Protein-plastic interactions: The driving forces behind the high affinity of a carbohydrate-binding module for polyethylene terephthalate

(cid:129) A method was developed to study CBM binding to plastics. (cid:129) A CBM2 was shown to have a remarkably high af ﬁ nity for crystalline PET ﬁ lms. (cid:129) Af ﬁ nity of the CBM for the ﬁ lm is dependent on temperature and crystallinity. (cid:129) CBMs can be tuned to modulate the substrate af ﬁ nity of plastic degrading enzymes


Introduction
Plastics play an integral role in the world economy.460 million tonnes were produced globally in 2019 (OECD, 2019), and 1.5 million jobs in Europe alone depend on the industry (Plastics europe, 2018), demonstrating their importance.The high durability and resistance to chemical and microbial degradation make plastics an ideal material for myriad applications, but also a persistent pollutant in the environment (Geyer et al., 2017).One of the major plastic pollutants is poly(ethylene terephthalate) (PET), with up to 40 % of the plastic debris in some open water areas being made up of this polymer (Choy et al., 2019).PET is generally used to produce single use food and beverage containers, and fibers for textiles.It is crucial due to its resistance to biodegradation, is often produced in a highly crystalline form (Kawai et al., 2020).With the accumulation of PET in the environment, we not only harm the biosphere, but also disperse a valuable carbon source that could have many uses if degraded and used to either make new plastic or higher value materials (Kim et al., Science of the Total Environment 870 (2023) 161948 2019).In order to ensure this useful material is kept in a closed loop economy, a cost effective recycling method of PET is required.Given the high energy costs in traditional plastic recycling, bioprocessing has been identified as a promising avenue of sustainable PET recycling in recent work.
During the past decade increasing research focus has been on discovery of enzymes that have the ability to degrade PET (Jenkins et al., 2019;Kawai et al., 2020).These enzymes (PET hydrolases) are predominantly cutinases, which originally evolved to have activity on the waxy polyesters found in leaves and fruits (Chen et al., 2013).Many studies have been performed in recent years to engineer PET hydrolases with increased stability or activity (Cui et al., 2021;Lu et al., 2022;Rennison et al., 2021;Tournier et al., 2020), with a number of enzymes now showing promising rates of degradation.However, relatively less attention has been paid to surface adsorption and the affinity of these enzymes for their non-native targets.Recent work has shown that the affinity of PET hydrolases for the plastic has been shown to be highly important for their activity (Arnling Bååth et al., 2022;Badino et al., 2022).This is in accordance with the Sabatier principle, which states that the highest activity of an enzyme is often not synonymous with the highest affinity for the target, but that affinity should be tuned to an intermediate in which complexation and dissociation are balanced to increase activity (Kari et al., 2018).
In nature, enzymes that degrade insoluble polymers such as polysaccharides are in often found in conjunction with substrate binding domains (SBDs).These help to direct the enzyme toward a target substrate and tune the affinity of the enzyme into the most productive range.SBDs, therefore, may be useful in attempts to engineer optimal activity of enzymes on synthetic polymers.A limited amount of work has shown that fusion of SBDs to PET hydrolases can improve activity, however the mechanistic basis for this remains elusive (Ribitsch et al., 2013(Ribitsch et al., , 2015)), Furthermore, there has been little scrutiny of the properties of the lone SBDs.In 2019, a Bacillus anthracis carbohydrate-binding module (CBM) from family 2 (BaCBM2) was identified to have a high affinity for crystalline PET (Weber et al., 2019).However, the binding strength for PET under different conditions was not quantified.The full spectrum of ligands for CBM2s have not been explored, but they have been shown to bind mostly to insoluble polysaccharides, such as cellulose or xylan (Abbott and van Bueren, 2014;McLean et al., 2002).BaCBM2, in particular, is expected to be a chitin binding domain, given that it was originally found as part of a chitinase enzyme (Weber et al., 2019).
In this study, we have developed a quantitative assay for PET-CBM interactions.We have used this to characterize BaCBM2 binding as function of temperature and the crystallinity.Furthermore, we have produced a number of variants, which helped us to identify key residues for PET interactions, and allowed us to tune the adsorption of the protein onto PET.This work can further inform the development of CBM-PET hydrolase fusions, and help to develop plastic recycling technology as part of a transition to the green economy.

