# Growing Crystals for X-ray Free-Electron Laser Structural Studies of Biomolecules and Their Complexes

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. Quantitative Relationship between Crystal Number Density and Mean Crystal Size

^{3}of solution, established during the nucleation stage remains constant during the subsequent crystal growth, the quantitative relationship between N and the mean crystal size l (cm) can be calculated easily by assuming a cubic crystal shape [17,18]. Under such conditions, at any time point during the crystal growth, the cumulative volume of all growing crystals totals Nl

^{3}, where l is the approximate edge length of a cubic crystal reached at that point of growth: To calculate l, we consider the mass of the uncrystallized solute. While the initial crystallizable mass m

_{o}(g) decreases gradually during the growth of the crystals, an uncrystallized mass m

_{t}(g) remains in the solution at any time point t during the growth process. Thus, the difference (m

_{o}− m

_{t}) is the mass of solute that is consumed to grow N crystals to the mean size l. To convert the cumulative crystalline volume Nl

^{3}into mass, we divide Nl

^{3}by the specific volume υ (cm

^{3}/g):

_{e}(when no crystal growth is possible) is eventually reached; the maximum achievable mean crystal size λ is thus:

_{m}is the mass that (approximately) corresponds to solubility c

_{e}.

_{t}corresponds to m

_{t}.

^{1/3}. This dependence is very weak, and even an approximate N value can enable estimation of the desired crystal sizes l and the maximum achievable crystal size λ. (Due to the stochastic nature of the nucleation process, such an estimate is sufficient.) Knowing c

_{e}and υ of the crystallizing substance, Equation (2) enables estimation of the solute mass m

_{o}, which is needed to obtain the desired theoretical crystal yield Nλ

^{3}. If the time required to reach solubility c

_{e}proves to be unacceptably long, there is the possibility to stop the crystallization process at any desired (mean) crystal size l, according to Equation (1). To this end, the time needed for growing crystals to size l is calculated as described in the following subsection.

#### 2.2. Growing Crystals Suitable for X-ray Free-Electron Laser Studies

_{o}is a constant, we obtain:

_{t}. The latter diminishes during the growth of the crystal, but the effect of this decrease (i.e., a decrease in the driving force for growth) is somewhat counterblanced by the increase in the crystal surface.

_{o}and m

_{m}are constants, we obtain:

_{1}. The process of crystal growth can be conceptually divided in two consecutive stages: the first covers the growth of the crystal from size l* until the maximum crystal size L

_{max}for which the Gibbs–Thomson law is valid. (According to the Gibbs–Thomson law, small clusters of molecules, including crystals, are in equilibrium with their mother phase at a higher supersaturation than larger crystals). The second stage is the growth of that crystal beyond L

_{max}, to its final size. The time for growth from l* to L

_{max}is denoted τ

_{1}, while the final size l

_{1}is reached after additional growth time τ

_{2}. Thus, time (τ

_{1}+ τ

_{2}) is needed for growing crystals larger than those corresponding to the upper limit of the Gibbs–Thomson effect.

_{max}.

_{1}can be calculated using the equation for the rate of crystal growth [19]:

^{2}/s) the diffusion coefficient of the solute, and δ

_{N}[cm] the thickness of the Nernst diffusion layer [20]; c

_{t}is the actual solute concentration at the surface of the growing crystal, and c

_{e}is the equilibrium concentration with respect to an “infinitely” large crystal.

_{B}is the Boltzmann constant and T the absolute temperature.

