J. Phys. Chem. B 2008, 112, 7111–7119
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Growth Inhibition Mechanism of an Ice–Water Interface by a Mutant of Winter Flounder Antifreeze Protein: A Molecular Dynamics Study Hiroki Nada*,† and Yoshinori Furukawa‡ National Institute of AdVanced Industrial Science and Technology (AIST), 16-1 Onogawa, Tsukuba 305-8569, Japan, and Institute of Low Temperature Science, Hokkaido UniVersity, Sapporo 060-0819, Japan ReceiVed: December 21, 2007; ReVised Manuscript ReceiVed: February 25, 2008
Molecular dynamics (MD) simulations of a growing ice–water interface of a pyramidal {202¯1} plane in the presence of a mutant of winter flounder antifreeze protein (AFP) were conducted. Simulation results indicated that the AFP was partially surrounded by ice grown at the pyramidal interface. The AFP stably bound to the interface only when AFP hydrophobic residues bound to ice. Simulation results also indicated a drastic decrease in the growth velocity of the ice surrounding the stably bound AFP, in agreement with ice growth inhibition processes that have been observed in real systems. We confirmed that the decrease in the growth velocity of ice was attributable to the melting point depression caused by the Gibbs–Thomson effect. Simulation results suggested that the growth of ice surrounding the AFP is needed to promote stable AFP binding to the interface and subsequent ice growth inhibition. MD simulations of a growing ice–water interface of a prismatic {101¯0} plane were also conducted. Neither the stable binding of the AFP to the interface nor the decrease in the growth velocity occurred for the prismatic plane. These results agree with the fact that AFPs inhibit the growth of ice only on the pyramidal planes in real systems. 1. Introduction Antifreeze proteins (AFPs) dissolved in the sera of organisms living in cold climates inhibit the growth of ice within these organisms’ bodily water.1 In the presence of AFPs, the freezing point of water becomes lower than the melting point of ice. This discrepancy between the freezing and melting points, known as thermal hysteresis, suggests that ice growth inhibition occurs by a noncolligative mechanism, which originates from the binding of AFPs to ice.2 AFPs are classified into four structural types (I-IV). The winter flounder type I AFP (wf-AFP) is the most extensively studied AFP.3 Experimental studies of ice crystal growth in water in the presence of wf-AFPs have shown that a spherical ice seed gradually changes to a hexagonal bipyramidal ice crystal containing 12 equivalent flat {202¯1} planes (Figure 1a) before ceasing growth entirely.4 This morphological change of the ice crystal indicates that wf-AFPs inhibit the growth of ice on the pyramidal plane. Several theoretical models have been proposed to explain how wf-AFPs inhibit the growth of ice on the pyramidal plane. Knight et al. proposed a model of ice growth inhibition based on the melting point depression caused by the Gibbs–Thomson (or Kelvin) effect at curved ice interfaces, which grow between bound wf-AFPs.5 Other theoretical models have also attributed ice growth inhibition to the melting point depression caused by the Gibbs–Thomson effect.6,7 These models suggest that the stable binding of wf-AFPs to the pyramidal plane is a necessary condition for ice growth inhibition. Thus far, the most stable binding conformation has been determined by considering a structural match between a wf* To whom correspondence should be addressed. Telephone: +81-29861-8231. Fax: +81-29-861-8722. E-mail:
[email protected]. † AIST. ‡ Hokkaido University.
Figure 1. (a) Shapes of an ice crystal grown from liquid water in the presence of the wf-AFPs (a hexagonal bipyramid that has 12 equivalent {202¯1} planes) (left) and the location of the {201} plane in a hexagonal column ice crystal (right). (b) Mutant AFP used for the simulation. Large red, purple, ivory, and blue spheres represent carbon atoms of Val, Lys, Glu, and Arg, respectively. Carbon atoms of other residues are shown as large green spheres (most of them are of Ala). For all the residues depicted, small dark purple spheres represent nitrogen atoms and very small blue spheres represent oxygen atoms. Hydrogen atoms are not depicted.
