Growth of Ice Crystals in the Presence of Type III Antifreeze Protein

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Growth of ice crystals in the presence of type III antifreeze protein Dmitry A. Vorontsov, Gen Sazaki, Evgeniia K. Titaeva, Ekaterina L. Kim, Maddalena Bayer-Giraldi, and Yoshinori Furukawa Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b00172 • Publication Date (Web): 26 Feb 2018 Downloaded from http://pubs.acs.org on February 27, 2018

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Crystal Growth & Design

Growth of ice crystals in the presence of type III antifreeze protein Dmitry A. Vorontsov*,1,2, Gen Sazaki2, Evgeniia K. Titaeva1, Ekaterina L. Kim1, Maddalena Bayer-Giraldi3, Yoshinori Furukawa2 1

Lobachevsky State University of Nizhny Novgorod, Gagarin Ave., 23, Nizhny Novgorod,

603950 Russia 2

Institute of Low Temperature Science, Hokkaido University, Kita-19, Nishi-8, Kita-ku,

Sapporo, 060-0819 Japan 3

Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Am Alten Hafen,

26, Bremerhaven, 27568, Germany

KEYWORDS ice crystallization, growth rates, antifreeze protein, AFP-III, freezing point depression, adsorption, Cabrera-Vermilyea model ABSTRACT. The morphology and growth kinetics of ice single crystals in aqueous solutions of type III antifreeze protein (AFP-III) have been studied in detail over a range of AFP-III concentrations and supercoolings. In pure water, the shape of ice crystals changes from the circular disk-like to planar dendritic with increasing supercooling. In AFP-III solutions, ice

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crystals in the form of faceted plates, irregular dendrites with polygonized tips and needles appear with increasing supercooling and AFP-III concentration. The growth rate of ice crystals in the crystallographic a direction is two orders of magnitude higher than that in the c direction. AFP-III molecules cause the stoppage of the growth of the prismatic and basal faces at low supercoolings. When supercooling exceeds the critical value, AFP-III favours the acceleration of the growth in both a and c directions. The observed behaviour of AFP-III is explained in terms of the Cabrera-Vermilyea pinning model and the specificity of the dissipation of latent heat from the growing crystals with different shapes.

INTRODUCTION Antifreeze proteins (AFPs) depress the freezing temperature of water and exhibit a strong ability to control the growth of ice crystals mainly by changing their growth rates and growth shapes. The inhibition effect of AFPs on the recrystallization and growth of ice helps living organisms (sea fish, plants, insects, microorganisms) to survive in a subfreezing environment. A great interest in the properties of AFPs in biology, physics, chemistry and engineering is explained by high perspectives of AFP applications in food industry,1,2 medicine and cryobiology.3 The difference between the melting and freezing points of ice in AFP solution is called thermal hysteresis (TH). Typically the antifreeze activity of AFPs is determined by the ability to depress the freezing point of water. AFPs, according to their activity, can be classified into two groups: moderate AFPs with a TH value up to 1−1.5 K and hyperactive AFPs which rise the TH up to 6 K or more.4,5 The former have been broadly discovered in sea fish6 and plants7, the latter are typical for insects, like beetles8. Depending on the amino acid sequences, the AFPs from fish are


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subdivided into several groups called types I−IV6,9−12 and antifreeze glycoproteins (AFGP).13,14 Moderate AFPs bind only prismatic and bipyramidal faces without attaching basal faces of ice crystals,15−17 whereas hyperactive AFPs bind also basal faces15,18 and, therefore, show higher TH activity. The depression of the freezing point in the presence of AFPs is commonly explained on the basis of the protein adsorption and the Gibbs-Thomson effect.6 However, it was found that the action of some AFGPs could not be fully explained within the framework of the GibbsThomson model.19 In spite of the fact that every AFP is expected to modify the growth kinetics and shapes of ice crystals in a specific way due to its unique characteristics of the adsorption-desorption processes on ice crystal surfaces, many studies have focused only on the TH activity of different AFPs without paying attention to growth rates and shapes of ice crystals. The available data on the ice crystal shapes in the presence of AFP-III are limited to the smallest crystal size of 10−40 µm and specified protein concentration.20 Only one study21 reported the measurement of the growth rate of the basal faces of ice, however, restricted to the AFP-III concentration of 5 µg/ml. Regarding other AFPs, we found published results on the growth rates of ice crystals in the a direction only for AFGP solutions.22 Therefore, our research is the first aimed to explore in detail the effects of AFP-III on the morphology and growth kinetics of ice crystals over a range of supercoolings and protein concentrations, and to reveal the specificity and the action mechanisms of AFP-III.

