A linear relationship between crystal size and fragment binding time observed crystallographically: implications for fragment library screening using acoustic droplet ejection

Abstract

High throughput screening technologies such as acoustic droplet ejection (ADE) greatly increase the rate at which X-ray diffraction data can be acquired from crystals. One promising high throughput screening application of ADE is to rapidly combine protein crystals with fragment libraries. In this approach, each fragment soaks into a protein crystal either directly on data collection media or on a moving conveyor belt which then delivers the crystals to the X-ray beam. By simultaneously handling multiple crystals combined with fragment specimens, these techniques relax the automounter duty-cycle bottleneck that currently prevents optimal exploitation of third generation synchrotrons. Two factors limit the speed and scope of projects that are suitable for fragment screening using techniques such as ADE. Firstly, in applications where the high throughput screening apparatus is located inside the X-ray station (such as the conveyor belt system described above), the speed of data acquisition is limited by the time required for each fragment to soak into its protein crystal. Secondly, in applications where crystals are combined with fragments directly on data acquisition media (including both of the ADE methods described above), the maximum time that fragments have to soak into crystals is limited by evaporative dehydration of the protein crystals during the fragment soak. Here we demonstrate that both of these problems can be minimized by using small crystals, because the soak time required for a fragment hit to attain high occupancy depends approximately linearly on crystal size.

Figure 1. Lysozyme crystals have a cubic habit and thermolysin crystals have an elongated habit.

Lysozyme forms cubic crystals which were measured along the longest sides as shown (panel A). One large and one medium sized lysozyme crystal are shown. Thermolysin crystals have an elongated habit and were measured along the long axis (panel B). One large and one small crystal are shown. Occasionally a small piece of a crystal broke off (yellow highlight). In these cases, the longest crystal fragment was measured (without adjusting the length to account for the missing piece). The soaking time should correlate with the shortest crystal dimension, but the short side is difficult to measure accurately. Fortuitously, it was possible to grow lysozyme and thermolysin crystals with a very consistent crystal habit. The long crystal axis (which was easy to measure) was a good proxy way to compare the short crystal axis (which was difficult to measure).

Figure 2. Electron density for NAG bound to lysozyme and for ASN bound to thermolysin.

Panel A: N-acetyl glucosamine is shown bound to lysozyme (difference omit map is contoured at 3.0 σ). The lysozyme data comes from a 310 µm crystal that was soaked for 750 seconds, with a refined occupancy of 74% and occupancy calculated using Eq. 1 of 68%. Panel B: Asparagine is shown bound to thermolysin (difference omit map is countered at 3.0 σ). The thermolysin data comes from a 220 µm crystal that was soaked for 601 seconds, with a refined occupancy of 99% and occupancy calculated using Eq. 1 of 84%.

Figure 3. Refined occupancies (y axes, %) as a function of soak time (x axes, seconds).

Two dimensional slices are shown for the three dimensional relationship between crystal size, ligand soak time, and occupancy (O_calc and O_refine). In each panel, the crystal size variable is excluded by grouping crystals of similar sizes. Lysozyme + NAG crystals are grouped by size (0–60 µm in box A, 60–120 µm in box B, 120–180 µm in box C, 180–240 µm in box D, 240–360 µm in box E, 360–480 µm in box F). Thermolysin + asparagine crystals are grouped into two sizes (0–150 µm in box α, and 150–300 µm in box β). Each data point represents the observed soak time and occupancy of one crystal + ligand. The average size for crystals in each range is indicated. The average number of calculated structure factors that were added into the data () is also shown (larger crystals had more overloads and consequently more added reflections). Inspection of the relationship between soak time and refined occupancy revealed a linear relationship between crystal length and the time needed to reach 50% maximum occupancy (t_1/2), so that t_1/2 = Lτ, where L is the crystal length and τ is a fixed constant. Best fits for lysozyme (R² = 78%) and thermolysin (R² = 88%) were calculated using least squares applied to Eq. 1. In each panel, a solid line shows Eq. 1 with the average size of crystals in that panel assigned to L (fitting parameters taken from Table 2). Note that the data in each panel come from crystals with similar but not identical sizes. Consequently, the data fit Eq. 1 much better than these graphs suggest. The average residual between calculated occupancies from Eq. 1 and refined occupancies from the X-ray diffraction data was 9.76% for lysozyme + NAG and 6.51% for thermolysin + ASN.

Figure 4. Higher order terms not accounted for by Eq. 1 may exist.

The residual (O_refine−O_calc) between refined occupancies and calculated occupancies as a function of crystal size (µm) for lysozyme + NAG suggests that small crystals may bind even faster than predicted by Eq. 1. Each crystal data set is represented as one point (x-axis hash marks represent 100 µm of crystal size). The average absolute difference between refined occupancy and calculated occupancy is 9.73%. A polynomial best fit to the residual (solid line) indicates that there may be higher order terms (R² = 6%). If Eq. 1 fully described the relationship between ligand occupancy, soaking time, and crystal size then the residual should show shapeless noise. Ten very large crystals (over 480 µm) were soaked with NAG to further investigate the size dependence of the discrepancy (these data points are on the right side of the figure, and were not used for any other purpose). This possible limitation of Eq. 1 finds weak support in the data; we do not assert that it is the best or only evidence that Eq. 1 is incomplete. Despite these possible limitations, we believe that Eq. 1 relates soak time and crystal length sufficiently to help plan high throughput screening experiments.