_{1}for isothermal crystal growth from a crystal nucleus of negligible size to a crystal of size l, we use the average value ${\left(\frac{\mathrm{d}m}{\mathrm{d}t}\right)}_{avg}$:

^{2}, where K is the number of faces, the solute concentration around the growing crystal simultaneously decreases, i.e., $\left({c}_{\mathrm{t}}-{c}_{\mathrm{e}}\right)$ diminishes. For cubic crystals K = 6, and substituting $S=6{{l}^{*}}^{2}$ and ${c}_{\mathrm{t}}-{c}_{\mathrm{e}}=\frac{{4\Omega \gamma c}_{\mathrm{e}}}{{k}_{\mathrm{B}}T{l}^{*}}$, we obtain Equation (10) from Equations (8) and (9):

_{1}, the crystal of size l* grows to size L

_{max}. As m is obtained by multiplying ${\left(\frac{\mathrm{d}m}{\mathrm{d}t}\right)}_{avg}$ by τ

_{1}, if we multiply both sides of Equation (10) by τ

_{1}and replace l* with L

_{max}, we obtain:

_{max}depends merely on m/τ

_{1}—all other factors are constants.

^{3}) is the density of the crystal, we can also write:

_{1}depends proportionally on the surface area.

_{1}is smaller. Very roughly, m/τ

_{1}decreases in proportion to the number of surrounding crystals, but it also depends on their relative distances. Thus, the relation m/τ

_{1}is case specific, and can hardly be determined with any precision.

_{max}.

_{max}. Therefore, to calculate the additional growth time τ

_{2}for the crystal to grow to size l

_{1}> L

_{max}, we use again the average growth rate ${\left(\frac{\mathrm{d}m}{\mathrm{d}t}\right)}_{avg}$ expressed by Equation (9). Knowledge of the quantitative relationship between S and ${c}_{\mathrm{t}}-{c}_{\mathrm{e}}$ is again needed. This relationship is provided in Equation (1), rewritten in the form:

_{m}(which is the mass of solute at solubility c

_{e}), we write:

^{2}(for cubic crystals), the solute concentration around the growing crystal simultaneously decreases, i.e., $\left({c}_{\mathrm{t}}-{c}_{\mathrm{e}}\right)$ diminishes. Substituting $S={6l}^{2}$ in Equation (9), we obtain the average crystal growth rate ${\left(\frac{\mathrm{d}m}{\mathrm{d}t}\right)}_{avg}$ for crystals of average size l—starting from negligible size, i.e., from l ≈ 0, right up to the attainment of ${c}_{\mathrm{e}}$:

_{N}, N, $\upsilon $, V, c

_{o}, and c

_{e}are considered constant, performing definite integration, the solution of Equation (14) is:

_{1}> L

_{max}, i.e., above the upper limit of the Gibbs–Thomson effect (${\tau}_{1}$ being the time during which the crystal grows to size L

_{max}).

_{max}to l

_{1}for time τ

_{2}, we rewrite Equation (16) as:

#### 2.3. Impurity Inclusion in the Grown Protein Crystals

^{2}/s) to mass diffusivity D (cm

^{2}/s), i.e., the ratio of momentum diffusivity to molecular diffusivity:

^{1/3}Re

^{1/2}<<1. For liquids, ν is on the order of 0.01 cm

^{2}s

^{−1}(for instance, the kinematic viscosity of water at 20 °C is 1.003 mm

^{2}s

^{−1}), and with the diffusion coefficient for lysozyme D ≈ 1.06 × 10

^{−6}cm

^{2}/s [27], Sc is, according to Equation (21), of the order of 10

^{4}. Therefore, Sc

^{1/3}≈ 21.5, and for Sc

^{1/3}Re

^{1/2}<< 1, Re

^{1/2}must be at least 10

^{−3}.

^{−6}, the speed of the convective flow for L = 10

^{−3}cm must be u = 10

^{−5}cm/s. This is a creeping flow for which boundary layer flow and plumes above such crystals are hardly expected. In other words, it is reasonable to assume that the supply of impurities to crystals of size equal or smaller than 10 μm is restricted merely to diffusional supply.