AFP and the pyramidal plane on the atomic scale.4,5,8–11 Computer simulation studies have also been used to search for the most stable binding conformation between a wf-AFP and the pyramidal plane.12–20 These studies suggest that the binding becomes the most stable when the R-helical axis of the wf-
10.1021/jp711977g CCC: $40.75 2008 American Chemical Society Published on Web 05/14/2008
7112 J. Phys. Chem. B, Vol. 112, No. 23, 2008 AFP aligns with the 〈011¯2〉 vector of the pyramidal plane. Hydrogen bonds12,13,15,17 and hydrophobic interactions11,14,19 between the wf-AFP and the pyramidal plane, as well as the effect of the surrounding liquid water on the stability of the wf-AFP’s binding to the pyramidal plane,17,18,20 have also been considered in earlier studies. Nevertheless, elucidation of the most stable binding conformation between a wf-AFP and the pyramidal plane is not sufficient to understand the mechanism of ice growth inhibition in real systems. Ice growth inhibition occurs through the binding of wf-AFPs to a “growing” ice–water interface of the pyramidal plane.21 Therefore, elucidating the growth kinetics of the ice–water interface of the pyramidal plane in the presence of wf-AFPs is of particular importance to understand the mechanism of ice growth inhibition. Thus far, a few molecular dynamics (MD) simulations have been carried out for an equilibrium ice–water interface of the pyramidal plane in the presence of a wf-AFP.16,22 However, as far as we know, no one has yet studied the molecular-level growth kinetics of the ice–water interface of the pyramidal plane in the presence of a wf-AFP. In this study, we carried out MD simulations of a growing ice–water interface of the pyramidal plane in the presence of a mutant of wf-AFP. Simulation results indicated a drastic decrease in the ice growth velocity, corresponding to ice growth inhibition, only when the mutant wf-AFP stably bound to ice. In this article, we will discuss the mechanism of ice growth inhibition and its relationship to the binding conformation of the mutant wf-AFP at ice as determined from the results of the MD simulations. 2. Simulation Methods 2.1. Models of AFP and H2O. The purpose of this study was to qualitatively study the growth kinetics of an ice–water interface of the pyramidal plane in the presence of a wf-AFP, rather than to elucidate a detailed wf-AFP conformation and detailed structures of its surrounding H2O molecules. Therefore, a simple model of a wf-AFP was sufficient for our purposes, and thus we used a rigid model of a wf-AFP. Note that the conformation of a wf-AFP is stable and is not significantly influenced by its surrounding H2O molecules.18 In this study, we chose the VVVV2KE mutant of wf-AFP, which was synthesized by Haymet et al.,23 as the model for the simulations. In this mutation, the Thr residues of wf-AFP were substituted by Val residues, which are strongly hydrophobic (i.e., the OH of each Thr residue of wf-AFP was replaced by a CH3 group). Moreover, two additional Lys-Glu sale bridges were introduced in this mutant. The helical conformation of this mutant was similar to that of wf-AFP, except that this mutant showed a slight R-helix bent.24 We chose this mutant because all its atomic coordinates were determined precisely by an experimental study (Figure 1b),24 making the creation of a rigid model straightforward. Note that this mutant also inhibited the growth of ice on the pyramidal plane.11 The stable binding conformation to the pyramidal plane was the same for both this mutant and wf-AFP.20 Moreover, the antifreeze activity of this mutant was also similar to that of wf-AFP.11 Therefore, the mechanism of ice growth inhibition associated with wf-AFP was believed to be essentially the same as that associated with this mutant (referred to herein as AFP). Intermolecular interactions were estimated as the sum of the Coulombic interactions between point charges plus the sum of the Lennard-Jones (LJ) interactions between atoms. Potential parameters of the AFP were determined according to the
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Figure 2. Number of hydrogen bonds between each residue of the AFP and its surrounding H2O molecules, NHB, obtained by an MD simulation of the AFP dissolved in liquid water at 298 K and 1 atm. The solid and dotted lines show the NHB for the CHARMM six-site parameters and for the CHARMM-TIP3P parameters, respectively. The 37 AFP residues are D-VASDAKAAAEL-VAANAKAAAEL-VAANAKAAAEA-VAR, listed in sequence.23
