INTRODUCTIONThe biopolymer complex of plant tissue cell wallsis a complex conglomerate of intertwined branchedsupramolecular networks of the protopectin complexand the hemicellulose. The complex is permeated withcellulose microfibrils and protein extensin (Fig. 1) [1, 2].All its components are linked to each other by ester,salt, combined, and hydrogen bonds. Each componentpossesses valuable physicochemical properties with agood potential for food industry [3–7].Pectins have the most attractive and numerousfunctional properties among all the carbohydrates ofplant cell walls [5, 8]. They owe these useful propertiesdue to their molecular structure. In their native form,pectins have a water-insoluble supramolecular structurecalled the protopectin complex. The structure is anextended and highly branched linear and lateral networkof polymer fragments (Fig. 2). Lateral branches alsohave a complex structure and can be interconnected withsalt and borate bonds [9–18].Contemporary science knows eight types offragments of the protopectin complex: homo-galacturonan,rhamnogalacturonan-I, rhamnogalacturonan-II, xylogalacturonan, apiogalacturonan, andarabinogalacturonan [19].Homogalacturonans are linear polymeric fragmentsof α-D(+)-galacturonic acid residues, linked by(1 → 4)-glycosidic bonds (Fig. 3) [19, 20]. Each residuecontains a carboxyl group, which naturally may existin a free, esterified, or amidated state. Free carboxylgroups are capable of dissociation, while acquiring apartial negative charge. Carboxyl groups esterified withmethanol demonstrate inactivated charge formation.Amidated carboxyl groups, due to the donor-acceptorbond of the lone-pair electrons, accept cation H+ andacquire a partial positive charge.In positions C1 and C2, hydroxyl groups can formglycosidic bonds with the residues of xylose, ribose,arabinose, and galactose, as well as ester bonds withcarboxylic acids and aromatic compounds. The state andtotal amount of carboxyl groups in the pectin moleculefragment define the physicochemical propertiesof pectins, while the degree and the nature of thesubstitution of hydroxyl groups define the inhibitiondegree.The practical use of pectins depends on the chemicalstructure of homogalacturonans.Ramnogalacturonan-I is the second most commonfragment of pectins. Its content can reach 45% insugar beet pectin [5, 19, 20]. These fragments includesequences from the residue of α-L-rhamnose andα-D(+)-galacturonic acid, linked by a (1 → 4)-glycosidicbond. In the rhamnosyl residue, the pair can be linkedwith other pairs or with the end of the homogalacturonanby a rhamnosyl-uronic (1 → 2)-glycosidic bond. In theuronic residue, the pair can be linked with other pairby a rhamnosyl-uronic (1 → 2)-glycosidic bond orwith the end of homogalacturonan by a uronic-uronic(1 → 4)-glycosidic bond. As a result, rhamnosyl residuesof rhamnogalacturonan-I are the branching zones of thepectin molecule, where free functional groups can formglycosidic bonds with either residues of neutral sugars,or their polymer sequences, i.e. arabinans, galactans,arabinogalactans, and galactoarabinans-I and II (Fig. 4).The basis of the protopectin complex of planttissue cell walls is a network of regions formedby linear sequences of homogalacturonans andrhamnogalacturonans-I. Of course, this assumptionexcludes two types of lateral branches: the rhamnosilfreelateral branches (rhamnogalacturonan-II),which may contain residues of L-rhamnoseand/or α-D(+)-galacturonic acid with proportionof ≤ 2–3%, and branches formed by neutral sugarsand their oligo- and polymers [16, 19]. Molecularproperties of homogalacturonan fragments define thephysicochemical properties of plant