X RAY DIFFRACTION STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE

Transcription

1 X RAY DIFFRACTION STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE By JOHN M. SQUIRE* AND CARLO KNUPP { *Biological Structure & Function Section, Biomedical Sciences Division, Imperial College Faculty of Medicine, London SW7 2AZ London, United Kingdom; { Structural Biophysics Group, School of Optometry and Visi00on Sciences, Cardiff University, Cardiff University, Cardiff CF10 3NX, United Kingdom I. Introduction A. Muscle Structure and Diffraction B. Factors Affecting Diffraction Patterns C. Diffraction from Actin Filaments D. Diffraction from the Myosin Head Array E. The Z Band Contribution F. Diffraction from the Myosin Filament Backbone II. Modeling of Rigor Muscle A. Introduction B. Labeling of Actin in Rigor Muscle C. The Weak Binding State D. Summary: Take Home Messages III. Time Resolved Events in Contracting Muscles A. Changes in the Equatorial Reflections IV. X Ray Interference Measurements and Their Implications A. Introduction to the Idea of Interference B. Interference Observations and Their Possible Interpretations C. Interference Changes During Muscle Transients D. Further Details of the Interference Experiments E. Temperature Jump Experiments and Isotonic Contractions V. Summary References I. Introduction The basic assembly of striated muscles has been described in detail in Squire et al. (2005), Granzier and Labeit (2005), and Brown and Cohen (2005) and ideas about the crossbridge cycle were described in Geeves and Holmes (2005). Many of the ideas about the crossbridge mechanism have come from X ray diffraction studies of muscle, but to many people such studies are difficult to understand and, even to some practitioners of the technique, it is easy to be misled by certain types of results. The technique itself is immensely powerful and may be one of the very few approaches that can actually probe molecular structural changes that occur in intact muscles while they are undergoing their usual function, namely, tension ADVANCES IN 195 Copyright 2005, Elsevier Inc. PROTEIN CHEMISTRY, Vol. 71 All rights reserved. DOI: /S (04) /05 $35.00

2 196 SQUIRE AND KNUPP production and shortening. This article explores some of the issues involved in X ray diffraction studies of muscle and attempts to separate what has actually been shown unambiguously from what may be merely either conjecture or just one plausible interpretation among a panoply of very different ones. A. Muscle Structure and Diffraction The discussion here starts with the structure of vertebrate striated muscles, the basic components of which were described in Squire et al. (2005; see also Squire, 1981, 1992, 1997). The vertebrate sarcomere consists of bipolar myosin filaments with threefold rotational symmetry and myosin heads organized in the bridge regions on three co axial roughly helical strands with nine head pairs per turn of the helix, giving a true repeat of 429 Å and an axial separation between crowns of heads averaging 143 Å (see Squire et al., 2005, Fig. 16). The myosin filaments are organized in hexagonal arrays across the myofibril, with those in bony fish muscle having identical orientations around their long axes in a simple lattice arrangement and those in higher vertebrates having a statistical mixture of two orientations 60 apart giving a superlattice (see Squire et al., 2005, Fig. 6). A band lattice structure is defined and stabilized by bridging structures in the M band (Squire et al., 2005, Figs. 23 and 24). Interdigitating with these myosin filaments are actin filaments (Squire et al., 2005, Fig. 9) with a helical symmetry that in vertebrate striated muscles is close to, but not exactly, that of a 13/6 helix of actin subunits, which would have an axial repeat of Å. The actin filaments carry strands of tropomyosin molecules and troponin complexes (Squire et al., 2005, Fig. 2.9, and see Brown and Cohen, 2005). The actin filaments are arranged at the trigonal points of the hexagonal lattice of myosin filaments in the A band, but through the I band there is a transition to a square array in the Z band. The giant protein titin (Granzier and Labeit, 2005) interacts systematically with myosin filaments in the A band and then spans the I band and interacts with the Z band through its Z repeats and other adjacent sequences. In thinking about X ray diffraction from this assembly, a number of the sarcomere components contribute to the observed patterns in ways that have been the subject of detailed analysis. In the A band, these include the myosin filament backbone, where the coiled coil a helical myosin rods pack together, the myosin head arrays in the bridge regions of the myosin filaments, the non myosin A band proteins titin and C protein (MyBP C), and the A band parts of the actin filaments. Very little has been seen in X ray patterns so far that appears to be related to the M band, probably

3 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 197 because the M band carries relatively little mass. In the I band, the contributors are the remainder of the actin filaments, the tetragonal Z band, and possibly the I band parts of titin. In order to explain and understand the various contributions that these different structures make, the following section assesses the diffraction effects of each of the major components. The background ideas about muscle structure and the crossbridge cycle, together with some historical perspectives, are discussed in this volume in Squire et al. (2005) and Geeves and Holmes (2005) and also, for example, in Huxley (1969, 2004), Holmes (1997), Geeves and Holmes (1999), and the special Royal Society issue on Myosin, Muscle and Motility (Phil. Trans. Roy. Soc. B. volume 359, pp ). B. Factors Affecting Diffraction Patterns 1. General Ideas About Diffraction Although this volume is not primarily intended as a techniques book, it will probably be helpful here to summarize in a qualitative way for those who are non experts in the basic aspects of diffraction theory that are used later in this article. Those who already have a thorough understanding of the technique should proceed directly to Section I.C. Figure 1 summarizes the basic concept underlying all diffraction methods. Whether the radiation being used is X rays, neutrons, electrons, or visible light, it can be described in terms of a wave of oscillating amplitude (y) with a maximum amplitude a, and with a wavelength l. These waves can be imagined as propagating across space in the x direction as in Fig. 1A. If two such waves with the same wavelength arrive at the same point with their peaks and troughs in step (they are said to be in phase), then the amplitudes add and a wave of larger amplitude results (Fig. 1B). This is called constructive interference. However, if the peaks of one coincide with the troughs of the other (they are exactly out of phase), then destructive interference occurs (Fig. 1C). Often such peaks will be neither exactly in phase nor exactly out of phase and they sum to give an intermediate or partial amplitude as in Fig. 1D. If a beam of light with a wavelength of, say 5000 Å, falls onto a card with two small holes a distance d apart (Fig. 2), then each hole will scatter the light in all directions. In a particular direction at the angle f the ways that the light scattered from the two holes adds up depends on how in phase or out of phase the two beams are. This can be determined by the size of d sinf, which is the extra distance the beam from X must travel relative to the beam from Y. Obviously, if the two waves add up after being

4 198 SQUIRE AND KNUPP Fig. 1. Summary of the ideas of interference. (A) Wave profile with wavelength l and amplitude a. (B) Constructive interference from waves moving in the x direction where the amplitude (a) of the two waves varies in step (or in phase). (C) destructive interference by waves out of step by half a wavelength (l/2), and (D) partial reinforcement by waves not exactly in phase or out of phase. shifted by a whole wavelength or any integer multiple of the wavelength (nl), then constructive interference will occur (Fig.1B). So if d sinf is the same as nl, then an intense peak will be seen on a screen placed on the right hand side of Fig. 2A. In general, if d sinf 6¼ nl, then partial or destructive interference occurs. Fig. 2B E show various situations where the path difference d sinf is (B) 0 (n ¼ 0), (C) l/2 (n ¼ 0.5), (D) l (n ¼ 1), and (E) 2l (n ¼ 2). In summary, the condition d sinf ¼ nl produces a series of intensity peaks on the screen for varying values of n. This is described as the diffraction pattern from the array of holes. The condition d sinf ¼ nl, sometimes known as the grating equation, has some interesting implications. For a given wavelength of radiation, if the separation of the holes d is larger, then the value of f needed for constructive interference is smaller and vice versa (i.e., sinf / 1/d). This is often described in terms of the reciprocal nature of diffraction. Also noteworthy is that if the wavelength increases, then the whole diffraction pattern gets bigger as well. Most importantly, if f can be measured and l is known, then the distance d can be calculated.

