Pit Formation on the Basal Plane of Ice in Antifreeze Protein Type III

Jun 1, 2016 - Synopsis. Pit formation process on the basal plane of ice in antifreeze protein (AFP) type III solution was observed, and the growth rat...
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Pit Formation on the Basal Plane of Ice in Antifreeze Protein Type III Solution for Different Growth Mechanisms of Ice Takaaki Inada,*,† Toshie Koyama,† and Kunio Funakoshi‡ †

National Institute of Advanced Industrial Science and Technology (AIST), Namiki 1-2-1, Tsukuba, Ibaraki 305-8564, Japan National Institute of Technology, Suzuka College, Shiroko, Suzuka, Mie 510-0294, Japan

‡

S Supporting Information *

ABSTRACT: When a single crystal of ice that has the basal plane several tenths of mm2 in area grows in a moderately active antifreeze protein (AFP) solution, numerous pits consisting of six pyramidal planes are formed on the basal plane. This pit formation suggests some interactions between the AFPs and the basal plane. In this study, we observed pit formation on the basal plane of ice growing in a 5 mg/mL fish AFP (type III) solution and examined three growth mechanisms (normal, spiral, and two-dimensional (2D) nucleation) of the basal plane by measuring the relationship between the growth rate and the degree of supercooling. We also measured the number density of pits in ice and found that the number density of pits for normal growth mode on molecularly rough surfaces was lower than that for spiral growth mode on relatively smooth surfaces, whereas pit formation was not observed during 2D nucleation growth mode. On the basis of these results, we proposed a model of pit formation during spiral growth mode. In this model, if only reversible adsorption of the AFP molecules on the smooth surfaces is considered to occur, then pit formation can be explained without assuming irreversible adsorption on the smooth surfaces.

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as a “stones on a pillow” or “buttons on a mattress” model, in which AFP molecules are irreversibly adsorbed on an ice surface (even if rough), thus pinning the growth normal to the surface.12,21−23 Despite the diversity of AFPs, ice binding surfaces of most AFP molecules are relatively flat and hydrophobic.2,5,9 For irreversible binding, the ice binding surfaces of AFPs are considered to fit complimentarily with specific ice planes.5,6 In addition, it has been recently suggested that the ice binding surfaces might organize water molecules into ice-like ordered structures before binding and thus bind to specific ice surfaces or quasi-liquid layers at ice/water interfaces.9,24,27−32 Before a single crystal of ice completely stops growing and melting in AFP solution within the TH gap, the crystal grows into a unique morphology, which depends on the type of AFP. This morphology is dominated by specific ice planes to which AFP molecules preferentially bind.17,20 In solutions of “moderately active” AFPs,9,17 such as fish AFPs (Figure 1), a single crystal of ice generally grows into a bipyramidal shape with a hexagonal cross-section when the crystal size is small (typically, < 1 mm).15,17,20,33−39 On the contrary, in solutions of “hyperactive” AFPs,9,17,40 such as insect or some bacterium AFPs, a single crystal of ice grows into a hexagonal plate-shape

INTRODUCTION Antifreeze proteins (AFPs) discovered in various organisms living in subzero-temperature environments, such as bacteria, plants, insects, and fish,1−9 protect these organisms from freezing. In AFP solutions, the freezing temperature at which an ice crystal starts to grow is depressed below the equilibrium melting point,1−11 whereas the melting temperature of ice is slightly elevated from the equilibrium melting point.9,12−14 The thermal hysteresis (TH) gap is defined as the temperature difference between these nonequilibrium freezing and melting temperatures.9,15 Below the nonequilibrium freezing temperature, ice crystals start to grow explosively,16−20 whereas above the nonequilibrium melting temperature, ice crystals melt and disappear suddenly.14 Within the TH gap, however, ice growth and melting can be completely stopped by AFP molecules in a noncolligative manner.9 To explain TH activity, an adsorption−inhibition model is generally used,1,5,11,12,21−24 in which AFP molecules are irreversibly adsorbed on a growing ice surface, thus producing local curvature of the ice surface by pinning the growth.24 This curvature makes further growth energetically unfavorable. The original adsorption−inhibition model supposed that AFP molecules are adsorbed on a step, thus pinning the step flow.11 However, this supposition can be applied only to the basal plane, because other ice surfaces growing in water under atmospheric pressure are thermally roughened near the melting temperature.21−23,25,26 Therefore, the model has been modified © XXXX American Chemical Society