EXPERIMENTAL TECHNIQUE Ice crystals were grown in a laboratory designed observation cell (Fig. 1) filled with an AFPIII aqueous solution with a concentration of 0−800 µg/ml. The detailed information about the


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construction and principles of the function of the cell can be found in.23,24 The volume of the growth chamber was about 1 cm3, and the accuracy of temperature control was ± 0.02 K. Fresh pure water with a resistivity of 18 MΩ·cm was used for the preparation of the AFP-III solutions. Commercially available purified AFP-III extracted from Anarhichas lupus was purchased from A/F Protein Inc. and used without further purification.

Figure 1. Construction of the cell for observations. (1 − growth chamber, 2 − tripled glass windows, 3 − Peltier elements, 4 − water heat exchangers, 5 − capillary holder, 6 − tubes for solution supply, 7 − inlet for cold spray, 8 − area with seed ice crystals, 9 − glass capillary, 10 − thermistor, 11 − ice crystal).

The cell and tubes were washed with 0.1 mol/l nitric acid to delete residual AFP-III remained in the previous experiment. Then, the chamber was filled with the AFP-III solution and cooled down to a certain temperature in the range of −0.02 ~ −1.5 °C. After that, cold spray was carefully injected through the inlet 7 to freeze the liquid in this part of the capillary and to nucleate ice crystals. The temperature in this area was much lower than that in the chamber, and the ice micro-crystals inside the capillary grew towards the growth chamber. During this process,


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because of the geometrical selection only one ice single crystal remained, and finally appeared on the tip of the capillary. We could keep the temperature inside the chamber constant until the moment when the growing ice single crystal reached the inner wall of the chamber. After that, ice rapidly covered the inner wall. As a result, temperature sharply increased because of the release of large amount of latent heat, and we had to stop the experiment. Before starting a new experiment, we increased the temperature to melt all ice crystals in the chamber. The images of the growing ice crystal were recorded by a computer video system as a sequence of graphic files which were used for the calculation of growth rates. Depending on supercooling and AFP-III concentration, an observed ice crystal of hexagonal modification had a plate-like or planar dendritic shape. In Fig. 2a, the crystallographic a and c directions were located parallel and perpendicular to the crystal plane, respectively. When a crystal with a clearly visible shape started to form, we first rotated the capillary to orient the basal face perpendicular to a screen, as shown in Fig. 2b, and recorded a side-view image of the ice crystal. This picture helped us to determine the angle ϕ between the basal face and the capillary oriented parallel to the image (screen) plane (Fig. 2b). We used this angle (usually it did not exceed 30 degrees) for the correction of the growth rates calculated from the sequence of crystal images. Then, we rotated the capillary by 90 degrees and recorded the subsequent growth process. The growth rate along the a axis was determined by ordinary optical microscopy from temporal change of a position either of a dendrite tip or a lateral surface of the disk (in the case of a disk-like shape). The description of the procedure of the growth rate calculation in the a direction can be found in our previous work.23 The growth rate along the c axis was measured by Mach-Zehnder interferometry. We used a laser diode with a wavelength of 670 nm and power of 5 mW for this purpose. An example of the interference picture of a growing ice crystal is shown


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in Fig. 2a. Here, two opposite basal faces {0001} are located in the image plane, and the laser beam passes through the crystal perpendicular to the screen. The interference fringes moved when the thickness of the crystal changed. We used a time dependence of the intensity I(t) of the laser irradiation passed through the crystal in order to find the growth rate in the c direction. The changes in I(t) as a function of time were calculated from the time sequence of recorded images (Fig. 2c).

