David J.
Sparks
a,
Maria E.
Romero-González
*b,
Elfateh
El-Taboni
c,
Colin L.
Freeman
a,
Shaun A.
Hall
a,
Gabriella
Kakonyi
b,
Linda
Swanson
d,
Steven A.
Banwart
b and
John H.
Harding
*a
aDepartment of Materials Science and Engineering, University of Sheffield, Sir Robert Hadfield Building, Mappin Street, Sheffield, S1 3JD, UK. E-mail: j.harding@sheffield.ac.uk
bDepartment of Civil and Structural Engineering, Kroto Research Institute, University of Sheffield, Broad Lane, Sheffield, S3 7HQ, UK. E-mail: m.e.romero-gonzalez@sheffield.ac.uk
cDepartment of Chemistry, University of Benghazi, Libya
dDepartment of Chemistry, University of Sheffield, Sheffield, S3 7HF, UK
First published on 24th September 2015
Macromolecular binding to minerals is of great importance in the formation of biofilms, and carboxylate functional groups have been found to play a pivotal role in the functioning of these macromolecules. Here we present both fluorescence time-resolved anisotropy measurements and simulation data on the conformational behaviour and binding of a poly acrylic acid polymer. In solution the polymer exhibits a pH dependent behaviour, with a coiled conformation at a low pH and extended conformation at higher pH values. The polymer is readily adsorbed on the surface of calcite, preferring to bind in an extended conformation, with the strength of the adsorption dependent on the pH and presence of counter ions. We discuss the reasons why the calculated adsorption free energy differs from that obtained from a Langmuir isotherm analysis, showing that they refer to different quantities. The enhanced binding of the extended conformations shows the importance of flexibility in the binding of macromolecules.
The design of the experiments set out in this paper is focused on the importance of carboxylate groups found on macromolecules from bacteria cell walls and EPS secreted by bacteria to promote adhesion, such as lipopolysaccharides and mycolic acid. The well-known polymer of acrylic acid (polyacrylic acid, PAA) can be used as a simple model for these more complex EPS components.6,13,14 In this work both experimental fluorescence studies and computer simulations have been employed to analyse the binding of PAA macromolecules to the surface of calcite. Fluorescence time-resolved anisotropy measurements (TRAMS) were used to collect the experimental data used in this study. TRAMS is a powerful technique that monitors the segmental motion of a polymer in solution and at the polymer–solid interface.15–17 The difficulty with studying large macromolecules in computer simulations is the number of degrees of freedom that the macromolecule has and the large energy barriers between the different conformations that it can adopt. It is difficult to sample all the conformational configurations using straightforward molecular dynamics simulations, and in order to increase the efficiency of sampling this phase space, a different approach must be used. There are several methods available that increase the sampling of a system, such as replica exchange molecular dynamics18 (REMD) and umbrella sampling.19 REMD is a sampling technique that uses duplicate simulations at different temperatures to overcome energy barriers between conformations. Umbrella sampling uses a biased potential to drive a simulation towards certain reaction coordinates. In this work we have utilised the metadynamics method to increase the sampling of the system. This method was developed in 2002 by Laio and Parrinello20 and also uses a biased potential to drive a simulation forward. The simulation methodology developed here will be a useful tool in future projects to study the behaviour of other macromolecules, such as polymers and peptides, in solution and on mineral surfaces.
A PAA chain with a number average molar mass of Mn = 19580 g mol−1 (272-mers) was used in the experimental work reported here. Due to the difficulty of simulating such a large polymer in molecular dynamics simulations, a short chain, 28-mers of PAA with molecular weight of ca. 2000 g mol was used in the simulation work. This shorter chain polymer is expected to behave slightly differently to the larger chain polymers. PAA is a well-studied polymer and has been the focus of several experimental and computational studies in the past. Laguecir et al.21 studied the behaviour of PAA in solution and found a decrease in the degree of ionisation when increasing the chain length of the polymer, a decrease in the diffusivity of PAA with increasing chain length, and a decrease in diffusivity with increasing pH. Bulo et al.22 investigated the interaction between short chain PAA and calcium ions in solution using computational simulations and found that at high ionic strengths the PAA chains exhibit a extended conformation stabilised by calcium ions. The same research group23 also performed computational studies on the complexation of PAA with calcium and carbonate ions, showing that PAA chains strongly bind to calcium carbonate species. Computational simulations in vacuum of longer PAA chains by Liu et al.24 show the favourable absorption of the polymer onto calcite surfaces due to the interaction between the functional groups and the surface. Aschauer et al.25 later showed that the binding of PAA must have a high entropic contribution due to the disruption of the highly ordered water layer on the calcite surface, a conclusion shared by Geffroy et al.,26 who also showed that small molecular weight polymers will have a greater affinity for the surface than large molecular weight polymers. Our study analyses the adsorption of PAA to calcite surfaces and the conformation of the polymer at varying pH values, comparing experimental data with simulation results.