pectin. Therefore,enzymatic fragmentation is the most effective methodfor the protopectin complex. It is a selective hydrolyticcleavage of rhamnosyl-uronide (1 → 2) and (1 → 4)glycosidic bonds.Figure 1 Primary cell wall of higher plants [1]However, the physicochemical properties of pectinalso depend on the polymerization degree of thefragmentation products [21]. The maximal possibledegree of polymerization depends on the polymerizationdegree of the native homogalacturonan fragments inthe protopectin complex. In each specific case, theexperimental determination of this indicator is a difficultresource- and time-consuming task.Therefore, a criteria assessment would be theoptimal approach to evaluate the potential efficiencyof the directed enzymatic fragmentation of a particularplant protopectin complex. Such assessment can alsodefine the boundary conditions that determine thedegree of the targeted physicochemical properties ofthe fermentolysis products. This approach could alsodetermine the conditions for processing any plant tissueor its derivatives. The approach consists of some stepby-step stages. The first stage was a system of criteriafor assessing the transformation potential of a plantbiopolymer complex [22].As a next stage, the present research objective was todevelop a system of criteria for assessing the enzymatictransformation potential of a plant biopolymer complexas in the case of pectin substances. The researchincluded the following tasks:– developing the abovementioned assessment criteriasystem, based on the use of zoned criteria space;– developing a system of boundary conditions for theclassification of plant raw materials according to theapplicability of the enzymatic transformation of itsprotopectin complex.STUDY OBJECTS AND METHODSThe protopectin complex of the plant tissue consistsof three main types of fragments: homogalacturonan,rhamnogalacturonan-I, and rhamnogalacturonan-II. Thelatter type was disregarded as its mass fraction in theprotopectin complex is ≤ 2%.Rhamnogaracturonan-I has linear polynalacturonansites. As a result, the homogalanic component of theprotopectin complex can be considered as part ofrhamnogalacturonan-I fragments.A pectin molecule can be classified asrhamnogalacturonan-I only if, in addition to thehomogalacturonan component, it contains at leastone branch formed by at least one rhamnosyl residue.Consequently, a polymer molecule has at least twohomogalacturonan regions with at least one terminallink (rhamnosyl residue) each.Linear and homogalacturonan regions of themolecular network alternate in the protopectin complexin a particular order. This order presumably dependson the taxonomy of the raw material and the functionFigure 4 Fragment of rhamnogalacturonan-I of pectin molecule [19]. Lateral branches: A – arabinan, B – galactan,C – arabinogalactan, D – galactoarabinanFigure 3 Homogalacturonan fragment of pectin molecule [20]of the plant parts. The structural features of thefragments of rhamnogalacturonan-I are such that thenatural boundaries of the homogalacturonan regionsare L-rhamnose residues connected to the terminaluronid links (1 → 2) and (1 → 4) by glycosidic bonds.The fragment can be roughly described by the followingsequence: “terminal link of homogalacturonan –rhamnose residue (the branching starts) – branchingsite – rhamnose residue (the branching ends) –homogalacturonan region – … – section ofhomogalacturonan – rhamnose residue (the branchingstarts) – branching site – rhamnose residue (thebranching ends) – terminal link of homogalacturonan”.In the simplest case, the rhamnogalacturonan-Ifragment has only one branching site ( 1 r b = ). Dependingon its structure, the