2.1. Ice Nucleation and Its Hindering in the Presence of an Ice-Binding Protein
We have studied the action of an antifreeze protein on the temperature of initiation of ice formation in the presence and in the absence of potent ice nucleators.
The ice-binding protein used in our experiments is the mutant mIBP83 [
46,
47] of the natural ice-binding protein cfAFP isoform 337 [
48,
49,
50]; the cfAFP is an antifreeze protein from a spruce budworm
Choristoneura fumiferana, a moth whose larvae winter at temperatures below –30 °C [
51]. This mutant was used because while retaining the ability of ice-binding [
46,
47], it is less susceptible to aggregation during isolation and purification than the wild-type cfAFP, thus being more convenient for experiments. The mutant mIBP83 has one SS bond
vs. four of the wild-type cfAFP and a slightly truncated C-terminus (for details, see [
46,
47]).
To visualize the results of some of our experiments, we used the fusion protein mIBP83-GFP [
46,
47], where “GFP” means the cycle3 mutant form of the green fluorescent protein [
52]. The cycle3 mutant remains monomeric and fluorescent under our experimental conditions [
53].
The fusion protein mIBP83-GFP, as well as mIBP83 itself, was expressed in
E. coli cells, isolated, and purified [
46,
47]. The ice-binding ability of this fusion protein and the lack of such ability of GFP (
Figure 1A) have already been shown by some of us [
46,
47].
Experiments on sample freezing in the thermostat (the device was described in detail at [
56], see also Materials and Methods) show the impact of mIBP83 on ice nucleation. The experiments were carried out as follows (for details, see Materials and Methods). In the thermostat, a plastic (polypropylene) test tube with 1 mL of a sample was cooled from +10 °C to –18 °C at a rate of 0.24 °C/min and then heated at the same rate; the temperature was measured in the center of the sample. In
Figure 1B, we show the change in temperature of sodium phosphate water buffer without any protein in several cooling/heating cycles using the same sample portion and the same test tube. Freezing of the sample can be noticed as a sharp increase in the sample temperature during the cooling because the sample starts to receive the latent heat released by the freezing liquid. The beginning of each peak, i.e., the nucleation event, is indicated by an arrow. After the ice freezing is completed, the temperature drops back to the thermostat temperature. One can see that all three nucleation events shown in
Figure 1B occur at a temperature of about –10 °C. These nucleation temperatures are very well reproducible from cooling to cooling, provided neither the sample portion nor the test tube has been changed during the experiment.
Similar experiments—with similar results [
54]—were performed by two of us previously with distilled water.
In
Figure 1C, four blue curves stand for freezing of the same buffer, but with different 1 mL portions of the sample in different test tubes. We present an individual freezing curve for each portion of the sample; the point of ice nucleation, i.e., the beginning of the temperature peak, is indicated with a blue arrow. One can see that here, the range of nucleation temperatures is wider than in the case of several nucleation events observed for one and the same sample portion (
Figure 1B). Four red curves with red arrows correspond to the solution of the antifreeze mIBP83 in the same buffer. There is no significant change in the average nucleation temperature between the sole buffer and the buffer with added mIBP83 (
Figure 1C,
Table 1).
Similar experiments with the same results were performed, as a control, with 0.6 mg/mL solution of carbonic anhydrase B, a protein that has never been considered as an antifreeze protein, in the same phosphate buffer: again, we saw no change in the nucleation temperature between the sole buffer and the buffer with carbonic anhydrase B.
In contrast, in the presence of the nucleating agents CuO and
P. syringae, we observed significant changes in the nucleation temperature upon the addition of mIBP83 (see Figures 1D, 1E, and
Table 1).
The ranges of nucleation temperatures for all studied samples are given in
Table 1. This Table and
Figure 1 show that the antifreeze protein mIBP83 decreases the ice initiation temperature in the presence of a potent ice nucleating agent.
It follows from
Figure 1 and
Table 1 that the freezing of all studied solutions occurs not at 0 °C but, in the absence of nucleators, below –7.9 °С. This means, by the way, that in the absence of nucleators, the blood freezing
per se cannot happen to any polar fish since the ocean temperature is never below –2 °C [
57]; see also the “Temperature of Ocean Water” website:
https://www.windows2universe.org/earth/Water/temp.html.
In all the above cases, the initiation of freezing occurred in supercooled liquids. The phenomenon of liquid supercooling before freezing is well-known [
38,
39]. Below, it is discussed in association with the ice nucleation kinetics.
