Crystal-plane-dependent effects of antifreeze glycoprotein impurity for ice growth dynamics

Abstract

An impurity effect on ice crystal growth in supercooled water is an important subject in relation to ice crystal formation in various conditions in the Earth's cryosphere regions. In this review, we consider antifreeze glycoprotein molecules as an impurity. These molecules are well known as functional molecules for controlling ice crystal growth by their adsorption on growing ice/water interfaces. Experiments on free growth of ice crystals in supercooled water containing an antifreeze protein were conducted on the ground and in the International Space Station, and the normal growth rates for the main crystallographic faces of ice, namely, basal and prismatic faces, were precisely measured as functions of growth conditions and time. The crystal-plane-dependent functions of AFGP molecules for ice crystal growth were clearly shown. Based on the magnitude relationship for normal growth rates among basal, prismatic and pyramidal faces, we explain the formation of a dodecahedral external shape of an ice crystal in relation to the key principle governing the growth of polyhedral crystals. Finally, we emphasize that the crystal-plane dependence of the function of antifreeze proteins on ice crystal growth relates to the freezing prevention of living organisms in sub-zero temperature conditions.

This article is part of the theme issue ‘The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets’.

1. Introduction

Crystal growth and morphology are modified by various external factors such as diffusion field, convection (gravity) and impurities [1]. The effect of impurities is very important when discussing various aspects of crystals such as their shape, internal structures and morphological instabilities [2]. The impurity effect is also important for industrial crystallization because it controls the size distribution and shape of crystalline particles. Recently, much interest has been shown in crystallization in living organisms, which is controlled by biological macromolecules such as proteins and amino acid molecules [3]. Consequently, the impurity effect of biological molecules, which is the essence of the so-called bio-mineralization, is a fundamental but advanced topic in the current research field of crystal growth. In order to clarify the impurity effect, it is essential to precisely measure the growth rate as a function of growth conditions such as the temperature and impurity concentration. However, it is easier said than done. Actually, it is difficult to obtain precise growth rates that are sufficient for discussing impurity effects for crystal growth because growth rates are easily changed by other external factors such as convection, which occurs around the growing crystal under the condition of gravity.

Impurity effects for ice crystal growth are also very important during the ice formation process in nature. For example, sea ice formation, inhibition of freezing living bodies and formation of frozen foods are basically controlled by inorganic or organic molecules added as an impurity [4]. It is known that if we use biological molecules as an impurity for ice crystal growth, the impurity effect for ice crystal growth is more critical than that in the case of inorganic molecules. In this review article, we discuss the impurity effect for ice crystal growth in supercooled water containing an antifreeze glycoprotein 7–8 (abbreviated as AFGP) as an impurity. This protein is well known as one of the functional proteins that control ice crystal growth and prevent freezing of living bodies in a sub-zero temperature environment [5–10]. In order to understand the antifreeze mechanism, we have measured the growth rates for both basal {0001} and prismatic $\{10\overline{1}0\}$ faces during free growth of ice crystals in supercooled water containing an antifreeze glycoprotein. We also discuss the functions of antifreeze glycoproteins for ice crystal growth and the dynamic mechanism of ice growth inhibition. Hereafter, a water sample containing AFGP molecules is called an AFGP solution. Note that our experiments are not on the solution growth of ice but on the melt growth of ice.

2. Biological macromolecules with an antifreeze function

There exist at least five distinct classes of these proteins found in polar fish bodies, ranging in structure from a short α-helical rod to extended helices and even larger globular forms with distinct compositions [5]. Here, we focus on the most popular antifreeze glycoprotein found in fish serum. It is well known that ice crystals growing in pure supercooled water take on thin circular discs or thin dendrites depending on the supercooling temperature [11–15]. In contrast to this, the growth forms in AFGP solution become highly faceted and form needle-type crystals, greatly depending on the concentration of AFGP and the supercooling. It means that the modifications of crystal forms occur via some interaction between the adsorbed AFGP molecules and the ice crystal at the ice/water interface.