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c


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Figure 2. (a) Interferogram of an ice crystal growing at supercooling ∆T=0.1 K; (b) determination of the inclination of an ice crystal; (c) schematic representation of the time dependence of the intensity I(t) of laser irradiation transmitted through the crystal at the designated point O.

The change in the intensity I(t) for one period ∆t corresponds to the change of the crystal thickness in the c direction for a value ∆h, which is determined by the following expression ∆h =

λ n w − ni

,

where λ is the wavelength of laser irradiation, nw and ni are the refractive indices of water and ice, respectively. The refractive indices are nw = 1.3327, ni = 1.3078 at the temperature T = 273.15 K. The variation of the refractive indices of water and ice within the temperature range of 272.15−273.15 K is negligible. Thus, the changes in the intensity for one period correspond to the change in the crystal thickness ∆h ≈ 26.9 µm (λ = 670 nm). The crystal thickness depends on the development of the two opposite basal faces. The normal growth rate of the basal face can be calculated as Rc = 0.5·∆h/∆t. This formula gives the averaged growth rate because of the simultaneous record of the growth of the two opposite (0001) faces. In the majority of the experiments, the crystallographic a direction of a growing ice crystal was oriented parallel to the capillary, and the c direction was nearly perpendicular to the capillary.


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When supercooling of AFP-III solution was set below some critical level ∆Tcr = Tm − Tcr, where Tm = 273.15 K was the melting point, an ice crystal stopped growing in the a direction. The critical supercooling ∆Tcr above which the crystal resumed growing in the a direction was determined in the following way. At first, temperature was stepwise increased close to the melting point to ensure the prismatic faces stopped their advancement. Then, after 3 minutes to 2 hours (depending on the experiment) of waiting, supercooling was gradually increased by 0.015 K steps. The waiting time between adjacent steps was about 20−25 seconds.

EXPERIMENTAL RESULTS Morphologies of ice crystals The images in Fig. 3 show various morphologies of ice crystals grown under different supercooling ∆T and AFP-III concentration CAFP-III. An ice crystal exhibited a rounded-disk shape in pure water and at small supercoolings up to 0.2 K (Fig. 3a1). Both planes of the disk were the {0001} basal faces which were perpendicular to the c axis. The crystallographic a axis was parallel to the basal faces. The side surface of the disk-like crystal was not faceted under this condition. Further increase in supercooling of pure water led to the formation of planar dendrites with the branches parallel to the {0001} faces (Figs. 3a2-a3). The dendrite tip grew along the crystallographic a direction. The side surface of the disk-like crystal became faceted even at CAFP-III = 1 µg/ml and consisted of twelve prismatic faces (Fig. 3b1). The growth morphologies of the crystals were gradually transformed from a bulk disk-like shape to planar dendrites and needles with increase in supercooling and protein concentration (Figs. 3a1-e3). The dendrite tips were slightly polygonized in the AFP-III solutions, whereas in pure water they were rounded. A very ragged


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side surface was formed within the supercooling range of ∆T = 0−0.2 K and at CAFPIII

≈100 µg/ml (Fig. 3c1). The growth in the a direction almost ceased at CAFP-III >100 µg/ml

(Figs. 3d1-e1). When supercooling was 0.7−1.0 K and CAFP-III was about 800 µg/ml, needle crystals elongated along the c axis appeared (Fig. 3e3).


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Figure 3. Growth shapes of ice crystals in AFP-III aqueous solutions at different supercooling ∆T and AFP-III concentration CAFP-III. Crystallographic orientations are shown in the images.


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In contrast to the growth in pure water where the basal face was very flat, AFP-III within the concentration rage of 5−20 µg/ml caused the formation of clearly visible macrosteps on the basal face (Fig. 4a). During the growth along the c axis in AFP-III solutions at small supercoolings, the bipyramidal faces frequently appeared in the crystal habitus (Fig. 4b). Sometimes exposure of the ice crystal in the 20 µg/ml AFP-III solutions at low supercoolings below ~0.2 K led to the formation of hexagonal pits (marked by arrows in Fig. 4c) on the basal faces as reported by Inada et al.21 The side walls of these pits were bipyramidal surfaces.

a

b

c

Figure 4. Ice crystals in AFP-III solutions: (a) macrosteps on the basal face at CAFP-III = 5 µg/ml; (b) formation of the basal (1), bipyramidal (2) and prismatic (3) faces at CAFP-III = 5 µg/ml and ∆T = 0.09 K; (c) hexagonal pits on the basal face at CAFP-III = 20 µg/ml and ∆T = 0.15 K.

