Molecular Recognition of Ice by Fully Flexible Molecules - The Journal

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Molecular Recognition of Ice by Fully Flexible Molecules Pavithra Madhavi Naullage, Laura Lupi, and Valeria Molinero J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10265 • Publication Date (Web): 10 Nov 2017 Downloaded from http://pubs.acs.org on November 19, 2017

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The Journal of Physical Chemistry

Molecular Recognition of Ice by Fully Flexible Molecules Pavithra M. Naullage, Laura Lupi, and Valeria Molinero* Department of Chemistry, The University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850, United States

Abstract Cold acclimatized organisms produce antifreeze proteins that enable them to prevent ice growth and recrystallization at subfreezing conditions. Flatness and rigidity of the ice-binding sites of antifreeze proteins are considered key for their recognition of ice. However, the most potent synthetic ice recrystallization inhibitor (IRI) found to date is polyvinyl alcohol (PVA), a fully flexible molecule. The ability to tune the architecture and functionalization of PVA makes it a promising candidate to replace antifreeze proteins in industrial applications ranging from cryopreservation of organs to deicing of turbine blades. However, an understanding of how does PVA recognize ice remains elusive, hampering the design of more effective IRIs. Here we use large-scale molecular simulations to elucidate the mechanism by which PVA recognizes ice. We find that the polymer selectively binds to the prismatic faces of ice through a cooperative zipper mechanism. The binding is driven by hydrogen bonding, facilitated by distance matching between the hydroxyl groups in PVA and water at the ice surface. Strong, cooperative binding to ice results from the different scaling of the free energy gains on binding per monomer, and the loss of translational and configurational entropy of the chain. We explain why branching of PVA does not improve its IRI activity, and use the new molecular understanding to propose principles for the design of macromolecules that bind efficiently to the basal and prismatic planes of ice, producing hyperactive synthetic antifreeze molecules that could compete with the most effective antifreeze proteins.

*

corresponding author, e-mail: [email protected]

ACS Paragon Plus Environment

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1. Introduction Antifreeze proteins (AFPs) and glycoproteins (AFGPs) are produced by many organisms that thrive at sub-freezing temperatures.1-11 Ice etching studies reveal that AFPs and AFGPs preferentially recognize certain planes of ice crystals.2, 12-14 Molecular recognition of ice by antifreeze proteins has long been considered a puzzle: how does a molecule immersed in water recognize ice, which has the same type of interactions as the liquid?15-16 Although the role of hydrogen bonding on ice recognition by proteins is not fully established,17 it is known that many ice binding proteins have hydrogen-bonding residues at distances that match those between water molecules in specific ice planes.18-19 Most antifreeze proteins have quite flat and rigid binding sites;20 it has been proposed that this characteristic are important for ice binding.21-22 Consistent with that conjecture, a recent study demonstrates that fluctuations of an ice binding surface decrease the strength of its binding free energy to ice.23 These findings would suggest that flexible molecules cannot efficiently recognize and bind to ice. However, experiments indicate that polyvinyl alcohol (PVA), a flexible molecule with persistence length just 7 Å,24 recognizes the prismatic planes of ice and acts as a potent ice recrystallization agent.25-26 The mechanism of interaction of PVA with ice is still debated. There are conflicting hypothesis on whether PVA actually binds to ice,27 or it merely affects the structure of liquid water close to the ice interface.28 Lu et al. found well defined cylindrical grooves on the surface of ice in the presence of PVA in scanning tunneling microscopy (STM) experiments, consistent with direct binding of the polymer to ice.29 Moreover, ice growth-habit experiments identified that the prismatic ice planes grow slower in the presence of PVA, while the basal and pyramidal planes are unaffected.27 These results point to highly selective interactions between PVA and ice. Based on these experiments, Budke and Koop proposed that PVA binds to the prismatic faces of ice through hydrogen bonds.27 It has also been hypothesized30 that PVA binds to ice similarly to antifreeze proteins, via an anchored clathrate31 binding motif. To date there have not been studies with molecular resolution to determine the mode of binding of PVA to ice. An alternative hypothesis is that PVA prevents the growth of ice by disruption of the structure of liquid water near the ice-liquid interface, without directly binding to ice.25,