5 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 199 Fig. 2. (A) Scattering from two small holes at points X and Y a distance d apart in an opaque card, and (B) to (E) the effects of the angle of scatter (f) on whether the two waves are in phase or out of phase. Path differences are (B) zero (in phase), (C) l/2 (out of phase), (D) l (in phase), (E) 2l (in phase). 2. Diffraction from Crystals The next step to think about is what happens if the radiation is, say, an X ray beam (with a wavelength of 1 2 Å) and this falls onto an array of atoms in a crystal rather than holes. This situation is illustrated in Fig. 3A. What happens when the X rays arrive at the atoms is that the electrons in the atoms are caused to oscillate by the alternating electric field in the X ray beam and such oscillating charged particles themselves radiate at the same wavelength as the incident radiation, but in all directions. Considering the top plane of atoms in Fig. 3A, including the atom at O, then each of these atoms will be stimulated by the incoming X ray beam and will radiate in all directions at the same wavelength l. It is easy to show that the radiation incident at a particular angle y is scattered most strongly in a

6 200 SQUIRE AND KNUPP Fig. 3. (A) Scattering of an X ray beam from planes of atoms in a crystal. Scattering from the atoms (atom planes) at O and B has a path difference of 2d siny, giving rise to Bragg s law (nl ¼ 2d siny). The angle of incidence is y; the diffraction angle between the incident and diffracted beam is 2y. (B) Geometry of a typical fiber diffraction experiment. The radiation used (e.g., X rays or neutrons) comes in from the left and passes through the fiber. Molecules in the fiber scatter the radiation onto a film or detector at a distance D from the fiber. The pattern of spots on the detector can be related to the organization of the molecules in the fiber. Spots at a position S from the center of the diffraction pattern are diffracted through an angle given by Tan 2y ¼ S/D. This, combined with Bragg s law can yield the value of d corresponding to the peak at S. Typical fiber patterns have a meridian, parallel to the fiber axis through the undiffracted beam direction (center), an equator at right angles to this through the center, and a series of layer lines (horizontal) parallel with the equator. These layer lines may have continuous intensity along them, or if the fiber is well ordered they may be sampled on vertical row lines to give diffraction spots along the layer lines.

7 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 201 direction that is also at an angle y to the plane of atoms. In most other directions there is destructive interference. It is almost as if the X rays have been reflected by the plane of atoms. What happens now if there is a second plane a distance d below the first plane and reflecting like the first? Fig. 3A shows the geometry involved. In this case, the two beams going off to the right at angle y are such that the beam from B has had to travel the extra distance AB þ BC relative to the beam from O to reach a screen or film on the right. Obviously if AB þ BC is a whole number of wavelengths, l,thena constructive interference would be expected to occur. From the figure it is clear that AB and BC are both d sin y, so we now have the rule for diffraction (constructive interference) from a crystal: 2d siny ¼ nl. This is Bragg s law. Note that as well as the reciprocal relationship that we had before, and the change of size of the diffraction pattern with l, there is an additional condition in this case. The condition is that if the crystal planes of spacing d are not at the angle y as in Bragg s law above, then those particular planes will not diffract. A single crystal needs to be turned relative to the incident direction of a monochromatic (single wavelength) X ray beam in order to get diffraction from particular planes of atoms. However, when diffraction is seen, measurement of the angle of diffraction (the angle 2y between the incident and diffracted beams) then permits calculation of the value of d for those planes, assuming that the wavelength is known (Fig. 3B). 3. Description of Lattice Planes A 3D crystal has its atoms arranged such that many different planes can be drawn through them. It is convenient to be able to describe these planes in a systematic way and Fig. 4 shows how this is done. It illustrates a 2D example, but the same principle applies to the third dimension. The crystal lattice can be defined in terms of vectors a and b, which have a defined length and angle between them (it is c in the third dimension). The box defined by a and b (and c for 3D) is known as the unit cell. The dashed lines in Fig. 4A show one set of lines that can be drawn through the 2D lattice (they would be planes in 3D). It can be seen that these lines chop a into 1 piece and b into 1 piece, so these are called the 11 lines. The lines in B, however, chop a into 2 pieces, but still chop b into 1 piece, so these are the 21 lines. If the lines are parallel to an axis as in C, then they do not chop that axis into any pieces so, in C, the lines chopping a into 1 piece and which are parallel to b are the 10 lines. This is a simple rule. The numbers that are generated are known as the Miller indices of the plane. Note that if the structure in Fig. 6.4 was a 3D crystal viewed down the c axis, the lines would be planes. In these cases, the third Miller index would be zero (i.e., the planes would be the 110 planes in A, the 210 planes in B, and the 100

8 202 SQUIRE AND KNUPP Fig. 4. Demonstration of the definitions if Miller indices describing different planes through a lattice. For details, see text. planes in C). The Miller indices are also represented in general by the italic letters h, k, and l. 4. Intensity of Diffraction Peaks: The Convolution Theorem One of the obvious features of diffraction patterns is that the diffracted peaks do not all have the same intensity. We can see partly why this is from the illustration in Fig. 5. Figure 5A represents a 2D lattice (as in Fig. 4), and D shows the sort of diffraction pattern that would be observed if the scattering object in Fig. 2A was a mask of holes arrayed as in Fig. 5A and the diffraction pattern was viewed on the screen. The positions of the spots in Fig. 5D are totally defined by the arrangement of the objects in A, that is, by a, b, and the angle between them. However, real crystals have some

9 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 203 Fig. 5. Illustration of the convolution theorem applied to a crystal structure and its diffraction pattern. (A) is a lattice and (B) is the motif or repeating unit on the lattice. The full crystal (C) is a convolution of (A) and (B). The diffraction pattern (F) of the crystal (C) is the product of the diffraction patterns (Fourier transforms) (D) and (E) from (A) and (A), respectively. For details, see text. (Based on Squire, 1981.) interesting objects (e.g., Fig. 5B) within each unit cell (Fig. 5C). It is convenient to think about the full crystal (C) as what is termed a convolution. Literally this means folding together. If the object in B is picked up and placed on every point on the lattice in A, then the structure in C is generated. This is called the convolution ( * ) of B with A. In short, C ¼ (A) * (B). It can be shown mathematically, and is illustrated in Fig. 5D F, that the diffraction pattern (G(C)) from C is then the product of the diffraction patterns G(A) and G(B) from A and B, respectively. In short: If (c) ¼ (a) * (c), then G(c) ¼ G(a) G(c); or, in words, as in Fig. 5, IF lattice * object ¼ crystal, THEN lattice transform object transform ¼ crystal transform. The term transform here is the mathematical equivalent of the diffraction pattern. This rule is known as the convolution theorem. The way that the product of the two diffraction patterns D and E is produced is such that they are placed on top of each other with their centers together and then multiplied point for point. This means that where there is zero in either pattern there is zero also in F. The result is

10 204 SQUIRE AND KNUPP that F consists of peaks in the positions defined by D, but the intensities of these peaks are determined by the intensities in E at those particular positions. The take home message from this is that the positions of observed diffraction peaks tell us about the lattice and unit cell in the crystal (A), whereas the intensities of the peaks tell us about the structure of the object (B) on the lattice. This object is variously described in the literature as the motif, or the unit cell contents, or the asymmetric unit. Following from this, if the intensities of the peaks in (F) can be measured for a real crystal, then it is possible to work out the structure of the object in (B). This is what is done in the technique of protein crystallography (e.g., Blow, 2002). 5. Effects of the Extent of a Lattice Before embarking on the diffraction patterns produced by the objects in the muscle sarcomere, it is necessary to illustrate one other feature of diffraction patterns. Figure 6 shows various objects as in Fig. 2A and their computed diffraction patterns. The objects are like the mask of holes a distance d apart as in Fig. 2A, but this time there are different numbers of holes. In Fig. 6A there are 3 holes, in C there are 7 holes, and in E there are 10 holes. Since it is assumed that the wavelength of the light being scattered in these examples is the same, and all the objects have the same interhole spacing d, the grating equation d sinf ¼ nl from Fig. 2A still applies to each of them. This means that the diffraction patterns on the right of Fig. 6 all have peaks in exactly the same place. However, the width of the peaks changes. If there are only three objects as in Fig. 6A, then there are many directions each side of the main peaks in the pattern where the partial interference still leaves a significant amount of intensity. The peaks in Fig. 6B are therefore quite broad. On the other hand, as the number of objects increases, the partials become much weaker and the diffraction peaks become progressively narrower. If the length of the whole array is W, then the width of the observed peaks can be expected to be related to 1/W (the reciprocal nature of diffraction). 1/W 10 is therefore very small compared with 1/W 3, with 1/W 7 lying between the two. In summary, the width of an observed diffraction peak can be related to the length of the array giving rise to the peak. Short arrays give broad peaks, large arrays give sharp peaks. This armory affords consideration of the diffraction from the components of the muscle sarcomere. Note first that muscles are not single crystals of the kind illustrated in Fig. 3A. The sarcomeres themselves can have varying degrees of order; some, like insect flight muscle and bony fish muscle, are almost crystalline within an A band or sarcomere. But, whatever the muscle, both different myofibrils within a fiber, and different