The relationship between the supercooling of AFGP solution and the ice crystal morphology is summarized as follows:

• (1)The existence of AFGP molecules lowers the freezing temperature (T_f) of water, inhibiting the growth of existing ice crystals, but keeps the melting temperature (T_e) of ice at the equilibrium melting point, as shown schematically in figure 1.
• (2)In the temperature region between T_e and T_f, which is called the ‘thermal hysteresis’ region, the ice crystals take on dodecahedral shapes surrounded by 12 pyramidal $\{10\overline{1}1\}$ faces with lengths of a few tens of micrometres at most, and the growth completely stops. Many ice particles with this crystalline shape are actually observed in the blood of fish living in a sub-zero temperature environment [16].

Figure 1.

Schematic illustration to explain the establishment of freezing inhibition by antifreeze proteins. The solid and broken lines with arrows in the illustration indicate the cooling and heating processes of the AFGP solution, respectively. The water never freezes in the temperature range between the equilibrium melting point, T_e, and the freezing temperature, T_f. When the temperature reaches T_f, the water suddenly starts to freeze. This temperature range between T_e and T_f is defined as the thermal hysteresis region. It has been known that many ice particles with a dodecahedral shape, as shown in the centre of this figure, are actually observed in the blood of living organisms in this temperature range. (Online version in colour.)

3. Importance of growth rate measurements to clarify impurity effect

In general, the growth rate of a crystal varies as function of its position on a surface and growth time as shown in figure 2. The crystal morphology at any time is determined as a consequence of the accumulation of these crystal-plane-dependent and/or time-dependent growth rates. It should be noted that, for example, morphological instability at the growing surface is mainly related to the growth rate difference according to positions on the surface. In contrast to this, the impurity effect causes change in the growth rate at an arbitrary point as a function of growth time, because growth rate modification by an impurity depends on the number of adsorbed impurity molecules that can work as pinning points for growth step propagation on a growing interface. Consequently, precise measurements of growth rates at any position and time are essential for understanding the mechanisms of such varied phenomena related to the crystal growth as the morphological instability and the impurity effect.

Figure 2.

Schematic illustration to explain the factors that control the growth rates of crystals. Normal growth rate (V) is determined as functions of the position (p) along the crystal surface and the growth time (t). Growth rate change mainly depending on the surface position triggers morphological instability, but the impurity effect is related to the growth rate change depending on the growth time. M-S instability means Mullins–Sekerka instability [17]. (Online version in colour.)

4. Growth inhibition for prismatic faces by AFGP molecules

Growth experiments of an ice crystal in a growth cell with water containing fluorescence-labelled protein molecules are useful for observing the growth form and the distribution of molecules near the growing ice/water interfaces at the same time. Zepeda et al. [18–20] conducted experiments on free growth of single ice crystals in supercooled water containing 5 µg ml⁻¹ of an AFGP labelled by fluorescein isothiocyanate (FITC), while the supercooling temperature of the AFGP solution was kept at less than 0.05 K.

Figure 3a shows a frame captured from a video recording ice crystal growth at the tip of a glass capillary, observed by a laser confocal fluorescent microscope. The ice crystal takes the form of a thin hexagonal plate surrounded by basal and prismatic faces. The most notable characteristic is that the prismatic faces indicated by 1, 3 and 4 are bordered by bright rims along the faces and their growth is completely stopped, but no bright rim is seen along prismatic face 2, which continuously grows. This observation directly shows that inhibition of growth for the prismatic face is caused by the interfacial adsorption of AFGP molecules. Figure 3b shows the profile of average concentrations along the rectangle indicated as ‘b’ in figure 3a, which was calculated from the intensity of fluorescent emission in the laser focal region of 100 µm in thickness, as illustrated in figure 3c. The local peak at the surface originates from the adsorbed AFGP molecules on the prismatic faces located in the direction perpendicular to the picture.

Figure 3.

