Laue diffraction and time-resolved crystallography: a personal history

Abstract

A personal, historical view is presented of Laue X-ray diffraction and its application to time-resolved studies of dynamic processes, largely in light-sensitive biological systems. In Laue diffraction, a stationary crystal is illuminated by a polychromatic X-ray source. Laue diffraction has inherent complications largely absent in monochromatic diffraction, and consequently fell into disuse for quantitative structure determination. However, the advent of naturally polychromatic, intense, pulsed storage ring X-ray sources in the 1970s led to re-examination at Daresbury and elsewhere of its underlying principles. Laue diffraction has been successfully applied at storage ring sources to time-resolved, pump–probe crystallographic studies, whose exposure time and time resolution were progressively reduced from minutes to seconds, milliseconds, nanoseconds and 100 ps. Most recently, hard X-ray free electron laser sources have been used to generate narrow bandpass Laue diffraction patterns. The femtosecond X-ray pulses from such sources are completely destructive, generate only one diffraction pattern per tiny crystal and have unusual properties. However, they too are being applied to time-resolved crystallography to explore, for example, isomerization and rapid tertiary structural changes on the chemical, femtosecond timescale.

This article is part of the theme issue ‘Fifty years of synchrotron science: achievements and opportunities’.

1. Introduction

The geometrical foundations of Laue diffraction are reviewed by Amoros et al. [1], and its development and application to static and dynamic crystallography by Moffat [2] and by the authors in the book edited by Cruickshank et al. [3]. Helliwell [4] presents the principles and applications of synchrotron-based, macromolecular X-ray crystallography. Recent studies that use hard X-ray free electron laser sources to probe the nanosecond to femtosecond timescale on biological systems are reviewed by authors in Sections II and III of [5].

Since the conference at which this work was presented had historical origins, this article is explicitly both historical and personal, illustrated largely by references to the author and close colleagues.

2. Laue diffraction

Diffraction of X-rays occurs when a beam of X-rays falls on a crystal. During the earliest years of crystallography by Bragg, Dickinson and Dickinson's student Pauling, Laue diffraction was widely used for semi-quantitative structure determination of structures containing only a few atoms. In Laue diffraction, the X-rays are polychromatic with wavelengths ranging from λ_min to λ_max and the crystal is stationary throughout the exposure. In monochromatic diffraction (now much more widely used), the X-rays have a single X-ray energy/wavelength λ and the crystal is rotated during the exposure.

For structure determination of the molecules in all but the very simplest crystals, the structure amplitudes |F(hkl)| associated with each reciprocal lattice point (RLP) with indices hkl must be accurately extracted from the intensities of the diffraction spots. However, the relationship between diffraction spots and RLPs differs between monochromatic and Laue diffraction. For a monochromatic diffraction pattern, the relationship is relatively straightforward: each RLP is associated with a single diffraction spot in the overall pattern. The intensity of that spot can be accurately measured and the desired structure amplitude directly extracted. That is, monochromatic diffraction maps individual RLPs on to the X-ray detector that records the pattern. By contrast, for a Laue diffraction pattern, several RLPs may be associated with each Laue spot (e.g. [6], fig. 1). These RLPs all lie on a line in reciprocal space passing through the origin (000) and through a radial array of RLPs: (hkl), (2h2k2 l), …. (nhnknl) … This line is known as a central ray. In the array, h, k and l are co-prime, i.e. they have no common factor greater than 1; (hkl) denotes a first order RLP, (2h2k2 l) a second order RLP, and so on. Laue diffraction maps central rays on to the X-ray detector. The mapping is thus quite different for monochromatic and Laue diffraction.

