Theoretical study of interaction of winter flounder antifreeze protein with ice

Abstract

Antifreeze proteins (AFPs) are synthesized by various organisms to enable their cells to survive subzero environment. These proteins bind to small ice crystals and inhibit their growth, which if left uncontrolled would be fatal to cells. The crystal structures of a number of AFPs have been determined; however, crystallographic analysis of AFP–ice complex is nearly impossible. Molecular modeling studies of AFPs’ interaction with ice surface is therefore invaluable. Early models of AFP–ice interaction suggested H-bond as the primary driving force behind such interaction. Recent experimental evidence, however, suggested that hydrophobic interactions could be the main contributor to AFP–ice association. All computational studies published to date were carried out to verify the H-bond model, and no works attempting to verify the hydrophobic interaction model have been published. In this work, we Monte Carlo–minimized complexes of several AFPs with ice taking into account nonbonded interactions, H-bonds, and the hydration potential for proteins. Parameters of the hydration potential for ice were developed with the assumption that the free energy of the water–ice association should be close to zero at equilibrium melting temperature. Our calculations demonstrate that desolvation of hydrophobic groups in the AFPs upon their binding to the grooves at the ice surface is indeed the major stabilizing contributor to the free energy of AFP–ice binding. This study is consistent with available structural and mutation data on AFPs. In particular, it explains the paradoxical finding that substitution of Thr residues with Val does not affect the potency of winter flounder AFP whereas substitution with Ser abolished its antifreeze activity.

To survive subzero temperatures, living organisms have to protect themselves from fatal ice crystal growth (DeVries 1974). Some of these organisms produce antifreeze proteins (AFPs), which depress the freezing point of their bodily fluids. The freezing point of a solution at a given pressure is the temperature at which liquid and solid phases have the same free energy. Some antifreeze compounds, such as ethylene glycol, lower the freezing point by an amount proportional to their molar concentration. In contrast, AFPs exhibit antifreeze activity at molar concentrations 300×–500× lower than that of small compounds (Harding et al. 1999). This unusual antifreeze activity is apparently due to the binding of AFP to specific surfaces on the ice seed crystals (Wilson 1994).

AFPs were first found in the blood of polar fish living in the subzero Antarctic waters (Scholander et al. 1957; DeVries 1980 DeVries 1982 DeVries 1983). Currently, structures of five types of AFPs have been determined (Davies and Sykes 1997). Type I AFPs are alanine-rich α-helical proteins of 3.3–4.5 kD (Duman and DeVries 1974,Duman and DeVries 1976; Hew et al. 1985). Type II AFPs are cysteine-rich globular proteins containing five disulfide bonds (Slaughter et al. 1981; Ng et al. 1986; DeLuca et al. 1996). Type III AFPs are globular proteins of ~6 kD (Ng an Hew 1992; Jia et al. 1995; Sonnichsen et al. 1996). Type IV AFPs are glutamate- and glutamine-rich α-helical proteins (Deng et al. 1997). The fifth category comprises hyperactive AFPs from insects (Graham et al. 1997; Liow et al. 2000).

Type I AFPs are the best studied AFP type and have been isolated from shorthorn sculpin, winter flounder, and other organisms. The winter flounder AFP HPLC6 (Sicheri and Yang 1995) has 37 amino acids arranged in three 11-residue repeats ThrX₂AsxX₇, where Asx is Asp or Asn, and X is usually Ala (Table 1). This protein is further referred to as WF AFP. CD and NMR studies revealed that WF AFP has an α-helical structure with disordered amino and carboxy termini. The X-ray study of WF AFP (Sicheri and Yang 1995) confirmed its α-helical structure and revealed an amino-terminal cap formed by Asp 1, Thr 2, Ser 4, Asp 5, a carboxy-terminal cap formed by the amidated Arg³⁷, and a salt bridge Lys¹⁸—Glu²² apparently stabilizing the α-helix (Fig. 1A ▶). When WF AFP is viewed along the α-helical axis, three faces may be distinguished: a hydrophobic face formed by alanines and methyl groups of threonines, a hydrophilic face formed by Arg, Glu, Ser, and Asn residues, and a Thr–Asx face formed by hydrophilic groups of Thr and Asx residues (Fig. 1B,C ▶).

Table 1.

