The kinetic dose limit in room-temperature time-resolved macromolecular crystallography

Abstract

Protein X-ray structures are determined with ionizing radiation that damages the protein at high X-ray doses. As a result, diffraction patterns deteriorate with the increased absorbed dose. Several strategies such as sample freezing or scavenging of X-ray-generated free radicals are currently employed to minimize this damage. However, little is known about how the absorbed X-ray dose affects time-resolved Laue data collected at physiological temperatures where the protein is fully functional in the crystal, and how the kinetic analysis of such data depends on the absorbed dose. Here, direct evidence for the impact of radiation damage on the function of a protein is presented using time-resolved macromolecular crystallography. The effect of radiation damage on the kinetic analysis of time-resolved X-ray data is also explored.

Figure 1

The PYP photocycle. After absorption of a blue photon the photocycle proceeds through a number of intermediates that are occupied on different time-scales. Red dashed arrow: part of the photocycle covered by our short time-series consisting of eight time delays from 256 µs to 32 ms plus the dark data.

Figure 2

(a) Geometry of the crystal setting and X-ray and laser illumination. The X-ray beam (red ellipse) probes the volume near the surface of the crystal that is illuminated by the laser light. The laser beam (blue) is substantially larger than the X-ray beam to facilitate alignment. Arrow: positive y′-displacement of the crystal. The region shaded orange shows the new beam position after y′-displacement. The crystal translation along the long axis is 440 µm. The length L is used for the dose calculation. Dashed box: approximation of the beam with a rectangular box. Dotted box: displacement of the box to the new beam position. (b) Model used to determine the common area F _C used to calculate the common volume V _C. A rectangular X-ray beam (red) whose vertical size is smaller than half the crystal diameter falls on a crystal with a circular cross section. As the crystal is re-oriented by Δθ it is irradiated from another direction (yellow). The orange area is the common area F _C that determines the common volume V _C. F _S is the first term and 2F _T the second term in equation (1), respectively (see also the supplementary material). (c) A sequence of angular settings (in degrees). The angular settings are also separated by translations of 22 µm. Five settings are fully or partially exposed given the horizontal size of the X-ray beam. The orange bars denote the relative sizes of the common volumes V _C, for each angular setting, values of which are given as a percentage at the bottom.

Figure 3

Simple kinetic mechanism with a source S and two rate coefficients k ₁ and k ₂ for kinetic refinement with posterior analysis. Dashed box: mechanism used if no rising phase is detected in the RSV.

Figure 4

(a) Raw mean intensities 〈I〉 (solid squares) and 〈I/σ_I〉 (open squares) as a function of the uncorrected dose. Black and dashed lines: fits by exponential functions. Vertical dashed and dashed-dotted lines indicate the D _1/2 obtained with the uncorrected dose. (b) Normalized quantities M _n plotted as a function of adjusted dose. Average intensity 〈I〉_free (red solid squares) and 〈I/σ_I〉_free (red open squares) are plotted as a function of adjusted dose. Red solid line: fit by a straight line. Thin dotted line: fit by an exponential function. The dashed vertical line indicates the corresponding D _1/2. Black solid and black open triangles: variation of the mean intensity 〈I〉_L and 〈I/σ_I〉_L, respectively, observed in the control experiment as a function of virtual dose. The black solid and dashed lines are fits by a straight line. (c) Normalized R ^AO values (black spheres) as a function of adjusted dose. Black dashed curve: fit by a single exponential. The horizontal/vertical dashed lines indicate and the corresponding kinetic dose limit . (d) Red squares: relaxation times τ_RSV1 from the SVD analysis as a function of adjusted dose. The red dashed line is a guide to the eye. Green triangles: inverse of the rate coefficient (relaxation time τ_post) obtained from posterior analysis. The green dashed line is a guide to the eye. Black spheres: difference between τ_post and τ_RSV1. The dashed vertical line indicates the kinetic dose limit .

Figure 5

Right singular vectors (RSV) resulting from the SVD analysis of the short time-series. All singular vectors are shown. (a) First short time-series with the lowest absorbed dose. Solid spheres: first singular vector; solid squares: second singular vector; solid triangles: third singular vector; blue crosses: fourth singular vector. RSV 5 to 8 are shown as thin lines. Solid black line: fit of two exponentials with a source and decaying phase. Vertical dashed line: relaxation time of the decaying phase from a fit of the sum of two exponentials; long dashed line: fit of only one exponential with the same relaxation time; vertical dashed-dotted line: amplitude of RSV1; horizontal dashed-dotted line: offset of RSV1. Insert: red dashed curve: concentration profile of pB1; black dashed line: relaxation time from the inverse of the rate coefficient k ₂. (b) Tenth short time-series with a high absorbed dose. Solid spheres: first singular vector; solid squares: second singular vector; solid triangles: third singular vector; blue crosses: fourth singular vector. RSV 5 to 8 are shown as thin lines. Vertical dashed line: relaxation time of the decaying phase from fit of only one exponential; vertical dashed-dotted line: amplitude of RSV1; horizontal dashed-dotted line: offset of RSV1. Insert: red dashed curve: concentration profile of pB1; black dashed line: relaxation time from the inverse of the rate coefficient k ₂.

Figure 6

Three-dimensional plot of first right singular vectors for all 12 short time-series shown as a function of dose. is reached after 36 datasets or four short time-series. The offsets in the RVS are indicated by the dotted lines. Green dotted line: small offsets; orange dotted line: offset increases slightly; red dotted line: offset increases strongly. The orange regime ends after 72 datasets. The red line indicates that posterior analysis of the data beyond this dose will not be possible. D _1/2 is also indicated. (b) Three-dimensional plot of all fitted time courses from the posterior analysis as a function of dose. The green, orange and red regimes as well as the approximate relaxation times that can be expected in these regimes are marked. , D _1/2 as well as Owen’s limit are also shown.