11 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 205 Fig. 6. Illustration of the effects of array length on the thickness (width) of observed diffraction peaks. The arrays on the left all have the same spacing (d) between points. The peaks in the diffraction patterns on the right therefore have peaks centered in the same places, despite the varying array lengths. What changes is the thickness of the lines; short arrays (A) give thick diffraction peaks (B); long arrays (E) give relatively narrow diffraction peaks (F); and intermediate length arrays (E) have intermediate effects (D). Calculated and displayed using MusLABEL (Squire and Knupp, 2004). fibers within a whole muscle, can have random rotations about the fiber long axis, thus presenting different Bragg planes to the incoming X ray beam. This means that the muscle diffraction pattern is actually a so called fiber pattern that possesses rotational symmetry around the fiber axis direction (the meridian in Fig. 3B). The effect of this is that Bragg s law

12 206 SQUIRE AND KNUPP is satisfied simultaneously for different diffraction planes in myofibrils with different orientations around the fiber axis, and, ideally, all possible diffraction peaks out to a certain resolution can be seen in a diffraction pattern from a stationary muscle or fiber. In other words, it is not usually necessary to adjust the orientation of a muscle or fiber to see all of the low angle X ray diffraction pattern. C. Diffraction from Actin Filaments Actin filaments are typical of many elongated biological particles in that they have their subunits arranged in a helical manner. Figure 7 illustrates some general features of helical structures. First, the helix is thought of first as a continuous uniform wire. The wire will turn around the axis by some angle and, at the same time, will rise along this axis by an amount determined by the angle. The amount traveled along the helix axis in one complete turn of the helix around its axis is the helix pitch (P). Helical molecules or filaments are made up from subunits, such as an actin monomer or a myosin molecule, and the axial separation between monomers (h) is called the subunit axial translation or unit rise. It may be that there is an exact number of subunits in one pitch, in which case the helix is said to be integral. B DNA is an example of this with exactly 10 nucleotide pairs (each being one unit) in one pitch. It is described as a 10 1 or 10/1 helix. However, other structures are not integral and it may be necessary to traverse several helix pitches before a subunit is reached that is at an exactly equivalent azimuthal position (i.e., at the same angle measured around the filament long axis) to the starting subunit. In this case a repeat C is defined. The structure in Fig. 7A has exactly five subunits in two turns of the helix. It is a 5 2 or 5/2 helix where C ¼ 2P ¼ 5h. It is not appropriate to go into the full mathematics of helical diffraction theory, which is done well elsewhere (Chandrasekaran and Stubbs, 2001; Harford and Squire, 1997; Holmes and Blow, 1965; Squire, 2000). However, some of the important features can be noted. The diffraction pattern has the form illustrated in Fig. 7B. One can imagine a fiber of helical molecules or filaments being in the path of an X ray beam (Fig. 7C) and diffracting the X rays onto a screen or detector a distance D from the fiber (Fig. 3B). The axis in the diffraction pattern that is parallel to the fiber axis and goes through the undiffracted beam position (i.e., the center of the pattern) is called the meridian. The axis at right angles to this through the center is called the equator. The helical diffraction pattern as exemplified by Fig. 7B consists of a series of spots along the meridian at positions related to m/h where h is the subunit axial translation as above and m is an integer number, which can be positive, negative, or zero. The spots at m ¼ 0 and m

13 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 207 Fig. 7. Geometry of a helical structure (A) and the form of its diffraction pattern (B). In (A), the pitch (P) of the helix is like the wavelength of a sine wave. The radius (r) of the helix is like the amplitude of the sinewave. The subunit axial translation (h) is the rise along the helix axis from one monomer to the next. If there is not a whole number of monomers in one turn of the helix (said to be a non integral helix), then there may be a longer repeat (C). In the case illustrated C ¼ 2P. Dimensions in the helix in (A) have their counterparts in the diffraction pattern illustrated in (B), but dimensions in (B) are reciprocal to those in (A). Meridional reflections occur at positions m/h from the equator, where m is an integer. Each of these positions is the center of a so called helix cross consisting of layer lines, which are n/p up or down from the meridional peaks, where n is another integer. All of the resulting layers of intensity can be related to orders of l/c, where C is the repeat of the helix and l is the layer line number. ¼1 are shown in the figure. For a perfectly helical structure, these and peaks at other values of m are the only intensities that occur along the meridian. Off the meridian is a series of so called layer lines (horizontal), which occur at axial positions (i.e., measured in the direction parallel to the meridian), which are orders of the repeat C: they are at l/c, where l, known as the layer line number, is an integer that is positive, negative, or zero. Particularly strong layer lines occur when l/c is equal to 1/P (l ¼2), 2/P (l ¼2), and so forth. They also occur at the same distances above

14 208 SQUIRE AND KNUPP and below the meridional reflections at different values of m. In other words there are strong peaks at: l ¼ m/h þ n/p, where n is another integer that can be positive, negative, or zero (in mathematical treatments n is actually the order of a Bessel function describing the intensity along the layer line). Measurement of the axial positions of the meridional reflections (related to 1/h) and of the layer lines (related to 1/C) can determine the number of subunits h in one repeat C. An explanation of the origins of the helical diffraction pattern is given in Fig. 8 and its legend. In the case of 13/6 actin filaments, the subunit axial translation h is 27.5 Å and the repeat C is after 13 subunits at Å, which is also after 6 turns of the helix. The strongest layer lines are where l ¼ 6 or 7. This is because the pitch P of the 13/6 actin helix is C/6 at 59 Å. The sixth layer line is therefore 1/P up from the origin, where m ¼ 0, and the seventh layer line at 51 Å is 1/P down (i.e., 6 layer lines down) from the m ¼þ1 position, which occurs on layer line 13. These structural features of an actin filament are illustrated in Fig. 9 (see, for example, Parry and Squire, 1973; Holmes et al., 1990; Lorenz et al., 1993). This figure also shows a convenient representation of helical structures in terms of a radial projection or helical net. This is obtained (A) by imagining a piece of paper wrapped round the filament and marking wherever there is a subunit on the helix. This paper is then unwrapped (B) and the helical strands of the filament become straight lines. The leftand right hand edges of the radial projection represent the same line along the filament. Marked on the radial net in Fig. 9C are the 27.5 Å subunit axial translation between actin monomers and the pitch of the genetic helix (i.e., the helix that runs through all the monomers) of 59 Å. The fact that the azimuthal rotation between successive subunits along the helix is not far from 180 (it is at 360 6/13 ¼ ) shows why the actin filament appears as two slowly twisting strands of monomers, like two strings of beads twisting around each other (see Fig. 3A and Fig. 9 in Squire et al. of this volume). In terms of spacing, the first actin layer line (A1 in Fig. 10B) from a 13/6 helix occurs at 1/357.5 Å 1, the second (A2) at 2/357.5 ¼ 1/ Å 1, the sixth (A6) at 1/59.58 Å 1, the seventh at 1/51.07 Å 1, and the thirteenth (A13) at 1/27.5 Å 1. Not all actin filaments have 13/6 helical symmetry. For example, in insect flight muscle, as exemplified by Lethocerus, the actin filaments form a 28/13 helix. This also occurs in the vertebrate striated muscle Z band (Squire et al., this volume. Section III.E; Luther and Squire, 2002). The differences between the diffraction patterns from helices with 13/6 and 28/13 symmetry are illustrated in Fig. 10. The diffraction patterns were generated by the program HELIX (Knupp and Squire, 2004), but the program MusLabel can also be used (Squire and Knupp, 2004). Another

15 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 209 Fig. 8. Generation of the form of the helical diffraction pattern. (A) shows that a continuous helical wire can be considered as a convolution of one turn of the helix and a set of points (actually three dimensional delta functions) aligned along the helix axis and separated axially by the pitch P. (B) shows that a discontinuous helix (i.e., a helical array of subunits) can be thought of as a product of the continuous helix in (A) and a set of horizontal density planes spaced h apart, where h is the subunit axial translation as in Fig. 7. This discontinuous set of points can then be convoluted with an atom (or a more complicated motif ) to give a helical polymer. (C) (F) represent helical objects and their computed diffraction patterns. (C) is half a turn of a helical wire. Its transform is a cross of intensity (high intensity is shown as white). (D) A full turn gives a similar cross with some substructure. A continuous helical wire has the transform of a complete helical turn, multiplied by the transform of the array of points in the middle of (A), namely, a set of planes of intensity a distance n/p apart (see Fig. 7). This means that in the transform in (E) the helix cross in (D) is only seen on the intensity planes, which are n/p apart. (F) shows the effect of making the helix in (E) discontinuous. The broken helix cross in (E) is now convoluted with the transform of the set of planes in (B), which are h apart. This transform is a set of points along the meridian of the diffraction pattern and separated by m/h. The resulting transform in (F) is therefore a series of helix crosses as in (E) but placed with their centers at the positions m/h from the pattern center. (Transforms calculated using MusLabel or HELIX.)