Each Laue spot associated with a central ray contains contributions from all RLPs that lie in the volume between three limiting spheres: the Ewald spheres corresponding to 1/λ_min and 1/λ_max, and a sphere centred on the origin representing the limiting resolution of the crystal, d*_max. Each RLP within this volume selects the X-ray energy that satisfies Bragg's Law for that RLP. For a given X-ray beam and crystal resolution, the number of RLPs on each central ray and their specific indices that satisfy these constraints varies with crystal orientation. There may be only one RLP, e.g. with indices (hkl) or (3h3k3 l); the spot is said to be single, containing a single order. There may be two RLPs, e.g. (2h2k2 l) and (3h3k3 l); or many more than two; the spot is said to be multiple, containing multiple orders. The individual orders overlap exactly on the detector and cannot be spatially separated. Each RLP within a multiple spot selects the appropriate X-ray energy according to Bragg's Law from the polychromatic X-ray spectrum. Multiple Laue spots thus contain more than one X-ray energy. The total intensity of a Laue spot is the sum of the intensities arising from each RLP within that spot.

However, isolation of the intensities arising from all individual RLPs is necessary if the corresponding structure amplitudes |F(hkl)|, required for all subsequent quantitative crystallographic analyses, are to be obtained. This does not pose a problem if the Laue spots are single, but is highly non-trivial for multiple spots. Unfortunately, a full treatment of the distribution of single and multiple Laue spots, an assessment of the extent of the overlapping orders problem and of experimental or computational approaches to resolving it had not been developed by the 1930s. For quantitative measurements of more complicated structures, Laue diffraction was thus largely superseded by the somewhat simpler monochromatic diffraction. However, monochromatic diffraction too has limitations. Rotation is required to ensure that all regions of the crystal diffract X-rays from all areas of the X-ray source, thus generating ‘integrated’ intensities associated with each RLP: integration over angle. Each RLP diffracts for only a small fraction of the rotation, corresponding to a small fraction of the exposure time. In Laue diffraction, by contrast, these intensities are automatically achieved by integration over X-ray energy in the polychromatic beam. No rotation is necessary; the crystal remains stationary throughout the exposure. All constituent RLPs within each Laue spot select and diffract the appropriate X-ray energy for the entire exposure time. Thus compared with monochromatic diffraction, Laue diffraction typically requires shorter exposure times and, if a wider range of wavelengths is used, surveys a larger volume of reciprocal space in a single exposure.

3. Structural dynamics

Crystallography is normally thought of as a purely static experimental approach. However, the atomic structures that are its ultimate goal are a space average over all molecules in the crystal, and a time average over all molecular conformations (such as differing side chain orientations and backbone fluctuations) present during the X-ray exposure. If the structures are dynamic, changing with a time constant τ, then an X-ray exposure time less than, say, 0.1 τ is required to resolve the changes in the associated structure amplitudes. Time-resolved crystallography of rapid reactions characterized by low values of τ (say milliseconds, characteristic of many enzymatic reactions) thus requires short X-ray exposure times (say, tens of microseconds). It also requires at least equally rapid means of initiating the reaction, uniformly across all molecules in the crystal and with high efficiency. These requirements vary among crystals and can be challenging to meet [2,3].

We now take for granted the critical role of structural dynamics in function but this was by no means always the case. When the first few protein structures of myoglobin, haemoglobin and lysozyme were determined by static crystallography in the 1960s, the coordinates of atoms were laboriously determined and brass models built according to those coordinates were (literally) bolted down tight. This supported a static, ‘brass model mentality’. However, the necessity for some molecular flexibility and structural dynamics was evident even in the very first structure, of the oxygen-binding protein, myoglobin [7]. Its time- and space-average structure did not reveal a pathway by which an oxygen-sized molecule might diffuse from the solvent to the Fe atom in the fully buried haem; some structural changes were clearly required for oxygen binding and release. This generated a fundamental question: Was the crystal structure of myoglobin, and indeed of biomolecules more generally, of physiological relevance?