Received: November 10, 2015 Revised: April 28, 2016

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DOI: 10.1021/acs.cgd.5b01596 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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EXPERIMENTAL SECTION

Materials. A moderately active AFP (AFP type III, A/F Protein), which is a 7-kDa globular protein from fish (Figure 1C), was purchased and used without further purification. Water was purified by a purification system (Elix-UV-3 and Academic-A10, Millipore) and used to produce single crystals of ice and to prepare AFP solutions. Preparation of Single Crystal of Ice. A single crystal of ice was produced from pure water in an open acrylic vessel (90 mm inner diameter and 120 mm high) placed in a constant-temperature room (Figure S1). The side and bottom walls of the vessel were equipped with a jacket, in which ethylene glycol solution (50 wt %) was supplied from a thermostat bath (RC 20 CS, Lauda) to control the wall temperature. The room temperature was controlled between −2.5 and −2.0 °C to induce spontaneous ice nucleation on the water surface, and the temperature of the ethylene glycol solution was controlled at 1.5 °C to prevent freezing on the walls. Once an ice crystal nucleated, it was slowly grown into a thin layer laterally along the water surface. Before this crystal covered the water surface, other ice crystals frequently nucleated on the water surface. These unfavorable crystals were removed by using tweezers or a pipet, to allow only this single crystal to grow. It took a few hours for the ice layer to cover the water surface except for the periphery, near the vessel walls. Then, the ice layer was grown further in the vertical direction until its thickness reached at least about 1 mm. In the single crystal, the c-axis was normal to the water surface.58 Finally, as a sample for observation, a small disk-shaped crystal (3−6 mm diameter and 1 mm thick) was cut from this single crystal by using a copper pipe heated by hand. Observation of Ice Growth. In a constant temperature room controlled at −3.0 °C, using the following process, this sample ice crystal was frozen to a cover glass (18 mm diameter), oriented with the c-axis approximately normal to the cover glass surface, namely, with the basal plane approximately parallel to the cover glass surface. To facilitate freezing to the glass surface, first, a piece of 50-μm thick stainless steel film (0.5 × 0.5 mm) was placed between the sample ice and the cover glass. Then, the sample ice was heated gently by touching the backside of the cover glass with our finger, so that the sample ice was slightly melted only around the stainless steel film and then tightly refroze to the cover glass. Finally, the cover glass was adhered (using adhesive tape) onto an acrylic sample support that had been fitted beforehand with an acrylic sample cell (30 × 30 × 30 mm) (Figure 2A). The sample cell was removed from the constant temperature room and then installed upside down in an acrylic vessel, in which a transparent coolant (Novec 7100, 3M) was circulated from a thermostat bath (RP 1840, Lauda) (Figure 2B). The coolant temperature in the thermostat bath could be set in increments of 0.01 °C. Then, 5 mg/mL AFP type III solution cooled to −0.4 °C in advance was slowly injected into the sample cell by using a syringe, until the cell was filled with the solution, taking about 3 min. During the injection, to maintain the size and shape of the sample ice as much as possible, the solution temperature was kept between 0.00 and 0.25 °C in the sample cell by controlling the coolant temperature. The solution temperature in the sample cell was measured by a platinum resistance thermometer (Fast Response RTDs 5622-05 and CHUBE4, Hart Scientific). Because the solution temperature was slightly higher than the melting point Tm (= −0.006 °C at 5 mg/mL) of the AFP solution just after filling the sample cell, the sample ice partly melted and thus temporarily detached from the cover glass. Soon after that, the degree of supercooling ΔT was promptly controlled between 0.000 and 0.010 °C and kept in this range for more than 0.5 h. Then, ΔT was set at a prescribed value (seven different values between 0.019 ≤ ΔT ≤ 0.059 °C), and the basal plane of the sample ice was observed and the images were recorded from the bottom by a digital microscope (VHX900 and VH-Z35, Keyence) and simultaneously from the side by a microscopic lens (VB-G25, Keyence), CCD camera (XC-77RR-CE, Sony), and a hard disk drive recorder (VDH-8000, Sanyo Electric), unless otherwise specified. While ΔT was kept constant (with a