Prior to use, 4-amino naphthalene-1-sulfonic acid (AmNS) (Aldrich, 97%) was purified by extraction with warm hexane. The residue was removed and dried under vacuum over CaCl2 to produce a yield of ca. 74% with a melting point of 300–302 °C, which was stored in a dark coloured bottle in a cold place. Acenaphthylene (ACE) (Lancaster, 90%) was purified by multiple recrystallisations from methanol, followed by vacuum sublimation. The purified fluorophore (ACE) with a melting point of 86.5–87.0 °C was stored at −10 °C. Before use, a monomer of acrylic acid (AA) was vacuum distilled at room temperature to remove the gas phase inhibitors (monomethyl ether hydroquinone) that are included in the supplied material to prevent polymerisation. The distillation was carried out with the distillate flowing into an iced vessel. The purified AA was stored at −10 °C. Solutions with a monomer to solvent weight ratio of approximately 1:
4 were made using 1–4 dioxane as solvent. The monomer solutions were poured into ampoules, then degassed to remove dissolved oxygen using a freeze–pump–thaw cycle on a vacuum line. Finally the ampoules were placed in a water bath at 60 °C to polymerise for one day. The reactions were polymerised by a free radical mechanism using azobisisobutyronitrile (AIBN, 1000 mg L−1) as initiator. The polymers were purified by multiple dissolutions (three times) and subsequent precipitation using methanol as the solvent and diethyl ether as non-solvent. The polymers produced were then dried in a vacuum oven for at least 24 hours before being weighed. The polymers were labelled with the fluorescent labels AmNS and ACE following a modified procedure described elsewhere.29 The products were washed with dichloromethane (Sigma-Aldrich) and the aqueous layers were evaporated to dryness at reduced pressure to yield the fluorescently labelled PAA. The amount of fluorescent label content was AmNS = 1.55 mol% and ACE = 1.28 mol%. The labelled polymers were characterised by gel permeation chromatography with a refractive index detector to have a molar mass distribution of: number average molar mass Mn = 19
580 g mol−1; weight average molar mass Mw = 47
458 g mol−1 and viscosity average molar mass Mv = 37
778 g mol−1 (the estimated accuracy of Mn, and Mv is ±5%).
To sample the conformational space of the polymer, its radius of gyration was used as the CV for the metadynamics simulations. The radius of gyration is the average distance from the centre of mass of the polymer to each individual monomer and describes the size and shape of the polymer. The radius of gyration is taken as an ensemble average and can be written as
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![]() | (2) |
The polymer was inserted into a periodic box of 40000 TIP3P water molecules,31 packed together randomly using the Packmol code,32 and placed on top of a slab of (10.4) oriented calcite with a surface area of 104 × 108 Å and depth of 32 Å (chosen to ensure a density of water of 0.99 g cm−3). At pH 6.5 and 9.5 the PAA will have a differing degree of ionisation of the acid groups. The ionisation process cannot be directly modelled in standard classical simulations and therefore it is necessary to set the molecule with the appropriate ionisation at the beginning of the simulation. This was taken from experimental titration data21 which indicated ionisation degrees of 0.75 and 1.0 at pH values of 6.5 and 9.5 respectively. Therefore for the polymer at pH 6.5, 20 side chains were ionised and distributed randomly throughout the polymer to spread out the charge. For the polymer at pH 9.5 all side chains were ionised. All atomic charges were calculated using AMBER Antechamber33 using the AM1-BCC method,34 a semi-empirical method that calculates the electronic structure in combination with bond charge corrections. To ensure a neutral simulation box 10 and 14 Ca2+ cations were added to the simulation cells for pH 6.5 and 9.5 respectively. The dissolution of calcite gives Ca2+ ions to the solution that can form PAA–Ca complexes in solution. Due to the relatively short length of the simulations and the potentially sizable energetic barriers it is entirely possible that the Ca2+ cations will not displace to or from the PAA molecule i.e. they are likely to remain complexed if they begin the simulation complexed and non-complexed if they begin the simulation non-complexed. Over the experimental timeframe we would expect the cations to reach the more stable (lower energy) arrangement. To account for this we ran two sets of simulations. In the first the Ca2+ cations were randomly placed within <5 Å of the PAA molecule (complexed) and in the second they were placed randomly >10 Å away from the PAA (non-complexed). The polymer was placed either close to the surface of calcite (<3 Å – close) or further away from the surface (>15 Å – far) to simulate the polymer being adsorbed on the surface or in solution. Collectively this made a total of eight different simulations (pH 6.5-close-complexed, pH 6.5-close-non-complexed, pH 6.5-far-complexed, pH 6.5-far-non-complexed, pH 9.5-close-complexed, pH 9.5-close-non-complexed, pH 9.5-far-complex, pH 9.5-far-non-complexed).
