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Electrophoretic Behavior of Copolymeric Galacturonans Including Comments on the Information Content of the Intermolecular Charge Distribution Martin A. K. Williams,*,†,‡ Aure´lie Cucheval,†,§ Anna Stro¨m,| and Marie-Christine Ralet⊥ Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand, MacDiarmid Institute for Nanotechnology and Advanced Materials, New Zealand, Fonterra Research Centre, Palmerston North, New Zealand, Unilever R&D Colworth, Sharnbrook, MK44 1LQ, Bedford, United Kingdom, and UR1268 Biopolyme`res Interactions Assemblages, INRA, F-44300 Nantes, France Received January 28, 2009; Revised Manuscript Received March 26, 2009
Capillary electrophoresis has been used to characterize samples of the copolymeric anionic polysaccharides homoand rhamno-galacturonan (HG and RGI, respectively). In the case of HG, the ratios of the two component sugar residues, galacturonic acid and its methylesterified analogue, have been controlled chemically to produce samples comprised of varying degrees of methylesterification (DM). The mapping of the measured electrophoretic mobilities to the biopolymer charge density has been considered in some detail and for HG substrates with random intramolecular patterns of methylesterification it is shown that the experimentally extracted intermolecular DM distribution agrees well with the predictions of calculations based on the binomial theorem. This demonstrates that the intermolecular distribution of the methylesterification of pectin samples contains information on the intramolecular pattern by virtue of the fact that they are both manifestations of the same statistical process.
Introduction The ubiquitous occurrence of the polysaccharide pectin in the cell walls of land plants, taken together with the large number of pectin-modifying enzymes encoded in the genomes of plants1 and their pathogens,2 clearly points to the importance of pectin in many diverse aspects of plant physiology. Among other things, this complex carbohydrate polymer plays an instrumental role in regulating the mechanical properties of the plant cell wall. It has long been appreciated that indeed biopolymer networks mediated by the interaction between such ionic polysaccharides and specific metal ions play crucial roles in fulfilling the structural physiological requirements of both land and marine plants.3-5 These adapted structuring solutions have been exploited in vitro for many decades using extracted biopolymers such as pectins, alginates, and carrageenans, mixed with relevant cations.6,7 Applications of this soft-materials engineering are diverse8 and include systems used as cell immobilization matrices,9-11 ion-exchange media,12,13 controlled drug delivery vehicles,14,15 and rheology modifiers for the textural design of food products.16-18 While the detailed structure of the pectin macromolecular assembly in vivo is still a matter of debate to some extent,19 most commercially available pectin samples can be considered as a collection of polymer chains each consisting of extended regions of homogalacturonan (HG) interspersed sparsely with regions of rhamonogalacturonan I (RGI).20 HG consists of a linear backbone of (1,4)-linked R-D-galacturonic acid (GalA) residues, commonly partly methyl-esterified at C-6, while the RG-I backbone consists of [2)-R-L-Rhap-(1,4)-R-D-GalpA-(1] repeats with no strong evidence that GalA units in RG-I domains * Corresponding author. E-mail:
[email protected]. † Massey University. ‡ MacDiarmid Institute for Nanotechnology and Advanced Materials. § Fonterra Research Centre. | Unilever R&D Colworth. ⊥ INRA.
are methyl-esterified.21 The rhamnosyl (Rha) residues of RG-I backbone are substituted, mainly at O-4, with several types of arabinose (Ara) and galactose (Gal)-containing neutral sugar side-chains.21 (Further, some information on the three-dimensional molecular structures of the components is available.22) Even at this level of description complexity and heterogeneity abound. In particular, the relative amount of methylesterified GalA residues (degree of methylesterification, DM) and the distribution of the methylesterification of the HG, both among chains, and along individual polymer backbones, is a key determinant of molecular functionality. Indeed, cell wall enzymes routinely tailor methylesterification distributions to exploit structure-function relationships based on the dependence of molecular association on the pattern of methylesterification.23,24 The measurement of such distributions is then vital in order to understand the role that fine structure modifications play in determining the functionality of pectin both in vivo and in vitro. Capillary electrophoresis has been shown to be a useful tool for the investigation of just such pectin methylester distributions.25-32 Most simply it can used to measure the average DM of a pectin sample, because a linear relationship between the electrophoretic mobility and the average charge per sugar residue has been observed over a large range of methylesterification degree.25,26 While many other methods perform this sample averaged DM measurement equally well,33-38 an advantage of the electrophoretic method is its inherent separation quality. For chains with lengths in excess of around 25 residues a symmetrical scaling of charge and hydrodynamic friction coefficient with the degree of polymerization (DP) is found. This means that larger polymeric chains, regardless of their DP, elute according to their average charge density and, therefore, that each CE migration time marks species with a unique DM. Peak shapes thus reflect the intermolecular methylesterification distribution (the methylesterification distribution among chains) of the sample.30
10.1021/bm900119u CCC: $40.75 2009 American Chemical Society Published on Web 04/22/2009
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Table 1. Chemical and Macromolecular Characteristics of the HG and RGI Samples Used in this Study
GalA (mol %) Rha (mol %) DM ζ Mw DPw I (Mw/Mn) a
HG 93
HG-B82
HG-B69
HG-B57
HG-B40
HG-B20
RGI
>99 99 99 99 99 99 75 Fluka Biochimica 78 Copenhagen Pectin 55.8 89.0 f-PME Copenhagen Pectin 31.1 85.2 f-PME This Work - Homemade Samples CP-Kelco (Initial DM 83%) 60 ∼85 base 40 ∼85 base 30 ∼85 base A Stro¨m Thesis, University of Cork, 2006 Copenhagen Pectin 77.8 84.5 f-PME Copenhagen Pectin 65 81.5 f-PME Copenhagen Pectin 55.8 89.0 f-PME Copenhagen Pectin 31.1 85.2 f-PME CP-Kelco (Initial DM 83%) 25 ∼85 base 20 ∼85 base 15 ∼85 base 10 ∼85 base 5 ∼85 base Copenhagen Pectin Copenhagen Pectin Copenhagen Pectin Copenhagen Pectin
