Many copolysaccharides are compositionally heterogeneous, containing variations in monosaccharide composition and sequence distributions [1], [2], [3], [4]. This heterogeneity may originate from different sources: 1) It can be caused by variations in biosynthesis due to different stages of plant maturation, seasonal variations, or differences in temperature, drought, and nutrient profile during plant growth. 2) Different plant varieties or cultivars may produce copolymers with slightly different composition. 3) The process of extraction of the polysaccharides from a plant or downstream processing may vary, leading to minor differences in composition. 4) If the polysaccharide has been subjected to post-harvest modification (e.g. alkaline hydrolysis, enzymatic reaction, or chemical derivatization), the variations in reaction conditions or process fluctuations may cause changes in composition and sequence distribution. 5) Sometimes a commercial material may be a blend of different batches of materials. In view of the possibility of heterogeneity, NMR analysis of these polysaccharides should be done with care. Frequently the NMR sequence information (e.g., diad and triad sequence intensities) is fitted to simple Bernoullian (**B**), first-order Markovian (**M1**) or second-order Markovian (**M2**) models. For compositionally heterogeneous polymers, the use of these conventional models can be misleading.

A number of NMR methodologies have been developed to address compositional heterogeneity [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. For simplicity, these treatments can be grouped into two general types: continuous function and discrete-component approaches.

In the continuous function treatment, one can use the perturbed Markovian models, such as symmetric [11] and non-symmetric functions [15] or the general (function-independent) formalism [15]. For example, the exponentially modified Gaussian (EMG) function [15] can be utilized, where the Bernoullian probability is represented not by one value but by a distribution of values, f(z):

$f\mathrm{(}z\mathrm{)}=\frac{N}{\tau \sigma \sqrt{2\pi}}{\displaystyle \underset{0}{\overset{\infty}{\int}}\mathrm{exp}\left[-\frac{{\mathrm{(}z-P1-z\prime \mathrm{)}}^{2}}{2{\sigma}^{2}}-\frac{z\prime}{\tau}\right]}dz\prime $

where z is the Bernoullian probability, N the area under the Gaussian, σ the standard deviation, τ the skew factor, z′ the dummy variable of integration, and P_{1} the average value of Bernoullian probability in the absence of exponential modification. The EMG model for the first-order Markovian probabilities can be similarly expressed [15]. For these models, the theoretical expressions for polymer composition, diad, triad, and tetrad sequences have been previously derived [15]. The observed NMR sequence intensities can be fitted to the theoretical expressions to obtain P_{1}, σ, and τ.

In the discrete-component approaches [7], [8], [9], the polymer is regarded as the mixture of two or more discrete components. The components may be separate chains or joined together as a block copolymer. In this approach, the composition and the sequence intensities are the weighted averages of the corresponding compositions and sequence intensities of all the components.

${I}_{\beta}={\displaystyle \sum _{\kappa}{w}_{\kappa}\cdot {I}_{\beta \kappa}}$

where I_{β} is the total intensity for sequence β, w_{κ} is the weight fraction for component κ, and I_{βκ} is the intensity for sequence β and component κ. In simple cases, the observed and the calculated NMR sequence intensities can be fitted to the two-component **B**/**B** or **M1**/**M1** model; if NMR sequence data on polymer fractions are available, it may be possible to combine the NMR data of the fractions and fit them to three- or four-component models.

The methodologies described above were initially developed to treat compositional heterogeneity observed in synthetic polymers [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. The same approaches have also been shown to be applicable to copolysaccharides [18], [19], [20], [21], [22]. In this work a review is made of the NMR analysis of three polysaccharides that exhibit compositional heterogeneity.

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