One way of examining relevance to physiology was to ask whether molecules in the crystal were active, retaining biological function. This question was incisively attacked by the biophysicist Quentin Gibson and his postdoc Larry Parkhurst at Cornell University [8]. They subjected the CO complex of haemoglobin—closely related to myoglobin—to flash photolysis that ruptured the light-sensitive Fe–CO bond. The kinetics of CO rebinding to the newly liberated deoxyhaemoglobin could be readily observed by following the time course of optical absorption, which differs markedly between the CO and deoxy forms. They found that the rebinding reaction spanned a few tens of microseconds (figure 1). More significantly, its kinetics were closely similar under three very distinct experimental conditions: in the red blood cell (the physiologist's favourite environment for haemoglobin), in a dilute solution (the biophysicist's favourite environment) and in a thin film containing a polycrystalline slurry (resembling the crystallographer's favourite environment). At least for this reaction, the haemoglobin molecules in the crystal fully and quantitatively retain function. The crystal structure of haemoglobin, and by implication those of other biomolecules, are indeed highly relevant to physiology—and of course to chemistry.

Figure 1.

The kinetics of recombination of CO with a slurry of tiny haemoglobin crystals, after flash photolysis. The flash profile is shown in the right panel. Fig. 6 of Parkhurst & Gibson [8].

As a crystallography research student of Max Perutz, these kinetic results raised questions in my mind: Could the CO rebinding reaction be monitored, not optically through the time dependence of optical absorption as Gibson had done, but crystallographically? That is, could structural dynamics be directly visualized through time-resolved crystallography? Enthusiasm said the answer was ‘yes’! On arrival in Gibson's lab as a postdoc in 1969, we spent a long, hard afternoon arguing about the experimental aspects of this candidate experiment. Although our scientific backgrounds were very different, Gibson was wonderful to argue with. We convinced each other that, although time-resolved crystallography of haemoglobin was indeed scientifically desirable, it was at that date experimentally unfeasible, for several reasons: the lack of intense X-ray sources that might offer microsecond time resolution, the necessity for very large crystals approximately 1 mm, and the difficulty of initiating the reaction uniformly and rapidly in such large, optically dense crystals. Realism prevailed over enthusiasm.

Though it was painful to reach this conclusion at the time, hindsight shows it was correct. I pursued more conventional, lower-risk, lower-reward projects in haemoglobin kinetics during my brief postdoc. On joining the Cornell faculty as an Assistant Professor, I established a research programme in conventional, static, macromolecular crystallography. Dreams of time-resolved crystallography were filed away.

4. Synchrotrons, the redevelopment of Laue diffraction and time-resolved crystallography

A few years later, synchrotrons were being developed as promising, intense X-ray sources at Hamburg, Stanford and Daresbury [9,10]. A seminal workshop at Brookhaven in 1972 considered applications of synchrotron radiation in many areas of research including materials science, chemistry and biology [11]. The biology-related speakers Stephen Harrison (Harvard), Harold Wyckoff (Yale) and Gerd Rosenbaum (Hamburg) presciently identified such applications as fast data collection, enzyme kinetics and study of small crystals to exploit the high intensity of synchrotron sources; and anomalous dispersion and Laue diffraction to exploit their naturally polychromatic radiation. The high intensity offered particular promise for attacking time-resolved crystallography with shorter X-ray exposures, and potentially on smaller crystals. Synchrotrons themselves had drawbacks as radiation sources, but early experiments in the early 1970s at the Stanford Positron-Electron Accelerator Ring demonstrated that in a storage ring, the more stable, continuously circulating electrons at higher current overcame these drawbacks.

My laboratory in the biochemistry department at Cornell directly overlooked an intramural playing field—and under that field was a tunnel housing a high energy electron synchrotron, devoted to experiments in fixed target, high energy physics. In 1976, the Cornell high energy physicists were actively planning to convert the synchrotron into a colliding beam storage ring, whose high electron energy would make it an ideal source for hard X-ray experiments in many disciplines, definitely including biology. Two carefully coordinated, parallel grant applications to the High Energy Physics and Materials Science Programs at NSF led to construction and commissioning of the Cornell Electron-positron Storage Ring (CESR) and the Cornell High Energy Synchrotron Source (CHESS). Our first monochromatic diffraction experiments at CHESS in 1981 indeed required exposure times shorter than those required with a rotating anode source, but remained in the range of a few minutes for a typical crystal of a macromolecule. This was an important step, in the right direction towards rapid time-resolved measurements. However, there was a long way to go to reach the more biological and biophysical timescale of nanoseconds to seconds, let alone the chemical timescale of picoseconds to femtoseconds characteristic of elementary steps such as electron transfer, bond breaking and isomerization. (For timescales, see, e.g. fig. 5.1 of [5]).