^{−5}cm/s and L = 10

^{−3}cm, Pe = 0.01, i.e., the convective mass transfer is only 1% of the diffusive mass transfer, and the larger the crystal, the slower the flow that is sufficient for transferring the same convective mass (amounting to 1%). Indeed, a flow rate u = 10

^{−5}cm/s (i.e., 0.6 μm/min) for L = 10

^{−3}cm is hardly measurable, but Pusey et al. [25] observed (and measured) growth plumes above larger lysozyme crystals, of 0.3, 0.5, 1.2, and 1.7 mm across the (110)face. Figure 3 in ref. [25] indeed shows that the apex plume velocities increase with the increase in crystal size. This observation favors our hypothesis that, while impurities brought by convective plumes can be an obstacle for growing large protein crystals, these impurities can hardly stop the growth of microcrystals that are needed for XFEL crystallography.

#### 2.4. Experimental Results

_{1}and τ

_{2}do not provide an exact answer to the question of how long the growth time must be for reaching the desired crystal sizes. Firstly, due to natural convection [25], the solution around sufficiently large crystals can be replenished, leading to faster growth of these crystals. On the other hand, natural convection brings more impurities to the surface of the growing crystals, which delay crystal growth. These are processes that defy accurate theoretical description. Secondly, the nucleation induction time (if appreciable) must be added to τ

_{1}and τ

_{2}. To evaluate the overall effect of all these factors and to verify some of the theoretical results, we conducted experimental studies with lysozyme, which, because of the availability of accurate solubility data at various conditions and of the ease with which its crystallization can be fine-tuned and controlled, has become the standard model protein for crystallization studies.

^{3}ranges from 0.25 × 10

^{−4}to 2 × 10

^{−4}cm

^{3}. From Equation (2), Nλ

^{3}= υ(m

_{0}− m

_{m}). The initial mass of lysozyme in 2 μL of a 50 mg/mL solution is m

_{o}= 0.05 × 2 × 10

^{−3}= 10

^{−4}g. The solubility of lysozyme in a 5% NaCl solution c

_{e}= 2.16 mg/mL = 2.16 × 10

^{−3}g/cm

^{3}[28], so at solubility we have m

_{m}= 2.16 × 10

^{−3}× 0.002 = 0.4 × 10

^{−5}g in 2 μL. The density of a lysozyme crystal at 1 M NaCl is ρ = 1.24 g/cm

^{3}[29], so its specific volume υ = 0.81 cm

^{3}/g. Thus, Nλ

^{3}= υ(m

_{o}− m

_{m}) = 0.81 × (0.9 × 10

^{−4}) = 0.78 × 10

^{−4}cm

^{3}, which is in excellent agreement with the range of values obtained above from counting and measuring the crystals.

^{3}ranges from 300 × (2.5 × 10

^{−3})

^{3}= 4.7 × 10

^{−6}cm

^{3}to 1000 × (5 × 10

^{−3})

^{3}= 1.25 × 10

^{−4}cm

^{3}. This is a much wider range than for the crystals grown from 5% NaCl, but, looking at the data in Table 1 in greater detail, we may assume the lower value is an underestimate, whereas the higher value appears closer to the average situation.

_{e}= 1.5 × 10

^{−3}g/cm

^{3}[28]. Therefore, Nλ

^{3}= υ(m

_{o}− m

_{m}) = 0.81 × (0.05 − 1.5 × 10

^{−3}) × 2 × 10

^{−3}= 0.81 × 0.97 × 10

^{−4}≈ 0.79 × 10

^{−4}cm

^{3}, which is virtually the same as for 5% NaCl and is again in excellent agreement with the above range of values from counting and measuring the crystals.

_{1}:

_{B}T ≈ 4.05 × 10

^{−14}erg per molecule (at 20 °C), γ

_{c}≈ 1 erg/cm

^{2}, D ≈ 10

^{−6}cm

^{2}s

^{−1}, and ${\delta}_{\mathrm{N}}$ ≈ 10

^{−2}cm [20]. The lysozyme molecule can be described as a prolate ellipsoid of rotation with axes of lengths 9 and 1.8 nm [30]. Dynamic light scattering gives a hydrodynamic diameter of ca. 3.6 nm, so Ω ≈ 10

^{−19}cm

^{3}. Replacing all these in Equation (12), we have:

_{1}= C(m/L

_{max}) = C[(L

_{max}

^{3}ρ)/L

_{max}] = C L

_{max}

^{2}ρ,

_{max}; C ≈ 1.172 × 10

^{11}cm.s/g for 5% NaCl and 1.69 × 10

^{11}cm.s/g for 6% NaCl.