CHARMM force field 19.25 Note that parameter values for a protein in the CHARMM force field were developed by applying the TIP3P model of H2O26 to the protein’s surrounding H2O molecules. However, the TIP3P model was not suitable for simulations of ice growth, because the melting point of ice in the TIP3P model (146 K)27 is much lower than the real melting point of 273.15 K. Instead, we used a six-site model of H2O28 because this model satisfactorily reproduces ice growth near the real melting point.29,30 The H2O-AFP LJ parameters were determined according to the Lorentz–Berthelot rules. As with previous studies,21,29–31 all intermolecular interactions were smoothly truncated at the intermolecular distance from 0.95 to 1 nm using a switching function.32 Because potential parameters in the CHARMM force field were not developed with the six-site H2O model, we confirmed that the combination of the CHARMM parameters with the sixsite model parameters (CHARMM six-site parameters) satisfactorily reproduced interactions between the AFP and H2O molecules, by comparing the results of an MD simulation of liquid water in the presence of the AFP between the CHARMM six-site parameters and the combination of the CHARMM parameters with the TIP3P model parameters (CHARMMTIP3P parameters). The potential energy between the AFP and its surrounding H2O molecules was 15% higher for the CHARMM six-site parameters than for the CHARMM-TIP3P parameters. This higher potential energy for the six-site model reflected a smaller dielectric constant for the six-site model than for the TIP3P model.28 Nevertheless, the number of hydrogen bonds, NHB, between each residue of the AFP and the H2O molecules was almost the same for both the CHARMM six-site and CHARMMTIP3P parameters, as shown in Figure 2 for each of the 37 AFP residues. Therefore, we concluded that the structural properties of liquid water surrounding the AFP as determined by the CHARMM six-site parameters were, at least qualitatively, the same as those determined by the CHARMM-TIP3P parameters. In addition, we analyzed the most energetically stable binding conformation of the AFP to an ideal pyramidal plane surface, in which all of the H2O molecules were fixed at the lattice sites of ice using the CHARMM six-site parameters. This analysis was carried out by a two-step process: the position and orientation of the AFP were varied to create a binding conformation at the surface, and then the local energy minimum conformation was obtained by a Monte Carlo (MC) simulation. For the first step, the binding conformation of the AFP at the surface was described by its center-of-mass coordinates (x, y, and z) and two rotation angles (θ and φ).33 Then, for a fixed
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Figure 3. Initial binding conformations of AFP-1, AFP-2, AFP-3, and AFP-4 at the pyramidal interface.
value of θ, the binding conformation of the AFP at the surface that led to the lowest potential energy was searched by changing x, y, and z with a 0.1-nm step size and φ with a 5° step size.34 This searching procedure was performed for all values of θ at every 5° from 0 to 360°. For the second step, an MC simulation was carried out at 0 K for each of the binding conformations that were determined in the first step to obtain the local energy minimum confirmation. Finally, the most stable binding conformation was determined by comparing these local energy minimum values. The most stable binding conformation was obtained when the R-helical axis of the AFP was aligned along the 〈011¯2〉 vector and each Val residue fitted in the “groove” at the pyramidal surface (see AFP-1 in Figure 3). This conformation was the same as that obtained from a combination of the AMBER force field parameters with the TIP3P model parameters.20 Furthermore, the CHARMM-TIP3P parameters produced the same most stable binding conformation as that obtained from the CHARMM six-site parameters. Thus, we believe that the CHARMM six-site parameters satisfactorily reproduce interactions between the AFP and H2O molecules and are applicable to this simulation study. 2.2. MD Simulations. MD simulations were carried out for a rectangular-parallelepiped system in which an ice crystal was sandwiched between two liquid water phases. The ice crystal was oriented in the system so that its pyramidal planes were in contact with liquid water. That is, the system contained two ice–water interfaces of the pyramidal plane. The AFP was oriented at the surface of each of the pyramidal interfaces. The
