (The diagram is simplified – the laser is focused at the back focal plane of the objective and provides collimated, above-critical-angle illumination of a wide area in the focal plane.) The evanescent field extends into the sample by only about 100 nm. TIRF facilitates the measurement of fluorescence from single molecules immobilised at the glass surface or diffusing or transported into the illuminated layer. The limited penetration of the exciting light greatly reduces the background resulting from fluorescence of molecules in solution, away from the interface.

    Slide 5 includes a brief reminder of TIR. In the glass cover slip (refractive index n1):

    Equation 1
    Equation 1

    Equation 2
    Equation 2

    Similarly in the specimen/water (n2):

    Equation 3
    Equation 3

    Equation 4
    Equation 4

    The condition for TIR is:

    Equation 5
    Equation 5

    The upper diagram in Slide 5 illustrates ‘through-objective’ TIRF, in which the laser beam is focused off-axis at the back focal plane of a high numerical aperture objective. (Rays passing through the back focal plane nearer the optical axis strike the interface below the critical angle and are transmitted, as shown in blue in Slide 5.) The objective is also used to collect light emitted from the specimen.

    In an alternative configuration, the evanescent field is produced by total internal reflection of a laser beam introduced through a prism above the sample, on the opposite side from the objective. This has the advantage of avoiding laser light scattered inside the objective, or emitted by fluorescence of the immersion oil or of the glass in the objective. However, it requires a closed sample and extra optical components above the sample, and observation of the surface furthest from the objective. For these reasons, ‘through-objective’ TIRF is the more popular method.

    A DNA helicase is a motor protein that uses energy from ATP to unwind DNA duplexes into two single strands. In the simple single-molecule experiment shown in Slide 6, DNA helicases are immobilised on the glass cover slip. There are dye molecules in solution that bind preferentially to single-strand DNA. The intensity of fluorescence from the volume surrounding a helicase molecule is therefore a measure of the amount of ssDNA that it has produced – that is, its progress in unwinding the duplex. Each fluorescent spot corresponds to a single helicase, so many molecules can be observed in parallel in real time. Below Slide 6 is a movie illustrating this.

    Notice that the spots get gradually brighter as more ss-DNA is produced by the helicase, allowing more fluorescent dye molecules to bind, despite photobleaching of the fluorescent molecules,which would tend to make the spots dimmer.

    Slide 7 shows a classic example of single-molecule enzymatic dynamics – an experiment in which, by observing the time-dependent behaviour of individual molecules, it is possible to obtain information that would be lost in an ensemble measurement.

    In this experiment, molecules of cholesterol oxidase are loosely trapped in an agarose gel (the gel localises them but does not affect their function). These enzymes (catalytic proteins) catalyze the oxidation of cholesterol by oxygen. They are fluorescent during part of their catalytic cycle. By observing individual molecules over time it is possible to detect individual catalytic events and to calculate correlations between them. Switching events are stochastic, reflecting the stochastically distributed waiting times for the diffusion of reactants or products or for thermal activation. The average behaviour of many molecules over long periods of observation is consistent with the enzyme kinetics deduced from ensemble measurements. However, analysis of single-molecule data reveals information that could not be obtained otherwise.

    Static inhomogeneity All molecules behave in qualitatively the same way, but the rate constants associated with individual molecules are different.

    Dynamic inhomogeneity The behaviour of a given molecule during successive catalytic cycles is correlated at short times – the molecules display memory, consistent with slow conformational fluctuations.

    3.1.3 Beating diffraction-limited resolution

    Subwavelength resolution can be achieved by localising single fluorescent molecules. By fitting the intensity profile of the image of an isolated fluorophore to the appropriate point spread function (e.g. an Airy function or Gaussian), the centroid can be determined with an uncertainty of

    δx = σ/√N ,

    Equation 6

    where N is the number of photons counted and

    σ ≈ λ /(2AN)

    Equation 7

    is the diffraction-limited spot size (AN ≡ numerical aperture of the objective). (Resolution is further reduced by the fluorescence background and digitisation error resulting from the pixellated structure of the camera.) It is possible to determine the position of a single fluorophore to a resolution of 1 nm, typically limited either by the integration time (determined by the time resolution required) or by the lifetime of the fluorophore. This is similar to the method used in Slide 3 with scattering by gold particles on F1-ATPase, except that single-molecule fluorescence is much less bright, requiring much longer exposure times to achieve the same spatial resolution.