Plastic substrates
All plastic substrates, PET, polystyrene (PS), Nylon 6,6 and polyurethane (PUR), used in this study were obtained from Goodfellow (UK), with details of each in Table S1.The molecular weight (Mw) of the bulk PET used in all of the experiments is expected to be approximately 38 kDa (Wei et al., 2019).

Bacterial strains and plasmids
All protein expression and plasmid storage was carried out in Escherichia coli BL21(DE3) and DH5α strains, respectively, except for the D45C/A61C variant, which was expressed in the E. coli T7 Shuffle strain.The backbone plasmid for expression was pET-21b(+), with the BaCBM2 variants fused to the C-terminal of sfGFP.A construct with BaCBM2 at the N-terminal was also produced, in order to compare expression levels between the two, however only the construct with BaCBM2 at the C terminus was used, as it had higher soluble expression levels.6xHis and StrepII affinity tags were added to the N and C termini of all constructs, respectively.All gene synthesis, cloning and mutagenesis was performed by GenScript (USA), and transformation was done following standard protocols.The sequence for BaCBM2 was taken from the NCBI database (Genbank Accession: MK349005) (Weber et al., 2019), whereas the sequence for the C terminal extended variant was taken from the CAZy database, extending the length from 72 to 93 residues.

Expression and purification of proteins
Single clones of E. coli BL21(DE3) cells containing the relevant plasmid were inoculated into 10 mL of LB medium with 100 μg/L of ampicillin at 37 °C, 200 rpm, E. coli T7 cells were also supplemented with 25 μg/L of streptomycin.This overnight culture was then used to inoculate 750 mL of LB media in 3 L shake flasks, to an OD of 0.1, and incubated under the same shaking and temperature conditions.After the culture reached an OD 600 of 0.4-0.6, the temperature was reduced to 16 °C and expression was induced with 0.1 mM Isopropyl β-D-1-thiogalactopyranoside (IPTG) and allowed to grow for 24 h.The cells were harvested by centrifugation, 4000 g for 30 min at 4 °C, and the pellet stored at −20 °C until purification.The stored pellet was then resuspended in binding buffer (10 mM HEPES, 150 mM NaCl, 10 % glycerol, pH 7.5) and lysed by sonication, before separating the cell debris by centrifugation, 40,000 g for 30 min at 4 °C.The supernatant was then filtered through a 0.45 μm filter, and passed through a His-Trap FF 5 mL column (Cytiva, USA) using a peristaltic pump.The column was washed with 10 mL binding buffer, and then protein was eluted in three steps of 15 mL binding buffer containing 10 mM, 80 mM and 240 mM of imidazole, respectively.Imidazole was then removed by overnight dialysis using a 3.5 kDa MWCO standard dialysis tubing (Spectrum Labs, USA) in binding buffer, and the protein concentration determined by a BCA assay (Thermofisher, USA).

Disc-based affinity assay
Discs were cut out of plastic films using an office hole punch to give a surface area of 0.64 cm 2 , or in the case of PUR, individual pellets were weighed before analysis.The substrates were then placed into a low protein binding fluorescent suitable 96-well plate, and washed once with 10 % SDS and then twice with deionized water.The substrates were then incubated in binding buffer for approx.30 min, before 300 μL protein was added to each well containing the substrate, over a titration series between 50 nM and 1000 nM in binding buffer.The plate was then covered with adhesive sheets and shaken at 300 rpm for 60 min over a range of six temperatures between 20 °C and 70 °C in a thermomixer (Eppendorf, Germany) with an insulating lid.Following this, the liquid in each well was immediately removed to another neighboring well, and allowed to cool.The concentration of unbound protein was then determined by fluorescence using a FP-8500 Spectrofluorimeter equipped with an FMP-825 plate reader (JASCO Corporation, Japan) with excitation at 450 nm and emission at 510 nm.Standard curves of each protein were prepared by adding protein to wells without substrate, and treating standards with the exact conditions as the samples before removing them to neighboring wells.The amount of bound protein in each well was calculated by subtracting the unbound from the total protein added, and the dissociation constant (K d ) was determined by fitting Eq. (1) to a one site specific binding isotherm (GraphPad Prism,version 9).
where [BP] and [FP] are the concentrations of the bound and unbound protein, respectively.For the isotherms, the concentration of bound protein was expressed as nmol/cm 2 , or nmol/g in the case of PUR.A minimum of seven points were used to produce each binding isotherm for K d determination.