Winter flounder HPLC6 and its mutants

Code	Sequence					Hysteres, % to WF AFP at 2 mM	α-Helicity,%	Reference
	1	2	13	24	35
HPLC6	D	TASDAAAAAAL	TAANAKAAAEL	TAANAAAAAAA	TAR	100	98	Loewen et al. (1999)
S23	D	TASDAAAAAAL	NAATAKAAAEL	TAAAAANAAAA	TAR	17	95.3	Wen and Laursen (1993)
TSST	D	TASDAAAAAAL	SAANAKAAAEL	SAANAAAAAAA	TAR	0.11	100	Haymet et al. (1998)
SSSS	D	SASDAAAAAAL	SAANAKAAAEL	SAANAAAAAAA	SAR	0	100	Haymet et al. (1998)
STSS	D	SASDAAAAAAL	TAANAKAAAEL	SAANAAAAAAA	SAR	0	105	Zhang and Laursen (1998)
SSSS2KE	D	SASDAKAAAEL	SAANAKAAAEL	SAANAKAAAEA	SAR	0	100	Haymet et al. (1998)
TVVT	D	TASDAAAAAAL	VAANAKAAAET	VAANAAAAAAA	TAR	85	100	Chao et al. (1997)
VVVV2KE	D	VASDAKAAAEL	VAANAKAAAEL	VAANAKAAAEA	VAR	100	100	Haymet et al. (1998)
AAAA2KE	D	AASDAKAAAEL	AAANAKAAAEL	AAANAKAAAEA	AAR	17	100	Haymet et al. (1998)
S21	D	TASADAAAAAN	LAANAKAAAEL	TAAAAANAAAA	TAR	0	106.2	Wen and Laursen (1993)
S22	D	TASDAAAAAAN	LAATAKAAAEL	TAAAAANAAAA	TAR	30	96.4	Wen and Laursen (1993)
S41	D	TASDAALAAAA	TAANKLAAAEA	TAANAAAAAAA	TAR	0	103	Wen and Laursen (1993)
S42	D	TASDAAAAAAA	TAANLKAAAEA	TAANAAAAAAA	TAR	0	102	Wen and Laursen (1993)
A17L	D	TASDAAAAAAL	TAANLKAAAEL	TAANAAAAAAA	TAR	0		Baardsnes et al. (1999)
A19L	D	TASDAAAAAAL	TAANAKLAAEL	TAANAAAAAAA	TAR	80		Baardsnes et al. (1999)
A20L	D	TASDAAAAAAL	TAANAKALAEL	TAANAAAAAAA	TAR	100		Baardsnes et al. (1999)
A21L	D	TASDAAAAAAL	TAANAKAALEL	TAANAAAAAAA	TAR	10		Baardsnes et al. (1999)

Figure 1.

(A,B) Perpendicular views at the X-ray structure of WF AFP. (C) Schematic representation of the AFP viewed along the helical axis. The scheme shows hydrophobic, hydrophilic, and Thr–Asx faces. Side chains of Thr, Asx, and Glu–Arg residues are shown as protrusions on the cylindrical surface of the α-helix.

The major characteristics of AFP activity are thermal hysteresis and modification of ice crystal growth morphology. AFPs inhibit thermodynamically favorable growth of ice crystals by creating a heterogeneous layer between the solid ice and liquid water. The difference between the freezing and melting temperature of the AFP solution is defined as the temperature of thermal hysteresis. The thermal hysteresis curve has a hyperbolic form. Inhibition of ice growth has been explained as a kinetically controlled process (Burcham et al. 1986) due to the effect of AFP molecules covering the water-accessible surfaces of ice.

Early models suggested H-bonding of AFPs’ Thr residues to ice was the major driving force of AFP–ice association (DeVries 1974; Raymond and DeVries 1977; Brooke-Taylor et al. 1996; Haymet et al. 1999) with AFP binding to ice via the Thr–Asx face. However, mutational experiments demonstrated that substitution of Thr residues by Val did not change the AFP activity significantly (Haymet et al. 1999), whereas substitution of the same Thr residues by Ser eliminated the AFP activity (see Table 1; Zhang and Laursen 1998). Furthermore, mutation of Ala 19 and Ala 21 at the hydrophobic side of the AFP helix to Leu residues reduced the WF AFP activity, whereas mutation of Ala 17 and Ala 20 did not (Baardsnes et al. 1999). These experiments suggested that the Thr–Asx face of WF AFP helix is not involved in AFP’s binding to ice, thus questioning the H-bond model of AFP action. As an alternative to the H-bond model, van der Waals and hydrophobic interactions were suggested to play important roles in AFP binding (Haymet et al. 1999).

Several molecular modeling studies of AFP–ice complexes were performed with the aim to understand the atomic mechanisms of AFP–ice association. The earlier modeling studies attempted to explain how AFPs’ binding affects the morphology of growing ice crystals. In the absence of AFP, ice crystals grown from solution exhibit only basal {000̄1} and prism {101̄0} faces (Fig. 2 ▶) and appear as round and flat discs. AFPs modify the disc into a crystal that displays other faces. DeVries and Lin (1977) suggested that the change in crystal morphology is due to binding of AFPs to the prism faces of ice via H-bonds. They reasoned that the distance of 4.5 Å between Thr and Asx in WF AFP matches the distance between oxygen atoms on the prism face of ice. However, this model did not explain the specificity of AFP binding to the prism face because the 4.5 Å distance can be found in many different crystallographic faces of ice.

Figure 2.

Side views at the surface (202̄1) of ice. Loosely bound waters are defined as those that have a single H-bond to the ice. In our computations, we used the surface that has no loosely bound waters.