Since synchrotron sources are naturally polychromatic, monochromatic diffraction experiments required the insertion into the X-ray beam of a narrow bandpass Si monochromator which transmits only a very small fraction of the full radiation spectrum. Most of the X-ray energy is rejected. What happens if the monochromator is removed and the full spectrum falls on a crystal? The head of CHESS, Boris Batterman, said ‘You get a Laue diffraction pattern with many spots. They're beautiful but no use, you can't extract quantitative information. The orders of most spots overlap and can't be separated!’ The CHESS scientist Don Bilderback and I decided to try a Laue diffraction experiment anyway on a stationary haemoglobin crystal. It was immediately obvious that only a very short exposure was necessary to obtain spectacular—and beautiful—Laue diffraction patterns, even with crystals substantially smaller than usual (figure 2). Fast time-resolved crystallography shot back into my mind [6,12].

Figure 2.

One of the first Laue diffraction patterns from a protein, a single crystal of horse methemoglobin, recorded on Polaroid film with an exposure of 1 min at CHESS. Adapted from Fig. 2b of Moffat et al. [6].

With the crystallographer Marian Szebenyi, we were immediately able to solve the spatially complex, geometrical problem of the location of the Laue spots on the film detector. From these locations and knowing approximate unit cell dimensions and angles from earlier monochromatic data, we could refine these dimensions and angles, derive the crystal orientation, index each Laue spot on the diffraction pattern and distinguish those spots that arose from only one RLP and were single from those that arose from several RLPs and were multiple. With some knowledge of the synchrotron radiation spectrum, reasonably accurate structure amplitudes could be obtained for those Laue spots that were single, which in this particular example were a substantial majority (approx. 96%) of the diffraction pattern. But for those spots that were multiple, this was not possible. How might accurate extraction of structure amplitudes be achieved, for each of the overlapping orders within a multiple spot?

We were not the only ones encountering this problem. Laue diffraction patterns from single crystals of an aluminium phosphate had also been obtained with short exposures at the new Synchrotron Radiation Source at Daresbury Laboratory by Wood et al. [13], and its structure successfully refined. Also at Daresbury, the protein crystallographer John Helliwell and his colleagues were commissioning beamline SRS9.6 for protein crystallography, similar to our beamlines at CHESS. Helliwell (JR Helliwell 1983, personal communication) immediately noticed our Science paper [6], and its important implications for structure and function studies by macromolecular crystallography. He noted excitedly that his design of the SRS9.6 wiggler protein crystallography station, with its straight through beam to the sample for tunable applications, also allowed Laue diffraction. These early developments are described by Helliwell [14]. Daresbury seemed exactly the right place to attack the problems of Laue diffraction, and so it proved. I spent a sabbatic leave there and at the University of York with John and his senior crystallographic collaborator Durward Cruickshank (University of Manchester Institute of Science and Technology). The three of us initiated a close and extremely stimulating collaboration on the theoretical and experimental foundations of Laue diffraction (figure 3). Our success—and the fun we had—ensured that the collaboration continued after my return to Cornell and subsequent move to the University of Chicago, where Zhong Ren joined our effort. Together, we quantitated and resolved the overlapping orders problem [15], examined in detail the spatial distribution of Laue spots on the detector [16], showed experimentally how to extract the spectrum of the polychromatic, incident radiation from the dependence of symmetry-related Laue spot intensities [17], used this information to show that structure amplitudes derived from Laue diffraction could be just as accurate as those from monochromatic diffraction [18] and finally, obtained structure amplitudes from each order in multiple Laue spots [19]. Helliwell [20] has emphasized the equally valuable application of the Laue approach to neutron crystallography.

Figure 3.

Durward Cruickshank, John Helliwell and Keith Moffat (left to right) in 1986. Photo courtesy of John Helliwell. (Online version in colour.)