Protein stability
Aliquots of sfGFP-BaCBM2 at approximately 20 μM in assay buffer were assayed by differential scanning calorimetry (DSC) on Nano DSC calorimeter (TA Instruments, USA).Samples were heated from 20 °C to 100 °C, at 1 °C/min at a pressure of 3 atm, with assay buffer in the reference cell.

Modification of PET by thermal annealing
PET discs were produced, using a standardized assay (Thomsen et al., 2022), over a range of crystallinities in order to test how binding affinity was affected by crystallinity.Amorphous PET discs were incubated dry in an Eppendorf tube at 115 °C for predefined periods of time, before quenching by plunging the tube into ice-water.

Determination of PET crystallinity
The degree of crystallinity (X c ) of annealed discs was determined by differential scanning calorimetry (DSC).Triplicate samples of discs from each batch were placed into a Pyris 1 DSC (Perkin-Elmer, USA) and the temperature increased by 10 °C/min from 20 °C to 270 °C.The X c of the sample was then calculated according Eq. ( 2) (Thomsen et al., 2022): Where ΔH m is the heat of melting, ΔH cc is the cold crystallization enthalpy (numerical value), and ΔH 0 m is the heat of melting of a pure crystalline sample, which has the literature value of 140 J/g (Mehta et al., 1978).

Validation of disc based affinity assay
sfGFP-BaCBM2 was expressed in E. coli BL21 cells and purified to over 95 % purity with a yield of approximately 10 mg per L of growth culture.Following this, several steps were taken to ensure that the methodology was sound.Firstly, the use of the sfGFP domain as an indicator was assessed.Binding assays were run using a lone sfGFP protein, over the same range of concentrations as to be used in the BaCBM2 binding assays, for each substrate to be tested.The sfGFP protein did not show any measurable affinity for any of the substrates featured in this study, with binding isotherms included in the supplementary material (Fig. S1).Secondly, the binding of sfGFP-BaCBM2 to the wells in the low protein binding fluorescence suitable 96-well plate was also shown to be negligible when treated under the same conditions.Furthermore, the production of standard curves using samples treated in exactly the same way as the samples would also ensure any binding measured was to the PET disc substrate.

BaCBM2 has nM affinity for PET films which is highly temperature dependent
As mentioned, much of the research into CBM affinities for PET has focused on CBM-PET hydrolase fusions, and as such, there are few studies measuring the affinity of these proteins for the plastic itself.As shown in Fig. 1, the K d of BaCBM2 for a crystalline PET film was measured here to be 189 nM at 20 °C, with the binding module demonstrating a remarkable affinity for this synthetic substrate.
Considering that the final goal of SBDs use is as fusion constructs with PET hydrolases, the binding properties of BaCBM2 for PET was measured over the range of temperatures commonly used in PET hydrolysis (Cui et al., 2021;Zhong-Johnson et al., 2021).High crystallinity PET (X c = 31.6% ± 2.2 %) was incubated in storage buffer at temperatures between 20 °C and 70 °C, before sfGFP-BaCBM2 was applied, with the K d and B max at each temperature shown in Fig. 1.
The affinity, which varies inversely with K d , over the temperature range shows an initial increase in K d to 408 nM at 30 °C, after which the K d decreases to a minimum of 75 nM at the upper temperature of 70 °C.This decline and increase of affinity suggests two different effects upon binding as the temperature is increased.The thermal stability of the sfGFP-BaCBM2 construct was determined using DSC, in order to confirm that this change in affinity was not due to any non-specific binding to the PET surface by unfolded protein.Two unfolding peaks were seen in the DSC plot, at approximately 77 °C and 91 °C, which correspond to the unfolding of each domain in the protein, and demonstrate suitability of assays up to 70 °C.DSC curves for the WT sfGFP-BaCBM2 variant studied at higher temperatures can be found in Fig. S3.
Molecular dynamics (MD) simulations of BaCBM2 binding to PET films have suggested that binding is driven by the three tryptophan residues W9, W44 and W63 (Weber et al., 2019).This is in accordance with a typical Type A CBM binding mechanism, in which binding is driven by a gain in entropy arising from dehydration of the binding surface (Creagh et al., 1996;Georgelis et al., 2012).It would be expected, therefore, that a maximum affinity would be seen at lower temperatures, contrary to what is seen here at the higher tested temperatures.However, this standpoint does not take into account any effects that increasing temperature would have on the substrate, in particular an increase in crystallinity.A maximum crystallinity in the substrate may occur at the glass transition temperature (T g ) where increased mobility in the polymer chains allows a slow relaxation of amorphous material to the thermodynamically stable crystalline structure.For PET in aqueous suspension, T g is approximately 60 °C (Roudaut et al., 2004).However, this value only refer to the bulk properties, rather than any surface effects, which would be more relevant to binding.Atomic Force Microscopy (AFM) studies of PET have shown that surface crystals may develop at temperatures well below T g (Shinotsuka and Assender, 2016).The increased affinity of BaCBM2 for PET at higher temperatures could therefore be explained by the increase in the number of crystalline regions on the surface of the film at higher temperatures.Furthermore, CBMs from family 2 have been shown to have a higher affinity for crystalline cellulose rather than the amorphous forms (McLean et al., 2002), which could possibly also be the case for PET binding.The increase of B max as higher temperatures also indicates that the binding capacity of each film is Points represent the mean of two replicates, while error bars represent the standard deviation between them.Individual binding isotherms for each replicate can be found in Fig. S2.
increasing, further demonstrating the increase of surface crystalline regions as the temperature increases.