Unilever Research 77.8 84.5 70.3 85.1 65.0 81.5 62.2 83.9
Copenhagen Pectin Copenhagen Pectin
55.8 42.6
89.0 85.7
CP-Kelco (LM-12) Copenhagen Pectin
35.0 31.1
∼85 85.2
f-PME f-PME f-PME f-PME (Ca-sensitive fraction) f-PME f-PME (Ca-sensitive fraction) base f-PME
cooled, and filtered (PVDF filter 13 mm diameter, 0.45 µm pore size; Whatman Inc., Sandford, ME, U.S.A.) prior to analysis. Samples were injected automatically through a 50 µL loop. Data for molar mass determinations were analyzed using Astra 1.4 software (Wyatt, Santa Barbara, CA) taking dn/dc 0.146. Unsmoothed Mw and Mn were obtained from raw data. Pectin Samples. In addition to collecting data on pectin samples from the literature, a number of samples were also run in this work, and in addition, previously unpublished data from Ph.D. thesis work and experiments carried out at Unilever research have also been included. These samples are detailed in Table 2. While some of these samples may have formed part of previously reported studies, rerunning some of these samples and including further experimental data permits a better assessment of the reproducibility across laboratories. “Homemade” refers to standard base-catalyzed demethylesterification as amply described in literature cited herein. With the exception of two calciumsensitive samples, all the pectins in Table 2 are believed to have close to random distributions of methylesterification, being generated either by a fungal pectinmethylesterase (f-PME) or by base saponification. Molecular weights of all these samples are between 40 and 120 kDa. Capillary Electrophoresis. Experiments carried out in this work used an automated CE system (HP 3D), equipped with a diode array detector. Electrophoresis was carried out in a fused silica capillary of internal diameter 50 µm and a total length of 46.5 cm (40 cm from inlet to detector). The capillary incorporated an extended light-path detection window (150 µm) and was thermostatically controlled at 25 °C, although in reality it is possible that the temperature in the capillary during electrophoresis could exceed this value by several degrees.58 Phosphate buffer at pH 7.0 was used as a CE background electrolyte (BGE) and was prepared by mixing 0.2 M Na2HPO4 and 0.2 M NaH2PO4 in appropriate ratios and subsequently reducing the ionic strength to 50 or 90 mM. At pH 7.0, the unmethylated GalA residues are fully charged, and while the samples are susceptible to basecatalyzed β-elimination above pH 4.5, no problems were encountered
Figure 1. Electrophoretic mobilities, µ, for HGs, RGI, and a number of pectin samples, measured herein or gathered from the literature, as a function of the fraction of the sugar rings charged, z, and the typical dimensionless polyelectrolytic charge density parameter, ζ (50 mM BGE, 298 K, existing data originally measured at different I and T has been scaled as described in the main text).
during the CE runs of some 20 min at room temperature. All new capillaries were conditioned by rinsing for 30 min with 1 M NaOH, 30 min with a 0.1 M NaOH solution, 15 min with water, and 30 min with BGE. Between runs, the capillary was washed for 2 min with 1 M NaOH, 2 min with 0.1 M NaOH, 1 min with water, and 2 min with BGE. Detection was carried out using UV absorbance at 191 nm with a bandwidth of 2 nm. Samples were loaded hydrodynamically (various injection times at 5000 Pa, typically giving injection volumes of the order of 10 nL) and typically electrophoresed across a potential difference of 20 kV. All experiments were carried out at normal polarity (inlet anodic) unless otherwise stated. Electrophoretic mobilities, µ, are related to the migration times of the injected samples relative to a neutral marker, t and t0, respectively, by the equation
µ ) µobs-µeo ) (lL/V)(1/t - 1/t0) where L is the total length of the capillary, l is the distance from the inlet to detector, V is the applied voltage, µobs is the observed mobility, and µeo is the mobility of the electroosmotic flow (EOF).59
Results and Discussion Electrophoretic Mobility Measurement. Figure 1 shows the electrophoretic mobilities measured in this work for HGs, RGI, and a series of pectin samples in 50 mM BGE at 298 K. The fractional charges against which these values are plotted have been measured by at least one other independent (not electrophoretic) method, typically titration, chromatographic assessment of released methanol, or FT-IR, and are estimated to be known to the order of (3%. The mobilities have been calculated as number averages over the CE peaks (after normalization to account for the different lengths of time that species with different electrophoretic velocities spend passing the detection window60). The error bars show what are considered as the largest realistic uncertainties. Typical reproducibility is around 2-3%, with the largest uncertainties arising from the estimation of the EOF, typically signaled by a drop in the absorbance signal originating from the refractive index change concurrent with the passage of water from the sample plug moving past the detection window. The occasional use of a UV-absorbing neutral marker did improve the situation somewhat when running experiments with very low charge density samples, where elution was in close proximity to neutral species. Other
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uncertainties caused by electromigration dispersion were exacerbated at high charge densities, but could be ameliorated up to a point by modifying the sample concentration and the ionic strength of the BGE. Dimensionless Charge Density Parameter. The mobilities are plotted against the fraction of the sugar rings charged, z, and in addition against the typical dimensionless polyelectrolytic charge density parameter given by:
ξ)
lb e2 ) 4πεkTb b
(1)