Concentration distribution of AFGP 7–8 molecules during the growth of an ice crystal. (a) A snapshot of an ice crystal in the form of a hexagonal plate growing in an AFGP solution at a concentration of 5 µg ml⁻¹. The AFGP samples used in this experiment were purified from the Antarctic fishes and consumed from the A/F Protein Inc. Supercooling temperature of the solution sample was 0.05 K at the beginning of ice growth. This image is a snapshot taken from a video movie recorded by a confocal and fluorescent microscope system. The fluorescent intensity depends on the spatial number density of FITC-labelled AFGP molecules. The small picture shows a side view of the ice crystal. The movie corresponding to this snapshot has been shown in the supplementary data of [18]. (b) AFGP concentration distribution along the longer direction of the rectangular region ‘b’ indicated in (a). An intensity peak observed at the interface region is originated from AFGP molecules adsorbed on the prismatic faces. (c) Schematic illustration of the side view of an ice crystal. The thickness of the laser focal region for the confocal optical system was about 100 µm, and the thickness of the ice crystal was 40 µm. Consequently, the fluorescent intensity at an ‘ice + solution’ region was about 60% of that at a solution region. Modified from [18]. (Online version in colour.)

Zepeda et al. [18] also estimated the adsorption density on the prismatic faces based on the fluorescent intensity profiles and reported that the average distance between the nearest neighbouring AFGP molecules was about 21 ± 4 nm in this particular case, which was much larger than the diameter of AFGP molecules (about 3 nm). Thus, the prismatic faces are not completely covered by the adsorbed AFGP molecules. The coverage by AFGP molecules is only less than 10% for the prismatic faces.

The further growth process of this ice crystal is shown as successive pictures in figure 4a–c. The prismatic face indicated by 2 continuous advances in the growth direction perpendicular to this face and then the surface areas of its neighbouring halted faces, 1 and 2, expand. As a result, the advancing prismatic face, 2, disappears from the external shape of the crystal. It is to be emphasized that, at this moment, the prismatic face indicated by 3, for which growth halted suddenly, started to grow again as shown in figure 4c, and the bright rim of the fluorescent emission simultaneously disappeared at this face. Figure 4e shows the fluorescent intensity profiles in front of prismatic face 3 as a function of growth time. The increase of the AFGP concentration was clearly observed in front of face 3 in the profile indicated by ‘b’ (yellow line). This result strongly suggests that AFGP molecules adsorbed on face 3 desorbed on starting the regrowth. If the adsorbed AFGP molecules are incorporated into the crystal after the beginning of regrowth, we may observe the fluorescent image inside the crystal. However, we never observe such an image inside the crystal. Namely, these observations indicate that the adsorption of AFGP molecules on the prismatic faces may occur in a reversible manner. A recent computer simulation study carried out by Mochizuki et al. [21] also indicated reversible adsorption of AFGP molecules on prismatic faces. These results also indicate that the growth of prismatic face in an AFGP solution may occur in a periodically varying manner, that is, the growth rates of prismatic faces are periodically changed.

Figure 4.

Growth process of an ice crystal in an AFGP solution and the diffusion process of AFGP molecules desorbed from prismatic faces. (a–c) Growth of an ice crystal proceeding with time. The prismatic face indicated by 2 continues to grow and finally disappears from the external shape of the ice crystal. At that moment, the other prismatic face indicated by 3, which has stopped growing, starts to grow again. This observation means that the growth of prismatic faces should be periodic. (d) Concentration profiles of AFGP in front of the prismatic face indicated by 3. When the growth of prismatic faces starts again, the AFGP molecules adsorbed on those faces are detached and diffuse away in the solution in front of the growing faces. The concentration increase in front of the interface is clearly observed in the profile just before the restart of growth, which is indicated by ‘b’. This result indicates that the AFGP molecules are not incorporated into the ice crystal. (Online version in colour.)