BaCBM2 binding to PET films is dependent on substrate crystallinity
In an attempt to demonstrate empirically this effect of crystallinity on BaCBM2 binding, a number of PET discs of varying crystallinity were investigated.All of these assays were performed at 20 °C in order to minimize any temperature effects upon the crystallinity of the discs.As these discs were produced using a thermal annealing process, rather than the stretching process used to make the biaxially oriented film used in the previous experiment, the results between the two are not comparable.However, within this experiment, there is a clear trend for higher affinity at higher crystallinity, as seen in Fig. 2.
Fig. 2 demonstrates a sharp increase in affinity as the PET discs reach approximately 20 % bulk crystallinity.While this is lower than the biaxially oriented discs used in the previous assays, the DSC assay used to measure crystallinity can only describe the bulk material and not the formation of surface crystals.However, as surface crystals are known to form before the onset of bulk crystallinity (Shinotsuka and Assender, 2016), it can be expected that the local crystallinity of the surface of each of these discs is higher than the values measured for the bulk.Nevertheless, a clear increase of binding affinity is seen at higher crystallinities, suggesting that BaCBM2 binds preferentially to crystalline regions on the PET surface.

Determination of residues important for BaCBM2 binding
The binding of type A CBMs to crystalline substrates such as chitin and cellulose is well described (Boraston et al., 2004;Georgelis et al., 2012).While it is to be expected that a related binding mechanism is displayed between BaCBM2 and PET, this has only been shown in MD simulations (Weber et al., 2019).Therefore, a number of mutations were made to BaCBM2 in order to elucidate residue specific contributions to binding affinity (Fig. 3).Each of these variants expressed well, with yields between 9 mg and 35 mg per L of growth culture.
The three aromatic residues expected to be central to binding, W9, W44 and W63, are confirmed as such in this experiment, with binding completely lost when these are substituted for alanine.MD simulations have suggested, however, that of these three residues only W9 and W44 bind to the PET surface initially, with W63 binding later after a conformational change of the loop it sits on (Weber et al., 2019).Indeed, this seems to be confirmed by the reduction, but not complete loss of binding when only W63 is substituted for alanine.W63, therefore, could be posited as a target for protein engineering to try to tune the affinity of BaCBM2, as will be discussed later.The proline residue at position 69 sits at the end of the mobile loop containing W63, as seen in Fig. 4D.This residue could potentially stabilize the loop after binding, which is again indicated by the decrease in affinity of the P69A variant compared to the WT BaCBM2.N64 was also suggested in MD simulations to form hydrogen bonds with the PET substrate once the major binding is undertaken by the aromatic triad (Weber et al., 2019), which is again backed up by the relatively Fig. 2. BaCBM2 binding to PET over a range of crystallinities.The K d and B max of BaCBM2 binding to PET films of different crystallinities.Discs were thermally annealed using the process described by (Thomsen et al., 2022), and bulk crystallinity measured by DSC.All assays were performed at 20 °C.Points represent the mean of two replicates, while error bars represent the standard deviation between them.Individual binding isotherms for each replicate can be found in the supplementary materials (Fig. S4).Fig. 3. Affinity of BaCBM2 variants to probe the binding mechanism (A) and to tune affinity (B) for crystalline PET.All assays were performed at 20 °C.Bars represent the mean of two replicates (values above), while error bars represent the standard deviation between them.Lower values of K d represent a higher affinity, while higher values represent a lower affinity.Missing data represents no measurable affinity over the protein concentration range tested (50-1000 nM).Individual binding isotherms for each replicate can be found in Fig. S5.Structures used for the interpretation of the binding affinity of these variants were solved using AlphaFold2, and can be found in Fig. 4. small reduction in affinity, when the asparagine is substituted for alanine (Fig. 3A).