where e is the electron charge, ε is the permittivity of the fluid, and k is the Boltzmann constant; lb is known as the Bjerrum length (the separation of electrons at which the electrostatic interaction energy is equivalent to kT), and b is the average axial distance between charged groups on the polymer backbone. At room temperature, in typical aqueous electrolytes, whose viscosity and dielectric constant are not significantly different from water, this means that ζ ) 1 corresponds to approximately b ) 0.7 nm and, therefore, that this condition is typically exceeded by polysaccharides when more than around 65% of the sugar rings bear a charge. A brief description of theory will follow in due course but it is worthy at this juncture to note the significant implications of the value of this parameter: (i) for ζ < 1 the Debye-Hu¨ckel linearization of the Poisson-Boltzmann equation is valid, and (ii) Manning’s counterion-condensation theory advocates that, above ζ ) 1, tight binding (“condensation”) of counterions to the chain effectively limits the charge density from increasing further. Comparison of Mobility Measurements with Literature. It can be seen that there is, on the whole, excellent agreement in Figure 1, not only between the data reported herein, but also when compared with a large amount of further data taken from the existing literature. It should be noted that, in the literature data, a small number of the experiments had been carried out in different ionic strength BGE or at a different temperature (i.e., not at 50 mM BGE or at 298 K), and these data have been scaled according to the predictions of theoretical calculations, which will be described in detail in due course. There is also a data point from the literature for polygalacturonic acid that should be noted was made using an alternative experimental setup to CE and using sodium chloride as an electrolyte.61 Mobility of RGI Compared with HG. It is also noteworthy that the RGI mobility agrees well with that of a 50% methylesterified HG, suggesting that, at least in the regime where mobilities are not dependent on DP, the nature of the linkage between the sugar rings does not have a large impact on the electrophoretic mobility. It also suggests that the overall charge density of the chain is significantly more important than the intramolecular arrangement of the charged groups, as the RGI polymeric backbone consists of the strictly alternating dimer Rha-GalA, as described above, while the HG sample has a random placement of the charged groups along the chain. Such an independence of the electrophoretic mobility on intramolecular sequence has also previously been found when comparing results obtained from sister pectin samples that had been demethylesterified chemically or by processive enzymes.30 Mobility of HGs Compared with Pectins. It is also worthy of comment that the data from the pectin samples have had their charge densities calculated from measured DM values without taking account of any neutral sugars that might be present in the molecule. The first study carried out on the CE of pectins also found that the proportion of the pectin
sample that was claimed to be GalA did not seem to be overly important in determining the electrophoretic mobility,25 despite the fact that the addition of neutral sugars attached to the polymeric backbone would be expected to increase the frictional forces acting on the molecule. Certainly it would be expected that the pectin samples would, at the very least, contain a small amount of Rha in the RGI regions that are hypothesized to connect the otherwise fairly monodisperse HG regions (of around DP 100) 51,62 Despite this approximation, the pectin and HG mobilities shown in Figure 1 do not appear different by more than a few percent at most. This effectively limits the RGI content of the pectins studied to less than around 10%. For example, a pectin consisting of 10% RGI and 90% HG (DM 50) has 95% GalA groups of which 45% are methylesterified, a DM of 47.4%. Taking this DM value, which might be obtained by say titrametry, neglecting the RGI regions and naively calculating the % of charged residues (100-DM), gives 52.6% compared to the real 50%. Even if the RGI backbone carries an equal weight of neutral sugar side chains, then a pectin consisting of 5% RGI in the backbone carrying a further 5% Gal and Ara substituents and 90% HG (DM 50) has 92.5% GalA groups, of which 45% are methylesterified, giving a measured DM of 48.6% and a naı¨ve 51.4% charged residues. From these simple considerations it is clear that for typical RGI and neutral sugar contents of extracted pectin samples, the electrophoretic mobility is consistent within experimental uncertainty (a few %) with that predicted simply using the measured DM value to calculate the fractional charge, thus, explaining the good agreement observed in Figure 1. This is certainly reasonable but does suggest that in commercial samples (typically quoted GalA contents are of the order of 85% by weight) the weight that is not GalA is not all likely to be sugars covalently attached to the pectic polymer and does not in fact play a significant role in influencing its electromigration (water, ions, and possibly free sugars could account for a large amount of this ∼15%). Calculation of the Dependence of Mobility on Charge Density. It is clear that in the region in which previous work has been carried out, corresponding to z ∼ 0.2-0.7, there is a well-defined consistent relationship wherein simple linear regression analysis based on the mobility of surrounding standards can yield a reasonable estimate of the DM of an unknown sample from its electrophoretic mobility. Indeed, in the region 0 < z < 0.6, a single linear regression is a reasonable description of the data. However, it is also abundantly clear from data presented in Figure 1 that at lower DM the dependence of electrophoretic mobility on fractional charge is modified. Indeed, above around z ) 0.8 it is not possible within our experimental uncertainties to confidently assert whether there is any dependence on DM at all or whether the electrophoretic mobility is constant. It is noteworthy that this large change in behavior occurs at a charge density, ζ, close to that of 1, reminiscent of the postulates of Manning’s counterion condensation theory. Although there continues to be debate and legitimate concerns around the ad hoc nature of its assumptions,63 Manning’s theory has previously been found to be useful for the description of the behavior of a number of polyelectrolytes of both synthetic and biological origin,48,64-66 and as such, it is briefly examined as a framework for capturing the features of Figure 1. It is worth noting at the outset that, while experimental data have been compared with modeling studies of the electrophoretic mobilities of polyelectrolytes previously, this has largely focused on the dependence on ionic strength or molecular weight
