Self-terminating diffraction gates femtosecond X-ray nanocrystallography measurements

Abstract

X-ray free-electron lasers have enabled new approaches to the structural determination of protein crystals that are too small or radiation-sensitive for conventional analysis¹. For sufficiently short pulses, diffraction is collected before significant changes occur to the sample, and it has been predicted that pulses as short as 10 fs may be required to acquire atomic-resolution structural information^1-4. Here, we describe a mechanism unique to ultrafast, ultra-intense X-ray experiments that allows structural information to be collected from crystalline samples using high radiation doses without the requirement for the pulse to terminate before the onset of sample damage. Instead, the diffracted X-rays are gated by a rapid loss of crystalline periodicity, producing apparent pulse lengths significantly shorter than the duration of the incident pulse. The shortest apparent pulse lengths occur at the highest resolution, and our measurements indicate that current X-ray free-electron laser technology⁵ should enable structural determination from submicrometre protein crystals with atomic resolution.

Figure 1. Femtosecond X-ray diffraction from Photosystem I nanocrystals

A suspension of nanocrystals flows in a liquid jet across the X-ray beam, and diffraction is recorded using a pair of 512 × 1,024 pixel pnCCD detectors with 75 μm pixel pitch. The lower half detector is placed further from the beam centre than the upper half detector to increase the accessible range of scattering angles. The detector module is located 64.7 mm downstream of the interaction region, giving a maximum measurable resolution of 0.76 nm. Thousands of individual diffraction patterns are recorded from single nanocrystals with pulse lengths up to 300 fs to a resolution of d =0.76 nm, and summed to produce virtual powder patterns, which are radially integrated to produce one-dimensional powder plots.

Figure 2. Dynamics of exploding crystals

a, Onset of disorder in a crystalline lattice during an ultra-intense X-ray pulse with a duration of 100 fs, which, for the sake of visual clarity, is shown here for the case of a small molecule (lysergic acid diethylamide). Individual atoms are randomly displaced by atomic displacements (calculated using Cretin). For this small molecule, crystalline order is largely destroyed by 100 fs; however, by this time, Bragg diffraction from the initial ordered crystalline structure has already been measured. b, Plot of the one-dimensional component of the r.m.s. displacement, $\sigma (t)=\sqrt{\langle D^2(t)\rangle }$, of atoms in Photosystem I calculated using Cretin for constant-irradiance X-ray pulses with a photon energy of 2 keV. Black triangles show the predicted component of r.m.s. displacement at the end of pulses of a constant fluence of 4 kJ cm⁻². The turn-off time for our highest-resolution length d =0.76 nm occurs when σ(t) reaches a value of d/(2π) =0.12 nm (dashed horizontal line).

Figure 3. Self-terminating Bragg diffraction

a, Plot of relative accumulation of Bragg signal, tg(q; T), using σ(t) values from Fig. 2b at I₀ = 1 × 10¹⁷ W cm⁻² and a pulse duration T =150 fs. Bragg peaks initially accumulate signal at the same rate proportional to the irradiance I₀ (relative to the undisturbed case); however, accumulation of counts into higher-resolution peaks ends as crystal disorder grows. Termination of signal accumulation can occur before the X-ray pulse itself has terminated, leading to apparent pulse lengths shorter than the duration of the incident pulse. The vertical black line at 40 fs indicates the pulse duration experimentally realized at this fluence, which is close to the turn-off time for the highest-resolution peaks at d =0.76 nm. b, Visualization of the dynamic disorder factor g(q; T) given by equation (2). The black line shows the turn-off time for Bragg peaks of different resolution. The zero-frequency signal, which depends only on the total electron mass of the crystal, is unaffected by the crystal explosion.

Figure 4. Bragg termination observed at approximately constant X-ray pulse fluence I₀T

a, ‘Virtual powder pattern’ formed by summing 3,792 single-pulse patterns obtained with X-ray pulses with a duration of 300 fs. The spots in the pattern are Bragg peaks, which are visible out to the corners of the detector, corresponding to a resolution of d =0.76 nm. Because of the large unit cell size of the crystal, Debye–Scherrer rings overlap and are not resolved at q >0.5 nm⁻¹. b, Bragg signal I(q; T) of Photosystem I nanocrystals averaged over q shells of virtual powder patterns for nominal pulse durations T varying between 70 fs and 300 fs. c, Bragg signal relative to the shortest pulses, plotted as solid lines. Dashed lines give the computed ratios of I(q; T)/I(q; T =40 fs) from the Cretin simulations of Fig. 2. Previous experiments at LCLS indicate that the nominal ‘70 fs’ pulses are shorter than indicated. We achieve a best fit assuming these pulses have a duration of 40 fs (see Supplementary Information). d, Comparison of the calculated dynamic disorder factor g(q; T) (solid lines) compared to a Debye–Waller factor best-fit to the same data (dashed lines).

Figure 5. Dynamic disorder factor at atomic resolution

a, Plot of the one-dimensional component of atomic displacement in a Photosystem I protein sphere for constant-irradiance 8 keV X-ray pulses (wavelength, 0.15 nm). Higher irradiances than 2 keV are required to achieve similar diffraction signals. The turn-off time for 0.3 nm resolution occurs when σ(t) reaches 0.05 nm. b, Plot of g(q; T) for 8 keV pulses at 100 kJ cm⁻² fluence (8 × 10¹¹ photons μm⁻²), for different pulse durations. At 100 fs duration, the pulse irradiance is 1 × 10¹⁸ W cm⁻². The highest diffraction efficiency and signal-to-background is reached with the shortest pulses, but longer pulses do not preclude the observation of Bragg peaks.