The Molecular Dynamics package DL POLY Classic35 was used for all simulations, with the plug-in Plumed36 for the metadynamics simulations. The forcefield for the mineral phase was described by the CaCO3 potentials developed by Raiteri et al.37 and the interactions of the organic molecules described with the AMBER forcefield.38 To model the interactions between the mineral and organic phase a generic method39 to produce cross term potentials was used to generate a reliable potential for our system without the need for fitting the interaction terms. All the potential cross term values are listed in the ESI.† All systems were equilibrated for 1.0 ns with a timestep of 0.1 fs, using an NVT ensemble with a Nosé–Hoover thermostat40 with a relaxation time of 0.5 ps and a temperature of 295 K. Subsequent metadynamics simulations were performed for 2.0 ns, and gaussians of height 0.05 kJ mol−1 and width 0.35 were added every 0.5 ps. All 2.0 ns of the simulation time was used to collect data to reconstruct the free energy surfaces. To calculate the adsorption energies of the polymer, the lowest energy configuration from each configuration was simulated using Molecular Dynamics simulation without metadynamics, in an NVT ensemble with a timestep of 0.1 fs and a Nosé–Hoover thermostat with a relaxation time of 0.5 ps. These simulations were equilibrated for 0.5 ns, followed by a simulation of 1.0 ns for data collection.
Eadsorption = Ewater−polymer−calcite − Ewater−calcite − Ewater−polymer |
In this work, AmNS- and ACE-labelled PAA were investigated at various pH values between 1 and 12 using TRAMS. Anisotropy decay data for each pH was modelled using a single exponential function as detailed in the ESI.† The resultant τc data are shown as a function of pH in Fig. 1. The AmNS data can be contrasted with the ACE data and with previous anisotropy studies of fluorescence labelled PAA:15 clearly the conformational transition for the AmNS-labelled PAA sample is very slight compared to that of the ACE-labelled polymer. The τc for AmNS-labelled PAA at low pH is ca. 2.3 ns compared to ca. 8.5 ns for the ACE-labelled polymer. Presumably this difference stems from the mode of attachment of each label to the polymer and the resultant motions that the respective label can monitor. The ACE label is attached at two points to the polymer backbone and so can only report on macromolecular backbone motion. With the AmNS label, on the other hand, backbone motion is not being exclusively monitored in the current experiments: free rotation about the bond of attachment to the polymer is possible which is reflected in a much shorter τc. Nonetheless, this label is still of value in revealing the conformational behaviour of PAA since it is likely to be sensitive to the microviscosity of its environment. Previous work16,41 has revealed that various fluorescent labels attached to poly(methacrylic acid) were sensitive to the conformational switch of the polymer through changes in the microviscosity of the medium. The AmNS label on PAA rotates freely at pH values above 8 due to the fact that the polymer is in its extended conformation. Below pH 6, the polymer contracts into its partially coiled structure. Under these conditions of macromolecular crowding, the microviscosity is increased slightly which results in a decrease of the free rotation of the label, reflected in a slightly longer τc. The τc data from AmNS–PAA are, in effect, an indirect measure of the conformational change of PAA. The current anisotropy results also confirm the findings of Laguecir et al.21 who studied a PAA chain of molecular weight = 50000 Da with a Rhodamine 123 fluorescence tag in fluorescence correlation spectroscopy experiments. The decrease in correlation time observed in the current experiments is consistent with polymer expansion at high pH, and faster motion through the solution. This change from a coiled conformation with a small radius of gyration to a more extended conformation is also visible in the computational simulations of PAA.