ice crystal and each of the water phases consisted of 2160 and 3240 H2O molecules, respectively. Periodic boundary conditions were imposed on all three axes (x, y, and z) of the system. Computation was carried out using an implicit leapfrog algorithm proposed by Fincham.35 The time step was 1 fs, and the total run was 4 ns. Temperature, T, and pressure, P, were maintained at 268 K and 1 atm, respectively, by a thermostat method proposed by Berendsen et al.36 P was controlled by changing the dimension of the system in the direction normal to the interface (z axis) only, whereas the dimensions in the directions parallel to the interface (x and y axes) were fixed at their equilibrium values. Our previous MD simulation study of the growth of ice in pure liquid water suggested that the melting point, Tm, of ice in the six-site model is located in the range of 281–285 K.30 However, Tm of ice in the present system was lower than that in the pure liquid water system because the Gibbs free energy of liquid water decreases in the presence of the AFP. To determine Tm of ice in the present system, we carried out MD simulations with a run of 2 ns or shorter at 273, 278, and 283 K. Ice grew at 273 K but melted at 283 K. At 278 K, neither growth nor melting occurred. Therefore, we assumed that Tm of ice in the present system was 278 K; therefore, the simulation T of 268 K corresponded to -10 °C. In the MD simulations, we examined four initial binding conformations of the AFP at the pyramidal interface. The initial binding conformations were selected from the results of the analysis of the AFP’s binding energy to the ideal pyramidal plane surface, as described in the previous subsection. The initial
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Figure 4. Snapshots of AFP-1 and AFP-2, and their surrounding H2O molecules, at the pyramidal interface at 0.1 and 4.0 ns. The dashed lines show the initial positions of the interfaces. Icelike H2O molecules are shown in gray. Each solid line connecting a pair of H2O molecules represents a hydrogen bond.
binding conformations that we selected are shown in Figure 3 and are labeled AFP-1, -2, -3, and -4. For AFP-1, which had the most energetically stable binding conformation, each Val residue fitted in the groove at the pyramidal plane. Therefore, the binding face of AFP-1 had hydrophobic properties. The binding faces of AFP-2 and AFP-3 also had hydrophobic properties because hydrophobic Val and Ala residues bound to ice. Note that each Val residue of AFP-2 also slightly fitted in the groove at the pyramidal plane, causing the binding conformation of AFP-2 to resemble that of AFP-1. For AFP-4, a hydrophilic Arg residue bound to ice, meaning that the binding face of AFP-4 was hydrophilic. The estimated binding energies for AFP-1, AFP-2, AFP-3, and AFP-4 were -4.1 × 105, -3.7 × 105, -3.8 × 105, and -3.3 × 105 K, respectively. 3. Results and Discussion 3.1. Ice Growth around AFP. Figures 4 and 5 show snapshots of the AFP and surrounding H2O molecules at the pyramidal interface during the growth of ice. Snapshots of “icelike” H2O molecules, which were defined as H2O molecules that were connected via hydrogen bonds to each of their four nearest neighbors, are shown as gray spheres. Here, the number of nearest neighbors around a selected H2O molecule was estimated by counting the number of H2O molecules included in a sphere of 0.35-nm radius from the selected one. An energetic definition was used to determine whether a pair of H2O molecules was connected by a hydrogen bond.37 As seen in Figures 4 and 5, the AFP was partially surrounded by the ice that had grown during the simulation. Growth of the surrounding ice around a wf-AFP was also reported in lattice model simulations by Wathen et al.38 We observed that most of the H2O molecules surrounding the AFP-1 Val residues were arranged in the lattice structure of ice, whereas H2O molecules surrounding the hydrophilic residues did not form the structure