16 210 SQUIRE AND KNUPP Fig. 9. Representation of a 13/6 actin filament together with its illustration by means of a radial net. In (A) an imaginary piece of paper is wrapped round the filament and on it are marked all the positions of the actin monomers. The paper is then unwrapped as in (B) and the helical tracks in (A) become straight lines. The final result in (C) is the radial projection or radial net. The 59 Å pitch length (P) and 27.5 Å subunit axial translation (h) are indicated in (C). way of thinking about a 13/6 helix is that it has 26 subunits in 12 turns of the helix. A helix with 28 subunits in 13 turns is therefore very closely related just obtained by slight untwisting of a 26/12 (i.e., 13/6) helix. For this reason, the two diffraction patterns in Fig. 10 are remarkably similar and distinguishing between them experimentally is not easy. Note that there is also a further important feature of actin filaments in muscle, namely, that they are rather flexible. Not only can their long axes be curved, but they can also twist azimuthally in a random way so that even along a helix that is a 13/6 filament on average there can be local twisting and untwisting, which makes the so called coherence length along the filaments rather short (Egelman et al., 1982; it is known as the random variable twist). The coherence length can be thought of as being a length

17 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 211 Fig. 10. Comparison of 13/6 (A) and 28/13 (C) actin filaments and their diffraction patterns, (B) and (D), respectively. The pattern in (B) shows characteristic features such as a strong first layer line (A1; P ¼ Å); a significant second layer line (A2; 179 Å); strong layer lines, which are the sixth (59.58 Å) and seventh (51.07 Å) orders of the repeat C (357.5 Å); and the first meridional reflection at h ¼ 27.5 Å on layer line 13. The pattern in (D) has similar features to (B), but the layer line numbering is different. The first few layer lines are the A2 at 385 Å, A4 at Å, A13 at 59.2 Å, A15 at Å, and A28 at 27.5 Å.

18 212 SQUIRE AND KNUPP over which the positions of, say, the crossovers of different parts of the two long pitched strands in actin are well enough related for the diffraction from these two parts of the filament to interfere in phase. It should be remembered that diffracting arrays that are relatively short (see Fig. 6)give diffraction peaks that are relatively broad. For this reason, the layer lines from the short coherence length actin filaments in muscle diffraction patterns are often quite broad axially. This makes it even harder to measure their axial position exactly and thus to define the helical symmetry precisely. In fact, vertebrate striated muscle diffraction patterns appear to be such that the crossover spacing is actually slightly longer than the Å expected for an exact 13/6 helix; it is more likely Å (Huxley and Brown, 1967; Harford and Squire, 1986). Note that in terms of Bragg s law, and assuming a wavelength l for the X rays of say 1.5 Å, which is quite common for both laboratory based and synchrotron X ray sources, the value of the angle of diffraction 2y for an actin filament repeat of Å is very small. It is 2y ¼ 2 sin 1 (1.5/ ) ¼ Since the myosin filament repeat in vertebrate striated muscles is of the same order of magnitude as the actin repeat (it is 429 Å), diffraction from muscle filaments that shows their helical structure is often called low angle diffraction (LAD) or small angle diffraction (SAD). Such diffraction patterns need to be recorded with the specimen to detector distance (see D in Fig. 3B) long enough (1 to 10 m depending on the X ray beam diameter) for the pattern to expand to a useful size that matches the pixel resolution in the detector being used. As discussed later, useful highangle diffraction information can also be obtained from muscle (Squire, 1986). This arises from the myosin filament backbone structure and also from the detailed internal structure of actin filaments (Holmes et al., 1990). As seen earlier (in Fig. 5), it is the lattice shape and size in a crystal that define the location of the diffraction spots and it is the repeating unit on the lattice that defines the relative intensities of these spots. So it is with actin filaments. It is the symmetry of the array of actin subunits that determines where the layer lines will be (as in Fig. 10), but it is the shape and orientation of the actin subunits on each point along the helix that define the relative intensities of these actin layer lines. The actin monomer (as discussed in Squire et al. in this volume; see Section II.A.3 and Fig. 9) has four subdomains in which subdomains 3 and 4 lie close to the helix axis and subdomains 1 and 2 are on the outside of the helix. Subdomain 1 is relatively large and is where myosin heads bind, whereas subdomain 2 is relatively small and its precise role is not clear. However, it can be shown (e.g., Harford and Squire, 1997) that even quite small movements of subdomain 2 can have their effect on the intensities of the low angle actin layer lines. In terms of resolution, which is often all important in structural

19 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 213 studies, the actin layer lines very definitely occur at low resolution. However, the crystal structure of the actin monomer is known, so we have a great deal of additional very high resolution information. When the low angle layer lines from the actin filament are modeled in terms of the relative positions of the actin subdomains, the intensities of the low angle actin layer lines are seen to be sensitive to sub domain movements of only a few angstroms. The sensitivity of the technique is therefore very high. Before leaving the discussion of actin filaments it is necessary to discuss the effects of tropomyosin and troponin. Tropomyosin strands run along the long period helices of actin where one tropomyosin molecule interacts pseudo equivalently with seven actin monomers. Successive tropomyosin molecules link end to end along the filament to form more or less continuous strands of density. In the case of a 13/6 actin helix, one of these strands has a pitch of ¼ 715 Å, but because there are two essentially continuous strands of tropomyosin, the tropomyosin repeat appears to be halved to Å. The tropomyosin strands therefore contribute strongly to the low angle actin layer lines A1 at 1/357.5 Å 1, A2 at 2/357.5 Å 1, A3 at 3/357.5 Å 1, and so on. The tropomyosin strands do not contribute strongly elsewhere because the density appears continuous along the strands, so there are no helix crosses apart from the one at m ¼ 0. However, the tropomyosin diffraction pattern and the actin diffraction pattern interfere with each other and this is how it was realized that the tropomyosin strands might move across the actin monomers as a result of muscle activation (Haselgrove, 1972; Huxley, 1972; Parry and Squire, 1973). The A2 reflection was weak in patterns from resting muscle but became stronger in patterns from active muscle when the A3 layer line became slightly weaker. This was consistent with a movement of the tropomyosin from a position well out of the groove between the two strands of actin to one where it was closer into the groove (see analysis in Parry and Squire, 1973). This was because the actin and tropomyosin patterns interfered with each other in different ways when the tropomyosin was in the two positions. This kind of model now enjoys a great deal of support (Al Khayat et al., 1995; Brown and Cohen, 2005; Craig and Lehman, 2002; Squire and Morris, 1998; Vibert et al., 1997). The diffraction pattern from troponin is very different. Here, there is one troponin complex for each tropomyosin molecule, but the end to end repeat along the tropomyosin strands is about 385 Å It is longer than the actin filament crossover repeat of just over 357 Å in vertebrate muscles (Fig. 11A and B). Because much of the troponin complex is globular, unlike tropomyosin, it shows very marked discontinuous density every 385 Å along each strand of the actin filament, with the troponins in opposite strands axially shifted by the actin monomer subunit translation h of

20 214 SQUIRE AND KNUPP Fig. 11. (A) Radial net for an actin filament (blue) with tropomyosin strands (green) and troponin added at 385 Å intervals along each strand (red) and a possible line of nebulin (gray) shown here along one strand only of the long period actin helices. In fact, there may be nebulins on both strands. (B) As in (A) but shown as a 3D model with the same color code. (C) Left hand half of a low angle X ray diffraction pattern from bony fish muscle, and (D) calculation of the diffraction pattern of a structure similar to that in (B), but with a slightly different pitch to show that some features in (C) could be due to troponin. (Based on Squire et al., 2004.) 27.5 Å. In vertebrate striated muscles, the troponin repeat is slightly longer than the actin crossover repeat, so the troponin subunits appear to lie on two very slowly twisting helices around the actin filament. The effect on the diffraction pattern is shown in Fig. 11C and D. The troponin complexes can be thought of as lying on helices of pitch ¼ 715 Å, but with a subunit axial translation of 385 Å (Fig. 11A and B). Thus, part of the diffraction pattern consists of a series of meridional reflections at orders m ¼ 0, 1, 2, 3, etc. of 385 Å. These occur at spacings 1/385 Å 1, 2/ 385 [¼ 1/192.5 Å 1 ], 3 /385 [¼ 1/128.3 Å 1 ], etc. In addition, there are layer lines up and down from these positions by an amount n/715 Å 1. Since 385 is not far from half of 715, the layer lines (n ¼1, 3, etc.) appear about halfway between the meridional reflections (Fig. 11C and D). However, the layer lines for n ¼2, 4, etc. appear very close to the equator and to the meridional reflections for different values of m, so the whole pattern appears as meridional peaks with very closely spaced layer lines above and below them forming a very shallow cross, together with offmeridional layer lines about halfway between the meridional reflections.

