You might recall the television series in the 1960th called “the twilight zone”, where the actors claimed that there is a dimension additional to the “normal” four dimensions space and time. This fifth dimension was called “the twilight zone”. Not that we are claiming to restore the twilight zone by crystallography but we are heading towards a fifth dimension that will of course not be called “the twilight zone” but much simpler. Lets start with the 3 dimensions usually found in crystallography. These are the usual x,y,z coordinates or, in reciprocal space, the h k l components of the reciprocal vectors. Due to the periodicity of the crystal, we can, fortunately, restore the electron density at any arbitrary position x, y, z in real space with structure factors sampled only at discrete integer steps in reciprocal space. Although Max von Laue remarked sceptically in his famous book “Roentgenstrahlinterferenzen” that the determination of the electron density of objects like proteins is a hopless venture in the first place, 10 years later John Kendrew came up with the structure of Myoglobin and Max Perutz with that of Hemoglobin. This was basically the beginning of modern biophysics. Another 25 years later a student of Max Perutz, Keith Moffat, had the idea to add a fourth dimension to crystallography, time; and he had just obtained the tool to do so: Macromolecular Laue Crystallography. With this technique the crystal does not need to be rotated to obtain the integral reflection intensity. This of course came with a price. Polychromatic radiation used for the Laue images produced thousands of reflections on the detector. Even worse, some of the reflections exactly overlapped and methods had to be developed to cope with these data. That meant that powerful computer software needed to be developed for that. After many bootstrapping iterations, the first fully functional software package was the Chicago LaueView suite in 1995. With this, even complicated data sets could be successfully processed. Around 2000 Michael Wulff and colleagues at the ESRF and Keith Moffat’s group at the University of Chicago showed that the best device to produce X-rays for time-resolved crystallographic experiments is actually the undulator and not the wiggler as previously anticipated.

Time-resolved crystallography is a pump-probe type of experiment. The pump starts a reaction. The probe examines the structure. The pump pulse is usually an intense laser pulse that is absorbed by a chemical that is either added artificially to the crystal or is intrinsic to the protein that forms the cyrstal. The probe is a brilliant X-ray pulse that determines the distribution of electrons in the crystal as quickly as possible. Since rotation of the crystal is almost always impossible during the short time of data aquisition, the Laue method must be used. Already in 1990 Ilme Schlichting and colleagues investigated the enzymatic activity of the onco-protein RAS by time resolved crystallography. At that time, the time resolution was only seconds but the synchrotron delivered X-ray pulses in the order of 100 picoseconds, the ultimate time-resolution to date. The first experiment with single 100 ps X-ray pulses was conducted by Vukica Srajer and colleagues in Keith Moffat’s group. Their laser pulses were 4 ns long. Hence, their best time-resolution was 4 ns and they could characterize the dissociation and rebinding of CO to wild-type myoglobin. It took another 7 years to the first time-resolved crystallographic experiment with 100 ps time-resolution. In 2003 Phil Anfinrud, Friedrich Schotte and colleages from the NIH realized that for the first time at Micheal Wulff’s beamline at the ESRF using streched pulses from a femtosecond laser to initiate a reaction in L29F mutant myoglobin crystals.

The ultimate goal of time-resolved crystallography is to determine structure and kinetics at the same time. Increasing the time-resolution is crucial to extract the kinetics, since processes in biological macromolecules can stretch from femtoseconds to seconds and longer. A time-resolved data set consist of a comprehensive time-series of complete Laue data sets that cover multiple orders of magnitude in time; from the fastest to the slowest processes that take place within the protein. The kinetics is hidden in these data. Already in 2001 Keith Moffat’s group at the UofC had obtained a comprehensive time-resolved time series on myoglobin. The kinetics was extracted by simply integrating the difference electron density features. This integrated density was then plotted as a function of time. The kinetics was clearly visible and could be analyzed globally by fitting trial functions to the data. But there was also the Photoactive Yellow Protein (PYP) that drove the analysis further. PYP shows a photocycle with several reaction intermediates characterized previously by time-resolved (absorption) spectroscopy. The question was, how do these intermediates look like. Time-resolved crystallography should give an answer. Analyzing only single difference electron density features was suddenly not an option since from that the structures of the intermediates cannot be extracted. The main difficulty was (and still is) the temporal overlap of the intermediates in a chemical kinetic mechanism. That leads to mixtures of states. Almost every map in the time course has contributions from more than one intermediate. It is impossible to visually spearate the features since they do not carry a flag saying, intermdiate 1, me!, intermediate 2, me!, and so on. The time-information must rather be used to extract the intermediates. But how? Fortunately, there are methods from linear algebra which just deal with this. A powerful method is the singular value decomposition (SVD). Programs needed to be developed that applied the SVD to time-resolved crystallographic data. You find the relevant programs on this web-page. The first SVD analysis of time-resolved data was published in 2004 in PNAS. Since then, the SVD analysis has been further refined and applied to many more time-resolved data sets. With the advent of the SVD, time-resolved crystallography truly unifies structure with kinetics wouldn’t there be a small detail that makes the determination of a unique chemical kinetic mechanism from a single time course impossible. At a single temperature, the chemical kinetic mechansim is mathematically underdetermined since it contains more parameters than observables that can be extracted from the data. Multiple mechanism will fit the data equally well. One may also say, the mechanism is degenerate. And that drives us into the “twilight zone“. By changing a 5th variable, the temperature, there is a chance that we can resolve this degeneracy. Most importantly, since time-resolved X-ray data bear not only structural but also kinetic information, by varying the temperature barriers of activation can be extracted from crystallographic data alone!

Here is a comprehensive time-series on the L29W myoglobin mutant we measured in 2005. This mutant shows the longest time-window between photodissociation of CO and rebinding of all myoglobin mutants. It is an ideal case for time-resolved crystallography.