Three of the substitutions apart from the aromatic triad seem to have destroyed any binding of BaCBM2 to the PET substrate, suggesting they have a role approaching the influence of W9 and W44 in binding.The residues two positions prior and five positions after the first aromatic binding residue, in this case S7 and N14, have been shown to have a large effect on the affinity of chitin binding CBM2s (Nakamura et al., 2008), we therefore wished to determine if the same was true for PET binding.These two residues are thought to form a negative patch on the surface of the protein, promoting hydrogen bonding with the substrate (Nakamura et al., 2008).However, these residues both sit at the beginning and end, respectively, of the loop where W9 is situated, and their two side chains are close enough to form hydrogen bonds with each other, as seen in Fig. 4B.We propose, therefore, that these two residues help to stabilize the loop on which one of the primary binding residues sit, and any loss of the bonding with either the substrate or each other is responsible for the complete loss of affinity in these variants.In the vast majority of CBM2s, the residue found three positions after the first aromatic binding residue is either an arginine or a glycine.This residue is known to control the planar conformation of this aromatic side chain, with a glycine leading to it being in the same plane as the other two aromatic binders, and arginine causing a 90°shift out of the plane.This shift is seen in the AlphaFold model in Fig. 4C, but has also been confirmed by crystal structures in other CBM2 structures (Simpson et al., 2000).This then consequently leads to the binding module switching affinity between cellulose and chitin to xylan, for glycine and arginine respectively (Simpson et al., 2000).Of course, the effect of this substitution and subsequent planar rearrangement of the aromatic binding side chain was not known for PET binding, and we therefore decided to study this.BaCBM2, as a chitin-binding module, already has a glycine in this position, and it seems that this is also the residue required for PET binding, as the G12R variant displays no affinity for the substrate.

Protein engineering to tune BaCBM2 affinity for PET
One of the goals of CBM fusions with PET degrading enzymes is to tune the affinity of the overall protein to an ideal, yet unknown, value.We therefore attempted to engineer BaCBM2 to either increase or decrease the affinity for PET, with the knowledge then available for use when designing fusion constructs.Each of these variants expressed well, with yields of approximately 10 mg per L of growth culture.The affinities of these engineered variants is shown in Fig. 3B.
As discussed, the third (W63) of the thee aromatic binding residues in BaCBM2 is of less importance to the overall binding to PET, and therefore a good target for protein engineering.In fact, mutation of this residue to either another aromatic residue, such as tyrosine, or a hydrophobic residue, such as leucine, has been shown to increase the PET degrading efficiency of a CBM-cutinase fusion (Zhang et al., 2013).However, it is not known how this increase in activity is related to binding affinity, or even a different effect such as surface mobility.We therefore studied these two mutations to determine their effect on affinity for crystalline PET.In both cases, a reduction in affinity was seen with these substitutions.Interestingly, the loss of affinity was lessened with the substitution for a hydrophobic leucine compared to the aromatic tyrosine, suggesting that π-π interactions here are less important than shielding of a hydrophobic surface on the protein.In either case, this seems to be a demonstration of the reduction in affinity being beneficial for the overall activity of a protein, as proposed by the Sabatier principle.
Finally, a C-terminal extension was applied to BaCBM2 (CtermExt), in line with the sequence obtained from the Carbohydrate-active Enzyme (CAZy) Database (www.cazy.org)(Drula et al., 2022), see Fig. S6 for sequence.The sequence used in the original paper by Weber et al. (2019) (GenBank accession: MK349005) was approximately 20 amino acids shorter than the sequence defined by the CAZy database from the same chitinase B gene, seen in Fig. S4.We therefore decided to ascertain whether this different set of domain boundaries would have an effect on binding.As shown in Fig. 3B, the affinity was increased dramatically, to a K d of 31 nM, upon addition of the extension, demonstrating a very strong binding to the PET substrate.Furthermore, we also tested this protein for affinity to PET at the upper temperature limit of 70 °C, and found a similar increase in affinity, with a K d of 16 nM at this temperature.We recommend that the Cterminal extended variant would be very useful in increasing the affinity of a PET hydrolase with a very low affinity for PET, however this would have to be determined experimentally.Nonetheless, it does demonstrate the importance of correct boundary definition between domains in modular enzymes.A tightly binding domain could also be beneficial for construction of a cellulosome type PET degrading complex, as has been recently attempted (Hwang et al., 2022).