On the other hand, Meister et al. [22] recently published a paper in which they report irreversible adsorption of AFGP molecules on ice/water interfaces based on the results of microfluidic solution exchange experiments. Their results are completely different from the results described in the previous paragraph. Although they did not specify which crystallographic faces the AFGP molecules were adsorbed on, it seems that they observed adsorption of AFGP molecules on an ice crystal with a characteristic dodecahedral shape surrounded by pyramidal faces because the fluorescence image observed at the edge of the ice crystal does show a rather fat line in their picture (figure 1 of their paper [22]). Consequently, we can imagine that the irreversible adsorption preferentially occurred on pyramidal faces. It should be noted that the growth of faces with AFGP molecules irreversibly adsorbed may be completely stopped. Actually, computer simulation of ice crystal growth with the effect of antifreeze protein molecules carried out by Nada et al. [23,24] indicated that the molecules could be strongly adsorbed not on prismatic faces but on pyramidal faces.

5. Growth promotion for basal faces in AFGP solution

It is more difficult to measure the growth rates of basal faces than those of prismatic faces because special optical methods, using Mach–Zehnder or Michelson-type interferometers, are required for measuring the thickness of a thin circular or hexagonal plate. Consequently, results for the growth rates of basal faces have been limited. The first measurements for growth rates of basal faces were carried out for circular ice discs growing in supercooled pure water using a Mach–Zehnder interferometer in 1993 [12]. As an ultimate achievement, Furukawa et al. [25–27] carried out free growth experiments of ice crystals in supercooled pure water under a microgravity condition in the Japanese Experiment Module ‘Kibo’ of the International Space Station (abbreviated as ISS-KIBO) in 2008. Since the influence of thermal convection around a crystal during growth is completely avoided under a microgravity condition, they were able to perform accurate measurements of growth rates for basal faces.

Based on this technical development, free growth experiments on an ice crystal in supercooled AFGP solutions were also carried out in 2013 using newly developed space apparatus. Here, we summarize the results of space experiments for growth rate measurements of basal faces in an AFGP solution [28].

Growth conditions for this space experiment are summarized as follows. First, we prepared a spherical growth cell with a diameter of 42 mm for the space experiments. Since it was difficult to exchange the AFGP solution sample in this growth cell in space, we used the same solution sample for all of the space experiments. Namely, the concentration of AFGP for this solution was fixed at 0.07 mg ml⁻¹, which was the most appropriate concentration for the space experiments and was determined on the basis of reference measurements carried out on the ground. Consequently, the only controllable growth condition was the bulk supercooling (ΔT_∞) of the AFGP solution at the beginning of crystal growth and it was adjustable between 0.1 and 0.5 K within an accuracy of 0.01 K. The experiments were repeated 124 times for various values of supercooling in this temperature range, and the growth of a single ice crystal surrounded by flat interfaces was observed at the tip of a glass capillary inserted into the centre of a spherical growth cell for each experiment. Because of the difficulty in optical adjustment in space, measurements of growth rates were completed for only 24 experiments, but the success rate of 20% was very high. Ice crystal growth was stably maintained in space over a period of 30 min (more than one hour in some cases) and was observed using a Michelson interference microscope combined with a phase contrast microscope, which was newly developed for use in space. The apparatus was loaded in an operational system (Solution Crystallization Observation Facility, abbreviated as SCOF) of ISS-KIBO. Although the function of the phase contrast microscope was completely lost shortly after the beginning of the experiments due to an accident that occurred in the SCOF system, interference fringe images for ice crystal growth, which provided the most important experimental results, were normally acquired.

Figure 5a shows a snapshot taken from a video obtained by the ISS experiments, and figure 5b shows the three-dimensional geometry of the ice crystal. These video images were subjected to time-space plot analysis, and the growth rates of basal faces were measured as a function of growth time. Figure 5c shows the growth rates as a function of growth time, which were estimated from the translational velocity of interference fringes appearing on the basal face. It should be noted that the normal growth rate of the basal face, $V_b^{\text{top}}$, periodically varied as a function of growth time. This is the first direct observation of the oscillatory growth of a crystal resulting from the interfacial adsorption of impurity molecules. Such oscillatory growth caused by periodic adsorption of impurity molecules has been pointed out as the origin for the formation of striations [29], which are striped patterns frequently observed inside mineral crystals such as agate. The results of mathematical analysis have also indicated the occurrence of oscillatory growth under the effect of impurity molecules [30–33]. However, there is a lack of adequate experimental evidence for oscillatory growth, because the convection caused by gravity may mitigate or modify this effect. Consequently, it was a great achievement that observations of this effect were first made possible under long-term microgravity conditions.