_{1}≈ 1.172 × 10

^{11}× 1.24 × (10

^{−4})

^{2}= 1447 s = 0.4 h or 24 min for 5% NaCl.

_{max}, ${\tau}_{1}$ would be, counterintuitively, somewhat longer for 6% NaCl (35 min). However, although the rate of material deposition is overall greater at higher supersaturations, see Equation (6), the number density of crystals is also substantially larger, the crystals are thus appreciably closer to each other and therefore, as noted above, the mass incorporated into each growing crystal for a given time is, in fact, smaller. This variability leads to fluctuations in the actual ${\tau}_{1}$, which are, however, quite small compared with the usual statistical fluctuations expected in macromolecular crystallization. For an eightfold difference in crystal volume, i.e., L

_{max}= 0.5–1 μm, ${\tau}_{1}$ would still only range from 9 to 35 min, the kind of variability that would not be surprising, even between identical trials.

^{−2}g/cm

^{3}. For a 5% NaCl precipitating solution, ${c}_{\mathrm{e}}$ = 2.16 × 10

^{−3}g/cm

^{3}; N = 300 crystals and $l$ = 75 μm = 7.5 × 10

^{−3}cm (see Table 1). Replacing these experimental figures in Equation (16.1):

^{−3}g/cm

^{3}, and we may take N = 600 crystals and $l$ = 5 × 10

^{−3}cm (Table 1). In this case,

^{3}= 10,000 × (1.5 × 10

^{−3})

^{3}= 3.375 × 10

^{−5}cm

^{3}= υ(m

_{o}− m

_{m})

_{o}− m

_{m}) = (3.375 × 10

^{−5})/0.81 = 4.17 × 10

^{−5}g = 4.17 × 10

^{−2}mg

_{e}= 1.23 mg/mL [29], so in 1 μL, m

_{m}= 1.23 × 10

^{−3}mg.

_{o}= 4.17 × 10

^{−2}+ 1.23 × 10

^{−3}= 4.29 × 10

^{−2}mg in 1 μL, corresponding to c

_{o}≈ 43 mg/mL.

_{e}= 7.4 mg/mL [29], so in 1 μL, m

_{m}= 7.4 × 10

^{−3}mg. Then, m

_{o}= 4.17 × 10

^{−2}+ 7.4 × 10

^{−3}= 4.91 × 10

^{−2}mg in 1 μL, corresponding to c

_{o}≈ 49 mg/mL, which is very close to the above despite the sixfold difference in protein solubility between the two conditions. This condition indeed gives almost the same crystal mass, but concentrated within 1–2 crystals in our 2 μL drops.

_{0}obtained only gives a limit below which the risk of crystals being too few and/or too small for XFEL is appreciable. For example, in the worked example above, 7% NaCl was chosen as we already knew that lower supersaturations have yielded crystals that were too few and large for XFEL, whereas higher ones have resulted in amorphous precipitation.

_{o}= 43 mg/mL, the lysozyme solubility corresponding to 7% NaCl, and the required sizes and numbers of crystals stated above, we obtain:

_{e}= 3.2 mg/mL [29]. We obtain:

## 3. Concluding Remarks

## 4. Materials and Methods

^{TM}(Thermo Fischer Scientific Inc., Markham ON, Canada) protein concentration measurements that were made. As 2 μL droplets had yielded a higher crystal density than the 5 μL ones in the first set of trials, only 2 μL drops were set (in triplicates) for this series.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Crystal Size Distribution