Growth rates of ice crystals The normal growth rates R of ice crystals in the crystallographic a and c directions were measured at various ∆T and CAFP-III to study the effect of AFP-III on ice crystallization. Every experimental point in Figs. 5a-b and Figs. 6a-b shows the average value of the results of three to


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seven experiments. The areas of the existence of the different growth shapes of ice crystals are also shown in Fig. 5a and Fig. 6a. Thus, at supercoolings ∆T = 0.2−0.4 K the bulk and wellfaceted crystals grew. At higher ∆T, the planar dendrites with large or small branches were formed. Irregular dendrites and needle crystals appeared at larger concentrations of AFP-III. Fig. 5b shows that all Ra(∆Т) kinetic curves obtained in the presence of AFP-III had certain ranges of supercooling ∆Т ≤ ∆Tcr where the growth was completely blocked. When supercooling was above the critical value ∆Tcr, the growth in the a direction started suddenly with increasing ∆T. The growth rate at the same ∆T became higher with increasing protein concentration at supercoolings above ∆Tcr. The data in Fig. 6b demonstrate that the growth of the basal face also ceased below certain critical supercoolings. When supercooling of the AFP-III solution exceeded the critical value, the basal face became to grow faster with increasing AFP-III concentration (Fig. 6a). At CAFPIII

= 200 µg/ml, the growth in the c direction was extremely fast resulting in the formation of the

needle-shape crystals along the c axis (Figs. 3e2-e3). According to our experimental data, the growth rate of the dendrite tip versus supercooling in pure water could be described by the function Ra0(∆T) = 88·∆T 1.79 [µm/sec].


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b


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Figure 5. (a) Growth rates of ice crystals in the crystallographic a direction; (b) enlarged area A shown in panel (a) with growth rates at ∆T = 0−0.4 K. AFP-III concentration: 0, 1, 5, 20, 100 µg/ml.

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b Figure 6. (a) Growth rates of ice crystals in the crystallographic c direction (basal face); (b) enlarged area B shown in panel (a) with growth rates at ∆T = 0−0.4 K. AFP-III concentration: 0, 1, 5, 20, 100, 200 µg/ml.

For the growth of the basal face in pure water we obtained the following relation between the growth rate and supercooling Rc0(∆T) = 1.07·∆T 1.04 [µm/sec].

Critical supercooling in AFP-III aqueous solutions Since the molecular weight of AFP-III was 6.5 kDa, the colligative freezing point depression of ice in the aqueous AFP-III solutions could be neglected. For example, at the maximal CAFP-III of 800 µg/ml used in the experiments, the possible decrease in the melting point according to the


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formula dTm=1.86·C (C is the concentration of the AFP-III solution in mol/kg H2O) was dTm=2·10−4 K: i.e. two orders of magnitude smaller than the accuracy of the temperature control in the experiment. The freezing point of the AFP-III aqueous solutions was evidently lower than that for pure water. It was found that some critical supercooling ∆Tcr = 273.15 − Tcr existed below which the growth of the ice crystal ceased. In order to measure ∆Tcr, we gradually decreased the temperature from the value near the melting point. Since the growth rate in the a direction is about two orders of magnitude higher than that in the c direction (Fig. 5 and Fig. 6), the thermal hysteresis activity of AFP-III is dominated by the suppression of the growth in the a direction. Hence, we measured the critical supercooling only in the a direction. The value of ∆Tcr for the growth in the a direction increased non-linearly with AFP-III concentration (Fig. 7). When supercooling exceeded ∆Tcr, the prismatic faces resumed the growth. The recovery of the growth in the a direction began from the moment when a macrostep suddenly started its movement. The example of the successive stages of this process is shown in Fig. 8. Here, the macrostep emerged at the junction (marked by an ellipse) of the prismatic and lower basal faces. Then, it started to move towards the prismatic surface and caused the formation of new macrosteps there with the further recommencement of the growth. The lines of macrosteps on the prismatic faces were oriented mainly along or slightly aslant to the c axis.