Subsequent models of AFP–ice complexes attempted to explain the results of ice etching experiments that demonstrated specific binding of WF AFP to ice’s pyramidal planes {202̄1} with the protein aligned along the 〈011̄2〉 vectors (Knight et al. 1991). In one study, the use of Monte Carlo (MC) simulated annealing and energy minimization in vacuum (Chou 1992) predicted WF AFP binding to pyramidal planes in a zipperlike fashion with Thr side chains H-bonded to ice. In this model, the predicted distance of 16.1 Å, which separates two Thr residues on the protein’s surface, matched the repeat distance of 16.7 Å, which separates two oxygen atoms along the [011̄2] vector, on the pyramidal plane of ice (Chou 1992). Other molecular dynamics (MD) simulation studies of WF AFP in water also indicated the involvement of H-bonds in AFP–ice interaction (Haymet and Kay 1992; McDonald et al. 1992; Jorgensen et al. 1993).

Lal et al. (1993) combined MC and MD methods to simulate AFPs’ binding to explicit models of the pyramidal and basal planes of ice crystals in vacuum. Only a small difference in the H-bond energy of WF AFP with the pyramidal and basal planes was predicted, whereas the energy of van der Waals interactions of AFP with the pyramidal plane was found to be considerably larger than that with the basal plane. Consequently, a “lock and key” mechanism based on the high complementarity was proposed to explain why WF AFP binds to the pyramidal plane. The predicted binding energy for WF AFP to the pyramidal plane was rather high (−84 kcal/mole). The authors suggested the omission of solvation in the simulation studies could be the cause of this high value. MD simulation at 0°C by Brooke-Taylor et al. (1996) found that water around the hydrophobic regions of AFP tends to form H-bonded clusters. The authors proposed that WF AFP interacts with ice through H-bonds, while hydrophobic groups of AFP impede further binding of water molecules to ice and therefore prevent the growth of the ice crystal.

MD simulation of WF AFP at the (202̄1) surface of ice in the presence of explicit water molecules (Cheng and Merz 1997) predicted ice–AFP binding energy of −157 kcal/mole. This is about twice as large as the energy reported by Lal et al. (1993). Furthermore, the predicted energy of interaction of AFP with ice and waters (−1062 kcal/mole) was higher than the energy of complete hydration of AFP (−1167.4 kcal/mole). The model predicted that methyl groups of Thr and Leu dock in the grooves on the ice surface, suggesting that hydrophobic interactions may contribute to the AFP binding via reducing penalty for exposure of these groups in water.

In contrast with the H-bond model of AFP–ice binding, mutation studies demonstrated that Thr substitution by Val does not eliminate AFP activity (Zhang and Laursen 1998; Haymet et al. 1999), suggesting that van der Waals interactions may determine WF AFP binding to ice. Dalal and Sonnichsen (2000) tested this hypothesis by minimizing the energy of WF AFP with ice from ~250,000 starting points. In the lowest energy complex, the Thr–Asx face aligns along vector 〈11̄02̄〉 at surface {202̄1}. The authors concluded that van der Waals interactions alone could not explain structure–activity relationships of WF AFP and its mutants.

In this study, we estimated free energy of AFP–ice binding |Δ_GAFP–ice| from an analysis of experimental antifreeze activity data. Our deduced |Δ_GAFP–ice| value is smaller than 5 kcal/mole. This small free energy of binding is a difference of two large components, the energy of interaction between AFP and ice binding surfaces in vacuum and the energy of hydration of these surfaces. Simulation of the AFP–ice system with explicit waters is unlikely to reproduce this small energy for two reasons. First, parameters of the force fields are not perfect. Second, thousands of explicit water molecules must be added to the system of AFP and ice to ensure their complete hydration. However, during a MD trajectory, such a large system is unlikely to move far from the starting geometry in a reasonable time of simulation.

In this study, we model AFP binding the ice surface 202̄1, the preferred binding surface for winter flounder AFP (Knight et al. 1991). We treat the water environment implicitly and use a Monte Carlo energy minimization (MCM) method (Li and Scheraga 1987). Hundreds of MCM trajectories launched from randomly generated starting points predict optimal orientations of WF AFP at ice. Our models explain most of the available experimental data on structure–activity relationships of WF AFP and their mutants.

Results

Experimental binding energy of WF AFP to ice

Free energy of binding of AFP to ice (Δ_GAFP–ice) is not available in the literature. We estimated Δ_GAFP–ice from the data on thermal hysteresis ΔT.

Let us consider a typical thermal hysteresis experiment, in which an ice crystal of radius r is embedded in a drop of AFP solution of radius R. A projection of an α-helix of WF AFP of 50 Å in length and 10 Å in diameter on the ice surface area is 5•10⁻¹² mm². The surface the ice sphere can accommodate 4πr²/5•10⁻¹² = 8π•10¹¹ × r² molecules of AFP. When AFP concentration (C_AFP) equals 0.5 mM, the drop would contain 4π•10¹⁴ × R³ molecules of AFP. The ratio between the number of AFP molecules in the drop and the number of available AFP binding sites on the ice crystal can be calculated as:

In a typical experiment when R ≈1 mm and r ≈ 0.2 mm, the number of AFP molecules would be 1.25•10⁴. In other words, the number of AFP molecules in solution exceeds the number of binding sites at the ice surface by at least three orders of magnitude. In other words, the fraction of AFP molecules bound to the ice surface is always negligible when compared to the total number of AFP molecules in solution. Let us consider the following process at equilibrium condition:

The number of AFP molecules that are attaching to the ice surface (N_k+) should be equal to the number of AFP molecules that are dissociating from the ice surface (N_k−):