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predicted for polymers of a fixed charge density.67,68 There appear to be few cases of comparisons of experiment and models where the charge density is systematically varied, possibly owing to the experimental difficulty of wielding such control. In this regard, the charged polysaccharides studied herein from ideal test systems. While more complicated (and it should be added more rigorous) models than Manning’s do exist,68-70 these do not presently appear to be able to capture the rapidity of the change in mobility observed experimentally in a relatively small region of charge density, around ζ ) 1. Further work on detailed mobility calculations for these charged sugar polymers is ongoing, including modeling a dependence on DP measured for pectic oligomers, and will be submitted for publication in due course. In essence, these models seek to balance forces owing to the electric field and the frictional forces. Here, the hydrodynamics are treated with the polymer considered a sequence of structural units, each of which is a point source of friction, although it is worth noting that more complex models involving more realistic wormlike chains give remarkably small differences in the predictions.68 Essentially, as we take our pectin chain and progressively introduce charges through demethylesterification, the average charge spacing, b, is modified according to 0.445 nm divided by the fractional charge; so that, for example, the minimum spacing structurally possible would be 0.445 nm (crystallographically determined 71), while a 50% methylesterifed structure would have twice that spacing (0.445 nm/0.5). This spacing is then used in eq 1 to determine the dimensionless polyelectrolytic charge density, ζ, and thus ζeff (equivalent to ζ when ζ < 1, or taken to be equal to 1 when ζ > 1) is determined. This value is then used in the following expression, based on eq 37 of ref 68, extended to include ionic strength dependence of the friction coefficient of a structural unit to calculate the electrophoretic mobility
µ)
[
( ))]
(
2RAξeff κlb lb - ln 1 - exp 2 β ξeff 2ξeff(as + as κ)
where the Debye length, κ
κ-1 )
(
-1
(2)
, is given by
εkT 2
eL
)
1/2
∑ ck(zk)
2
(3)
with L ) Avagrado’s number and ck ) the concentration of ion k with valence zk. While
A)
2εkT 3ηe
(4)
is simply the “normalization factor” to be applied to the reduced dimensionless electrophoretic mobility given by the expression in the square brackets (η is the solvent viscosity and all other symbols with their usual meaning), and R and β are Manning’s “relaxation parameters”,72 which account for the symmetry breaking of the ion-cloud and subsequent dipole formation. These are calculated within a Debye-Hu¨ckel formulation, and it is here that the mobility of the ions enters the expression; these values have been obtained from the conductance of the appropriate ionic solutions and their temperature dependence (in addition to the temperature dependence of the viscosity and dielectric constant of water) from the literature has also been included. It should be noted that the β term also carries a dependence on charge spacing and thereby on ζeff. Figure 2 shows the results of the calculation with no adjustable parameters, where the Stokes radius of a “frictional unit” is taken to be half the charge spacing. It can be seen that
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Figure 2. Data from Figure 1 compared with the results of calculations described in the text (solid line: the Stokes radius, as, equal to half the charge spacing; dotted line: using prolate spheroids; dashed line: as scaled to fit at ζ ) 1; thick solid line: empirical fit to the data). Τhe inset shows the variation of Stokes radii required to fit the data exactly, as described in the text.
while some general features are captured the agreement is on the whole rather poor. In particular, prior to the linear section of the calculated curve being reached, the gradient of the modeled relationship can be seen to be increasing notably. Although this feature of the model can be noticed in previous works it appears to have been generally ignored owing to data being plotted to higher values of ζ. In fact, over a similar range of ζ, the comparison between the model and the experimental data shown here closely resembles previous such attempts to model polyelectrolyte mobilities.48 So that even though a region of linear dependence that shallows and possibly disappears as ζ climbs above one is arguably a feature captured by the model, it seems clear that in the low charge density region the data deviates substantially from the model. Applying different hydrodynamic considerations, for example, where the frictional elements are considered as prolate ellipsoids with a fixed minor axis and a major axis determined by the charge spacing does not improve the situation nor does scaling the size appropriately to force a fit at z ) 1, as demonstrated in Figure 2. It might be argued that how the hydrodynamic friction of “singly charged elements” changes as their size is modified relative to the chain is complex,73 and a fit of the data to the model can of course be forced, point by point, by allowing the effective Stokes radius to vary. Such a procedure has been carried out using a simple zero-crossing routine, and the inset in the figure shows the values required for the data to match the theory. That is, if the effective Stokes radius varied, as shown in the inset, the model would fit the data points exactly. However, bearing in mind the many inherent approximations in the model, this should not be taken too seriously as an extraction of the real hydrodynamic radius of the singly charged structural units. Dependence of Mobility on Temperature and Ionic Strength. Despite the shortcomings of the model (when the Stokes radius of a “frictional unit” is taken to be half the charge spacing) in capturing the dependence of the mobility with charge density the predictions of the ionic strength and temperature dependence of electrophoretic mobility were further compared with experiments. Figure 3 shows the predictions of the model along with a limited number of data points obtained in this work. The data from experiments carried out on a DM 55% pectin are fortuitously close to the model, while results for DM 78% polymers have been arbitrarily scaled, simply to compare how
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Figure 3. Electrophoretic mobilities, µ, calculated as a function of I and T, from the model given as the solid line in Figure 2 (DM 78% result scaled, as described in the text).