Figure 1. 3D structure of moderately active fish AFPs. (A) Type I from winter flounder (Protein Data Bank (PDB): 1WFA). (B) Type II from sea raven (PDB: 2AFP). (C) Type III from ocean pout (PDB: 1MSI) with the ice-binding surface highlighted in red.15,45

surrounded by the basal and prism planes or into a lemonshape without distinct facets.17,18,20,35,40−42 On the basis of these observations of growth shapes, it has been often argued that moderately active AFPs have no interaction with the basal plane, whereas hyperactive AFPs bind to the basal plane.17,20,43,44 These arguments have been supported by direct evidence of AFP adsorption onto specific ice planes, evidence obtained either by an etching assay using a hemispherical single crystal of ice grown in AFP solution,15,21,35,38,45,46 or by direct visualization of AFP molecules tagged with fluorescent proteins.42,43,47−49 Several reports implicitly suggest, however, some interactions of moderately active AFP molecules with the basal plane.50−55 In those reports, a single crystal of ice that has the basal plane on the order of tenth of mm2 or larger was prepared in advance and then immersed in moderately active AFP solutions within the TH gap. The result was that numerous pits, each consisting of six pyramidal planes, were left on the growing basal plane, which gradually disappeared due to being covered with pits. If the basal plane grew as a molecularly rough surface, such pit formation does not seem unusual because at the nanoscale level, AFP molecules find any preferential orientation of ice surface for binding.34 If the basal plane grew as a molecularly smooth surface, however, some interaction of moderately active AFP molecules with the basal plane seems to be necessary for pit formation; otherwise, the basal plane would grow while maintaining its smooth surface without pits. Therefore, to discuss the interaction of AFP molecules with the basal plane, it is essential to understand the molecular picture, or growth mechanism, of the basal plane. Previous studies on pit formation by moderately active AFPs,50−55 however, do not discuss whether the basal plane was molecularly smooth or rough in those studies, because it is extremely difficult to observe growing ice surfaces directly at the molecular scale. Despite recent successful observations of advancing elementary steps at ice/air interfaces,56,57 clear observation of elementary steps at ice/water interfaces has not been reported to date to our knowledge. In this study, we deduced the molecular picture of the basal plane of ice in moderately active AFP solutions based on macroscopic measurement of the growth rate. First, using optical microscopy, we observed pit formation on the basal plane growing in a 5 mg/mL fish AFP (type III) solution within the TH gap. Then, we examined three growth mechanisms (normal, spiral and two-dimensional (2D) nucleation) of the basal plane by measuring the relationship between the growth rate and the degree of supercooling. Finally, we discussed the pit formation mechanism by measuring the number density of pits for different growth mechanisms. B

DOI: 10.1021/acs.cgd.5b01596 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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where h represents the downward-growth height and t is the time. From the side-view of pits (Figure S3), the apex of a pit was confirmed to be immobile and 2θ was estimated to be approximately 70°. Because the value of 2θ could not be exactly determined due to the resolution limit of the images, it is doubtful if the assumption of constant 2θ is valid.50 However, because 2θ satisfied at least 65° ≤ 2θ ≤ 75° irrespective of ΔT throughout the experiments, the error of vb due to the change in 2θ was within ±10%.