Figure 5.

Analysis of interference fringes observed on the basal faces of ice under the microgravity condition in ISS-KIBO. The AFGP concentration was 0.7 mg ml⁻¹ and the initial supercooling temperature was 0.3 K. (a) Snapshot of an ice crystal growing at the end of a capillary in the AFGP solution. Corresponding video is provided as Supplementary Video 1 of [28]. The region where the interference fringes lined up in parallel appear corresponds to the basal face. The fringes clearly observed on the top basal face come from the interference between the reflection from that face and a reference mirror. The bright region at the centre is caused by the overlap of images from the top and bottom basal faces. (b) Illustration of the three-dimensional geometry for the ice crystal shown in (a). This illustration was drawn from the arrangement of flat interfaces surrounding the external crystal shape based on the interference fringe images, in which only the top and bottom basal faces that orthogonally crossed the optical axis are visible. Numbers 1–4 indicate the corners of the crystal, and the places corresponding to the corners appear in the image in (a). Normal growth rate of this face, $V_b^{\text{top}}$, is estimated from the translational velocity of the interference fringes. (c) Growth rate of the basal face, $V_b^{\text{top}}$, as a function of growth time. Growth rates varied periodically and the time average of growth rate is shown by the broken line (0.58 µm s⁻¹), almost three to four times larger than that observed in pure water (about 0.17 µm s⁻¹)[28]. Details of experimental results are given in the literature [28]. (Online version in colour.)

The time average for the growth rate of basal faces was also estimated from the experimental results and we found that the average growth rates were 3–5 times larger than the growth rates measured for ice crystal growth in pure supercooled water. We thus concluded that the growth rates of basal faces were strongly enhanced by the effect of AFGP molecules. Since adsorbed impurity molecules are generally considered to work as ‘inhibitors’ of the crystal growth, this is a new finding with regard to the impurity effect for crystal growth.

6. Mechanisms of crystal-plane-dependent effect of AFGP molecules for ice crystal growth dynamics

Here, let us consider the mechanisms of the inhibition and promotion of growth by AFGP molecules adsorbed on prismatic and basal faces, respectively. First, we consider the mechanism of growth inhibition for prismatic faces. Based on the results of fluorescent observation as shown in figures 3 and 4, Zepeda et al. found that the spacing of adsorbed AFGP molecules was around 20 nm. The Gibbs-Thomson model predicts a 5°C lowering of the freezing temperature for this spacing. Despite the existence of many adsorbed molecules, the largest freezing depression observed was less than 1°C, contrary to prediction. This discrepancy was explained by the partial adsorption of molecules on prismatic faces. Namely, only the proteins first adsorbed are responsible for the inhibition of growth and subsequent over-adsorption does not play a role in the inhibition process.

The results suggest that the adsorption of AFGP molecules on prismatic faces occurs in a phased step from weak adsorption to strong adsorption, namely two-stepped reversible adsorption. The weakly adsorbed AFGP molecules do not work as pinning points for the advance of faces and can be reversibly desorbed from the face. In contrast, the strongly adsorbed molecules can work as pinning points. Figure 6 schematically shows the adsorption states of AFGP molecules at basal, prismatic and pyramidal faces. The illustration at the lower left of this figure shows that only the strongly adsorbed molecules contribute to the inhibition of growth of prismatic faces.

Figure 6.