the values vary with I and T. Although, as discussed above, the absolute values of the predicted mobilities are not, in general, well described by the model, nevertheless, the theory does a reasonable job of capturing the electrophoretic mobility dependence on T and I, at least over the limited range of temperatures (20-30 °C) and ionic strengths (50-90 mM) relevant to the available data. In this way, experimental data measured at different temperatures and ionic strengths was mapped onto the conditions used herein, and as conjectured this methodology works well, as evidenced by the consistency of Figure 1. Measured Dependence of Mobility on Charge Density. With Figure 1 in hand and in lieu of a theoretical description that quantitatively captures the data in detail (while employing sensible values of the Stokes radius), an empirical fit to the data was carried out to obtain an electrophoretic mobility versus fractional charge relationship, yielding
µ ) A + B(1 - exp(-Cz))
(5)
where A ) -0.9179 × 10-10, B ) 4.6101 × 10-8, and C ) 1.719. While this relationship can be confidently used when 0 < z < 0.8, at higher charge densities, caution should be exercised as the current data set is unable, within experimental uncertainties, to determine whether there is any variation in this regime. When such a µ to z mapping is used, it has previously been discussed in some detail how to convert measured electropherograms into intermolecular distributions of DM. To date, the relationship used to perform this task was a locally linear one, obtained from a calibration run containing three standard samples. By expanding the range of samples previously reported and amalgamating measurements across different laboratories and instruments, a universal electrophoretic mobility versus charge relationship has been derived that might be used without recourse to standards and can be confidently used to generate intermolecular DM distributions. Intermolecular Distributions. Randomly Demethylesterified Monodisperse Homogalacturonans. Having confidently measured a relationship between electrophoretic mobility and charge (or for HGs equivalently DM), it is trivial, at least
for chains with DMs above 25-30%, to convert an experimentally measured electrophoregram into a full intermolecular DM distribution. With this in mind the expected nature of such a distribution for randomly demethylesterified HG samples was considered. Under the assumption that the charged residues are indeed distributed randomly along the backbone of the polysaccharide then the binomial theorem predicts that the distribution of the number of chains containing different numbers of charged residues is Gaussian. Furthermore, the full width at half-height of these distributions (in DM %) can be calculated as 235.5 × ((1 - p)p/n), where p is the probability of the residue being methylesterified and n is the DP of the chain. (Just as the likelihood of achieving an equal number of heads or tails in classical coin-tossing depends on the number of trials, so the chances that an individual chain will have the sample average DM depends on its DP.) This demonstrates that far from simply being a complicating factor to be taken into account in interpreting results from other experimental methodologies designed to infer the intramolecular distribution of charges, the intermolecular distribution itself contains information regarding the statistical properties of the process that generated the charged residues. Furthermore it is our contention that, on the whole, the intermolecular DM distribution is easier to measure experimentally. In particular, as described above, if the process that generated the charged sites is entirely random then the resultant intermolecular charge distributions should be Gaussian. Figure 4a shows the predicted full width at half-height of a 50% methylesterified sample as a function of its DP and Figure 4b the fraction by which this width would be reduced as DM increases or decreases either side of 50%. It is clear from Figure 4b why most experimentally measured distributions (of pectins with random methylester distributions) look similar; samples with DM values between 30 and 70% are predicted to have widths less than 10% different from one another. Unfortunately the nature of the relationship between electrophoretic mobility and charge density at high fractional charge, as discussed above, means that for samples below around 25% DM, the interpretation becomes more complex and precludes us from confidently measuring the widths in this region. The electropherograms of these samples clearly show that the observed peaks are narrower but at present a sufficiently precise relationship does not exist in this area to tease out how much of that reduction is due to the fact that the resolution itself is decreasing rather than originating from actual changes in the statistical width. These low DM samples reach a width of a couple of DM units, similar to that found for RGI, and represents the chromatographically obtainable limit. At the high DM limit where the DM distributions are again predicted to become substantially narrower, experiments are limited by the number of available samples in this region (methylesterifying samples to close to 100% is potentially possible but not trivial); and the fact that (for pectins) the effects of charged residues in the RGI regions becomes more important. However, using reasonably monodisperse, well-characterized HG samples of known DP and DM, as described in this work, provides an excellent test for the proposed hypotheses. Figure 5a shows the comparisons of the calculated (Gaussian distributions with fwhh values given by the theory displayed in Figure 4a,b, assuming DP ) 80) and the experimentally measured distributions for a set of HG samples obtained as described in the Experimental Section, and the agreement can be seen to be good. It is particularly noteworthy that the sample with the highest DM does indeed possess a narrower intermolecular DM distribution as predicted. For reasonably monodis-
Electrophoretic Behavior of Copolymeric Galacturonans
Figure 4. (a) Predicted full width at half-height of the intermolecular DM distribution of a 50% methylesterified sample as a function of its degree of polymerization (DP); (b) the fraction by which the width given in (a) will be reduced as degree of methylesterification increases or decreases either side of 50%.