- −
- The competition for material (needed for growth) between crystals that are positioned close to each other. There are indications [33], however, that presumably due to the relatively slow protein crystal growth, the competition for solute is not very intense and this alone can hardly be the major cause for protein crystal polydispersity and its gradual increase during prolonged growth.
- −
- The plumes [23,25] that arise because solution with lower solute concentration around the growing crystal rises, and fresh, more concentrated solution from farther away invades that space; the larger the growing crystal, the larger the plume forming above it, in other words the more extensive the solution replenishment around the crystal.
- −
- Step sources of increased growth activity (such as closely spaced screw dislocations of the same and opposite signs) are present in some large crystals while absent in others [33]. Such defects should be absent in nanocrystals, and this has been explained by estimating the equilibrium distance between two dislocations [34]; with crystal size decreasing below the equilibrium separation distance, dislocations inside such nanocrystals become unstable.
- −
- The crystals that are born first in the solution bulk sediment (Figure A1), which brings them into the non-depleted solution where they grow faster. Crystal sedimentation occurs when the viscous resistance cannot counterbalance the gravitational drag force acting on the protein crystal. Therefore, when crystals grow to sizes between 1.6 μm [35] and 2 to 6 μm [36], most of them settle to the bottom and continue to grow there. However, sedimentation also destroys the Chernov ”self-purifying” zones and exposes the growing crystals to increased impurity delivery.

**Figure A1.**A crystal, born in the solution bulk, sediments (shown by the arrow); thus, the crystal leaves the depleted solution zone (yellow) formed around it. As a result, the crystal starts growing faster in the nondepleted solution (green). However, when they reach the bottom of the container, the crystals can land either in nondepleted or in already-depleted solution. Microphotograph of a real (interference contrasted) crystal of apoferritin (edge length 0.25 mm) is used for showing the settling crystal. Reprinted with permission from [17].

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**Figure 1.**Crystals of hen egg-white lysozyme grown in microbatch at very similar conditions and different incubation times, showing the difficulty of fine-tuning the conditions to the desired result. (

**A**) Crystals that are too large for XFEL crystallography but quasi-ideal for conventional crystallography. Grown from 4% NaCl and incubated for 24 h; ca. 150–200 µm in each dimension. (

**B**) Crystals that are still too large for XFEL crystallography but can be improved for conventional crystallography. Grown from 5% NaCl and incubated for 24 h; ca. 50–100 µm in each dimension. (

**C**) Crystals of approximately adequate size for XFEL crystallography but with too low number density in the solution. Grown from 6% NaCl and incubated for 1.5 h; <40 µm in each dimension. (

**D**) Crystals of adequate size for XFEL crystallography growing together in ”hedgehog” clusters, thus making their harvesting very difficult. Grown from 6% NaCl and incubated for 48 h. (

**E**) Crystals of adequate size and number density for XFEL crystallography. Grown from 6% NaCl and incubated for 4 h; <25 µm in each dimension.

**Table 1.**Numbers and sizes of lysozyme crystals for two different precipitating agent concentrations and at different times of incubation after setup; (a)–(c) correspond to each drop of the triplicates set up at each condition, wherever these drops are not identical.

5% NaCl | 6% NaCl | |
---|---|---|

t = 0 | clear after centrifugation | clear after centrifugation |

t = 0.5 h | tiny visible crystals | tiny visible crystals |

t = 1.5 h | (a) 100s of crystals 50 × 50 × 50 μm (b) ca. 200 crystals 75 × 75 × 75 μm (c) ca. 200 crystals 50 × 50 × 50 μm | (a) 100s of crystals, 25 × 25 × 25 μm (b) 100s of crystals (but fewer than a), 25–50 μm in each dimension (c) 100s of crystals (but fewer than a), 25–50 μm in each dimension |

t = 3.5–4 h | (a) as at t = 1 h 30 min (b) ca. 200 crystals 75–100 μm in each dimension (c) as at t = 1 h 30 min | (a) as at t = 1 h 30 min (b) as at t = 1 h 30 min (c) as at t = 1 h 30 min |

t = 45–48 h (growth completed) | (a) 100s of crystals 50 × 50 × 50–75 × 50 × 50 μm (b) ca. 200 crystals 75–100 μm in each dimension + very small ones (<25 μm) (c) as at t = 1 h 30 min | (a) as at t = 1 h 30 min (b) as at t = 1 h 30 min (c) 100s of crystals (but fewer than a), 25–75 μm in each dimension |