of ice during the simulation. These results indicate that the binding of hydrophobic Val residues to ice did not markedly damage the ice lattice structure, whereas hydrophilic residues impeded the growth of ice in the surrounding liquid water. As expected, the growth of the surrounding ice significantly influenced the stability of the AFP’s binding to the pyramidal interface. The stability of binding was reflected in the dynamics of the AFP at the pyramidal interface during growth, which we discuss in section 3.2. 3.2. Stability of AFP Binding. Figure 6 shows square displacements of the AFP’s center of mass in the z direction from the beginning of the simulation, ∆rz2, as a function of time, t. Figure 7 shows shifts of θ and φ from their initial values (∆θ and ∆φ, respectively) as functions of t. The ∆rz2, ∆θ, and ∆φ values for AFP-1 were consistently small over the whole run, whereas these values for the other AFPs substantially changed with increasing t. These results strongly suggest that AFP-1 bound to the pyramidal interface much more stably than the other AFPs during ice growth. The ∆rz2, ∆θ, and ∆φ values for AFP-2 gradually increased with increasing t for a period of 0-2 ns. However, after 2 ns, these increases stopped and ∆rz2 decreased with t. These results indicate that the binding conformation of AFP-2 became much more stable after 2 ns had elapsed. As seen in Figure 4, the binding conformation of AFP-2 approached that of AFP-1 as time elapsed during the simulation; that is, each AFP-2 Val residue fitted in the groove at the pyramidal plane at 4 ns. This observed behavior for AFP-2 reflects a relaxation process resulting in AFP-2’s rearrangement to conform to the binding orientation of AFP-1. The changes in ∆rz2, ∆θ, and ∆φ with increasing t for AFP-3 and AFP-4 also corresponded to relaxation processes for these AFP’s rearrangements to better match the binding conformation of AFP-1. The fact that AFP-3 and AFP-4 did not stably bind
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Figure 5. Snapshots of AFP-3 and AFP-4, and their surrounding H2O molecules, at the pyramidal interface at 0.1 and 4.0 ns. Line and color representations are the same as those in Figure 4.
Figure 6. Square displacements of the AFP center of mass from its initial position, ∆rz2, as a function of t for AFP-1, AFP-2, AFP-3, and AFP-4. lz is the cell length in the z direction.
to the pyramidal interface is attributable to a short run time of 4 ns, which was apparently too short for these AFPs to adequately rearrange themselves into a stable binding conformation like that observed for AFP-1. Consequently, we concluded that AFP-1 had the most stable binding conformation at the growing pyramidal interface. 3.3. Growth Velocity of Ice. Figure 8 shows the fraction of icelike H2O molecules in the system, fi, as a function of t. The increase in fi with increasing t reflects the growth of ice, and the slope of the fi-t relationship corresponds to the growth velocity of ice, Vg. The values of Vg (in cm/s) that we estimated from the slopes of the fi-t relationships were 19.0 (0–2 ns) and 5.9 (2–4 ns) for AFP-1, 16.9 (0–2 ns) and 6.3 (2–4 ns) for AFP2, 10.4 (0–2 ns) and 14.1 (2–4 ns) for AFP-3, and 8.7 (0–2 ns) and 12.5 (2–4 ns) for AFP-4. Notably, the Vg values for AFP2, AFP-3, and AFP-4 were smaller than that for AFP-1 for the period of 0-2 ns. These results indicate that the growth of ice surrounding the rearranging, or “moving”, AFPs was slower than that observed for the ice surrounding the stably bound AFP. Notably, Vg for AFP-1 and AFP-2 drastically decreased after 2 ns, whereas Vg for AFP-3 and AFP-4 did not decrease during the simulations. These results suggest that the drastic decrease
Figure 7. Shifts of θ and φ from their initial values, ∆θ and ∆φ, as a function of t for AFP-1 (s), AFP-2 (- - -), AFP-3 (b), and AFP-4 (0).
in Vg occurred only for the ice surrounding the AFP that stably bound to the pyramidal interface. Note that the ice interfaces surrounding AFP-1 and AFP-2 were curved, as shown in Figure 4. Therefore, we suspected that the decrease in Vg observed for AFP-1 and AFP-2 originated from the decrease in Tm at the curved interfaces due to the Gibbs–Thomson effect. Using the parameters associated with the Gibbs–Thomson effect, we estimated the decrease of Tm (δT) using δT ) VγTm/ r∆Hm, where γ is the excess interface free energy, V is the molar volume, ∆Hm is the latent heat, and r is the radius of curvature.5 Here, we assumed that the shape of ice grown around AFP-1 and AFP-2 was a column with r ) 3.45 nm, which roughly corresponded to half of the dimension of the system in the y direction. By using γ ) 2 × 10-13 erg/nm2, ∆Hm ) 10-13 erg, and V ) 3.2 × 10-2 nm3,6 we obtained δT ) 5 K. Since T for
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Figure 9. ∆rz2 for AFP-1 as a function of t for the equilibrium (3) and growing (s) pyramidal interfaces.