perse samples with a fairly low DP Figure 4a suggests that the DP dependence of the width of the intermolecular distribution should be strong enough to give a reasonable estimate of the molecular weight of the sample. In Figure 5b we explicitly demonstrate the sensitivity in this region by plotting the experimental distribution obtained versus the calculation obtained for a variety of DPs for the DM 69% sample, and the agreement with the prediction based on the independently measured DP ) 80 can indeed be seen to be reasonable. Simply taking the experimentally measured width and using Figure 4 to obtain a DP gives around (120 ( 10). For real pectin samples the DPs are likely to be higher than those of the HGs, so that the sensitivity of the intermolecular DM distribution width to molecular weight will be reduced somewhat (Figure 4a), and additionally there is likely to be a degree of polydispersity. However, such measurements might still provide a reasonable average molecular weight estimate for pectin samples that could be of interest. Although techniques such as HPSEC-MALLS are routinely exploited to obtain molecular weight distributions for biopolymers these experiments are by no means trivial74 and having a secondary independent estimate could be advantageous. To investigate how the polydispersity of chain lengths would effect the intermolecular distribution of DM, numerical simulations were conducted. A set of chains with a chosen DP distribution was modeled in silico, each one as a one-
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Figure 5. (a) Calculated (Gaussian distributions with fwhh values given by the theory displayed in Figure 4a,b, assuming DP ) 80) and experimentally measured distributions for a set of HG samples. (b) Calculation obtained for a variety of degrees of polymerization for the DM 69% sample compared with the experimental data.
dimensional array of a length determined according to the chosen molecular weight distribution. Demethylesterification was simulated simply by selecting a residue at random from the entire set and labeling the array element G rather than M. The process was continued until a sample average DM was reached and the resulting distribution of number of chains with DM was plotted. First the simulation was carried out for a set of 104 monodisperse chains of DP ) 500, demethylestrified to 50%, and the results compared with those predicted by the analytical theory. As expected, the agreement can be seen to be excellent (Figure 6a), validating the algorithm and confirming the number of chains used is sufficient. Next, the same simulation was run numerically but now with polydispersity introduced into the chain lengths. Initially, Gaussian distributions were used with full widths at half-height given in brackets in Figure 6. Similarly, Figure 6b shows the analytical theory compared with mono- and polydisperse numerical simulations for DP ) 100. It can be seen that, for such distributions at least, the result is that the width of the intermolecular distribution obtained is not significantly different from the monodisperse case; that is, if there is polydispersity in the DP, fitting the width of the intermolecular distribution of copolymers might still extract a useful number average molecular weight. The numerical simulation described here, simple as it is, is the focus of ongoing work. Here, it has been experimentally demonstrated for the first time, using well-characterized sub-
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methylesterification it is shown, for the first time, that the experimentally extracted intermolecular distributions agree well with the predictions of calculations based on the binomial theorem. This confirms previous speculations about the minor effect of chromatographic parameters in determining the measured widths, validates the derived relation between electrophoretic mobility and methylesterification, supports the assumption that the chemical manipulations used to sculpt the fine structure of the polymers can indeed be considered as random, and most importantly demonstrates that the intermolecular distribution of the methylesterification of pectin samples contains information on the intramolecular pattern, by virtue of the fact that they are both manifestations of the same statistical process. In addition, this means that for substrates for which the generation of the copolymeric pattern was known to be random, the width of the intermolecular distribution also allows an estimate of the molecular weight to be obtained. Acknowledgment. The authors acknowledge the financial support from Fonterra and FRST for the Ph.D. scholarship of A.C. R. D. Keenan is acknowledged for performing preliminary calculations of electrophoretic mobility. G. Mouille and H. North (Institut Jean-Pierre Bourgin, INRA Versailles) are acknowledged for the gift of Arabidopsis seeds. We thank Marie-Jeanne Cre´peau for skillful technical assistance in the preparation and characterization of HG samples.
References and Notes
Figure 6. Comparison of the predicted distributions for a 50% DM substrate obtained from the analytical expression and numerical simulations, additionally incorporating polydispersity in DP (fwhh given in brackets) for (a) DP ) 500 and (b) DP ) 100.
strates, that the randomness of the demethylesterification process leaves its signature not only in the intramolecular sequence of methylesters, but in the measurable intermolecular distribution of DM. We now aim to use the numerical simulation to investigate a variety of nonrandom demethylesterification mechanisms and assess their affect on the intermolecular DM distribution. If something of the generating processes can be inferred from this intermolecular DM distribution then reconstruction of the concomitant intramolecular sequences may be possible. Such nonrandom processes are indeed thought to occur naturally during enzymatic processing and, tantalizingly, intermolecular DM distributions have been reported for pectin samples demethylesterified by pectinmethylesterase (PME) that show clear deviation from the Gaussian shapes reported here for randomly demethylesterified polymers.