32

That

hypothesis was proposed to explain the similar ice recrystallization inhibition (IRI) activity of branched PVA molecules and their linear counterparts.30, 32 However, it is challenging to explain the


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selectivity of PVA for specific ice planes through a mode of action in which the molecule does not bind to ice crystals. While important advances have been made in establishing the effect of length and chemical functionalization on the IRI activity of PVA,25, 33 the design of new –more effective– molecular architectures is hampered by a lack of molecular understanding of the mechanism by which PVA recognizes ice and inhibits its melting and growth. Molecular dynamics simulations have the spatial and temporal resolution to elucidate the mechanism of recognition of ice by fully flexible molecules such as PVA. However, the slow dynamics and relatively large simulation cells required to study the interaction of polymers in twophase, ice-liquid systems, have hindered their use. To date there has not been any molecular simulation study demonstrating how PVA, or any other water-soluble fully flexible macromolecule, interacts with ice. Here we use large-scale molecular dynamics simulations with accurate and computationally efficient coarse-grained models to unravel how does a flexible molecule effectively recognize and bind to ice and its selectivity to the prismatic plane. Our findings provide a molecular foundation for the design of more effective synthetic ice binding molecules that could be used for environmental and industrial applications.

2. Methods A. Simulation settings We perform molecular dynamics simulations using LAMMPS.34 The equations of motion are integrated with the velocity Verlet algorithm using a time step of 5 fs. The simulation cell is periodic in the three Cartesian directions. All simulations are performed in the isobaric isoenthalpic ensemble (NpH) preceded by equilibration of the system in the isobaric isothermal (NpT) ensemble at 273 K and 1 atm. The pressure and temperature are regulated with the Nose-Hoover thermostat and barostat35, 36 with time constants 2.5 ps and 12.5 ps, respectively. The pressure is set to 1 atm, and is controlled independently in each direction, except for the one-phase simulations used to compute the radii of gyration, where a single barostat was used to control the pressure in all directions. B. Models Water is modeled with the monoatomic water model mW, in which each molecule is represented by a single particle that interacts only through short-range anisotropic interactions.37 mW mimics the hydrogen-bonded order of water through a non-bonded three body interaction that


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encourages tetrahedral configurations.37 The mW model has been extensively validated to reproduce the structure,37-41 thermodynamics,37, 41-47 interfacial properties,37, 48-54 and phase transitions of water.23, 37-39, 42, 44, 54-62

The equilibrium melting temperature of hexagonal ice in the mW model Tm = 273 ± 0.5

K.47 PVA is modeled with a united atom model, i.e. without hydrogen atoms. The nonbonded interactions between the CH3, CH2 and CH groups are represented by the UA-OPLS force field,63 based on Lennard-Jones interactions, while the hydroxyl group is modeled with mW,37 based on the Stillinger-Weber potential.64 Here we call “C” the UA CH3, CH2 and C, and “O” the UA OH. The bonds, angles and dihedrals were taken from UA-OPLS,63 with the following modifications: i) the strength constants for the bonds and angles were softened as in ref. 50 to allow for integration of the equations of motion with 5 fs time step, and ii) the parameters for the CCCO dihedral were considered to be identical to those of the CCCC. Following ref. 23, the interactions between hydroxyl groups and water are modeled as identical to those between water molecules. Non-bonded interactions between UA-OPLS carbon types, mW water, and hydroxyl groups are modeled with Lennard-Jones potentials, assuming that all alkane moieties interact in an identical manner with mW. The size of the water-hydrocarbon interaction σWC = 0.3536 nm is taken from ref. 23. Here we tune the strength εWC of that interaction to reproduce the experimental65 radius of gyration (Rg) of PVA in water at 308 K as a function of the molecular weight. We compute the radius of gyration (Rg) of PVA with degrees of polymerization (DP) from 30 to 240 in mW water at 308 K and 1 bar. The initial strength of the water-hydrocarbon interactions, εWC = 0.17 kcal mol-1, was parameterized to reproduce surface tension of the nonane-water interface.50 We find that a strengthening to εWC = 0.204 kcal mol-1 provides good agreement between the computed radii of gyration and the experimentally reported ones (Figure 1). In modeling the two-armed and three-armed PVA architectures, the UA phenyl group and its interaction with mW water are taken from ref. 66, and the bonded interactions between the chain and the phenyl group are adopted from the AMBER unitedatom force field,67 with the softened strength constants from ref. 66.