**Table 2.**Numbers and sizes of lysozyme crystals for various different precipitating agent concentrations and at different times of incubation after setup, in the first series of trials (see Materials and Methods); (a)–(c) correspond to each drop of the 2 μL triplicates and (i)–(iii) to each drop of the 5 μL triplicates set up at each condition.

3% NaCl | 4% NaCl (Regular) | 4% NaCl (Pre-Mixed) | 5% NaCl (Pre-Mixed) | 6% NaCl (Regular) | 6% NaCl (Pre-Mixed) | 8% NaCl | |
---|---|---|---|---|---|---|---|

t = 0 | All clear for at least 10 days | Shock nucleation, then slowly clarified | clear | Very light precipitate, then slowly clarified | Heavy precipitate everywhere—no crystals | Light precipitate | Heavy precipitate everywhere—no crystals |

t = 1.5 h | (a) 18 xtals, 50 × 25 × 25–75 × 50 × 50 μm (b) 30 xtals, 75 × 30 × 30–75 × 75 × ? μm (c) 16 xtals, 75 × 25 × 25–75 × 50 × 50 μm (i) 32 xtals, 50 × 25 × 25–75 × 75 × ? μm (ii) 58 xtals, 50 × 30 × 30–75 × 75 × ? μm (iii) 45 xtals, 50 × 30 × 30–75 × 50 × 50 μm | (a) 12 xtals, 30 × 20 × 20–50 × 40 × 40 μm (b) 13 xtals, 25 × 25 × 25–35 × 35 × 35 μm (c) 5 xtals, 50 × 25 × 25–50 × 40 × 40 μm (i) 10 xtals, ca. 30 × 20 × 20 μm (ii) 16 xtals, 50 × 25 × 25–75 × 50 × 50 μm (iii) 19 xtals, 25 × 25 × 25–50 × 50 × 50 μm | (a) 26 xtals, 50 × 25 × 25–50 × 50 × 50 μm (b) 34 xtals, 50 × 25 × 25–50 × 50 × 50 μm (c) 43 xtals, 30 × 15 × 15–50 × 50 × 50 μm (i) 90 xtals, 50 × 25 × 25–50 × 50 × 50 μm (ii) 70 xtals, 50 × 25 × 25–50 × 50 × 50 μm (iii) 67 xtals, 50 × 25 × 25–75 × 50 × 50 μm | (a) 38 xtals, 25–50 μm in each dimension (b) 43 xtals, same (c) 38 xtals, same (i) ca. 65 xtals, same (ii) ca. 70 xtals, same (iii) ca. 70 xtals, same (plus light precipitate) | |||

t = 2.5 h | (a) 24 xtals, 75 × 50 × 50–125 × 75 × ? μm (b) 35 xtals, 125 × 50 × 50–125 × 125 × ? μm (c) 18 xtals, 75 × 50 × 50–125 × 125 × ? μm (i) 49 xtals, 125 × 50 × 50–175 × 125 × 125 μm (ii) 66 xtals, 50 × 50 × ?–125 × 125 × ? μm (iii) 65 xtals, 75 × 50 × 50–125 × 75 × 75 μm | ||||||