Figure 8. Fraction of the icelike H2O molecules in the system, fi, as a function of t for the four AFPs. fi0 is the fi at the beginning of the simulation.
the system was set to -10 °C, T at the curved growing interfaces surrounding AFP-1 and AFP-2 was expected to be -5 °C according to our obtained value of δT. To infer whether T at the curved growing interfaces surrounding AFP-1 and AFP-2 was actually -5 °C, we compared Vg values for ice at -5 °C between the present simulation study and an experimental study of the ice growth.39 The experimental Vg value at -5 °C is about 2 cm/s. By contrast, the Vg values obtained at a period of 2–4 ns in our simulations were 5.9 and 6.3 cm/s for AFP-1 and AFP-2, respectively. We note that simulation Vg values often exceed experimental values because the constant temperature MD algorithm instantly removes the latent heat, causing an observed increase in Vg.29,30 Moreover, a small system in which three-dimensional periodic boundary conditions are imposed is advantageous for the growth of ice. Thus, we concluded that T at the curved growing interfaces surrounding AFP-1 and AFP-2 corresponded to about -5 °C. Consequently, we confirmed that the decrease in Vg for the ice surrounding AFP-1 and AFP-2 can be explained by the decrease in Tm caused by the Gibbs–Thomson effect, as suggested in earlier reports.5–7 The observation that Vg did not decrease for the ice surrounding AFP-3 and AFP-4 is attributable to the migration of those AFPs during growth. In other words, the migration of these AFPs hindered the formation of a curved interface, so the decrease in Tm caused by the Gibbs–Thomson effect was negligibly small. 3.4. Effect of Grown Ice on the Stability of AFP Binding. The most stable binding conformation of the AFP at the growing pyramidal interface obtained in this study (i.e., the binding conformation of AFP-1) was the same as the most stable binding conformation at an “equilibrium” pyramidal interface obtained by Jorov et al.20 In the stable binding conformation of AFP-1, hydrophobic Val residues bound to ice and hydrophilic residues were exposed to the surrounding liquid water. Here, we discuss why the binding conformation of AFP-1 was the most stable conformation observed. Jorov et al. explained that the most stable binding conformation at the equilibrium pyramidal interface occurs as follows:20 The binding of hydrophobic protein residues to ice produces an entropy gain as compared with the case in which those residues are exposed to liquid water, because liquid H2O molecules surrounding each hydrophobic residue tend to form
Figure 10. Potential energy, U, between AFP-1 and its surrounding icelike H2O molecules as a function of t for the growing pyramidal interface.
a cagelike structure, causing loss of entropy. Moreover, the number of hydrogen bonds between H2O molecules and each hydrophilic residue becomes larger when the hydrophilic residues are exposed to liquid water rather than ice, because H2O molecules in liquid water rearrange to form hydrogen bonds with the hydrophilic residues. Therefore, the exposure of hydrophilic residues to liquid water produces an enthalpy gain. These entropy and enthalpy gains explain why the binding conformation of AFP-1 was the most stable. Nevertheless, simulation results indicated that AFP-1 was partially surrounded by the ice that had grown during the simulation. Therefore, the explanation for the most stable binding conformation at the equilibrium pyramidal interface might not be sufficient for describing binding conformation at the growing pyramidal interface. To determine the effect of the surrounding ice on the stability of the AFP’s binding at the growing pyramidal interface, we also conducted an MD simulation of an equilibrium pyramidal interface for the binding conformation of AFP-1.40 Figure 9 shows ∆rz2 as a function of t for the equilibrium pyramidal interface. The increase in ∆rz2 with increasing t is clearly observed, meaning that AFP-1 did not stably bind to the equilibrium pyramidal interface. These results indicate that the attractive interaction between AFP-1 and the equilibrium pyramidal interface was not sufficient to produce a stable binding conformation. Actually, as seen in Figure 10, the attractive interaction between AFP-1 and ice significantly increased after the growth of the surrounding ice. Thus, we concluded that the growth of ice surrounding the AFP is needed to promote stable AFP binding to the pyramidal interface and subsequent ice growth inhibition. In the present simulation of the growing pyramidal interface, the AFP-1 conformation did not shift from its initial position even before the growth of the surrounding ice. This observation indicates that the surrounding ice grew before the migration of AFP-1, reflecting a very slow migration of AFP-1 at the interface. Although we did not measure the diffusion coefficient
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Figure 11. Initial binding conformations of AFP to the prismatic interface. The AFPs shown here represent the most stable and metastable binding conformations at the ideal prismatic plane surface. The estimated binding energies to the ideal prismatic surface for the most stable and metastable binding structures were -3.7 × 105 and -3.5 × 105 K, respectively.