(1)

Burcham et al. (1986) applied the equation of Langmuir (1918) to relate θ, a fraction of the ice surface covered by AFP with concentration C_AFP and the rate constants of the direct (k₊) and reverse (k₋) reactions of AFP binding to ice:

(2)

Rearranging (2) gives expressions for the association constant K_a:

(3)

Further rearrangement gives an expression for θ in which K_d = 1/K_a is the dissociation constant:

(4)

We define fractional hysteresis activity (ΔT_F) as the ratio between thermal hysteresis temperature at the given concentration of AFP (ΔT_C) and the maximal attainable thermal hysteresis temperature of an AFP solution (ΔT_max). Let us assume that ΔT_F is a function of θ:

(5)

Combining equations 5 and 4 gives us equation 6, in which ΔT_C is a function of CAFP:

(6)

Equation 6 fits the experimentally observed thermal hysteresis curves when

(7)

suggesting that equation 7 can be used as a first approximation of the function ψ. Combining equations 6 and 7 gives the final equation for ΔT_C:

(8)

Equation 8 shows that K_d is equal to C_1/2, the concentration of AFP at which ΔT_C is half of ΔT_max. ΔG_AFP–ice is related to K_d by the fundamental Arrhenius equation

(9)

Using equation 9 with the experimental value of C_1/2 ~ 0.5 mM for WF AFP²⁸, R ≈ 1.99 cal mole-1 K⁻¹, and T = 273 K gives the estimate of the free energy of binding:

Earlier predictions of AFP–ice binding energy in vacuum were on the level of hundreds of kilocalories per mole (see, e.g., Cheng and Merz 1997). A reasonable way to bring this huge energy to the neighborhood of the above estimate of ~4 kcal/mole is to include the hydration energies of AFP and ice into consideration. It is understood that the hydration energies of AFP and ice are large and therefore can easily compensate for the huge binding energy as predicted by published studies. Before addressing computation of the hydration energies, we describe our results of simulations in vacuum.

MC-minimizing AFP–ice complexes in vacuum

First, we attempted to estimate van der Waals, electrostatic, and H-bond interactions that stabilize AFP–ice complexes by calculating MCM trajectories in vacuum from many starting positions of AFP at different ice slabs. Many minima with different orientations of AFP on ice were found (data not shown). In the MC-minimized structures, AFPs H-bond to the ice surface via the Thr–Asx face (Fig. 3 ▶). These results are consistent with earlier theoretical studies that predicted H-bonds to be the major driving force of AFP–ice association in vacuum. As in the earlier studies, our MC-minimization in vacuum also could not explain why mutation of Thr to Val did not affect the AFP activity whereas mutation of Thr to Ser did (Table 1).

Figure 3.

(A) MC-minimized complex of WF AFP bound to surface (202̄1) computed in vacuum. AFP binds by the Thr–Asx face, forming H-bonds. The binding energy is −57.3 kcal/mole. (B) Conformations of Thr residues found in the complex have χ₁ ~ −60° (left), 60° (middle), and 180° (right). In the conformation with the strongest binding energy in vacuum (χ₁ ~ −60°), Thr accepts an H-bond from ice and donates an H-bond to the AFP carbonyl four position upstream. Van der Waals interactions of the methyl group in Thr and ice additionally stabilize the complex.

Second, we explored systematically the steric complementarity between ice and different faces of AFP. A reasonable measure of AFP–ice complementarity is van der Waals energy of their complex. The torsional component was also included to keep AFP side chain torsions near their canonical conformations. When considering the AFP helix as a rigid body, its position and orientation are characterized by six variables that govern three translational and three rotational degrees of freedom. All these parameters were varied in the MC-minimizations (see Materials and Methods). Fewer than six parameters are needed to describe the mutual disposition of the AFP and ice. Indeed, in the ice-bound AFP, the helix axis is approximately parallel to the ice surface, and mutual disposition of ice and AFP may be described by three variables: distance from the ice surface to the helical axis d, angle ψ between the helical axis and the a axis on the basal plane of ice, and angle ϕcharacterizing rotation of AFP around the helical axis. We define ϕ as the angle between the ice plane and the unit vector V, which is normal to the AFP helical axis and passes through the midpoint of the salt bridge Lys 18–Gly 22. Variation of ϕ would cause different AFP faces to approach the ice surface. A plot of MC-minimized energy against ϕ would characterize complementarity of ice to different AFP faces. Building such a plot requires imposing target values of ϕ, ϕ_t. To do that, we introduced a torque penalty function sin (ϕ − ϕ_t). The penalty function imposes penalty forces to a pair of pseudo atoms at the ends of vectors V and −V. To keep AFP within the ice slab’s boundary, C^α of Ala 19 of AFP was constrained via a flat-bottom penalty function to an axis drawn normal to the ice surface and originating from the slab center. Angle ϕ_t was sampled from 0° to 360° with a 20° step. For a given value of ϕ_t, the sum of van der Waals and torsional energies was MC-minimized in the space of six parameters specifying position and orientation of AFP and all side chain torsions. The plot of MC-minimized energy against ϕ_t is shown in Figure 4 ▶. Values of ϕ_t between 80° and 280° correspond to low-energy complexes in which the WF AFP helical axis aligns parallel to vector [011̄2] on surface (202̄1). In the apparent global minimum, WF AFP binds to ice by the Thr–Asx face (Fig. 5A ▶). AFP binding by its hydrophobic (Fig. 5B ▶) and hydrophilic (Fig. 5C ▶) faces is weaker by 20% and 30%, respectively. The small energy difference of the three binding modes indicates that geometric complementarity alone cannot explain the specificity of AFP–ice association.