Conclusions When carefully extracted, manipulated, and characterized samples of HGs, RGI, and pectins are used, a universal electrophoretic mobility versus fractional charge plot has been generated for copolymeric galacturonans. Based on an empirical relationship describing this data, intermolecular DM distributions of well-characterized HG samples have been extracted. For these substrates, which possess random intramolecular patterns of
(1) Henrissat, B.; Coutinho, P. M.; Davies, G. J. Plant Mol. Biol. 2001, 47 (1-2), 55–72. (2) DeVries, R. P.; Visser, J. Microbiol. Mol. Biol. ReV. 2001, 65 (4), 497–522. (3) Draget, K. I. In Handbook of hydrocolloids; Williams, P. A., Phillips, G. O., Eds.; Woodhead Publishing Limited/CRC Press LLC: Cambridge, 2000; pp 379-395. (4) McCann, M. C.; Roberts, K. In Pectins and Pectinases; Visser, J., Voragen, A. G. J., Eds.; Elsevier Science B.V.: New York, 1996; Vol. 9, pp 1-107. (5) William, G. T. W.; McCartney, L.; Mackie, W.; Knox, J. P. Plant Mol. Biol. 2001, 47, 9. (6) Lawrence A. A. Edible Gums and Related Substances; Noyes Data Corporation: Park Ridge, NJ, 1973. (7) Thickening and Gelling Agents for Food, 2nd ed.; Imeson, A., Ed.; Blackie Academic and Professional: London, 1997. (8) Skjaˇk-Bræk, G. Biochem. Soc. Trans. 1992, 20, 27. (9) Draget, K. I.; Østgaard, K.; Smidsrød, O. Appl. Microbiol. Biotechnol. 1989, 31, 79. (10) Thu, B.; Bruheim, P.; Espevik, T.; Smidsrød, O.; Soon-Shiong, P.; Skjaˇk-Bræk, G. Biomaterials 1996, 17, 1031. (11) Vassilev, N.; Vassileva, M.; Azcon, R.; Medina, A. J. Biotechnol. 2001, 91, 237. (12) Chen, J. P.; Hong, L.; Shunnian, W.; Wang, L. Langmuir 2002, 18, 9413. (13) Franco, C. R.; Chagas, A. P.; Jorge, R. A. Colloids Surf., A 2002, 204, 183. (14) Iskakov, R. I.; Kikuchi, A.; Okano, T. J. Controlled Release 2002, 80, 57. (15) El-Gibaly, I. Int. J. Pharm. 2002, 232, 1999. (16) Gilsenan, P. M.; Richardson, R. K.; Morris, E. R. Carbohydr. Polym. 2000, 41, 339. (17) Abdumola, N. A.; Richardsson, R. K.; Morris, E. R. Food Hydrocolloids 2000, 14, 569. (18) Picout, D. R.; Richardsson, R. K.; Morris, E. R. Carbohydr. Polym. 2000, 43, 133. (19) Vincken, J. P.; Schols, H. A.; Oomen, R. J. F. J.; McCann, M. C.; Ulvskov, P.; Voragen, A. G. J.; Visser, R. G. F. Plant Physiol. 2003, 132 (4), 1781–1789. (20) Ralet, M. C.; Thibault, J.-F. Biomacromolecules 2002, 3, 917–925. (21) Voragen, A. G. J.; Pilnik, W.; Thibault, J.-F.; Axelos, M. A. V.; Renard, C. M. G. C. Pectins. In Food Polysaccharides and Their Applications; Stephen, A. M., Ed.; Marcel Dekker: New York, 1995; pp 287-339.
Electrophoretic Behavior of Copolymeric Galacturonans (22) Engelsen, S. B.; Cros, S.; Mackie, W.; Perez, S. Biopolymers 1996, 39, 417–433. (23) Willats, W. G. T.; Orfila, C.; Limberg, G.; Buchholt, H. C.; van Alebeek, G. J. W. M.; Voragen, A. G. J.; Marcus, S. E.; Christensen, T. M. I. E.; Mikkelson, J. D.; Murray, B. S.; Knox, J. P. J. Biol. Chem. 2001, 276 (22), 19404–19413. (24) Vincent, R. R.; Cucheval, A.; Hemar, Y.; Williams, M. A. K. Eur. J. Phys. E 2009, 28, 79-87. (25) Zhong, H.-J.; Williams, M. A. K.; Keenan, R. D.; Goodall, D. M.; Rollin, C. Carbohydr. Polym. 1997, 32 (1), 27–32. (26) Zhong, H.-J.; Williams, M. A. K.; Goodall, D. M.; Hansen, M. E. Carbohydr. Res. 1998, 308 (1-2), 1–8. (27) Jiang, C.-M.; Wu, M.-C.; Chang, W.-H.; Chang, H.-M. J. Agric. Food Chem. 2001, 49, 5584–5588. (28) Williams, M. A. K.; Buffet, G. M. C.; Foster, T. J. In Gums and Stabilisers for the Food Industry; Williams, P. A., Philips, G. O., Eds.; The Royal Society of Chemistry: Cambridge, 2002; Vol. 11, pp 1328. (29) Williams, M. A. K.; Buffet, G. M. C.; Foster, T. J. Anal. Biochem. 2002, 301 (1), 117–122. (30) Williams, M. A. K.; Foster, T. J.; Schols, H. A. J. Agric. Food Chem. 2003, 51 (7), 1777–1782. (31) Stro¨m, A.; Williams, M. A. K. Carbohydr. Res. 2004, 339 (10), 1711– 1716. (32) Stro¨m, A.; Ralet, M.-C.; Thibault, J.-F.; Williams, M. A. K. Carbohydr. Polym. 2005, 60, 467–473. (33) Maness, N. O.; Ryan, J. D.; Mort, A. J. Anal. Biochem. 1990, 185 (2), 346–352. (34) Massiot, P.; Perron, V.; Baron, A.; Drilleau, J. F. Food Sci. Technol. 1997, 30 (7), 697–702. (35) Synytsya, A.; Copikova, J.; Matejka, P.; Machovic, V. Carbohydr. Polym. 2003, 54 (1), 97–106. (36) Rosenbohm, C.; Lundt, I.; Christensen, T. M. I. E.; Young, N. W. G. Carbohydr. Res. 2003, 338, 637–649. (37) Be´douet, L.; Courtois, B.; Courtois, J. Carbohydr. Res. 2003, 338 (4), 379–383. (38) Huisman, M. M. H.; Oosterveld, A.; Schols, H. A. Food Hydrocolloids 2004, 18 (4), 665–668. (39) Neiss, T. G.; Cheng, H. N.; Daas, P. J. H.; Schols, H. A. Macromol. Symp. 1999, 140, 165–178. (40) Lee, H.; Rivner, J.; Urbauer, J. L.; Garti, N.; Wicker, L. J. Sci. Food Agric. 2008, 88 (12), 2102–2110. (41) Daas, P. J. H.; Arisz, P. W.; Schols, H. A.; DeRuiter, G. A.; Voragen, A. G. J. Anal. Biochem. 1998, 257, 195–202. (42) Daas, P. J. H.; Meyer-Hansen, K.; Schols, H. A.; DeRuiter, G. A.; Voragen, A. G. J. Carbohydr. Res. 1999, 318, 135–145. (43) Ko¨rner, R.; Limberg, G.; Christensen, T. M. I. E.; Mikkelson, J. D.; Roepstorff, P. Anal. Chem. 1999, 71, 1421–1427. (44) Goubet, F.; Jackson, P.; Deery, P. J.; Dupree, P. Anal. Biochem. 2002, 300, 53–68. (45) Goubet, F.; Morriswood, B.; Dupree, P. Anal. Biochem. 2003, 321 (2), 174–182.