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RESULTS AND DISCUSSION Pit Formation on Basal Plane. The pit formation process on the basal plane of a single crystal of ice was observed when the ice crystal grew in 5 mg/mL AFP type III solution for the seven different ΔT (0.019 ≤ ΔT ≤ 0.059 °C). These ΔT were much smaller than the TH gap of 5 mg/mL AFP type III solution (about 0.56 °C) (Figure S4). Typical images of pit formation at ΔT = 0.026 °C as an example are shown in Figure 3: entire images of ice observed from the side (Figure 3A−C) and magnified images of the basal plane observed from the bottom (Figure 3D−F). The time at which ΔT reached a prescribed value (here, ΔT = 0.026 °C) was defined as t = 0. First, just after T became lower than Tm (when t < 0), the ice crystal began to grow both upward and downward in the c-axis direction, while stopping the growth in the a-axis direction, thus being surrounded by two basal planes with multiple pits and 12 pyramidal planes (Figure 3A). After the top basal plane was tightly frozen to the cover glass, water was no longer provided between the top basal plane and the cover glass. Therefore, only the bottom basal plane continued growing downward (Figure 3A−C). The pits were pyramidal in shape with a hexagonal crosssection, confirmed by side-view images (Figure S3). As previously reported,50,54 the hexagonal symmetry of the pyramidal planes forming the pits was shifted by about 30° relative to the symmetry of the external pyramidal shape of the ice crystal, with respect to the c-axis (Figure S5); the six pyramidal planes of each pit were approximately represented as {112̅x}, in contrast to the external pyramidal planes of the ice crystal as {101̅y}, where the values of x and y could not be exactly determined due to the resolution limit of the images. Strictly speaking, the number of pyramidal planes forming a pit was sometimes not six, but rather 12 (Figure 3E,F), as

Figure 2. Experimental apparatus. (A) Single crystal of ice frozen to cover glass fixed in acrylic sample cell. (B) Sample cell equipped with acrylic vessel. precision of ±0.005 °C) by carefully controlling the coolant temperature in the thermostat bath, the crystal was observed for more than 24 h or until the basal plane disappeared. Evaluation of Ice Growth Rate. The growth rate vb of a separate area of the basal plane surrounded by chains of pits (as shown as areas (i), (ii), and (iii) in Figure 3F) was evaluated based on the change in the width w of the separate basal area. A schematic cross-sectional view explaining the relationship between vb and w is shown in Figure S2. Assuming the apex of a pit is immobile and the opening angle 2θ of a pit is constant, vb can be represented as

vb =

dh cot θ dw =− dt 2 dt

Figure 3. Images of pit formation on the basal plane of ice growing in 5 mg/mL AFP type III solution at constant degree of supercooling (ΔT = 0.026 °C as an example). (A−C) Side-view images of entire ice crystal. (D−F) Magnified bottom-view images. (D, E) Number of pits gradually increased, and then (F) the basal plane was separated into several areas surrounded by chains of pits, as shown by the color lines (i−iii). C

DOI: 10.1021/acs.cgd.5b01596 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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previously reported.50 Pits appeared to form randomly on the basal plane, and then gradually increased in number during growth of the basal plane (Figure 3D,E). The basal plane eventually separated into several areas by chains of pits (Figure 3F). Bottom-view images of the basal plane after such separation are shown in Figure S6. Although the surfaces of the pyramidal planes of pits appeared smooth during the first few hours (Figures 3D−F and S6A), they gradually developed complicated undulations (Figure S6B−D), which made it much more difficult to accurately determine the index of the pyramidal planes. Growth Rate of Basal Plane. Among the several separate basal planes, we focused on three areas labeled (i), (ii), and (iii) observed in Figure 3F (ΔT = 0.026 °C). The growth profiles for these three areas are shown in Figure 4, where h represents