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Figure 1. Radius of gyration Rg of PVA in liquid water at T = 308 K as a function of molecular weight of the polymer. Red circles are experimental values, from ref. 65. Geen circles are simulation values with strength of the water-hydrocarbon interaction εWC = 0.204 kcal mol-1.

Simulations cells that contain liquid water and a single PVA molecule are evolved for 200 ns for the calculation of the radii of gyration. The simulation boxes have dimensions of 5 nm × 5 nm × 5 nm for DP 30, 10 nm × 5 nm × 5 nm for DP 60 and 10 nm ×10 nm × 10 nm for DP 120 and 240. To elucidate the interaction of PVA with ice, we prepare two-phase simulation cells in which ice exposes either the basal

0001 , primary prismatic

1010 , or secondary prismatic

1120 planes to the liquid. The two-phase simulation cells contain approximately the same amount of water molecules in the liquid and ice phases. A single PVA molecule is initially placed and equilibrated in the liquid phase, and the simulations are evolved for times up to 600 ns, during which we monitor the binding of PVA to ice. The molecules considered in this study are i) linear PVA with DP 20, 30 or 60, with most of the studies performed for DP 20 as it already exhibits strong IRI activity25 while requiring smaller simulation cells, ii) two-armed and three-armed star PVA molecules with the architectures of ref. 32, in which a central phenyl group is functionalized with two or three arms of DP 10 PVA in 1,3 and 1,3,5 positions, respectively. The simulation cells exposing the prismatic plane have dimensions 9.4 nm × 5.4 nm × 5.7 nm, and contain 9216 water molecules for the studies with DP 20, and dimensions 9.2 nm × 5.3 nm × 11.4 nm, with 18432 water molecules for those involving DP 30. We use simulation cells containing 36864 water molecules, with dimensions 9.3 nm × 10.6 nm × 11.4 nm, for the studies with DP 60. For the two-armed and threearmed architectures, the simulation cells have dimensions 9.4 nm × 5.3 nm × 5.7 nm, and contain 9216 water molecules. The simulation cells that expose the basal plane of ice have dimensions 4.6 nm × 5.3 nm × 11.4 nm for the studies with DP 20 and 30, while the simulation cells that expose the secondary prismatic plane of ice have dimensions 4.7 nm × 10.7 nm × 5.7 nm and contain 9216 water molecules. C. Analysis


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We use the bond-orientational order parameter q668 > 0.57 to identify ice54,

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69

and the

hydroxyl groups of the PVA molecule bound to it. We use the CHILL+ algorithm and visual inspection of the bound configurations to identify clathrate-like order at the ice-water interface.69 The CHILL+ algorithm is very accurate at identifying clathrates and ice.69 However, we found it difficult to extend it to identify the OH groups of PVA bound to it, as the bound OH have a broad distribution of neighbor-correlated bond order parameters. The number of hydroxyl groups bound to the surface are presented as running averages of data collected over 1 ns windows, to filter out fast fluctuations in order parameter that arise from vibrations of the PVA at the ice surface and do not lead to unbinding. We use the function QuickSurf70 of Visual Molecular Dynamics (VMD)71 to map the topography of the ice interface identified with CHILL+.

3. Results and discussion A. PVA hydrogen bonds to the prismatic plane of ice, assisted by lattice matching. To elucidate how does PVA recognize ice, we perform molecular dynamics simulations of ice-liquid phase coexistence in which hexagonal ice exposes the prismatic or basal planes to liquid water containing a PVA molecule with degree of polymerizations (DP) 20, 30 or 60. A recent study demonstrates that the promotion of ice nucleation by dilute solutions of PVA72 is not due to a heterogeneous nucleation mechanism, but to an enhancement of the rate of homogeneous nucleation due to an increase in the activity of liquid water.73 Consistent with those results, we do not find ice-like order around the PVA molecules in solution. In this section we focus on the interaction of PVA with the prismatic and secondary prismatic faces of ice at 273 K. The ice surface exposing the secondary prismatic plane to the liquid is significantly rougher than the one exposing the prismatic plane. The roughness of the secondary prismatic plane arises from the continuous growth and dissolution of the interface, and results in slow and reversible binding of PVA, which remains bound for at most 200 ns of the 600 ns long simulation. On the contrary, the primary prismatic plane offers a flatter surface with much slower fluctuations, which leads to irreversible binding of PVA in the 600 ns simulations (Figure 2). Binding of PVA to the prismatic plane starts at a random hydroxyl group in the chain and progresses through binding of contiguous segments of the molecule along the direction parallel to the c axis (Figure 2). The sequential nature of the binding process to the prismatic plane is indicative of a cooperative zipper mechanism.74