Figure 4.

MC-minimized energy of AFP–ice interaction plotted against angle ϕ that characterizes the helix rotation around the helical axis. Angle ϕ is counted between the ice plane and the vector normal to the AFP helical axis and drawn from the axis to the middle of the salt bridge Lys¹⁸—Gly²². Once defined for the X-ray structure of AFP, the vector does not depend on the AFP conformation in models. The energy is a sum of van der Waals and torsional components.

Figure 5.

Complexes of WF AFP with the surface (202̄1) of ice corresponding to various values of ϕ in the plot of MC-minimized energy E of van der Waals and torsional interactions in Figure 4 ▶. (A) The lowest energy complex. AFP interacts with the ice surface by its Thr–Asx face. Both methyl and hydroxyl groups of Thr stabilize the complex. AFP aligns along vector 〈011̄2〉 on ice surface. (B) The complex in which AFP interacts with the ice surface by its hydrophobic face involving methyl groups of Thr residues. (C) The complex in which AFP interacts with the ice surface by its hydrophobic face that involves both hydrophobic methyl and hydrophilic hydroxyl groups of Thr.

MC-minimizing AFP–ice complexes in water

Baardsnes et al. (1999) suggested that hydrophobic interactions drive AFP–ice interaction. Theoretical study of this scenario requires computing of free energy of the complex system that include ice, AFP, and explicit waters. This would involve huge computational resources. One such study is being carried out at the Pittsburgh Supercomputer Center by Madura et al., who reported preliminary results on this exciting simulation experiment at a recent meeting (Madura et al. 2003). Simulation of the binding of WF AFP to two surfaces took months of supercomputer time. In the present study, we avoided huge computational cost by using an energy scoring function to estimate relative probabilities of different AFP–ice complexes. For this purpose, we adopted an implicit-waters method proposed by Augspurger and Scheraga (1996) for computing hydration energy of proteins. This required development of certain parameters as described below.

Parameters for computing the hydration energy scoring function

The method developed by Augspurger and Scheraga (1996) for computing the dehydration energy cannot be applied directly to the AFP–ice system for two reasons. First, three important parameters required by the Augspurger and Scheraga method are not available readily. These three parameters are δ_ice, the free energy required to remove a water molecule from the hydration shell of ice; R^h_ice, radius of the hydration shell of an ice water molecule; and R_VR, the reduced van der Waals radius of the ice water. Second, parameters for protein dehydration were derived for room temperature and therefore cannot be applied directly to 0°C. We made the following modifications in order to adopt the Augspurger and Scheraga method to the AFP–ice system. First, we assumed that at the melting temperature (thermodynamic equilibrium point) the free energy of a water molecule in the bulk should be very close to the free energy of a water molecule at the ice surface and therefore δ_ice can be assigned a value of zero. A direct consequence of this assumption is that the value of R^h_ice also becomes irrelevant. Second, our preliminary computation of a series of MCM trajectories of the WF AFP–ice complex with R_VR varied between 1 and 3 Å found the ice–AFP dehydration energy to be highly sensitive to R_VR. The earlier estimated binding energy of 4.1 kcal/mole was reproduced with R_VR = 1.95 Å. The adoption of this calibrated value of R_VR should also compensate for errors resulting from applying protein-dehydration parameters derived at 25°C to the AFP–ice system at 0°C.

Using thus calibrated hydration-energy scoring function along with van der Waals, electrostatic, and torsional energy components, we calculated 50 MCM trajectories from randomly generated starting points. Only five trajectories converged to complexes within 3 kcal/mole from the apparent global minimum, whereas other trajectories were trapped in high-energy local minima. The energy landscape had a highly rugged shape. Further analysis revealed that the rugged shape is due to electrostatic interactions between AFP and ice that are highly sensitive to orientation of individual ice molecules. Apparently, reorientation of the ice molecules upon AFP binding could smooth the energy landscape; however, in this study we used a rigid model of ice (see Materials and Methods) for reducing the number of degrees of freedom, and, hence, computation time. Because reorientation of ice molecules was not allowed in our simulation, it resulted in a highly rugged energy landscape. Another observation from the preliminary calculations was that increasing the dielectric constant ɛ improved convergence of MCM trajectories with little effect on the optimal orientation of AFP on ice. Based on these two observations, we decided to improve convergence by excluding the electrostatic term from the energy expression. To compensate for this change, we recalibrated R_VR as described above and arrived at a new value of R_VR = 1.9 Å with which calculations reproduced the estimated binding energy of 4.1 kcal/ mole. This new force field, VS (van der Waals and solvation), was used in all subsequent calculations. Using the VS force field, we launched 50 MCM trajectories from random starting points and found that 40 trajectories converged to structures within 3 kcal/mole of the apparent global minimum. Importantly, the optimal structures found with the VS force field were similar to those found with electrostatics and R_VR = 1.95 Å.