    The experiment illustrated in Slide 8 revealed the stepping mechanism of myosin V(‘five’), a two-headed (footed) motor protein that ‘walks’ along an actin filament (on its heads). A fluorophore was attached to one of the two legs. The attachment position was different on different molecules, but the pattern of step lengths was consistently (x0δ) followed by (x0+ δ), where the period of stepping is 2x0 (74 nm). This is consistent with a stepping mechanism in which the two heads alternately take the leading position.

    There are many related super-resolution optical imaging techniques that are based on the principle that isolated emitters can be localised to very high resolution. The image in Slide 9 is reconstructed from many separate images in which only a small, well-separated subset of the total population of fluorophores is active. Individual spots are identified in each individual image by a computer algorithm, and their position is determined as described in Slides 3 and 8.

    To reconstruct the image, a point is drawn at the location of each spot (similar to the artistic style pointillism), but with a width equal to the uncertainty in that location. Because each point is smaller than the diffraction limit by a factor of width of √N, a densely labelled object (DNA in the example of Slide 9) can in principle be imaged with a resolution up to √N times better than the diffraction limit – if enough photons are collected from enough images of enough fluorescent molecules. At the time of writing (2011), resolution is limited in practice to ~10 nm by factors such as the density and mobility of the fluorescent labels, the total number of photons that can be collected from each label before it photo bleaches, and the noise and pixellation of the original images. This limit will decrease as improvements are made.

    3.1.4 Fluorescence resonance energy transfer

    Fluorescence resonance energy transfer (FRET) (also known as Förster resonance energy transfer) allows the detection of nanometre-scale relative motions between two fluorophores, and in certain cases the absolute measurement of distances of a few nanometres. It is based on the resonant coupling of two different fluorophores attached to the molecule of interest (see Slide 10).

    The donor is generally a ‘bluer’ fluorophore than the acceptor; the emission spectrum of the donor must overlap the excitation spectrum of the acceptor. If the excitation spectrum of the donor is sufficiently blue-shifted relative to that of the acceptor then the donor can be selectively excited by a laser (or by a narrow band of frequencies selected from a continuous light source by an interference filter). When excited, the donor may decay radiatively or non-radiatively – and one non-radiative decay channel is transfer of energy by near-field dipole-dipole coupling to the acceptor. The rate of energy transfer scales as r –6, where r is the separation between fluorophores, so the efficiency, E, of transfer scales as:

    Equation 8
    Equation 8

    E is estimated experimentally via the ratio of light detected at wavelengths characteristic of the donor and acceptor fluorescence emission. (See also the discussion of activation energy in the supplementary lecture ‘Chemical reaction kinetics and equilibrium’.)

    The Förster radius Ro is typically in the range 2~6 nm, so displacements in the range 1~10 nm can be observed. Ro depends on the overlap between the spectra of the fluorophores and on their relative orientations.

    Slide 11 shows studies of a catalytic RNA molecule or ribozyme. A ribozyme is an RNA molecule that can function as a catalyst. The name comes from ribonucleic acid enzyme. (It is not to be confused with ribosome, although the ribosome is a ribozyme because it catalyzes peptide bond formation and is made largely of RNA.) Its substrate is another molecule of RNA (S in the diagram on the left) that hybridises to the ribozyme. The ribozyme catalyzes the hydrolysis of the substrate, cleaving it at a precisely defined position. FRET labels attached at two positions on the ribozyme allow the time-dependent conformational changes of individual ribozymes to be observed and interpreted in terms of a catalytic cycle.

    3.2 Optical tweezers

    Optical tweezers (Slide 12) use a focused laser beam to trap transparent (dielectric) spheres with radiation pressure. This technique has revolutionised the study of molecular motors by allowing direct study of the energy landscape associated with motion (see, for example papers by Ashkin and by Mehta et al.).

    The optical force on the bead results from exchange of momentum with scattered photons and is proportional to the gradient of the optical intensity: particles with higher dielectric constants than the surrounding medium are attracted to the region of maximum intensity. Slide 12 (left) illustrates momentum exchange in optical tweezers in the ray optics regime (particle much larger than wavelength), with black arrows for light rays and light momentum and red arrows for momentum transfer, which is proportional to the force on the particle. Slide 12 (right) is a schematic diagram of a simple optical tweezers setup.

    For small displacements from the equilibrium position, the trap is close to harmonic – that is, the force exerted on the bead increases linearly with distance from the trap centre. The position of the bead can be detected optically, by detecting scattered light from the trapping laser or by means of a separate detection laser. Spatial resolution of 0.1 nm is possible.