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c axis a)

b)

c)

d)

e) d

Figure 2. PVA binds to the prismatic plane of ice through a zipper mechanism. Panels a) to d) show the progression in binding of a PVA molecule with a DP 20 to the prismatic plane of ice. Binding in this simulation starts with the 5th OH group of PVA and propagates from there in the two directions along the c axis. Ice is represented with silver sticks, bound OH groups with red balls, the unbound OH groups in the chain with blue balls, and the hydrocarbon backbone of PVA with green sticks. Liquid water is not shown, for clarity. Panel e) shows the corresponding number of hydroxyl groups bound to the prismatic plane (red line). The letter labels in panel e correspond to the snapshots in the four upper panels. The black dashed line shows the maximum number of hydroxyl groups in DP 20 that can bind to the prismatic plane in a 2:1 binding pattern.

c b a

The simulations indicate that PVA binds to the prismatic plane via direct hydrogen bonding to the crystal surface. The binding follows a regular pattern, with two out of every three hydroxyl groups hydrogen bonded to ice in the direction parallel to the c axis. Irregularities in the ice surface, such as steps, can disrupt the binding pattern (see Figure 2). Although the united atom model of PVA does not have a well-defined tacticity, on binding to ice it adopts an isotactic configuration, with all the methylene groups oriented in the same direction (Figure 3). We find no evidence of clathrate-like order or anchored-clathrate motifs around the methylene groups. Nevertheless, each methylene loses in average 5.2 water molecules from its liquid hydration shell as it transfers from the liquid to the ice surface. This may contribute to the binding through their entropy of desolvation, enhancing the enthalpic contribution of the hydrogen bonding.


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b)

a)

c)

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Figure 3. PVA directly hydrogen bonds to the prismatic plane of ice following a pattern in which 2 consecutive OH are bound and 1 OH is unbound. The figure shows three views of PVA with DP 20 bound to ice. Ice is represented with silver sticks, bound OH groups with red balls, unbound OH groups with blue balls, and the hydrocarbon backbone with green balls. a) Side view of the binding motif. b) Front view showing the hydrocarbon backbone lying along the prismatic plane parallel to the c axis, with all methylene groups oriented in the same direction. c) The 2:1 binding pattern of the hydroxyl groups is well preserved, except when there are irregularities in the ice surface.

The simulations confirm the binding pattern Budke and Koop27 proposed based on matching of the distances between OH groups in PVA and the water molecules in the prismatic planes of ice. The average distance between two consecutive OH groups of PVA in liquid water is 2.92±0.46 Å in the simulations. This is comparable to the nearest oxygen-oxygen distance in the primary prismatic plane in the direction parallel to c axis, 2.70 Å in the mW model (2.76 Å in experiments,75 Figure 4). The distance between two consecutive oxygen groups in the prismatic plane perpendicular to the c axis is 4.43 Å in the mW model (4.52 Å in experiments75), hindering the hydrogen bonding of PVA to the prismatic plane in that direction. Distance matching between the hydroxyl groups in PVA and the oxygen atoms in the prismatic planes in the direction parallel to the c axis explains the preference in binding and the 2:1 binding pattern27 (Figure 4). We note that the distances between OH groups in PVA matches equally well the flat secondary prismatic and prismatic planes (Figure 4). Nevertheless, the rough surface of ice exposing the secondary prismatic plane makes it difficult for PVA to bind and develop the 2:1 pattern expected from distance matching (Figure 5). The difference in binding for the prismatic and secondary prismatic planes indicates that lattice matching to a flat surface is not sufficient to predict the binding efficiency; the molecular roughness of the ice surface also plays an important role.