To elucidate the mechanism of freezing initiation and especially functioning of ice-binding proteins, i.e., antifreeze proteins and ice-nucleators, we address the theory of the first order phase transitions [
38,
39,
40,
41] describing the nucleation of crystals, e.g., ice. We use this theory to evaluate the rate of ice formation in water, as well as in bodily fluids, at different temperatures, and in particular, “biological” ones.
We focus on the nucleation, which is a crucial step of ice formation (because “there is no pregnancy without conception”) and pay little attention to the growth of ice, which, at “biological” temperatures, usually takes much less time than the ice nucleation event [
43].
2.2. Ice Nucleation: A Theoretical Consideration
We consider the ice nucleation in conditions that are most interesting for biology: at high subzero temperatures, i.e., just below 0 °C (=273 K), where the ice and the liquid water phases are close to the equilibrium; and we ignore shock waves which are rare in organisms but, in principle, can trigger the freezing in supercooled liquids [
37]).
As reported previously [
38,
39,
42,
43,
54,
58], the "3-dimensional case" of ice nucleation—nucleation within a body of bulk water—can only happen, for kinetic reasons, at rather low temperatures (experimentally: below ≈–35 °C [
59]), which are not of interest here.
Therefore, we consider the most “biology-related” case of ice formation that occurs at high subzero temperatures on the surfaces that are in contact with water. The basic estimates of the nucleation time of this "2-dimensional case" of the first order phase transition can be obtained using the classical theory of nucleation [
40,
60,
61,
62]. To do so, one must find the activation free energy corresponding to the transition state, i.e., the maximum value
of the free energy
that changes with growing
n, the number of particles in the
d-dimensional (
d = 3 or 2) piece of the new phase:
here
is the chemical potential of a molecule in the “new” (arising) solid phase minus that in the “old” (liquid) one (so that
at the point of thermodynamic equilibrium of phases),
is the additional free energy of one molecule on the border of the “new” phase, i.e., on its surface for the 3-dimensional (
) or perimeter for the 2-dimensional (
) case, and
(where
,
, see [
43]) is the number of molecules on the border of a compact piece of the new phase of
particles. Then
and
, while the diameter of the ice “seed” (i.e., the minimal stable piece of arising ice) is
in both cases [
43], 3Å being the size of an H
2O molecule.
The value of the temperature-depended term
is estimated as follows. At the temperature
(
=273 K, i.e., 0 °C, is the water/ice equilibrium point, and
),
according to the classical thermodynamics, where
and
are the entropy and enthalpy of water freezing per 1 molecule at the absolute temperature
. Taking
and
values from [
63], we obtain [
43]:
being the Boltzmann constant. Thus,
with the value
≈ 0.85
that follows from the experimental value of the ice/water interface free energy ≈32 erg/cm
2 [
64] and the fact that an H
2O molecule occupies ≈10 Å
2 of the interface, we obtain
The time of appearance of the ice seed around
one given H
2O molecule is
where
τ (the time of the border H
2O molecule diffusive inclusion in or exclusion from the ice surface at about 0 °C) is a fraction of a microsecond [
39,
43]. It is clear that
is the main temperature-depended term here (when
→0 and thus
→0, i.e., close to 0 °C,
can be huge), while the temperature dependence of the term
is relatively weak [
43] and can be ignored.
The time of nucleation, i.e., of appearance of an ice seed around
some one of the N water molecules contained in (at
d=3) the vessel or on its borders (at
d=2) is
and
is much larger than the time of ice growth after the seeding, especially close to 0 °C. Both theoretically and experimentally, the growth of ice in a ~1 mL test tube at ≈–10 °C usually takes seconds, while the ice nucleation time (
) at temperatures higher than –10 °C is usually minutes, hours or much more [
39,
43,
54].
Note that if, as observed experimentally, the time of ice appearance in a test tube,
, is much longer than
seconds, and
which corresponds to the volume of a tiny droplet or the water layer on walls of a ~1 mL test tube, then
, the appearance of the ice seed around
one given H
2O molecule, takes
billions of years, like a decay of a uranium nucleus. Comparison of this
years with the experimental times of ice nucleation in a ~1 mL test tube (
seconds at the temperature of ice nucleation, see the end of this Section and
Section 2.2.2) and the subsequent ice growth time there (also ~10 seconds, see [
54]) shows that all ice in a ~1 mL test tube usually arises from one or two, rarely three ice seeds.