disappeared by being covered by pits. Although it was difficult to evaluate the variation in vb during the growth due to insufficient data points, vb always showed non-negligible values (Figure S7D−F). Ice Growth Mechanism. The growth mechanism of the basal plane in AFP type III solution is discussed here based on the measured growth profiles. The variation in vb at a constant ΔT (Figures 4 and S7A−C) primarily reflects the variation in surface roughness or growth mechanism. When ΔT ≤ 0.038 °C, vb reached several hundred μm/h just after ΔT reached a prescribed value (t = 0). This vb was a few orders in magnitude higher than the minimum vb (vb,min), which was reached in the later stage of the measured growth profile; for example, at ΔT = 0.026 °C, vb averaged a value of 210 μm/h between t = 1.0 h (Figure 3D) and 1.7 h (Figure 3E), whereas vb,min was lower than 0.1 μm/h when t > 20 h (Figure 4). The high vb obtained just after t = 0 clearly indicates that in the early stage of the measured growth profile, the basal plane was molecularly rough and normal growth was dominant.59 This roughness was probably due to the initial state of the surface, which was cut from an original larger single crystal. An initially rough surface tends to smoothen at the ΔT used in this study (0.019 ≤ ΔT ≤ 0.059 °C) because neither the thermal roughening transition nor kinetic roughening transition occurs on the basal plane in this temperature range; thermal roughening does not occur on the basal plane in water even near the melting temperature,26 and kinetic roughening temperature on the basal plane in water is about −0.3 °C,60 which is much lower than the solution temperatures used in this study. As the surface becomes smooth, the layer growth caused by dislocations or 2D nucleation becomes dominant.59 Such a surface transition led to a sudden decrease in vb (Figures 4 and S7A−C). The time ttr at which vb suddenly decreased due to the surface transition from rough to smooth was 1.8 h at ΔT = 0.019 °C (Figure S7A), 2.2 h at ΔT = 0.026 °C (Figure 4), 1.2 h at ΔT = 0.027 °C (Figure S7B), and 0.6 h at ΔT = 0.038 °C (Figure S7C). Although strictly speaking, ttr depended on the specific separate area of the basal plane, the difference was at most a few minutes. When ΔT ≤ 0.038 °C, after the basal plane separated into different areas (h > 0) and changed from rough to smooth (t > ttr), each area showed a different vb profile that discontinuously increased or decreased (Figures 4 and S7A−C). The distinct difference in vb profile even between areas separated by only less than 200 μm (Figures 3F and S6) was caused not by the difference in solution temperature or concentration, but by the difference in step sources for layer growth.61 We speculate that the discontinuous change in vb was caused by the formation and elimination of dislocations, and therefore spiral growth caused by dislocations was dominant during this observed discontinuous change in vb. Because the surface area of a separate basal area shrunk as the growth continued (Figures 3D−F and S6), dislocations would often disappear in a manner similar to the Dash-necking process.62 On the contrary, dislocations might be newly formed due to the adsorption of impurity molecules (i.e., AFP molecule), even if the adsorption was reversible.63,64 Dislocations might also be formed by stacking faults produced on the growing basal planes.65−68 Such a discontinuous change in vb was previously reported in heavy water without any additives and was also attributed to the change in step sources on the basal plane.69 Figure 5 shows the combined data of vb from Figures 4 and S7 as a function of 1/ΔT (or ΔT), where vb,min at each 1/ΔT is

Figure 4. Growth profile of three separate basal planes ((i−iii) shown in Figure 3F) in 5 mg/mL AFP type III solution at constant degree of supercooling (ΔT = 0.026 °C). Here, h is the downward-growth height (see Figure S2) and t is the elapsed time, where t = 0 is defined as the time at which ΔT reached 0.026 °C. The slope (dh/dt) corresponds to the growth rate (vb) of the basal plane, and ttr represents the time at which vb suddenly decreased.