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a)

2.92 Å

7.46 Å

b)

4.52 Å (4.43 Å)

c)

2.76 Å (2.70 Å) 7.35 Å (7.21 Å)

Figure 4. Binding of PVA to ice is controlled by distance matching between hydroxyl groups in PVA and water molecules in the ice planes. a) Sketch of the PVA molecule showing the distances between consecutive hydroxyl groups (blue balls). Water molecules in the b) Prismatic, c) secondary prismatic, and d) basal faces of ice (water molecules shown as blue balls, and their hydrogen bonds as sticks). Distances on the prismatic and secondary prismatic planes along the c axis are shown in read, while other distances are shown in green. In all cases, the distances for mW ice are shown in parentheses.

2.62

4.52 Å (4.43 Å) 4.43Å

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2.74 Å (2.69 Å) 7.24 Å (7.1 Å) d) 4.52 Å (4.43 Å)

a) Prismatic

c)

b) Secondary Prismatic

Figure 5. Prismatic and secondary prismatic ice surfaces have widely different roughness. Instantaneous surfaces of the a) prismatic and b) secondary prismatic surfaces of ice in coexistence with liquid water at 273 K. The dimensions of the prismatic and secondary prismatic areas shown are 5.4 nm × 5.7 nm and 4.6 nm × 5.3 nm, respectively. c) Time evolution of the number of hydroxyl groups of PVA with DP 20 bound to the secondary prismatic plane. Binding to the rough surface is more difficult than to the smoother prismatic surface (Figure 2), despite having essentially the same distance matching to PVA (Figure 4).


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Simulations of PVA with DP 20, 30 and 60 result in binding to the prismatic plane in which the molecules are fully stretched along the c axis (Figure 2). STM experiments provide evidence that PVA molecules of lengths in between 520 and 580 nm bind to ice in stretched conformations.29 It may be expected that binding of very long PVA molecules could be initiated independently from different regions of the chain, leading to linear binding regions separated by coiled unbound polymer. This could result in a plateauing of the ice recrystallization inhibition activity of polymers with very long chain lengths. We interpret that the strong binding of PVA to the prismatic face of ice arises from a different scaling of the enthalpy and entropy of binding as a function of the number of OH groups bound. Each OH of PVA that binds to ice contributes to the binding free energy ΔGbmono, which has enthalpic and entropic contributions at the monomer level. In PVA, we expect that the enthalpic contribution ΔHbmono is controlled mostly by hydrogen bonding, with strength modulated by the distance mismatch between the OH in PVA and in ice, and that the main entropic contribution to ΔSbmono originates in partial desolvation of the methylene groups upon binding. The contributions of individual monomers to the total binding free energy scale linearly with the number of OH groups bound. However, as the polymer binds to ice, the translational and configurational entropy of the chain decrease in a non-linear way: on binding the first OH, PVA loses the translational entropy of center of mass, and subsequent binding of OH groups results in loss of configurational entropy of the chain. The shorter the unbound portion of the chain, the smaller are these entropy loses.76 We conjecture that the dwindling unfavorable contributions from the configurational entropy of the polymer result in a binding free energy per OH that becomes more favorable as the binding progresses. This would result in cooperative binding, consistent with the zipper mechanism observed in the simulations. To estimate the strength of the binding of PVA to the prismatic plane, we investigate the evolution of the number of bound hydroxyl groups with time. This is shown for PVA with DP 20 in Figure 2e. Through the analysis of multiple binding trajectories for polymers of various lengths, we find that once PVA binds to the prismatic plane through more than 6 OH groups, it stays bound throughout the 600 ns long simulations. We estimate that the binding free energy ΔGbinding of DP 20 is at least ~35 kJ mol-1, using transition state theory to relate the characteristic bound time τ to ΔGbinding, τ = h/(kbT) exp(ΔGbinding/RT), where h, kb and R are respectively Heisenberg’s,