Searching optimal orientation of AFP and its mutants on ice surface (202̄1)

In the search of optimal complexes with the use of the VS force field, many starting positions of AFP were randomly generated. In addition to keeping the AFP within the ice boundary as previously described, we constrained amino and carboxy termini of AFP to within 15 Å of the ice surface plane by flat-bottom penalty functions. To preserve the α-helical structure of WF AFP, the backbone torsions were fixed, whereas all side chain torsions were allowed to vary. These constraints did not bias AFP orientation on ice, but improved convergence of MCM trajectories. The maximal length of the MCM trajectories was limited to 10,000 steps. Usually, an apparent global minimum was found in ~3000 steps, but an additional 7000 steps were computed to ensure that no better minimum was missed.

Figure 6A ▶ shows superposition of snapshots of MCM trajectories. During a single trajectory, AFP moves from a randomly generated starting point to the ice surface. In the MC-minimized complexes, AFP molecules have different orientations on the ice surface, but AFP side chains always fill ice grooves (Fig. 6A ▶). Figure 6B ▶ shows snapshots of a typical MCM trajectory taken at every energy drop, and Figure 6C ▶ shows how energy changes during the trajectory. AFP rapidly approaches the ice surface and then finds an optimal orientation at the surface. In the low-energy complexes, the α-helix extends along the 〈011̄2〉 vector, forming tight contact with the ice surface by its hydrophobic face (Fig. 6D ▶). Methyl groups of Thr are found in the ice grooves and hydroxyl groups are exposed to the solution. Thr residues have χ₁ ≈ −60°, as in the crystal structure, with the side chain hydroxyl H-bonded to the main chain carbonyl. Hydrophilic side chains of Asp and Asn are exposed to water.

Figure 6.

Searching optimal complexes of WF with surface (202̄1) of ice. (A) Superposition of snapshots of MCM trajectories generated from random starting points. (B) Snapshot of a single MCM trajectory. (C) Energy convergence in a typical MCM trajectory. (D) Structure of a typical MC-minimized complex.

An interesting feature in structure-activity relationships of AFPs is that substitution of Thr by Val does not decrease the antifreeze activity whereas substitution to Ser and Ala does (see Introduction). To rationalize these experimental observations, we simulated the ice complexes with the three mutants. The predicted optimal complexes of ice with the Thr→Val mutant are similar to those with the wild type except that both methyl groups of Val are in the ice grooves (Fig. 7A ▶). The stronger interaction of this mutant with ice (Table 2) apparently due to the extra interaction with the second methyl group of Val would imply higher AFP activity. This, however, is not seen in experiments (Table 1). A possible explanation is that the mutant molecules aggregate at the higher concentration because of the increased hydrophobicity (Loewen et al. 1999) and therefore prevent the ice-binding surface from interacting with ice.

Figure 7.

MC-minimized complexes of mutants of WF AFP with surface (202̄1) of ice computed using the VS force field. (A) Complex of the Thr → Val mutant is similar to that of wild-type WF AFP. Favorable dehydration of the methyl group in Val results in a stronger binding affinity. (B) Complex of the Thr → Ser mutant does not have specificity to the ice. The binding energy is weak because large Leu residues fail to fit the grooves at the ice surface and their exposure to water destabilizes the complex. (C) The Thr → Ala mutant has a higher binding affinity than the Thr → Ser mutant. However, in contrast to the wild-type WF AFP and its Val mutants, methyl groups of Ala residues form rather weak contacts with the ice grooves; this results in weaker van der Waals contacts with ice.

Table 2.

AFP–ice interaction energies in MC-minimized complexes of WF AFP and its mutants with the (202̄1) face of ice

AFPa	van der Waals energy	Solvation energy	Total
TTTT	−18.4	13.5	−4.9
VVVV	−20.3	12.4	−7.9
SSSS	−4.8	2.3	−2.5
AAAA	−15.9	12.4	−3.5

^a Residues in positions 2, 13, 24, and 35. Residues in other positions correspond to HPLC6 (Table 1).

MC-minimized complexes of the Thr → Ser mutant with ice have weaker binding energy (Table 2), which agrees with the low antifreeze activity (Table 1). Favorable interactions of Ser residues with water caused the AFP helix to turn from the orientation observed in the wild type so that Leu 12 and Leu 23 contacted the ice surface. These, however, do not fit in the ice grooves (Fig. 7B ▶). Thus, the Thr → Ser mutant contributes more solvation energy, but less van der Waals energy than the wild type to interaction with ice. The total binding energy of the mutant is smaller than that of the wild type (Table 2).

In the optimal complexes of the Thr → Ala mutant with ice, the AFP orientation is similar to that in the wild type (Fig. 7C ▶). However, the side chain of Ala is too small to fill the ice groove, bringing a smaller van der Waals contribution to the binding energy (Table 2).