    The trap stiffness can be calibrated by measuring the variance or frequency spectrum of the Brownian motion of the trapped bead or by measuring its response to viscous drag induced by a known fluid flow. Stiffnesses are typically in the range 0.01 – 1 pN nm–1 , and applied forces in the range 0.1 – 100 pN.

    Near-infrared wavelengths are often used, because biological specimens are near-transparent in this spectral region and because the low photon energy minimises photochemical damage.

    Slide 13 shows the results of a study of myosin II. This is skeletal muscle myosin (see ‘Molecular Machines’ Lecture 1). There are many other types of myosin in eukaryotic cells.

    In this three-bead assay, an actin filament is suspended between two beads held in optical traps and is lowered down towards a third bead on which myosin is bound. The beads are ~1 μm in diameter (the actin filament is 6 nm in diameter and the myosin molecule is ~ 10 nm). The position of the filament is measured by imaging one of the beads onto a quadrant photodiode.

    When a myosin molecule binds to the filament, it adds to the two traps a third, stiff spring restraining the filament: the thermal fluctuations in the position of the filament therefore decrease in amplitude. The power stroke of the motor produces a lateral displacement of the filament. The centroid of a histogram of displacements measured during binding corresponds to the myosin power stroke of 5 nm.

    The force generated in the power stroke can also be measured by applying feedback, by moving the optical traps, to keep the beads in fixed positions. The distance between the trap and the (fixed) beads is then proportional to the force exerted by the motor. Power strokes generate about 6 pN under these conditions (see Finer et al. 1994).

    Kinesin is a processive motor protein. This means that it takes many steps (it has two heads) before detaching from its microtubule track. The movie linked to Slide 1 shows kinesin ‘walking’ along a microtubule. In Slide 14 the motor is attached to a single, trapped bead and ‘walks’ along an immobilised track. Feedback is applied to maintain a constant bead-trap separation (constant force) to measure the dependence of motor speed on retarding force.

    3.3 Atomic force microscopy

    Atomic force microscopy (AFM) (Slide 15) is a type of scanning probe microscopy and is most frequently used as an imaging tool. A sharp tip on the end of a flexible cantilever is scanned over a surface while feedback is used to move the tip up and down to keep the deflection of the cantilever (and therefore the force between the tip and surface) constant. Scanning and tip height are controlled by piezoelectric transducers with subnanometre (ångstrom) sensitivity. A map of height, or more generally tip–surface interaction, is generated. On the right of Slide 15 is a collection of high-resolution AFM images of native membrane proteins in situ.

    The cantilever can also be oscillated at resonance and either the amplitude or phase of the oscillation used as the feedback signal – both are affected by the proximity and nature of the surface. Cantilever deflection is usually monitored by measuring the position of a laser beam reflected from the cantilever (sometimes optical interferometry is used instead).

    The resolution is determined by the sharpness of the tip, which is usually determined by an accidental asperity rather than by the designed shape. When imaging in water, it is critical to adjust the ionic composition of the solution to screen long-range electrostatic tip–surface interactions without generating a strongly attractive tip–surface interaction. In the best cases, subnanometre lateral resolution and 0.1 nm vertical resolution can be achieved in AFM imaging of proteins.

    AFM can also be used to measure mechanical properties of individual molecules, as shown in Slide 16. See ‘Biological Molecules’ Lecture 1 for a description of this experiment, in which an AFM is used to unfold the giant muscle protein titin.

    The compliant cantilever can be used as a sensor to monitor the force exerted as a single molecule is compressed or stretched between the tip and surface. The cantilever is a linear spring. Its stiffness can be calibrated by measuring the power spectrum of thermal vibrations and is typically in the range 10 – 100 pN nm–1 for single-molecule force experiments.

    High-speed AFM can capture the behaviour of individual molecules with sufficient spatial and temporal resolution to reveal mechanistic detail. In Slide 17 and the linked movie, molecules of myosin V, a processive two-headed motor protein, are imaged with a frame rate of 7 Hz while they ‘walk’ down actin filaments.

    3.4 Other techniques in single-molecule biology

    This lecture has highlighted only a small selection of single-molecule methods and experiments. Other important single-molecule techniques (Slide 18) include:

  • patch clamp: for the detection of ionic currents through single ion channels in biological membranes;
  • super-resolution optical microscopies with active control of fluorophore emission;
  • fluorescence polarisation: for detection of the orientation of single molecules;
  • magnetic tweezers: to exert torque on single molecules;
  • imaging by cryoelectron microscopy, electron tomography: for reconstruction of the structure of large molecular complexes.