BaCBM2 has strong affinity for a number of environmentally relevant plastics
Finally, we wanted to ascertain whether BaCBM2, and therefore potentially CBMs in general, have any affinity for other environmentally relevant plastics.The surface affinity assay was used to determine affinity for PS, Nylon 6,6 and PUR (Fig. 5).BaCBM2 demonstrates a similarly high affinity for all three of these plastics as for PET, with the protein binding to PS particularly strongly.As it was not possible to produce polymers of varying Mw, it is not known whether the Mw of PS, Nylon 6,6 and PUR has any effect upon the adsorption of BaCBM2 to the surface.While there are currently few enzymes known to have activity on any of these plastics, it is reasonable to expect that these will be discovered with further research, at which point the awareness of binding domains to fuse with these enzymes will be of great interest.

Conclusion
This study has characterized in detail the binding of a known CBM for PET.During the application of this work, we have developed a robust method with a moderate throughput, which can be used in future work of this kind.We have shown that the affinity of BaCBM2 for PET is highly influenced by both temperature, and in turn crystallinity of the substrate.We have successfully identified a number of residues within the protein that have a larger or lesser effect on binding, and used this knowledge to engineer this binding module and tune its affinity for the substrate.Variants have been produced that both increase and decrease the affinity, in the extreme case reducing the dissociation constant by 6-fold.Furthermore, we have shown that this binding module has a similarly high affinity for other environmentally relevant plastics, knowledge of which will be indispensable when engineering future enzymes for their degradation.These results indicate that binding modules, in particular CBMs, have the potential to play a role in the development of enzymes for plastic degradation in general, and can contribute to development of sustainable recycling schemes for PET in particular.

Fig. 1 .
Fig. 1.BaCBM2 binding to crystalline PET over a range of temperatures.The K d (left axis) and B max (right axis) for binding of BaCBM2 onto biaxially oriented PET films.Points represent the mean of two replicates, while error bars represent the standard deviation between them.Individual binding isotherms for each replicate can be found in Fig. S2.

Fig. 4 .
Fig. 4. Alpha fold simulated models of BaCBM2.(A) BaCBM2 with three binding tryptophans highlighted in blue, and all residues mutated in this study in red, C-terminal extension in orange; (B) Close up of W9 with stabilizing S7 and N14; (C) Close up of changes to W9 planar angle in WT and G12R; (D) Close up of W63 and stabilizing P69.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) This work was supported by the Danish Independent Research Council (DFF) [grant number: 1032-00273B].CRediT authorship contribution statement Andrew Philip Rennison: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writingoriginal draft, Writingreview & editing.Peter Westh: Supervision, Writingreview & editing.Marie Sofie Møller: Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Supervision, Writingreview & editing.

Fig. 5 .
Fig. 5. BaCBM2 binding to polystyrene (PS), Nylon 6,6 (A) and polyurethane (PUR) (B), with red representing K d , and blue representing B max .All assays were performed at 20 °C.Bars represent the mean of two replicates, while error bars represent the standard deviation between them.Individual binding isotherms for each replicate can be found in Fig. S7.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)