If the time of appearance of the ice seed around one given H2O molecule is , the probability that a seed does not appear around the given H2O molecule in time t is , and the probability that a seed arises around this H2O molecule is if . Under the condition that , the probability of the appearance of m seeds in time t in an ensemble of N water molecules follows from the Poisson probability distribution = , which gives the average expected value of m as , and its variance as . Thus, the expected value of m is . So, at , is the range of expected seed numbers at the characteristic moment (see Equation (5)) of the appearance of the first ice seed in the ensemble. This means that the expected characteristic time range of appearance of the first ice seed at a fixed temperature is approximately .
2.2.1. Ice Nucleation in Bulk Water Is Only Possible at Rather Low Temperatures
For the 3-dimensional case corresponding to the ice nucleation in a body of bulk water, the transition state free energy is:
[
43]; where
≈0.85
, see above.
Equations (4), (6) show that the time of ice appearance is extremely temperature-sensitive: it turns to infinity when →0, and, unlike most molecular processes, the freezing is accelerated not with increasing but with decreasing temperature, at least, when it is not too far from 0 °C.
The time of ice appearance within 1 mL of resting pure water containing
H
2O molecules not surrounded by solid walls (e.g., inside a water droplet), should take (theoretically) very many years at about –35 °C, and a fraction of microsecond at about –50 °C [
43]; this is in agreement with numerous experimental observations that ice never appears within a droplet of resting pure water at –35 °C and above [
59].
2.2.2. Ice Nucleation on the Ice-Binding Surfaces at High Subzero Temperatures
Now we address a more biologically interesting case of ice formation on the ice-binding walls of a vessel filled with water or on the surfaces of ice-binding dust particles in water. Unlike the ice nucleation inside a body of bulk water, the ice nucleation on a surface can occur at rather high subzero temperatures [
38,
39,
41,
43].
On the ice-binding surface, an ice nucleus (and seed) arises not as a 3
d (
Figure 2A) but as a 2
d (Figures 2B, 2C) object. This (cf. Equation (6) with Equation (7) below) drastically decreases [
43] the transition state free energy when
:
If it is assumed that
for a 2
d nucleus, as it is for the 3
d one, then
, and, according to Equations (4, 5), the characteristic time of appearance of an ice seed somewhere on the 1 mL vessel walls accommodating
10
15 water molecules is
where
and, at
,
This means that with , the freezing of water in a 1 mL vessel should, theoretically, take a second at ≈6°, that is, at a temperature of –6 °C, and a minute at –5.5 °C. Thus, any ice-binding surface can be considered as a kind of ice nucleator. The time is highly temperature-sensitive: at a temperature of 1° higher than –6 °C, the appearance of an ice seed would take hours, while at a temperature of 1° lower than –6 °C, it would take a millisecond.
However, the experimentally measured [
64] value
represents the average free energy of the ice/water interface per interface molecule, while different facets of an ice crystal may have somewhat different values of this interface free energy due to different orientation of molecules relative to different crystal facets [
39,
65]. Then, if, for instance,
, we have
instead of
in Equation (8), and theoretically, the initiation of water freezing in a 1 mL vessel should take seconds at about –10 °C and minutes at about –9 °C (the freezing initiation temperature of –9 ÷ –10 °C was observed in our experiments, see
Figure 1B). With
, Equation (8) has the form
The value of
can be experimentally measured at a given fixed temperature
. However, our experiments on water cooling use a constant decrease in temperature with time
t, where
and
with
(see
Section 2.1). Therefore, the total time from the beginning of the experiment to the appearance of an ice seed at a temperature of
can be calculated as
. The minimum of this calculated time must correspond to the experimental value of
.
The first derivative of with respect to equals to , which must be equal to zero at the extremum of . With , this extremum corresponding just to is the minimum because the second derivative of with respect to is positive. At , the optimal time of freezing nucleation calculated from Eq. (8a) is about 40 seconds.
2.2.3. Ice-Binding Surfaces
As mentioned above, the emergence of ice is catalyzed by ice-binding surfaces, i.e., the surfaces that bind ice stronger than liquid water. However, the catalytic effect is not affected by the strength of ice binding to the “non-ice” underlay, so far as this binding is stronger than the binding of liquid water. This is because the second and all further layers of ice form on the ice already bound to the “non-ice” underlay, and, if the ice strongly binds to the “non-ice” underlay, a monomolecular ice layer exists even at temperatures > 0 °C; but a massive ice growth, our sole interest, can arise on this icy underlay only at temperatures below 0 °C.