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Fig. 1 Correlation time for PAA labelled with AmNS and ACE in solution as a function of pH, measured using time resolved anisotropy measurements (TRAMS). |
Throughout the simulations where the polymer is complexed by counter ions, the Ca2+ ions that are bound to the carboxylate groups of the polymer stay bound and do not tend to dissociate. In the simulations where the polymer is not complexed, the counter ions are further away (>10 Å) and do not associate at all with the polymer during the simulation time. Therefore the metadynamics sampling of the polymer does not affect the degree of complexation. The complexation of PAA in solution is an energetically favourable reaction when the conformational energies of both systems are compared. The energy difference when complexing the polymer is −23.7 ± 16.6 kJ mol−1 (pH 6.5) and −37.5 ± 20.9 kJ mol−1 (pH 9.5). Therefore we would expect the polymer to be complexed throughout the experiments. We continue to discuss all eight different scenarios, however, as the complexation could vary depending on the presence of the surface and the solution conditions.
The free energy surface of the polymer in solution (Fig. 2), generated with metadynamics simulations demonstrates the influence of Ca2+ counter ions present in solution on the conformation of the polymer in the energetically preferred complexed system. At higher pH values, above the point of zero charge of carboxylate groups in the molecule, the net surface charge of the polymer is expected to be negative and the acidic groups mainly deprotonated on all the experiments performed. In the vicinity of Ca2+ ions, the polymer adopts an open and extended conformation as shown by the obtained radius of gyration values for the simulations conducted at initial pH of 6.5 and 9.5 respectively (labelled as complexed). The strong binding of the Ca2+ ions to the carboxylate groups of the polymer induces a local rigidity in the structure, causing the chain to be less flexible. Similar results were seen by Bulo et al.22 with similar simulations of Ca2+ ions and PAA chains in water. The removal of Ca2+ ions from solution forces the polymer to contract and adopt a random-coiled configuration, evident from the small radius of gyration and the deep well in the energy surface of 6 kJ mol−1 obtained for the non-complexed simulations. The configuration of the polymer in solution is thus greatly influenced by the presence of positively charged ions that impart rigidity to the polymer that is supported by the high density of charges on the polymer backbone.
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Fig. 2 Free energy surface of the radius of gyration of the polymer in solution, as calculated with the metadynamics simulations. |
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Fig. 3 Correlation time for PAA labelled with AmNS on calcite surface, measured using time resolved anisotropy measurements (TRAMS). |
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Fig. 4 Sorption isotherm of PAA on calcite surface at pH 7, 9 and 11 quantified using steady state fluorescence spectroscopy. |
The sorption of a polyacrylate to calcite has been previously reported43–45 to follow a similar trend to the one observed here and the general model of sorption of electrolyte on oxide.45 At low polyacrylate concentration in solution a monolayer of polymer is formed on the surface of calcite until saturation is reached at higher concentration of polymer in solution.43,44 The amount of polyacrylate sorbed to the surface of calcite is affected by the pH of the solution, where more polyacrylate is sorbed at pH values lower than the pHpzc of calcite. The reduction of sorption of polyacrylate and/or PAA to calcite at pH values higher than 7 indicates a change in binding mechanism from simple electrostatic interactions between molecule and surface, since PAA would be negatively charged and calcite would have an overall positive charge producing strong binding. At pH < pHpzc−calcite the PAA chains are negatively charged due to the deprotonation of carboxyl groups of PAA resulting in the ionization of PAA.21 The degree of ionization increases with increasing pH to values above the pHpzc−calcite resulting in an overall negative charge on the surface of polyacrylic acid. The degree of ionization for PAA of Mw = 50000 g mol−1 (similar to the one used in this study) at pH 7 was reported to be α = 0.55, suggesting that more than 50% of the carboxyl groups on the PAA are negatively charged. At pH 11, α = 1.0 and therefore PAA is fully ionized in solution.21 This suggests that the sorption of PAA to calcite is favourable at pH 7, as observed from the sorption isotherm obtained.