Different effects of AFGP molecules adsorbed on basal, prismatic and pyramidal faces of an ice crystal. AFGP molecules preferentially adsorb on the pyramidal and prismatic faces. The adsorption on pyramidal faces is irreversible, but the adsorption on prismatic faces is reversible. Consequently, the growth of pyramidal faces will completely stop, whereas the growth of prismatic faces still continues slowly. AFGP molecules can also absorb along the edges of growth steps propagating on the basal faces, because the edge faces are composed of prismatic and/or pyramidal faces. These molecules can work as new sources of growth steps on the basal faces and their growth is strongly enhanced. Based on the crystal-plane-dependent functions of AFGP molecules, the fundamental relation for growth rates, $V_b\gg V_{\text{pri}}>V_{\text{pyr}}\sim 0$, is reasonably proposed. (Online version in colour.)

The behaviours of AFGP molecules on prismatic faces have been investigated by other experiments and computer simulations. For example, Uda et al. [34] confirmed by ATR-FTIR analysis of adsorbed AFGP molecules that the conformational change of adsorbed AFGP molecules may occur from the flexible extended helix to the α-helix in the wake of initial adsorption on the ice/water interface. As we already pointed out, molecular dynamics simulations also showed that molecules with α-helix conformation can be strongly adsorbed on the pyramidal face [23,24] and the adsorption of AFGP molecules on the prismatic faces [21] is reversible. These results strongly suggest the two-step reversible adsorption on prismatic faces, which should be crucial for understanding the adsorption–inhibition mechanism of AFGP molecules.

However, we consider the mechanism by which AFGP molecules promote the growth of ice basal faces. It is well known that ice morphology in an AFGP solution takes a polyhedral shape surrounded by two basal faces, six prismatic faces and trapezoidal pyramidal faces connecting the basal and prismatic faces (figure 1). AFGP molecules are thought to be adsorbed on prismatic or pyramidal faces, but not on basal faces, and to have the ability to smoothen the rough interfaces. It prompted us to speculate that AFGP molecules can be adsorbed on the edges of the growth steps propagating on the basal faces because those should be constituted by faces including prismatic and/or pyramidal faces. Since the average size of AFGP molecules (approx. 3 nm in length) is much larger than the height of the elementary step (0.37 nm) on the basal face, the adsorbed AFGP molecules would protrude from the growth steps and may work as sources of growth steps for the basal face, as shown schematically at the upper left of figure 6. This process may thus enhance growth rates through the adsorption–promotion effect of impurity molecules on crystal growth.

Finally, let us refer to the origin of the oscillation of growth rates induced by the adsorption of AFGP molecules. The mechanism previously discussed for growth oscillations has been based on growth depression due to the pinning effect of AFGP molecules adsorbed on the growing faces. Oscillatory growth observed on prismatic faces may be explained by this mechanism, but it is no longer applicable to the growth oscillation observed on the basal faces, which is induced by the growth promotion of AFGP molecules. We should propose a new mechanism to explain the growth oscillation based on the adsorption–promotion effect of impurity molecules. Although we do not further discuss this issue here, we would like to point out that the kinetic processes originating from the interactive variation between interfacial supercooling (i.e. the driving force) and the concentration of adsorbed impurity molecules at the interface will become a key component of the new model.

7. Relationship between ice crystal shape and freezing prevention of living organisms

As stated in the previous section, AFGP molecules adsorbed on the faces of an ice crystal affect in the different mode for the growth kinetics of each face. The molecules are reversibly adsorbed on prismatic faces but irreversibly adsorbed on pyramidal faces. Furthermore, the growth for both pyramidal and prismatic faces was strongly depressed but that for the basal faces was strongly enhanced. As a consequence, we can expect that the magnitude relationship for normal growth rates among these three crystallographic faces will be given by $V_b\gg V_{\text{pri}}>V_{\text{pyr}}\sim 0$, where V_b, V_pri and V_pyr are the normal growth rates of basal, prismatic and pyramidal faces, respectively, as shown in figure 7.

Figure 7.