Biomacromolecules, Vol. 10, No. 6, 2009
1531
(46) Goubet, F.; Stro¨m, A.; Quemener, B.; Stephens, E.; Williams, M. A. K.; Dupree, P. Glycobiology 2006, 16 (1), 29–35. (47) Coenen, G. J.; Kabel, M. A.; Schols, H. A.; Voragen, A. G. J. Electrophoresis 2008, 29 (10), 2101–2111. (48) Hoagland, D. A.; Smisek, D. L.; Chen, D. Y. Electrophoresis 1996, 17, 1151–1160. (49) McCormick, L. C.; Slater, G. W. Electrophoresis 2007, 28, 674–682. (50) Nedelcu, S.; Meagher, R. J.; Barron, A. E.; Slater, G. W. J. Chem. Phys. 2007, 126, 175104. (51) Thibault, J.-F.; Renard, C. M. G. C.; Axelos, M. A. V.; Roger, P.; Cre´peau, M.-J. Carbohydr. Res. 1993, 238, 271–286. (52) Deng, C.; O’Neill, M. A.; York, W. S. Carbohydr. Res. 2006, 341, 474–484. (53) Macquet, A.; Ralet, M.-C.; Kronenberger, J.; Marion-Poll, A.; North, H. M. Plant Cell Physiol. 2007, 48 (7), 984–999. (54) Thibault, J.-F. Lebensm. Wiss. Technol. 1979, 12, 247–251. (55) Blakeney, A. B.; Harris, P. J.; Henry, R. J.; Stone, B. A. Carbohydr. Res. 1983, 113, 291–299. (56) Ralet, M.-C.; Dronnet, V.; Buchholt, H. C.; Thibault, J.-F. Carbohydr. Res. 2001, 336, 117–125. (57) Levigne, S.; Thomas, M.; Ralet, M.-C.; Quemener, B.; Thibault, J.-F. Food Hydrocolloids 2002, 16, 547–550. (58) Rathore, A. S. J. Chromatogr., A 2004, 1037, 431. (59) Weinberger, R. Practical Capillary Electrophoresis, 2nd ed.; Academic Press: San Diego, CA, 2000. (60) Goodall, D. M.; Williams, S. J.; Lloyd, D. K. Trends Anal. Chem. 1991, 10, 272–279. (61) Tuffile, F. M.; Ander, P. Macromolecules 1975, 8, 789. (62) Hellı´n, P.; Ralet, M.-C.; Bonnin, E.; Thibault, J.-F. Carbohydr. Polym. 2005, 60 (3), 307–317. (63) Allison, S. A.; Stigter, D. Biophys. J. 2000, 78, 121–124. (64) Winzor, D. J.; Carrington, L. E.; Deszczynski, M.; Harding, S. E. Biomacromolecules 2004, 5, 2456–2460. (65) Dong, Q.; Stellwagen, E.; Dagle, J. M.; Stellwagen, N. Electrophoresis 2003, 24, 3323–3329. (66) Peric, I. M.; Rivas, B. L.; Pooley, A.; Rifffo, E.; Basez, L. A. Bol. Soc. Chilena Quim. 1999, 44. (67) Hoagland, D. A.; Arvanitdou, E.; Welch, C. Macromolecules 1999, 32, 6180–6190. (68) Cleland, R. L. Macromolecules 1991, 24, 4391–4402. (69) Stigter, D. J. Phys. Chem. 1978, 82, 1417–1423. (70) Stigter, D. J. Phys. Chem. 1979, 83, 1663–1670. (71) Cros, S.; Du Penhoat, C.H.; Bouchemal, N.; Ohassan, H.; Imberty, A.; Perez, S. Int. J. Biol. Macromol. 1992, 14, 313. (72) Manning, G. S. J. Phys. Chem. 1981, 85, 1506–1515. (73) Fossey, M. A.; Marques dos Santos, C. C.; Chahine, J.; Neto, J. R. J. Phys. Chem. B 2000, 104, 12174–12178. (74) Berth, G.; Vukovic, J.; Lechner, M. D. J. Appl. Polym. Sci. 2008, 110 (6), 3508–3524.
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