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Boltzmann’s and the gas constant. Strong binding of antifreeze molecules to ice is a requisite for their action through an adsorption-inhibition mechanism.4 Consistent with that scenario, in a separate study we demonstrate that the strong binding of PVA to the prismatic face of ice pins the crystal surface.77 This results in the development of curvature under supercooled conditions, which halts the growth of ice through the Gibbs-Thomson effect. Our analysis suggests that the potent IRI activity displayed by PVA with DP 20 or longer25 is due to cooperative binding. B. Branched architectures do not improve binding of PVA to ice. Recent studies show that increasing the length of linear PVA chains up to at least DP 350 results in increasingly more powerful inhibition of ice recrystallization.25 The degree of polymerization of PVA can also be increased by adding multiple branches to a central core. However, Congdon et al. found that having three or two PVA arms of a given DP attached to a phenyl core results in identical IRI activity, despite the difference in their total number of hydroxyl groups.32 More recently, Luuk et al. found similar IRI activity for a densely grafted PVA bottlebrush and a linear PVA molecule with the same degree of polymerization than each graft.30 To understand why branching of PVA does not improve its IRI, we investigate the ice binding of the two architectures of ref. 32: a central phenyl core functionalized with two arms of PVA with DP 10 in 1,3 positions (Figure 6a) or with three arms of PVA with DP 10 in 1,3,5 positions (Figure 6b). We find that the number of hydroxyl groups bound to ice is comparable for both architectures (Figure 6c). This result is explained by the linear, one dimensional (1D) binding of PVA to the prismatic plane: when the three-armed PVA binds to the prismatic plane (Figure 6b), two arms of the molecule bind parallel to the c axis of ice, same as in the two-armed architecture (Figure 6a), while the third arm lays perpendicular to the c axis, to which it does not bind due to large lattice mismatch (Figure 4). As the number of OH bound to the ice surface is a measure of both the strength of their binding and their footprint on the ice surface, the simulations concur with the experiments32 that the addition of the third arm does not improve the IRI of PVA, and demonstrate that this results from the onedimensional binding of PVA to the prismatic plane.


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a)

b)

c) Parallel to c axis

Perpendicular to c axis

c axis

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Figure 6. Branched PVA molecules and their linear counterparts bind to the prismatic plane of ice through similar number of hydroxyl groups, irrespective of their total DP. Configurations of the bound a) two-armed and b) three-armed star PVA, with DP 10 arms. Bound hydroxyl groups are shown with red balls, unbound hydroxyl groups with blue balls, and the central phenyl ring and hydrocarbon backbone with green sticks. c) Evolution of the number of hydroxyl groups of the PVA bound to the prismatic plane for the two-armed (red line) and three-armed (blue lines) architectures. The number of OH groups bound in the direction parallel and perpendicular to the c axis is shown separately.

We interpret that the similar IRI activity of a heavily grafted PVA bottlebrush and a linear PVA molecule with the same DP as each graft30 arises from their lattice mismatch to the prismatic plane in the direction perpendicular to the c axis. We expect that the IRI activity of PVA bottlebrushes would be enhanced if the separations between grafted PVA chains are integers of 4.52 Å, the distance between water molecules in the direction perpendicular to c (Figure 4b). This condition would also remove the limitations that prevent PVA from binding to the basal plane (Figure 4c and section C, below). Our analysis indicates that if the separation between the PVA branches matches the periodicity of the prismatic plane in the two directions, cooperative hydrogen bonding could be achieved in two dimensions, resulting in hyperactive synthetic antifreeze molecules that strongly bind to the prismatic and basal planes of ice. C. Binding of PVA to the basal plane is weak and non-cooperative. Growth habit experiments indicate that PVA does not interact strongly with the basal plane.27 Likewise, in our simulations PVA dissolved in water binds only weakly to the basal surface. Different from the binding to the prismatic plane, the binding to the basal plane is reversible in the time scale of the simulations and does not follow a well-defined spatial pattern or orientation (Figure 7). This is consistent with a lack of distance matching between PVA and the basal surface (Figure 4d), which does not allow binding of consecutive segments. Figure 7e demonstrates that PVA binds and unbinds from the basal surface within a few nanoseconds even when several OH groups are


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involved in the binding. It also shows that an increase in the degree of polymerization does not improve the binding of PVA to the basal face. We interpret that the enthalpy gain from binding random OH groups along the polymer does not compensate for the loss of conformational entropy of the chain. We conclude that mismatch in the distance between the water molecules in the basal face and the hydroxyl groups in PVA is responsible for the weakness of the interaction of PVA with the basal surface and the lack of cooperativity in binding.

a)

b)

c)

d)

