Biotechnology Techniques 13: 325–328, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands.
325
Hydrolytic gain during hydrolysis reactions; implications and correction procedures L.M. Marchal∗ & J. Tramper Food and Bioprocess Engineering Group, Department of Food Technology and Nutritional Sciences, Wageningen Agricultural University, Bomenweg 2, 6703 HD Wageningen, The Netherlands ∗ Author for correspondence (Fax: +31 598 665427; E-mail:
[email protected]) Received 26 February 1999; Revisions requested 2 March 1999; Revisions received 31 March 1999; Accepted 31 March 1999
Key words: beta-amylase, glucoamylase, hydrolytic gain, starch, structure
Abstract Some of the structural parameters of starch (e.g. % beta- or gluco-hydrolysis) were influenced by the increase in mass during the hydrolysis reactions (hydrolytic gain). Procedures were derived to correct this apparent % of hydrolysis to actual % of hydrolysis. These analytically derived equations are not only valid for the hydrolysis of starch but also for the hydrolysis of lower molecular weight saccharides (i.e. α-limit dextrin). With a small modification, these equations can be used to correct for hydrolytic gain which occurs during the hydrolysis of other (bio)polymers.
Introduction
Method
During the hydrolysis of starch the cleavage of each glycosidic linkage results in the net addition of one molecule of water, thus increasing the mass of the solute (hydrolytic gain). This addition is not negligible. When, for example 162 g starch is totally converted to its monomers (dextrose), the dry mass of the solute increases by some 11% to 180 g. The partial hydrolysis of amylopectin and amylose (both components of starch), using various enzymes (i.e., β-amylase, glucoamylase), is widely used to determine structural parameters of these molecules. It is shown that the hydrolytic gain influences these values. Previously relations were derived which describe the dry-weight increase during hydrolysis as a function of dextrose equivalent, degree of polymerization, or mean-average molecular weight (Marchal et al. 1996). In this paper, relations are derived for the hydrolytic gain as a function of both the % of glycosidic linkages hydrolyzed and the % of monomers liberated from the starting material. Furthermore a correction equation to convert the reported apparent % of hydrolysis to the actual % of hydrolysis is presented.
In this article no materials but analytically derived equations are used. The following abbreviations, which definitions are explained in the text for reasons of clarity, are used in these calculations. CL = chain length [−] DE = dextrose equivalent [−] DPn = degree of polymerization (n) [−] [−] DPx = degree of polymerization liberated oligomer (x) HG = hydrolytic gain [g/g] ICL = inner chain length [−] Mn = number-average molecular weight [g/mol] Mx = molecular weight of saccharide (x) [g/mol] nx = amount of saccharide (x) [mol] OCL = outer chain length [−]
326 Results and discussion Implications of hydrolytic gain The implications of hydrolytic gain can be illustrated as follows. Consider the hydrolysis of 162 g of amylopectin (degree of polymerization of 1 × 105 ) with a β-amylase to the extent where 50% of the glucose units are split off (as maltose). This will yield 81 g branched, high molecular mass carbohydrate and 81 × (342/324) = 85.5 g of maltose. The numberaverage molecular weight (Mn ) of the hydrolyzate is now (nx = amount (moles) of saccharide; Mx = molecular weight of saccharide): n1 M1 + n2 M2 Mn ≡ = n1 + n2 0.25 × 342 + 1.10−5(162 × 1.105 × 0.5 = 666 0.25 + 1.10−5 h g i . (1) mol In literature several methods are described to determine the % β-amylolysis after complete hydrolysis of starch with a β-amylase. In general, two categories of methods are used: (1) Determination of the weight percentage of maltose in the hydrolyzate by chromatographic methods (Bender et al. 1982, Bertoft 1989a). The % of βhydrolysis is calculated by dividing the peak area of maltose by the total amount of carbohydrates [g/g]. In our example this would yield a % β-amylolysis of 85.5/(81+85.5)×100% = 51.35%. (2) Determination of the mean number-average molecular weight by titration methods (dextrose equivalent) or enzymatic methods (Banks & Greenwood 1959, Bathgate & Manners 1966, Bertoft 1989b, Peat et al. 1956; Thorn & Mohazzeb 1990). The % of β-amylolysis is then given by (DE hydrolysate/DE maltose) or (Mn maltose/Mn hydrolysate). Both expressions are equivalent since the DE is defined as (180/Mn hydrolysate)×100. In our example both expressions yield a % β-amylolysis of 51.35%. Therefore, in both examples the % of actual hydrolysis is overestimated by 1.35% due to the hydrolytic gain, and a higher apparent % of hydrolysis is determined. This has several implications. The % of β-amylolysis is for example used to calculate several structural parameters of amylopectin. Amylopectin is a branched macromolecule in which linear chains of about 24 (1→4)-α-linked D-glucose residues on average are linked by (1→6)-α-D-glucosidic linkages to
Fig. 1. A schematic representation of a small part of the amylopectin structure. R = the reducing end of the amylopectin, A = unsubstituted chain, B = chain substituted by a least one other chain.