rhamnogalacturonan-I can includeonly one rhamnosyl residue ( 1 Rh z = ). In a more complexcase, the rhamnogalacturonan-I may contain severalrhamnosyl residues (zRh = q, where q = 1, 2, 3, ...), whichalternate with galacturonid residues (Fig. 5).The number of branching sites may also depend, tosome extent, on the plant species and the functional typeof the plant tissue.Figure 5 features no fragments of rhamnogalacturonan-I as their lateral branches are representedmainly by the nonuronic component.The conditional assumption is that the uronidecontainingpart of rhamnogalacturonan-I is completelydetermined by the following variables: HG n is totalhomogalacturonan sites, Rh n is total rhamnosyl unitsin the branching sites, GalA(b) n is total uronid residues inthe branching sites, Rh z is number of rhamnosyl residuesper branching site, GalA(b) z is number of uronid residuesper branching site, and br n is total branch sites. Table 1demonstrates the numerical values of the variables inparticular cases of the distribution of homogalacturonanand branching sites in Fig. 5.The ratios in Table 1 can be expressed by thefollowing formulae:( 1) Rh HG Rh n = n − ⋅ z , (1)Figure 5 Distribution of homogalacturonan and branching sites in rhamnogalacturonan-I at br = 1–4. Not to scale. а) 2 Rh z = ;b) 3 Rh z = ; c) 4 Rh z =Table 1 Particular cases of the distribution of variables that determine the structure of rhamnogalacturonan-I,at different values of brNumberof branchingsites, r bCasesА B CHG n Rh n GalA(b) n HG n Rh n GalA(b) n HG n Rh n GalA(b) n1 2 2 1 2 3 2 2 4 32 3 4 2 3 6 4 3 8 63 4 6 3 4 9 6 4 12 94 5 8 4 5 12 8 5 16 12… ... … … … … … … … …br n ( 1) 2 Rh HG n = n − ⋅( ) ( 1) 1 GalA b HG n = n − ⋅( )12RhGalA bnn⋅=( 1) 3 Rh HG n = n − ⋅( ) ( 1) 2 GalA b HG n = n − ⋅( )23RhGalA bnn⋅=( 1) 4 Rh HG n = n − ⋅( ) ( 1) 3 GalA b HG n = n − ⋅( )34RhGalA bnn⋅=a bchomogalacturonan regionrhamnosyl residueα-(D+)-galacturonic acid residuenGalA(b) = (nHG −1) ⋅ zGalA(b) (2)The structure of the rhamnogalacturonan-Ifragments suggests that the main structural unit is theamount of rhamnosyl residues in the branching sites. Asa result, formulae (1) and (2) take the following form:Rh 1 Rh RhHGRh Rhn n znz z+= + = , (3)( )( )Rh GalA bGalA bRhn znz⋅= (4)Based on the data in Table I,( ) 1 GalA b Rh z = z − (5)Thus, the final formula (4) is:( )( 1) Rh RhGalA bRhn znz⋅ −= (6)These dependences give an approximate quantitativeidea of the structure of rhamnogalacturonan-I. For theirpractical use, they have to be linked to the real chemicalcomposition of a particular raw material.The line of reasoning follows the next path.Considering that the molecular weight of therhamnosyl residue is Rh M (Da) and the mass fraction ofrhamnose in the composition of the natively insolublepart of the raw material is Rh ω (%), the amount ofrhamnosyl residues in the mass of the natively insolublepart of the raw material m (g) can be calculatedaccording to the formula below:100RhRhRhmnM a⋅ω=⋅ ⋅(7)where a is the atomic mass unit (1.66053892×10–24g/Da).A combination of formulae (6) and (7) gives thenumber of moles of α-D(+)-galacturonic acid residues inthe branch sites:( )( 1)100 ( 1)100RhRhRh Rh RhGalA bRh Rh Rhm zM a m znz M z aωω⋅⋅ −⋅ ⋅ ⋅ ⋅ −= =⋅ ⋅ ⋅(8)Consequently, the mass fraction of α-D(+)-galacturonic acid residues in the insoluble part of theraw material in the branching sites is:( )( )100 100 ( 1)100GalA GalA b GalA Rh RhGalA bRh RhM n a M a m zm m M z aωω⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ −= = ⋅ ⇒⋅ ⋅ ⋅×× 100 100 ( 1)100GalA Rh RhRh Rha M a m zm M z aω⋅ ⋅ ⋅ ⋅ ⋅ −= ⋅ ⇒⋅ ⋅ ⋅( 1) GalA Rh RhRh RhM zM z⋅ω ⋅ −⇒⋅(9)where GalA M is the molar mass of