Figure 12. Snapshots of AFP and its surrounding H2O molecules at the prismatic interface at 0.1 and 4.0 ns. Line and color representations are the same as those in Figure 4.
of AFP-1 at the pyramidal interface in this simulation, it would be much smaller than the diffusion coefficient in liquid water.41 Therefore, we expected that even if AFP-1 migrated from its initial position before the ice growth, the growing pyramidal interface would contact AFP-1, causing AFP-1 to stably bind to the pyramidal interface. 3.5. MD Simulations of the Prismatic Interface. Investigating the growth kinetics of an ice–water interface for other crystallographic planes in the presence of the AFP is also important because the growth of a hexagonal bipyramidal ice crystal reflects the anisotropy of Vg. In this study, we also conducted MD simulations of an ice–water interface of a prismatic {101¯0} plane using two different initial binding conformations of the AFP. The two initial binding conformations were energetically the most stable binding conformation and
another relatively stable (metastable) binding conformation at the ideal prismatic plane surface (Figure 11). Figure 12 shows snapshots of the AFP and its surrounding H2O molecules at the prismatic interface. Figure 13 shows ∆rz2 and fi as functions of t for the prismatic interface. The values of Vg (cm/s) estimated from the slopes of the fi-t relationships were 18.6 (0–2 ns) and 14.9 (2–4 ns) for the most stable binding structure and 13.2 (0–2 ns) and 17.0 (2–4 ns) for the metastable binding structure. For both conformations, the AFP migrated from its initial position and Vg did not substantially change during the simulation, as in the cases of AFP-3 and AFP-4 for the pyramidal interface. The changes in ∆θ and φ with increasing t were also seen for both conformations (not shown). These results indicate that, for both conformations, the AFP
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Nada and Furukawa AFP, whereas the growth of ice on the prismatic interface was not. However, a molecular-scale process of the morphological change to the hexagonal bipyramid still remains unclear. More extensive studies of the anisotropic growth kinetics of an ice–water interface in the presence of the AFP are needed to elucidate this process. Nevertheless, we believe that the present study contributes greatly to our understanding of the mechanism of ice growth inhibition by the AFPs in real systems. 4. Conclusions
Figure 13. (a) ∆rz2 of the most stable and metastable binding conformations of AFP as a function of t for the prismatic interface. (b) fi as a function of t for the prismatic interface.