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Figure 7. Critical supercooling ∆Tcr for the growth in the a direction in AFP-III solutions.

The basal faces could continue advancing even after the stoppage of the growth of the prismatic faces. Many rough macrosteps appeared on the basal face at supercooling smaller than ∆Tcr. When ∆T was close to ∆Tcr, the macrosteps visible in optical microscope disappeared, and the growth of the crystal along the c axis became pronounced. In a series of the experiments, we intentionally kept the ice crystal at small supercoolings below ∆Tcr for various periods from 3 minutes to 2 hours. Then, we decreased the temperature below Tcr to test whether the ∆Tcr depended on the exposure time of a non-growing crystal in the a direction in AFP-III solutions. We found that the critical supercooling for the prismatic faces did not depend on the exposure time of 3 minutes − 2 hours within the accuracy of temperature measurements.


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Figure 8. The recovery of the growth in the a direction after the movement of the macrostep marked by an arrow: 1 − basal face {0001}; 2 − prismatic face {10 1 0}; ∆T ≈ 0.09 K; CAFP-III = 100 µg/ml; (a) 0, (b) 1, (c) 2, (d) 3, (e) 5, and (f) 6 sec.

DISCUSSION The observed morphological changes in the shapes of ice crystals in AFP-III solutions (Fig. 3) show that AFP-III drastically affects the crystallization processes of ice. The rounded faces were changed to faceted faces in the crystallographic a direction even at 1 µg/ml of AFPIII. The growth was stopped at ∆T < ∆Tcr. The regular growth was disturbed at CAFPIII

≥ 100 µg/ml. These facts clearly indicate that AFP-III molecules are adsorbed on the prismatic

faces of ice crystals. Although it has been previously discovered by fluorescent microscopy25 that AFP-III molecules do not adhere to the ice basal planes, the results of our current study suggest the existence of a certain amount of interaction between AFP-III and the basal faces, as well. For example, we did not detect any growth of the basal faces at low supercoolings in the presence of AFP-III. Also we found that rough macrosteps started to appear on the basal faces when CAFP-III became 5 µg/ml or higher (Fig. 4a), whereas this surface was very smooth in pure water. Inada et al.21 observed the appearance of faceted pits on the basal faces of ice growing in the AFP-III solution. According to the molecular dynamics simulation studies at water-ice interfaces,26 the basal faces seem to be flat at the molecular level and grow by the layer-by-layer mechanism. Thus, we assume that in our case the basal faces of the ice crystals in pure water also have lowheight or elementary steps which, however, are invisible by ordinary optical microscopy. In the AFP-III solution, the AFP-III molecules do not adhere to the basal planes,25 but they can be attached to the edges of steps on the basal faces, depressing their lateral movement and


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subsequently forming step bunches and rough macrosteps (Fig. 4a), since the structure of the step edges on the basal faces is similar to that of the prismatic faces. The deceleration of the step movement on the basal face due to the interaction with AFP-III molecules leads to the appearance of the bipyramidal faces in crystal habitus (Fig. 4b) and explains the formation of needle crystals at high AFP-III concentrations of 400−800 µg/ml (Fig. 3). The shape of the ice crystal shown in Fig. 4b has two hexagonal bipyramids. In contrast, in the presence of other isoforms of AFP-III, the upper and lower pyramids of an ice crystal can be shifted relatively with each other by 30 degrees rotation on the c axis.27 This difference is due to the amino acid changes in the molecule structure of AFP-III isoforms. The formation of the hexagonal pits at low supercoolings (Fig. 4c) is also caused by the adsorption of AFP-III at the step edges on the basal faces. Inada et al.21 observed the pits of similar geometry. The data in Fig. 5b, Fig. 6b and Fig. 7 show that AFP-III molecules suppress the growth of ice in both the a and c directions under low supercoolings. In contrast, AFP-III promotes crystal growth when supercooling exceeds the critical value, i.e. the growth rate of the prismatic and basal faces increases with the increase in AFP-III concentration at higher supercoolings. At first, let us discuss the promotion of ice growth by AFP-III. We suppose two possible reasons to explain this phenomenon. The first one is that AFP-III molecules being adsorbed on the crystal decrease the surface free energy of the ice-AFP-III solution interfaces. When the growth occurs by the two-dimensional nucleation mechanism, the activation energy barrier to create a nucleus is directly proportional to the square of the surface free energy. Hence, the decrease in the surface free energy results in the promotion of the growth. In the case of the spiral growth mechanism, the normal growth rate of the face is expressed as28