Illustrative process for the formation of an ice crystal with a dodecahedral external shape based on the fundamental relation $V_b\gg V_{\text{pri}}>V_{\text{pyr}}\sim 0$. At the initial state, tiny ice crystals are nucleated in the water. At that moment, those crystals are surrounded by various crystallographic faces. The ice crystals are surrounded by faces with relatively slow growth rates, actually basal, prismatic and pyramidal faces. Finally, the basal and prismatic faces, which grow faster than the pyramidal faces, disappear from the external crystal form and then dodecahedral shapes surrounded by 12 pyramidal faces with the slowest growth rate are finally formed. In this figure, ice crystal shapes predicted from the other magnitude relationships for growth rates are shown at the bottom. Note that the dodecahedral shape is not formed in these cases. (Online version in colour.)

Now, let us consider how this magnitude relationship of growth rates is relevant to the ice crystal shapes. It is well known that many tiny ice particles with a dodecahedral shape (several tens of micrometres in size) surrounded by only pyramidal faces are observed in the blood of fish living in a sub-zero temperature environment, but they do not continue to grow. The reason why the dodecahedral ice particles can stably exist in serum is explained by a key principle governing the growth of polyhedral crystals: ‘Flat faces with faster growth rates are truncated by the faces with slower growth rates and finally the polyhedral crystal is surrounded by only flat faces with the lowest growth rates’. Based on this principle, we conclude that the formation of a dodecahedral ice shape is realized only when the growth rates for individual faces maintain the relationship of $V_b\gg V_{\text{pri}}>V_{\text{pyr}}\sim 0$. Furthermore, both angles of the basal-to-pyramidal faces and the prismatic-to-pyramidal faces are not right angles. Consequently, as shown in figure 7, all of the basal and prismatic faces on an ice crystal are truncated by the neighbouring pyramidal faces as they grow, and finally, both faces disappear from the external shape of ice crystals. As a result, a dodecahedral shape surrounded only by pyramidal faces with the slowest growth rate is formed. Since all of the faces with faster growth rates disappear from the external shape of the ice crystal, the further growth of the dodecahedral crystal is completely inhibited and the water is thus kept in a supercooled state. It should be noted that the growth enhancement by adsorbed AFGP molecules was not an obstructive factor but an absolute requirement for the development of the antifreeze function for these proteins.

8. Conclusion

The growth rates of prismatic and basal faces of ice crystals growing in supercooled water-containing AFGP molecules as an impurity were precisely measured by various methods including space experiments. As a result, the growth inhibition by the impurity effect was observed for the prismatic faces, but the growth enhancements and oscillatory changes of growth rates for the basal faces were elucidated for the first time. Namely, the AFGP impurity had different effects for ice crystal growth depending on the adsorbed crystallographic faces.

It was emphasized that the growth rates for the main crystallographic faces of an ice crystal, namely, basal, prismatic and pyramidal faces, should satisfy the magnitude relation of $V_b\gg V_{\text{pri}}>V_{\text{pyr}}\sim 0$ by the crystal-plane-dependent effects of antifreeze glycoprotein impurity. This relation was essential to form a dodecahedral external shape of an ice crystal, which is the predominant ice crystal shape observed in the serum of living fishes under the sub-zero temperature conditions. Namely, the prevention of freezing in living organisms cannot be solely explained by the growth depression effect of protein molecules for ice crystals. Promotion of the growth of the basal face is essential to fulfil the freezing inhibition function for living organisms.

Our findings will lead to a better understanding of a novel kinetic process for growth oscillation in relation to growth promotion due to the adsorption of protein molecules and shed light on the role of crystal growth kinetics at the onset of the mysterious antifreeze effect in living organisms; that is, how this protein prevents fish from freezing, but the detailed mechanism of the oscillatory growth remains to be determined.

Data accessibility

This article has no additional data.

Authors' contributions

Y.F. conceived the study and wrote the paper. S.N. and S.Z. assisted in the development of the growth apparatus. K.N., Y.F., S.Z., K.M. and G.S. performed the experiments and analysed the experimental data. All authors discussed the results and contributed to the interpretation of the data. All authors gave final approval for publication.

Competing interests

The authors declare they have no competing interests.

Funding

Y. Furukawa is grateful for the financial support provided by the Japan Society for the Promotion of Science (JSPS), grant nos. 26287095, 25600081 and 18K04961.