21 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 215 Note that in insect flight muscle, since the actin filaments have 28/13 symmetry with a repeat of 385 Å (which is the same as the troponin repeat), in this muscle the troponins lie in regular positions along each side of the actin filament, almost like a ladder; they fit precisely into the regular A band lattice geometry (see Fig. 10C in Squire et al., this volume) where each actin filament lies exactly between two myosin filaments. This gives rise to interesting interference effects between the troponins and any myosin heads that bind to actin (Tregear et al., 1998). D. Diffraction from the Myosin Head Array Myosin filament structure has been described by Squire et al. (2005). In vertebrate striated muscles the myosin filaments can be described approximately as three stranded 9/1 helices. The helix pitch is 1287 Å, but, because there are three strands and nine subunits in each strand, the structure repeats after C ¼ 1287/3 ¼ 429 Å. Figure 12 shows the expected form of the low angle diffraction pattern from such filaments. The modeling of this structure by X ray diffraction was described by Squire et al. in terms of the three crowns of heads within each 429 Å repeat. The crown repeat of 143 Å gives rise to an m ¼þ1 meridional reflection, which has been labeled as the M3 reflection in many muscle studies (as in Fig. 12). The myosin head array also gives rise to layer lines at orders of the repeat of 429 Å. The first myosin layer line (ML1) is at 1/429 Å 1, the second (ML2) at 2/429 ¼ 1/ Å 1, and so on. The M3 reflection occurs on the third layer line at 3/429 ¼ 1/143 Å 1. It was shown in Fig. 27 of Squire et al. (this volume) that the myosin filaments in different muscle types, particularly in invertebrate muscles, have their heads arranged on different surface lattices. There can be different numbers of helical strands and also different axial repeats. However, in all of these other cases the head arrays appear to be perfectly helical. The vertebrate striated muscle myosin filaments are different in that their heads do not lie on perfect helical tracks; there is a perturbation (described in Squire et al., this volume, see Fig. 20) that makes the three crowns within a 429 Å repeat nonequivalent. This shows up very obviously in the X ray diffraction patterns from vertebrate striated muscles. If the structure was helical, meridional reflections would be expected to occur only at positions where m ¼ 0, 1, 2, etc., that is, at multiples of 3/429 Å 1. In fact, meridional reflections are observed on all of the first few orders of the 429 Å repeat, in particular with a strong peak on the second myosin layer line at Å (M2), and with others at M4, M5, M7, and so on. These are all indications that the helix is not quite perfect.

22 216 SQUIRE AND KNUPP Fig. 12. (A) The left half of a low angle diffraction pattern from bony fish muscle (similar to that in Fig. 11C) but showing the layer lines, which are thought to come from the array of myosin heads on the myosin filaments. This array has a repeat C of 429 Å and a subunit axial translation (intercrown spacing) of 143 Å. The observed layer lines are therefore ML1 at 429 Å, ML2 at Å, and so on with meridional reflections at M3 (h ¼ 143 Å). Other forbidden meridional reflections occur at M2, M4, M5, and so on. (B) Simulation of the layer line pattern in (A) produced by MusLabel for the myosin filament structure illustrated in Fig. 16 in Squire et al. (this volume) and in 3D in Fig. 14 here. The reason for this perturbation could be that the myosin filaments in vertebrate striated muscles carry titin, which has a repeating pattern along it which itself probably has a 429 Å spacing, and C protein (MyBP C), which in the C zone region of the A band appears to label every third crown level. Squire et al. (2003d) showed that the outer, N terminal, end of C protein could also bind to actin, in addition to the C terminal part binding to myosin and to titin, and this may be why there are particular features of the X ray pattern from striated muscles with an apparent

23 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 217 spacing that is just longer than the 429 Å repeat of the myosin filaments (Fig. 13). In particular, there is a meridional reflection at about 440 Å, which has been shown to come from C protein (Rome et al., 1973a), and there is evidence from electron microscopy that appears to show C protein with a slightly longer spacing than myosin (Sjostrom and Squire, 1977; Squire et al., 1982). The diffraction pattern from C protein is discussed further when the effects of interference between the two halves of the A band are considered. To summarize the results so far, Fig. 14 shows a stereo view of part of the A band in bony fish muscle with the myosin heads organized on the myosin filament surface as in the X ray analysis of Hudson et al. (1997), with the actin filaments as described in Fig. 6.10, and with the C protein strands running with the C6 C10 C terminal region aligned parallel to the myosin filament axis and the N terminal C5 C0 regions crossing over to binding sites on adjacent actin filaments. Note that this arrangement of the C terminal region is different from that shown in Fig. 13A, B. Based on evidence for binding between domains 7 and 10 and 5 and 8, Moolman Smook et al. (2002) have suggested that this part of C protein may form a collar around the myosin filament backbone. The alternative arrangement in Fig. 14 is based on X ray diffraction evidence (Squire et al., 2003d). As yet it is not known which model is correct. E. The Z Band Contribution As detailed by Squire et al. (this volume; see Section II.C.6), one of the curious features of the vertebrate muscle sarcomere is that, although the A band lattice is hexagonal, the Z band lattice is square. The transition between the two structures in the I band has been discussed by Squire et al. (see their Fig. 14, this volume). There is relatively very little material in the Z band itself to give very strong diffraction unless the Z band is very thick (e.g., in the midshipman fish swim bladder; Lewis et al., 2003). However, the actin filaments in the muscle I band appear to be relatively straight for 0.1 mm on each side of the Z band and these regions might well diffract strongly. In muscle diffraction patterns the equator is the part of the pattern that shows what the sarcomere looks like in a view down the filament axis. The hexagonal lattice in the A band gives rise to equatorial reflections, the first few of which index as the 100, 110, 200, 210, and 300 reflections from a hexagonal lattice of side a ¼ bof420 to 450 Å, depending on the muscle type and the sarcomere length. Such a pattern is shown in Fig. 15. Note that often for brevity the third index is omitted, so these reflections are often referred to as the 10, 11, 20, 21, and 30 reflections.

24 218 SQUIRE AND KNUPP Fig. 13. Illustrations of the possible arrangement of C protein (MyBP C) on the myosin filament backbone in projection down the axis (A) and in axial view (B). Of particular importance here is the possibility that the N terminal half of C protein extends out and binds to actin in relaxed muscle. (C) Simulation of the possible interactions of C protein with binding sites on actin generated using the program MusLABEL (Squire and Knupp, 2004). (D) Left: left half of the low angle X ray diffraction pattern from bony fish muscle (as in Fig. 11C), showing (right) the possible positions where the C protein array in (D) might contribute. (From Squire et al., 2003d.) Also apparent in Fig. 15A is a peak (shown with arrows) that is not part of the A band series, but in fact comes from the Z band/i band part of the sarcomere. This peak at a spacing of 290 Å is between the 10 and 11

25 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 219 Fig. 14. Model of the A band filament lattice in bony fish muscle, based on Hudson et al. (1997) and Squire et al. (2003d), showing the central myosin filament with its projecting myosin heads, together with C protein in orange and actin filaments colored as in Fig. 11A and B. A band peaks, which to avoid confusion can be referred to as AB10 and AB11. The 290 Å peak is the 10 reflection from the tetragonal I/Z lattice and so can be called the Z10 reflection. As realized by Harford et al. (1994), this spacing puts the Z band 11 reflection in exactly the same spot as the A band 20 reflection; the Z11 and AB20 peaks overlap. This can be a nuisance if one is trying to use the equatorial reflections to determine the mass distribution in the A band by carrying out what is known as Fourier synthesis (e.g., Harford et al., 1994; Squire, 1981; Yu and Brenner, 1989). This is p a means of using the observed intensities (actually the amplitudes / ffiffi I ), and their estimated relative phases, to compute the

26 220 SQUIRE AND KNUPP Fig. 15. Intensity profiles along the equator of the bony fish muscle low angle X ray diffraction pattern from muscles at rest (A), fully active (B), and in rigor (C). The indexing in (A) is based on the hexagonal A band lattice, and the arrows indicate peaks that come from the Z band. (C) to (F) are computed electron density maps based on the amplitudes of the A band peaks in (A) to (A), respectively. The simple lattice unit cell is outlined in (D). (From Harford and Squire, 1997.) contents of the unit cell. Harford et al. (1994) devised a method to unscramble the AB20 and Z11 peaks and were able to compute separate density maps for the A band (Fig. 15D F) and Z band (not shown).