In parallel with these basic advances we, Janos Hajdu, Louise Johnson, John Helliwell, Ilme Schlichting and others [3] began to apply experimental, time-resolved crystallographic approaches to specific biological problems. Four advances were beginning to be available around 1992:

• (1)Crystals of protein molecules whose structural dynamics are of biological interest and are light-sensitive in the visible region of the spectrum, thus providing a convenient means of reaction initiation in the crystal. Examples are the long-studied CO complexes of haem-containing proteins such as haemoglobin, and newer examples of signalling photoreceptors such as the bacterial blue light photoreceptor known as photoactive yellow protein (PYP);
• (2)A very bright light source to initiate the reaction in light-sensitive systems, i.e. a pulsed laser in the visible, whose short pulses are the ‘pump’ in a pump–probe dynamic experiment;
• (3)An extremely bright X-ray source to generate excellent X-ray Laue diffraction patterns from a stationary crystal with a very brief exposure, initially a storage ring and now a hard X-ray laser, the structural ‘probe’ in the pump–probe experiment; and
• (4)Development of experimental design, hardware and software technology: put the pieces together for an ‘X-ray movie camera’. The time delay between the pump and probe pulses corresponds to one frame of a ‘movie’ and by varying this time delay, the reaction course of the molecules in the crystal can be swept out. The phases from a previously determined, static structure prior to reaction initiation are combined with the time-dependent difference in structure amplitudes to produce time-resolved (difference) electron density maps. Such difference Fourier maps clearly reveal small, time-dependent changes in density [21], and could be interpreted in terms of changes in atomic structure.

A further development in conventional protein crystallography at around this date was the freezing of crystals to around 100 K, which greatly minimizes secondary radiation damage. This advance is unfortunately not applicable to time-resolved studies since the desired structural changes are themselves literally ‘frozen out’ and largely abolished. Time-resolved studies are therefore conducted at near-physiological temperatures where the molecules in the crystal remain active and retain their essential structural changes.

5. Enhancement of the time resolution

Time resolution is one of the experimental frontiers of time-resolved crystallography. In a pump–probe experiment, the time resolution is determined by the longest of the (visible) pump pulses, the (X-ray) probe pulse, and the timing jitter between the pump and probe pulses. The X-ray probe pulse is usually the longest, particularly if this is set by the open time of an X-ray shutter. Using multiple X-ray pulses from a bending magnet at a synchrotron source such as the National Synchrotron Light Source (NSLS) at Brookhaven (similar to the Daresbury synchrotron), millisecond time resolution was achieved for the decay of the longest-lived intermediate in the photocycle of PYP [22].

If the inherently pulsed nature of synchrotron sources can be directly exploited to isolate a single X-ray probe pulse, the accessible time resolution in a pump–probe experiment is immediately reduced by four decades in time from microseconds, the typical circulation time of a single bunch of electrons at NSLS, Daresbury or CHESS, to around 100 ps, the typical duration of the single X-ray pulse emitted by that bunch. This time resolution is characteristic of rapid tertiary structural changes in proteins, for example, those evident in fluorescence decay on the nanosecond timescale. Since a single X-ray pulse is of much lower intensity than a train of pulses, an even more intense undulator X-ray source is essential. We developed a very fast X-ray shutter train capable of isolating a single X-ray pulse from those emitted by adjacent electron bunches in the storage ring. When the first hard X-ray undulator (a prototype for undulator A at the Advanced Photon Source) was installed briefly at CESR, we obtained a Laue diffraction pattern—admittedly of low quality—from a large single crystal of hen egg white lysozyme with a single X-ray pulse of 120 ps duration [23]. When this shutter was adapted to isolate single, 100 ps X-ray pulses at the European Synchrotron Radiation Facility, a time-resolved series of difference electron density maps was obtained of the photolysis and rebinding reaction of the CO complex of myoglobin [24,25]. The nanosecond time resolution was now set by the duration of the pump laser pulse. It had taken us 30 years to finally achieve the X-ray equivalent of the Parkhurst & Gibson experiments [8] and explore structural dynamics directly.

