A Single-Entity Method for Actively Controlled Nucleation and High-Quality Protein Crystal Synthesis

Lack of controls and understanding in nucleation, which proceeds crystal growth and other phase transitions, has been a bottleneck challenge in chemistry, materials, biology, and other fields. The exemplary needs for better methods for biomacromolecule crystallization include (1) synthesizing crystals for high-resolution structure determinations in fundamental research and (2) tuning the crystal habit and thus the corresponding properties in materials and pharmaceutical applications. Herein, a deterministic method is established capable of sustaining the nucleation and growth of a single crystal using the protein lysozyme as a prototype. The supersaturation is localized at the interface between a sample and a precipitant solution, spatially confined by the tip of a single nanopipette. The exchange of matter between the two solutions determines the supersaturation, which is controlled by electrokinetic ion transport driven by an external potential waveform. Nucleation and subsequent crystal growth disrupt the ionic current limited by the nanotip and are detected. The nucleation and growth of individual single crystals are measured in real time. Electroanalytical and optical signatures are elucidated as feedbacks with which active controls in crystal quality and method consistency are achieved: five out of five crystals diffract at a true atomic resolution of up to 1.2 Å. As controls, those synthesized under less optimized conditions diffract poorly. The crystal habits during the growth process are tuned successfully by adjusting the flux. The universal mechanism of nano-transport kinetics, together with the correlations of the diffraction quality and crystal habit with the crystallization control parameters, lay the foundation for the generalization to other materials systems.

. Conductivity size measurements of nine 150-nm-radius pipettes. Table S2. X-ray diffraction data from five crystals synthesized under optimized NanoAC controls. Table S3. Structure refinement results. Table S4. Lists of bonding interactions of acetate ions with water molecules and neighboring residues. Table S5. The NanoAC control parameters for the syntheses of the crystals in Table S1. Table S6. The NanoAC control parameters result in lower diffraction quality (3~4 Å). Table S7. Nucleation rates determined by current decrease (V N, C ) and noise reduction (V N, N ) from four 40-nm-radius pipettes. Table S8. Nucleation rate determined by current decrease (V N, C ) from six 150-nm-radius pipettes. Table S9. Growth rates of face (110) from four 40-nm-radius pipettes. Table S10. Growth rates of face (110) from nine 150-nm-radius pipettes. Table S11. The growth kinetics of individual crystals under varied electric current controls. Figure S1. Current-time trace under different potentials to induce the domain formation using a 150-nm-radius pipette. Figure S2. Current-time traces from three pipettes with different reagent gradients across the nanotip. Figure S3. Electric current features of three distinct phase transition periods from two 40-nm-radius pipettes. Figure S4. Electric current features of three distinct phase transition periods from two 150-nm-radius pipettes. Figure S5. Electric signatures for nucleation kinetics from two 40-nm-radius nanopipettes. Figure S6. Electric signatures for nucleation kinetics from one 150-nm-radius nanopipette. Figure S7. Current-time and potential-time profiles corresponding to the crystal growth in Fig. 5. Figure S8. Crystal growth controlled at single-entity levels under different current amplitudes. Figure S9. Crystal growth and corresponding current/potential-time curves under less electric field manipulation.
The conductivity size characterization of a conical nanopore is summarized in a recent review (ref. 44): Here, is the Ohmic resistance of the nanopore; Λ is electrical conductivity of the electrolyte; is the radius of a nanopipette; is the half cone angle (Scheme S1). A 1 M KCl solution is generally used in conductivity size characterizations: linear ohmic current-potential curve confirms the surface effects being insignificant and allows for the volumetric resistance calculation. Access resistance 1 4 was not considered at this concentration. The was determined to be 3.5° by SEM and assumed consistent. The Λ was 10.9 S/m for 1 M KCl solution. Conductivity size measurements for nine 150-nm-radius pipettes were summarized in Table 1.
Scheme S1 The geometry of a conical nanopore.