form a branched structure as schematically illustrated in Figure 1. Two main groups of chains in amylopectin have been defined, namely A-chains (unsubstituted) and B-chains (substituted by other chains). A β-amylase releases maltose (DP2 ) starting from the non-reducing ends of the amylopectin and is not capable to cleave or bypass the (1→6)-α-D-glucosidic linkages. The total amount of maltose units released starting from the non-reducing end of a chain depends on the type of chain (A or B) and the number of glucose units (odd or even) in the chain. After hydrolysis with a β-amylase there are one (odd) or two (even) glucose units left connected to an A-chain and two (even) or three (odd) glucose units left connected to a B-chain. The % of β-amylolysis is used to calculate the average chain length of the outer chains (OCL) of the amylopectin according to (Hizukuri 1996): OCL = (% β-hydrolysis) × CL + 2,
(2)
where CL is the average chain length of the amylopectin chains and the number 2 is the average amount of glucose units left connected to a (1→6)linkages after β-amylolysis (assuming an A/B ratio of 1 and an equal amount of odd and even chains). An overestimation of the % of β-amylolysis leads thus to an overestimation of the value for the outer chain length. In our example of 50% hydrolysis of amylopectin (taking an average chain length of 24), this leads to an overestimation of the OCL with 0.324 glucose units. Another parameter related to this is the average inner chain length (ICL), which is defined as (Hizukuri 1996): ICL ≡ CL − OCL − 1.
(3)
The overestimation of the OCL thus leads to an equivalent underestimation of this inner chain length, both caused by an overestimation of the % of β-amylolysis. The % of β-amylolysis, OCL and ICL are often used to compare different varieties and botanical sources
327 of starches with respect to their chemical structural (Hizukuri 1996). Since the overestimation of % βamylolysis is not linear with the % of hydrolysis (see below), the differences in % of β-amylolysis, OCL and ICL are not directly proportional to the differences in branching characteristics of the polymer. Because of these implications, it is important to derive correction procedures to convert the apparent % of hydrolysis to an actual % of hydrolysis.
in which DPx is the degree of polymerization of the liberated oligomers. Multiplying Equation (5) with Equation (6) and (7) gives the hydrolytic gain (in g/g starting material) as a function of % of hydrolysis, now defined as the amount of monomeric units liberated from the starting material: HG =
Hydrolytic gain as a function of % of hydrolysis One mol of a glucose polymer with degree of polymerization n (DPn ) has a molecular weight of (162 × DPn + 18) g/mol. One mol of polymer (DPn ) is linked by (DPn -1) mol glycosidic bonds. The amount (mols) of bonds per g of polymer is thus given by: DPn − 1 DPn × 162 + 18
mol . g
% actual bond hydrolysis × 18 100% DPn − 1 g × . DPn × 162 + 18 g
(5)
mol . (6) mol
When the monomeric units are split off from the polymer as glucose units (DP1 ), the ratio between the amount of linkages hydrolyzed and monomeric units liberated is 1. When the monomeric units are split off from the polymers as maltose (DP2 ), as in the case with β-amylolyis, the ratio between the amount of linkages hydrolyzed and monomeric units liberated becomes 12 . Or, in a general form: mol linkages hydrolyzed 1 = mol monomeric units liberated DPx
A higher degree of polymerization of the hydrolysis product (DPx ) leads to a lower amount of hydrolytic gain. Hydrolysis to glucose (DP1 ) thus leads to a higher increase in dry weight then hydrolysis to, for example, maltose (DP2 ). Correcting apparent % of hydrolysis to actual % of hydrolysis As illustrated in the example of β-amylolyis, the overestimation of the % of actual hydrolysis is caused by hydrolytic gain. The determined apparent % of β-amylolysis actually consists of: % apparent = 100%
Since in most cases the % of hydrolysis is defined as % of monomeric units liberated from the starting material, Equation (5) has to be converted. In a polymer, the ratio between the amount of monomeric units and amount of linkages is given by: DPn mol monomeric units = mol linkages DPn − 1
(8)
(4)
Per mol of bonds hydrolyzed the total dry weight increases with 18 g. The hydrolytic gain (HG, in g per g starting material) as a function of % of bonds hydrolyzed is then given by: HG =
% actual hydrolysis 18 × 100% DPx DPn g × . DPn × 162 + 18 g
mol ,(7) mol
mass of maltose (as monomeric units) + hydrolytic gain mass starting material + hydrolytic gain [−].