The metadynamics simulations of the PAA chain on the surface of calcite show a similar, but less pronounced behaviour than the polymer in solution. The radius of gyration of the macromolecule is dependent on both the pH of the solution and the presence of counter ions. The free energy of the polymer on the surface of calcite as a function of the radius of gyration is shown in Fig. 5. The relatively strong interaction between the surface of calcite and the short chain polymer prevents the latter from desorbing from the surface during the metadynamics simulations. This surface binding also has an effect on the complexation of the Ca2+ counter ions, which have less effect on the configuration than in solution, as the interaction between the calcite surface and the polymer dominates.
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Fig. 5 Free energy surface of the radius of gyration of the polymer on the surface of calcite solution, as calculated with the metadynamics simulations. |
The adsorption free energy (ΔG) of the PAA adsorption process on the calcite surfaces can be calculated using the equilibrium constant obtained from the isotherm fitted to the data in Fig. 4. A Langmuir isotherm model was fitted to the data to produce adsorption gibbs free energies of −2.12, −1.41 and −1.18 kJ mol−1 at pH 7, 9 and 11 respectively. The negative values for ΔG indicates a favourable binding of PAA to the surface of calcite, with the polymer binding more strongly to the surface at lower pH values, when less functional groups are ionised. These experimental adsorption energies are within the same range of those obtained by Geffroy et al.,26 who measured an adsorption enthalpy of +2 kJ mol−1 for PAA adsorption onto calcite.
The simulations show that binding occurs through several of the acid groups of the polymer which interact with the calcite surface. A wide range of adsorption energies of PAA on calcite have been obtained from previous simulations. Using a PAA dimer in a simulation with a TIP3P water model and a flat (104) calcite surface, Zhu et al.14 calculated an adsorption energy of −45 kJ mol−1 for a dimer where both carboxyl groups interact with the surface mediated by water. On the other hand, Aschauer et al.25 obtained a positive binding energy of +395 kJ mol−1 for simulations of a 10 monomer PAA chain on acute stepped calcite. The authors offer two possible explanations for this surprising result: the presence of a strongly layered water layer that keeps the PAA molecule at a distance from the surface (ca. 0.4 nm) and formation of complexes which stabilise the PAA in a coiled configuration in solution. Our metadynamics simulations do show the existence of complexation effects, but this does not prevent strong binding to the calcite surface. The advantage of using metadynamics over standard molecular dynamics simulations is that it compels the system to sample a wide range of configurations both in the solution and at the surface. This supports the suggestion that barriers resulting from a combination of complexation and strongly layered surface water was preventing the calculations of Aschauer et al.25 from finding the low-energy binding state found in our simulations.
When calculating the energy of adsorption of molecules to a mineral surface from the computational simulations, standard practice is to calculate the configurational energy of adsorption. This method only takes into account the enthalpic contribution of the system and ignores the entropic contribution to the binding. Adsorption of macromolecules to the surface of calcite will be a positive entropic process, as the binding process will disrupt the highly ordered water layers on the surface of calcite. In order to calculate an estimate of the free energy of adsorption, the entropic energy of the release of these water molecules needs to be taken into account. An estimate of the Helmholtz free energy, A, (the free energy without the contribution from the pressure volume term as these simulations are performed within the NVT ensemble) of the system can be made by assuming the most important entropy term arises from the displacement of water molecules from the surface. Given that our metadynamics simulations showed similar conformational behaviour in solution and on the surface, it is reasonable to assume there is a very small entropy change between the polymer on the surface on in solution, and therefore the estimated free energy of the system can be written as A = U − TnS, where U is the internal energy of the system, T is the temperature, n is the number of water molecules displaced from the calcite surface during adsorption and S is the entropic contribution arising from the displacement of a single water molecule from the calcite surface. Freeman and Harding46 estimated this entropic contribution for a water molecule on the surface of (10.4) calcite to be ca. 6 J mol−1 K−1.