did not stably bind to the prismatic interface and hence did not inhibit the growth of ice. These results alone might not be enough to conclude whether the AFP inhibits the growth of ice on the prismatic interface. However, we believe that the AFP does not inhibit the growth of ice on the prismatic interface, because the AFP did not stably bind to the interface, even in its most energetically favorable conformation in the present simulations. Notably, the present results are qualitatively consistent with the fact that the AFPs inhibit the growth of ice only on the pyramidal planes in real systems. 3.6. Comparison with Real Systems. Finally, we compared ice growth inhibition observed in the present simulations with that observed in real systems. According to an experimental study,42 the AFP-AFP distance, d, at an ice–water interface is on the order of 10 nm, which is much larger than the d ≈ 6.9 nm used in the present simulations (i.e., the dimensions of the system in the x and y directions). This difference in d results in a much larger δT for the simulations than that for the experiment, as δT is inversely proportional to d. Supposing that the ice growth inhibition in real systems originates from the Gibbs–Thomson effect and supposing that δT ) 1 °C in real systems, the value of d that leads to δT ) 1 °C is estimated to be 34.5 nm, which is consistent with the experimentally determined d. Therefore, we believe that the ice growth inhibition in real systems also originates mainly from the Gibbs–Thomson effect, as suggested by earlier works.5–7 In real systems, the growth of ice on the pyramidal plane in the presence of the AFPs almost stops (i.e., Vg ≈ 0). However, the growth of ice did not stop in the present simulations, even after Vg decreased. This observation is attributable to the much lower simulation T of -10 °C, as compared with the experimental T, which is normally higher than -1 °C. That is, since the simulation T was very low, the curved interface surrounding the AFP was still in the undercooling state even if the decrease in Tm caused by the Gibbs–Thomson effect occurred. MD simulations at T values much higher than -10 °C are needed to observe the cessation of ice growth. In real systems, the shape of an ice crystal changes during growth from a sphere to a hexagonal bipyramid containing flat pyramidal planes.4 These experimental observations are qualitatively consistent with the present results, which show that the growth of ice on the pyramidal interface was inhibited by the
MD simulations of a growing pyramidal ice–water interface in the presence of a mutant winter flounder AFP were conducted using four initial binding conformations of the AFP at the pyramidal interface. Simulation results clearly indicated the growth of ice surrounding the AFP on the pyramidal interface. The AFP was partially surrounded by the grown ice and was stably bound to the pyramidal interface only when hydrophobic AFP Val residues fitted into the grooves at the pyramidal plane. The decrease in Vg, which corresponds to ice growth inhibition, occurred only for the ice surrounding the AFP that stably bound to the pyramidal interface. We confirmed that the decrease in Vg was attributable to the decrease in Tm caused by the Gibbs–Thomson effect at the curved interface surrounding the AFP, as suggested by earlier works.5–7 Notably, this study is the first to investigate the molecular-scale process of ice growth inhibition by an AFP with an MD simulation. The most stable binding conformation of the AFP at the growing pyramidal interface obtained in this study was the same as the most stable binding conformation at the equilibrium pyramidal interface obtained by Jorov et al.20 However, in the present simulations, the AFP did not stably bind to the equilibrium pyramidal interface. Our results suggest that the growth of ice surrounding hydrophobic AFP Val residues is necessary to promote the stable binding of the AFP to the pyramidal interface and to promote subsequent ice growth inhibition. MD simulations of the prismatic interface were also conducted. Neither stable binding of the AFP to the prismatic interface nor a decrease in Vg was observed. These results agree with the fact that, in real systems, the AFPs inhibit the growth of ice only on the pyramidal planes. More extensive studies of the anisotropic growth kinetics of ice–water interfaces are necessary for elucidating the growth of hexagonal, bipyramidal ice in real systems. Though the mechanism of ice growth inhibition is believed to be essentially the same for both wf-AFP and the mutant AFP that we examined in this study,11 MD simulations for wf-AFP should be conducted to confirm that the results obtained in the present study are accurate. Moreover, our results should also be compared with results obtained with a flexible AFP model, as we used a rigid AFP model in this study. Nevertheless, the present results qualitatively agree with ice growth inhibition caused by wf-AFPs in real systems. In conclusion, the present study proposed a molecular-scale mechanism of ice growth inhibition by the mutant AFP, which might qualitatively explain ice growth inhibition by wf-AFPs in real systems. Acknowledgment. We thank Dr. Salvador Zepeda for his helpful comments about the relationship between the experimental results of ice growth in the presence of AFP and the present simulation results. This work was financially supported by a Grant-in-Aid for Scientific Research (C) (No. 17540385) from the Japan Society for the Promotion of Science. This work was part of a Joint Research Program of the Institute of Low Temperature Science, Hokkaido University. Some of the
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