(9)
Or rewritten in a general form: (% actual/100%) + HG % apparent = [−]. (10) 100% 1 +HG Substituting Equation (8) in Equation (10) leads to a relation to calculate the actual % of hydrolysis from the apparent % of hydrolysis: % actual = 100% 1+
18 DPx
[−].
(% apparent/100%) % apparent DPn × DPn ×162+18 × 1− 100% (11)
Figure 2 illustrates the (non-linear) overestimation of the actual % of hydrolysis of starch (DPn = 100 000)
328
Fig. 2. The overestimation of the real % of hydrolysis of starch (DPn = 100 000 as a function of the apparent % of hydrolysis for two hydrolysis products maltose (DP2 ) and glucose (DP1 ).
as a function of the apparent % of hydrolysis for two hydrolysis products maltose (DP2 ) and glucose (DP1 ). With Equation (11) or Figure 2 values reported in literature can be corrected to the actual % of hydrolysis. If the difference in the chemical structure (e.g., between different starches of botanical origin) is investigated, this non-linear overestimation of the actual % of hydrolysis has to be corrected for. Equation (11) can, with a minor modification, also be used for the hydrolysis of other polymers. The molecular weight of the monomeric units (162 for starch) has to be changed in the molecular weight of the monomeric units of the polymer considered.
Acknowledgements The authors wish to thank Avebe and the Dutch Ministry of Economic Affairs (PBTS-Biotechnology Project No. BIO94043) for funding of this research.
References Banks W, Greenwood CT (1959) Physicochemical studies on starches. Part XX. The existence of an anomalous amylopectin in starch. J. Chem. Soc.: 3436–3439. Bathgate GN, Manners DJ (1966) Mutiple branching in glycogens. Biochem. J. 101: 3c–5c. Bender H, Siebert R, Stadler-Szöke A (1982) Can cyclodextrin glycosyltransferase be useful for the investigation of the fine structure of amylopectins?: characterisation of highly branched clusters isolated from digests with potato and maize starches. Carbohydr. Res. 110: 245–259. Bertoft E (1989a) Investigation of the fine structure of amylopectin using alpha- and beta-amylase. Carbohydr. Res. 189: 195–207. Bertoft E (1989b) Partial characterisation of amylopectin alphadextrins. Carbohydr. Res. 189: 181–193. Hizukuri S (1996) Starch: Analytical aspects. In: Eliasson AC ed. Carbohydrates in Food. New York: Marcel Dekker, pp. 347–429. Marchal LM, Jonkers J, Tramper J (1996) The use of freezing point depression to determine the theoretical dextrose equivalent. Starch. 48: 220–224. Peat S, Whelan WJ, Thomas GJ (1956) The enzymatic synthesis and degradation of starch. Part XXII. Evidence of multiple branching in waxy-maize starch. A correction. J. Chem. Soc.: 3025–3030. Thorn W, Mohazzeb S (1990) Molecular weights, lengths, and distribution of side-chains in alpha-D-polyglucanes. Starch 42: 373–376.