27 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 221 It was mentioned by Squire et al. (2005) that the myosin filament lattice spacing changes when the sarcomere length changes to give an almost constant volume for the sarcomere. When the sarcomere length is increased, the A band equatorial reflections move to smaller d spacings (further from the meridian). An interesting observation by Yu et al. (1977) was that the Z band spacing also changes in the same direction and by proportionately the same amount, so that the AB10/Z10 ratio remains constant. There presumably are lateral forces on the Z band that make this happen, probably due to the organization of titin in the I band (see Squire et al., 2005; Granzier and Labeit, 2005). F. Diffraction from the Myosin Filament Backbone Before leaving this discussion of the basic contributors to the muscle diffraction pattern, there are two other parts of the sarcomere that make a significant contribution at high diffraction angles. One is the internal structure of the actin monomers in the actin filaments, which can give rise to a rich and quite sharp meridional pattern out to d spacings of a few angstroms, and also some diffuse off meridional high angle intensities. This rich, high angle pattern can be recorded from oriented gels of actin filaments (Holmes et al., 1990), but can also be seen in high angle patterns from muscle (see Squire, 1981). The other contributor is the backbone of the myosin filaments where the myosin rods are packed. These rods are two chain coiled coil a helical structures, each of diameter 20 Å, which pack together quite tightly to give a sturdy filament backbone. Evidence from paramyosin filaments suggests that the rods might prefer to pack with the wide parts of the coiled coil of one molecule side onto the narrow part of its neighbor, thus giving rise to a pseudo body centered lattice. This may be (pseudo ) tetragonal in molluskan muscles with large diameter thick filaments in which paramyosin is abundant (see Squire et al., this volume, Figs. 10 and 27), but must be more close packed in the much smaller diameter, tighter myosin surface layer, filaments of vertebrate or insect flight muscles (see Squire, 1973). Low angle X ray diffraction data has revealed the distribution of myosin heads on the myosin filament surfaces of different muscles, and the myosin rods must be organized in the backbone so as to produce this arrangement of heads on the surface. However, the precise mode of rod organization is not fully determined. Various models have been proposed that have been tested in depth by Chew and Squire (1995) against the quite rich high angle X ray diffraction patterns from bony fish and

28 222 SQUIRE AND KNUPP other muscles (Squire, 1986). Here there are two main features; one is the 5.1 Å meridional reflection from the slightly distorted a helix pitch in the coiled coil structure and the other is a set of rather diffuse equatorial peaks at 20 Å and 10 Å due to the lateral packing of the myosin rods, together with diffuse near equatorial peaks due to the axial repeat of the coiled coils. Chew and Squire found that the model proposed by Squire (1973) for the packing of these rods was in fact the most consistent with the observations of all the models tested, but direct proof is still needed. This model is also consistent with the molecular overlaps predicted from the distribution of charges along the myosin rods. In addition to this high angle X ray diffraction, the myosin rods together with titin and C protein undoubtedly contribute to the low angle meridional diffraction pattern. Part of this is due to the peaks already discussed as coming from C protein (440 Å; see later discussion). However, they also contribute to some of the otherwise forbidden meridional reflections, such as M2, M4, M5, etc., and to the proper meridionals at M3, M6, M9, and so on. Since the M3 reflection and some of its orders are used to probe the movement of myosin heads in active muscle, knowledge of the contribution from the myosin filament backbone is important. Note that the eleventh order meridional peak (M11) at 429/11 ¼ 39 Å is relatively strong, possibly because of the myosin packing itself (see Squire et al., 2005) and possibly because of the eleven domains in the 429 Å repeat along the titin (Labeit and Kolmerer, 1995; Cantino et al., 2002). II. Modeling of Rigor Muscle A. Introduction With the structure of resting muscle established as far as we know it, it is appropriate to think about how the myosin heads can interact with actin. Before thinking about contracting muscle and force production, this section briefly describes current knowledge of the well documented static state after the relaxed state, namely, the nucleotide free rigor state. This can be induced in intact muscle by allowing the muscle to die (as would occur in rigor mortis), but a more controlled and useful procedure is to skin the muscle in some way, perhaps by glycerination or by detergentskinning, and then to bathe the muscle in an ATP free solution so that all of the heads end up in the AM (rigor) state. A controlled reduction of the ATP level and the use of such things as BDM (2,3 butanedione monoxime) or NEM (N ethylmaleimide) can help to produce a relatively well ordered

29 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 223 rigor structure (e.g., Bershitsky et al., 1996; Yagi, 1992). The myosin head interaction with actin in this state in skinned muscles or fibers has been studied by a variety of methods including X ray diffraction, electron microscopy, and analysis of the orientation of fluorescent probes. However, the most detailed modeling of the rigor head conformation on actin has come from image processing of isolated actin filaments labeled with S1 moieties (e.g., Rayment et al., 1993a,b). A reconstruction of this type is shown as Fig. 16C. The most recent analysis of S1 labeled actin using cryoelectron microscopy and energy filtering (Holmes et al., 2003; 2004) produced a density map at Å resolution and showed both the tilted configuration of the rigor head, as in Fig. 16C, and the suggestion that the cleft in the motor domain should be closed in this strong actin binding configuration (see discussion and references in Geeves and Holmes, 2005). This rigor conformation is more or less consistent with previous maps from electron microscopy. So, if we know how isolated myosin heads like to interact with actin in the rigor conformation, the question then is, what happens in rigor muscle? The most direct indication of mass transfer from myosin to actin in rigor muscle comes from analysis of the equatorial part of the low angle X ray diffraction pattern (e.g., Harford and Squire, 1992; Harford et al., 1994; Haselgrove and Huxley, 1973; Huxley, 1968; Millman and Irving, 1988; Yu et al., 1977, and many others). Fig. 15A C show the intensity profiles along the equator of bony fish muscle in three different states: relaxed, active, and rigor. The AB10 and AB11 reflections from the A band hexagonal lattice are seen with the AB10 relatively strong and the AB11 relatively weak in patterns from relaxed muscle (A), but the intensities reversed in patterns from rigor muscle (C). Alongside these profiles are computed electron density maps based on these equatorial patterns and showing the changing mass distribution in the A band unit cell in the different states (D F). These maps depend on an assumption about the phases of the reflections as discussed in detail in, for example, Harford et al. (1994) and Harford and Squire (1997). In the maps in Fig. 15, there is relatively little mass at the actin filament position in relaxed muscle (Fig. 15D), there is a great deal of mass at actin in rigor (Fig. 15F), and there is something in between in active muscle (Fig. 15E). The equatorial reflections can therefore be taken as indicators of head attachment to actin. However, it should be noted that it is also true that for a given number of myosin heads attached, the actual shape and configuration of the heads on actin will also change these equatorial intensities (e.g., Lymn, 1978); in principle, the equatorial intensities can also be used to monitor head shape as well as attachment number.