Details for crystallization
A 3D printed ABS chamber (25×50 mm 2 ) was used, consisting of a 1-mm-depth well, a 1-mm slit channel on the top that accommodates pipette and a narrow channel at the bottom for a Ag/AgCl WE. Once the WE was placed, a plastic coverslip was attached to the bottom of the well by vacuum grease. Then, a pipette loaded with the precipitant solution was inserted into the well through the slit channel, and 10-20 µL mother solution was added until the WE and pipette tip were immerged. After that, the chamber was sealed with a coverslip on the top to reduce evaporation.
The crystallization solution was freshly made by mixing equal volumes of the protein stock solution and a 1.1 M NaCl and centrifuged at 15,000 rpm for 10 min. The choice of 1.1 M NaCl to approach supersaturation is based on the screening using 1.0 M, 1.1 M and 1.2 M NaCl. By using the 1.0 M NaCl instead of 1.1 M to prepare the sample for nanopipette experiments, nucleation is not observed within one day under otherwise comparable conditions in NanoAC controlled crystallization. In comparison as summarized in Table S7 and S8, the induction time, starting from the application of the positive potential till the start of nucleation t S , is much faster within several hours.
Growth rate measurement A series of time-lapsed images were taken during the growth of individual crystals. Image size/scale was calibrated with a Stage Micrometer KR868 (Klarmann Ruling) and analyzed with ImageJ. The crystal sizes in the lengths of M and L A ( Fig.  1 and Fig. 3) were used to calculate the crystal growth rates of the (101) and (110)  Electroanalytical data processing The electric current over the whole phase transition was generally recorded at ten points per second rate (can be faster or slower if needed) and used directly without denoising or outlier removal. The noise level is represented by 5-second (50point) moving standard deviation of the raw current. To resolve the transition point times, continuous piecewise linear regression with two breakpoints was performed using Origin. With enough sampling points for the pre-N and post-N baselines, i.e., 8 min, the breakpoints can be determined with P < 0.0001. If spikes/oscillations were continuously presented in the current (Fig. S5B, Noise level), data was smoothed by 20% percentile filter using 1% points prior to piecewise fitting.
Crystallography and data processing Crystals were synthesized one at a time. After the size reaches about 70-90 µm of length in L A , the pipette with a crystal still attached on tip was removed from the sample droplet and quickly inserted in LV CryoOil (MiTeGen) for 20-30 s prior to flash-cooling in liquid nitrogen. Ten tetragonal lysozyme crystals were harvested in this manner for X-ray crystallography. Five of them grown at 1.8±0.9 nm/s generated high diffraction quality, and five of them grown at a higher growth rate showed poor diffraction. The results are summarized in Tables S2 and S3. X-ray diffraction data were collected at 100 K from beamline 8.2.1 (λ=1.0000 Å) at the Advanced Light Source (ALS, Berkeley, CA). Diffraction data were indexed, integrated and scaled using HKL-2000 program package based on a Chi 2 =0.5 cutoff. Molecular replacement and refinement of the reduced scalepack files were performed using Phenix 1.20 and Coot 0.9.2. X-ray data collection and refinement statistics are listed in Table S3. Ramachandran favored 98.43%, allowed 1.57%, outliers 0.00%. Table S1. Conductivity size measurements of nine 150-nm-radius pipettes. Nine pipettes were measured with 1 M KCl solution inside and outside of the nanopore. is the Ohmic resistance of the nanopore; is the radius of a nanopipette; is the half cone angle (Scheme S1) at 3.5°; Λ is electrical conductivity of the 1 M KCl solution at 10.9 S/m.  Table S2. X-ray diffraction data from five crystals synthesized under optimized NanoAC controls. Crystal 4 here is crystal 1 in Table S8 and S10. Crystal 5 here corresponds to the current and growth in Figure S9B.   Table S4. Lists of bonding interactions of acetate ions with water molecules and neighboring residues. The residue number is from the peptide sequence, and the number for water molecules is generated by software during refinement.  3  Table S5. The NanoAC control parameters for the syntheses of the crystals in Table S2. Crystal 4 here is crystal 1 in Table S8 and S10. Crystal 5 here corresponds to the current and growth in Figure S9B.    Table S2 and S5 (crystallography). Crystal 5 here is the crystal grown at ca. +2 nA in Figure 5 (growth habit). Crystal 1-6 correspond to crystal 1-6 in Table S10. Crystal 2 1.9 3 1.8 4 2.0 Mean 1.8 SD 0.3 Table S10. Growth rates of face (110) from nine 150-nm-radius pipettes. The growth rates were measured during the linear growth period when the length of L A grow from about 3 µm to 20 µm or larger. Crystal 4 here is crystal 4 in Table  S2 and S5 (crystallography). Crystal 5 here is the crystal grown at ca. +2 nA in Figure 5 (growth habit). Crystal 1-6 correspond to crystal 1-6 in Table S8.

Crystal
Grow rate, G 110 (nm/s) 1 0.9 7 2 1.1 3 0.8 6 4 0.6 6 5 1.1 6 0.8 9 7 0.8 8 8 0.9 0 9 0.8 7 Mean 0.9 SD 0.1 2 Table S11. The growth kinetics of individual crystals under varied electric current controls (data in Figure 5A-C   Precondition potential at -0.1 V was applied, followed by several potential adjustments. Current was near constant in those three conditions, and no domain formation was optically resolved. A and B were from two ca. 150nm-radius pipettes and C was from one ca. 40-nm-radius pipette.      The lengths can only be measured after reaching two pixels or more (single pixel 250 nm; optical limit). Scale bars are 4 m. Crystal 5 in Table S2 and S5 corresponds to the crystal in B.