the downward-growth height (Figure S2). Because h = 0 is defined here as the height at the last moment when all three areas were still connected together within the field of view, the plots for these three areas are in agreement when h ≤ 0. In contrast, after the basal plane was separated into the different areas (h > 0), each area exhibited its own growth profile. The growth rate vb of each area, which corresponds to the slope (dh/dt) of the growth profile in Figure 4, discontinuously increased or decreased at intervals of typically several hours. For all three areas, when t > 20 h, vb became lower than 0.1 μm/h. Similar tendencies of the growth profile were observed also at ΔT = 0.019 and 0.027 °C (Figure S7A,B). Also at ΔT = 0.038 °C, vb discontinuously increased or decreased after the basal plane was separated into several areas (Figure S7C). At this ΔT, however, vb never decreased below 1 μm/h, and thus all the separate areas eventually disappeared within several hours by being covered by pits. When ΔT ≥ 0.047 °C, because vb was so high that all the separate areas of the basal plane disappeared within several minutes by being covered by pits, it was difficult to discuss the growth mechanism. Therefore, to facilitate analysis of the growth mechanism for ΔT ≥ 0.047 °C, first we reduced vb to below 0.1 μm/h by keeping ΔT ≤ 0.027 °C to ensure a smooth surface at the molecular scale (discussed in detail in the following section) and then quickly changed ΔT to a prescribed value (ΔT = 0.047, 0.055, and 0.059 °C). As a result, all the separate areas started to grow again and continued until they D

DOI: 10.1021/acs.cgd.5b01596 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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molecules to some extent. Such suppression is probably due to the step pinning effect caused by the AFP molecules adsorbed reversibly on the basal plane (schematically shown in Figure 8A). The data vb in AFP type III solution were also reported by others, although pits were not observed in that study probably because the crystal used was as small as about 10 μm.20 Those data, plotted as solid triangles in Figure 5, showed a temperature dependency almost identical to vb,min obtained in the present study. Note that those previously obtained vb decreased as the surface area of the basal plane decreased, suggesting the dominance of 2D nucleation growth.20 Pit Formation Mechanism. Here, we correlate the pit formation with the growth mechanism. In the early stage of the measurements (t < ttr), vb was quite high, indicating that the surface condition was rough at the molecular scale and that normal growth was dominant. During normal growth, numerous pits formed on the basal plane (Figure 3D,E). Because steps and kinks exist anywhere on such rough surfaces, there are apparently various surfaces with arbitrary orientations at the nanoscale. Therefore, AFP molecules easily irreversibly bind to such rough surfaces and thus form pits by stopping the growth of specific pyramidal planes to which AFP molecules bind. As discussed in the previous section, when ΔT ≤ 0.027 °C, spiral growth caused by dislocations was dominant when t > ttr. Here we examine if pits were newly formed on the basal planes during spiral growth (t > ttr), by focusing on area (ii) in Figure 3F (ΔT = 0.026 °C) as an example. In the observed images (Figure 6), two pits were newly recognized on area (ii) during

Figure 5. Growth rate of the basal planes of ice in 5 mg/mL AFP type III solution, as a function of 1/ΔT, where ΔT is the degree of supercooling. Here, vb,min represents the minimum growth rate at each ΔT, vb,rough represents the growth rate on molecularly rough surfaces, and vb represents other data. For reference, also shown are the growth rate of the basal plane in pure water (plotted as crosses)60 and that in AFP type III solution when using a small ice crystal of about 10 μm (plotted as solid triangles).20 Lines are the linear fits to the measured vb,min (red) and to the data in pure water (green).