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R=

mh v, ωα T 0 19 + 2L h0 ∆T

(1)

where mh is the screw component of the Burgers vector, m is the number of elementary steps, h is the height of elementary step, ω is the volume of a water molecule in a crystal lattice, α is the specific surface free energy of the step edge, T0 = 273.15 K is the melting point, and h0 is the specific latent heat of fusion, 2L is the perimeter of the contour surrounded the outcrops of the dislocation group, v is the velocity of step movement. Thus, with the decrease in the surface free energy one should expect the increase in the growth rate at a certain supercooling ∆T. Hence, in the cases of both the growth mechanisms, the decrease in the surface free energy causes the promotion of the growth. The suppression of the recrystallization processes of polycrystalline ice by AFP in the references29−33 is another evidence that AFPs decrease the surface free energy of ice-water interfaces. The second reason for the promotion of ice growth at high supercooling of the AFP-III solutions in our study is due to the change in the crystal morphology. As it can be seen in Fig. 3, the crystal shapes transform from the bulk crystal to planar dendrites, irregular dendrites and needles with the increase in ∆T and CAFP-III. The branches of the dendrites in the AFP-III solutions are thinner than those in pure water. Therefore, the shape of the ice crystals was changed so that the ice crystals had larger amount of openings that gave better conditions for the dissipation of latent heat from the growing crystal and, finally, resulted in higher growth rate. Indeed, the growth rate of the basal face (Fig. 6a) jumped up within the 0.2−0.5 K supercooling range in which the bulk crystals became dendritic. In addition to the promotion so far discussed, AFP-III also suppresses the growth of ice at low supercoolings. The suppression of ice growth by AFP-III can be understood on the basis of the


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classical pinning model by Cabrera-Vermilyea34 previously applied to the explanation of the effect of angstrom size ionic impurities on inorganic crystal growth.35−37 According to this model, AFP-III molecules adsorbed on ice surfaces can be considered as obstacles for the growing surface. The parts of the crystal surface penetrating through the adsorbed AFP-III molecules become more curved. From the Gibbs-Thomson law, the curved surface requires higher supercooling to continue the growth. The larger the concentration of AFP-III, the smaller is the average distance between AFP-III molecules adsorbed on the ice surface. Therefore, the critical supercooling increases with the increase in CAFP-III. The data in Fig. 7 confirm this tendency. The sharp rise in the growth rates in Fig. 5b near the critical supercooling is explained by the break of the surface pinning by the adsorbed AFP-III molecules. The ∆Tcr values in Fig. 7 for the a direction are bigger than the critical supercoolings taken from the growth rate curves Ra(∆T) in Fig. 5b at the same AFP-III concentrations. This difference is due to the following reason. In Fig. 7, in order to find ∆Tcr, we increased the supercooling stepwise from the value near the melting point to the ∆Tcr. But in Fig. 5b, the supercooling was changed in the opposite direction from high to lower values. When the supercooling is bigger, the growth rate is higher, resulting in the shorter exposure time of a crystal surface to an AFP-III solution, and hence, the smaller amount of the AFP-III adsorbed on this surface. Therefore, during the decrease in the ∆T (Fig. 5b), the surface density of adsorbed AFP-III was relatively small at the beginning and then gradually increased as ∆T decreased. In contrast, during the increase in the ∆T (Fig. 7), the surface density of adsorbed AFP-III was relatively high at the beginning, resulting in the larger amount of the suppression of the growth than in the opposite case (Fig. 5b). Thus, AFP-III causes the appearance of hysteresis for the growth in the a direction.