30 224 SQUIRE AND KNUPP Fig. 16. (A) Low angle X ray diffraction pattern from permeabilized bony fish muscle with exogenous myosin heads (S1) added under rigor conditions. The actin layer lines are enhanced, but no new layer lines appear compared with patterns from relaxed muscle. The arrowed peak is the M3 reflections at 143 Å. (B) A similar pattern to (A) but from permeabilized fish muscle in rigor, but without added exogenous myosin heads. A new set of layer lines appears. (C) Helical reconstruction of labeled actin

31 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 225 B. Labeling of Actin in Rigor Muscle Figu re 16A shows a low angle X ray diffr action pattern from a fish muscle into which an exces s of exogeno us m yosin S1 had been soaked under ri gor con ditions (from Squ ire et al., 2005b ). Such a procedur e should ran domly label any availa ble actin sites, at th e limit produ cing actin filam ents through the I band and overlap reg ion of the A band that are total ly S1 labeled. The effec t on the diffracti on pattern is as pre dicted. The acti n layer lines ( Fig. 16A ) all become stron ger and their pea k intensi ty moves in toward the meridi an, consist ent with the head s produci ng an actin like heli x of rel atively large radius. No new lay er lines are se en, since there is no new lattice geomet ry present. The 3D recon struction in Fig. 16C is actual ly a helical recon struction based on th e observed X ray amp litudes from Fig. 16A combined with phases obtained from Dr. R. Milligan. The diffraction pattern from the S1 labeled structure should be compared with Fig, 16B, wh ich is from a skinn ed fish m uscle without any exogenous heads, but in the rigor state. Of course, the original actin layer lines are enhanced once again, but, in addition, the M3 reflection is much stronger. It also extends along the layer line away from the meridian, and there are new layer lines that are not present in patterns from either relaxed muscle or S1 labeled muscle. The reason that these new features are present is that in the overlap region of the vertebrate A band there are not enough heads to fully decorate actin filaments. The positions of attachment of the heads that do find a binding site are heavily dependent on the relative positions of the origin of the myosin head on the myosin filament and the position of the nearest available binding site on actin (Squire, 1972). Since the rigor attachment is one that is described as stereo specific (i.e., its geometry is fully determined in three dimensions; Fig. 16C, D), it is easier for a given head to attach to some actin monomers, which present the binding site in an appropriate orientation for myosin attachment, than it is to attach to other actin monomers, which may be relatively hard to reach. This constraint was fully described and illustrated by Squire (1972) in his analysis of the results of Reedy (1968) on insect flight muscle. It gave rise to what are termed actin target areas within which it is relatively easy for heads to bind. Subsequent independent analysis has supported the idea of target areas (e.g., Squire and Harford, 1988; Yagi, 1996; Koubassova and Tsaturyan, 2002; Steffen et al., 2001). filaments based on the X ray amplitudes from (A) and phases courtesy of Dr. R. Milligan. This shows the general form of the rigor head shape on actin as in the green head shape in (D). Also shown in (D) is the lever arm in the pre powerstroke position (blue) discussed in detail in Geeves and Holmes (2005).

32 226 SQUIRE AND KNUPP The new layer lines observed in X ray patterns from rigor vertebrate muscle can be explained approximately as orders of a repeat of about Å ¼ Å ¼ 2145 Å, where 429 Å is the myosin repeat, 715 Å is the actin filament pitch, and 2145 Å is the beat period between the two. The first myosin layer line (ML1 in Fig. 11) would then be the fifth order of this; the first actin layer line (A1; Fig. 9) would be the sixth order, and the M3 or ML3 layer line would be the fifteenth order. In the observed rigor pattern, intensity is seen on orders 5, 6, 9, 10, 11, 12, and 15 of the roughly 2145 Å repeat. The tenth and eleventh order peaks are relatively close to the meridian (shown with arrows in Fig. 16D). One way to analyze this process is to use the program MusLabel, mentioned earlier, and to set up the appropriate geometry for the vertebrate muscle A band overlap region. The search ranges for the axial and azimuthal reach of a myosin head and the size of the actin target area can then be chosen and the program used to show what happens to the computed diffraction pattern. We know from previous studies (e.g., Lovell et al., 1981) that in rigor vertebrate striated muscles there is labeling of actin by virtually 100% of the available heads, so the MusLabel program can be used to determine which geometrical constraints on head movement are needed to yield 100% labeling. In fact, Squire et al. (2005b) assumed 98% labeling and obtained results such as those in Fig. 17, which shows a set of computed diffraction patterns from just the actin binding sites that are labeled by at least 98 % of the myosin heads under different search conditions. The first point is that there are many different ways to get virtually 100% labeling of actin by the heads. However, not all of these ways give strong layer lines where they are observed in the pattern from rigor muscle. In other words, the observed pattern can start to tell us which factors are dominant when a head is searching for a binding site on actin. Three distinct regions are outlined in the set of computed diffraction patterns shown in Fig. 17. Even though these patterns are computed from putative sites on actin filaments, region A is such that it gives rise to strong layer lines at positions 5, 10, and 15 (i.e., 429 Å, 215 Å, and 143 Å), which are the same as those from resting myosin filaments (see Fig. 12). In other words, myosin like layer lines can be produced by myosin heads on actin. The unifying feature of these patterns in region A is that the angular size of the target area (twice the inset number in each frame) is generally very large. In summary, if the actin target area concept and the idea of stereo specificity are relaxed, the myosin heads just reach out and bind to the nearest actin monomer regardless of its azimuthal orientation. Heads attached to actin non stereo specifically will give rise to a strong M3 reflection and to other myosin like layer lines, as well as making a contribution to the first actin layer line (A1).

33 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 227 F ig. 17. Sets of computed diffraction pattern simulations for different patterns of labeling of myosin heads on actin, defined by the head angular search range y, the head axial search range Z, and the actin target area angular size (twice the large number on each pattern), in each case with at least 98% of the available myosin heads bound to actin. For details of parameters and regions A, B, and C, see text. (Based on Squire et al., 2005 b.) Are a B in Fig. 17 shows th at the M3 layer line is very weak o r abse nt, the other myosin like lay er lines and the new low radius layer line s on orders 9 12 of Å are prac tically nonexist ent, but the acti n like layer lines (i.e., 6, 12 [high radius], 18, etc; 357.5, 179, 119 Å ) are very strong and at ever increa sing radius. The partic ular poi nt abo ut this region is that the target areas on actin are very small and the heads need to search a large distance axially to reach a binding site. In doin g this, they effecti vely wa sh

34 228 SQUIRE AND KNUPP out the 143 Å ness of th eir crown spacin g and the myosin like fea tures of th e pattern disappea r. The remai ning reg ion C is so mewhere between these two extrem es. All patter ns in C have a strong fir st acti n layer line (order 6 of 2145), th ey have a strong fifteen th ord er at 143 Å, they have inten sity at low radius on layer line s 9 and 12, and in som e cas es they have a weak remnan t of the fifth layer line (42 9 Å ) at relativel y low radi us, as ob served. The extend ed nature of th e obs erved 143 Å layer line in Fig is reprod uced in region C, where th e axial excursion ( Z) of the head s is small, the azi muthal excursi on ( y) is qui te large, and the actin ta rgets for the better model s are of the ord er of 2 75 ¼ 150. (The low est box in reg ion C of Fig. 17 has the fif teenth layer line muc h strong er than the sixth, wh ich is not observed ). In one half turn of a long per iod actin heli x contai ning 6.5 actin m onomers, th e actin mono mer azimuth cha nges by 180, so this analysi s sugg ests that a gi ven head can bind within a reg ion that is 4 or 5 actin m onomers long on one strand only (obviou sly the near er) of the fila ment. Note fina lly that all o f this ana lysis so far is inde pende nt of the shap e of th e myosin head. The analysis is like defin ing the lattice on which the head s are arranged (s ee Fig. 5 ) thereby defining whic h layer lines will be domi nant. The shape of the head will then be a kind of moti f convoluted wit h this latti ce of binding sites. Electr on tomograph ic analysi s of ri gor insect fligh t muscle by C hen et al. (2002 ) and Liu et al. (20 04) has suggested th at the strains on differen t myosin heads in rigor muscle will make the neck parts of th e head s tilt bac k in differen t directio ns toward th eir own partic ular ori gins on the myosin filament, so not all attached heads will neces sarily have th e unstrain ed confor mation in Fig. 15C and D. If this is gener ally true, this distribut ion of shap es will have its effect on the relative intensities of the rigor layer lines, but it will not generate new layer lines in addition to those on the 2145 Å lattice. A more detailed examination of head shapes in rigor will require full modeling of the rigor X ray diffraction pattern from either bony fish muscle or insect flight muscle where the lattice sampling is good. This has yet to be done. C. The Weak Binding State The ana lysis of the crossbridge cycl e in Geeves and Hol mes (2005 ) empha - sized the probable existence of a weak binding (non stereo specific, prepowerstroke) myosin head state before transition to a strong binding (stereo specific; post powerstroke) state. It would make sense if myosin heads can first dock loosely to actin, then become stereo specifically bound, and then go through their force producing cycle on actin. A highly populated weak binding state was, in fact, observed and studied in skinned