When a picosecond pump laser pulse is used to initiate the reaction, the time resolution of pump–probe experiments with even the best storage ring sources is limited by the X-ray probe pulse length of approximately 100 ps. That pulse length is in turn established by the characteristics of the RF cavities that maintain the energy of the electrons. Hundred picoseconds still does not approach the chemical timescale of femtoseconds to approximately 1 ps associated with fundamental chemical processes in biology such as electron transfer (e.g. photosynthesis), isomerization (e.g. of retinal in vision, or of the p-cinnamic acid chromophore in PYP) and the formation and breaking of covalent bonds (enzymes and haem proteins). A radically new type of X-ray source has been developed: the hard X-ray free electron laser (see e.g. Section I of [5]), the first example of which is the Linac Coherent Light Source at the Stanford Linear Accelerator Laboratory. A single-pass laser, this represents truly disruptive technology. Individual ultrashort X-ray pulses in the femtosecond time range are so intense that atoms become fully ionized and all experiments are destructive. What saves the day is that destruction is not instantaneous. A brief time window in the 100 fs range exists between illumination by the X-ray pulse of a tiny crystal of a biomolecule, typically 1–10 µm in dimensions, and complete loss of its structure and diffraction pattern. In this time window, an excellent diffraction pattern can be recorded ([26]; see e.g. Section II of [5]). One tiny crystal yields one diffraction pattern; then replace the crystal and repeat many times, to carry out the essential averaging and cover all of reciprocal space. The crystal does not have time to rotate, hence its diffraction of necessity gives rise to the Laue pattern characteristic of a stationary crystal. As in more conventional laser sources, the X-ray pulse from a free electron laser is (nearly) monochromatic and this pattern may be described as a very narrow bandpass Laue diffraction pattern. The bandpass is so narrow that all Laue spots are single, as long ago our Daresbury-derived theory showed [15]. However, a downside of the narrow bandpass is that ‘integrated’ intensities have to be produced by extensive averaging over hundreds or even thousands of individual observations of each Laue spot [27]. The problem of obtaining accurate integrated intensities in a complicated experimental geometry remains an active research topic (e.g. [28]). Further complications arise because the X-ray lasing process is based on the amplification of noise in the spatial distribution of electrons in the single bunch that generates the X-ray pulse. As a result, both the intensity of the X-ray pulse on the few femtosecond timescale and its spectrum are extremely spiky (see, e.g. Section I of [5]).

Given these unusual features, it is remarkable that any accurate, quantitative measurements of spot intensities can be made on the femtosecond timescale—but they can. Although individual measurements of partial spot intensities are extremely noisy, the noise distribution is such that averaging over a sufficient number of measurements leads to convergence to an accurate mean spot intensity, and hence to accurate structure amplitudes. Time-resolved measurements are further aided by the use of tiny crystals in which reaction initiation by light can be nearly complete and uniform throughout the crystal [29]. Indeed, these advances have permitted pump–probe, time-resolved measurements on the femtosecond timescale of the protein quake that ensues upon photodissociation of CO from myoglobin [30], of isomerization about the single double bond of the chromophore of PYP in the earliest stage of its photocycle [29,31], and of chromophore twisting of a fluorescent protein in an electronically excited state [32]. All present direct observations of very diverse femtosecond transitions in structural chemistry.

With a rotating anode source in 1965, X-ray exposures of at least 1.5 min on a very large, strongly scattering protein crystal were required for a Laue still, limiting the time resolution to roughly that duration. Fifty years later with a hard X-ray free electron laser source, a time resolution of 150 fs on a tiny, weakly scattering crystal is possible, also for a Laue still. That represents a gain in time resolution by a factor of 6 × 10¹⁴, on a crystal smaller in volume by a factor of roughly 10⁶.

Research at Daresbury without a doubt played an important part in the (re)development of the foundations and applications of Laue diffraction.

Data accessibility

This article has no additional data.

Competing interests

We declare we have no competing interests.

Funding

This study was supported by NIH grant no. EY024363.