α-D(+)-galacturonicacid residue, Da.The conditional assumption is that all the residuesof α-D(+)-galacturonic acid in the insoluble part belongexclusively to the protopectin complex and are presentonly in the composition of homogalacturonan fragmentsand branch points of rhamnogalacturonan-I. Then,the mass fraction of α-D(+)-galacturonic acid residuesin homogalacturonan fragments can be calculated asfollows:( ) ( )( 1) GalA Rh RhGalA HG GalA GalA b GalARh RhM zM zωω ω ω ω⋅ ⋅ −= − = −⋅( ) ( )( 1) GalA Rh RhGalA HG GalA GalA b GalARh RhM zM zωω ω ω ω⋅ ⋅ −= − = −⋅ (10)As the plant tissue grows, the protopectin complex ofcell walls and intercellular spaces changes continuously.As a result, the structure of the complex becomesheterogeneous. Assuming that all homogalacturonanregions of the protopectin complex are a nativecomponent of rhamnogalacturonan fragments, thewhole protopectin complex can be represented asconsisting almost entirely of rhamnogalacturonan-Ifragments. The length of the homogalacturonan regionsdiffers in different parts of the protopectin complex.Consequently, a particular homogalacturonan molecularmass is in fact a certain mean value. The molecularweight of any arbitrarily taken (i-th) homogalacturonanregion of the protopectin complex is related to itspolymerization degree by the following ratio:HG(i) GalA i M = M ⋅ k (11)where i k is the polymerization degree of the i-thhomogalacturonan region.Consequently, the formula for the average molecularweight of homogalacturonan sites is as follows:( )1 1 1( )N N NHG i GalA i ii i iHG av GalA GalA avM M k kM M M kN N N= = =⋅= = = ⋅ = ⋅Σ Σ Σ( )1 1 1( )N N NHG i GalA i ii i iHG av GalA GalA avM M k kM M M kN N N= = =⋅= = = ⋅ = ⋅Σ Σ Σ (12)where av k – average polymerization degree ofhomogalacturonan regions and N – total homogalacturonanregions amount.The mass fraction of the homogalacturonancomponent in the insoluble part can be expressed asfollows:( ) 100 HG av HGHGM n amω⋅ ⋅ ⋅= (13)A combination of formulae (3) and (13) gives thefollowing result:( )( )100 ( ) 100Rh RhHG avRh HG av Rh RhHGRhM n z a z M n z am z mω+⋅ ⋅ ⋅⋅ + ⋅ ⋅= = ⋅( )( )100 ( ) 100Rh RhHG avRh HG av Rh RhHGRhM n z a z M n z am z mω+⋅ ⋅ ⋅⋅ + ⋅ ⋅= = ⇒⋅( ) 100100RhHG av RhRhRhM m z aM az m ⋅ω ⋅ +  ⋅ ⋅  ⋅ ⋅  ⇒ ⇒⋅( )100 Rh RhHG av RhRh RhM M a zmM zω ⋅ ⋅ ⋅  ⋅ + ⇒  ⋅(14)However, the following inequation occurs atm ≥ 10−6g and 103 Rh z ≤ :100 10Rh Rh 10 M a zm− ⋅ ⋅ ⋅<<which makes it possible to disregard the sum of100 Rh Rh M a zm⋅ ⋅ ⋅ as insignificant, in which case formula (14)can be simplified as follows:HG(av) RhHGRh RhMM zωω⋅≈⋅(15)The mass fraction of homogalacturonan fragmentsand the mass fraction of α-D(+)-galacturonic acidresidues that make up the homogalacturonan fragmentsare the same, which leads to the following identicalequation:HG(av) Rh GalA Rh ( Rh 1)GalARh Rh Rh RhM M zM z M zω ωω⋅ ⋅ ⋅ −≅ −⋅ ⋅(16)Added to formula (12), the equation assumes thefollowing form:( 1) GalA av Rh GalA Rh RhGalARh Rh Rh RhM k M zM z M zω ωω⋅ ⋅ ⋅ ⋅ −≅ −⋅ ⋅(17)Applying formula (17) to kav makes it possibleto calculate the average polymerization degree ofhomogalacturonan regions in the protopectin complex:( 1)Rh GalA Rh GalA Rh Rh Rh GalA 1 1av RhGalA Rh GalA RhM z M z Mk zM Mω ω ωω ω⋅ ⋅ − ⋅ ⋅ −  ⋅ = =  −  ⋅ + ⋅  ⋅ ( 1)Rh GalA Rh GalA Rh Rh Rh GalA 1 1av RhGalA Rh GalA RhM z M z Mk zM Mω ω ωω ω⋅ ⋅ − ⋅ ⋅ −  ⋅ = =  −  ⋅ + ⋅  ⋅ (18)Thus, the mass fractions of galacturonide andrhamnosyl residues in the plant cell can help todetermine the average polymerization degree ofthe homogalacturonan regions in the protopectincomplex.RESULTS AND DISCUSSIONLet the dimentionless criterion ν is uniquelydetermined on the basis of chemical