Thus, any ice-binding surface, including that of a plastic test tube or some dust particles, serves as an ice nucleator but its catalytic effect on the ice emergence is determined solely—see Equations (8), (8a)—by the temperature and the free energy of the border of the arising ice, i.e., by the
B2 factor. The latter depends on the orientation of molecules forming the layer of ice arising on the underlay. A special shape of the underlay (cf.
Figure 2C with
Figure 2B) can significantly weaken the contacts between ice molecules inside the newly arising ice layer, and accordingly, reduce the values of the boundary
factors. In turn, the smaller
strongly decreases the freezing temperature, thereby drastically shortening the freezing time at a given temperature. The faster ice formation on surfaces corrugated at an atomic scale has been already experimentally observed [
66]. Thus, a special atomic structure of the underlay can create a strong “ice nucleator”—like, e.g., CuO powder [
43]—unlike while "weak ice nucleators”, such as plastic walls of test tubes.
If strong ice nucleators are added to water in a test tube with ice-binding walls, then there are two parallel freezing nucleation reactions: one is generated by the walls of the test tube, and the other by the added nucleators. If the initiation time of the freezing generated by the tube walls alone is
, and the initiation time of the freezing generated by the added nucleators alone is
, then the initiation time of the freezing in the test tube with added nucleators is
Here, is the number of water molecules on the tube walls, is the number of water molecules on the surfaces of the added nucleators, and , are the activation free energies for nucleation on the tube walls and on the added nucleators, respectively. If is large enough and is small enough, then the freezing time is determined mainly by the added ice nucleators.
If the antifreeze protein is added, it reduces in proportion to the antifreeze concentration and the antifreeze-wall binding constant, and it reduces in proportion to its concentration and the antifreeze-nucleator binding constant.
2.2.4. Can an Antifreeze Protein Bind to Something That Was Not Evolved to Be an Ice Nucleator?
Since the activity of the antifreeze protein so clearly manifests itself in the blocking of ice nucleators, we hypothesized that antifreeze proteins could evolve to bind to any surfaces which are or may serve as ice nucleators. Some ice nucleators (e.g., in
P. syringae) are thought to be used as a weapon [
67] or, in some plants, as a natural thermostat utilizing, in frost, the latent heat released during the nucleators-induced freezing to save other parts of the plant [
68]. But one cannot expect that ice nucleators could evolve, e.g., in mice, though it has been already shown [
69] that ice arises in tails of mice at –22 °C (while ice cannot arise at temperatures higher than –35 °C without nucleators, see above), and that an antifreeze protein induced by transfection protects the mice tails from frostbite damage. Thus, the observed ice-nucleating activity in mice is apparently an incidental side effect of something with another function.
In this connection, we checked if human cells have binding sites for mIBP83.
Since mIBP83-GFP allows visualization of the mIBP83 location, we transfected human breast cancer cells SKBR-3 by plasmids encoding either the fused protein mIBP83-GFP or sole GFP as a control. The transfected cells were cultured under standard conditions (see Experiments with the Human Cell Culture in Materials and Methods).
To test the response of the transfected cells to cold, they were kept at +37 °C and then incubated at +2 °C for 2 hours, followed by immediate fixation with 4% formaldehyde to prevent protein redistribution during the imaging procedure. The temperature of +2 °C was chosen as the lowest temperature at which the cells remained spread out, attached to the substrate, and accordingly, convenient for the research using a laser scanning microscope, see Materials and Methods.
The pattern of intracellular location of mIBP83-GFP clearly differs from that of the sole GFP namely at a low positive (+2 °C) temperature (
Figure 3). At +37 °C, both proteins do not show a clear location in the cell. The cooling down to +2 °C leads to drastic changes in the mIBP83-GFP but not in the GFP distribution. The amount of diffusely distributed mIBP83-GFP decreases, and it accumulates mainly in central regions of the cytoplasm, including a part of the perinuclear regions. Although no region in the considered cells evolved as a natural target for the given antifreeze protein, mIBP83-GFP is concentrated in small areas that are clearly visible in the cells. This suggests that mIBP83-GFP binds to some cellular structures upon the cooling down to almost zero.