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An existence of the critical supercooling on the Rc(∆T) curves in Fig. 6b proves that AFP-III can block the growth of the basal faces, as well. Since AFP-III molecules do not bind terraces of the basal faces of ice crystals25, we conclude that the inhibition effect of AFP-III for the growth in the c direction is related to the adsorption of AFP-III on the step edges of the basal faces. When all steps are pinned by AFP-III, the growth of the basal face is still possible due to the formation of new layers of ice by two-dimensional nucleation on the terraces between the steps on the basal plane. In contrast to the basal faces, the prismatic and bipyramidal surfaces can collect larger amount of AFP-III adsorbate25. Therefore, due to the specificity of the AFP-III adsorption on the ice surfaces with different indices, the TH activity of AFP-III for the a direction should be higher than those for the c direction. At this time, we do not have any experimental data on the distances between adjacent AFP-III molecules adsorbed on the surface of ice crystals. Hence, we can not analyze the results in Fig. 7 quantitatively. The shape of the dependence of ∆Tcr(C) represented in Fig. 7 qualitatively agrees with the data for other AFPs (TmAFP,5,15 AFGP,38 AFP-I,39 AFP-II40,41), but our experimental values of critical supercooling are smaller than, for example, those reported in the work42 for AFP-III. This is probably due to the non-use of buffer solutions in this study. The measurements in the studies25,42 were performed in the AFP-III solutions with a saline buffer. But, we have confirmed in the trial experiments that the buffer components give additional contribution to the total depression of the freezing point of AFP aqueous solutions. Furthermore, Bayer-Giraldi et al.43 showed effects of salinity on AFP activity with the enhancement of the thermal hysteresis gap due to the increase in the salt concentration. Therefore, we used pure water instead of the saline buffer in our experiments. It was possible because the antifreeze activity of AFP-III molecules remained constant within a wide pH range of 2−11.44 The ∆Tcr values in Fig. 7 for


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AFP-III concentrations of 400 and 800 µg/ml are smaller than the results of the study45 because of the absence of the saline buffer in our solutions. The data in Fig. 7 can not explain the square root dependence on CAFP-III that was observed in the previous study.45 In AFP-III solution, the basal faces of an ice crystal can essentially affect the growth process of the prismatic faces by the following mechanism. The macrostep appeared on the basal face has a probability to reach the prismatic face blocked by AFP-III and cause the formation of growing steps on the prismatic surface. We found that the prismatic surface usually resumed growth at ∆Tcr after the appearance of macrostep at the junction of the basal-prismatic faces (Fig. 8). Thus, the critical supercooling for the prismatic faces is expected to be lower when they are in contact with the bulk solution. The clear correlation between the ∆Tcr values for the prismatic faces and AFP-III concentration was not found in the reference25 because both the basal and prismatic faces of ice crystals contacted with the solution. In our study, we measured the ∆Tcr for the prismatic faces when the ice crystal was located inside the capillary near the tip, so that the growth of the basal faces was blocked by the capillary walls. As a result, the critical supercooling for the prismatic surface in the capillary was about 0.2 K (Fig. 7) and exceeded the ∆Tcr = 0.09 K measured on the crystal with natural shape (Fig. 8) at the same AFP-III concentration. When all faces of an ice crystal are in contact with AFP-III solution, the value of critical supercooling should be smaller for the ice crystals of bigger size. The larger the basal face of an ice crystal, the bigger the total length of the basal-prismatic junction line, and consequently, the higher the probability of onset of growth at smaller ∆Tcr. This conclusion agrees with the results of the study25. In our experiments, the exposure of the ice surface in the AFP-III solutions during 3 minutes to 2 hours did not influence the value of critical supercooling for the a direction. We can explain


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this fact by quick adsorption of AFP-III molecules. Our results agree with the observations by Drori.15 The correlation between ∆Tcr and the exposure period varied from 2 to 60 minutes also was not found in that work, but ∆Tcr depended on supercooling at which the ice crystal was preserved. Opposite results were reported in the study by Takamichi et al.,42 where nfeAFP8, an isoform of AFP-III, was used. After the storage of a non-growing ice crystal in the nfeAFP8 solution at ∆T

Growth of Ice Crystals in the Presence of Type III Antifreeze Protein

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