Figure 7. PVA binds weakly and reversibly to the basal plane of ice, irrespective of its DP. Panels a) to d) display snapshots along a simulation trajectory and evidence of binding and unbinding of PVA with DP 20 to the basal plane. Ice is shown with silver sticks, hydroxyl groups with red balls if bound and with blue balls if unbound, and the hydrocarbon backbone with green sticks. Liquid water is not shown, for clarity. e) Evolution of the number of hydroxyl groups bound to the basal plane of ice with time for two PVA molecules, with a DP 20 (red line, with labels corresponding to the snapshots of the upper panels) and DP 30 (green line).

e) DP 30 DP 20 b

d c

a


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4. Conclusions In this work we use molecular simulations to elucidate the mechanism of binding of PVA to ice and explain its selectivity for the prismatic plane. To our knowledge this is the first molecular simulation study demonstrating recognition and binding of ice, by PVA or any other fully flexible macromolecule. We use this molecular understanding to propose principles for design of PVAbased macromolecules that bind efficiently to the basal and prismatic planes of ice. It has been proposed that ice-binding molecules induce ice order in their interfacial water, and that this is key for their recognition and binding to ice crystals.31, 78-79 We find that although PVA strongly binds to ice, it does not induce ice-like structures in the liquid. We conclude that ice-like order is not needed for ice recognition. Molecular recognition of ice by PVA involves cooperative hydrogen bonding through a zipper mechanism facilitated by matching of the distances between water molecules in the ice surface and the OH groups along the chain. The simulations indicate that PVA binds to the prismatic plane along the c direction in a pattern that involves 2 consecutive OH bound and 1 unbound (2:1 pattern), as proposed by Budke and Koop.27 Lattice matching to ice –probably assisted by a decrease in the liquid hydration shell of the methylene groups and the flatness of the prismatic plane- results in a strong binding free energy per monomer, ΔGbmono. This is sufficient to offset the losses in configurational and translational entropy of the flexible polymer upon binding, and yield a large negative binding free energy for the whole chain. We interpret that the different scaling of the enthalpic and entropic contributions with the number of OH groups bound to ice is responsible for the cooperative mechanism that leads to strong binding of PVA to the prismatic plane. This implies that PVA molecules with high degree of polymerization should have stronger total binding free energy per monomer, consistent with the increase in IRI with the DP of PVA chains.25 We predict that rigid ice binding molecules –which pay a low configurational entropy cost upon binding– would have the stronger binding to ice. This may explain why most antifreeze proteins have evolved quite rigid ice-binding sites. Lattice matching to the secondary prismatic plane is as good as for the prismatic plane. However, the roughness and extent of structural fluctuations in the secondary prismatic plane result in slower binding of PVA, which does not develop the characteristic 2:1 binding pattern within the 500 ns simulations of this study. Different from the prismatic planes, the basal plane does not


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expose water molecules at distances that match those between OH groups in PVA. That results in a weak ΔGbmono that cannot offset the loss in configurational entropy of the chain. The outcome is a non-cooperative, weak and reversible binding of PVA to the basal plane of ice. Our work reconciles the results of ice recrystallization inhibition experiments of two- and three-armed PVA molecules32 with the hypothesis of direct hydrogen bonding of PVA to ice.27 We show that three-armed and two-armed star PVA molecules bind to the prismatic plane through similar number of hydroxyl groups because the third arm is positioned perpendicular to the c axis, where the binding is weak and reversible due to lattice mismatch. We propose that to design hyperactive architectures that efficiently bind to both prismatic and basal planes, the separation between PVA branches connected to a molecular rod should be multiples of 4.52 Å. That would allow the hydroxyl groups in the chain to match the distances between water molecules in the prismatic plane in the direction perpendicular to the c axis of ice as well as the distances in the basal plane. These hyperactive synthetic molecules may be able to compete with hyperactive antifreeze proteins in preventing the growth and melting of ice. Our findings provide a molecular foundation for the design of ice binding molecules with enhanced antifreeze and ice recrystallization inhibition activities.

Acknowledgements. We are grateful to Ido Braslavsky for fruitful discussions. This work was supported by the National Science Foundation through award CHE-1305427 “Center for Aerosol Impacts on Climate and the Environment”. We thank the Center for High Performance Computing at the University of Utah for technical support and grant of computer time.

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Bound&OH Unbound&OH


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Molecular Recognition of Ice by Fully Flexible Molecules - The Journal

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