plotted as open circles, vb,rough on molecularly rough surfaces (t < ttr) as open squares, and other data (vb) as small dots. To avoid complexity, error bars are shown only for vb,min. Horizontal error bars correspond to the precision of temperature control. Vertical error bars were calculated based on the spatial resolution of side-view images (for 2θ) and bottom-view images (for w) (Figure S2). The large scatter in vb even at the same ΔT (especially at relatively small ΔT) suggests the existence not only of single or double bilayer steps (0.37 or 0.74 nm height), which are generally observed on the growing basal plane,67 but also of step bunches or macrosteps of various heights. When ΔT ≤ 0.027 °C, vb,min is on the order of 0.1 μm/h (10−4 mm/h) or less, which is on the same order of the detection limit (i.e., vertical error bars in Figure 5). This indicates that when ΔT ≤ 0.027 °C, 2D nucleation did not occur, and all the dislocations that can induce spiral growth already disappeared from the basal plane when vb,min was measured. On the contrary, when ΔT ≥ 0.038 °C, vb,min is higher than 1 μm/h (10−3 mm/h), which is significantly higher than the detection limit (Figure 5). This indicates that even if spiral growth was stopped by disappearance of dislocations, 2D nucleation would inevitably occur and thus always provide step sources for layer growth at this ΔT. (Strictly speaking, 2D nucleation might be stopped when the basal plane becomes too narrow for a critical 2D nucleus to form: for example, the critical radius is 6 μm at −0.1 °C.19) Therefore, the critical degree of supercooling ΔT* for 2D nucleation must be within the range of 0.027 < ΔT* < 0.038 °C, which is almost identical to ΔT* reported for pure water.25,60 Theoretically, vb caused by 2D nucleation is proportional to exp (−1/ΔT).60 Actually, the measured vb,min can be well fitted by exp(−1/ΔT) (linear fitting represented by the red line in Figure 5). Reference data vb for pure water, plotted as crosses in Figure 5, were reportedly caused by 2D nucleation growth, because they could also be fitted by exp(−1/ΔT) (represented by the green line).60 The vb,min values obtained in the present study were lower than vb for pure water, indicating that 2D nucleation growth on the basal plane was suppressed by AFP type III

Figure 6. (A, B) Images of pits formed on the basal plane (area (ii) shown in Figure 3F) growing in 5 mg/mL AFP type III solution at a constant degree of supercooling (ΔT = 0.026 °C). Pit (b) emerged after ttr (= 2.2 h), whereas pit (a) emerged before ttr, although not visible yet at ttr due to the resolution limit of the image. Here, ttr represents the time at which vb suddenly decreased.

spiral growth (pits (a) and (b) in Figure 6B). On the basis of the growth profile of area (ii) (Figure 4), the pit formation time was 2.1 h for pit (a) and 13.2 h for pit (b). These times indicate that in practice, pit (a) emerged when t < ttr (= 2.2 h), namely, when the surface was still rough, although this pit was not visible in Figure 6A (t = 2.2 h) due to the resolution limit of the image. Therefore, in area (ii), only pit (b) actually emerged during spiral growth. The number N of pits formed during each of the three growth modes was determined and then converted into the number density per unit volume of ice, N/V (Table 1 and E

DOI: 10.1021/acs.cgd.5b01596 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Table 1. Number of Pits (N) Formed in 5 mg/mL AFP Type III Solution during Each Growth Mode and the Corresponding Number Density Per Unit Volume of Ice (N/ V) degree of supercooling, ΔT [°C]

number of pits, N

volume of ice, V [mm−3]

number density of pits, N/V [mm−3]

normal growth

0.019

136

0.466

2.9 × 102

spiral growth

0.026 0.027 0.038 0.019 0.026 0.027 0.038

114 70 142 38 33 9 0

0.571 0.798 0.871 0.013 0.011 0.028 0.002

2.0 8.8 1.6 3.0 3.0 3.3 0

0.047 0.055 0.059

0 0 0

0.003 0.011 0.003

0 0 0

growth mode

2D nucleation growth

× × × × × ×

102 101 102 103 103 102

Figure 7). Although N for normal growth mode was higher than that for spiral growth mode, N/V was lower. These results

Figure 8. Model of pit formation on the basal plane of ice during spiral growth in AFP type III solution. Ice binding surface of AFP type III molecules (PDB: 1MSI) are highlighted in red.15,45 (A) AFP molecules are adsorbed reversibly on an elementary step, thus delaying the step flow by pinning. (B) Other steps behind catch up with the delayed step and develop into a macrostep. AFP molecules recognize this macrostep as a pyramidal plane, thus stopping the growth by being adsorbed irreversibly on the macrostep.

steps behind would then successively catch up with the pinned step, and consequently a macrostep would gradually develop (Figure 8B). Such a macrostep formation by impurity adsorption is a common phenomenon and often observed in crystal growth in solutions.70,71 If the macrostep has a substantial thickness on the same order as the size of an AFP type III molecule (