Figure 8 ▶ illustrates the relationship of the experimentally measured hysteresis of WF AFP and three mutants with the predicted fractional density ϕ of these proteins on the ice surface (202̄1). The fractional density was calculated from the binding energy by applying equations 4 and 9 and is related to the experimentally observed fractional hysteresis ΔT_F according to equations 5 and 7. Two proteins demonstrating the largest hysteresis (WF AFP and its TTTT mutant) are predicted to have the largest fractional density. Both AAAA and SSSS mutants demonstrate much lower hysteresis, and calculations predict lower fractional density for these proteins.

Figure 8.

Calculated fractional density ϕ and experimentally observed temperature of thermal hysteresis (relative to WF) for WF AFP and its mutants.

Discussion

The driving force of AFP–ice binding

When hydration of AFP and ice was ignored, previous simulation studies predicted large binding energy with major contributions from H-bonds and electrostatic interactions. Addition of explicit waters to the AFP–ice system (Cheng and Merz 1997), however, resulted in a too complex system that was not expected to move far away from starting points in a limited time of simulation. The implicit-waters approach adopted in this study allows the detection of small changes of large hydration energies upon AFP–ice binding in a relatively short simulation time.

The basic question addressed in this study is the nature of the driving force of AFP–ice association. In terms of binding energy, what could ice offer to AFP that water could not? We reason that “soft” molecules of bulk water can form close contacts with AFP, which are optimal in terms of van der Waals, electrostatic, and H-bond energy. “Rigid” water molecules of ice, however, are unlikely to form optimal contacts with AFP because the geometric requirement of H-bonds are less likely to be completely satisfied. In other words, van der Waals, electrostatic, and H-bond potential of AFP should be satisfied by “soft” water better than by “rigid” ice. This leaves hydrophobic interactions as the most likely energy component to drive the AFP–ice association.

Entropic in nature, hydrophobic interactions occur because hydrophobic groups at the water-accessible area do not form H-bonds with water molecules. Water molecules around hydrophobic groups maximize the number of H-bonds by forming entropically unfavorable “cages.” Hydrophobic groups gather together to minimize the net hydrophobic area exposed to water and thus minimize the number of water molecules in the cages. This process apparently drives protein folding, aggregation, and binding to surfaces.

Upon AFP–ice association, the AFP hydrophobic groups dip into the grooves on the ice surface, releasing the caged waters to the bulk phase, an entropically favorable process. It is possible that there is a small enthalpic price because van der Waals and electrostatic interactions of a water molecule with the “soft” bulk water is stronger than with “rigid” waters in ice. The overall enthalpic price however is unlikely to override the entropic gain.

Structure–activity relationships

In this work, we modified a standard force field by developing a solvation energy scoring function and calibrated it to reproduce the experimental AFP–ice binding energy. No considerations of structure–activity relationships have been taken into account at the stage of development of the scoring function. With the force field thus calibrated, we computed the optimal structures of four AFP molecules on the ice surface. The analysis of these results allows understanding of the interesting peculiarities of structure–activity relationships of AFP molecules.

Several structural properties of AFPs are crucially important for their function. First, AFPs should obviously be water-soluble. Second, the AFP ice-binding surface needs hydrophobic groups that can provide large entropic gain to the ice–AFP binding energy. Third, AFPs should have rather rigid backbone conformation to prevent hydrophobic collapse of these groups in water. Fourth, the ice-binding surface of AFPs should be complementary to an ice surface. In lack of complementarity, poor van der Waals contacts between ice and AFP would not compensate for the loss of van der Waals contacts between AFP and water. Fifth, the AFP hydrophobic face should not be self-complementary; otherwise self-aggregation would occur (Fig. 9A ▶). The latter restriction explains why WF AFP binds preferably to rough surfaces of ice, such as {202̄1}. WF AFP has all of the above features. Thr residues at the hydrophobic face form protrusions 16.5 Å apart, a distance large enough to prevent AFP dimerization but short enough to fit in the parallel ice grooves (Fig. 9C ▶). To avoid self-aggregation, WF AFP is not complementary to the smooth surface {0001}. Among other ice surfaces, surface {202̄1} observable in the ice etching experiment has the best binding affinity to WF AFP. The Lys–Glu salt bridge stabilizes the α-helix; introduction of additional salt bridges makes AFP even more rigid as was shown by CD experiments (Chakrabartty and Hew 1991). Apparently, the salt bridge along with Asp and Asn residues increases solubility and prevents self-aggregation. Mutational studies suggested the importance of Asn residues for WF AFP solubility and Leu residues for preventing α-helix aggregation (Loewen et al. 1999).

Figure 9.

Possible scenarios of aggregation and binding to ice surfaces for different AFP structures. (A) A flat hydrophobic surface of AFP interacts with a flat ice surface. This structure would yield AFP–AFP aggregation. (B) The hydrophobic surface of AFP is complementary to itself. This scenario would also result in AFP–AFP aggregation. (C) The structure of the AFP surface that allows interaction with certain ice surfaces, but is not complementary to itself. Such an AFP is unlikely to aggregate. (D) Another possible way to avoid aggregation is to introduce hydrophilic groups at the hydrophobic surface. Upon binding of AFP on ice, formation of hydrogen bonds may partially compensate for a loss of contact with water for hydrophilic groups of AFP. On the other hand, the inability of hydrophobic groups to offer a hydrogen bond disfavors the aggregation.