analysis of thenative water-insoluble plant tissue component:RhGalAωνω= (19)As a result, formula (18) looks as follows:Rh 1 1av RhGalAMk zM ν =  −  ⋅ +  ⋅ (20)In (20), constituent RhGalAMM is constant. Subsequently,formula (20) is a mathematical description of functionaldependence kav = f (ν , zRh ) (Fig. 6). Thus, analyticallyobtained ωRh and ωGalA can define the weighted averagedegree of polymerization of homogalacturonan regionsof pectins.Figure 6 Weighted average polymerization degree of homogalacturonan sites of the rhamnogalacturonan fraction in pectins:functional dependence260Kondratenko V.V. et al. Foods and Raw Materials, 2021, vol. 9, no. 2, pp. 254–261Figure 7 Zoned criteria space of molecular characteristics of homogalacturonan fractions in pectinsIn a same time, homogalacturonan regions in therhamnogalacturonan fraction of pectin are possible onlyat kkaavv≥≥11.As a result, the rational condition for criterion ν is:( 1)Rh RhGalA av RhM zM k zν⋅≤ − + (21)Provided that there are homogalacturonan regions inthe rhamnogalacturonan fraction of pectin substances,the range for determining the numerical values of thiscriterion can be represented as 0; RhGalAMMν ∈  . The functionaldependence can be reduced to a criterion space incoordinates ν and zRh, where kav is boundary zoningconditions (Fig. 7).Within this criterion space, zone I is the absenceof homogalacturonan regions in pectins. Zone II isthe presence of regions with the weighted averagepolymerization degree of homogalacturonan region inthe range of 1–5; zone III – 5–10; and zone IV – ≥ 10.Homogalacturonan regions with kav > 10 are oftheir own practical importance. Therefore, the useof homoenzyme preparations for fragmentation ofthe native protopectin complex makes sense only forplant tissues in zone IV. In other cases, the use ofhomogalacturonan-specific enzyme preparations forprotopectin complex fragmentation has no sense.The new criteria-based approach makes it possibleto unambiguously define the effectiveness of targetedenzymatic fragmentation of the plant protopectincomplex within the boundary conditions that determinethe degree of the targeted physicochemical propertiesof the final product. This approach is universal andrepresents the second stage of the decision tree startedin [22] as a science-based technology for pectinproduction.CONCLUSIONThe research produced a criteria space to assessthe potential effectiveness of the homoenzymatictransformation of a plant biopolymer complex as in thecase of pectin substances. The method was based on atwo-dimensional criteria space, zoned according to thekey factor, i.e. the targeted polymerization degree ofhomogalacturonan fragments in the native protopectincomplex.We found that the compliance with the first criteriazone (at kav ≥ 10) determined the feasibility of usinghomogalacturonan-specific enzyme preparations toisolate of homogalacturonan (targeted) regions of theplant protopectin complex. The compliance with thesecond criteria zone (at 1 ≤ kav < 10) determined theexpediency of non-enzymatic fragmentation of theprotopectin complex. The compliance with the thirdzone (at kav < 1) meant that the fragmentation of theprotopectin complex would neither increase the massfraction of pectin substances in the medium, nor releasepectins.The new criteria approach is an integral part of thetechnologies for obtaining pectin and its products withtargeted physical and chemical properties.CONTRIBUTIONAll authors contributed equally to the manuscript andare equally responsible for any possible plagiarism.CONFLICT OF INTERESTThe authors state that there is no conflict of interestsrelated to the publication of this article.