35 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 229 rabbit psoa s muscle fibers by immer sing the fibe rs in low ionic streng th relaxing solution ( Brenner et al., 1984; Yu and Brenner, 1989 ). The e xistence of this state wa s ded uced from th e follow ing observa tions. First, the muscle wa s not stiff to slow stretches, but became stiffer as th e speed of stretch was incr eased. This imp lied that a substa ntial numb er of heads were reversibl y and tran siently bound to acti n even in relaxing solution, so that in slow stretches a subse t of actin at tached head s could qui ckly come off actin and others could reattac h so mewhere else so that little stif fness would be rec orded. On th e con trary, in very fast stretche s, many of the attached subset of head s would be attached essential ly for the who le time and the muscle would appear stiff. Eve n faste r stret ches woul d trap eve n more heads and the muscle would appea r st iffer. Second, equator ial diffracti on patterns from thes e low ionic streng th fibers show ed relative intensi ties for the AB 10 and AB 11 equatorial reflec tions, which were m idway betwe en relaxed and rigor; they were in fact not unlike pattern s from active muscle (see Fig. 15B ) with the AB10 and AB11 intens ities about the same as each other, even thoug h no tension was being produ ced. Third, even thoug h these head s were clearly atta ching to actin, henc e the rapid stif fness, they still gave rise to myosin li ke layer line s in the low angle X ray patter ns (e.g., Xu et al., 2002 ). We would interpret this ( Squ ire and Harford, 1988 ) as indicating the prese nce o f non stereo spec ifical ly boun d actin attached heads which, as in reg ion A of Fig. 17 ( Squ ire et al., 2005b ), would gi ve myosin like layer line s. D. Summary: Take Home Messages Wor k by Xu et al. (19 99 ; and references to others there) has ten ded to confirm that good heli cal o rdering of th e myosin heads o n rabbi t psoas muscle thick filaments requ ires the heads to be in the M.ADP.P i state at temperatu res above 20 C. This pro bably occurs in oth ers m uscles, too, but fish and frog muscles, for exam ple, normall y opera te at muc h lower tempe ratur es (5 15 C) than rabbit (37 C ), whic h preclud es the possibilit y of taking them ove r 17 C down from their normal opera ting temperatu re to test this. However, assuming that M.ADP.P i is the predominant stat e in ord ered resti ng m uscles, then th e next step in the Lym n Taylor (19 71) schem e is AM. ADP.P i, a stat e discussed in some detai l in Geeves and Hol mes (2005 ). The AM. ADP.P i st ate is taken to be init ially a non stereo specific, tran siently attached, stat e largely controlled by electrostatic interactions (Wong et al., 1999). The strong states such as AM.ADP and AM follow from this. A number of attempts to trap heads in the elusive AM.ADP.P i state in intact muscle, sometimes using ATP analogues (e.g., AMP.PNP), as well as

36 230 SQUIRE AND KNUPP other studies with heads largely in defined states (e.g., Xu et al., 2002; Yagi et al., 1998; and others) have tended to confirm this general picture of varying populations of non stereo specific states and stereo specific states in the crossbridge cycle. Results from steady state muscles have led to the following general conclusions: 1. Stereo specifically attached heads as in rigor give rise to a mixed population of myosin like and actin like layer lines, including a 143 Å (M3) reflection. They show good evidence for actin target areas. 2. Non stereo specifically attached (such as weak binding) heads, even though on actin, give a myosin like layer line pattern including a 143 Å (M3) reflection. This also includes a contribution to the first myosin layer line (ML1) and the first actin layer line (A1; Ferenczi et al., 2005; Harford and Squire, 1992; Xu et al., 1999). 3. Both stereo specifically attached and non stereo specifically attached heads can change the equatorial intensities. For a given attachment number, the observed intensities depend on the nature of the binding and shape of the myosin head (Lymn, 1978; Squire and Harford, 1988). The AB11/AB10 intensity ratio increases with increasing attachment number, and, for a given attachment number, it increases with increased relative populations of rigor like or stereo specifically attached heads. 4. Following on from (3) above, non stereo specifically attached heads give an AB11/AB10 ratio of about 1, as in the low ionic strength relaxed state of Brenner et al. (1984). Transition to the strongly attached state reduces the AB10 intensity, which therefore changes in step with tension, but does not greatly alter the AB11 intensity. 5. In active or rigor muscle, heads that do not overlap actin filaments become disordered (Cantino et al., 2002; Padron and Craig, 1989). They therefore contribute little to the observed low angle X ray diffraction patterns. This population increases with increasing sarcomere length (reduced filament overlap). III. Time Resolved Events in Contracting Muscles A. Changes in the Equatorial Reflections Following the pioneering, laboratory based, time resolved X ray diffraction studies of muscle by H. E. Huxley and separately by G. F. Elliott (Elliott et al., 1965; 1967; Huxley, 1972; Huxley and Brown, 1967; Huxley et al., 1965), a number of groups, including that of Huxley, have followed

37 STUDIES OF MUSCLE AND THE CROSSBRIDGE CYCLE 231 up these experim ents on frog and se veral other muscle ty pes, in rec ent years using muc h strong er and bri ghter synchr otron beam line s and very high speed elec tronic dete ctors (e.g., RAPID ; Lewis et al., 1996, 1997 ). These include furth er stud ies by Huxle y et al. (19 80, 1981, 1983, 2003) and by many others, includ ing Ba gni et al. ( 2001); Bord as et al. (19 93); Cecchi et al. (1991, 2003) ; Ma rtin Ferna ndez et al. (1994 ); Piazzes i et al. (1999) ; Juanhi x et al. (2001); and Kraft et al. (19 99; 2002). Further studies of very fast transients in intact frog single fibers have been carried out by (Dobbie et al., 1998; Irving et al., 1992, 1995, 2000; Linari et al., 2000; Lombardi et al., 1995; Piazzesi et al., 2002; Reconditi et al., 2003, 2004) and studies of permeabilized rabbit fibers with applied temperature jumps and other interventions (Bershitsky et al., 1996; 1997; Ferenczi et al., 2005; Tsaturyan et al., 1999a,b). We have made use of the muscles of bony fish, because of their high degree of order and well sampled diffraction patterns (Harford and Squire, 1986; 1990; 1992; 1997; Harford et al., 1991; Mok et al., 2005; Squire, 1998; Squire et al., 1994; 2003a,b,c; 2005a) and have carried out related time resolved experiments with tetanically contracting intact muscles. The reasons for preferring bony fish muscles is the very high degree of simple lattice order in the bony fish muscle A band (discussed in Squire et al., 2005; Luther and Squire, 1980; Luther et al., 1981; Harford and Squire, 1986), which makes the diffraction patterns highly sampled and therefore much more amenable to proper interpretation (e.g., Hudson et al., 1997) than superlattice muscles. Figure 18 shows a difference fish muscle diffraction pattern, active minus relaxed, between the tetanus plateau and the resting phase before stimulus, and Fig. 19 shows intensity and tension time courses on a millisecond time scale in the early part of fish muscle tetanic contractions (from Mok et al., 2005). Note that these are all shown as normalized changes, with rest as 0% and the plateau set as 100% for intensities that increase on activation and vice versa for decreasing intensities; they are not absolute changes. Both figures illustrate the kinds of changes that are observed in most of the quoted X ray studies. A number of characteristic features are observed in the difference map in Fig. 18. Generally, as a result of activation, the myosin layer lines become weaker (black arrows), whereas much of the actin pattern becomes stronger (white arrows), particularly the second actin layer line (A2), which is associated with the tropomyosin shift discussed in Squire et al. (2005) and Brown and Cohen (2005). However, the outer part of the first actin layer line drops a little (black double arrow). These features are put on a quantitative basis in Fig. 19. As expected from the intensity changes seen in Fig. 15(C E), the effect on the equator is that during the rising phase of tension the AB10 intensity decreases and the AB11 intensity increases as more heads become attached to actin. However,

38 232 SQUIRE AND KNUPP Fig. 18. Difference intensity map between diffraction patterns from a fully active and a relaxed fish muscle (Mok et al., 2005). Generally, dark colors show intensity drops and green, yellow, and red show intensity increases. Generally, the myosin layer lines have dropped in intensity (black arrows), and many of the actin layer lines have increased in intensity (white arrows), especially layer line A2. However, the outer part of A1 has dropped in intensity (double headed black arrow). There are also clearly some shifts in axial spacing of the peaks; these are especially visible along the meridian. an interesting observation is that the time courses of the intensity changes of these two reflections are not the same. The AB10 intensity changes almost in step with tension (even though one increases while the other reduces), whereas the change in the AB11 reflection is well ahead of tension (about 20 1 ms before tension (T) at level of 50% change; Fig. 19A). The time to 50% tension and AB10 change was 37 1 ms after activation. Another feature that increases rapidly and well before tension is the intensity of the second actin layer line (25 1 ms before T; A2 in Fig. 19A), interpreted as showing that tropomyosin moves as an early event