t = 3.5–4 h | (a) 13 xtals, 100 × 100 × 50–180 × 100 × 100 μm (b) 14 xtals, 125 × 125 × 125–180 × 125 × 125 μm, but also some smaller ones (125 × 50 × 50 μm) (c) 9 xtals, 125 × 50 × 50–150 × 150 × 125 μm (i) 15 xtals, 125 × 100 × 100–125 × 125 × 125 μm (ii) 22 xtals, 100 × 100 × 100–160 × 160 × 160 μm (iii) 21 xtals, 125 × 100 × 100–180 × 180 × ? μm | (a) 30 xtals, 150 × 100 × 100–150 × 150 × 150 μm (b) 37 xtals, 150 × 125 × 100–200 × 200 × 200 μm (c) 49 xtals, 125 × 100 × 60–175 × 125 × 125 μm (i) ca. 100 xtals, 125 × 75 × 75–180 × 180 × ? μm (ii) ca. 80 xtals, 180 × 100 × 100–200 × 150 × 150 μm (iii) ca. 85 xtals, 180 × 100 × 100–180 × 180 × 180 μm | |||||

t = 45–48 h (growth completed) | (a) 25 xtals, with 2 distinct morphologies: 180 × 180 × 180 and 180 × 125 × 50 μm (b) 31 xtals, as in A1 but there are 2 much smaller ones (ca. 75 × 75 × 50 μm) (c) 17 xtals, 200 × 125 × 125–200 × 200 × 180 μm (i) ca. 55 xtals, 200 × 200 × ? μm (ii) ca. 60 xtals, 200 × 125 × ?–200 × 200 × ? μm (iii) ca. 60 xtals, ca. 180 × 180 × 125 μm | (a) 12 xtals, 225 × 225 × ?–225 × 225 × 225 μm (b) 14 xtals, 250 × 180 × 180–200 × 200 × ? μm, but also some smaller ones (180 × 180 × 125 μm) (c) 9 xtals, 250 × 180 × ?–200 × 200 × ? μm (i) 17 xtals, 125 × 100 × 100–125 × 125 × 125 μm (ii) 22 xtals, 100 × 100 × 100–160 × 160 × 160 μm (iii) 21 xtals, 125 × 100 × 100–180 × 180 × ? μm | (a) 34 xtals, with 2 distinct morphologies: 200 × 180 × 180–180 × 180 × 100 μm (b) 40 xtals, 125 × 125 × 125–180 × 180 × ? μm (c) 65 xtals, 100 × 100 × 100–150 × 125 × 125 μm (i) ca. 90 xtals, 180 × 180 × 180 μm (mostly) (ii) ca. 85 xtals, 125 × 125 × 125–225 × 180 × 180 μm (iii) ca. 75 xtals, 200 × 125 × 125–200 × 200 × 150 μm | All drops had both single crystals and “hedgehog” clusters over them. That made the single crystals impossible to count. Only dimensions could be measured: (a) 75 × 50 × 50–100 × 75 × 75 μm (b) 75 × 75 × ? 125 × 50 × 50 μm (c) 125 × 75 × 50–175 × 100 × 100 μm (i) ca. 100 × 50 × 50 μm (ii) and (iii) 100 × 75 × ?–180 × 125 × ? μm |

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**MDPI and ACS Style**

Nanev, C.N.; Saridakis, E.; Chayen, N.E.
Growing Crystals for X-ray Free-Electron Laser Structural Studies of Biomolecules and Their Complexes. *Int. J. Mol. Sci.* **2023**, *24*, 16336.
https://doi.org/10.3390/ijms242216336

**AMA Style**

Nanev CN, Saridakis E, Chayen NE.
Growing Crystals for X-ray Free-Electron Laser Structural Studies of Biomolecules and Their Complexes. *International Journal of Molecular Sciences*. 2023; 24(22):16336.
https://doi.org/10.3390/ijms242216336

**Chicago/Turabian Style**

Nanev, Christo N., Emmanuel Saridakis, and Naomi E. Chayen.
2023. "Growing Crystals for X-ray Free-Electron Laser Structural Studies of Biomolecules and Their Complexes" *International Journal of Molecular Sciences* 24, no. 22: 16336.
https://doi.org/10.3390/ijms242216336