The above five criteria of antifreeze activity may be applicable to other AFPs. Interestingly, insect AFPs with a rather flat hydrophobic surface managed to stay as monomers in solution. Dimers are only found under crystallization conditions. In the case of AFP from spruce budworm (Choristoneura fumiferana) elevated temperature (318 K) is required to produce crystals. It is reasonable to assume that the increased hydrophobic interaction at the elevated temperature is responsible for stabilizing the dimer formation for crystallization to occur (Liou et al. 2000). The hydrophobic surface of these AFPs has polar groups that can form H-bonds with water and ice but not with other AFPs, as shown in Figure 9D ▶.

In conclusion, Monte Carlo minimization with an implicit-solvent method allows prediction of optimal AFP–ice complexes that highlight the importance of hydrophobic interactions in AFP–ice binding and explain interesting peculiarities in structure–activity relationships of WF AFP and its mutants.

Materials and methods

The energy scoring function was calculated with nonbonded (van der Waals), electrostatic, and torsion terms as well as the free energy of hydration of ice and AFP. The latter was computed by the method of Augspurger and Scheraga (1996), which treats the water environment implicitly. The method was adapted to the system under consideration by introducing parameters of ice hydration as described in Results. Nonbonded interactions were calculated using the AMBER force field (Weiner et al. 1984) with a cutoff distance of 8 Å. Bond lengths and bond angles involving hydrogen atoms were fixed at their standard values (Momany et al. 1975). Electrostatic energy was calculated with the standard partial charges at atoms in amino acids (Momany et al. 1975) and a distance-dependent dielectric (Weiner et al. 1984). The partial charges of oxygen and hydrogen atoms of ice were assigned values of −0.5 and 0.25, respectively. Molecular mechanics calculations were performed in the space of generalized coordinates using the ZMM program (Zhorov 1981). In particular, three generalized coordinates that specify the position of AFP are Cartesian coordinates of its root atom, which is the C^α in the first residue. Orientation of AFP is specified by three Euler angles of the local system of coordinates defined by the root atom and its bonded neighbors. The RASMOL program was used for visualization.

Monte Carlo–minimization protocol (Li and Scheraga 1987) was used for the search of optimal conformations as described earlier (Zhorov and Ananthanarayanan 1996). Minimum-energy complexes found during an MCM trajectory were accumulated in a stack. Usually, a trajectory was terminated when the last 1000 consecutive energy minimizations did not lower the energy of the apparent global minimum in the stack and did not add a new minimum to the stack. In some trajectories, the energy converged rather fast, but the number of minima in the stack kept growing. Such trajectories were terminated after 10,000 energy minimizations.

The starting geometry of WF AFP was obtained by the energy minimization of the crystallographic structure (Sicheri and Yang 1995). The minimization structure had a straight α-helix, H-bonds Thrⁱ_OH•O_Alaⁱ⁻⁴, and χ₁ ≈ −60° in all Thr residues. This structure was also used to build homology models of WF AFP mutants. The ice was modeled as a cylindrical slab with a diameter of 80 Å and a thickness of 7.5 Å. Such a slab is large enough to accommodate a 50 Å–long molecule of WF AFP and to offer extra area to simulate translation of AFP along the ice surface. Coordinates of the oxygen atoms of the slab were generated using the program SLAB (D. Yang, unpubl.). The ZMM program was used to add hydrogen atoms, to assign random starting Euler angles to all water molecules, and to optimize their orientation in a MCM trajectory of 10,000 steps with fixed coordinates of oxygen atoms. The MC-minimized structure of ice was used in subsequent models as a rigid body. To prevent large unproductive separation of AFP from the ice slab that could occur during MC sampling, the distance r between the slab and any end of the α-helical axis was restrained within an interval d_l < r < d_h. For this purpose, a flat-bottom penalty function (Brooks et al. 1985) with d_l = 5 Å, d_h = 15 Å, and the force constant 100 kcal mole⁻¹ Å⁻² was used.

Surfaces {202̄1} of ice have a characteristic geometrical profile (Fig. 2C ▶). It has deep grooves that seemingly fit large side chains protruding from the WF AFP helix. Importantly, the depth and the profile of the grooves depend on how water molecules at the border between the ice and bulk water are treated. We define that a water molecule belongs to the ice slab if it forms at least two H-bonds with the slab (top and bottom slabs in Fig. 2C ▶). The ice surfaces thus defined do not contain loosely bound waters. Recent models of ice–AFP complexes involved explicit water molecules that can form only one H-bond with the ice surface (Cheng and Merz 1997; Dalal and Sonnichsen 2000). The weakly bound waters flatten the ice surface, decreasing the geometrical complementarity between the ice and AFP. In contrast, the geometrical complementarity between ice and AFP is important in our models, which do not include explicit water molecules that form a water pillow between AFP and ice. Ignoring the water pillows that smooth the energy hypersurface makes the search for the lowest energy structures more difficult computationally, but the optimal structures are least biased by the starting approximations.

Abbreviations

• AFP, antifreeze protein

• WF, winter flounder

• MC, Monte Carlo

• MCM, Monte Carlo minimization

• MD, molecular dynamics