The configurational energy of adsorption and estimated Helmholtz free energy of adsorption are shown in Table 1. The predicted binding energy decreases with increasing pH values, indicating that the polymer binds more strongly to the calcite surfaces at lower pH values.
pH | ΔHa [kJ mol−1] | n | (TnS)c [kJ mol−1] | A [kJ mol−1] | ||||
---|---|---|---|---|---|---|---|---|
Extended | Coiled | Extended | Coiled | Extended | Coiled | Extended | Coiled | |
a Enthalpy of adsorption. b Number of displaced water molecules. c Entropic contribution due to displaced water molecules. d Estimated free energy of adsorption. | ||||||||
6.5 | −325 ± 28.9 | −203 ± 40.2 | 30.1 | 15.4 | 53.8 | 27.5 | −118.1 | −30.2 |
9.5 | −317 ± 33.0 | −178 ± 35.5 | 30.7 | 14.8 | 54.9 | 26.5 | −112.1 | −15.6 |
We finally address the issue of the difference between the free energy obtained from a Langmuir isotherm analysis of the experimental absorption curve and the calculated energy of absorption for the PAA molecule. It is clear from the great difference in values that they must refer to different quantities. The free energy value estimated using the Langmuir isotherm constant may include mediated bonding through calcium ions and even a contribution from PAA molecules that are loosely attached to already absorbed PAA molecules that are loosely attached to an absorbed PAA layer. This is supported by the TRAMS data that suggests that the calcite is saturated with PAA chains during the experiment with more than one type of bonding between the PAA molecules and the mineral unlike the simulation where we bind one isolated polymer. It should be pointed out that saturation does not imply that all the binding sites are occupied. Jamming, whereby the molecules block large number of possible sites, is almost inevitable in a system of this kind.47 The simulation refers (necessarily) to a smaller molecule than that used in experiment that is in isolation on the surface and the binding functional groups are directly attached to the surface with no intermediate water present between the group and the mineral. This individual binding will give a much larger binding energy than the average response collected in the experiment.
The number of functional groups interacting with the calcite surface upon binding can be calculated from the computational simulations and is displayed in Table 2. The number of displaced water molecules depends strongly on the conformation adopted by the PAA chain, with twice as many water molecules displaced when the polymer adopts an extended conformation than for a coiled conformation. Similarly, the number of functional groups involved with the binding process changes depending on the adopted conformation. In an extended conformation (Fig. 6) the average number of carboxylic acid groups interacting with the surface is 6.9, corresponding to 25% of the total number of functional groups on the polymer. This number drops to 4.0 (14%) for a more coiled conformation (Fig. 6). The configurational binding energies per functional group interacting with the surface at pH 9.5 are −45.7 kJ mol−1 (coiled) and −47.3 kJ mol−1 (extended), suggesting that there is a much larger entropic gain with the adsorption of the extended conformation on the surface of calcite than with the coiled conformation.
The values presented in Table 2 show that only up to a quarter of the functional groups present in the polymer are involved with the binding process, and that this number does not drastically increase when increasing the number of charged functional groups when increasing the pH of the environment. When analysing a typical binding motif of an extended polymer chain on the surface of calcite (e.g.Fig. 6) it can be seen that only the central part of the polymer stays in constant contact with the surface and that the ends of the polymer are often found floating up into the solution. Additionally, only alternating functional groups in the central section of the polymer are involved in the binding process. This behaviour suggests that not only the number of charged functional groups present will dictate the binding of a molecule to surfaces, but also the spacing between these groups. On the surface of (104) calcite there are a lot of exposed CO32− ions present, which could hinder the adsorption of molecules with a high density of negative charges. The complexation of the polymer with positively charged calcium ions might therefore be aiding the adsorption of the polymer to the calcite surface by shielding these negative charges. The counter ions are complexed to the polymer for extended periods of time and continue to be associated with the polymer when bound to the surface, indicating this complexation could be a mechanism of calcium transport to the surface.
Footnote |
† Electronic supplementary information (ESI) available: Details of the simulation parameters are available. See DOI: 10.1039/c5cp00945f |
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